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18

To add to Lutz Lehmann's answer, you can look up the latency for the CPU instructions in this comprehensive table by Anger Fog. For example, on the Intel Ivy Bridge processors: FADD / FSUB (floating point add and subtract) both take 3 cycles FMUL (multiply) takes 5 cycles FDIV (divide) takes 10-24 cycles FYL2X ($y \cdot \log_2(x)$) takes 90-106 cycles F2XM1 ...


11

$\exp$, $\sin$, $\tan$ and their inverse and otherwise related functions are transcendental, defined by an infinite power series. Meaning it takes some effort to evaluate uniformly good approximations. This is done via argument simplification using the properties of these functions, and polynomial approximations, or using quotients of polynomials à la Padé ...


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