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Stock-Based Compensation - Narrative (Details) - USD ($)
$ in Millions
12 Months Ended
Jul. 08, 2022
Jan. 01, 2022
Sep. 30, 2023
Sep. 30, 2022
Sep. 30, 2021
Mar. 18, 2021
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]            
Number of shares authorized (in shares)     6,204,720      
Employee Stock Option            
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]            
Intrinsic value of options exercised     $ 12.2 $ 27.6 $ 66.9  
Stock-based compensation expense     8.4 10.8 12.4  
Unrecognized pre-tax compensation expense     $ 2.9      
Weighted average period to recognize pre-tax compensation expense     4 months 24 days      
Restricted Stock Units (RSUs)            
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]            
Stock-based compensation expense     $ 69.7 $ 113.6 $ 64.2  
Weighted average period to recognize pre-tax compensation expense     1 year 7 months 6 days      
Granted (in shares)     1,243,644      
Share-based payment award (in shares)     4,241,640 4,069,931    
Unrecognized pre-tax compensation expense     $ 94.4      
Restricted Stock Units (RSUs) | Chief Executive Officer            
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]            
Share-based payment award (in shares) 99,521          
Restricted Stock Units, Market-Based | Chief Executive Officer            
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]            
Granted (in shares)   800,000        
Equity award value $ 38.4          
Performance-Based Restricted Stock Units | Chief Executive Officer            
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]            
Share-based payment award (in shares) 149,282          
2004 Plan            
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]            
Shares reserve for issuance (in shares)     0      
2004 Plan | Restricted Stock Units (RSUs)            
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]            
Share-based payment award (in shares)     0      
2013 Plan            
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]            
Shares reserve for issuance (in shares)     3,408,707      
Number of shares forfeited (in shares)     217,922      
2013 Plan | Restricted Stock Units (RSUs)            
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]            
Share-based payment award (in shares)     1,886,500      
2021 Plan            
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]            
Number of shares authorized (in shares)           8,000,000
Number of shares forfeited (in shares)     1,979,364      
2021 Plan | Restricted Stock Units (RSUs)            
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]            
Share-based payment award (in shares)     1,671,315      
Outside Of Equity Compensation Plans | Employee Stock Option            
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]            
Shares reserve for issuance (in shares)     707,432      
Outside Of Equity Compensation Plans | Restricted Stock Units (RSUs)            
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]            
Shares reserve for issuance (in shares)     683,825