work out vs add up

work out and add up both are verbs.

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

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

Other hypernyms of work out include amount, come, number, total.

work out (verb)	add up (verb)
do physical exercise	determine the sum of
give a workout to	be reasonable or logical or comprehensible
come up with	to measure up to in kind or quality
work out in detail	add up in number or quantity
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