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Share-Based Compensation - Additional Information (Details) - USD ($)
$ / shares in Units, shares in Thousands, $ in Millions
12 Months Ended
Sep. 30, 2020
Sep. 30, 2020
Sep. 30, 2019
Sep. 30, 2018
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Shares granted 9,200 9,200    
Weighted average fair values of options granted (usd per share)   $ 16.61 $ 18.60 $ 14.16
Stock option expense   $ 13.0 $ 21.0 $ 22.6
Intrinsic value of stock option exercises   42.6 51.2 116.7
Total fair values of options vested   $ 21.3 $ 22.7 25.8
Nonvested options outstanding (shares) 2,129 2,129 3,265  
Expected future compensation expense relating to nonvested options outstanding $ 10.3 $ 10.3    
Weighted average period over which expected future compensation expense relating to nonvested options outstanding will be recognized 1 year 8 months 12 days      
Employee options        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Vesting period (in years)   4 years    
Expiration period (in years)   7 years    
Non-employee options        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Vesting period (in years)   3 years    
Expiration period (in years)   10 years    
Restricted stock units        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Restricted stock expense   $ 39.8 $ 29.2 26.8
Total fair values of restricted shares vested   $ 26.4 $ 14.5 15.8
Nonvested shares outstanding (shares) 1,512 1,512 1,222  
Expected future compensation expense relating to restricted shares outstanding $ 43.4 $ 43.4    
Weighted average period over which expected future compensation expense relating to restricted shares outstanding will be recognized 1 year 4 months 24 days      
Performance stock units        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Vesting period (in years)   3 years    
Nonvested shares outstanding (shares) 288 288 283  
Performance stock unit expense   $ 21.5 $ 8.5 $ 12.8
Performance stock units | Minimum        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Vesting percentage   0.00% 0.00%  
Performance stock units | Maximum        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Vesting percentage   200.00% 150.00%