Amount of cash outflow for license agreement.

No definition available.

Name:	cmpx_CashPaymentForLicenseAgreement
Namespace Prefix:	cmpx_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of expenses to be recognized under license and research agreement.

+ References

No definition available.

+ Details

Name:	cmpx_LicenseAndResearchAgreementExpensesToBeRecognized
Namespace Prefix:	cmpx_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

The maximum amount of commercial milestone payments and royalties.

+ References

No definition available.

+ Details

Name:	cmpx_MaximumCommercialMilestonePaymentsAndRoyalties
Namespace Prefix:	cmpx_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

The maximum amount of development and regulatory milestone payments.

+ References

No definition available.

+ Details

Name:	cmpx_MaximumDevelopmentAndRegulatoryMilestonePayments
Namespace Prefix:	cmpx_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of obligation for milestone payments.

+ References

No definition available.

+ Details

Name:	cmpx_MilestonePaymentObligation
Namespace Prefix:	cmpx_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of cash outflow for milestone payments.

+ References

No definition available.

+ Details

Name:	cmpx_MilestonePaymentsPaid
Namespace Prefix:	cmpx_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of cash outflow for upfront payment.

+ References

No definition available.

+ Details

Name:	cmpx_UpfrontPayment
Namespace Prefix:	cmpx_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Carrying value as of the balance sheet date of liabilities incurred (and for which invoices have typically been received) and payable to vendors for goods and services received that are used in an entity's business. Used to reflect the current portion of the liabilities (due within one year or within the normal operating cycle if longer).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.19(a))
-URI https://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

Reference 2: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 852
-SubTopic 10
-Section 55
-Paragraph 10
-URI https://asc.fasb.org/extlink&oid=84165509&loc=d3e56426-112766

+ Details

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

- Definition

The aggregate costs incurred (1) in a planned search or critical investigation aimed at discovery of new knowledge with the hope that such knowledge will be useful in developing a new product or service, a new process or technique, or in bringing about a significant improvement to an existing product or process; or (2) to translate research findings or other knowledge into a plan or design for a new product or process or for a significant improvement to an existing product or process whether intended for sale or the entity's use, during the reporting period charged to research and development projects, including the costs of developing computer software up to the point in time of achieving technological feasibility, and costs allocated in accounting for a business combination to in-process projects deemed to have no alternative future use.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 912
-SubTopic 730
-Section 25
-Paragraph 1
-URI https://asc.fasb.org/extlink&oid=6472174&loc=d3e58812-109433

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 985
-SubTopic 20
-Section 50
-Paragraph 1
-URI https://asc.fasb.org/extlink&oid=6501960&loc=d3e128462-111756

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 730
-SubTopic 10
-Section 50
-Paragraph 1
-URI https://asc.fasb.org/extlink&oid=6420194&loc=d3e21568-108373

+ Details

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

- Details

Name:	us-gaap_TypeOfArrangementAxis=cmpx_ABLBioAgreementMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_ProductOrServiceAxis=cmpx_OncologyMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_ProductOrServiceAxis=cmpx_OphthalmologyMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_TypeOfArrangementAxis=cmpx_AdimabAgreementMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_TypeOfArrangementAxis=cmpx_FujifilmDiosynthBiotechnologiesAgreementMember
Namespace Prefix:
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Note 10 - License, Research and Collaboration Agreements (Details Textual) - USD ($) $ in Thousands	1 Months Ended	3 Months Ended	6 Months Ended
	Nov. 30, 2018	Jun. 30, 2022	Jun. 30, 2022	Dec. 31, 2021
Accounts Payable, Current, Total		$ 6,532	$ 6,532	$ 867
ABL Bio Agreement [Member]
Upfront Payment	$ 5,000
Maximum Development and Regulatory Milestone Payments	110,000
ABL Bio Agreement [Member] \| Oncology [Member]
Maximum Commercial Milestone Payments and Royalties	295,000
ABL Bio Agreement [Member] \| Ophthalmology [Member]
Maximum Commercial Milestone Payments and Royalties	$ 185,000
Accounts Payable, Current, Total		6,000	6,000
Adimab Agreement [Member]
Milestone Payments Paid			0
Milestone Payment Obligation		2,000	2,000
FUJIFILM Diosynth Biotechnologies Agreement [Member]
Cash Payment for License Agreement		488	500
Research and Development Expense, Total		2,200	2,800
License and Research Agreement, Expenses to be Recognized		$ 600	$ 600