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Income Taxes - Additional Information (Details) - USD ($)
$ in Thousands
12 Months Ended
Sep. 30, 2024
Sep. 30, 2023
Sep. 30, 2022
Jun. 30, 2022
Income Taxes [Line Items]        
U.S. federal statutory rates 21.00% 21.00% 21.00%  
Income tax expense (benefit) $ 3,468 $ 19,865 $ 112,075  
Deferred tax assets valuation allowance 167,314 162,966    
Uncertain tax positions 87,400 85,172 76,590  
Uncertain tax positions cumulative translation adjustments 4,000 5,000    
Deferred Tax Assets Net 50,820 46,039    
Increases related to tax positions taken from prior periods 216      
Interest related to uncertain tax positions 1,300 600 $ (300)  
Recognized interest income $ 5,600 4,200    
Minimum        
Income Taxes [Line Items]        
Operating loss carryforwards expiration year 2026      
Minimum | Research and Development        
Income Taxes [Line Items]        
Operating loss carryforwards expiration year 2025      
Maximum | Research and Development        
Income Taxes [Line Items]        
Operating loss carryforwards expiration year 2041      
U.S. Federal | Research and Development        
Income Taxes [Line Items]        
Net operating loss carryforwards $ 7,000 7,600    
Uncertain tax positions 5,200 7,400    
State        
Income Taxes [Line Items]        
Net operating loss carryforwards 9,800 8,400    
State | Research and Development        
Income Taxes [Line Items]        
Net operating loss carryforwards 300 300    
Netherlands        
Income Taxes [Line Items]        
Net operating loss carryforwards 360,700 350,500    
Domestic        
Income Taxes [Line Items]        
Deferred Tax Assets Net   8,200    
Foreign        
Income Taxes [Line Items]        
Deferred tax assets valuation allowance 167,300      
Net operating loss carryforwards 433,600 385,800    
Uncertain tax positions 270,200 256,000    
Deferred Tax Assets Net   154,800    
Foreign | Research and Development        
Income Taxes [Line Items]        
Net operating loss carryforwards $ 7,200 $ 5,500    
Foreign Jurisdiction        
Income Taxes [Line Items]        
Deferred tax assets valuation allowance       $ 107,600