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You can’t use exponentially in the colloquial sense in a post about software performance.

If my barista says that his new coffee is exponentially better, it’s ok to use it colloquially.

If my git hosting provider writes about an impactful performance improvement, it’s not.

Thank you.

(I don't think that anyone should use "exponentially" that way: it is an art term with a specific and particular meaning, so find another word if you mean something else! Like misusing specific legal or sporting terms...)

Which term is appropriate here? What would you suggest? (honest question)

"hugely" or "a lot" or "to O(XXX)" whatever the new XXX complexity is.

"to O(xxx)" is a good idea, in terms of keeping it mathematical and accurate. I like that best. "hugely" makes me giggle, because I really hear "bigly" when I see/hear it.

Art term?

https://en.wiktionary.org/wiki/term_of_art

Ah, thanks. I could only think of art as in literal, artistic art.

If you have that tendency, you just need to think of TAOCP, this industry's best distillation of intellectual achievement, with the word "art" in its name.

I'm disappointed that the page has not been fixed...