Stock-Based Compensation - Additional Information (Detail) - USD ($) | | | 1 Months Ended | 3 Months Ended | 9 Months Ended | 12 Months Ended |
Jan. 01, 2022 | Feb. 28, 2021 | Feb. 28, 2022 | Sep. 30, 2022 | Mar. 31, 2022 | Sep. 30, 2021 | Jun. 30, 2021 | Sep. 30, 2022 | Sep. 30, 2021 | Dec. 31, 2021 |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] | | | | | | | | | | |
Number of additional shares available for grant (in shares) | 20,500,000 | | | | | | | | | |
Stock based compensation expense | | | | $ 50,100,000 | | $ 71,100,000 | | $ 173,100,000 | $ 292,900,000 | |
Intrinsic value of options | | | | | | | | $ 20,100,000 | $ 97,600,000 | |
Market price per share (in dollars per share) | | | | $ 2,320,000 | | | | $ 2,320,000 | | $ 9,090,000 |
Shares authorized to be repurchased (in shares) | | | | 100,000 | | | | 100,000 | | |
Options early exercised (in shares) | | | | | | | | 0 | | |
Unrecognized stock-based compensation expense | | | | $ 367,200,000 | | | | $ 367,200,000 | | |
Unrecognized stock-based compensation, period of recognition | | | | | | | | 2 years 7 months 6 days | | |
Accrued Expenses And Other Current Liabilities | | | | | | | | | | |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] | | | | | | | | | | |
Proceeds received for unvested shares of common stock | | | | | | | | $ 600,000 | | |
Other Current Liabilities | | | | | | | | | | |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] | | | | | | | | | | |
Proceeds received for unvested shares of common stock | | | | | | | | $ 200,000 | | |
Common Class A | | | | | | | | | | |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] | | | | | | | | | | |
Market price per share (in dollars per share) | | | | $ 23.14 | | | | $ 23.14 | | |
2021 Equity Incentive Plan | | | | | | | | | | |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] | | | | | | | | | | |
Number of shares available for grant (in shares) | | 29,700,000 | | 37,900,000 | | | | 37,900,000 | | |
2021 Agent Equity Program | | | | | | | | | | |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] | | | | | | | | | | |
Stock based compensation expense | | | | | $ 100,000,000 | | | $ 15,200,000 | | $ 84,800,000 |
Outstanding stock options | 2012 Stock Incentive Plan | | | | | | | | | | |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] | | | | | | | | | | |
Expiration period | | | | | | | | 10 years | | |
Restricted Stock Units | | | | | | | | | | |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] | | | | | | | | | | |
Nonvested stock options (in shares) | | | | 46,357,027 | | | | 46,357,027 | | 54,517,930 |
Award vesting rights conditions | | | | | | | | The performance-based vesting conditions provide that 12.5% of the shares subject to the RSUs will vest subject to the achievement of a market price per share of $23.14 of the Company's Class A common stock. An additional 12.5% of the shares subject to the RSUs will vest upon the achievement of a market price per share of the Company's Class A common stock at each of 200%, 250%, 300%, 350%, 400%, 450% and 500% of the reference price. | | |
Percentage of options (in percent) | | | | | | | | 12.50% | | |
Granted (in shares) | | | | | | | | 32,008,264 | | |
Restricted Stock Units | Service-based and Performance-based | | | | | | | | | | |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] | | | | | | | | | | |
Nonvested stock options (in shares) | | | | 17,200,000 | | | | 17,200,000 | | |
Restricted Stock Units | Common Class A | | | | | | | | | | |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] | | | | | | | | | | |
Shares issued in period (in shares) | | | | | | | | 23,200,000 | | |
Restricted Stock Units | Common Class A | Share-based Payment Arrangement, Tranche One | | | | | | | | | | |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] | | | | | | | | | | |
Vesting rights threshold (in percent) | | | | | | | | 200% | | |
Restricted Stock Units | Common Class A | Share-based Payment Arrangement, Tranche Two | | | | | | | | | | |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] | | | | | | | | | | |
Vesting rights threshold (in percent) | | | | | | | | 250% | | |
Restricted Stock Units | Common Class A | Share-based Payment Arrangement, Tranche Three | | | | | | | | | | |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] | | | | | | | | | | |
Vesting rights threshold (in percent) | | | | | | | | 300% | | |
Restricted Stock Units | Common Class A | Share-based Payment Arrangement, Tranche Four | | | | | | | | | | |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] | | | | | | | | | | |
Vesting rights threshold (in percent) | | | | | | | | 350% | | |
Restricted Stock Units | Common Class A | Share-based Payment Arrangement, Tranche Five | | | | | | | | | | |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] | | | | | | | | | | |
Vesting rights threshold (in percent) | | | | | | | | 400% | | |
Restricted Stock Units | Common Class A | Share-based Payment Arrangement, Tranche Six | | | | | | | | | | |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] | | | | | | | | | | |
Vesting rights threshold (in percent) | | | | | | | | 450% | | |
Restricted Stock Units | Common Class A | Share-based Payment Arrangement, Tranche Seven | | | | | | | | | | |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] | | | | | | | | | | |
Vesting rights threshold (in percent) | | | | | | | | 500% | | |
Restricted Stock Units | 2012 Stock Incentive Plan | | | | | | | | | | |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] | | | | | | | | | | |
Expiration period | | | | | | | | 7 years | | |
Restricted Stock Units | 2021 Agent Equity Program | | | | | | | | | | |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] | | | | | | | | | | |
Deferred compensation share-based arrangements, liability | | | | | | | | | | $ 100,000,000 |
Restricted Stock Units | 2021 Agent Equity Program | Common Class A | | | | | | | | | | |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] | | | | | | | | | | |
Granted (in shares) | | | 13,600,000 | | | | | | | |
Restricted Stock Units | 2022 Agent Equity Program | | | | | | | | | | |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] | | | | | | | | | | |
Deferred compensation share-based arrangements, liability | | | | $ 19,400,000 | | | | $ 19,400,000 | | |
Shares subject to the Employee Stock Purchase Plan | 2021 Equity Incentive Plan | | | | | | | | | | |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] | | | | | | | | | | |
Increase in the shares authorized for issuance as a percentage of shares outstanding (in percent) | | 5% | | | | | | | | |
Shares subject to the Employee Stock Purchase Plan | 2021 Employee Stock Purchase Plan | | | | | | | | | | |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] | | | | | | | | | | |
Increase in the shares authorized for issuance as a percentage of shares outstanding (in percent) | | 1% | | | | | | | | |
Number of ESPP shares authorized (in shares) | | 7,400,000 | | | | | | | | |
Number of additional ESPP shares authorized (in shares) | 3,900,000 | | | | | | | | | |
Purchase period | | 6 months | | | | | | | | |
Purchase price of common stock, percent of market price (in percent) | | 85% | | | | | | | | |
Stock based compensation expense | | | | 700,000 | | | | 1,700,000 | | |
Employee withholdings for future purchases under the ESPP | | | | $ 700,000 | | | | $ 700,000 | | |
Shares subject to the Employee Stock Purchase Plan | 2021 Employee Stock Purchase Plan | Common Class A | | | | | | | | | | |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] | | | | | | | | | | |
Number of shares available for grant (in shares) | | | | 10,700,000 | | | | 10,700,000 | | |
Maximum employee subscription amount | | $ 12,500 | | | | | | | | |
Shares issued in period (in shares) | | | | 600,000 | | | | 600,000 | | |
Shares subject to the Employee Stock Purchase Plan | 2021 Employee Stock Purchase Plan | Maximum | | | | | | | | | | |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] | | | | | | | | | | |
Number of ESPP shares authorized (in shares) | | 150,000,000 | | | | | | | | |
IPO Based Restricted Stock Units [Member] | | | | | | | | | | |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] | | | | | | | | | | |
Stock based compensation expense | | | | | | | $ 148,500,000 | | | |