The number of operating leases.

No definition available.

Name:	cmpx_NumberOfOperatingLeases
Namespace Prefix:	cmpx_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	instant

- Definition

Discount rate used by lessee to determine present value of operating lease payments.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (c)(3)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147478964/842-20-50-3

+ Details

Name:	us-gaap_LesseeOperatingLeaseDiscountRate
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Remaining lease term of operating lease, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (a)(1)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147478964/842-20-50-3

+ Details

Name:	us-gaap_LesseeOperatingLeaseRemainingLeaseTerm
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	instant

- Definition

Term of lessee's operating lease, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (a)(3)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147478964/842-20-50-3

+ Details

Name:	us-gaap_LesseeOperatingLeaseTermOfContract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	instant

- Definition

Amount of cash outflow from operating lease, excluding payments to bring another asset to condition and location necessary for its intended use.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 45
-Paragraph 5
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479041/842-20-45-5

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 4
-Subparagraph (g)(1)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147478964/842-20-50-4

+ Details

Name:	us-gaap_OperatingLeasePayments
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

Note 7 - Commitments and Contingencies (Details Textual) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2023 USD ($)	Sep. 30, 2022 USD ($)	Sep. 30, 2023 USD ($)	Sep. 30, 2022 USD ($)	Dec. 31, 2022	Dec. 31, 2020
Number of Operating Leases						1
Lessee, Operating Lease, Term of Contract (Year)					4 years 5 months 1 day
Lessee, Operating Lease, Discount Rate					6.25%
Lessee, Operating Lease, Remaining Lease Term (Year)	1 year 7 months 28 days		1 year 7 months 28 days
Operating Lease, Payments	$ 0.3	$ 0.3	$ 1.0	$ 1.0