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Stock-Based Compensation - Additional Information (Detail) - USD ($) |  | 1 Months Ended | 3 Months Ended | 9 Months Ended | 12 Months Ended | 21 Months Ended |
--- | --- | --- | --- | --- | --- | --- | ---
Feb. 28, 2021 | Jan. 31, 2023 | Sep. 30, 2024 | Sep. 30, 2023 | Sep. 30, 2024 | Sep. 30, 2023 | Dec. 31, 2022 | Sep. 30, 2023 | Jan. 01, 2024
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |
Stock based compensation expense |  |  | $ 32,500,000 | $ 38,000,000.0 | $ 96,300,000 | $ 121,900,000 |  |  |
Intrinsic value of options |  |  |  |  | 7,300,000 | 5,900,000 |  |  |
Unrecognized stock-based compensation expense |  |  | $ 138,000,000.0 |  | $ 138,000,000.0 |  |  |  |
Unrecognized stock-based compensation, period of recognition |  |  |  |  | 2 years |  |  |  |
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 |  | 59,700,000 |  | 59,700,000 |  |  |  |
Number of additional shares available for grant (in shares) |  |  |  |  |  |  |  |  | 24,200,000
2022 Agent Equity Program |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |
Stock based compensation expense |  |  |  |  |  | 11,600,000 | $ 41,700,000 | $ 53,300,000 |
Outstanding stock options | 2012 Stock Incentive Plan |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |
Expiration period |  |  |  |  | 10 years |  |  |  |
RSUs |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |
Granted (in shares) |  |  |  |  | 24,238,196 |  |  |  |
RSUs | Common Class A |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |
Shares issued in period (in shares) |  |  |  |  | 18,200,000 |  |  |  |
RSUs | 2012 Stock Incentive Plan |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |
Expiration period |  |  |  |  | 7 years |  |  |  |
RSUs | 2022 Agent Equity Program |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |
Deferred compensation share-based arrangements, liability |  | $ 53,300,000 |  |  |  |  |  |  |
RSUs | 2022 Agent Equity Program | Common Class A |  |  |  |  |  |  |  |  |
Share-based Compensation Arrangement by Share-based Payment Award [Line Items] |  |  |  |  |  |  |  |  |
Granted (in shares) |  | 14,100,000 |  |  |  |  |  |  |
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) | 5.00% |  |  |  |  |  |  |  |
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) | 1.00% |  |  |  |  |  |  |  |
Number of additional shares available for grant (in shares) |  |  |  |  |  |  |  |  | 4,700,000
Number of ESPP shares authorized (no more than) (in shares) | 7,400,000 |  |  |  |  |  |  |  |
Purchase period | 6 months |  |  |  |  |  |  |  |
Purchase price of common stock, percent of market price (in percent) | 85.00% |  |  |  |  |  |  |  |
Stock based compensation expense |  |  | $ 200,000 | $ 400,000 | $ 700,000 | $ 1,000,000.0 |  |  |
Employee withholdings for future purchases under the ESPP |  |  | $ 400,000 |  | $ 400,000 |  |  |  |
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) |  |  | 18,100,000 |  | 18,100,000 |  |  |  |
Maximum employee subscription amount | $ 12,500 |  |  |  |  |  |  |  |
Shares issued in period (in shares) |  |  |  |  | 700,000 |  |  |  |
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 (no more than) (in shares) | 150,000,000.0 |  |  |  |  |  |  |  |

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