Altair Engineering (ALTR) 10-K 20 Feb 25 2024 FY Annual report Financial data

Document and Entity Information

Document and Entity Information - USD ($) $ in Billions	12 Months Ended
	Dec. 31, 2024	Feb. 03, 2025	Jun. 30, 2024
Document And Entity Information [Line Items]
Document Type	10-K
Amendment Flag	false
Document Period End Date	Dec. 31, 2024
Document Fiscal Year Focus	2024
Document Fiscal Period Focus	FY
Trading Symbol	ALTR
Entity Registrant Name	ALTAIR ENGINEERING INC.
Entity Central Index Key	0001701732
Current Fiscal Year End Date	--12-31
Entity Well-known Seasoned Issuer	Yes
Entity Current Reporting Status	Yes
Entity Interactive Data Current	Yes
Entity Voluntary Filers	No
Entity Filer Category	Large Accelerated Filer
Entity Public Float			$ 5.8
Entity Small Business	false
Entity Emerging Growth Company	false
ICFR Auditor Attestation Flag	true
Document Financial Statement Error Correction [Flag]	false
Entity Shell Company	false
Entity File Number	001-38263
Entity Tax Identification Number	38-2591828
Entity Address, Address Line One	1820 East Big Beaver Road
Entity Address, City or Town	Troy
Entity Address, State or Province	MI
Entity Address, Postal Zip Code	48083
City Area Code	248
Local Phone Number	614-2400
Entity Incorporation, State or Country Code	DE
Document Annual Report	true
Document Transition Report	false
Title of 12(b) Security	Class A Common Stock $0.0001 par value per share
Security Exchange Name	NASDAQ
Auditor Name	Ernst & Young LLP
Auditor Firm ID	42
Auditor Location	Detroit, Michigan
Documents Incorporated by Reference	Portions of the registrant’s Proxy Statement relating to the 2025 Annual Meeting of Stockholders, scheduled to be filed with the Securities and Exchange Commission within 120 days after the end of the registrant’s fiscal year ended December 31, 2024, are incorporated by reference into Part III of this Annual Report on Form 10-K.
Auditor Opinion [Text Block]	Opinion on the Financial Statements We have audited the accompanying consolidated balance sheets of Altair Engineering Inc. and subsidiaries (the Company) as of December 31, 2024 and 2023, the related consolidated statements of operations, comprehensive loss, changes in stockholders' equity (deficit) and cash flows for each of the three years in the period ended December 31, 2024, and the related notes (collectively referred to as the “consolidated financial statements”). In our opinion, the consolidated financial statements present fairly, in all material respects, the financial position of the Company at December 31, 2024 and 2023, and the results of its operations and its cash flows for each of the three years in the period ended December 31, 2024, in conformity with U.S. generally accepted accounting principles. We also have audited, in accordance with the standards of the Public Company Accounting Oversight Board (United States) (PCAOB), the Company's internal control over financial reporting as of December 31, 2024, based on criteria established in Internal Control-Integrated Framework issued by the Committee of Sponsoring Organizations of the Treadway Commission (2013 framework) and our report dated February 20, 2025 expressed an unqualified opinion thereon.
Class A Common Stock [Member]
Document And Entity Information [Line Items]
Entity Common Stock, Shares Outstanding		60,401,224
Class B Common Stock [Member]
Document And Entity Information [Line Items]
Entity Common Stock, Shares Outstanding		25,393,574

Consolidated Balance Sheets

Consolidated Balance Sheets - USD ($) $ in Thousands	Dec. 31, 2024	Dec. 31, 2023
CURRENT ASSETS
Cash and cash equivalents	$ 561,898	$ 467,459
Accounts receivable, net	173,509	190,461
Income tax receivable	21,513	16,650
Prepaid expenses and other current assets	28,058	26,053
Total current assets	784,978	700,623
Property and equipment, net	41,008	39,803
Operating lease right of use assets	31,117	30,759
Goodwill	462,459	458,125
Other intangible assets, net	72,937	83,550
Deferred tax assets	8,770	9,955
Other long-term assets	44,378	40,678
TOTAL ASSETS	1,445,647	1,363,493
CURRENT LIABILITIES
Accounts payable	7,316	8,995
Accrued compensation and benefits	50,328	45,081
Current portion of operating lease liabilities	7,876	8,825
Other accrued expenses and current liabilities	56,058	48,398
Deferred revenue	139,085	131,356
Current portion of convertible senior notes, net	227,106	81,455
Total current liabilities	487,769	324,110
Convertible senior notes, net	0	225,929
Operating lease liabilities, net of current portion	24,141	22,625
Deferred revenue, non-current	28,531	32,347
Other long-term liabilities	48,017	47,151
TOTAL LIABILITIES	588,458	652,162
Commitments and contingencies
STOCKHOLDERS’ EQUITY
Preferred stock ($0.0001 par value), authorized 45,000 shares, none issued or outstanding	0	0
Additional paid-in capital	1,010,789	864,135
Accumulated deficit	(116,328)	(130,503)
Accumulated other comprehensive loss	(37,281)	(22,309)
TOTAL STOCKHOLDERS’ EQUITY	857,189	711,331
TOTAL LIABILITIES AND STOCKHOLDERS' EQUITY	1,445,647	1,363,493
Class A Common Stock [Member]
STOCKHOLDERS’ EQUITY
Common stock	6	5
Class B Common Stock [Member]
STOCKHOLDERS’ EQUITY
Common stock	$ 3	$ 3

Consolidated Balance Sheets (Pa

Consolidated Balance Sheets (Parenthetical) - $ / shares	Dec. 31, 2024	Dec. 31, 2023
Preferred stock, par value	$ 0.0001	$ 0.0001
Preferred stock, shares authorized	45,000,000	45,000,000
Preferred stock, shares issued	0	0
Preferred stock, shares outstanding	0	0
Class A Common Stock [Member]
Common stock, par value	$ 0.0001	$ 0.0001
Common stock, shares authorized	513,797,000	513,797,000
Common stock, shares issued	60,181,000	55,240,000
Common stock, shares outstanding	60,181,000	55,240,000
Class B Common Stock [Member]
Common stock, par value	$ 0.0001	$ 0.0001
Common stock, shares authorized	41,203,000	41,203,000
Common stock, shares issued	25,394,000	26,814,000
Common stock, shares outstanding	25,394,000	26,814,000

Consolidated Statements of Oper

Consolidated Statements of Operations - USD ($) shares in Thousands, $ in Thousands	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Total revenue	$ 665,788	$ 612,701	$ 572,221
Total cost of revenue	124,803	121,791	122,889
Gross profit	540,985	490,910	449,332
Operating expenses
Research and development	221,161	212,645	202,542
Sales and marketing	184,280	176,138	163,884
General and administrative	90,150	70,887	72,288
Amortization of intangible assets	33,022	30,851	27,510
Other operating (income) expense, net	(5,313)	146	(9,955)
Total operating expenses	523,300	490,667	456,269
Operating income (loss)	17,685	243	(6,937)
Interest expense	5,836	6,116	4,377
Other (income) expense, net	(20,781)	(18,492)	16,899
Income (loss) before income taxes	32,630	12,619	(28,213)
Income tax expense	18,455	21,545	15,216
Net income (loss)	$ 14,175	$ (8,926)	$ (43,429)
Loss per share:
Income (loss) per share, basic	$ 0.17	$ (0.11)	$ (0.55)
Income (loss) per share, diluted	$ 0.16	$ (0.11)	$ (0.55)
Weighted average shares
Weighted average shares , basic	84,085	80,596	79,472
Weighted average shares , diluted	88,558	80,596	79,472
Total Software [Member]
Total revenue	$ 611,900	$ 549,974	$ 506,508
Total cost of revenue	79,113	71,182	72,443
License [Member]
Total revenue	435,288	393,144	363,520
Total cost of revenue	15,099	15,088	20,497
Maintenance and Other Services [Member]
Total revenue	176,612	156,830	142,988
Total cost of revenue	64,014	56,094	51,946
Engineering Services And Other [Member]
Total revenue	53,888	62,727	65,713
Total cost of revenue	$ 45,690	$ 50,609	$ 50,446

Consolidated Statements of Comp

Consolidated Statements of Comprehensive Loss - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Statement of Comprehensive Income [Abstract]
Net Income (Loss)	$ 14,175	$ (8,926)	$ (43,429)
Other comprehensive (loss) income, net of tax:
Foreign currency translation (net of tax effect of $0 for all periods)	(15,490)	9,011	(24,084)
Retirement related benefit plans (net of tax effect of $(251), $177 and $(308), respectively)	518	(1,318)	3,032
Total other comprehensive (loss) income	(14,972)	7,693	(21,052)
Comprehensive loss	$ (797)	$ (1,233)	$ (64,481)

Consolidated Statements of Co_2

Consolidated Statements of Comprehensive Loss (Parenthetical) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Statement of Comprehensive Income [Abstract]
Foreign currency translation, tax effect	$ 0	$ 0	$ 0
Retirement related benefit plans, tax effect	$ (251)	$ 177	$ (308)

Consolidated Statement of Chang

Consolidated Statement of Changes in Stockholders' Equity (Deficit) - USD ($) shares in Thousands, $ in Thousands	Total	Cumulative Effect, Period of Adoption, Adjustment [Member]	Common Stock [Member] Class A Common Stock [Member]	Common Stock [Member] Class B Common Stock [Member]	Additional Paid-in Capital [Member]	Additional Paid-in Capital [Member] Cumulative Effect, Period of Adoption, Adjustment [Member]	Accumulated Deficit [Member]	Accumulated Deficit [Member] Cumulative Effect, Period of Adoption, Adjustment [Member]	Accumulated Other Comprehensive Loss [Member]
Beginning balance at Dec. 31, 2021	$ 613,197		$ 5	$ 3	$ 724,226		$ (102,087)		$ (8,950)
Beginning balance (in shares) at Dec. 31, 2021			51,524	27,745
Net Income (Loss)	(43,429)						(43,429)
Settlement of convertible senior notes	(29,756)				(29,756)
Repurchase and retirement of common stock, Shares			(461)
Repurchase and retirement of common stock	(21,658)				(21,658)
Reclassification of mezzanine equity to permanent equity	784				784
Issuance of common stock for acquisitions	224				224
Issuance of common stock for acquisitions (in shares)			111
Issuance of common stock for employee stock purchase program (in shares)			185
Issuance of common stock for employee stock purchase program	8,723				8,723
Exercise of stock options	3,577				3,577
Exercise of stock options (in shares)			440
Vesting of restricted stock (in shares)			478
Stock-based compensation	85,196				85,196
Foreign currency translation, net of tax	(24,084)								(24,084)
Retirement related benefit plans, net of tax	3,032								3,032
Ending balance at Dec. 31, 2022	569,736	$ (26,070)	$ 5	$ 3	721,307	$ (50,009)	(121,577)	$ 23,939	(30,002)
Ending balance (in shares) at Dec. 31, 2022			52,277	27,745
Net Income (Loss)	(8,926)						(8,926)
Repurchase and retirement of common stock, Shares			(91)
Repurchase and retirement of common stock	(4,256)				(4,256)
Issuance of common stock for acquisitions	17,570				17,570
Issuance of common stock for acquisitions (in shares)			349
Issuance of common stock for employee stock purchase program (in shares)			183
Issuance of common stock for employee stock purchase program	7,793				7,793
Exercise of stock options	36,140				36,140
Exercise of stock options (in shares)			1,052
Vesting of restricted stock (in shares)			539
Conversion from Class B to Class A common stock			931	(931)
Stock-based compensation	85,581				85,581
Foreign currency translation, net of tax	9,011								9,011
Retirement related benefit plans, net of tax	(1,318)								(1,318)
Ending balance at Dec. 31, 2023	711,331		$ 5	$ 3	864,135		(130,503)		(22,309)
Ending balance (in shares) at Dec. 31, 2023			55,240	26,814
Net Income (Loss)	14,175						14,175
Settlement of convertible senior notes (in shares)			797
Issuance of common stock for acquisitions	4,020				4,020
Issuance of common stock for acquisitions (in shares)			259
Issuance of common stock for employee stock purchase program (in shares)			125
Issuance of common stock for employee stock purchase program	8,549				8,549
Exercise of stock options	66,406		$ 1		66,405
Exercise of stock options (in shares)			1,808
Vesting of restricted stock (in shares)			532
Conversion from Class B to Class A common stock			1,420	(1,420)
Stock-based compensation	67,680				67,680
Foreign currency translation, net of tax	(15,490)								(15,490)
Retirement related benefit plans, net of tax	518								518
Ending balance at Dec. 31, 2024	$ 857,189		$ 6	$ 3	$ 1,010,789		$ (116,328)		$ (37,281)
Ending balance (in shares) at Dec. 31, 2024			60,181	25,394

Consolidated Statements of Cash

Consolidated Statements of Cash Flows - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
OPERATING ACTIVITIES:
Net income (loss)	$ 14,175	$ (8,926)	$ (43,429)
Adjustments to reconcile net income (loss) to net cash provided by operating activities:
Depreciation and amortization	42,164	39,124	35,504
Stock-based compensation expense	67,680	85,581	84,787
Deferred income taxes	(707)	(2,319)	(4,164)
Loss (gain) on mark-to-market adjustment of contingent consideration	476	5,706	(7,153)
Expense on repurchase of convertible senior notes	0	0	16,621
Other, net	2,015	1,943	2,179
Changes in assets and liabilities:
Accounts receivable	14,560	(19,141)	(34,175)
Prepaid expenses and other current assets	(7,622)	(1,915)	1,014
Other long-term assets	2,431	(52)	2,852
Accounts payable	(2,127)	(1,878)	3,771
Accrued compensation and benefits	7,013	1,783	280
Other accrued expenses and current liabilities	7,791	9,068	(59,463)
Deferred revenue	6,235	18,333	40,946
Net cash provided by operating activities	154,084	127,307	39,570
INVESTING ACTIVITIES:
Payments for acquisition of businesses, net of cash acquired	(27,070)	(3,236)	(134,541)
Capital expenditures	(14,086)	(10,193)	(9,648)
Other investing activities, net	(4,974)	(2,423)	(10,322)
Net cash used in investing activities	(46,130)	(15,852)	(154,511)
FINANCING ACTIVITIES:
Settlement of convertible senior notes	(81,729)	0	0
Proceeds from the exercise of common stock options	65,537	36,140	3,577
Proceeds from employee stock purchase plan contributions	9,157	7,978	8,976
Payments for repurchase and retirement of common stock	0	(6,255)	(19,659)
Proceeds from issuance of convertible senior notes, net of underwriters' discounts and commissions	0	0	224,265
Repurchase of convertible senior notes	0	0	(192,422)
Payments for issuance costs of convertible senior notes	0	0	(1,523)
Other financing activities	0	(97)	(233)
Net cash (used in) provided by financing activities	(7,035)	37,766	22,981
Effect of exchange rate changes on cash, cash equivalents and restricted cash	(6,453)	1,397	(5,094)
Net increase (decrease) in cash, cash equivalents and restricted cash	94,466	150,618	(97,054)
Cash, cash equivalents and restricted cash at beginning of year	467,576	316,958	414,012
Cash, cash equivalents and restricted cash at end of period	562,042	467,576	316,958
Supplemental disclosures of cash flow:
Interest paid	4,339	4,242	2,425
Income taxes paid	9,306	11,291	8,941
Supplemental disclosure of non-cash investing and financing activities:
Issuance of common stock in connection with acquisitions	4,020	17,570	224
Promissory notes issued and deferred payment obligations for acquisitions and investments	7,774	3,201	1,350
Property and equipment in accounts payable and other current liabilities	$ 1,049	$ 1,019	$ 659

Pay vs Performance Disclosure

Pay vs Performance Disclosure - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Pay vs Performance Disclosure
Net Income (Loss)	$ 14,175	$ (8,926)	$ (43,429)

Insider Trading Arrangements

Insider Trading Arrangements	3 Months Ended
	Dec. 31, 2024 shares
Trading Arrangements, by Individual
Material Terms of Trading Arrangement	During the fiscal quarter ended December 31, 2024 , James R. Scapa , our Chairman and Chief Executive Officer , terminated his previously adopted Rule 10b5-1 plan. The trading arrangement provided for the sale of up to 156,000 shares of our Class A common stock, was set to expire no later than May 28, 2025 , and was intended to satisfy the affirmative defense of Rule 10b5-1. During the quarter ended December 31, 2024, except as provided above, none of the Company’s directors or officers adopted or terminated a “Rule 10b5-1 trading arrangement” or “non-Rule 10b5-1 trading arrangement,” as those terms are defined in Regulation S-K, Item 408, that was intended to satisfy the affirmative defense conditions of Rule 10b5-1(c).
Rule 10b5-1 Arrangement Adopted	false
Non-Rule 10b5-1 Arrangement Adopted	false
Rule 10b5-1 Arrangement Terminated	false
Non-Rule 10b5-1 Arrangement Terminated	false
James R. Scapa [Member]
Trading Arrangements, by Individual
Name	James R. Scapa
Title	Chairman and Chief Executive Officer
Rule 10b5-1 Arrangement Terminated	true
Termination Date	December 31, 2024
Expiration Date	May 28, 2025
Aggregate Available	156,000

Insider Trading Policies and Pr

Insider Trading Policies and Procedures	3 Months Ended
	Dec. 31, 2024
Insider Trading Policies and Procedures [Line Items]
Insider Trading Policies and Procedures Adopted	true

Cybersecurity Risk Management,

Cybersecurity Risk Management, Strategy, and Governance	12 Months Ended
	Dec. 31, 2024
Cybersecurity Risk Management, Strategy, and Governance [Line Items]
Cybersecurity Risk Management Processes for Assessing, Identifying, and Managing Threats [Text Block]	Item 1C. Cybersecurity We believe cybersecurity is a necessity for operating our business. As a global leader in computational science and artificial intelligence, we face many cybersecurity threats that range from common attack patterns, such as ransomware and denial-of-service, to attacks from sophisticated and persistent adversaries, including nation state actors, that target companies with innovative technology. Our customers, vendors and other third-party partners face similar cybersecurity threats, and a cybersecurity incident impacting us or any of these entities could materially adversely affect our operations, performance and results of operations. These cybersecurity threats and related risks make it imperative that we carefully execute our cybersecurity operations, strategy and governance. The Board of Directors are informed of cybersecurity risks and provide oversight to the executive management team with the day-to-day responsibility of cybersecurity functions, auditing and budget. Senior leadership, including our Chief Information Security Officer (CISO), regularly briefs the Board of Directors on our cybersecurity and information security posture and the Board of Directors is apprised of cybersecurity incidents deemed to impair data confidentiality, integrity and/or availability. In the event of an incident, we intend to follow our customized incident response playbooks, which outline the steps to be followed from incident detection to mitigation, recovery and notification, including notifying functional areas (e.g. legal), as well as senior leadership and the Board, as appropriate. Our procedures vary slightly depending on the type of incident at issue (e.g., account compromise, malware, data loss) as well as the data compromised. Our corporate information security team, led by our CISO, is responsible for our overall information security strategy, policy, security engineering, security operations (as a second line of defense) and cyber threat detection and response. The current CISO has more than ten years’ experience in cybersecurity and 35 years as an information technology professional. Given that our CISO has more than 25 years at the Company in multiple positions, he helped incubate and grow our corporate information security team into what it is today. During 2024 Altair chose to grow its security team further, recognizing the ever-increasing threats; a Director for IT Security was brought on board and a number of global staff were added to the Security Operations team. Our information security management philosophy is one of cyber risk prevention and we have the ultimate goal of preventing cyber incidents. Simultaneously, our information security team focuses on increasing our system resilience to minimize data breach (or other compromise) business impact should an incident occur. Cybersecurity is not the sole responsibility of our information security team. During 2024 and into 2025 we have increased the Security team involvement with business leaders. Our Security team works closely with internal departments to keep security at the forefront. Our employees and vendors also play a role in our company’s cybersecurity efforts. Through our cybersecurity awareness training and other team training we are fostering a culture that all employees and vendors have a role in our cybersecurity defenses. The corporate information security team has implemented a governance structure and processes to assess, identify, manage and report cybersecurity risks. We also have threat intelligence and insider threat programs to identify external and internal threats, and to mitigate those threats in a timely manner to the best of our ability. In addition, we have further developed security corporate practices, controls, and frameworks, which we believe enhance our ability to identify and manage cybersecurity risks. We employ a data privacy counsel to specifically improve our responses to growing international privacy laws. We believe that this enhances our data control and thus may reduce risk. Third parties also play a role in our cybersecurity and supplement our program. We engage third-party services in some vital areas of our business to conduct evaluations of our security controls, whether through penetration testing, independent audits or consulting on best practices to address new challenges. Additionally, we leverage a Security Operations Center ("SOC")-as-a-Service provider to ensure continuous monitoring and rapid response to potential threats, enhancing our ability to maintain a robust security posture at all times. We employ risk management functionality and document enterprise information security risks. Our information security team maintains documentation to assess risk and mitigate cyber risk in alignment with risk (understanding general impact and likelihood of risk exploitation), resources, and business process. Cybersecurity risks are tracked throughout the risk management process from risk mitigation to ultimate completion of remediation. From time-to-time significant risks may be escalated to the executive management team and/or the Board in the existing executive management processes for cybersecurity and Board briefing schedule. We rely on our indirect sales channel partners and supply chain to deliver our products and services to our customers, and a cybersecurity incident at a channel partner, supplier, subcontractor or joint venture partner could materially adversely impact us. We also contractually flow cybersecurity regulatory requirements to our subcontractors in alignment with legal and contractual obligations. Extensive international law and US-sector specific laws pertaining to privacy and data security may create challenges for our supply chain and increase costs as we continue to flow down legal obligations. Despite our careful planning, we may not be successful in preventing or mitigating a cybersecurity incident that could have a material adverse effect on us. While the Company maintains cybersecurity insurance, the costs related to cybersecurity threats or disruptions may not be fully insured. See Item 1A. “Risk Factors” for a discussion of cybersecurity risks.
Cybersecurity Risk Materially Affected or Reasonably Likely to Materially Affect Registrant [Flag]	false
Cybersecurity Risk Board of Directors Oversight [Text Block]	The Board of Directors are informed of cybersecurity risks and provide oversight to the executive management team with the day-to-day responsibility of cybersecurity functions, auditing and budget. Senior leadership, including our Chief Information Security Officer (CISO), regularly briefs the Board of Directors on our cybersecurity and information security posture and the Board of Directors is apprised of cybersecurity incidents deemed to impair data confidentiality, integrity and/or availability. In the event of an incident, we intend to follow our customized incident response playbooks, which outline the steps to be followed from incident detection to mitigation, recovery and notification, including notifying functional areas (e.g. legal), as well as senior leadership and the Board, as appropriate. Our procedures vary slightly depending on the type of incident at issue (e.g., account compromise, malware, data loss) as well as the data compromised. Our corporate information security team, led by our CISO, is responsible for our overall information security strategy, policy, security engineering, security operations (as a second line of defense) and cyber threat detection and response. The current CISO has more than ten years’ experience in cybersecurity and 35 years as an information technology professional. Given that our CISO has more than 25 years at the Company in multiple positions, he helped incubate and grow our corporate information security team into what it is today. During 2024 Altair chose to grow its security team further, recognizing the ever-increasing threats; a Director for IT Security was brought on board and a number of global staff were added to the Security Operations team. Our information security management philosophy is one of cyber risk prevention and we have the ultimate goal of preventing cyber incidents. Simultaneously, our information security team focuses on increasing our system resilience to minimize data breach (or other compromise) business impact should an incident occur. Cybersecurity is not the sole responsibility of our information security team. During 2024 and into 2025 we have increased the Security team involvement with business leaders. Our Security team works closely with internal departments to keep security at the forefront. Our employees and vendors also play a role in our company’s cybersecurity efforts. Through our cybersecurity awareness training and other team training we are fostering a culture that all employees and vendors have a role in our cybersecurity defenses.
Cybersecurity Risk Board Committee or Subcommittee Responsible for Oversight [Text Block]	The Board of Directors are informed of cybersecurity risks and provide oversight to the executive management team with the day-to-day responsibility of cybersecurity functions, auditing and budget. Senior leadership, including our Chief Information Security Officer (CISO), regularly briefs the Board of Directors on our cybersecurity and information security posture and the Board of Directors is apprised of cybersecurity incidents deemed to impair data confidentiality, integrity and/or availability.
Cybersecurity Risk Process for Informing Board Committee or Subcommittee Responsible for Oversight [Text Block]	We employ risk management functionality and document enterprise information security risks. Our information security team maintains documentation to assess risk and mitigate cyber risk in alignment with risk (understanding general impact and likelihood of risk exploitation), resources, and business process. Cybersecurity risks are tracked throughout the risk management process from risk mitigation to ultimate completion of remediation. From time-to-time significant risks may be escalated to the executive management team and/or the Board in the existing executive management processes for cybersecurity and Board briefing schedule.
Cybersecurity Risk Role of Management [Text Block]	Our corporate information security team, led by our CISO, is responsible for our overall information security strategy, policy, security engineering, security operations (as a second line of defense) and cyber threat detection and response. The current CISO has more than ten years’ experience in cybersecurity and 35 years as an information technology professional. Given that our CISO has more than 25 years at the Company in multiple positions, he helped incubate and grow our corporate information security team into what it is today. During 2024 Altair chose to grow its security team further, recognizing the ever-increasing threats; a Director for IT Security was brought on board and a number of global staff were added to the Security Operations team. Our information security management philosophy is one of cyber risk prevention and we have the ultimate goal of preventing cyber incidents. Simultaneously, our information security team focuses on increasing our system resilience to minimize data breach (or other compromise) business impact should an incident occur. Cybersecurity is not the sole responsibility of our information security team. During 2024 and into 2025 we have increased the Security team involvement with business leaders. Our Security team works closely with internal departments to keep security at the forefront. Our employees and vendors also play a role in our company’s cybersecurity efforts. Through our cybersecurity awareness training and other team training we are fostering a culture that all employees and vendors have a role in our cybersecurity defenses.
Cybersecurity Risk Management Positions or Committees Responsible [Flag]	true
Cybersecurity Risk Management Positions or Committees Responsible [Text Block]	Our corporate information security team, led by our CISO, is responsible for our overall information security strategy, policy, security engineering, security operations (as a second line of defense) and cyber threat detection and response.
Cybersecurity Risk Management Expertise of Management Responsible [Text Block]	The current CISO has more than ten years’ experience in cybersecurity and 35 years as an information technology professional. Given that our CISO has more than 25 years at the Company in multiple positions, he helped incubate and grow our corporate information security team into what it is today.
Cybersecurity Risk Process for Informing Management or Committees Responsible [Text Block]	We rely on our indirect sales channel partners and supply chain to deliver our products and services to our customers, and a cybersecurity incident at a channel partner, supplier, subcontractor or joint venture partner could materially adversely impact us. We also contractually flow cybersecurity regulatory requirements to our subcontractors in alignment with legal and contractual obligations. Extensive international law and US-sector specific laws pertaining to privacy and data security may create challenges for our supply chain and increase costs as we continue to flow down legal obligations.
Cybersecurity Risk Management Positions or Committees Responsible Report to Board [Flag]	true

Description of Business

Description of Business	12 Months Ended
	Dec. 31, 2024
Organization, Consolidation and Presentation of Financial Statements [Abstract]
Description of Business	1. Description of business Altair Engineering Inc. (“Altair” or the “Company”) is incorporated in the state of Delaware. The Company is a global leader in computational intelligence enabling organizations across broad industry segments to drive smarter decisions in an increasingly connected world. Altair delivers software and cloud solutions in the areas of simulation, high-performance computing (“HPC”), data analytics, and artificial intelligence (“AI”). Altair’s products and services leverage computational science to drive innovation and intelligent decisions for a more connected, safe, and sustainable future. The Company is based in Troy, Michigan. The Company’s simulation and AI-driven approach to innovation is powered by the Company’s broad portfolio of high-fidelity and high-performance physics solvers, our market leading technology for optimization and HPC, and our end-to-end platform for developing AI and Internet of Things (“IoT”) solutions. The Company’s integrated suite of software optimizes design performance across multiple disciplines encompassing structures, motion, fluids, thermal management, electromagnetics, system modeling, and embedded systems, while also providing AI solutions and true-to-life visualization and rendering. The Company's HPC solutions maximize the efficient utilization of complex compute resources and streamline the workflow management of compute-intensive tasks for applications including AI, modeling and simulation, and visualization. Altair's data analytics, AI, and IoT products include data preparation, data science, MLOps, orchestration, and visualization solutions that fuel engineering, scientific, and business decisions. Altair also provides Client Engineering Services to support its customers with long-term ongoing product design and development expertise. This has the benefit of embedding the Company within customers, deepening its understanding of their processes, and allowing the Company to quickly perceive trends in the overall market, helping the Company to better tailor its software products’ research and development and sales initiatives. The Company hires engineers and data scientists for placement at a customer site for specific customer-directed assignments. Pending Merger with Siemens Industry On October 30, 2024, Altair entered into an agreement and plan of merger (the “Merger Agreement”) with Siemens Industry Software, Inc. ("Siemens Industry") and Astra Merger Sub Inc., a wholly owned subsidiary of Siemens Industry (“Merger Sub”), pursuant to which Merger Sub will merge with and into Altair (the “Merger”), with Altair surviving the Merger as a wholly owned subsidiary of Siemens Industry. Altair stockholders will receive $ 113.00 per share in cash, representing an enterprise value of approximately $ 10.6 billion. The $ 113.00 per share cash consideration represents a 19 % premium to the closing price of Altair common stock on October 21, 2024. The transaction, which was unanimously approved by the Altair Board of Directors and obtained approval by Altair's stockholders, may close in the first half of 2025, following the receipt of certain regulatory approvals and foreign investment approvals and the satisfaction of customary closing conditions. Upon completion of the transaction, Altair’s common stock will no longer be listed on any public stock exchange. For the year ended December 31, 2024, the Company incurred approximately $ 22.3 million in expenses related to the pending Merger with Siemens Industry. These costs are included in Cost of revenue for $ 1.2 million, Research and development expense for $ 1.8 million, Sales and marketing expense for $ 1.3 million, and General and administrative expense for $ 18.2 million.

Summary of Significant Accounti

Summary of Significant Accounting Policies	12 Months Ended
	Dec. 31, 2024
Accounting Policies [Abstract]
Summary of Significant Accounting Policies	2. Summary of significant accounting policies Principles of consolidation The accompanying consolidated financial statements have been prepared using accounting principles generally accepted in the United States of America (“GAAP”). The consolidated financial statements include the results of the Company and its controlled subsidiaries. Intercompany accounts and transactions have been eliminated in the consolidated financial statements. Change in Presentation of Revenue and Cost of Revenue Effective in the first quarter of 2024, the Company changed the presentation of revenue and cost of revenue in its Consolidated Use of estimates The preparation of the consolidated financial statements in conformity with GAAP requires management to make estimates and assumptions that affect the reported amounts of assets and liabilities and disclosures of contingent assets and liabilities at the date of the financial statements, and reported amounts of revenue and expenses during the reporting periods. On an ongoing basis, management evaluates its significant estimates including the stand alone selling price, or SSP, for each distinct performance obligation included in customer contracts with multiple performance obligations, the incremental borrowing rate used in the valuation of lease liabilities, fair value of convertible senior notes, provision for expected credit losses, tax valuation allowances, liabilities for uncertain tax provisions, impairment of goodwill and intangible assets, retirement obligations, useful lives of intangible assets, revenue for fixed price contracts, and stock-based compensation. Actual results could differ from those estimates. Foreign currency translation The functional currency of the Company’s foreign subsidiaries is their respective local currency. The assets and liabilities of the subsidiaries are translated to U.S. dollars at the exchange rate as of the balance sheet date. Equity balances and transactions are translated using historical exchange rates. Revenues and expenses are translated at the average exchange rate during the period. Translation adjustments arising from the use of differing exchange rates from period to period are recorded as a component of accumulated other comprehensive loss within stockholders’ equity. All assets and liabilities denominated in a currency other than the functional currency are remeasured into the functional currency with gains and losses recognized in foreign currency losses, net, in the consolidated statements of operations. The Company has no transactions which hedge purchase commitments and no intercompany balances which are designated as being of a long-term investment in nature. Revenue recognition Software revenue Revenue is derived principally from the licensing of software products and from related maintenance contracts. The Company enters into contracts that include combinations of products, maintenance and services, which are accounted for as separate performance obligations with differing revenue recognition patterns. Revenue from term-based software licenses is classified as software revenue. Term-based licenses are sold only as a bundled arrangement that includes the rights to a term-based software license and post-contract customer support (PCS), which includes unspecified technical enhancements and customer support. Maximizing the use of observable inputs, the Company determined that a majority of the estimated standalone selling prices of the term-based license is attributable to the term-based license and a minority is attributable to the PCS. The license component is classified as license revenue and recognized as revenue upon the later of delivery of the licensed product or the beginning of the license period. PCS is classified as maintenance and other services and is recognized ratably over the term of the contract, as the Company provides the PCS benefit over time as a stand ready to perform obligation. In addition to term-based software licenses, the Company sells perpetual licenses. Software revenue is recognized upon the later of delivery of the licensed product or the beginning of the license period. Typically, the Company’s perpetual licenses are sold with PCS. The Company allocates value in bundled perpetual and PCS arrangements based on the value relationship between the software license and maintenance. Revenue from PCS is classified as maintenance and other services and is recognized ratably over the term of the contract, as the Company satisfies the PCS performance obligation over time as a stand ready to perform obligation. Revenue from training, consulting and other services is recognized as the services are performed and is classified as maintenance and other services in the consolidated statement of operations. For contracts in which the service consists of a single performance obligation, such as providing a training class to a customer, the Company recognizes revenue upon completion of the performance obligation. For service contracts that are longer in duration and often include multiple performance obligations (for example, point-in-time training and consulting), the Company measures the progress toward completion of the obligations and recognizes revenue accordingly. In measuring progress towards the completion of performance obligations, the Company typically utilizes output-based estimates for services with fixed fee arrangements, and estimates output based on the total tasks completed as compared to the total tasks required for each contract. Input-based estimates are utilized for services that involve general consultations with contractual billing arrangements based on time and materials, utilizing direct labor as the input measure. The Company also executes arrangements through indirect channel partners in which the channel partners are authorized to market and distribute the Company's software products to end users of the Company's products and services in specified territories. In sales facilitated by channel partners, the channel partner bears the risk of collection from the end-user customer. The Company recognizes revenue from transactions with channel partners in a manner consistent with the direct sales described above for both perpetual and term-based licenses. Revenue from channel partner transactions is the amount remitted to the Company by the channel partners. This amount includes a fee for PCS that is compensation for providing technical enhancements and the second level of technical support to the end user, which is recognized over the period that PCS is to be provided. The Company does not offer right of return, product rotation, or price protection to any of its channel partners. Non-income related taxes collected from customers and remitted to governmental authorities are recorded on the consolidated balance sheets as accounts receivable, net and other accrued expenses and current liabilities. These amounts are reported on a net basis in the consolidated statements of operations and do not impact reported revenues or expenses. Certain hardware revenue is included within software revenue and is recognized when all revenue recognition criteria stated above are met, which is generally when the products are delivered to end customers. Engineering services and other revenue Consulting services from product design and development projects are considered distinct performance obligations and are provided to customers on a time-and-materials (“T&M”) or fixed-price basis. The Company recognizes software services revenue for T&M contracts based upon hours worked and contractually agreed upon hourly rates using the input method. Revenue from fixed-price engagements is recognized using the output method based on the ratio of costs incurred to total estimated project costs. Client engineering services revenue are derived from professional services for staffing primarily representing engineers and data scientists located at a customer site. These professional services are considered distinct performance obligations and are provided to customers on a T&M basis. The Company recognizes this revenue for T&M contracts based upon hours worked and contractually agreed upon hourly rates using the input method. Revenue from the sale of LED products, primarily for the replacement of florescent tubes, is recognized when all revenue recognition criteria stated above are met, which is generally when the products are delivered to resellers or to end customers. Sales returns, which reduce revenue, are estimated using historical experience. Property and equipment, net Property and equipment are stated at cost, less accumulated depreciation and amortization. Equipment held under capital leases are stated at the present value of minimum lease payments less accumulated amortization. Depreciation is calculated using the straight-line method over the estimated useful lives of the assets. Expenditures for maintenance and repairs are charged to expense in the period incurred. Major expenditures for betterments are capitalized when they meet the criteria for capitalization. When assets are retired or otherwise disposed of, the cost and accumulated depreciation are removed from the accounts and any resulting gain or loss is reflected in the consolidated statements of operations in the period realized. Building and improvements are depreciated over an estimated useful life of five to thirty-nine years . Computer equipment and software is depreciated over an estimated useful life of three to five years . Office furniture and equipment is depreciated over an estimated useful life of five to fifteen years . Leasehold improvements and assets acquired under capital leases are amortized over the lease term or the estimated useful life of the related asset or improvement, whichever is shorter. Software development costs Software development costs incurred prior to the establishment of technological feasibility are expensed as incurred. Technological feasibility is established upon the completion of a detailed program design. Capitalization of software development costs may begin upon the establishment of technological feasibility and ends when the product is available for general release. Generally, the time between the establishment of technological feasibility and commercial release of software is short. As such, all internal software development costs have been expensed as incurred and included in research and development expense in the accompanying consolidated statements of operations. Impairment of long-lived assets Long-lived assets, such as property and equipment, and definite-lived intangible assets, including developed technology, customer relationships, and tradenames are reviewed for impairment whenever events or changes in circumstances indicate that the carrying amount of an asset may not be recoverable. If circumstances require a long-lived asset or asset group to be tested for possible impairment, the Company compares the undiscounted future cash flows expected to be generated by that asset or asset group to its carrying amount. If the carrying amount of the long-lived asset or asset group is not recoverable on an undiscounted cash flow basis, an impairment charge is recognized to the extent that the carrying amount exceeds its fair value. Fair value is determined through various valuation techniques, including discounted cash flow models and third-party independent appraisals. No impairment losses were recognized in 2024, 2023, or 2022. Goodwill Goodwill represents the excess of the consideration transferred for an acquired entity over the estimated fair values of the net tangible assets and the identifiable assets acquired. As described in Note 4 – Acquisitions, the Company has recorded goodwill in connection with certain acquisitions. Goodwill is not amortized but rather reviewed for impairment annually or more frequently if facts or circumstances indicate that the carrying value may not be recoverable. The Company has determined that there is one reporting unit with goodwill subject to goodwill impairment testing. An entity has the option to perform a qualitative assessment to determine whether it is more likely than not that the fair value of the reporting unit is less than its carrying amount prior to performing the quantitative two-step impairment test. The Company has the option to first assess qualitative factors to determine whether the existence of events or circumstances leads to a determination that it is more likely than not that the fair value of a reporting unit is less than its carrying amount prior to performing the quantitative two-step impairment test. The qualitative assessment evaluates various events and circumstances, such as macro-economic conditions, industry and market conditions, cost factors, relevant events and financial trends that may impact a reporting unit’s fair value. If, after assessing the totality of events or circumstances, an entity determines it is not more likely than not that the fair value of a reporting unit is less than its carrying amount, including goodwill, then additional impairment testing is not required. However, if an entity concludes otherwise, then it is required to perform the two-step goodwill impairment test. The impairment test involves comparing the estimated fair value of a reporting unit with its book value, including goodwill. If the estimated fair value exceeds book value, goodwill is considered not to be impaired. If, however, the fair value of the reporting unit is less than book value, then an impairment loss is recognized in an amount equal to the amount that the book value of the reporting unit exceeds its fair value, not to exceed the total amount of goodwill allocated to the reporting unit. The Company performs its annual impairment review of goodwill in the fourth quarter of each year and when a triggering event occurs between annual impairment dates. For 2024, the Company performed a qualitative assessment of goodwill and determined that it was not more likely than not that the fair value of its reporting unit with goodwill was less than its carrying amount. Accordingly, the Company determined that its goodwill was not impaired. Government assistance The Company receives incentives from federal, state and local governments in different regions of the world to primarily encourage the Company to establish, maintain, or increase investment or employment in the region. Government incentives are recorded in the consolidated financial statements in accordance with their purpose as a reduction of expense or other income based on the substance of the incentive received. Benefits are generally recorded when the conditions of the grant are met and there is reasonable assurance of receipt. The amounts are recorded in earnings as the expenses in which the incentive is meant to offset are incurred. For the years ended December 31, 2024, 2023 and 2022, respectively, other operating income includes $ 5.4 million, $ 5.6 million and $ 3.0 million of government related funding. Receivable for R&D credit The French government provides a research and development (“R&D”) tax credit known as Credit Impôt Recherche, or CIR, in order to encourage Companies to invest in R&D. The tax credit is deductible from the French income tax and any excess is carried forward for three years. After three years , any unused credit may be reimbursed to the Company by the French government. As of December 31, 2024, the Company had approximately $ 10.6 million of receivables from the French government related to CIR, of which $ 5.8 million was recorded in Income tax receivable and the remaining $ 4.8 million was recorded in Other long-term assets. As of December 31, 2023, the Company had approximately $ 12.1 million of receivables from the French government related to CIR, of which $ 5.7 million was recorded in Income tax receivable and the remaining $ 6.4 million was recorded in Other long-term assets. CIR is subject to customary audit by the French tax authorities. Other Investments Other investments include non-marketable equity investments in privately held companies, which do not have readily determinable fair values, and in which the Company does not have a controlling interest or significant influence. The Company applies the measurement alternative for non-marketable equity securities, measuring them at cost, less any impairment. These investments are presented within other long-term assets on our consolidated balance sheets and are periodically analyzed to determine whether there are indicators of impairment. Income taxes The Company accounts for income taxes under the asset and liability method. Deferred tax assets and liabilities are recognized for the future tax consequences attributable to differences between the financial statement carrying amounts of existing assets and liabilities and their respective tax basis and for operating loss and tax credit carryforwards. Deferred tax assets and liabilities are measured using enacted tax rates expected to apply to taxable income in the years in which those temporary differences are expected to be recovered or settled. The effect of a change in tax rates on deferred tax assets and liabilities is recognized in income in the period that includes the enactment date. The Company records net deferred tax assets to the extent it believes that these assets will more likely than not be realized. These deferred tax assets are subject to periodic assessments as to recoverability and if it is determined that it is more likely than not that the benefits will not be realized, valuation allowances are recorded which increase the provision for income taxes. In making such determination, the Company considers all available positive and negative evidence, including historical taxable income, projected future taxable income, the expected timing and reversal of existing temporary differences, ability to carryback losses, and tax planning strategies. If based upon the evidence, it is more likely than not that the deferred tax asset will not be realized, a valuation allowance is recorded. A valuation allowance is recognized to reduce deferred tax assets to the amount that management believes is more likely than not to be realized. The Company applies a more-likely-than-not recognition threshold to its accounting for tax uncertainties. The Company reviews all of its tax positions and makes determinations as to whether its tax positions are more likely than not to be sustained upon examination by the relevant taxing authorities. Only those benefits that have a greater than fifty percent likelihood of being sustained upon examination by taxing authorities are recognized. Interest and penalties related to uncertain tax positions are recorded in the provision for income taxes in the consolidated statements of operations. Research and development costs Research and development costs are expensed as incurred. Research and development expenses consist primarily of salaries and benefits of research and development employees and costs incurred related to the development of new software products and significant enhancements and engineering changes to existing software products. Advertising costs Advertising costs are expensed as incurred. Advertising expenses were $ 4.6 million, $ 5.1 million and $ 5.0 million for the years ended December 31, 2024, 2023 and 2022, respectively. Leases The Company determines if an arrangement is a lease at inception. Operating leases are included in operating lease right-of-use (“ROU”) assets, current portion of operating lease liabilities, and operating lease liabilities, net of current portion on the Company’s consolidated balance sheets. Stock-based compensation Employee stock-based awards, consisting of stock options, restricted stock units (RSUs) and employee stock purchase plan (ESPP) shares expected to be settled by issuing shares of Class A common stock, are recorded as equity awards. The fair value of stock options and ESPP shares on the date of grant is measured using the Black-Scholes option pricing model. The Company expenses the grant date fair value of its time-vested stock options subject to graded vesting using the straight-line method over the applicable service period. The Company expenses the fair value of ESPP shares over the offering period. The fair value of RSUs is measured using the fair value of the Company’s Class A common stock on the date of the grant. The fair value of RSUs is recognized as expense on a straight-line basis over the requisite service period, which is generally four years . Business combinations The Company accounts for business acquisitions using the acquisition method of accounting. The fair value of purchase consideration of the acquired businesses is allocated to the identifiable tangible and intangible assets acquired and liabilities assumed in the transaction based upon their estimated fair values as of the acquisition date. The excess of the purchase price over those fair values is recorded as goodwill. During the measurement period, which may be up to one year from the acquisition date, the Company may record adjustments to the assets acquired and liabilities assumed with the corresponding offset to goodwill. Upon the conclusion of the measurement period or final determination of the values of assets acquired or liabilities assumed, whichever comes first, any subsequent adjustments are recorded to the consolidated statements of operations. Recent accounting guidance Accounting standards adopted Reference Rate Reform – In March 2020, the Financial Accounting Standards Board ("FASB") issued Accounting Standards Update ("ASU") 2020-04 Reference Rate Reform (Topic 848) - Facilitation of the Effects of Reference Rate Reform on Financial Reporting. This ASU provides optional expedients and exceptions for applying U.S. GAAP to contract modifications and hedging relationships, subject to meeting certain criteria, that reference LIBOR or another rate that is expected to be discontinued. The Company adopted ASU 2020-04 on December 31, 2024. The adoption of this guidance did not have a material effect on the Company's consolidated financial statements. Segment Reporting – In November 2023, the FASB issued ASU 2023-07 Segment Reporting (Topic 280) - Improvements to Reportable Segment Disclosures. The update is intended to improve reportable segment disclosure requirements, primarily through enhanced disclosures about significant expenses. The ASU requires disclosures to include significant segment expenses that are regularly provided to the chief operating decision maker (CODM), a description of other segment items by reportable segment, and any additional measures of a segment's profit or loss used by the CODM when deciding how to allocate resources. The ASU also requires all annual disclosures currently required by Topic 280 to be included in interim periods. The Company adopted this update effective for fiscal year ended December 31, 2024. Accounting standards not yet adopted Income Taxes – In December 2023, the FASB issued ASU 2023-09, Income Taxes (Topic 740): Improvements to Income Tax Disclosures , which updates income tax disclosures related to the tax rate reconciliation and requires disclosure of income taxes paid by jurisdiction. The amendments are effective for fiscal years beginning after December 15, 2024. Early adoption is permitted. The amendments should be applied prospectively; however, retrospective application is permitted. The Company is currently evaluating this ASU to determine the effect on its related disclosures. Income Statement – In November 2024, the FASB issued ASU 2024-03, Income Statement - Reporting Comprehensive Income - Expense Disaggregation Disclosures (Subtopic 220-40): Disaggregation of Income Statement Expenses , which requires additional disclosures over certain expenses, including purchases of inventory, employee compensation, depreciation, intangible asset amortization, and other specific expense categories. This update also requires disclosure of the total amount of selling expenses and the Company's definition of selling expenses. This update is effective for fiscal years beginning after December 15, 2026, and interim periods within fiscal years beginning after December 15, 2027. Early adoption is permitted. The Company is evaluating this ASU to determine the effect on its related disclosures. Debt – In November 2024, the FASB issued ASU 2024-04, Debt - Debt with Conversion and Other Options (Subtopic 470-20): Induced Conversion of Convertible Debt Instruments , which clarifies the requirements for determining whether certain settlements of convertible debt instruments should be accounted for as an induced conversion. This update is effective for fiscal years beginning after December 15, 2025, including interim periods within those fiscal periods. Early adoption is permitted. The Company is evaluating this ASU to determine the effect on its related disclosures.

Revenue from Contracts with Cus

Revenue from Contracts with Customers	12 Months Ended
	Dec. 31, 2024
Revenue from Contract with Customer [Abstract]
Revenue from Contracts with Customers	3. Revenue from contracts with customers Significant judgments Software revenue The Company’s contracts with customers typically include promises to transfer licenses and services to a customer. Judgment is required to determine if the promises are separate performance obligations within the context of the arrangement, and if so, the allocation of the transaction price to each performance obligation. The Company’s determination of standalone selling price for performance obligations is based on the midpoint of the range of historical observable prices for goods and services sold separately. In addition, the Company estimates the standalone selling price for certain performance obligations where observable prices are not directly available, or a significant portion of historical prices are not within the range. In instances where standalone selling price was not determined based on the range of historical observable prices for goods and services sold separately, the Company used an adjusted market assessment approach to estimate the standalone selling price. In such cases the Company has considered market conditions and other observable inputs, such as internal price lists, peer data, and industry data for a similar or identical product or service. The Company estimates standalone selling price at contract inception considering all information that is reasonably available and is based on the amount of consideration for which the Company expects to be entitled in exchange for transferring the promised good or service to the customer. The corresponding revenues are recognized as the related performance obligations are satisfied. The Company’s contracts do not include a significant financing component requiring adjustment to the transaction price. Payment terms vary by contract type; however, arrangements typically stipulate a requirement for the customer to pay within 30 to 60 days. The Company rarely enters into agreements to modify previously executed contracts, which constitute contract modifications. The Company assesses each of these contract modifications to determine (i) if the additional products and services are distinct from the products and services in the original arrangement; and (ii) if the amount of consideration expected for the added products and services reflects the stand-alone selling price of those products and services, as adjusted for contract-specific circumstances. A contract modification meeting both criteria is accounted for as a separate contract. A contract modification not meeting both criteria is considered a change to the original contract and is accounted for on either (i) a prospective basis as a termination of the existing contract and the creation of a new contract; or (ii) a cumulative catch-up basis. Generally, the Company’s contract modifications meet both criteria and are accounted for as a separate contract, as adjusted for contract-specific circumstances. Disaggregation of revenue The Company disaggregates its revenue by type of performance obligation and timing of revenue recognition as follows (in thousands): Year ended December 31, 2024 2023 2022 Term licenses and other software products $ 388,751 $ 353,065 $ 320,181 Perpetual licenses 46,537 40,079 43,339 Maintenance 164,380 148,779 135,752 Professional software services 12,232 8,051 7,236 Software related services 25,367 28,032 30,661 Client engineering services 25,027 29,497 28,883 Other 3,494 5,198 6,169 Total revenue $ 665,788 $ 612,701 $ 572,221 T he Company derived approximately 13.3 %, 13.6 % and 13.9 % of its total revenue through indirect sales channels for the years ended December 31, 2024, 2023 and 2022, respectively. Costs to obtain a contract The Company pays commissions for new software product and PCS sales as well as for renewals of existing software and PCS contracts. Commissions paid to obtain renewal contracts are not commensurate with the commissions paid for new product sales and therefore, a portion of the commissions paid for new contracts relate to future renewals. The Company accounts for new product sales commissions using a portfolio approach and allocates the cost of commissions in proportion to the allocation of the transaction price of license and PCS performance obligations. Commissions allocated to the license and license renewal components are expensed at the time the license revenue is recognized. Commissions allocated to PCS are capitalized and amortized on a straight-line basis over a period of four years , reflecting the Company’s estimate of the expected period that it will benefit from those commissions. As of December 31, 2024 and 2023, respectively, capitalized costs to obtain a contract were $ 4.8 million and $ 4.3 million recorded in Prepaid and other current assets and $ 1.0 million and $ 0.9 million recorded in Other long-term assets. Sales commissions were $ 9.1 million, $ 8.8 million and $ 8.3 million for the years ended December 31, 2024, 2023 and 2022, respectively, and were included in Sales and marketing expense in the Company’s consolidated statements of operations. Contract assets As of December 31, 2024 and 2023, respectively, contract assets were $ 4.9 million and $ 5.2 million included in Accounts receivable and $ 2.1 million and $ 2.7 million included in Prepaid expenses and other current assets in the Company's consolidated balance sheets. Deferred revenue Deferred revenue consists of billings made or payments received in advance of revenue recognition from software license, PCS and professional services agreements. The timing of revenue recognition may differ from the timing of billings to customers. Payment terms vary by the type and location of customer and the products or services offered. The term between invoicing and when payment is due is not significant. The Company generally invoices its customers annually for the forthcoming year of software licenses, and more frequently for other products and services. Accordingly, the Company’s deferred revenue balance does not include revenue for future years of multiple year non-cancellable contracts that have not yet been billed. Approximately $ 131.2 million of revenue recognized during 2024 was included in the deferred revenue balances at the beginning of the year. Revenue allocated to remaining performance obligations represents contracted revenue that has not yet been recognized, which includes deferred revenue and amounts that will be invoiced and recognized as revenue in future periods. Contracted revenue not yet recognized was $ 270.6 million as of December 31, 2024, of which the Company expects to recognize approximately 71 % over the next 12 months and the remainder thereafter.

Acquisitions

Acquisitions	12 Months Ended
	Dec. 31, 2024
Business Combination, Asset Acquisition, and Joint Venture Formation [Abstract]
Acquisitions	4. Acquisitions 2024 Acquisitions During the year ended December 31, 2024, the Company completed four acquisitions that were accounted for as business combinations under the acquisition method. The preliminary aggregate transaction consideration of $ 36.8 million was allocated to the assets acquired and liabilities assumed at their estimated fair values. The fair values assigned to the identifiable intangible assets acquired were based on estimates and assumptions determined by management. The aggregate allocation included $ 21.4 million to developed technology, $ 3.1 million to customer relationships, and $ 13.0 million to goodwill, of which $ 5.1 million is deductible for tax purposes. All goodwill was recorded in the Software segment. The Company expects to finalize the purchase accounting as soon as practicable, but not later than one year from the respective acquisition dates. These acquisitions were financed with cash on hand. The operating results of each acquisition have been included in the consolidated financial statements since the respective dates of acquisition and were not material to the consolidated financial statements. The Company’s transaction costs related to these 2024 acquisitions were not material. Prior acquisitions The Company finalized the valuation of its 2023 acquisitions during the period ended December 31, 2024. There were no significant changes to the preliminary fair value of assets acquired and liabilities assumed, as previously reported. The Company recognized a $ 0.5 million loss, a $ 5.7 million loss and a $ 7.2 million gain, respectively, for the years ended December 31, 2024, 2023 and 2022, from a mark-to-market adjustments of contingent consideration associated with acquisitions. The mark-to-market adjustments were included in Other operating (income) expense, net in the consolidated statements of operations. As of December 31, 2022, the Company had a $ 12.0 million contingent consideration liability related to the World Programming acquisition. The Company settled the liability in October 2023 by issuing 257,382 shares of its Class A common stock in accordance with the acquisition agreement.

Supplementary Information

Supplementary Information	12 Months Ended
	Dec. 31, 2024
Supplementary Information [Abstract]
Supplementary Information	5. Supplementary Information Cash, cash equivalents and restricted cash The Company considers all highly liquid investments with original or remaining maturities of 90 days or less at the date of purchase to be cash equivalents. Cash and cash equivalents are recorded at cost, which approximates fair value. Restricted cash is included in Other long-term assets on the consolidated balance sheets. The following table provides a reconciliation of cash, cash equivalents and restricted cash reported in the consolidated balance sheets that sum to the total of the amounts reported in the consolidated statements of cash flows (in thousands): December 31, 2024 2023 Cash and cash equivalents $ 561,898 $ 467,459 Restricted cash included in other long-term assets 144 117 Total cash, cash equivalents, and restricted cash $ 562,042 $ 467,576 Restricted cash represents amounts required for a contractual agreement with an insurer for the payment of potential health insurance claims, and term deposits for bank guarantees. Accounts receivable, net Accounts receivable, net consisted of the following (in thousands): December 31, 2024 2023 Accounts receivable, trade $ 168,625 $ 185,275 Contract assets 4,884 5,186 Accounts receivable, net $ 173,509 $ 190,461 A provision for expected credit losses for groups of billed and unbilled receivables and contract assets that share similar risk characteristics is recorded based on an evaluation of historical loss experience, current conditions, and reasonable and supportable forecasts. Accounts are written off when it becomes apparent that such amounts will not be collected, generally when amounts are past due by greater than one year. Generally, the Company does not require collateral or charge interest on accounts receivable. Accounts receivable were reported net of a provision for credit loss of $ 1.7 million and $ 2.9 million at December 31, 2024 and 2023, respectively. Activity in the provision for credit loss was as follows (in thousands): Year ended December 31, 2024 2023 2022 Balance, beginning of year $ ( 2,941 ) $ ( 2,590 ) $ ( 2,539 ) Provision charged to expense ( 414 ) ( 299 ) ( 203 ) Write-off, net of recoveries 1,508 6 498 Effects of foreign currency translation 102 ( 58 ) ( 346 ) Balance, end of year $ ( 1,745 ) $ ( 2,941 ) $ ( 2,590 ) Property and equipment, net Property and equipment consisted of the following (in thousands): Estimated December 31, useful lives 2024 2023 Land Indefinite $ 8,371 $ 8,376 Building and improvements 5 - 39 years 17,903 17,528 Computer equipment and software 3 - 5 years 47,397 45,678 Office furniture and equipment 5 - 15 years 13,738 14,402 Leasehold improvements (1 ) 9,284 8,380 Total property and equipment 96,693 94,364 Less: accumulated depreciation and amortization 55,685 54,561 Property and equipment, net $ 41,008 $ 39,803 (1) Shorter of lease term or estimated useful life, generally ranging from five to ten years . Depreciation expense was $ 9.1 million, $ 8.3 million and $ 8.0 million for the years ended December 31, 2024, 2023 and 2022, respectively. Other liabilities The following table provides the details of other accrued expenses and current liabilities (in thousands): December 31, 2024 2023 Income taxes payable $ 13,965 $ 12,239 Accrued VAT 10,390 8,710 Accrued professional fees 5,718 2,436 Obligations related to acquisitions of businesses and technology 5,621 3,286 Employee stock purchase plan obligations 4,762 4,155 Accrued royalties 2,562 2,313 Non-income tax liabilities 2,335 2,473 Billings in excess of cost 2,138 2,385 Defined contribution plan liabilities 1,491 1,454 Other current liabilities 7,076 8,947 Total $ 56,058 $ 48,398 The following table provides the details of other long-term liabilities (in thousands): December 31, 2024 2023 Income tax reserves $ 11,902 $ 16,254 Pension and other post-retirement liabilities 16,052 15,815 Deferred tax liabilities 13,314 12,870 Other liabilities 6,749 2,212 Total $ 48,017 $ 47,151 Other (income) expense, net Other (income) expense, net consists of the following (in thousands): Year ended December 31, 2024 2023 2022 Interest income $ ( 22,995 ) $ ( 16,855 ) $ ( 4,127 ) Foreign exchange loss (gain) 2,214 ( 1,637 ) 4,405 Expense on repurchase of convertible senior notes — — 16,621 Other (income) expense, net $ ( 20,781 ) $ ( 18,492 ) $ 16,899

Goodwill and Other Intangible A

Goodwill and Other Intangible Assets	12 Months Ended
	Dec. 31, 2024
Goodwill and Intangible Assets Disclosure [Abstract]
Goodwill and Other Intangible Assets	6. Goodwill and other intangible assets Goodwill The changes in the carrying amount of goodwill, which is attributable to the Software reportable segment, are as follows (in thousands): Balance as of December 31, 2022 $ 449,048 Acquisitions 2,948 Foreign currency translation and other 6,129 Balance as of December 31, 2023 458,125 Acquisitions 13,027 Foreign currency translation and other ( 8,693 ) Balance as of December 31, 2024 $ 462,459 Other intangible assets A summary of other intangible assets is shown below (in thousands): December 31, 2024 Weighted Gross Accumulated Net carrying Developed technology 4 - 6 years $ 159,815 $ 112,494 $ 47,321 Customer relationships 4 - 10 years 60,556 44,524 16,032 Trade names and other intangibles 3 - 10 years 11,551 1,967 9,584 Total other intangible assets $ 231,922 $ 158,985 $ 72,937 December 31, 2023 Weighted Gross Accumulated Net carrying Developed technology 4 - 6 years $ 142,368 $ 90,729 $ 51,639 Customer relationships 7 - 10 years 58,316 37,779 20,537 Trade names and other intangibles 4 - 10 years 11,937 563 11,374 Total other intangible assets $ 212,621 $ 129,071 $ 83,550 Amortization expense related to amortizing intangible assets was $ 33.0 million, $ 30.9 million and $ 27.5 million for the years ended December 31, 2024, 2023 and 2022, respectively. Estimated amortization expense for the next five years as of December 31, 2024, is as follows (in thousands): Year ending December 31, 2025 $ 29,670 December 31, 2026 23,528 December 31, 2027 11,680 December 31, 2028 5,981 December 31, 2029 1,922 Thereafter 156 Total $ 72,937

Debt

Debt	12 Months Ended
	Dec. 31, 2024
Debt Disclosure [Abstract]
Debt	7. Debt Convertible senior notes 2027 Notes In June 2022, the Company issued $ 230.0 million aggregate principal amount of 1.750 % convertible senior notes due in 2027 (the "2027 Notes"), which includes the initial purchaser’s exercise in full of its option to purchase an additional $ 30.0 million principal amount of the 2027 Notes, in a private offering. The net proceeds from the issuance of the 2027 Notes was $ 224.3 million after deducting discounts, commissions and estimated issuance costs. The Company entered into an Indenture relating to the issuance of the 2027 Notes dated June 14, 2022 (the “Indenture”), by and between the Company and U.S. Bank Trust Company, National Association, as trustee. The Indenture includes customary covenants and sets forth certain events of default after which the 2027 Notes may be declared immediately due and payable and sets forth certain types of bankruptcy or insolvency events of default involving the Company after which the 2027 Notes become automatically due and payable. The 2027 Notes are senior unsecured obligations of the Company. The 2027 Notes mature on June 15, 2027, unless earlier repurchased, redeemed or converted. Prior to the consummation of the Merger, the Company may redeem for cash all or, subject to certain limitations, any portion of the 2027 Notes, at its option, on or after June 20, 2025 if the last reported sale price of Altair's Class A Common Stock has been at least 130 % of the conversion price then in effect for at least 20 trading days (whether or not consecutive) during any 30 consecutive trading day period, at a redemption price equal to 100 % of the principal amount of the notes to be redeemed, plus accrued and unpaid interest to, but excluding, the redemption date. Once the Merger is consummated, the Company will settle conversions solely in cash based upon the per share Merger Consideration payable under the Merger Agreement. The 2027 Notes bear interest at a rate of 1.750 % per year, payable semiannually in arrears on June 15 and December 15 of each year, which commenced on December 15, 2022 . The 2027 Notes have an initial conversion rate of 13.9505 shares of the Company's Class A common stock per $ 1,000 principal amount of 2027 Notes, which is equivalent to an initial conversion price of approximately $ 71.68 per share of Class A common stock. The conversion rate will be subject to adjustment upon the occurrence of certain events specified in the Indenture but will not be adjusted for any accrued and unpaid interest. In addition, upon the occurrence of a make whole fundamental change, which includes the Merger, or a redemption period (each as defined in the Indenture), the Company will, in certain circumstances, increase the conversion rate by a specified number of additional shares for a holder who elects to convert its 2027 Notes in connection with such make whole fundamental change or during the relevant redemption period. Prior to the Merger, holders of the 2027 Notes may convert all or any portion of their 2027 Notes at any time prior to the close of business on the business day immediately preceding December 15, 2026, in integral multiples of $ 1,000 principal amount, only under the following circumstances: • during any calendar quarter, if the last reported sale price of the Class A Common Stock for at least 20 trading days (whether or not consecutive) during a period of 30 consecutive trading days ending on, and including, the last trading day of the immediately preceding calendar quarter is greater than or equal to 130 % of the conversion price on each applicable trading day; • during the five business day period after any five consecutive trading day period (the “measurement period”) in which the trading price (as defined in the Indenture) per $ 1,000 principal amount of the 2027 Notes for each trading day of the measurement period was less than 98 % of the product of the last reported sale price of the Class A Common Stock and the conversion rate on each such trading day; • if the Company calls the 2027 Notes for redemption (which the Company may not do prior to June 20, 2025), at any time prior to the close of business on the scheduled trading day immediately preceding the redemption date but only with respect to the 2027 Notes called (or deemed called) for redemption; or • upon the occurrence of specified corporate events. On or after December 15, 2026 until the close of business on the business day immediately preceding the maturity date, holders may convert their 2027 Notes at any time, regardless of the foregoing circumstances. Upon conversion prior to the consummation of the Merger, the Company will pay or deliver, as the case may be, cash, shares of Class A Common Stock or a combination of cash and shares of the Class A Common Stock, at the Company’s election, in the manner and subject to the terms and conditions provided in the Indenture. During the period ended December 31, 2024, the conditions allowing holders of the 2027 Notes to convert were met. Therefore, the 2027 Notes were classified as current on the consolidated balance sheet as of December 31, 2024. During the period ended December 31, 2023, the conditions allowing holders of the 2027 Notes to convert were not met. Therefore, the 2027 Notes were classified as long-term debt on the consolidated balance sheet as of December 31, 2023. As of December 31, 2024, the “if converted value” of the 2027 Notes exceeded the principal amount by $ 120.1 million. 2024 Notes In June 2019, the Company issued $ 230.0 million aggregate principal amount of 0.25 % convertible senior notes maturing on June 1, 2024 (the "2024 Notes" together with the 2027 Notes "Convertible Notes"), which includes the underwriters’ exercise in full of their option to purchase an additional $ 30.0 million principal amount of the 2024 Notes, in a public offering. The net proceeds from the issuance of the 2024 Notes were $ 221.9 million after deducting the underwriting discounts and commissions and issuance costs. The 2024 Notes had an initial conversion rate of 21.5049 shares of the Company's Class A common stock per $ 1,000 principal amount of 2024 Notes, which was equivalent to an initial conversion price of approximately $ 46.50 per share of its Class A common stock. The interest rate was fixed at 0.25 % per year, payable semi-annually in arrears on June 1 and December 1 of each year, which commenced on December 1, 2019 . During the year ended December 31, 2022, using proceeds from the issuance of the 2027 Notes, the Company entered into separate privately negotiated transactions with certain holders of the 2024 Notes to repurchase and retire $ 148.2 million aggregate principal amount of the 2024 Notes for an aggregate amount of $ 192.4 million of cash including accrued and unpaid interest. The Company recognized expense of $ 16.6 million, representing the fair value of the consideration paid to certain holders of the 2024 Notes in excess of the value to which they were entitled to receive on the respective settlement dates. The amount is included in Other expense, net in the Company’s consolidated statement of operations. In June 2024, the Company settled the remaining principal amount of the 2024 Notes totaling approximately $ 81.7 million by paying cash for the principal amount of $ 81.7 million and issuing 796,817 shares of the Company’s common stock, with a fair value of $ 70.8 million. The net carrying value of the 2027 and 2024 Notes was as follows (in thousands): December 31, 2024 December 31, 2023 2027 Notes 2024 Notes 2027 Notes 2024 Notes Principal $ 230,000 $ — 230,000 $ 81,729 Less: unamortized debt issuance costs 2,894 — 4,071 274 Net carrying amount $ 227,106 $ — $ 225,929 $ 81,455 The interest expense related to the 2027 and 2024 Notes was as follows (in thousands): Year ended December 31, 2024 2023 2022 Contractual interest expense $ 4,110 $ 4,230 $ 2,452 Amortization of debt issuance cost and discount 1,452 1,806 1,745 Total $ 5,562 $ 6,036 $ 4,197 Credit agreement Revolving credit facility As of December 31, 2024, the Company had a $ 200.0 million credit agreement with a maturity date of December 31, 2025 (“2019 Amended Credit Agreement”) and there were no outstanding borrowings. The 2019 Amended Credit Agreement is available for general corporate purposes, including working capital, capital expenditures, and permitted acquisitions. Borrowings under the 2019 Amended Credit Agreement bear interest at a rate per annum equal to an agreed upon applicable margin plus, at the Company’s option, either the Alternate Base Rate (defined as the greatest of (1) the Prime Rate (as defined in the 2019 Amended Credit Agreement) in effect on such day, (2) the Federal Funds Effective Rate (as defined in the 2019 Amended Credit Agreement) in effect on such day plus 1/2 of 1.00% and (3) the Adjusted Term SOFR Rate (as defined in the 2019 Amended Credit Agreement) for one-month interest period as published two U.S. Government Securities Business Days prior to such day (or if such day is not a business day, the immediately preceding business day) plus 1.00 %) or the Adjusted Term SOFR Rate. The applicable margin for borrowings under the 2019 Amended Credit Agreement is based on the Company’s most recently tested senior secured leverage ratio and will vary from (a) in the case of Term Benchmark loans, 1.25 % to 2.00 %, and (b) in the case of ABR loans or swingline loans, 0.25 % to 1.00 %. The Company pays a commitment fee ranging from 0.15 % to 0.30 % on the unused portion of the 2019 Amended Credit Agreement. Collateral and guarantees The 2019 Amended Credit Agreement is secured by collateral including (i) substantially all of the Company’s properties and assets, and the properties and assets of the Company’s domestic subsidiaries but excluding any patents, copyrights, patent applications or copyright applications or any trade secrets or software products and (ii) pledges of the equity interests in all present and future domestic subsidiaries (subject to certain exceptions as provided for under the 2019 Amended Credit Agreement). The Company’s direct and indirect domestic subsidiaries are guarantors of all the obligations under the 2019 Amended Credit Agreement. Debt covenants The 2019 Amended Credit Agreement requires the Company to maintain a Senior Secured Leverage Ratio not greater than 3.00 to 1.00 as of the last day of each fiscal quarter. The Senior Secured Leverage Ratio is defined as the ratio of total indebtedness secured by a lien (net of unrestricted domestic cash in excess of $ 20.0 million) to EBITDA, as such terms are defined in the 2019 Amended Credit Agreement, for the rolling four quarter period ending on such date. As of December 31, 2024, the Company was in compliance with its financial covenants. Other The Company has available overdraft and line of credit facilities in several countries in which it operates. These credit facilities are with various domestic and international banks and are at quoted market rates. As of December 31, 2024 and 2023, the Company had $ 2.0 million and $ 2.4 million, respectively, of availability under these facilities and there were no outstanding commitments.

Leases

Leases	12 Months Ended
	Dec. 31, 2024
Leases [Abstract]
Leases	8. Leases The Company determines if an arrangement is a lease at inception. Operating leases are included in operating lease assets and operating lease obligations on the Company’s consolidated balance sheets. Right of use (“ROU”) assets represent the Company’s right to use an underlying asset for the lease term and lease liabilities represent the Company’s obligation to make lease payments under the lease. Operating lease ROU assets and operating lease liabilities are recognized based on the present value of the future minimum lease payments over the lease term at commencement date. At commencement date, the ROU asset also includes adjustments for lease prepayments, lease incentives received and the lessee's initial direct costs, if applicable. As most of the Company’s leases do not provide an implicit rate, the Company uses its incremental borrowing rate based on the information available at commencement date in determining the present value of future payments. The incremental borrowing rates are determined using rates specific to the term of the lease, economic environments where lease activity is concentrated, value of lease portfolio, and assuming full collateralization of the loans. Subsequent to the commencement date, the operating ROU asset is equal to the remeasured lease liability adjusted for cumulative prepaid or accrued rent if the lease payments are uneven throughout the lease term, unamortized lease incentives, unamortized initial direct costs and any impairment of the ROU assets. The lease terms may include options to extend or terminate the lease when it is reasonably certain that the Company will exercise that option. Lease cost for minimum lease payments is recognized on a straight-line basis over the lease term. The Company does not recognize a lease liability or ROU asset for short-term leases (leases with a term of twelve months or less). For contracts with lease and non-lease components, the Company does not allocate the contract consideration, and accounts for the lease and non-lease components as a single lease component. The Company’s operating leases consist of office facilities, office equipment and cars. The Company’s leases have remaining terms of less than one year to 15 years, some of which include one or more options to renew and some of which include options to terminate the leases within the next three years . The Company did not have any finance leases as of December 31, 2024. Operating lease cost was $ 14.0 million, $ 13.1 million and $ 13.4 million for the years ended December 31, 2024, 2023 and 2022, respectively. Operating lease cost includes short-term leases and variable lease costs, which are immaterial. Rent cost related to operating leases for office facilities was $ 11.7 million, $ 11.3 million and $ 11.7 million for the years ended December 31, 2024, 2023 and 2022, respectively. Other information related to operating leases for the years ended December 31, 2024, 2023 and 2022 is as follows: December 31, 2024 2023 Weighted average remaining lease term of operating leases 5.7 years 6 years Weighted average discount rate of operating leases 4.6 % 3.9 % Year ended December 31, (in thousands) 2024 2023 2022 Cash paid for amounts included in the measurement of lease liabilities: Operating cash flows from operating leases $ ( 10,641 ) $ ( 11,606 ) $ ( 12,949 ) ROU assets obtained in exchange for new operating lease obligations $ 9,150 $ 17,023 $ 12,455 Maturities of operating lease liabilities as of December 31, 2024, were as follows (in thousands): Year ending December 31, 2025 $ 9,550 2026 8,614 2027 6,277 2028 3,438 2029 2,669 Thereafter 7,492 Total future lease payments 38,040 Less: present value adjustment 6,023 Total operating lease liabilities $ 32,017

Fair Value Measurements

Fair Value Measurements	12 Months Ended
	Dec. 31, 2024
Fair Value Disclosures [Abstract]
Fair Value Measurements	9. Fair value measurements The accounting guidance for fair value, among other things, defines fair value, establishes a consistent framework for measuring fair value and expands disclosure for each major asset and liability category measured at fair value on either a recurring or nonrecurring basis. Fair value is defined as the price that would be received to sell an asset or paid to transfer a liability (an exit price) in an orderly transaction between market participants at the reporting date. The framework for measuring fair value consists of a three-level valuation hierarchy that prioritizes the inputs to valuation techniques used to measure fair value based upon whether such inputs are observable or unobservable. Observable inputs reflect market data obtained from independent sources, while unobservable inputs reflect market assumptions made by the reporting entity. The three-level hierarchy for the inputs to valuation techniques is briefly summarized as follows: Level 1— Quoted prices in active markets for identical assets and liabilities at the measurement date; Level 2— Observable inputs, other than the quoted prices in active markets, that are observable either directly or indirectly; and Level 3— Unobservable inputs in which there is little or no market data, which require the reporting entity to develop its own assumptions. An asset’s or liability’s fair value measurement level within the fair value hierarchy is based on the lowest level of any input that is significant to the fair value measurement. Valuation techniques used need to maximize the use of observable inputs and minimize the use of unobservable inputs. The carrying value of cash and cash equivalents, accounts receivable and accounts payable approximate fair value due to their short maturities. Interest on the Company’s line of credit is at a variable rate, and as such the debt obligation outstanding approximates fair value. The carrying value of the Company’s 2027 Notes are at face value less unamortized debt issuance costs. The estimated fair value of the 2027 Notes, which the Company has classified as Level 2 financial instruments, was determined based on quoted bid prices of the 2027 Notes on the last trading day of each reporting period. As of December 31, 2024, the estimated fair value of the 2027 Notes was $ 358.1 million, and is presented for required disclosure purposes only. For further information on the Convertible Notes see Note 7.

Stockholders' Equity

Stockholders' Equity	12 Months Ended
	Dec. 31, 2024
Equity [Abstract]
Stockholders' Equity	10. Stockholders’ equity Preferred stock As of December 31, 2024, the Company had authorized 45,000,000 shares of preferred stock, par value $ 0.0001 , of which no shares were issued or outstanding. The Board of Directors has the authority to issue the preferred stock in one or more series and to fix rights, preferences, privileges, and restrictions, including dividends and the number of shares constituting any series or the designation of such series, without any further vote or action by the stockholders. Common stock As of December 31, 2024, the Company had authorized 513,796,572 shares of Class A common stock, par value $ 0.0001 , and 41,203,428 shares of Class B common stock, par value $ 0.0001 . The rights of the holders of Class A common stock and Class B common stock are identical, except with respect to voting and conversion rights. Each share of Class A common stock is entitled to one vote per share. Each share of Class B common stock is entitled to ten votes per share and is convertible into one share of Class A common stock. The holders of Class A and Class B common stock are entitled to dividends at the sole discretion of the Board of Directors. No common stock dividends were declared or paid in 2024, 2023, or 2022. Stock repurchase program The Company has a stock repurchase program for up to $ 75.0 million of the Company's outstanding Class A Common Stock. As permitted by securities laws and other legal requirements and subject to market conditions and other factors, purchases under the program may be made from time to time in the open market at prevailing prices, or through privately negotiated transactions. The Company is not obligated to repurchase any dollar amount or number of shares, and the stock repurchase program may be suspended or terminated at any time. All shares repurchased under the stock repurchase program are retired. The Company intends to use the share repurchase plan to opportunistically return capital to shareholders while still focusing on its primary goal of investing in the business to drive growth. The Company did no t repurchase any shares in 2024. During the year ended December 31, 2023, under the Company's stock repurchase program, the Company repurchased 91,273 shares at an average price of $ 46.63 per share for a total cost of $ 4.3 million.

Stock-Based Compensation

Stock-Based Compensation	12 Months Ended
	Dec. 31, 2024
Share-Based Payment Arrangement [Abstract]
Stock-Based Compensation	11. Stock-based compensation 2001 stock-based compensation plans Nonqualified stock option plan In 2001, the Company established the Nonqualified Stock Option Plan (“NSO Plan”) under which 623,539 stock options with an exercise price of $ .000025 remain outstanding as of December 31, 2024. The NSO Plan was terminated in 2003. Stock options under the NSO plan were immediately vested and have a contractual term of 35 years from the date of grant. The outstanding awards will continue to be governed by their existing terms under the NSO Plan. The NSO Plan is accounted for as an equity plan. The following table summarizes the stock option activity under the NSO Plan: Number of Weighted Weighted Aggregate intrinsic value (in millions) Outstanding as of December 31, 2023 994,884 $ 0.000025 13.0 Exercised ( 371,345 ) $ 0.000025 Outstanding and exercisable as of December 31, 2024 623,539 $ 0.000025 12.0 $ 68.0 The total intrinsic value of the NSO Plan stock options exercised during the years ended December 31, 2024, 2023 and 2022, was $ 33.8 million, $ 11.5 million and $ 11.0 million, respectively. 2012 stock-based compensation plans During 2012, the Company established the 2012 Incentive and Nonqualified Stock Option Plan (“2012 Plan”) which permits the issuance of 5,200,000 shares of Class A common stock for the grant of nonqualified stock options and incentive stock options for management, other employees, and board members of the Company. The options are issued at a price equal to or greater than fair market value at date of grant. All options have a contractual term of 10 years from date of grant. The 2012 Plan is accounted for as an equity plan. For those options expected to vest, compensation expense is recognized on a straight-line basis over a four-year period, the total requisite service period of the awards. The following table summarizes the stock option activity under the 2012 Plan for the periods indicated as follows: Number of Weighted Weighted Aggregate intrinsic value (in millions) Outstanding as of December 31, 2023 271,359 $ 4.46 2.5 Exercised ( 111,992 ) $ 4.24 Outstanding and exercisable as of December 31, 2024 159,367 $ 4.62 1.9 $ 16.7 The total intrinsic value of the 2012 Plan stock options exercised during the years ended December 31, 2024, 2023 and 2022, was $ 10.1 million, $ 6.6 million and $ 8.5 million, respectively. 2017 stock-based compensation plan In 2017, the Company’s board of directors adopted the 2017 Equity Incentive Plan (“2017 Plan”), which was approved by the Company’s stockholders. The 2017 Plan provides for the grant of incentive stock options to the Company’s employees and any parent and subsidiary corporations’ employees, and for the grant of nonstatutory stock options, stock appreciation rights, restricted stock, restricted stock units, performance units, performance shares, other cash-based and stock-based awards to the Company’s employees, directors and consultants and the Company’s parent, subsidiary, and affiliate corporations’ employees and consultants. The 2017 Plan has 19,460,908 authorized shares of the Company’s Class A common stock reserved for issuance. As of December 31, 2024, the Company had 6,625,144 shares of its common stock available for future issuances under the 2017 Plan. The following table summarizes the restricted stock units, or RSUs, awarded under the 2017 Plan for the period: Number of RSUs Outstanding as of December 31, 2023 1,086,351 Granted 384,424 Vested ( 530,732 ) Forfeited ( 33,191 ) Outstanding as of December 31, 2024 906,852 The weighted average grant date fair value of the RSUs granted in 2024 was $ 80.60 and the RSUs generally vest in four equal annual installments. The fair value of RSUs that vested during the year ended December 31, 2024, was $ 47.2 million. Total compensation cost related to nonvested awards not yet recognized as of December 31, 2024, was $ 98.9 million and is expected to be recognized over a weighted average period of 2.2 years. The following table summarizes the stock option activity under the 2017 Plan for the period: Number of Weighted Weighted Aggregate intrinsic value (in millions) Outstanding as of December 31, 2023 7,602,078 $ 52.81 7.8 Granted 417,459 $ 79.19 Exercised ( 1,325,265 ) $ 49.91 Forfeited ( 124,821 ) $ 55.94 Outstanding as of December 31, 2024 6,569,451 $ 55.01 7.1 $ 355.4 Exercisable as of December 31, 2024 3,940,042 $ 51.61 6.5 $ 226.5 The total intrinsic value of the 2017 Plan stock options exercised during the years ended December 31, 2024, 2023 and 2022, was $ 58.6 million, $ 20.7 million and $ 1.1 million, respectively. Fair value of equity awards The Company measures the fair value of its stock options on the date of grant using the Black-Scholes option pricing model. This valuation model requires the Company to make certain estimates and assumptions, including assumptions related to the expected price volatility of the Company’s stock, the period under which the options will be outstanding, the rate of return on risk-free investments, and the expected dividend yield for the Company’s stock. The fair values of the Company’s stock options granted during the year ended December 31, 2024, 2023 and 2022, were estimated using the following assumptions: 2024 grants 2023 grants 2022 grants Weighted average grant date fair value per share $ 79.03 - 85.52 $ 65.19 - 67.65 $ 44.63 - 64.79 Expected volatility 35 % 35 % 35 % Expected term (in years) 6.25 6.25 6.25 Risk-free interest rate 4.2 % - 4.3 % 3.5 % - 4.3 % 1.7 % - 4.2 % Expected dividend yield 0 % 0 % 0 % These assumptions and estimates are as follows: • Fair Value of Common Stock . The Company used the publicly quoted price as reported on the Nasdaq Global Select Market as the fair value of its common stock. • Expected Term . The Company used the simplified method to determine the expected term. • Risk-Free Interest Rate . The Company based the risk-free interest rate on U.S. Treasury zero-coupon yield curves with a remaining term equal to the expected term of the option. • Expected Volatility . As the Company does not have an extensive trading history for its common stock, the expected volatility was derived using the historical volatility of the returns of comparable publicly traded companies combined with the brief trading history of the Company’s common stock. 2021 Employee Stock Purchase Plan The Company has an Employee Stock Purchase Plan (“ESPP”) which allows eligible employees to purchase shares of common stock through payroll deductions. As of December 31, 2024, the Company had 2,706,534 shares of its common stock available for future issuances under the ESPP. The purchase price for each share of common stock purchased under the ESPP will be 85 % of the lower of (a) the fair market value per share on the first day of the applicable offering period or (b) the fair market value per share on the applicable purchase date. Each offering period will last a number of months determined by the plan administrator, up to a maximum of 27 months. The final offering period began on July 15, 2024 , and ended on January 14, 2025 . The plan administrator has suspended all future offering periods. The ESPP allowed participants to purchase the Company’s common stock through payroll deductions, up to a maximum of 15 % of their eligible compensation or $ 25,000 , whichever is lower, and subject to limitations under Section 423 of the Internal Revenue Code. The plan administrator has limited participant contributions to $ 1,000 per month to prevent prejudicial advantages to higher compensated employees. Participants may withdraw from the ESPP and receive a refund of their accumulated payroll contributions at any time prior to a purchase date. The Company issued 125,686 , 182,883 and 184,897 shares of common stock under the ESPP during the years ended December 31, 2024, 2023 and 2022, respectively. As of December 31, 2024 and 2023, $ 4.8 million and $ 4.2 million, respectively, has been withheld on behalf of employees for future purchases under the ESPP due to the timing of payroll deductions and was reported in current liabilities. The Company recognized $ 2.9 million, $ 2.4 million and $ 2.6 million of stock-based compensation expense related to the ESPP for the years ended December 31, 2024, 2023, and 2022, respectively. Other In connection with the acquisition of World Programming in December 2021, per the World Programming stock purchase agreement, $ 29.5 million of the Company’s Class A Common Stock was issued to existing employees, subject to continuing employment and certain other contingencies. The accounting treatment for these shares in the context of the business combination was to recognize the expense as a post-combination expense, not as transaction consideration. As of December 31, 2024, the service period was met. Stock-based compensation expense includes $ 3.1 million, $ 8.0 million and $ 17.6 million for the years ended December 31, 2024, 2023 and 2022, respectively. In connection with the acquisition of Powersim Inc. in March 2022, per the Powersim stock purchase agreement, 68,792 shares of the Company’s Class A Common Stock were issued to existing employees, subject to continuing employment and certain other contingencies. The shares were issued on the one- and two-year anniversaries of the closing. The accounting treatment for these shares in the context of the business combination was to recognize the expense as a post-combination expense, not as transaction consideration. The post combination expense was determined to have a fair value of approximately $ 4.3 million and was recognized on an accelerated method over the employment period. As of December 31, 2024, the service period was met, and all shares have been issued. Stock-based compensation expense includes $ 0.2 million, $ 1.4 million and $ 2.7 million for the years ended December 31, 2024, 2023 and 2022, respectively. In connection with the acquisition of Concept Engineering in June 2022, per the Concept Engineering stock purchase agreement, 105,082 shares of the Company’s Class A Common Stock were issued to existing employees, subject to continuing employment and certain other contingencies. The shares were issued in installments of 52,541 shares on the one- and two-year anniversaries of the closing. The accounting treatment for these shares in the context of the business combination was to recognize the expense as a post-combination expense, not as transaction consideration. The post combination expense was determined to have a fair value of approximately $ 6.0 million and was recognized on an accelerated method over the employment period. As of December 31, 2024, the service period was met, and all shares have been issued. Stock-based compensation expense includes $ 0.6 million, $ 2.6 million and $ 2.7 million for the years ended December 31, 2024, 2023 and 2022, respectively. In connection with the acquisition of Research in Flight ("RIFL") in April 2024, the Company agreed to issue an aggregate of 18,000 shares of the Company' s Class A Common Stock to stockholders of RIFL, with 9,000 shares issuable on each of April 15, 2025, and April 2026, subject to potential reduction in certain circumstances. The accounting treatment for these shares in the context of the business combination was to recognize the expense as a post-combination expense, not as transaction consideration. The post combination expense was determined to have a fair value of approximately $ 1.5 million which is recognized over the two-year period. As of December 31, 2024, the weighted average remaining recognition period is 1.3 years. Stock-based compensation expense includes $ 0.8 million for the year ended December 31, 2024. Stock-based compensation expense The stock-based compensation expense was recorded as follows (in thousands): Year ended December 31, 2024 2023 2022 Cost of revenue-software $ 8,397 $ 10,095 $ 8,351 Research and development 25,630 33,842 36,250 Sales and marketing 19,459 28,376 30,370 General and administrative 14,194 13,268 9,816 Total stock-based compensation expense $ 67,680 $ 85,581 $ 84,787

Income Taxes

Income Taxes	12 Months Ended
	Dec. 31, 2024
Income Tax Disclosure [Abstract]
Income Taxes	12. Income taxes The components of income (loss) before income taxes are as follows (in thousands): Year ended December 31, 2024 2023 2022 U.S. $ ( 8,279 ) $ ( 21,803 ) $ ( 62,702 ) Non-U.S. 40,909 34,422 34,489 $ 32,630 $ 12,619 $ ( 28,213 ) The significant components of income tax expense are as follows (in thousands): Year ended December 31, 2024 2023 2022 Current U.S. Federal $ — $ — $ — Non-U.S. 19,168 22,746 18,759 U.S. State and Local ( 6 ) 1,118 621 Total current 19,162 23,864 19,380 Deferred U.S. Federal 36 35 23 Non-U.S. ( 773 ) ( 2,384 ) ( 4,206 ) U.S. State and Local 30 30 19 Total deferred ( 707 ) ( 2,319 ) ( 4,164 ) Income tax expense $ 18,455 $ 21,545 $ 15,216 The reconciliation of income taxes calculated at the U.S. Federal statutory income tax rate to income tax expense is as follows (in thousands): Year ended December 31, 2024 2023 2022 U.S. federal statutory rate 21 % 21 % 21 % Income taxes at U.S. federal statutory rate $ 6,852 $ 2,650 $ ( 5,925 ) Foreign income taxes at rates other than the federal statutory rate 2,626 1,733 2,249 U.S. state and local income taxes, net of U.S. federal tax benefit ( 3,054 ) ( 1,952 ) ( 5,976 ) U.S. effect of foreign operations 2,315 ( 9,931 ) 15,827 Change in valuation allowance 25,493 29,849 7,830 Foreign withholding taxes 8,501 7,444 6,738 U.S. foreign tax credit and deduction ( 8,261 ) ( 17,522 ) ( 12,315 ) Research and development tax credit 597 391 ( 326 ) Stock-based compensation ( 7,695 ) 1,361 8,649 Other 920 123 1,250 Uncertain tax positions ( 693 ) 6,370 472 FDII deduction ( 9,146 ) ( 169 ) ( 5,245 ) Mark-to-market adjustment of contingent consideration — 1,198 ( 1,502 ) Repurchase of convertible senior notes — — 3,490 Income tax expense $ 18,455 $ 21,545 $ 15,216 The Tax Cuts and Jobs Act, or the Tax Act, subjects a U.S. shareholder to current tax on global intangible low-taxed income (“GILTI”) earned by certain foreign subsidiaries. The impact of GILTI resulted in no incremental tax expense for the years ended December 31, 2024, 2023 and 2022 due to a full valuation allowance on U.S. net deferred tax assets. In addition, the Company has made an accounting policy election to treat taxes due under the GILTI provision as a current period expense. Deferred income tax assets and liabilities result from differences in the basis of assets and liabilities for tax and financial statements purposes. The approximate tax effect of each type of temporary difference, and operating losses and tax credit carryforwards that give rise to a significant portion of the deferred tax assets and liabilities are as follows (in thousands): December 31, 2024 2023 Deferred tax assets: Deferred revenue $ 6,419 $ 9,730 Net operating loss carryforwards 57,933 60,702 Tax credit carryforwards 39,987 48,752 Stock-based compensation 13,491 12,011 Capitalized research and development 87,261 58,946 Lease obligation 6,330 7,517 Employee benefits 7,994 6,955 Merger costs 4,288 — Other 3,704 3,910 Total gross deferred tax assets 227,407 208,523 Less: valuation allowances ( 204,954 ) ( 179,766 ) Net deferred tax assets (1) 22,453 28,757 Deferred tax liabilities: Prepaid royalties 1,609 3,602 Property and equipment and intangibles 13,174 16,610 Deferred tax on investment in subsidiary 3,220 1,950 Lease right of use asset 6,193 7,357 Other 2,801 2,153 Total deferred tax liabilities 26,997 31,672 Total net deferred tax liabilities $ ( 4,544 ) $ ( 2,915 ) (1) Reflects gross amount before jurisdictional netting of deferred tax assets and liabilities. Deferred tax assets and liabilities are determined separately for each tax jurisdiction on a separate or on a consolidated tax filing basis, as applicable, in which the Company conducts its operations or otherwise incurs taxable income or losses. A valuation allowance is recorded when it is more likely than not that some portion or all of the gross deferred tax assets will not be realized. The realization of deferred tax assets depends on the ability to generate sufficient taxable income of the appropriate character within the carryback or carryforward periods provided for in the tax law for each applicable tax jurisdiction. The Company considers the following possible sources of taxable income when assessing the realization of deferred tax assets: • taxable income in prior carryback years; • future reversals of existing taxable temporary differences; • future taxable income exclusive of reversing temporary differences and carryforwards; and • prudent and feasible tax planning strategies that the Company would be willing to undertake to prevent a deferred tax asset from otherwise expiring. The assessment regarding whether a valuation allowance is required or whether a change in judgment regarding the valuation allowance has occurred also considers all available positive and negative evidence, including but not limited to: • nature, frequency, and severity of cumulative losses in recent years; • duration of statutory carryforward and carryback periods; • statutory limitations against utilization of tax attribute carryforwards against taxable income; • historical experience with tax attributes expiring unused; and • near‑ and medium‑term financial outlook. The weight given to the positive and negative evidence is commensurate with the extent to which the evidence may be objectively verified. Accordingly, it is generally difficult to conclude a valuation allowance is not required when there is significant objective and verifiable negative evidence, such as cumulative losses in recent years. The Company uses the actual results for the last two years and current year results as the primary measure of cumulative losses in recent years. The evaluation of deferred tax assets requires judgment in assessing the likely future tax consequences of events recognized in the financial statements or tax returns and future profitability. The recognition of deferred tax assets represents the Company’s best estimate of those future events. Changes in the current estimates, due to unanticipated events or otherwise, could have a material effect on the Company’s results of operations and financial condition. In certain tax jurisdictions, the Company’s analysis indicates that it has cumulative losses in recent years. This is considered significant negative evidence, which is objective and verifiable and, therefore, difficult to overcome. However, the cumulative loss position is not solely determinative and, accordingly, the Company considers all other available positive and negative evidence in its analysis. Based on its analysis, the Company has recorded a valuation allowance for the portion of deferred tax assets where based on the weight of available evidence it is unlikely to realize those deferred tax assets. Based on the evidence available including a lack of sustainable earnings, the Company in its judgment previously recorded a valuation allowance against substantially all of its net deferred tax assets in the United States. If a change in judgment regarding this valuation allowance were to occur in the future, the Company will record a potentially material deferred tax benefit, which could result in a favorable impact on the effective tax rate in that period. The Company continues to record deferred foreign taxes on gross book-tax basis differences to the extent of foreign distributable reserves and excess cash balances for its subsidiary in India. Determining the amount of unrecognized deferred tax liability related to any remaining undistributed foreign earnings is not practicable. The following table summarizes the changes to the valuation allowance balance (in thousands): Year ended December 31, 2024 2023 2022 Beginning balance $ 179,766 $ 149,441 $ 119,981 Additions charged to expense 27,481 30,665 7,830 Deductions ( 1,988 ) ( 816 ) — Other ( 305 ) 476 21,630 Ending balance $ 204,954 $ 179,766 $ 149,441 The change in valuation allowance in Other for 2024 of $( 0.3 ) million is primarily related to currency translation. The change in valuation allowance in Other for 2023 of $ 0.5 million is primarily related to currency translation. The change in the valuation allowance in Other for 2022 of $ 21.6 million is primarily related to a $ 6.8 million increase from the adoption of ASU 2020-06 for convertible debt instruments, and a $ 13.1 million valuation allowance recorded on deferred tax assets established during purchase accounting from the RapidMiner acquisition. The following table summarizes the amount and expiration dates of operating loss and tax credit carryforwards as of December 31, 2024 (in thousands): Expiration dates Amounts U.S. general business credits and loss carryforwards 2025-Indefinite $ 62,990 Foreign general business credits and loss carryforwards 2025-Indefinite 13,029 U.S. foreign tax credits 2027 - 2033 21,901 Total operating loss and tax credit carryforwards $ 97,920 A reconciliation of the beginning and ending amounts of unrecognized tax benefits is as follows (in thousands): Year ended December 31, 2024 2023 2022 Unrecognized tax benefits—January 1 $ 38,219 $ 28,977 $ 16,376 Additions for tax positions of current period 50 9,435 50 Additions for tax positions of prior periods — 901 13,910 Reductions for tax positions of prior periods ( 4,891 ) ( 500 ) ( 1,334 ) Reductions due to statute of limitations ( 427 ) ( 594 ) ( 25 ) Unrecognized tax benefits—December 31 $ 32,951 $ 38,219 $ 28,977 As of December 31, 2024, the Company had $ 11.6 million of gross unrecognized tax benefits that if recognized would affect the effective tax rate. The Company expects a reduction over the next 12 months in the gross unrecognized tax benefits of approximately $ 12.8 million which if recognized would not impact the effective tax rate during 2025. The Company operates globally but considers its more significant tax jurisdictions to include the United States, India, Germany, Japan, and China. India has tax years open for examination from 2011 through 2024. All other significant jurisdictions have open tax years from 2017 through 2024. The Company records interest and penalties with respect to unrecognized tax benefits as a component of the provision for income taxes. For the years ended December 31, 2024, 2023, and 2022, accrued interest and penalties related to unrecognized tax benefits were approximately $ 0.6 million, $ 1.2 million, and $ 1.0 million, respectively, all of which if recognized would affect the effective tax rate.

Net Income (Loss) Per Share

Net Income (Loss) Per Share	12 Months Ended
	Dec. 31, 2024
Earnings Per Share [Abstract]
Net Income (Loss) Per Share	13. Net income (loss) per share Basic net income (loss) per share attributable to common stockholders is computed using the weighted average number of shares of common stock outstanding for the period, excluding dilutive securities, stock options, RSUs and ESPP shares. Diluted net income (loss) per share attributable to common stockholders is based upon the weighted average number of shares of common stock outstanding for the period and potentially dilutive common shares. The treasury stock method is used to calculate the effect of dilutive securities, stock options, RSUs and ESPP shares and the if-converted method is used to calculate the effect of convertible instruments. The following table sets forth the computation of the numerators and denominators used in the basic and diluted net income (loss) per share amounts (in thousands, except per share data): Year ended December 31, 2024 2023 2022 Numerator: Net income (loss) $ 14,175 $ ( 8,926 ) $ ( 43,429 ) Interest expense related to convertible notes, net of tax (1) — — — Numerator for diluted income (loss) per share $ 14,175 $ ( 8,926 ) $ ( 43,429 ) Denominator: Weighted average shares outstanding, basic 84,085 80,596 79,472 Effect of dilutive shares 4,473 — — Weighted average shares outstanding, diluted 88,558 80,596 79,472 Income (loss) per share, basic $ 0.17 $ ( 0.11 ) $ ( 0.55 ) Income (loss) per share, diluted $ 0.16 $ ( 0.11 ) $ ( 0.55 ) (1) Interest expense related to the convertible notes has been excluded from the numerator for diluted earnings per share because its effect would have been anti-dilutive. Anti-dilutive shares excluded from the computation of diluted net income (loss) per share were as follows (in thousands): Year ended December 31, 2024 2023 2022 Convertible shares 3,209 3,753 4,958 Stock options and ESPP shares — 3,293 961 Total shares excluded from calculation 3,209 7,046 5,919 Since the Company was in a net loss position for the years ended December 31, 2023 and 2022, basic net loss per share attributable to common stockholders is the same as diluted net loss per share for those periods as the inclusion of all potential common shares outstanding would have been anti-dilutive.

Retirement Benefits

Retirement Benefits	12 Months Ended
	Dec. 31, 2024
Retirement Benefits [Abstract]
Retirement Benefits	14. Retirement benefits The Company sponsors a 401(k)-profit sharing plan (the “Plan”) for all eligible U.S. employees. This Plan allows eligible employees to contribute up to 80 % of their compensation to the Plan. The Company makes discretionary matching contributions to the Plan provided the employee is employed on the last day of the year. Such discretionary contributions vest ratably over five years of service. The Company’s contributions to the Plan were $ 1.5 million, $ 1.6 million and $ 1.6 million for the years ended December 31, 2024, 2023 and 2022, respectively. The Company also participates in government-mandated retirement and/or termination indemnity plans, benefiting certain non-U.S. employees. Termination benefits are generally lump sum payments based upon an individual’s years of credited service and annual salary at retirement. These plans are generally unfunded, and employees receive payments at the time of retirement or termination under applicable labor laws or agreements. The amount of net benefit cost recorded in the consolidated statements of operations for these plans was $ 2.5 million, $ 2.6 million and $ 2.5 million in 2024, 2023 and 2022, respectively. The amount of benefits paid under these plans was $ 0.6 million, $ 0.4 million and $ 0.7 million in 2024, 2023 and 2022, respectively. The accumulated benefit obligation, unlike the projected benefit obligation, does not reflect expected benefit increases from future salary levels, and was $ 12.8 million and $ 11.6 million as of December 31, 2024 and 2023, respectively, under these plans. The projected benefit obligation, net of plan assets, was $ 17.3 million and $ 16.8 million as of December 31, 2024 and 2023, respectively. A summary of the components of the pension benefits obligation recorded in the consolidated balance sheets are as follows (in thousands): December 31, 2024 2023 Other long-term assets $ 19 $ 135 Accrued compensation and benefits 1,247 1,170 Other long-term liabilities 16,052 15,815 $ 17,280 $ 16,850 The estimated future benefit payments, which reflect expected future service that are expected to be paid for each of the next five years are as follows (in thousands): Year ending December 31, 2025 $ 1,319 December 31, 2026 $ 1,572 December 31, 2027 $ 1,372 December 31, 2028 $ 1,260 December 31, 2029 $ 1,114 Next five years $ 7,627

Accumulated Other Comprehensive

Accumulated Other Comprehensive Loss	12 Months Ended
	Dec. 31, 2024
Equity [Abstract]
Accumulated Other Comprehensive Loss	15. Accumulated other comprehensive loss The components of accumulated other comprehensive loss are as follows (in thousands): Foreign Retirement Total Balance as of December 31, 2021 $ ( 6,400 ) $ ( 2,550 ) $ ( 8,950 ) Other comprehensive (loss) income before reclassification ( 24,084 ) 87 ( 23,997 ) Amounts reclassified from accumulated other comprehensive loss — 3,253 3,253 Tax effects — ( 308 ) ( 308 ) Other comprehensive (loss) income ( 24,084 ) 3,032 ( 21,052 ) Balance as of December 31, 2022 ( 30,484 ) 482 ( 30,002 ) Other comprehensive income (loss) before reclassification 9,011 ( 16 ) 8,995 Amounts reclassified from accumulated other comprehensive loss — ( 1,479 ) ( 1,479 ) Tax effects — 177 177 Other comprehensive income (loss) 9,011 ( 1,318 ) 7,693 Balance as of December 31, 2023 ( 21,473 ) ( 836 ) ( 22,309 ) Other comprehensive loss before reclassification ( 15,490 ) ( 8 ) ( 15,498 ) Amounts reclassified from accumulated other comprehensive loss — 777 777 Tax effects — ( 251 ) ( 251 ) Other comprehensive (loss) income ( 15,490 ) 518 ( 14,972 ) Balance as of December 31, 2024 $ ( 36,963 ) $ ( 318 ) $ ( 37,281 )

Commitments and Contingencies

Commitments and Contingencies	12 Months Ended
	Dec. 31, 2024
Commitments and Contingencies Disclosure [Abstract]
Commitments and Contingencies	16. Commitments and contingencies Legal proceedings Stockholders of Altair have filed, and may in the future file, lawsuits against Altair and/or the directors and officers of Altair in connection with the Merger. These lawsuits could prevent or delay the completion of the Merger and result in significant costs to Altair, including any costs associated with the indemnification of directors and officers. From time to time, the Company may be subject to legal proceedings and claims in the ordinary course of business, unrelated to the Merger. The Company has received, and may in the future continue to receive, claims from third parties asserting, among other things, infringement of their intellectual property rights. Future litigation may be necessary to defend the Company, its partners and its customers by determining the scope, enforceability and validity of third-party proprietary rights, or to establish and enforce the Company’s proprietary rights. Effects of proceedings The results of any current or future litigation cannot be predicted with certainty and regardless of the outcome, litigation can have an adverse impact on the Company because of defense and settlement costs, diversion of management resources and other factors. Commitments The Company has entered into various renewable, nonexclusive license agreements under which the Company has been granted access to the licensor’s technology and the right to sell or use the technology in the Company’s products. Royalties are payable to developers of the software at various rates and amounts, which generally are based upon unit sales or revenue. Royalty fees were $ 12.8 million, $ 12.2 million, and $ 11.7 million for the years ended December 31, 2024, 2023 and 2022, respectively, and are reported in Cost of revenue—software. Additionally, the Company has current contractual purchase obligations for services supporting business operations, including non-cancelable agreements. The Company also has payment obligations related to recent acquisitions. The future purchase obligations for these agreements are as follows (in thousands): Year ending December 31, 2025 $ 22,085 2026 14,991 2027 2,708 2028 901 2029 364 Thereafter — Total $ 41,049 Contingencies The Company had contingent payment obligations for deferred professional fees of up to $ 135.2 million as of December 31, 2024, which may become payable in 2025, subject to certain terms which would cause such contingent amounts to become payable. The Company had contingent payment obligations for the purchase of a software license of $ 7.1 million as of December 31, 2024, which may become payable in 2025, subject to certain terms which would cause such contingent amounts to become payable.

Segment Information

Segment Information	12 Months Ended
	Dec. 31, 2024
Segment Reporting [Abstract]
Segment Information	17. Segment information The Company defines its operating segments as components of its business where separate financial information is available and used by the chief operating decision maker (“CODM”) in deciding how to allocate resources to its segments and in assessing performance. The Company’s CODM is its Chief Executive Officer . The Company has identified two reportable segments for financial reporting purposes: Software and Client Engineering Services. The primary measure of segment operating performance is Adjusted EBITDA, which is defined as net income (loss) adjusted for income tax expense (benefit), interest expense, interest income and other, depreciation and amortization, stock-based compensation expense, asset impairment charges and other special items as determined by management. Adjusted EBITDA includes an allocation of corporate headquarters costs. The Software reportable segment derives revenue from the sale and lease of software licenses and cloud solutions in the areas of simulation, high-performance computing, and artificial intelligence to design and optimize high-performance, efficient, innovative and sustainable products and processes for improved business performance. The software services and software-related services component of this segment includes consulting, implementation services, training, and software-related services focused on product design and development expertise and analysis from the component level up to complete product engineering at any stage of the lifecycle. To a much lesser extent, the Software segment includes revenue from the sale of hardware products. The Client Engineering Services reportable segment provides support to the Company’s customers with long-term ongoing expertise. The Company hires simulation specialists, industrial designers, design engineers, materials experts, development engineers, manufacturing engineers, data scientists, and information technology specialists for placement at customer sites for specific customer-directed assignments. "All Other” represents innovative services and products, including Toggled, the Company’s LED lighting business. Toggled is focused on developing and selling next-generation solid state lighting technology along with communication and control protocols based, in part, on intellectual property for the direct replacement of fluorescent tubes with LED lighting. Other businesses combined within "All other" include potential services and product concepts that are still in their development stages. Inter-segment sales are not significant for any period presented. The CODM does not review asset information by segment when assessing performance, therefore no asset information is provided for reportable segments. The accounting policies of the segments are the same as those described in Note 2—Summary of significant accounting policies. The following tables are in thousands: Year ended December 31, 2024 Software CES All other Total Revenue $ 637,267 $ 25,027 $ 3,494 $ 665,788 Less: Cost of revenue 90,674 21,315 2,640 114,629 Research and development 187,826 — 1,069 188,895 Sales and marketing 158,670 1,006 1,135 160,811 General and administrative 54,681 1,722 584 56,987 Other segment items ( 5,338 ) — ( 108 ) ( 5,446 ) Adjusted EBITDA $ 150,754 $ 984 $ ( 1,826 ) $ 149,912 Year ended December 31, 2023 Software CES All other Total Revenue $ 578,006 $ 29,497 $ 5,198 $ 612,701 Less: Cost of revenue 82,625 24,450 4,329 111,404 Research and development 172,954 — 1,247 174,201 Sales and marketing 143,406 761 1,034 145,201 General and administrative 53,966 1,998 837 56,801 Other segment items ( 4,109 ) — 65 ( 4,044 ) Adjusted EBITDA $ 129,164 $ 2,288 $ ( 2,314 ) $ 129,138 Year ended December 31, 2022 Software CES All other Total Revenue $ 537,169 $ 28,883 $ 6,169 $ 572,221 Less: Cost of revenue 85,589 23,577 4,988 114,154 Research and development 161,106 — 860 161,966 Sales and marketing 129,740 592 746 131,078 General and administrative 58,374 2,139 1,111 61,624 Other segment items ( 5,278 ) ( 1 ) 78 ( 5,201 ) Adjusted EBITDA $ 107,638 $ 2,576 $ ( 1,614 ) $ 108,600 Year ended December 31, 2024 2023 2022 Reconciliation of Adjusted EBITDA to GAAP income (loss) Adjusted EBITDA $ 149,912 $ 129,138 $ 108,600 Stock-based compensation expense ( 67,680 ) ( 85,581 ) ( 84,787 ) Interest expense ( 5,836 ) ( 6,116 ) ( 4,377 ) Depreciation and amortization ( 42,164 ) ( 39,124 ) ( 35,504 ) Special adjustments, interest income and other (1) ( 1,602 ) 14,302 ( 12,145 ) Income (loss) before income taxes $ 32,630 $ 12,619 $ ( 28,213 ) (1) The year ended December 31, 2024, includes $ 22.3 million of expenses related to the pending merger with Siemens Industry, $ 1.9 million currency losses on acquisition-related intercompany loans, $ 0.5 million losses from the mark-to-market adjustment of contingent consideration associated with acquisitions and $ 23.0 million of interest income. The year ended December 31, 2023, includes $ 3.2 million currency gains on acquisition-related intercompany loans, $ 5.7 million losses from the mark-to-market adjustment of contingent consideration associated with the World Programming acquisition and $ 16.9 million of interest income. The year ended December 31, 2022, includes $ 16.6 million expense on repurchase of convertible senior notes, $ 6.8 million currency losses on acquisition-related intercompany loans, $ 7.2 million gains from the mark-to-market adjustment of contingent consideration associated with the World Programming acquisition and $ 4.1 million of interest income. Revenue is attributed to geographic areas based on the country of origin. The following table provides sales to external customers and long-lived assets for each of the geographic areas in which the Company operates (in thousands): Revenue Long-lived assets (1) Year ended December 31, December 31, 2024 2023 2022 2024 2023 United States $ 323,905 $ 301,857 $ 274,635 $ 52,565 $ 55,230 Other countries 18,987 17,792 13,425 15,385 6,193 Total Americas 342,892 319,649 288,060 67,950 61,423 Germany 46,927 46,593 51,495 12,686 19,840 France 24,283 23,122 19,442 1,109 1,200 Other countries 76,459 66,903 69,769 24,485 34,561 Total Europe, Middle East and Africa 147,669 136,618 140,706 38,280 55,601 Japan 42,451 39,508 40,335 1,052 685 Other countries 132,776 116,926 103,120 6,663 5,644 Total Asia Pacific 175,227 156,434 143,455 7,715 6,329 Total $ 665,788 $ 612,701 $ 572,221 $ 113,945 $ 123,353 (1) Includes Property and equipment, net and Other intangible assets, net. Concentrations of credit risk The Company’s financial instruments that are potentially subject to concentrations of credit risk consist primarily of cash and trade receivables. The risk with respect to trade receivables is partially mitigated by the diversity, both by geography and by industry, of the Company’s customer base. The Company’s accounts receivable is derived from sales to a large number of direct customers and resellers around the world. No individual customer accounted for 10% or more of revenue in the years ended December 31, 2024, 2023 or 2022.

Summary of Significant Accoun_2

Summary of Significant Accounting Policies (Policies)	12 Months Ended
	Dec. 31, 2024
Accounting Policies [Abstract]
Principles of consolidation	Principles of consolidation The accompanying consolidated financial statements have been prepared using accounting principles generally accepted in the United States of America (“GAAP”). The consolidated financial statements include the results of the Company and its controlled subsidiaries. Intercompany accounts and transactions have been eliminated in the consolidated financial statements.
Change in Presentation of Revenue and Cost of Revenue	Change in Presentation of Revenue and Cost of Revenue Effective in the first quarter of 2024, the Company changed the presentation of revenue and cost of revenue in its Consolidated
Use of estimates	Use of estimates The preparation of the consolidated financial statements in conformity with GAAP requires management to make estimates and assumptions that affect the reported amounts of assets and liabilities and disclosures of contingent assets and liabilities at the date of the financial statements, and reported amounts of revenue and expenses during the reporting periods. On an ongoing basis, management evaluates its significant estimates including the stand alone selling price, or SSP, for each distinct performance obligation included in customer contracts with multiple performance obligations, the incremental borrowing rate used in the valuation of lease liabilities, fair value of convertible senior notes, provision for expected credit losses, tax valuation allowances, liabilities for uncertain tax provisions, impairment of goodwill and intangible assets, retirement obligations, useful lives of intangible assets, revenue for fixed price contracts, and stock-based compensation. Actual results could differ from those estimates.
Foreign currency translation	Foreign currency translation The functional currency of the Company’s foreign subsidiaries is their respective local currency. The assets and liabilities of the subsidiaries are translated to U.S. dollars at the exchange rate as of the balance sheet date. Equity balances and transactions are translated using historical exchange rates. Revenues and expenses are translated at the average exchange rate during the period. Translation adjustments arising from the use of differing exchange rates from period to period are recorded as a component of accumulated other comprehensive loss within stockholders’ equity. All assets and liabilities denominated in a currency other than the functional currency are remeasured into the functional currency with gains and losses recognized in foreign currency losses, net, in the consolidated statements of operations. The Company has no transactions which hedge purchase commitments and no intercompany balances which are designated as being of a long-term investment in nature.
Revenue recognition	Revenue recognition Software revenue Revenue is derived principally from the licensing of software products and from related maintenance contracts. The Company enters into contracts that include combinations of products, maintenance and services, which are accounted for as separate performance obligations with differing revenue recognition patterns. Revenue from term-based software licenses is classified as software revenue. Term-based licenses are sold only as a bundled arrangement that includes the rights to a term-based software license and post-contract customer support (PCS), which includes unspecified technical enhancements and customer support. Maximizing the use of observable inputs, the Company determined that a majority of the estimated standalone selling prices of the term-based license is attributable to the term-based license and a minority is attributable to the PCS. The license component is classified as license revenue and recognized as revenue upon the later of delivery of the licensed product or the beginning of the license period. PCS is classified as maintenance and other services and is recognized ratably over the term of the contract, as the Company provides the PCS benefit over time as a stand ready to perform obligation. In addition to term-based software licenses, the Company sells perpetual licenses. Software revenue is recognized upon the later of delivery of the licensed product or the beginning of the license period. Typically, the Company’s perpetual licenses are sold with PCS. The Company allocates value in bundled perpetual and PCS arrangements based on the value relationship between the software license and maintenance. Revenue from PCS is classified as maintenance and other services and is recognized ratably over the term of the contract, as the Company satisfies the PCS performance obligation over time as a stand ready to perform obligation. Revenue from training, consulting and other services is recognized as the services are performed and is classified as maintenance and other services in the consolidated statement of operations. For contracts in which the service consists of a single performance obligation, such as providing a training class to a customer, the Company recognizes revenue upon completion of the performance obligation. For service contracts that are longer in duration and often include multiple performance obligations (for example, point-in-time training and consulting), the Company measures the progress toward completion of the obligations and recognizes revenue accordingly. In measuring progress towards the completion of performance obligations, the Company typically utilizes output-based estimates for services with fixed fee arrangements, and estimates output based on the total tasks completed as compared to the total tasks required for each contract. Input-based estimates are utilized for services that involve general consultations with contractual billing arrangements based on time and materials, utilizing direct labor as the input measure. The Company also executes arrangements through indirect channel partners in which the channel partners are authorized to market and distribute the Company's software products to end users of the Company's products and services in specified territories. In sales facilitated by channel partners, the channel partner bears the risk of collection from the end-user customer. The Company recognizes revenue from transactions with channel partners in a manner consistent with the direct sales described above for both perpetual and term-based licenses. Revenue from channel partner transactions is the amount remitted to the Company by the channel partners. This amount includes a fee for PCS that is compensation for providing technical enhancements and the second level of technical support to the end user, which is recognized over the period that PCS is to be provided. The Company does not offer right of return, product rotation, or price protection to any of its channel partners. Non-income related taxes collected from customers and remitted to governmental authorities are recorded on the consolidated balance sheets as accounts receivable, net and other accrued expenses and current liabilities. These amounts are reported on a net basis in the consolidated statements of operations and do not impact reported revenues or expenses. Certain hardware revenue is included within software revenue and is recognized when all revenue recognition criteria stated above are met, which is generally when the products are delivered to end customers. Engineering services and other revenue Consulting services from product design and development projects are considered distinct performance obligations and are provided to customers on a time-and-materials (“T&M”) or fixed-price basis. The Company recognizes software services revenue for T&M contracts based upon hours worked and contractually agreed upon hourly rates using the input method. Revenue from fixed-price engagements is recognized using the output method based on the ratio of costs incurred to total estimated project costs. Client engineering services revenue are derived from professional services for staffing primarily representing engineers and data scientists located at a customer site. These professional services are considered distinct performance obligations and are provided to customers on a T&M basis. The Company recognizes this revenue for T&M contracts based upon hours worked and contractually agreed upon hourly rates using the input method. Revenue from the sale of LED products, primarily for the replacement of florescent tubes, is recognized when all revenue recognition criteria stated above are met, which is generally when the products are delivered to resellers or to end customers. Sales returns, which reduce revenue, are estimated using historical experience.
Property and equipment, net	Property and equipment, net Property and equipment are stated at cost, less accumulated depreciation and amortization. Equipment held under capital leases are stated at the present value of minimum lease payments less accumulated amortization. Depreciation is calculated using the straight-line method over the estimated useful lives of the assets. Expenditures for maintenance and repairs are charged to expense in the period incurred. Major expenditures for betterments are capitalized when they meet the criteria for capitalization. When assets are retired or otherwise disposed of, the cost and accumulated depreciation are removed from the accounts and any resulting gain or loss is reflected in the consolidated statements of operations in the period realized. Building and improvements are depreciated over an estimated useful life of five to thirty-nine years . Computer equipment and software is depreciated over an estimated useful life of three to five years . Office furniture and equipment is depreciated over an estimated useful life of five to fifteen years . Leasehold improvements and assets acquired under capital leases are amortized over the lease term or the estimated useful life of the related asset or improvement, whichever is shorter.
Software development costs	Software development costs Software development costs incurred prior to the establishment of technological feasibility are expensed as incurred. Technological feasibility is established upon the completion of a detailed program design. Capitalization of software development costs may begin upon the establishment of technological feasibility and ends when the product is available for general release. Generally, the time between the establishment of technological feasibility and commercial release of software is short. As such, all internal software development costs have been expensed as incurred and included in research and development expense in the accompanying consolidated statements of operations.
Impairment of long-lived assets	Impairment of long-lived assets Long-lived assets, such as property and equipment, and definite-lived intangible assets, including developed technology, customer relationships, and tradenames are reviewed for impairment whenever events or changes in circumstances indicate that the carrying amount of an asset may not be recoverable. If circumstances require a long-lived asset or asset group to be tested for possible impairment, the Company compares the undiscounted future cash flows expected to be generated by that asset or asset group to its carrying amount. If the carrying amount of the long-lived asset or asset group is not recoverable on an undiscounted cash flow basis, an impairment charge is recognized to the extent that the carrying amount exceeds its fair value. Fair value is determined through various valuation techniques, including discounted cash flow models and third-party independent appraisals. No impairment losses were recognized in 2024, 2023, or 2022.
Goodwill	Goodwill Goodwill represents the excess of the consideration transferred for an acquired entity over the estimated fair values of the net tangible assets and the identifiable assets acquired. As described in Note 4 – Acquisitions, the Company has recorded goodwill in connection with certain acquisitions. Goodwill is not amortized but rather reviewed for impairment annually or more frequently if facts or circumstances indicate that the carrying value may not be recoverable. The Company has determined that there is one reporting unit with goodwill subject to goodwill impairment testing. An entity has the option to perform a qualitative assessment to determine whether it is more likely than not that the fair value of the reporting unit is less than its carrying amount prior to performing the quantitative two-step impairment test. The Company has the option to first assess qualitative factors to determine whether the existence of events or circumstances leads to a determination that it is more likely than not that the fair value of a reporting unit is less than its carrying amount prior to performing the quantitative two-step impairment test. The qualitative assessment evaluates various events and circumstances, such as macro-economic conditions, industry and market conditions, cost factors, relevant events and financial trends that may impact a reporting unit’s fair value. If, after assessing the totality of events or circumstances, an entity determines it is not more likely than not that the fair value of a reporting unit is less than its carrying amount, including goodwill, then additional impairment testing is not required. However, if an entity concludes otherwise, then it is required to perform the two-step goodwill impairment test. The impairment test involves comparing the estimated fair value of a reporting unit with its book value, including goodwill. If the estimated fair value exceeds book value, goodwill is considered not to be impaired. If, however, the fair value of the reporting unit is less than book value, then an impairment loss is recognized in an amount equal to the amount that the book value of the reporting unit exceeds its fair value, not to exceed the total amount of goodwill allocated to the reporting unit. The Company performs its annual impairment review of goodwill in the fourth quarter of each year and when a triggering event occurs between annual impairment dates. For 2024, the Company performed a qualitative assessment of goodwill and determined that it was not more likely than not that the fair value of its reporting unit with goodwill was less than its carrying amount. Accordingly, the Company determined that its goodwill was not impaired.
Government assistance	Government assistance The Company receives incentives from federal, state and local governments in different regions of the world to primarily encourage the Company to establish, maintain, or increase investment or employment in the region. Government incentives are recorded in the consolidated financial statements in accordance with their purpose as a reduction of expense or other income based on the substance of the incentive received. Benefits are generally recorded when the conditions of the grant are met and there is reasonable assurance of receipt. The amounts are recorded in earnings as the expenses in which the incentive is meant to offset are incurred. For the years ended December 31, 2024, 2023 and 2022, respectively, other operating income includes $ 5.4 million, $ 5.6 million and $ 3.0 million of government related funding.
Receivable for R&D credit	Receivable for R&D credit The French government provides a research and development (“R&D”) tax credit known as Credit Impôt Recherche, or CIR, in order to encourage Companies to invest in R&D. The tax credit is deductible from the French income tax and any excess is carried forward for three years. After three years , any unused credit may be reimbursed to the Company by the French government. As of December 31, 2024, the Company had approximately $ 10.6 million of receivables from the French government related to CIR, of which $ 5.8 million was recorded in Income tax receivable and the remaining $ 4.8 million was recorded in Other long-term assets. As of December 31, 2023, the Company had approximately $ 12.1 million of receivables from the French government related to CIR, of which $ 5.7 million was recorded in Income tax receivable and the remaining $ 6.4 million was recorded in Other long-term assets. CIR is subject to customary audit by the French tax authorities.
Other Investments	Other Investments Other investments include non-marketable equity investments in privately held companies, which do not have readily determinable fair values, and in which the Company does not have a controlling interest or significant influence. The Company applies the measurement alternative for non-marketable equity securities, measuring them at cost, less any impairment. These investments are presented within other long-term assets on our consolidated balance sheets and are periodically analyzed to determine whether there are indicators of impairment.
Income taxes	Income taxes The Company accounts for income taxes under the asset and liability method. Deferred tax assets and liabilities are recognized for the future tax consequences attributable to differences between the financial statement carrying amounts of existing assets and liabilities and their respective tax basis and for operating loss and tax credit carryforwards. Deferred tax assets and liabilities are measured using enacted tax rates expected to apply to taxable income in the years in which those temporary differences are expected to be recovered or settled. The effect of a change in tax rates on deferred tax assets and liabilities is recognized in income in the period that includes the enactment date. The Company records net deferred tax assets to the extent it believes that these assets will more likely than not be realized. These deferred tax assets are subject to periodic assessments as to recoverability and if it is determined that it is more likely than not that the benefits will not be realized, valuation allowances are recorded which increase the provision for income taxes. In making such determination, the Company considers all available positive and negative evidence, including historical taxable income, projected future taxable income, the expected timing and reversal of existing temporary differences, ability to carryback losses, and tax planning strategies. If based upon the evidence, it is more likely than not that the deferred tax asset will not be realized, a valuation allowance is recorded. A valuation allowance is recognized to reduce deferred tax assets to the amount that management believes is more likely than not to be realized. The Company applies a more-likely-than-not recognition threshold to its accounting for tax uncertainties. The Company reviews all of its tax positions and makes determinations as to whether its tax positions are more likely than not to be sustained upon examination by the relevant taxing authorities. Only those benefits that have a greater than fifty percent likelihood of being sustained upon examination by taxing authorities are recognized. Interest and penalties related to uncertain tax positions are recorded in the provision for income taxes in the consolidated statements of operations.
Research and development costs	Research and development costs Research and development costs are expensed as incurred. Research and development expenses consist primarily of salaries and benefits of research and development employees and costs incurred related to the development of new software products and significant enhancements and engineering changes to existing software products.
Advertising costs	Advertising costs Advertising costs are expensed as incurred. Advertising expenses were $ 4.6 million, $ 5.1 million and $ 5.0 million for the years ended December 31, 2024, 2023 and 2022, respectively.
Leases	Leases The Company determines if an arrangement is a lease at inception. Operating leases are included in operating lease right-of-use (“ROU”) assets, current portion of operating lease liabilities, and operating lease liabilities, net of current portion on the Company’s consolidated balance sheets.
Stock-based compensation	Stock-based compensation Employee stock-based awards, consisting of stock options, restricted stock units (RSUs) and employee stock purchase plan (ESPP) shares expected to be settled by issuing shares of Class A common stock, are recorded as equity awards. The fair value of stock options and ESPP shares on the date of grant is measured using the Black-Scholes option pricing model. The Company expenses the grant date fair value of its time-vested stock options subject to graded vesting using the straight-line method over the applicable service period. The Company expenses the fair value of ESPP shares over the offering period. The fair value of RSUs is measured using the fair value of the Company’s Class A common stock on the date of the grant. The fair value of RSUs is recognized as expense on a straight-line basis over the requisite service period, which is generally four years .
Business combinations	Business combinations The Company accounts for business acquisitions using the acquisition method of accounting. The fair value of purchase consideration of the acquired businesses is allocated to the identifiable tangible and intangible assets acquired and liabilities assumed in the transaction based upon their estimated fair values as of the acquisition date. The excess of the purchase price over those fair values is recorded as goodwill. During the measurement period, which may be up to one year from the acquisition date, the Company may record adjustments to the assets acquired and liabilities assumed with the corresponding offset to goodwill. Upon the conclusion of the measurement period or final determination of the values of assets acquired or liabilities assumed, whichever comes first, any subsequent adjustments are recorded to the consolidated statements of operations.
Recent accounting guidance	Recent accounting guidance Accounting standards adopted Reference Rate Reform – In March 2020, the Financial Accounting Standards Board ("FASB") issued Accounting Standards Update ("ASU") 2020-04 Reference Rate Reform (Topic 848) - Facilitation of the Effects of Reference Rate Reform on Financial Reporting. This ASU provides optional expedients and exceptions for applying U.S. GAAP to contract modifications and hedging relationships, subject to meeting certain criteria, that reference LIBOR or another rate that is expected to be discontinued. The Company adopted ASU 2020-04 on December 31, 2024. The adoption of this guidance did not have a material effect on the Company's consolidated financial statements. Segment Reporting – In November 2023, the FASB issued ASU 2023-07 Segment Reporting (Topic 280) - Improvements to Reportable Segment Disclosures. The update is intended to improve reportable segment disclosure requirements, primarily through enhanced disclosures about significant expenses. The ASU requires disclosures to include significant segment expenses that are regularly provided to the chief operating decision maker (CODM), a description of other segment items by reportable segment, and any additional measures of a segment's profit or loss used by the CODM when deciding how to allocate resources. The ASU also requires all annual disclosures currently required by Topic 280 to be included in interim periods. The Company adopted this update effective for fiscal year ended December 31, 2024. Accounting standards not yet adopted Income Taxes – In December 2023, the FASB issued ASU 2023-09, Income Taxes (Topic 740): Improvements to Income Tax Disclosures , which updates income tax disclosures related to the tax rate reconciliation and requires disclosure of income taxes paid by jurisdiction. The amendments are effective for fiscal years beginning after December 15, 2024. Early adoption is permitted. The amendments should be applied prospectively; however, retrospective application is permitted. The Company is currently evaluating this ASU to determine the effect on its related disclosures. Income Statement – In November 2024, the FASB issued ASU 2024-03, Income Statement - Reporting Comprehensive Income - Expense Disaggregation Disclosures (Subtopic 220-40): Disaggregation of Income Statement Expenses , which requires additional disclosures over certain expenses, including purchases of inventory, employee compensation, depreciation, intangible asset amortization, and other specific expense categories. This update also requires disclosure of the total amount of selling expenses and the Company's definition of selling expenses. This update is effective for fiscal years beginning after December 15, 2026, and interim periods within fiscal years beginning after December 15, 2027. Early adoption is permitted. The Company is evaluating this ASU to determine the effect on its related disclosures. Debt – In November 2024, the FASB issued ASU 2024-04, Debt - Debt with Conversion and Other Options (Subtopic 470-20): Induced Conversion of Convertible Debt Instruments , which clarifies the requirements for determining whether certain settlements of convertible debt instruments should be accounted for as an induced conversion. This update is effective for fiscal years beginning after December 15, 2025, including interim periods within those fiscal periods. Early adoption is permitted. The Company is evaluating this ASU to determine the effect on its related disclosures.

Revenue from Contracts with C_2

Revenue from Contracts with Customers (Tables)	12 Months Ended
	Dec. 31, 2024
Revenue from Contract with Customer [Abstract]
Schedule of Disaggregation of Revenue	The Company disaggregates its revenue by type of performance obligation and timing of revenue recognition as follows (in thousands): Year ended December 31, 2024 2023 2022 Term licenses and other software products $ 388,751 $ 353,065 $ 320,181 Perpetual licenses 46,537 40,079 43,339 Maintenance 164,380 148,779 135,752 Professional software services 12,232 8,051 7,236 Software related services 25,367 28,032 30,661 Client engineering services 25,027 29,497 28,883 Other 3,494 5,198 6,169 Total revenue $ 665,788 $ 612,701 $ 572,221

Supplementary Information (Tabl

Supplementary Information (Tables)	12 Months Ended
	Dec. 31, 2024
Supplementary Information [Abstract]
Reconciliation of Cash, Cash Equivalents and Restricted Cash	The following table provides a reconciliation of cash, cash equivalents and restricted cash reported in the consolidated balance sheets that sum to the total of the amounts reported in the consolidated statements of cash flows (in thousands): December 31, 2024 2023 Cash and cash equivalents $ 561,898 $ 467,459 Restricted cash included in other long-term assets 144 117 Total cash, cash equivalents, and restricted cash $ 562,042 $ 467,576
Schedule of Accounts Receivable Net	Accounts receivable, net consisted of the following (in thousands): December 31, 2024 2023 Accounts receivable, trade $ 168,625 $ 185,275 Contract assets 4,884 5,186 Accounts receivable, net $ 173,509 $ 190,461
Schedule of Provision for Credit Loss	Activity in the provision for credit loss was as follows (in thousands): Year ended December 31, 2024 2023 2022 Balance, beginning of year $ ( 2,941 ) $ ( 2,590 ) $ ( 2,539 ) Provision charged to expense ( 414 ) ( 299 ) ( 203 ) Write-off, net of recoveries 1,508 6 498 Effects of foreign currency translation 102 ( 58 ) ( 346 ) Balance, end of year $ ( 1,745 ) $ ( 2,941 ) $ ( 2,590 )
Summary of Property and Equipment	Property and equipment consisted of the following (in thousands): Estimated December 31, useful lives 2024 2023 Land Indefinite $ 8,371 $ 8,376 Building and improvements 5 - 39 years 17,903 17,528 Computer equipment and software 3 - 5 years 47,397 45,678 Office furniture and equipment 5 - 15 years 13,738 14,402 Leasehold improvements (1 ) 9,284 8,380 Total property and equipment 96,693 94,364 Less: accumulated depreciation and amortization 55,685 54,561 Property and equipment, net $ 41,008 $ 39,803 (1) Shorter of lease term or estimated useful life, generally ranging from five to ten years .
Summary of Other Accrued Expenses and Current Liabilities	The following table provides the details of other accrued expenses and current liabilities (in thousands): December 31, 2024 2023 Income taxes payable $ 13,965 $ 12,239 Accrued VAT 10,390 8,710 Accrued professional fees 5,718 2,436 Obligations related to acquisitions of businesses and technology 5,621 3,286 Employee stock purchase plan obligations 4,762 4,155 Accrued royalties 2,562 2,313 Non-income tax liabilities 2,335 2,473 Billings in excess of cost 2,138 2,385 Defined contribution plan liabilities 1,491 1,454 Other current liabilities 7,076 8,947 Total $ 56,058 $ 48,398
Summary of Other Long-term Liabilities	The following table provides the details of other long-term liabilities (in thousands): December 31, 2024 2023 Income tax reserves $ 11,902 $ 16,254 Pension and other post-retirement liabilities 16,052 15,815 Deferred tax liabilities 13,314 12,870 Other liabilities 6,749 2,212 Total $ 48,017 $ 47,151
Schedule of Other (Income) Expense, Net	Other (income) expense, net consists of the following (in thousands): Year ended December 31, 2024 2023 2022 Interest income $ ( 22,995 ) $ ( 16,855 ) $ ( 4,127 ) Foreign exchange loss (gain) 2,214 ( 1,637 ) 4,405 Expense on repurchase of convertible senior notes — — 16,621 Other (income) expense, net $ ( 20,781 ) $ ( 18,492 ) $ 16,899

Goodwill and Other Intangible_2

Goodwill and Other Intangible Assets (Tables)	12 Months Ended
	Dec. 31, 2024
Goodwill and Intangible Assets Disclosure [Abstract]
Changes in Carrying Amount of Goodwill Attributable to Software Reportable Segment	The changes in the carrying amount of goodwill, which is attributable to the Software reportable segment, are as follows (in thousands): Balance as of December 31, 2022 $ 449,048 Acquisitions 2,948 Foreign currency translation and other 6,129 Balance as of December 31, 2023 458,125 Acquisitions 13,027 Foreign currency translation and other ( 8,693 ) Balance as of December 31, 2024 $ 462,459
Schedule of Other Intangible Assets	A summary of other intangible assets is shown below (in thousands): December 31, 2024 Weighted Gross Accumulated Net carrying Developed technology 4 - 6 years $ 159,815 $ 112,494 $ 47,321 Customer relationships 4 - 10 years 60,556 44,524 16,032 Trade names and other intangibles 3 - 10 years 11,551 1,967 9,584 Total other intangible assets $ 231,922 $ 158,985 $ 72,937 December 31, 2023 Weighted Gross Accumulated Net carrying Developed technology 4 - 6 years $ 142,368 $ 90,729 $ 51,639 Customer relationships 7 - 10 years 58,316 37,779 20,537 Trade names and other intangibles 4 - 10 years 11,937 563 11,374 Total other intangible assets $ 212,621 $ 129,071 $ 83,550
Summary of Estimated Amortization Expense	Estimated amortization expense for the next five years as of December 31, 2024, is as follows (in thousands): Year ending December 31, 2025 $ 29,670 December 31, 2026 23,528 December 31, 2027 11,680 December 31, 2028 5,981 December 31, 2029 1,922 Thereafter 156 Total $ 72,937

Debt (Tables)

Debt (Tables)	12 Months Ended
	Dec. 31, 2024
Debt Disclosure [Abstract]
Schedule of Net Carrying Value of the 2027 and 2024 Notes	The net carrying value of the 2027 and 2024 Notes was as follows (in thousands): December 31, 2024 December 31, 2023 2027 Notes 2024 Notes 2027 Notes 2024 Notes Principal $ 230,000 $ — 230,000 $ 81,729 Less: unamortized debt issuance costs 2,894 — 4,071 274 Net carrying amount $ 227,106 $ — $ 225,929 $ 81,455
Schedule of Interest Expense Related to 2027 and 2024 Notes	The interest expense related to the 2027 and 2024 Notes was as follows (in thousands): Year ended December 31, 2024 2023 2022 Contractual interest expense $ 4,110 $ 4,230 $ 2,452 Amortization of debt issuance cost and discount 1,452 1,806 1,745 Total $ 5,562 $ 6,036 $ 4,197

Leases (Tables)

Leases (Tables)	12 Months Ended
	Dec. 31, 2024
Leases [Abstract]
Schedule of Supplemental Balance Sheet Information Related to Lease Liabilities	December 31, 2024 2023 Weighted average remaining lease term of operating leases 5.7 years 6 years Weighted average discount rate of operating leases 4.6 % 3.9 %
Schedule of Supplemental Cash Flow Information Related to Leases	Year ended December 31, (in thousands) 2024 2023 2022 Cash paid for amounts included in the measurement of lease liabilities: Operating cash flows from operating leases $ ( 10,641 ) $ ( 11,606 ) $ ( 12,949 ) ROU assets obtained in exchange for new operating lease obligations $ 9,150 $ 17,023 $ 12,455
Schedule of Maturities of Operating Lease Liabilities	Maturities of operating lease liabilities as of December 31, 2024, were as follows (in thousands): Year ending December 31, 2025 $ 9,550 2026 8,614 2027 6,277 2028 3,438 2029 2,669 Thereafter 7,492 Total future lease payments 38,040 Less: present value adjustment 6,023 Total operating lease liabilities $ 32,017

Stock-Based Compensation (Table

Stock-Based Compensation (Tables)	12 Months Ended
	Dec. 31, 2024
Summary of Fair value of Company's Stock Options Granted	The fair values of the Company’s stock options granted during the year ended December 31, 2024, 2023 and 2022, were estimated using the following assumptions: 2024 grants 2023 grants 2022 grants Weighted average grant date fair value per share $ 79.03 - 85.52 $ 65.19 - 67.65 $ 44.63 - 64.79 Expected volatility 35 % 35 % 35 % Expected term (in years) 6.25 6.25 6.25 Risk-free interest rate 4.2 % - 4.3 % 3.5 % - 4.3 % 1.7 % - 4.2 % Expected dividend yield 0 % 0 % 0 %
Summary of Stock-Based Compensation	The stock-based compensation expense was recorded as follows (in thousands): Year ended December 31, 2024 2023 2022 Cost of revenue-software $ 8,397 $ 10,095 $ 8,351 Research and development 25,630 33,842 36,250 Sales and marketing 19,459 28,376 30,370 General and administrative 14,194 13,268 9,816 Total stock-based compensation expense $ 67,680 $ 85,581 $ 84,787
NSO Plan [Member]
Summary of Stock Option Activity	The following table summarizes the stock option activity under the NSO Plan: Number of Weighted Weighted Aggregate intrinsic value (in millions) Outstanding as of December 31, 2023 994,884 $ 0.000025 13.0 Exercised ( 371,345 ) $ 0.000025 Outstanding and exercisable as of December 31, 2024 623,539 $ 0.000025 12.0 $ 68.0
2012 Plan [Member]
Summary of Stock Option Activity	The following table summarizes the stock option activity under the 2012 Plan for the periods indicated as follows: Number of Weighted Weighted Aggregate intrinsic value (in millions) Outstanding as of December 31, 2023 271,359 $ 4.46 2.5 Exercised ( 111,992 ) $ 4.24 Outstanding and exercisable as of December 31, 2024 159,367 $ 4.62 1.9 $ 16.7
2017 Plan [Member]
Summary of Stock Option Activity	The following table summarizes the stock option activity under the 2017 Plan for the period: Number of Weighted Weighted Aggregate intrinsic value (in millions) Outstanding as of December 31, 2023 7,602,078 $ 52.81 7.8 Granted 417,459 $ 79.19 Exercised ( 1,325,265 ) $ 49.91 Forfeited ( 124,821 ) $ 55.94 Outstanding as of December 31, 2024 6,569,451 $ 55.01 7.1 $ 355.4 Exercisable as of December 31, 2024 3,940,042 $ 51.61 6.5 $ 226.5
Summary of Restricted Stock Units Awarded	The following table summarizes the restricted stock units, or RSUs, awarded under the 2017 Plan for the period: Number of RSUs Outstanding as of December 31, 2023 1,086,351 Granted 384,424 Vested ( 530,732 ) Forfeited ( 33,191 ) Outstanding as of December 31, 2024 906,852

Income Taxes (Tables)

Income Taxes (Tables)	12 Months Ended
	Dec. 31, 2024
Income Tax Disclosure [Abstract]
Components of Income (Loss) Before Income Taxes	The components of income (loss) before income taxes are as follows (in thousands): Year ended December 31, 2024 2023 2022 U.S. $ ( 8,279 ) $ ( 21,803 ) $ ( 62,702 ) Non-U.S. 40,909 34,422 34,489 $ 32,630 $ 12,619 $ ( 28,213 )
Schedule of Significant Components of Income Tax Expense	The significant components of income tax expense are as follows (in thousands): Year ended December 31, 2024 2023 2022 Current U.S. Federal $ — $ — $ — Non-U.S. 19,168 22,746 18,759 U.S. State and Local ( 6 ) 1,118 621 Total current 19,162 23,864 19,380 Deferred U.S. Federal 36 35 23 Non-U.S. ( 773 ) ( 2,384 ) ( 4,206 ) U.S. State and Local 30 30 19 Total deferred ( 707 ) ( 2,319 ) ( 4,164 ) Income tax expense $ 18,455 $ 21,545 $ 15,216
Reconciliation of Income Taxes Calculated at U.S. Federal Statutory Income Tax Rate	The reconciliation of income taxes calculated at the U.S. Federal statutory income tax rate to income tax expense is as follows (in thousands): Year ended December 31, 2024 2023 2022 U.S. federal statutory rate 21 % 21 % 21 % Income taxes at U.S. federal statutory rate $ 6,852 $ 2,650 $ ( 5,925 ) Foreign income taxes at rates other than the federal statutory rate 2,626 1,733 2,249 U.S. state and local income taxes, net of U.S. federal tax benefit ( 3,054 ) ( 1,952 ) ( 5,976 ) U.S. effect of foreign operations 2,315 ( 9,931 ) 15,827 Change in valuation allowance 25,493 29,849 7,830 Foreign withholding taxes 8,501 7,444 6,738 U.S. foreign tax credit and deduction ( 8,261 ) ( 17,522 ) ( 12,315 ) Research and development tax credit 597 391 ( 326 ) Stock-based compensation ( 7,695 ) 1,361 8,649 Other 920 123 1,250 Uncertain tax positions ( 693 ) 6,370 472 FDII deduction ( 9,146 ) ( 169 ) ( 5,245 ) Mark-to-market adjustment of contingent consideration — 1,198 ( 1,502 ) Repurchase of convertible senior notes — — 3,490 Income tax expense $ 18,455 $ 21,545 $ 15,216 The Tax Cuts and Jobs Act, or the Tax Act, subjects a U.S. shareholder to current tax on global intangible low-taxed income (“GILTI”) earned by certain foreign subsidiaries. The impact of GILTI resulted in no incremental tax expense for the years ended December 31, 2024, 2023 and 2022 due to a full valuation allowance on U.S. net deferred tax assets. In addition, the Company has made an accounting policy election to treat taxes due under the GILTI provision as a current period expense.
Schedule of Deferred Tax Assets and Liabilities	Deferred income tax assets and liabilities result from differences in the basis of assets and liabilities for tax and financial statements purposes. The approximate tax effect of each type of temporary difference, and operating losses and tax credit carryforwards that give rise to a significant portion of the deferred tax assets and liabilities are as follows (in thousands): December 31, 2024 2023 Deferred tax assets: Deferred revenue $ 6,419 $ 9,730 Net operating loss carryforwards 57,933 60,702 Tax credit carryforwards 39,987 48,752 Stock-based compensation 13,491 12,011 Capitalized research and development 87,261 58,946 Lease obligation 6,330 7,517 Employee benefits 7,994 6,955 Merger costs 4,288 — Other 3,704 3,910 Total gross deferred tax assets 227,407 208,523 Less: valuation allowances ( 204,954 ) ( 179,766 ) Net deferred tax assets (1) 22,453 28,757 Deferred tax liabilities: Prepaid royalties 1,609 3,602 Property and equipment and intangibles 13,174 16,610 Deferred tax on investment in subsidiary 3,220 1,950 Lease right of use asset 6,193 7,357 Other 2,801 2,153 Total deferred tax liabilities 26,997 31,672 Total net deferred tax liabilities $ ( 4,544 ) $ ( 2,915 ) (1) Reflects gross amount before jurisdictional netting of deferred tax assets and liabilities.
Summary of Changes to Valuation Allowance Balance	The following table summarizes the changes to the valuation allowance balance (in thousands): Year ended December 31, 2024 2023 2022 Beginning balance $ 179,766 $ 149,441 $ 119,981 Additions charged to expense 27,481 30,665 7,830 Deductions ( 1,988 ) ( 816 ) — Other ( 305 ) 476 21,630 Ending balance $ 204,954 $ 179,766 $ 149,441
Summary of Operating Loss and Tax Credit Carryforwards	The following table summarizes the amount and expiration dates of operating loss and tax credit carryforwards as of December 31, 2024 (in thousands): Expiration dates Amounts U.S. general business credits and loss carryforwards 2025-Indefinite $ 62,990 Foreign general business credits and loss carryforwards 2025-Indefinite 13,029 U.S. foreign tax credits 2027 - 2033 21,901 Total operating loss and tax credit carryforwards $ 97,920
Reconciliation of Beginning and Ending Amounts of Unrecognized Tax Benefits	A reconciliation of the beginning and ending amounts of unrecognized tax benefits is as follows (in thousands): Year ended December 31, 2024 2023 2022 Unrecognized tax benefits—January 1 $ 38,219 $ 28,977 $ 16,376 Additions for tax positions of current period 50 9,435 50 Additions for tax positions of prior periods — 901 13,910 Reductions for tax positions of prior periods ( 4,891 ) ( 500 ) ( 1,334 ) Reductions due to statute of limitations ( 427 ) ( 594 ) ( 25 ) Unrecognized tax benefits—December 31 $ 32,951 $ 38,219 $ 28,977

Net Income (Loss) Per Share (Ta

Net Income (Loss) Per Share (Tables)	12 Months Ended
	Dec. 31, 2024
Earnings Per Share [Abstract]
Computation of Numerators and Denominators Used in Basic and Diluted Net Income (Loss) Per Share Amounts	The following table sets forth the computation of the numerators and denominators used in the basic and diluted net income (loss) per share amounts (in thousands, except per share data): Year ended December 31, 2024 2023 2022 Numerator: Net income (loss) $ 14,175 $ ( 8,926 ) $ ( 43,429 ) Interest expense related to convertible notes, net of tax (1) — — — Numerator for diluted income (loss) per share $ 14,175 $ ( 8,926 ) $ ( 43,429 ) Denominator: Weighted average shares outstanding, basic 84,085 80,596 79,472 Effect of dilutive shares 4,473 — — Weighted average shares outstanding, diluted 88,558 80,596 79,472 Income (loss) per share, basic $ 0.17 $ ( 0.11 ) $ ( 0.55 ) Income (loss) per share, diluted $ 0.16 $ ( 0.11 ) $ ( 0.55 ) (1) Interest expense related to the convertible notes has been excluded from the numerator for diluted earnings per share because its effect would have been anti-dilutive.
Schedule of Anti-dilutive Shares Excluded from Computation of Diluted Net Income (Loss) Per Share	Anti-dilutive shares excluded from the computation of diluted net income (loss) per share were as follows (in thousands): Year ended December 31, 2024 2023 2022 Convertible shares 3,209 3,753 4,958 Stock options and ESPP shares — 3,293 961 Total shares excluded from calculation 3,209 7,046 5,919

Retirement Benefits (Tables)

Retirement Benefits (Tables)	12 Months Ended
	Dec. 31, 2024
Retirement Benefits [Abstract]
Schedule of Pension Benefits Obligation Recorded in Consolidated Balance Sheets	A summary of the components of the pension benefits obligation recorded in the consolidated balance sheets are as follows (in thousands): December 31, 2024 2023 Other long-term assets $ 19 $ 135 Accrued compensation and benefits 1,247 1,170 Other long-term liabilities 16,052 15,815 $ 17,280 $ 16,850
Schedule of Estimated Future Benefit Payments	The estimated future benefit payments, which reflect expected future service that are expected to be paid for each of the next five years are as follows (in thousands): Year ending December 31, 2025 $ 1,319 December 31, 2026 $ 1,572 December 31, 2027 $ 1,372 December 31, 2028 $ 1,260 December 31, 2029 $ 1,114 Next five years $ 7,627

Accumulated Other Comprehensi_2

Accumulated Other Comprehensive Loss (Tables)	12 Months Ended
	Dec. 31, 2024
Equity [Abstract]
Components of Accumulated Other Comprehensive Loss	The components of accumulated other comprehensive loss are as follows (in thousands): Foreign Retirement Total Balance as of December 31, 2021 $ ( 6,400 ) $ ( 2,550 ) $ ( 8,950 ) Other comprehensive (loss) income before reclassification ( 24,084 ) 87 ( 23,997 ) Amounts reclassified from accumulated other comprehensive loss — 3,253 3,253 Tax effects — ( 308 ) ( 308 ) Other comprehensive (loss) income ( 24,084 ) 3,032 ( 21,052 ) Balance as of December 31, 2022 ( 30,484 ) 482 ( 30,002 ) Other comprehensive income (loss) before reclassification 9,011 ( 16 ) 8,995 Amounts reclassified from accumulated other comprehensive loss — ( 1,479 ) ( 1,479 ) Tax effects — 177 177 Other comprehensive income (loss) 9,011 ( 1,318 ) 7,693 Balance as of December 31, 2023 ( 21,473 ) ( 836 ) ( 22,309 ) Other comprehensive loss before reclassification ( 15,490 ) ( 8 ) ( 15,498 ) Amounts reclassified from accumulated other comprehensive loss — 777 777 Tax effects — ( 251 ) ( 251 ) Other comprehensive (loss) income ( 15,490 ) 518 ( 14,972 ) Balance as of December 31, 2024 $ ( 36,963 ) $ ( 318 ) $ ( 37,281 )

Commitments and Contingencies (

Commitments and Contingencies (Tables)	12 Months Ended
	Dec. 31, 2024
Commitments and Contingencies Disclosure [Abstract]
Future Purchase Obligations	The future purchase obligations for these agreements are as follows (in thousands): Year ending December 31, 2025 $ 22,085 2026 14,991 2027 2,708 2028 901 2029 364 Thereafter — Total $ 41,049

Segment Information (Tables)

Segment Information (Tables)	12 Months Ended
	Dec. 31, 2024
Segment Reporting [Abstract]
Schedule of Segment Reporting Information	The following tables are in thousands: Year ended December 31, 2024 Software CES All other Total Revenue $ 637,267 $ 25,027 $ 3,494 $ 665,788 Less: Cost of revenue 90,674 21,315 2,640 114,629 Research and development 187,826 — 1,069 188,895 Sales and marketing 158,670 1,006 1,135 160,811 General and administrative 54,681 1,722 584 56,987 Other segment items ( 5,338 ) — ( 108 ) ( 5,446 ) Adjusted EBITDA $ 150,754 $ 984 $ ( 1,826 ) $ 149,912 Year ended December 31, 2023 Software CES All other Total Revenue $ 578,006 $ 29,497 $ 5,198 $ 612,701 Less: Cost of revenue 82,625 24,450 4,329 111,404 Research and development 172,954 — 1,247 174,201 Sales and marketing 143,406 761 1,034 145,201 General and administrative 53,966 1,998 837 56,801 Other segment items ( 4,109 ) — 65 ( 4,044 ) Adjusted EBITDA $ 129,164 $ 2,288 $ ( 2,314 ) $ 129,138 Year ended December 31, 2022 Software CES All other Total Revenue $ 537,169 $ 28,883 $ 6,169 $ 572,221 Less: Cost of revenue 85,589 23,577 4,988 114,154 Research and development 161,106 — 860 161,966 Sales and marketing 129,740 592 746 131,078 General and administrative 58,374 2,139 1,111 61,624 Other segment items ( 5,278 ) ( 1 ) 78 ( 5,201 ) Adjusted EBITDA $ 107,638 $ 2,576 $ ( 1,614 ) $ 108,600
Reconciliation of U.S. GAAP (Loss) Income Before Income Taxes to Adjusted EBITDA	Year ended December 31, 2024 2023 2022 Reconciliation of Adjusted EBITDA to GAAP income (loss) Adjusted EBITDA $ 149,912 $ 129,138 $ 108,600 Stock-based compensation expense ( 67,680 ) ( 85,581 ) ( 84,787 ) Interest expense ( 5,836 ) ( 6,116 ) ( 4,377 ) Depreciation and amortization ( 42,164 ) ( 39,124 ) ( 35,504 ) Special adjustments, interest income and other (1) ( 1,602 ) 14,302 ( 12,145 ) Income (loss) before income taxes $ 32,630 $ 12,619 $ ( 28,213 ) (1) The year ended December 31, 2024, includes $ 22.3 million of expenses related to the pending merger with Siemens Industry, $ 1.9 million currency losses on acquisition-related intercompany loans, $ 0.5 million losses from the mark-to-market adjustment of contingent consideration associated with acquisitions and $ 23.0 million of interest income. The year ended December 31, 2023, includes $ 3.2 million currency gains on acquisition-related intercompany loans, $ 5.7 million losses from the mark-to-market adjustment of contingent consideration associated with the World Programming acquisition and $ 16.9 million of interest income. The year ended December 31, 2022, includes $ 16.6 million expense on repurchase of convertible senior notes, $ 6.8 million currency losses on acquisition-related intercompany loans, $ 7.2 million gains from the mark-to-market adjustment of contingent consideration associated with the World Programming acquisition and $ 4.1 million of interest income.
Summary of Sales to External Customers and Long-Lived Assets by Geographical Areas	Revenue is attributed to geographic areas based on the country of origin. The following table provides sales to external customers and long-lived assets for each of the geographic areas in which the Company operates (in thousands): Revenue Long-lived assets (1) Year ended December 31, December 31, 2024 2023 2022 2024 2023 United States $ 323,905 $ 301,857 $ 274,635 $ 52,565 $ 55,230 Other countries 18,987 17,792 13,425 15,385 6,193 Total Americas 342,892 319,649 288,060 67,950 61,423 Germany 46,927 46,593 51,495 12,686 19,840 France 24,283 23,122 19,442 1,109 1,200 Other countries 76,459 66,903 69,769 24,485 34,561 Total Europe, Middle East and Africa 147,669 136,618 140,706 38,280 55,601 Japan 42,451 39,508 40,335 1,052 685 Other countries 132,776 116,926 103,120 6,663 5,644 Total Asia Pacific 175,227 156,434 143,455 7,715 6,329 Total $ 665,788 $ 612,701 $ 572,221 $ 113,945 $ 123,353 (1) Includes Property and equipment, net and Other intangible assets, net.

Description of Business - Addit

Description of Business - Additional Information (Details) - USD ($) $ / shares in Units, $ in Thousands		12 Months Ended
	Oct. 30, 2024	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022	Oct. 21, 2024
Business Acquisition [Line Items]
Payments to acquire businesses		$ 27,070	$ 3,236	$ 134,541
Siemens Industry Software Inc. [Member]
Business Acquisition [Line Items]
Business acquisiton, share price	$ 113				$ 113
Payments to acquire businesses	$ 10,600,000
Percentage of premium to closing price of common stock					19%
Merger related costs		22,300
Siemens Industry Software Inc. [Member] | Cost of Revenue [Member]
Business Acquisition [Line Items]
Merger related costs		1,200
Siemens Industry Software Inc. [Member] | Research and Development [Member]
Business Acquisition [Line Items]
Merger related costs		1,800
Siemens Industry Software Inc. [Member] | Sales and Marketing [Member]
Business Acquisition [Line Items]
Merger related costs		1,300
Siemens Industry Software Inc. [Member] | General and administrative [Member]
Business Acquisition [Line Items]
Merger related costs		$ 18,200

Summary of Significant Accoun_3

Summary of Significant Accounting Policies - Additional Information (Detail) - USD ($)	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Accounting Policies [Line Items]
Impairment losses	$ 0	$ 0	$ 0
Income tax receivable, current	21,513,000	16,650,000
Advertising expenses	4,600,000	5,100,000	5,000,000
Operating Income [Member]
Accounting Policies [Line Items]
Govenment funds	$ 5,400,000	5,600,000	$ 3,000,000
ASU 2019-12
Accounting Policies [Line Items]
Change in Accounting Principle, Accounting Standards Update, Adopted [true false]	true
Change in Accounting Principle, Accounting Standards Update, Immaterial Effect [true false]	true
ASU 2021-08
Accounting Policies [Line Items]
Change in Accounting Principle, Accounting Standards Update, Adopted [true false]	true
Change in Accounting Principle, Accounting Standards Update, Immaterial Effect [true false]	true
Restricted Stock Units (RSUs) [Member]
Accounting Policies [Line Items]
Stock-based compensation awards requisite service period	4 years
Ministry of the Economy, Finance and Industry, France [Member] | Research and Development Tax Credit Carryforward [Member]
Accounting Policies [Line Items]
Tax credit carryforward, period	3 years
Income tax receivable	$ 10,600,000	12,100,000
Income tax receivable, current	5,800,000	5,700,000
Income tax receivable, noncurrent	$ 4,800,000	$ 6,400,000
Building and Improvements [Member] | Minimum [Member]
Accounting Policies [Line Items]
Property and equipment, estimated useful life	5 years
Building and Improvements [Member] | Maximum [Member]
Accounting Policies [Line Items]
Property and equipment, estimated useful life	39 years
Computer Equipment and Software [Member] | Minimum [Member]
Accounting Policies [Line Items]
Property and equipment, estimated useful life	3 years
Computer Equipment and Software [Member] | Maximum [Member]
Accounting Policies [Line Items]
Property and equipment, estimated useful life	5 years
Office Furniture and Equipment [Member] | Minimum [Member]
Accounting Policies [Line Items]
Property and equipment, estimated useful life	5 years
Office Furniture and Equipment [Member] | Maximum [Member]
Accounting Policies [Line Items]
Property and equipment, estimated useful life	15 years

Revenue from Contracts with C_3

Revenue from Contracts with Customers - Schedule of Disaggregation of Revenue (Detail) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Disaggregation Of Revenue [Line Items]
Total revenue	$ 665,788	$ 612,701	$ 572,221
Term Licenses and Other Software Products [Member]
Disaggregation Of Revenue [Line Items]
Total revenue	388,751	353,065	320,181
Perpetual Licenses [Member]
Disaggregation Of Revenue [Line Items]
Total revenue	46,537	40,079	43,339
Maintenance [Member]
Disaggregation Of Revenue [Line Items]
Total revenue	164,380	148,779	135,752
Professional Software Services [Member]
Disaggregation Of Revenue [Line Items]
Total revenue	12,232	8,051	7,236
Software Related Services [Member]
Disaggregation Of Revenue [Line Items]
Total revenue	25,367	28,032	30,661
Client Engineering Services [Member]
Disaggregation Of Revenue [Line Items]
Total revenue	25,027	29,497	28,883
Other [Member]
Disaggregation Of Revenue [Line Items]
Total revenue	$ 3,494	$ 5,198	$ 6,169

Revenue from Contracts with C_4

Revenue from Contracts with Customers - Additional Information (Detail) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Revenue From Contracts With Customers [Line Items]
Percentage of net revenues through indirect channels	13.30%	13.60%	13.90%
Capitalized contract cost, amortization period	4 years
Capitalized contract cost, amortization method	straight-line basis
Contract assets	$ 4,884	$ 5,186
Deferred revenue, revenue recognized	131,200
Contracted revenue not yet recognized	$ 270,600
Revenue recognize percentage	71%
Sales and Marketing Expense [Member]
Revenue From Contracts With Customers [Line Items]
Sales commissions	$ 9,100	8,800	$ 8,300
Prepaid and Other Current Assets [Member]
Revenue From Contracts With Customers [Line Items]
Capitalized contract cost net, current	4,800	4,300
Contract assets	2,100	2,700
Other Long-Term Assets [Member]
Revenue From Contracts With Customers [Line Items]
Capitalized contract cost net, noncurrent	1,000	900
Accounts Receivable [Member]
Revenue From Contracts With Customers [Line Items]
Contract assets	$ 4,900	$ 5,200

Revenue from Contracts with C_5

Revenue from Contracts with Customers - Additional Information (Detail)1	Dec. 31, 2024
Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Start Date [Axis]: 2025-01-01
Revenue From Contracts With Customers [Line Items]
Revenue, remaining contractual obligation, expected to recognize, period	12 months

Acquisitions - Additional Infor

Acquisitions - Additional Information (Detail)	1 Months Ended	12 Months Ended
	Oct. 31, 2023 shares	Dec. 31, 2024 USD ($) Business	Dec. 31, 2023 USD ($)	Dec. 31, 2022 USD ($)
Business Acquisition [Line Items]
Loss (gain) on mark-to-market adjustment of contingent consideration		$ 476,000	$ 5,706,000	$ (7,153,000)
2024 Acquisitions [Member]
Business Acquisition [Line Items]
Number of business acquisitions completed | Business		4
Fair value of consideration transferred		$ 36,800,000
2024 Acquisitions [Member] | Goodwill [Member]
Business Acquisition [Line Items]
Fair value of consideration transferred		13,000,000
2024 Acquisitions [Member] | Goodwill Deductible for Tax Purpose [Member]
Business Acquisition [Line Items]
Business acquisition, goodwill, expected tax deductible amount		5.1
2024 Acquisitions [Member] | Developed Technology [Member]
Business Acquisition [Line Items]
Fair value of consideration transferred		21,400,000
2024 Acquisitions [Member] | Customer Relationships [Member]
Business Acquisition [Line Items]
Fair value of consideration transferred		3,100,000
Prior Acquisitions [Member]
Business Acquisition [Line Items]
Contingent consideration				12,000,000
Loss (gain) on mark-to-market adjustment of contingent consideration		$ (500,000)	$ (5,700,000)	$ 7,200,000
Prior Acquisitions [Member] | Class A Common Stock [Member]
Business Acquisition [Line Items]
Business acquisition, shares issued | shares	257,382

Supplementary Information - Rec

Supplementary Information - Reconciliation of Cash, Cash Equivalents and Restricted Cash (Detail) - USD ($) $ in Thousands	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022	Dec. 31, 2021
Supplementary Information [Abstract]
Cash and cash equivalents	$ 561,898	$ 467,459
Restricted cash included in other long-term assets	144	117
Total cash, cash equivalents, and restricted cash	$ 562,042	$ 467,576	$ 316,958	$ 414,012

Supplementary Information - Sch

Supplementary Information - Schedule of Accounts Receivable Net (Detail) - USD ($) $ in Thousands	Dec. 31, 2024	Dec. 31, 2023
Supplementary Information [Abstract]
Accounts receivable, trade	$ 168,625	$ 185,275
Contract assets	4,884	5,186
Accounts receivable, net	$ 173,509	$ 190,461

Supplementary Information - Add

Supplementary Information - Additional Information (Detail) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022	Dec. 31, 2021
Supplementary Information [Line Items]
Provision for credit loss	$ 1,745	$ 2,941	$ 2,590	$ 2,539
Depreciation expense, including amortization of right-of-use assets under finance leases	$ 9,100	$ 8,300	$ 8,000

Supplementary Information - S_2

Supplementary Information - Schedule of Provision for Credit Loss (Detail) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Accounts Notes And Loans Receivable [Line Items]
Balance, beginning of year	$ (2,941)	$ (2,590)	$ (2,539)
Provision charged to expense	(414)	(299)	(203)
Write-off, net of recoveries	1,508	6	498
Effects of foreign currency translation	102	(58)	(346)
Balance, end of year	$ (1,745)	$ (2,941)	$ (2,590)

Supplementary Information - Sum

Supplementary Information - Summary of Property and Equipment (Detail) - USD ($) $ in Thousands	Dec. 31, 2024	Dec. 31, 2023
Property, Plant and Equipment [Line Items]
Total property and equipment	$ 96,693	$ 94,364
Less: accumulated depreciation and amortization	55,685	54,561
Property and equipment, net	41,008	39,803
Land [Member]
Property, Plant and Equipment [Line Items]
Total property and equipment	8,371	8,376
Building and Improvements [Member]
Property, Plant and Equipment [Line Items]
Total property and equipment	$ 17,903	17,528
Building and Improvements [Member] | Minimum [Member]
Property, Plant and Equipment [Line Items]
Property and equipment, estimated useful life	5 years
Building and Improvements [Member] | Maximum [Member]
Property, Plant and Equipment [Line Items]
Property and equipment, estimated useful life	39 years
Computer Equipment and Software [Member]
Property, Plant and Equipment [Line Items]
Total property and equipment	$ 47,397	45,678
Computer Equipment and Software [Member] | Minimum [Member]
Property, Plant and Equipment [Line Items]
Property and equipment, estimated useful life	3 years
Computer Equipment and Software [Member] | Maximum [Member]
Property, Plant and Equipment [Line Items]
Property and equipment, estimated useful life	5 years
Office Furniture and Equipment [Member]
Property, Plant and Equipment [Line Items]
Total property and equipment	$ 13,738	14,402
Office Furniture and Equipment [Member] | Minimum [Member]
Property, Plant and Equipment [Line Items]
Property and equipment, estimated useful life	5 years
Office Furniture and Equipment [Member] | Maximum [Member]
Property, Plant and Equipment [Line Items]
Property and equipment, estimated useful life	15 years
Leasehold Improvements [Member]
Property, Plant and Equipment [Line Items]
Total property and equipment	$ 9,284	$ 8,380
Leasehold Improvements [Member] | Minimum [Member]
Property, Plant and Equipment [Line Items]
Property and equipment, estimated useful life	5 years
Leasehold Improvements [Member] | Maximum [Member]
Property, Plant and Equipment [Line Items]
Property and equipment, estimated useful life	10 years

Supplementary Information - S_3

Supplementary Information - Summary of Property and Equipment (Parenthetical) (Detail) - Leasehold Improvements [Member]	Dec. 31, 2024
Minimum [Member]
Property, Plant and Equipment [Line Items]
Property and equipment, estimated useful life	5 years
Maximum [Member]
Property, Plant and Equipment [Line Items]
Property and equipment, estimated useful life	10 years

Supplementary Information - S_4

Supplementary Information - Summary of Other Accrued Expenses and Current Liabilities (Detail) - USD ($) $ in Thousands	Dec. 31, 2024	Dec. 31, 2023
Other Liabilities Disclosure [Abstract]
Income taxes payable	$ 13,965	$ 12,239
Accrued VAT	10,390	8,710
Accrued professional fees	5,718	2,436
Obligations related to acquisitions of businesses and technology	5,621	3,286
Employee stock purchase plan obligations	4,762	4,155
Accrued royalties	2,562	2,313
Non-income tax liabilities	2,335	2,473
Billings in excess of cost	2,138	2,385
Defined contribution plan liabilities	1,491	1,454
Other current liabilities	7,076	8,947
Total	$ 56,058	$ 48,398

Supplementary Information - S_5

Supplementary Information - Summary of Other Long-term Liabilities (Detail) - USD ($) $ in Thousands	Dec. 31, 2024	Dec. 31, 2023
Other Liabilities Disclosure [Abstract]
Income tax reserves	$ 11,902	$ 16,254
Pension and other post retirement liabilities	16,052	15,815
Deferred tax liabilities	13,314	12,870
Other liabilities	6,749	2,212
Total	$ 48,017	$ 47,151

Supplementary Information - S_6

Supplementary Information - Schedule of Other (Income) Expense, Net (Detail) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Disclosure Supplementary Information Schedule Of Other Expense Income Net Detail [Abstract]
Interest income	$ (22,995)	$ (16,855)	$ (4,127)
Foreign exchange loss (gain)	2,214	(1,637)	4,405
Expense on repurchase of convertible senior notes	0	0	16,621
Other (income) expense, net	$ (20,781)	$ (18,492)	$ 16,899

Goodwill and Other Intangible_3

Goodwill and Other Intangible Assets - Changes in Carrying Amount of Goodwill Attributable to Software Reportable Segment (Detail) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023
Goodwill and Intangible Assets Disclosure [Abstract]
Beginning Balance	$ 458,125	$ 449,048
Acquisitions	13,027	2,948
Foreign currency translation and other	(8,693)	6,129
Ending Balance	$ 462,459	$ 458,125

Goodwill and Other Intangible_4

Goodwill and Other Intangible Assets - Schedule of Other Intangible Assets (Detail) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023
Summary Of Other Intangible Assets [Line Items]
Gross carrying amount	$ 231,922	$ 212,621
Accumulated amortization	158,985	129,071
Net carrying amount	72,937	83,550
Developed Technology [Member]
Summary Of Other Intangible Assets [Line Items]
Gross carrying amount	159,815	142,368
Accumulated amortization	112,494	90,729
Net carrying amount	$ 47,321	$ 51,639
Developed Technology [Member] | Minimum [Member]
Summary Of Other Intangible Assets [Line Items]
Weighted-average useful life of acquired finite-lived intangible assets	4 years	4 years
Developed Technology [Member] | Maximum [Member]
Summary Of Other Intangible Assets [Line Items]
Weighted-average useful life of acquired finite-lived intangible assets	6 years	6 years
Customer Relationships [Member]
Summary Of Other Intangible Assets [Line Items]
Gross carrying amount	$ 60,556	$ 58,316
Accumulated amortization	44,524	37,779
Net carrying amount	$ 16,032	$ 20,537
Customer Relationships [Member] | Minimum [Member]
Summary Of Other Intangible Assets [Line Items]
Weighted-average useful life of acquired finite-lived intangible assets	4 years	7 years
Customer Relationships [Member] | Maximum [Member]
Summary Of Other Intangible Assets [Line Items]
Weighted-average useful life of acquired finite-lived intangible assets	10 years	10 years
Trade names and other intangibles [Member]
Summary Of Other Intangible Assets [Line Items]
Gross carrying amount	$ 11,551	$ 11,937
Accumulated amortization	1,967	563
Net carrying amount	$ 9,584	$ 11,374
Trade names and other intangibles [Member] | Minimum [Member]
Summary Of Other Intangible Assets [Line Items]
Weighted-average useful life of acquired finite-lived intangible assets	3 years	4 years
Trade names and other intangibles [Member] | Maximum [Member]
Summary Of Other Intangible Assets [Line Items]
Weighted-average useful life of acquired finite-lived intangible assets	10 years	10 years

Goodwill and Other Intangible_5

Goodwill and Other Intangible Assets - Additional Information (Detail) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Goodwill and Intangible Assets Disclosure [Abstract]
Amortization of intangible assets	$ 33,022	$ 30,851	$ 27,510

Goodwill and Other Intangible_6

Goodwill and Other Intangible Assets - Summary of Estimated Amortization Expense (Detail) - USD ($) $ in Thousands	Dec. 31, 2024	Dec. 31, 2023
Goodwill and Intangible Assets Disclosure [Abstract]
December 31, 2025	$ 29,670
December 31, 2026	23,528
December 31, 2027	11,680
December 31, 2028	5,981
December 31, 2029	1,922
Thereafter	156
Net carrying amount	$ 72,937	$ 83,550

Debt - Additional Information (

Debt - Additional Information (Detail)	1 Months Ended			6 Months Ended	12 Months Ended
	Dec. 31, 2024 USD ($) Days $ / shares	Jun. 30, 2022 USD ($)	Jun. 30, 2019 USD ($) $ / shares shares	Jun. 30, 2024 USD ($) shares	Dec. 31, 2024 USD ($) Days $ / shares shares	Dec. 31, 2022 USD ($)	Dec. 31, 2023 USD ($)
Overdraft and Line of Credit [Member]
Debt Instrument [Line Items]
Loan outstanding	$ 0				$ 0		$ 0
Amount available under secured credit agreement	2,000,000				2,000,000		2,400,000
Convertible Senior Notes Due in 2024 [Member]
Debt Instrument [Line Items]
Debt instrument, aggregate principal amount	$ 0		$ 230,000,000		$ 0		81,729,000
Debt instrument interest rate	0.25%		0.25%		0.25%
Additional principal amount of notes to underwriters			$ 30,000,000
Net proceeds from issuance of costs			$ 221,900,000
Debt instrument frequency of periodic payment					semi-annually
Interest payment commencement date			Dec. 01, 2019
Debt instrument, description					The interest rate was fixed at 0.25% per year, payable semi-annually in arrears on June 1 and December 1 of each year, which commenced on December 1, 2019.
Debt conversion, converted instrument, shares issued | shares				796,817
Fair value of convertible notes				$ 70,800,000
Debt instrument, convertible, terms of conversion feature					The 2024 Notes had an initial conversion rate of 21.5049 shares of the Company's Class A common stock per $1,000 principal amount of 2024 Notes, which was equivalent to an initial conversion price of approximately $46.50 per share of its Class A common stock.
Debt instrument repurchased face amount						$ 148,200,000
Repayments of notes payable						192,400,000
Fair value expense recognized						$ 16,600,000
Debt instrument principal outstanding				$ 81,700,000
Convertible Senior Notes Due in 2024 [Member] | Class A Common Stock [Member]
Debt Instrument [Line Items]
Debt conversion, converted instrument, shares issued | shares			21.5049
Debt instrument conversion rate principal amount of notes			$ 1,000
Debt instrument convertible initial conversion price per share of common stock | $ / shares			$ 46.5
Convertible senior notes due in 2027 [Member]
Debt Instrument [Line Items]
Debt instrument, aggregate principal amount	$ 230,000,000	$ 230,000,000			$ 230,000,000		$ 230,000,000
Debt instrument interest rate	1.75%	1.75%			1.75%
Additional principal amount of notes to initial purchaser's		$ 30,000,000
Net proceeds from issuance of costs		$ 224,300,000
Debt instrument frequency of periodic payment					semiannually
Interest payment commencement date					Dec. 15, 2022
Debt instrument, description					The 2027 Notes mature on June 15, 2027, unless earlier repurchased, redeemed or converted. Prior to the consummation of the Merger, the Company may redeem for cash all or, subject to certain limitations, any portion of the 2027 Notes, at its option, on or after June 20, 2025 if the last reported sale price of Altair's Class A Common Stock has been at least 130% of the conversion price then in effect for at least 20 trading days (whether or not consecutive) during any 30 consecutive trading day period, at a redemption price equal to 100% of the principal amount of the notes to be redeemed, plus accrued and unpaid interest to, but excluding, the redemption date. Once the Merger is consummated, the Company will settle conversions solely in cash based upon the per share Merger Consideration payable under the Merger Agreement. The 2027 Notes bear interest at a rate of 1.750% per year, payable semiannually in arrears on June 15 and December 15 of each year, which commenced on December 15, 2022.
Fair value of convertible notes	$ 358,100,000				$ 358,100,000
Debt instrument conversion rate principal amount of notes	1,000				$ 1,000
Debt instrument, convertible, terms of conversion feature					The 2027 Notes have an initial conversion rate of 13.9505 shares of the Company's Class A common stock per $1,000 principal amount of 2027 Notes, which is equivalent to an initial conversion price of approximately $71.68 per share of Class A common stock.
Debt instrument, convertible, "if-converted value" in excess of the principal amount					$ 120,100,000
Convertible senior notes due in 2027 [Member] | Class A Common Stock [Member]
Debt Instrument [Line Items]
Debt conversion, converted instrument, shares issued | shares					13.9505
Debt instrument conversion rate principal amount of notes	$ 1,000				$ 1,000
Debt instrument convertible initial conversion price per share of common stock | $ / shares	$ 71.68				$ 71.68
Convertible senior notes due in 2027 [Member] | Class A Common Stock [Member] | Convertible Notes, Holders Conversion Rights, Circumstances 1 [Member]
Debt Instrument [Line Items]
Debt instrument conversion rate principal amount of notes	$ 1,000				$ 1,000
Debt instrument, convertible, business days | Days	5
Debt instrument, convertible, consecutive trading days | Days	30				30
Debt instrument, convertible, maximum threshold percentage of sale price of common stock during measurement period	98%
Debt Instrument, Redemption Price, Percentage					100%
Convertible senior notes due in 2027 [Member] | Class A Common Stock [Member] | Convertible Notes, Holders Conversion Rights, Circumstances 1 [Member] | Minimum [Member]
Debt Instrument [Line Items]
Debt instrument, convertible, trading days | Days	20				20
Debt instrument, convertible, threshold percentage of conversion price	130%				130%
Convertible senior notes due in 2027 [Member] | Class A Common Stock [Member] | Convertible Notes, Holders Conversion Rights, Circumstances 2 [Member]
Debt Instrument [Line Items]
Debt instrument, convertible, consecutive trading days | Days	5
Twenty Nineteen Credit Agreement
Debt Instrument [Line Items]
Maturity date					Dec. 31, 2025
Credit facility	$ 200,000,000				$ 200,000,000
Increase in unrestricted domestic cash					$ 20,000,000
Twenty Nineteen Credit Agreement | Federal Funds Effective Swap Rate [Member]
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate						0.50%
Twenty Nineteen Credit Agreement | Secured Overnight Financing Rate (SOFR) Overnight Index Swap Rate [Member]
Debt Instrument [Line Items]
Debt instrument, basis spread on variable rate					1%
Twenty Nineteen Credit Agreement | Minimum [Member]
Debt Instrument [Line Items]
Commitment fees on unused portion of the Revolving Credit Facility					0.15%
Twenty Nineteen Credit Agreement | Minimum [Member] | Term Benchmark Loans [Member]
Debt Instrument [Line Items]
Applicable margin for borrowings under new credit facility	1.25%				1.25%
Twenty Nineteen Credit Agreement | Minimum [Member] | Swingline Loans [Member]
Debt Instrument [Line Items]
Applicable margin for borrowings under new credit facility	0.25%				0.25%
Twenty Nineteen Credit Agreement | Minimum [Member] | ABR Loans [Member]
Debt Instrument [Line Items]
Applicable margin for borrowings under new credit facility	0.25%				0.25%
Twenty Nineteen Credit Agreement | Maximum [Member]
Debt Instrument [Line Items]
Commitment fees on unused portion of the Revolving Credit Facility					0.30%
Senior secured leverage ratio					3%
Twenty Nineteen Credit Agreement | Maximum [Member] | Term Benchmark Loans [Member]
Debt Instrument [Line Items]
Applicable margin for borrowings under new credit facility	2%				2%
Twenty Nineteen Credit Agreement | Maximum [Member] | Swingline Loans [Member]
Debt Instrument [Line Items]
Applicable margin for borrowings under new credit facility	1%				1%
Twenty Nineteen Credit Agreement | Maximum [Member] | ABR Loans [Member]
Debt Instrument [Line Items]
Applicable margin for borrowings under new credit facility	1%				1%
Secured Credit Agreement [Member]
Debt Instrument [Line Items]
Loan outstanding	$ 0				$ 0

Debt - Schedule of Net Carrying

Debt - Schedule of Net Carrying Value of the 2027 and 2024 Notes (Detail) - USD ($) $ in Thousands	Dec. 31, 2024	Dec. 31, 2023	Jun. 30, 2022	Jun. 30, 2019
Debt Instrument [Line Items]
Net carrying amount, current	$ 227,106	$ 81,455
Net carrying amount	0	225,929
Convertible Senior Notes Due in 2027 [Member]
Debt Instrument [Line Items]
Principal	230,000	230,000	$ 230,000
Less: unamortized debt issuance costs	2,894	4,071
Net carrying amount, current	227,106
Net carrying amount		225,929
Convertible Senior Notes Due in 2024 [Member]
Debt Instrument [Line Items]
Principal	0	81,729		$ 230,000
Less: unamortized debt issuance costs	0	274
Net carrying amount, current	$ 0	$ 81,455

Debt - Schedule of Interest Exp

Debt - Schedule of Interest Expense Related to 2027 and 2024 Notes (Detail) - Convertible Senior Notes Due in 2024 and 2027 [Member] - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Debt Instrument [Line Items]
Contractual interest expense	$ 4,110	$ 4,230	$ 2,452
Amortization of debt issuance cost and discount	1,452	1,806	1,745
Total	$ 5,562	$ 6,036	$ 4,197

Leases - Additional Information

Leases - Additional Information (Detail) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Lessee Lease Description [Line Items]
Operating lease cost	$ 14	$ 13.1	$ 13.4
Rent cost for operating leases	$ 11.7	$ 11.3	$ 11.7
Minimum [Member]
Lessee Lease Description [Line Items]
Leases, remaining lease term	1 year
Maximum [Member]
Lessee Lease Description [Line Items]
Leases, remaining lease term	15 years
Leases, options to terminate leases	3 years

Leases - Schedule of Other Info

Leases - Schedule of Other Information Related To Operating Leases (Detail)	Dec. 31, 2024	Dec. 31, 2023
Operating Leases [Abstract]
Weighted average remaining lease term of operating leases	5 years 8 months 12 days	6 years
Weighted average discount rate of operating leases	4.60%	3.90%

Leases - Schedule of Supplement

Leases - Schedule of Supplemental Cash Flow Information Related to Leases (Detail) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Cash paid for amounts included in the measurement of lease liabilities:
Operating cash flows from operating leases	$ (10,641)	$ (11,606)	$ (12,949)
ROU assets obtained in exchange for new operating lease obligations	$ 9,150	$ 17,023	$ 12,455

Leases - Schedule of Maturities

Leases - Schedule of Maturities of Operating Lease Liabilities (Detail) $ in Thousands	Dec. 31, 2024 USD ($)
Leases [Abstract]
2025	$ 9,550
2026	8,614
2027	6,277
2028	3,438
2029	2,669
Thereafter	7,492
Total future lease payments	38,040
Less: present value adjustment	6,023
Total operating lease liabilities	$ 32,017

Fair Value Measurements - Addit

Fair Value Measurements - Additional Information (Detail) $ in Millions	Dec. 31, 2024 USD ($)
Convertible Senior Notes Due in 2027 [Member]
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Fair value of convertible notes	$ 358.1

Stockholders' Equity - Addition

Stockholders' Equity - Additional Information (Detail) $ / shares in Units, $ in Millions	12 Months Ended
	Dec. 31, 2024 USD ($) Vote $ / shares shares	Dec. 31, 2023 USD ($) $ / shares shares	Dec. 31, 2022 $ / shares
Class of Stock [Line Items]
Preferred stock, shares authorized	45,000,000	45,000,000
Preferred stock, par value | $ / shares	$ 0.0001	$ 0.0001
Preferred stock, shares issued	0	0
Preferred stock, shares outstanding	0	0
Common stock dividends | $ / shares	$ 0	$ 0	$ 0
Class A Common Stock [Member]
Class of Stock [Line Items]
Class A common stock, shares authorized	513,796,572
Common stock, par value | $ / shares	$ 0.0001	$ 0.0001
Number of votes entitled per share | Vote	1
Number of shares repurchased	0	91,273
Stock repurchase program, Average price per share | $ / shares		$ 46.63
Stock repurchase program, Repurchase amount | $		$ 4.3
Class A Common Stock [Member] | Maximum [Member]
Class of Stock [Line Items]
Shares authorized to be repurchased amount | $	$ 75
Class B Common Stock [Member]
Class of Stock [Line Items]
Class B common stock, shares authorized	41,203,428
Common stock, par value | $ / shares	$ 0.0001	$ 0.0001
Number of votes entitled per share | Vote	10

Stock-based Compensation - Addi

Stock-based Compensation - Additional Information (Detail)		1 Months Ended				12 Months Ended
	Apr. 15, 2025 shares	Apr. 30, 2026 shares	Apr. 30, 2024 USD ($) shares	Jun. 30, 2022 USD ($) shares	Mar. 31, 2022 USD ($) shares	Dec. 31, 2024 USD ($) Installment $ / shares shares	Dec. 31, 2023 USD ($) $ / shares shares	Dec. 31, 2022 USD ($) shares	Dec. 31, 2021 USD ($)	Sep. 27, 2017 shares	Dec. 31, 2012 shares
World Programming [Member] | Stock Purchase Agreement [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Stock-based compensation expense						$ 3,100,000	$ 8,000,000	$ 17,600,000
Powersim Inc [Member] | Stock Purchase Agreement [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Stock-based compensation expense						200,000	1,400,000	2,700,000
Concept Engineering [Member] | Stock Purchase Agreement [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Stock-based compensation expense						$ 600,000	2,600,000	2,700,000
Research in Flight [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Weighted average remaining service period						1 year 3 months 18 days
Research in Flight [Member] | Stock Purchase Agreement [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Stock-based compensation expense						$ 800,000
Restricted Stock Units (RSUs) [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Weighted average remaining service period						4 years
2021 Employee Stock Purchase Plan [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Initial offering period beginning date						Jul. 15, 2024
Offering period expiration date						Jan. 14, 2025
Amount of eligible compensation for employee payroll deductions						$ 25,000
Monthly participant contributions limited to prevent prejudicial advantages to higher compensated employees						$ 1,000
Percentage of purchase price for each share of common stock purchased of lower of fair market value per share on first day of applicable offering period						85%
Stock-based compensation expense						$ 2,900,000	$ 2,400,000	$ 2,600,000
2021 Employee Stock Purchase Plan [Member] | Common Stock [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Issuance of common stock for employee stock purchase program (in shares) | shares						125,686	182,883	184,897
2021 Employee Stock Purchase Plan [Member] | The Timing of Payroll Deductions [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Amount withheld on behalf of employees for a future purchase						$ 4,800,000	$ 4,200,000
2021 Employee Stock Purchase Plan [Member] | Maximum [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Percentage of eligible compensation for employee payroll deductions						15%
2021 Employee Stock Purchase Plan [Member] | Maximum [Member] | Common Stock [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Common stock reserved for issuance | shares						2,706,534
Class A Common Stock [Member] | Common Stock [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Issuance of common stock for employee stock purchase program (in shares) | shares						125,000	183,000	185,000
Class A Common Stock [Member] | World Programming [Member] | Stock Purchase Agreement [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Business acquisition, shares issued fair value									$ 29,500,000
Class A Common Stock [Member] | Powersim Inc [Member] | Stock Purchase Agreement [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Business acquisition, shares issued | shares					68,792
Business acquisition, shares issued fair value					$ 4,300,000
Class A Common Stock [Member] | Concept Engineering [Member] | Stock Purchase Agreement [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Business acquisition, shares issued | shares				105,082
Business acquisition, shares issued fair value				$ 6,000,000
Class A Common Stock [Member] | Research in Flight [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Business acquisition, shares issued | shares			18,000
Business acquisition, shares issued fair value			$ 1,500,000
Class A Common Stock [Member] | Research in Flight [Member] | Forecast [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Business acquisition, shares issued | shares	9,000	9,000
Class A Common Stock [Member] | Employee [Member] | Concept Engineering [Member] | Stock Purchase Agreement [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Business acquisition, shares issued | shares				52,541
NSO Plan [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of options, outstanding | shares						623,539	994,884
Exercise price stock options outstanding | $ / shares						$ 0.000025	$ 0.000025
Contractual term						35 years
Intrinsic value of options exercised						$ 33,800,000	$ 11,500,000	$ 11,000,000
2012 Plan [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of options, outstanding | shares							271,359
Exercise price stock options outstanding | $ / shares							$ 4.46
Contractual term						10 years
Intrinsic value of options exercised						$ 10,100,000	$ 6,600,000	8,500,000
Weighted average remaining service period						4 years
2012 Plan [Member] | Class A Common Stock [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares authorized | shares											5,200,000
2017 Plan [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of options, outstanding | shares						6,569,451	7,602,078
Exercise price stock options outstanding | $ / shares						$ 55.01	$ 52.81
Intrinsic value of options exercised						$ 58,600,000	$ 20,700,000	$ 1,100,000
2017 Plan [Member] | Common Stock [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Common stock reserved for issuance | shares						6,625,144
2017 Plan [Member] | Restricted Stock Units (RSUs) [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Weighted average grant date fair value of RSUs | $ / shares						$ 80.6
Number of vesting equal annual installments | Installment						4
Compensation cost related to nonvested awards not yet recognized						$ 98,900,000
Weighted average period of recognition						2 years 2 months 12 days
Fair value of RSUs vested						$ 47,200,000
2017 Plan [Member] | Class A Common Stock [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Common stock reserved for issuance | shares										19,460,908

Stock-based Compensation - Summ

Stock-based Compensation - Summary of Stock Option Activity under NSO Plan (Detail) - NSO Plan [Member] - USD ($) $ / shares in Units, $ in Millions	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding [Roll Forward]
Number of options, Outstanding, Beginning Balance	994,884
Number of options, Exercised	(371,345)
Number of options, Outstanding and exercisable, Ending Balance	623,539
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Weighted Average Exercise Price [Abstract]
Weighted average exercise price per share, Outstanding, Beginning Balance	$ 0.000025
Weighted average exercise price per share, Exercised	0.000025
Weighted average exercise price per share, Outstanding and exercisable, Ending Balance	$ 0.000025
Share-based Compensation Arrangement by Share-based Payment Award, Options, Additional Disclosures [Abstract]
Weighted average remaining contractual term (years), Outstanding		13 years
Weighted average remaining contractual term (years), Outstanding and exercisable	12 years
Aggregate intrinsic value, Outstanding and exercisable	$ 68

Stock-based Compensation - Su_2

Stock-based Compensation - Summary of Stock Option Activity under 2012 Plan (Detail) - 2012 Plan [Member] - USD ($) $ / shares in Units, $ in Millions	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding [Roll Forward]
Number of options, Outstanding, Beginning Balance	271,359
Number of options, Exercised	(111,992)
Number of options, Outstanding and exercisable, Ending Balance	159,367
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Weighted Average Exercise Price [Abstract]
Weighted average exercise price per share, Outstanding, Beginning Balance	$ 4.46
Weighted average exercise price per share, Exercised	4.24
Weighted average exercise price per share, Outstanding and exercisable, Ending Balance	$ 4.62
Share-based Compensation Arrangement by Share-based Payment Award, Options, Additional Disclosures [Abstract]
Weighted average remaining contractual term (years), Outstanding		2 years 6 months
Weighted average remaining contractual term (years), Outstanding and exercisable	1 year 10 months 24 days
Aggregate intrinsic value, Outstanding and exercisable	$ 16.7

Stock-based Compensation - Su_3

Stock-based Compensation - Summary of Restricted Stock Units Awarded (Detail) - 2017 Plan [Member] - Restricted Stock Units (RSUs) [Member]	12 Months Ended
	Dec. 31, 2024 shares
Share-based Compensation Arrangement by Share-based Payment Award, Equity Instruments Other than Options, Nonvested, Number of Shares [Roll Forward]
Number of RSUs, Outstanding Beginning Balance	1,086,351
Number of RSUs, Granted	384,424
Number of RSUs, Vested	(530,732)
Number of RSUs, Forfeited	(33,191)
Number of RSUs, Outstanding Ending Balance	906,852

Stock-based Compensation - Su_4

Stock-based Compensation - Summary of Stock Option Activity under 2017 Plan (Detail) - 2017 Plan [Member] - USD ($) $ / shares in Units, $ in Millions	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding [Roll Forward]
Number of options, Outstanding, Beginning Balance	7,602,078
Number of options, Granted	417,459
Number of options, Exercised	(1,325,265)
Number of options, Forfeited	(124,821)
Number of options, Outstanding, Ending Balance	6,569,451	7,602,078
Number of options, Exercisable	3,940,042
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Weighted Average Exercise Price [Abstract]
Weighted average exercise price per share, Outstanding, Beginning Balance	$ 52.81
Weighted average exercise price per share, Granted	79.19
Weighted average exercise price per share, Exercised	49.91
Weighted average exercise price per share, Forfeited	55.94
Weighted average exercise price per share, Outstanding, Ending Balance	55.01	$ 52.81
Weighted average exercise price per share, Exercisable	$ 51.61
Share-based Compensation Arrangement by Share-based Payment Award, Options, Additional Disclosures [Abstract]
Weighted average remaining contractual term (years), Outstanding	7 years 1 month 6 days	7 years 9 months 18 days
Weighted average remaining contractual term (years), Exercisable	6 years 6 months
Aggregate intrinsic value, Outstanding	$ 355.4
Aggregate intrinsic value, Exercisable	$ 226.5

Stock-based Compensation - Su_5

Stock-based Compensation - Summary of Fair value of Company's Stock Options Granted (Detail) - $ / shares	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Expected volatility	35%	35%	35%
Expected term (in years)	6 years 3 months	6 years 3 months	6 years 3 months
Risk-free interest rate, minimum	4.20%	3.50%	1.70%
Risk-free interest rate, maximum	4.30%	4.30%	4.20%
Expected dividend yield	0%	0%	0%
Minimum [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Weighted average grant date fair value per share	$ 79.03	$ 65.19	$ 44.63
Maximum [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Weighted average grant date fair value per share	$ 85.52	$ 67.65	$ 64.79

Stock-based Compensation - Su_6

Stock-based Compensation - Summary of Stock-Based Compensation Expense (Detail) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Employee Service Share Based Compensation Allocation Of Recognized Period Costs [Line Items]
Total stock-based compensation expense	$ 67,680	$ 85,581	$ 84,787
Cost of revenue - software [Member]
Employee Service Share Based Compensation Allocation Of Recognized Period Costs [Line Items]
Total stock-based compensation expense	8,397	10,095	8,351
Research and Development [Member]
Employee Service Share Based Compensation Allocation Of Recognized Period Costs [Line Items]
Total stock-based compensation expense	25,630	33,842	36,250
Sales and Marketing [Member]
Employee Service Share Based Compensation Allocation Of Recognized Period Costs [Line Items]
Total stock-based compensation expense	19,459	28,376	30,370
General and administrative [Member]
Employee Service Share Based Compensation Allocation Of Recognized Period Costs [Line Items]
Total stock-based compensation expense	$ 14,194	$ 13,268	$ 9,816

Income Taxes - Components of In

Income Taxes - Components of Income (Loss) Before Income Taxes (Detail) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Income Tax Disclosure [Abstract]
U.S	$ (8,279)	$ (21,803)	$ (62,702)
Non-U.S	40,909	34,422	34,489
Income (loss) before income taxes	$ 32,630	$ 12,619	$ (28,213)

Income Taxes - Significant Comp

Income Taxes - Significant Components of Income Tax Expense (Detail) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Current
U.S. Federal	$ 0	$ 0	$ 0
Non-U.S.	19,168	22,746	18,759
U.S. State and Local	(6)	1,118	621
Total current	19,162	23,864	19,380
Deferred
U.S. Federal	36	35	23
Non-U.S.	(773)	(2,384)	(4,206)
U.S. State and Local	30	30	19
Total deferred	(707)	(2,319)	(4,164)
Income tax expense	$ 18,455	$ 21,545	$ 15,216

Income Taxes - Reconciliation o

Income Taxes - Reconciliation of Income Taxes Calculated at U.S. Federal Statutory Income Tax Rate (Detail) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Income Tax Disclosure [Abstract]
U.S. federal statutory rate	21%	21%	21%
Income taxes at U.S. federal statutory rate	$ 6,852	$ 2,650	$ (5,925)
Foreign income taxes at rates other than the federal statutory rate	2,626	1,733	2,249
U.S. state and local income taxes, net of U.S. federal tax benefit	(3,054)	(1,952)	(5,976)
U.S. effect of foreign operations	2,315	(9,931)	15,827
Change in valuation allowance	25,493	29,849	7,830
Foreign withholding taxes	8,501	7,444	6,738
U.S. foreign tax credit and deduction	(8,261)	(17,522)	(12,315)
Research and development tax credit	597	391	(326)
Stock-based compensation	(7,695)	1,361	8,649
Other	920	123	1,250
Uncertain tax positions	(693)	6,370	472
FDII deduction	(9,146)	(169)	(5,245)
Mark-to-market adjustment of contingent consideration	0	1,198	(1,502)
Repurchase of convertible senior notes	0	0	3,490
Income tax expense	$ 18,455	$ 21,545	$ 15,216

Income Taxes - Additional Infor

Income Taxes - Additional Information (Detail) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Income Tax Disclosure [Line Items]
Gross unrecognized tax benefits recognized would affect the effective tax rate	$ 11,600
Reduction in unrecognized tax benefits which if recognized would not impact effective tax rate in next 12 months	12,800
Accrued interest and penalties related to unrecognized tax benefits	600	$ 1,200	$ 1,000
Valuation Allowance of Deferred Tax Assets [Member]
Income Tax Disclosure [Line Items]
Valuation allowance in other	(305)	476	21,630
Issuance of Convertible Debt [Member]
Income Tax Disclosure [Line Items]
Valuation allowance in other			6,800
Currency Translation [Member]
Income Tax Disclosure [Line Items]
Valuation allowance in other	$ (300)	$ 500
Rapid Miner [Member]
Income Tax Disclosure [Line Items]
Valuation allowance in other			13,100
Rapid Miner [Member] | Valuation Allowance of Deferred Tax Assets [Member]
Income Tax Disclosure [Line Items]
Valuation allowance in other			$ 21,600

Income Taxes - Schedule of Defe

Income Taxes - Schedule of Deferred Tax Assets and Liabilities (Detail) - USD ($) $ in Thousands	Dec. 31, 2024	Dec. 31, 2023
Deferred tax assets:
Deferred revenue	$ 6,419	$ 9,730
Net operating loss carryforwards	57,933	60,702
Tax credit carryforwards	39,987	48,752
Stock-based compensation	13,491	12,011
Capitalized research and development	87,261	58,946
Lease obligation	6,330	7,517
Employee benefits	7,994	6,955
Merger costs	4,288	0
Other	3,704	3,910
Total gross deferred tax assets	227,407	208,523
Less: valuation allowances	(204,954)	(179,766)
Net deferred tax assets	22,453	28,757
Deferred tax liabilities:
Prepaid royalties	1,609	3,602
Property and equipment and intangibles	13,174	16,610
Deferred tax on investment in subsidiary	3,220	1,950
Lease right of use asset	6,193	7,357
Other	2,801	2,153
Total deferred tax liabilities	26,997	31,672
Total net deferred tax liabilities	$ (4,544)	$ (2,915)

Income Taxes - Summary of Chang

Income Taxes - Summary of Changes to Valuation Allowance Balance (Detail) - Valuation Allowance of Deferred Tax Assets [Member] - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Valuation Allowance [Line Items]
Balance at beginning of year	$ 179,766	$ 149,441	$ 119,981
Additions charged to expense	27,481	30,665	7,830
Deductions	(1,988)	(816)	0
Other	(305)	476	21,630
Balance at end of year	$ 204,954	$ 179,766	$ 149,441

Income Taxes - Operating Loss a

Income Taxes - Operating Loss and Tax Credit Carryforwards (Detail) $ in Thousands	12 Months Ended
	Dec. 31, 2024 USD ($)
Operating Loss and Tax Credit Carryforward [Line Items]
U.S. foreign tax credits, expiration year	2027 - 2033
U.S. foreign tax credits	$ 21,901
Total operating loss and tax credit carryforwards	$ 97,920
Foreign Tax Authority [Member]
Operating Loss and Tax Credit Carryforward [Line Items]
Foreign general business credits and loss carryforwards, expiration year	2025-Indefinite
Credits and loss carryforwards	$ 13,029
General Business Tax Credit Carryforward [Member]
Operating Loss and Tax Credit Carryforward [Line Items]
U.S. general business credits and loss carryforwards, expiration year	2025-Indefinite
Credits and loss carryforwards	$ 62,990

Income Taxes - Reconciliation_2

Income Taxes - Reconciliation of Beginning and Ending Amounts of Unrecognized Tax Benefits (Detail) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Income Tax Disclosure [Abstract]
Unrecognized tax benefits-January 1	$ 38,219	$ 28,977	$ 16,376
Additions (reductions) for tax positions of current period	50	9,435	50
Additions for tax positions of prior periods	0	901	13,910
Reductions for tax positions of prior periods	(4,891)	(500)	(1,334)
Reductions due to statute of limitations	(427)	(594)	(25)
Unrecognized tax benefits—December 31	$ 32,951	$ 38,219	$ 28,977

Net Income (Loss) Per Share - C

Net Income (Loss) Per Share - Computation of Numerators and Denominators Used in Basic and Diluted Net Income (Loss) Per Share Amounts (Detail) - USD ($) $ / shares in Units, shares in Thousands, $ in Thousands		12 Months Ended
		Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Numerator:
Net Income (Loss)		$ 14,175	$ (8,926)	$ (43,429)
Interest expense related to convertible notes, net of tax	[1]	0	0	0
Numerator for diluted income (loss) per share		$ 14,175	$ (8,926)	$ (43,429)
Denominator:
Weighted average shares outstanding, basic		84,085	80,596	79,472
Effect of dilutive shares		4,473	0	0
Weighted average shares outstanding, diluted		88,558	80,596	79,472
Income (loss) per share, basic		$ 0.17	$ (0.11)	$ (0.55)
Income (loss) per share, diluted		$ 0.16	$ (0.11)	$ (0.55)
[1] Interest expense related to the convertible notes has been excluded from the numerator for diluted earnings per share because its effect would have been anti-dilutive.

Net Income (Loss) Per Share - S

Net Income (Loss) Per Share - Schedule of Anti-dilutive Shares Excluded from Computation of Diluted Net Income (Loss) Per Share (Detail) - shares shares in Thousands	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Antidilutive Securities Excluded From Computation Of Earnings Per Share [Line Items]
Total shares excluded from calculation	3,209	7,046	5,919
Convertible Shares [Member]
Antidilutive Securities Excluded From Computation Of Earnings Per Share [Line Items]
Total shares excluded from calculation	3,209	3,753	4,958
Stock Options and ESPP [Member]
Antidilutive Securities Excluded From Computation Of Earnings Per Share [Line Items]
Total shares excluded from calculation	0	3,293	961

Retirement Benefits - Additiona

Retirement Benefits - Additional Information (Detail) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Retirement Benefits [Abstract]
Funded percentage	80%
Defined Benefit Plan, Contributions by Employer	$ 1,500	$ 1,600	$ 1,600
Net benefit cost	2,500	2,600	2,500
Benefit obligation benefits paid	600	400	$ 700
Accumulated benefit obligation	12,800	11,600
Defined benefit plan, benefit obligation	$ 17,280	$ 16,850

Retirement Benefits - Schedule

Retirement Benefits - Schedule of Pension Benefits Obligation (Detail) - USD ($) $ in Thousands	Dec. 31, 2024	Dec. 31, 2023
Defined Benefit Pension Plan [Abstract]
Other long-term assets	$ 19	$ 135
Accrued compensation and benefits	1,247	1,170
Other long-term liabilities	16,052	15,815
Components of pension benefits	$ 17,280	$ 16,850

Retirement Benefits - Schedul_2

Retirement Benefits - Schedule of Estimated Future Benefit Payments (Detail) $ in Thousands	Dec. 31, 2024 USD ($)
Defined Benefit Plan, Expected Future Benefit Payment [Abstract]
December 31, 2025	$ 1,319
December 31, 2026	1,572
December 31, 2027	1,372
December 31, 2028	1,260
December 31, 2029	1,114
Next five years	$ 7,627

Accumulated Other Comprehensi_3

Accumulated Other Comprehensive Loss - Components of Accumulated Other Comprehensive Loss (Detail) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	$ 711,331	$ 569,736	$ 613,197
Total other comprehensive (loss) income	(14,972)	7,693	(21,052)
Ending balance	857,189	711,331	569,736
Foreign Currency Translation [Member]
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	(21,473)	(30,484)	(6,400)
Other comprehensive (loss) income before reclassification	(15,490)	9,011	(24,084)
Amounts reclassified from accumulated other comprehensive loss	0	0	0
Tax effects	0	0	0
Total other comprehensive (loss) income	(15,490)	9,011	(24,084)
Ending balance	(36,963)	(21,473)	(30,484)
Retirement Related Benefit Plans [Member]
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	(836)	482	(2,550)
Other comprehensive (loss) income before reclassification	(8)	(16)	87
Amounts reclassified from accumulated other comprehensive loss	777	(1,479)	3,253
Tax effects	(251)	177	(308)
Total other comprehensive (loss) income	518	(1,318)	3,032
Ending balance	(318)	(836)	482
Accumulated Other Comprehensive Loss [Member]
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	(22,309)	(30,002)	(8,950)
Other comprehensive (loss) income before reclassification	(15,498)	8,995	(23,997)
Amounts reclassified from accumulated other comprehensive loss	777	(1,479)	3,253
Tax effects	(251)	177	(308)
Total other comprehensive (loss) income	(14,972)	7,693	(21,052)
Ending balance	$ (37,281)	$ (22,309)	$ (30,002)

Commitments and Contingencies -

Commitments and Contingencies - Additional Information (Detail) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Software and Other [Member]
Loss Contingencies [Line Items]
Royalty fees	$ 12.8	$ 12.2	$ 11.7
Software license [Member]
Loss Contingencies [Line Items]
Contingent payment obligations	7.1
Maximum [Member] | Professional fees [Member]
Loss Contingencies [Line Items]
Contingent payment obligations	$ 135.2

Commitments and Contingencies_2

Commitments and Contingencies - Future Purchase Obligations (Details) $ in Thousands	Dec. 31, 2024 USD ($)
Commitments and Contingencies Disclosure [Abstract]
2025	$ 22,085
2026	14,991
2027	2,708
2028	901
2029	364
Thereafter	0
Total	$ 41,049

Segment Information - Additiona

Segment Information - Additional Information (Detail)	12 Months Ended
	Dec. 31, 2024 Segment
Segment Reporting [Abstract]
Segment Reporting, CODM, Individual Title and Position or Group Name [Extensible Enumeration]	srt:ChiefExecutiveOfficerMember
Segment Reporting, CODM, Profit (Loss) Measure, How Used, Description	The primary measure of segment operating performance is Adjusted EBITDA, which is defined as net income (loss) adjusted for income tax expense (benefit), interest expense, interest income and other, depreciation and amortization, stock-based compensation expense, asset impairment charges and other special items as determined by management. Adjusted EBITDA includes an allocation of corporate headquarters costs.
Number of reportable segments	2

Segment Information - Schedule

Segment Information - Schedule of Segment Reporting Information (Detail) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Segment Reporting Information [Line Items]
Revenue	$ 665,788	$ 612,701	$ 572,221
Total cost of revenue	124,803	121,791	122,889
Research and development	221,161	212,645	202,542
Sales and marketing	184,280	176,138	163,884
General and administrative	90,150	70,887	72,288
Adjusted EBITDA	149,912	129,138	108,600
Adjusted EBITDA from revenue [Member]
Segment Reporting Information [Line Items]
Total cost of revenue	114,629	111,404	114,154
Research and development	188,895	174,201	161,966
Sales and marketing	160,811	145,201	131,078
General and administrative	56,987	56,801	61,624
Other segment items	(5,446)	(4,044)	(5,201)
Software [Member]
Segment Reporting Information [Line Items]
Revenue	637,267	578,006	537,169
Adjusted EBITDA	150,754	129,164	107,638
Software [Member] | Adjusted EBITDA from revenue [Member]
Segment Reporting Information [Line Items]
Total cost of revenue	90,674	82,625	85,589
Research and development	187,826	172,954	161,106
Sales and marketing	158,670	143,406	129,740
General and administrative	54,681	53,966	58,374
Other segment items	(5,338)	(4,109)	(5,278)
CES [Member]
Segment Reporting Information [Line Items]
Revenue	25,027	29,497	28,883
Adjusted EBITDA	984	2,288	2,576
CES [Member] | Adjusted EBITDA from revenue [Member]
Segment Reporting Information [Line Items]
Total cost of revenue	21,315	24,450	23,577
Research and development	0	0	0
Sales and marketing	1,006	761	592
General and administrative	1,722	1,998	2,139
Other segment items	0	0	(1)
All Other [Member]
Segment Reporting Information [Line Items]
Revenue	3,494	5,198	6,169
Adjusted EBITDA	(1,826)	(2,314)	(1,614)
All Other [Member] | Adjusted EBITDA from revenue [Member]
Segment Reporting Information [Line Items]
Total cost of revenue	2,640	4,329	4,988
Research and development	1,069	1,247	860
Sales and marketing	1,135	1,034	746
General and administrative	584	837	1,111
Other segment items	$ (108)	$ 65	$ 78

Segment Information - Reconcili

Segment Information - Reconciliation of U.S. GAAP Income (Loss) Before Income Taxes to Adjusted EBITDA (Detail) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Segment Reporting [Abstract]
Adjusted EBITDA		$ 149,912	$ 129,138	$ 108,600
Stock-based compensation expense		(67,680)	(85,581)	(84,787)
Interest expense		(5,836)	(6,116)	(4,377)
Depreciation and amortization		(42,164)	(39,124)	(35,504)
Special adjustments, interest income and other	[1]	(1,602)	14,302	(12,145)
Income (loss) before income taxes		$ 32,630	$ 12,619	$ (28,213)
[1] The year ended December 31, 2024, includes $ 22.3 million of expenses related to the pending merger with Siemens Industry, $ 1.9 million currency losses on acquisition-related intercompany loans, $ 0.5 million losses from the mark-to-market adjustment of contingent consideration associated with acquisitions and $ 23.0 million of interest income. The year ended December 31, 2023, includes $ 3.2 million currency gains on acquisition-related intercompany loans, $ 5.7 million losses from the mark-to-market adjustment of contingent consideration associated with the World Programming acquisition and $ 16.9 million of interest income. The year ended December 31, 2022, includes $ 16.6 million expense on repurchase of convertible senior notes, $ 6.8 million currency losses on acquisition-related intercompany loans, $ 7.2 million gains from the mark-to-market adjustment of contingent consideration associated with the World Programming acquisition and $ 4.1 million of interest income.

Segment Information - Reconci_2

Segment Information - Reconciliation of U.S. GAAP Income (Loss) Before Income Taxes to Adjusted EBITDA (Parenthetical) (Detail) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Segment Reporting Information [Line Items]
Currency losses on acquisition-related intercompany loans	$ 1,900		$ 6,800
Loss (gain) on mark-to-market adjustment of contingent consideration	476	$ 5,706	(7,153)
Interest income	23,000	16,900	4,100
Currency gains on acquisition-related intercompany loans		3,200
World Programming [Member]
Segment Reporting Information [Line Items]
Loss (gain) on mark-to-market adjustment of contingent consideration		$ 5,700	(7,200)
Siemens Industry Software Inc. [Member]
Segment Reporting Information [Line Items]
Merger related costs	$ 22,300
Convertible Senior Notes Due in 2024 [Member]
Segment Reporting Information [Line Items]
Fair value expense recognized			$ 16,600

Segment Information - Summary o

Segment Information - Summary of Sales to External Customers and Long-Lived Assets by Geographical Areas (Detail) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Revenues from External Customers and Long-Lived Assets [Line Items]
Revenue from Contract with Customer, Excluding Assessed Tax	$ 665,788	$ 612,701	$ 572,221
Long Lived Assets	113,945	123,353
United States [Member]
Revenues from External Customers and Long-Lived Assets [Line Items]
Revenue from Contract with Customer, Excluding Assessed Tax	323,905	301,857	274,635
Long Lived Assets	52,565	55,230
Other American Countries [Member]
Revenues from External Customers and Long-Lived Assets [Line Items]
Revenue from Contract with Customer, Excluding Assessed Tax	18,987	17,792	13,425
Long Lived Assets	15,385	6,193
Americas [Member]
Revenues from External Customers and Long-Lived Assets [Line Items]
Revenue from Contract with Customer, Excluding Assessed Tax	342,892	319,649	288,060
Long Lived Assets	67,950	61,423
Germany [Member]
Revenues from External Customers and Long-Lived Assets [Line Items]
Revenue from Contract with Customer, Excluding Assessed Tax	46,927	46,593	51,495
Long Lived Assets	12,686	19,840
France [Member]
Revenues from External Customers and Long-Lived Assets [Line Items]
Revenue from Contract with Customer, Excluding Assessed Tax	24,283	23,122	19,442
Long Lived Assets	1,109	1,200
Other Europe, Middle East and Africa Countries [Member]
Revenues from External Customers and Long-Lived Assets [Line Items]
Revenue from Contract with Customer, Excluding Assessed Tax	76,459	66,903	69,769
Long Lived Assets	24,485	34,561
Europe Middle East And Africa [Member]
Revenues from External Customers and Long-Lived Assets [Line Items]
Revenue from Contract with Customer, Excluding Assessed Tax	147,669	136,618	140,706
Long Lived Assets	38,280	55,601
Japan [Member]
Revenues from External Customers and Long-Lived Assets [Line Items]
Revenue from Contract with Customer, Excluding Assessed Tax	42,451	39,508	40,335
Long Lived Assets	1,052	685
Other Asia Pacific Countries [Member]
Revenues from External Customers and Long-Lived Assets [Line Items]
Revenue from Contract with Customer, Excluding Assessed Tax	132,776	116,926	103,120
Long Lived Assets	6,663	5,644
Asia Pacific [Member]
Revenues from External Customers and Long-Lived Assets [Line Items]
Revenue from Contract with Customer, Excluding Assessed Tax	175,227	156,434	$ 143,455
Long Lived Assets	$ 7,715	$ 6,329