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

Amount before allocation of valuation allowances of deferred tax asset attributable to deductible temporary differences from lease liabilities.

No definition available.

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

Amount, before allocation of valuation allowance, of deferred tax asset attributable to deductible temporary differences from section 174 capitalization..

No definition available.

Name:	cmpx_DeferredTaxAssetsSection174Capitalization
Namespace Prefix:	cmpx_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

Amount before allocation of valuation allowances of deferred tax asset attributable to deductible temporary differences and carryforwards.

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482685/740-10-50-2

Name:	us-gaap_DeferredTaxAssetsGross
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

Amount, after allocation of valuation allowances and deferred tax liability, of deferred tax asset attributable to deductible differences and carryforwards, without jurisdictional netting.

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482685/740-10-50-2

Name:	us-gaap_DeferredTaxAssetsLiabilitiesNet
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

Amount after allocation of valuation allowances of deferred tax asset attributable to deductible temporary differences and carryforwards.

Name:	us-gaap_DeferredTaxAssetsNet
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

Amount before allocation of valuation allowances of deferred tax asset attributable to deductible domestic operating loss carryforwards. Excludes state and local operating loss carryforwards.

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 6
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482685/740-10-50-6

Name:	us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsDomestic
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

Amount before allocation of valuation allowances of deferred tax asset attributable to deductible state and local operating loss carryforwards.

Name:	us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsStateAndLocal
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

Amount, before allocation of valuation allowance, of deferred tax asset attributable to deductible temporary differences, classified as other.

Name:	us-gaap_DeferredTaxAssetsOther
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

Amount before allocation of valuation allowances of deferred tax asset attributable to deductible research tax credit carryforwards.

Name:	us-gaap_DeferredTaxAssetsTaxCreditCarryforwardsResearch
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

Amount before allocation of valuation allowances of deferred tax asset attributable to deductible temporary differences from share-based compensation.

Name:	us-gaap_DeferredTaxAssetsTaxDeferredExpenseCompensationAndBenefitsShareBasedCompensationCost
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

Amount of deferred tax assets for which it is more likely than not that a tax benefit will not be realized.

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482685/740-10-50-2

Name:	us-gaap_DeferredTaxAssetsValuationAllowance
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

Amount of deferred tax liability attributable to taxable temporary differences from leasing arrangements.

Name:	us-gaap_DeferredTaxLiabilitiesLeasingArrangements
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

Amount of deferred tax liability attributable to taxable temporary differences classified as other.