work up vs work out

work up and work out both are verbs.

Word	Noun	Adjective	Verb	Adverb
work up	No	No	Yes	No
work out	No	No	Yes	No

As verbs, work up and work out are synonyms defined as:

work up (verb)	work out (verb)
develop	do physical exercise
form or accumulate steadily	give a workout to
come up with	come up with
bolster or strengthen	work out in detail
	find the solution to (a problem or question) or understand the meaning of
	make a mathematical calculation or computation
	be calculated
	happen in a certain way, leading to, producing, or resulting in a certain outcome, often well