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Income Taxes - Additional Information (Details) - USD ($)
$ in Millions
 3 Months Ended 6 Months Ended
Mar. 31, 2021
Mar. 31, 2020
Mar. 31, 2021
Mar. 31, 2020
Mar. 31, 2022
Sep. 30, 2020
Income tax expense $ 33.2 $ 38.3 $ 46.4 $ 59.0    
Effective income tax rate (as a percent) 25.00% 35.80% 21.50% 28.90%    
Income tax expense (benefit), tax credit, discrete items $ 1.4 $ 11.1 $ (5.3) $ 10.0    
Effective income tax rate reconciliation, other reconciling items, amount   (1.2)   (2.7)    
Income tax expense (benefit) related to uncertain tax reserve releases     4.4      
Income tax expense (benefit), interest income     2.1      
Unrecognized tax benefits 62.9   62.9     $ 79.8
Net unrecognized tax benefits, excluding interest and penalties that would affect the company's net income if recognized 17.6   17.6      
Interest and penalties     1.0 0.7    
Accruals for payment of interest and penalties 6.7   6.7      
Scenario Forecast            
Significant change in unrecognized tax benefits is reasonably possible, amount of unrecorded benefit         $ 3.9  
Foreign Tax Authority            
Valuation allowance on foreign or state net deferred tax assets   $ 11.4   $ 11.4    
State Tax Authority            
Charge related to state audit settlements $ 0.8   $ 0.8