work out vs add

work out and add both are verbs.

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

As verbs, add is a hyponym of work out; that is, add is a word with a more specific, narrower meaning than work out:

work out (verb)	add (verb)
do physical exercise	make an addition (to); join or combine or unite with others; increase the quality, quantity, size or scope of
give a workout to	make an addition by combining numbers
come up with	determine the sum of
work out in detail	state or say further
find the solution to (a problem or question) or understand the meaning of	bestow a quality on
make a mathematical calculation or computation	constitute an addition
be calculated
happen in a certain way, leading to, producing, or resulting in a certain outcome, often well