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Yeah, I once worked at a place where the compiler team was assigned the unpleasant task of implementing a long list of trigonometry functions. They struggled for many months to get the accuracy that was required of them, and when they did the performance was abysmal compared to the competition.
In hindsight, they probably didn't have anybody with the right background and should have contracted out the job. I certainly didn't have the necessary knowledge, either.
And similarly, entire generations of programmers were never taught Horner's scheme. You can see it in the article, where they write stuff like
(10 muls, 3 muladds)instead of the faster
(1 mul, 3 muladds)