Nature of Business and Summary of Significant Accounting Policies - Additional Information (Details) - USD ($) $ in Millions	12 Months Ended
Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2020
Accounting Policies [Abstract]
Depreciation and amortization, property and equipment	$ 15.2	$ 20.3	$ 23.5
Foreign exchange gains (losses)	1.9	0.0	(1.0)
Advertising and promotion costs	$ 8.1	$ 6.9	$ 8.7

No definition available.

Name:	us-gaap_AccountingPoliciesAbstract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

The current period expense charged against earnings on long-lived, physical assets not used in production, and which are not intended for resale, to allocate or recognize the cost of such assets over their useful lives; or to record the reduction in book value of an intangible asset over the benefit period of such asset; or to reflect consumption during the period of an asset that is not used in production.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 360
-SubTopic 10
-Section 50
-Paragraph 1
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=6391035&loc=d3e2868-110229

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 28
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=123570139&loc=d3e3602-108585

+ Details

Name:	us-gaap_DepreciationAndAmortization
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Amount before tax of foreign currency transaction realized and unrealized gain (loss) recognized in the income statement.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 830
-SubTopic 20
-Section 45
-Paragraph 1
-URI http://asc.fasb.org/extlink&oid=125521441&loc=d3e30690-110894

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 830
-SubTopic 20
-Section 35
-Paragraph 1
-URI http://asc.fasb.org/extlink&oid=123602790&loc=d3e30226-110892

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 830
-SubTopic 10
-Section 45
-Paragraph 17
-URI http://asc.fasb.org/extlink&oid=120253306&loc=d3e28228-110885

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 830
-SubTopic 20
-Section 50
-Paragraph 1
-URI http://asc.fasb.org/extlink&oid=124440516&loc=d3e30840-110895

+ Details

Name:	us-gaap_ForeignCurrencyTransactionGainLossBeforeTax
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

The total expense recognized in the period for promotion, public relations, and brand or product advertising.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section S99
-Paragraph 2
-Subparagraph (SX 210.5-03.4)
-URI http://asc.fasb.org/extlink&oid=123367319&loc=SL114868664-224227

+ Details

Name:	us-gaap_MarketingAndAdvertisingExpense
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration