Debt - Additional Information (Details) - USD ($)	3 Months Ended
Mar. 31, 2021	Mar. 31, 2020
Debt Instrument [Line Items]
Debt proceeds	$ 15,000,000
Credit Facility \| Pacific Western Bank, Inc
Debt Instrument [Line Items]
Debt proceeds	$ 15,000,000
Debt instrument, interest rate	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
Minimum cash balance	$ 6,000,000
Debt instrument, interest rate, effect plus percentage	5.00%
Interest expense	$ 100,000	$ 300,000
Prime Rate \| Credit Facility \| Pacific Western Bank, Inc
Debt Instrument [Line Items]
Debt instrument, applicable margin interest rate	2.00%

Debt instrument date of first required payment month and year.

No definition available.

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

- Definition

Minimum cash balance.

+ References

No definition available.

+ Details

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

- Definition

Success fee payment due.

+ References

No definition available.

+ Details

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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

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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

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-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
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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

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+ Details

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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

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-Name Accounting Standards Codification
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Balance Type:	na
Period Type:	instant

- Definition

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

+ References

No definition available.

+ Details

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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

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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

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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

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-Publisher FASB
-Name Accounting Standards Codification
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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.

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Balance Type:	na
Period Type:	duration

- Definition

Amount of the required periodic payments applied to principal.

+ References

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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

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Namespace Prefix:	us-gaap_
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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

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Namespace Prefix:	us-gaap_
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Balance Type:	debit
Period Type:	duration

- Details

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Balance Type:
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- Details

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