Debt instrument date of first required payment month and year.

No definition available.

Name:	cmpx_DebtInstrumentDateOfFirstRequiredPaymentMonthAndYear
Namespace Prefix:	cmpx_
Data Type:	xbrli:gYearMonthItemType
Balance Type:	na
Period Type:	duration

- Definition

Minimum cash balance.

+ References

No definition available.

+ Details

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

- Definition

Success fee payment due.

+ References

No definition available.

+ Details

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

- Definition

Percentage points added to the reference rate to compute the variable rate on the debt instrument.

+ References

No definition available.

+ Details

Name:	us-gaap_DebtInstrumentBasisSpreadOnVariableRate1
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Description of the frequency of periodic payments (monthly, quarterly, annual).

+ 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 210.5-02.22)
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 470
-Section 50
-Paragraph 3
-Subparagraph (c)
-URI http://asc.fasb.org/extlink&oid=75038535&loc=d3e64711-112823

+ Details

Name:	us-gaap_DebtInstrumentFrequencyOfPeriodicPayment
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

The average effective interest rate during the reporting period.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 835
-SubTopic 30
-Section 45
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=119993939&loc=d3e28551-108399

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-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.22(a)(1))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

Name:	us-gaap_DebtInstrumentInterestRateDuringPeriod
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Effective interest rate for the funds borrowed under the debt agreement considering interest compounding and original issue discount or premium.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 50
-Paragraph 6
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=120520924&loc=SL6036836-161870

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-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.22(a)(1))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

Name:	us-gaap_DebtInstrumentInterestRateEffectivePercentage
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Incremental percentage increase (decrease) in the stated rate on a debt instrument.

+ References

No definition available.

+ Details

Name:	us-gaap_DebtInstrumentInterestRateIncreaseDecrease
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Contractual interest rate for funds borrowed, under the debt agreement.

+ References

+ Details

Name:	us-gaap_DebtInstrumentInterestRateStatedPercentage
Namespace Prefix:	us-gaap_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

Name:	us-gaap_DebtInstrumentLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Date when the debt instrument is scheduled to be fully repaid, in CCYY-MM-DD format.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.22(a)(2))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 820
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (bbb)(2)
-URI http://asc.fasb.org/extlink&oid=117815213&loc=d3e19207-110258

+ Details

Name:	us-gaap_DebtInstrumentMaturityDate
Namespace Prefix:	us-gaap_
Data Type:	xbrli:dateItemType
Balance Type:	na
Period Type:	duration

- Definition

Description of the payment terms of the debt instrument (for example, whether periodic payments include principal and frequency of payments) and discussion about any contingencies associated with the payment.

+ 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 210.5-02.22(a)(3))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

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-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 470
-Section 50
-Paragraph 3
-Subparagraph (c)
-URI http://asc.fasb.org/extlink&oid=75038535&loc=d3e64711-112823

+ Details

Name:	us-gaap_DebtInstrumentPaymentTerms
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of the required periodic payments applied to principal.

+ References

+ Details

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

- Definition

Amount of the cost of borrowed funds accounted for as interest expense for debt.

+ References

+ Details

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

- Definition

The cash inflow during the period from additional borrowings in aggregate debt. Includes proceeds from short-term and long-term debt.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 14
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=121586364&loc=d3e3255-108585

+ Details

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

- Details

Name:	us-gaap_DebtInstrumentAxis=us-gaap_RevolvingCreditFacilityMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LineOfCreditFacilityAxis=cmpx_PacificWesternBankIncMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_VariableRateAxis=us-gaap_PrimeRateMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Debt - Additional Information (Details) - USD ($)	3 Months Ended		6 Months Ended
Debt - Additional Information (Details) - USD ($)	Jun. 30, 2021	Jun. 30, 2020	Jun. 30, 2021	Jun. 30, 2020
Debt Instrument [Line Items]
Debt proceeds			$ 15,000,000.0
Credit Facility \| Pacific Western Bank, Inc
Debt Instrument [Line Items]
Debt proceeds			$ 15,000,000.0
Debt instrument, interest rate	6.25%		6.25%
Debt instrument, interest rate during period			6.25%
Increase in interest rate in case of default			5.00%
Term loan facility payment terms			The Company made interest-only payments through March 31, 2020. In April 2020, the Company became obligated to make equal monthly principal payments of $625,000 through March 31, 2022 when the notes mature.
Frequency of periodic payment			monthly
Date of first required payment			2020-04
Equal monthly principal payments			$ 625,000
Debt instrument, maturity date			Mar. 31, 2022
Success fee payment due	$ 1,100,000		$ 1,100,000
Minimum cash balance	$ 6,000,000.0		$ 6,000,000.0
Debt instrument, interest rate, effect plus percentage	5.00%		5.00%
Interest expense	$ 100,000	$ 200,000	$ 300,000	$ 500,000
Prime Rate \| Credit Facility \| Pacific Western Bank, Inc
Debt Instrument [Line Items]
Debt instrument, applicable margin interest rate			2.00%