Subsequent Events - Additional Information (Details) - Subsequent Event $ / shares in Units, $ in Millions	Nov. 01, 2021 USD ($) $ / shares shares
Subsequent Event [Line Items]
Common shares issued under initial public offering	35,715,000
Public offering price per share | $ / shares	$ 3.50
Option to underwriter to purchase additional shares of common stock	5,357,250
Initial public offering description	common stock would begin trading on the Nasdaq Capital Market under the symbol “CMPX” at the opening of trading on November 2, 2021. The Offering closed on November 4, 2021.
Proceeds from the Offering, net of underwriting discounts and commissions and other offering expenses | $	$ 117.3
Granted period to purchase option	30 days