Income Taxes - Additional Information (Detail) - USD ($) $ in Millions	Dec. 31, 2019	Dec. 31, 2018
Income Tax Disclosure [Abstract]
Short term valuation allowance	$ 0.0	$ 0.1
Long term valuation allowance	$ 1.5	$ 1.0

Deferred Tax Asset Net Of Valuation Allowance, Noncurrent

No definition available.

Name:	cmpx_DeferredTaxAssetNetOfValuationAllowanceNoncurrent
Namespace Prefix:	cmpx_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant