I know I've had a few situations where the "play around with the numbers" part happened first. Usually once the actual goal was known the algebra (or similar details) would be obvious... but sometimes the inefficient/toy implementation was good enough.

Sometimes half-assed is ok, if it's the the right half of the ass.[1] The wrong half becomes yet another type of technical debt to be refactored "someday".

(this is not an excuse to ignore algebra or blindly assume the easiest/most-fun method is correct/useful/sane)

[1] https://twitter.com/jimweirich/status/29662011323326464 via https://www.youtube.com/watch?v=sCZJblyT_XM