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Stock-Based Compensation - Additional Information (Detail) - USD ($)
$ in Millions
12 Months Ended
Sep. 30, 2021
Sep. 30, 2020
Sep. 30, 2019
Mar. 18, 2021
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]        
Number of options outstanding 3,456,239 4,539,403    
RSU awards vesting, description At vesting, each outstanding RSU will be exchanged for one share of the Company’s Common Stock. RSU awards generally vest subject to the satisfaction of service requirements or the satisfaction of both service requirements and achievement of certain performance targets.      
Employee Stock Option        
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]        
Stock-based compensation expense $ 12.4 $ 9.7 $ 4.0  
Grant date fair value of the options granted 9.0 34.6 12.1  
Intrinsic value of options exercised 66.9 44.1 24.6  
Unrecognized pre-tax compensation expense $ 26.3      
Weighted average period to recognize pre-tax compensation expense 2 years 4 months 24 days      
Dividend yield 0.00%      
Restricted Stock Units (RSUs)        
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]        
Stock-based compensation expense $ 64.2 33.7 8.4  
Grant date fair value of the options granted $ 127.7 $ 149.4 $ 17.8  
Weighted average period to recognize pre-tax compensation expense 2 years 8 months 12 days      
Unrecognized pre-tax compensation expense $ 118.0      
Additional unrecognized pre-tax compensation expense $ 35.7      
2004 Equity Incentive Plan        
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]        
Shares reserve for issuance 429,141      
2004 Equity Incentive Plan | Employee Stock Option        
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]        
Number of options outstanding 429,141      
2013 Incentive Plan        
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]        
Shares reserve for issuance 5,225,983      
Number of shares forfeited 87,190      
2013 Incentive Plan | Employee Stock Option        
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]        
Number of options outstanding 2,066,533      
2013 Incentive Plan | Restricted Stock Units (RSUs)        
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]        
Number of restricted stock units outstanding 3,159,450      
Outside Of Equity Compensation Plans        
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]        
Shares reserve for issuance 957,565      
Outside Of Equity Compensation Plans | Restricted Stock Units (RSUs)        
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]        
Shares reserve for issuance 602,000      
2021 Incentive Plan        
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]        
Number of shares authorized 8,013,790     8,000,000
2021 Incentive Plan | Employee Stock Option        
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]        
Number of options outstanding 3,000      
2021 Incentive Plan | Restricted Stock Units (RSUs)        
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]        
Number of restricted stock units outstanding 70,400