go off half-cocked vs go off at half-cock

go off half-cocked and go off at half-cock both are verbs.

Word	Noun	Adjective	Verb	Adverb
go off half-cocked	No	No	Yes	No
go off at half-cock	No	No	Yes	No

As verbs, go off half-cocked and go off at half-cock are synonyms defined as:

go off half-cocked and go off at half-cock: act prematurely or without reflection or too soon

go off half-cocked (verb)	go off at half-cock (verb)
act prematurely or without reflection or too soon	act prematurely or without reflection or too soon