cook up vs cook

cook up is not a noun while cook is a noun.

Word	Noun	Adjective	Verb	Adverb
cook up	No	No	Yes	No
cook	Yes	No	Yes	No

As verbs, cook is a hypernym of cook up; that is, cook is a word with a broader meaning than cook up:

Other hypernyms of cook up include fix, make, prepare, ready.

cook up (noun)	cook (noun)
	someone who cooks food

cook up (verb)	cook (verb)
concoct something artificial or untrue	transform and make suitable for consumption by heating
prepare or cook by mixing ingredients	transform by heating
	prepare for eating by applying heat
	prepare a hot meal
	tamper, with the purpose of deception