Stock-based compensation expense - Valuation Assumptions (Detail)	12 Months Ended
	Sep. 30, 2023	Sep. 30, 2022	Sep. 30, 2021
Option
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Expected term (years)		6 years	6 years 1 month 6 days
Expected volatility		70.70%	64.40%
Risk-free interest rate		1.40%	1.00%
Dividend yield	0.00%	0.00%	0.00%
Performance Stock Options
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Expected term (years)		5 years 10 months 24 days	6 years 1 month 6 days
Expected volatility		70.90%	64.40%
Risk-free interest rate		2.80%	1.00%
Dividend yield		0.00%	0.00%