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Income Taxes - Effective Rate Reconciliation (Details) | 12 Months Ended
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Sep. 30, 2021 | Sep. 30, 2020 | Sep. 30, 2019
Income Tax Disclosure [Abstract] |  |  |
Federal statutory rate effect of: | 21.00% | 21.00% | 21.00%
U.S. State and local income taxes | 1.80% | 1.20% | (0.90%)
Foreign earnings and losses taxed at different rates | 1.00% | 0.90% | 0.20%
Change in valuation allowance | 1.90% | 1.00% | 0.90%
Income tax rate holiday | (0.50%) | (0.80%) | 0.50%
U.S. permanent items | (1.20%) | 0.60% | (0.50%)
Non-deductible compensation | 1.90% | 0.60% | 0.70%
Foreign permanent items | (0.20%) | 1.10% | 0.20%
U.S. bargain purchase gain | (0.50%) | (8.30%) | (1.00%)
GILTI | 0.60% | 0.70% | 2.20%
Income tax rate change | (1.20%) | 0.00% | 0.00%
Income tax rate change | 24.60% | 18.00% | 23.30%

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