Property and Equipment - Schedule of Property and Equipment (Detail) - USD ($) $ in Thousands	Jun. 30, 2022	Dec. 31, 2021
Property Plant And Equipment [Line Items]
Property plant and equipment, gross	$ 1,500	$ 1,196
Less: accumulated depreciation	(299)	(169)
Total property and equipment, net	1,201	1,027
Equipment
Property Plant And Equipment [Line Items]
Property plant and equipment, gross	1,101	870
Computers and Software
Property Plant And Equipment [Line Items]
Property plant and equipment, gross	164	109
Leasehold Improvements
Property Plant And Equipment [Line Items]
Property plant and equipment, gross	156	141
Furniture and Fixtures
Property Plant And Equipment [Line Items]
Property plant and equipment, gross	$ 79	$ 76

Amount of accumulated depreciation, depletion and amortization for physical assets used in the normal conduct of business to produce goods and services.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 360
-SubTopic 10
-Section 50
-Paragraph 1
-Subparagraph (c)
-URI https://asc.fasb.org/extlink&oid=6391035&loc=d3e2868-110229

Reference 2: 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(14))
-URI https://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

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

- Definition

Amount before accumulated depreciation, depletion and amortization of physical assets used in the normal conduct of business and not intended for resale. Examples include, but are not limited to, land, buildings, machinery and equipment, office equipment, and furniture and fixtures.

+ 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(13))
-URI https://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 360
-SubTopic 10
-Section 50
-Paragraph 1
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=6391035&loc=d3e2868-110229

+ Details

Name:	us-gaap_PropertyPlantAndEquipmentGross
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
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_PropertyPlantAndEquipmentLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount after accumulated depreciation, depletion and amortization of physical assets used in the normal conduct of business to produce goods and services and not intended for resale. Examples include, but are not limited to, land, buildings, machinery and equipment, office equipment, and furniture and fixtures.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 360
-SubTopic 10
-Section 50
-Paragraph 1
-URI https://asc.fasb.org/extlink&oid=6391035&loc=d3e2868-110229

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 944
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(a)(8))
-URI https://asc.fasb.org/extlink&oid=126734703&loc=d3e572229-122910

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 360
-Section 50
-Paragraph 1
-URI https://asc.fasb.org/extlink&oid=124429447&loc=SL124453093-239630

Reference 4: 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_PropertyPlantAndEquipmentNet
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Details

Name:	us-gaap_PropertyPlantAndEquipmentByTypeAxis=us-gaap_EquipmentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_PropertyPlantAndEquipmentByTypeAxis=tyra_ComputersAndSoftwareMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_PropertyPlantAndEquipmentByTypeAxis=us-gaap_LeaseholdImprovementsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_PropertyPlantAndEquipmentByTypeAxis=us-gaap_FurnitureAndFixturesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: