I find this whole discussion to be hilarious ;-)

"Approximate upper bound" is gibberish - "upper bound" is a crisp concept that means what it says.  It's not necessarily true that an upper bound is inaccurate - it may be exactly right.  So "this is not as accurate as ratio()" overstates the case.

"quick_ratio() returns an upper bound on what ratio() returns" is the truth, and can't be improved by adding more words.   Appealing to a "correct" result would also be misleading (what ratio() returns is a more-or-less arbitrary computation whose only claim to "correctness" is that ratio() returns what it's documented to return).

If people find the gloss in the docs confusing, remove the gloss entirely, leaving just the correct:

"Return an upper bound on ratio() relatively quickly."