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Equity-based Compensation - Employee Equity-Based Compensation Pre-Tax Expense (Detail) - USD ($) $ in Thousands | 12 Months Ended
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Sep. 30, 2023 | Sep. 30, 2022 | Sep. 30, 2021
Share-based Compensation Arrangement by Share-based Payment Award, Compensation Cost [Line Items] |  |  |
Equity-based compensation pre-tax expense | $ 89,698 | $ 71,807 | $ 54,249
Cost of Revenue [Member] |  |  |
Share-based Compensation Arrangement by Share-based Payment Award, Compensation Cost [Line Items] |  |  |
Equity-based compensation pre-tax expense | 42,969 | 32,096 | 22,691
Research and Development [Member] |  |  |
Share-based Compensation Arrangement by Share-based Payment Award, Compensation Cost [Line Items] |  |  |
Equity-based compensation pre-tax expense | 7,509 | 5,631 | 4,021
Selling, General and Administrative [Member] |  |  |
Share-based Compensation Arrangement by Share-based Payment Award, Compensation Cost [Line Items] |  |  |
Equity-based compensation pre-tax expense | $ 39,220 | $ 34,080 | $ 27,537

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