Average Error: 30.7 → 0
Time: 9.2s
Precision: 64
\[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
↓
\[\log \left(\mathsf{hypot}\left(re, im\right)\right)\]
\log \left(\sqrt{re \cdot re + im \cdot im}\right)
↓
\log \left(\mathsf{hypot}\left(re, im\right)\right)
double f(double re, double im) {
        double r820878 = re;
        double r820879 = r820878 * r820878;
        double r820880 = im;
        double r820881 = r820880 * r820880;
        double r820882 = r820879 + r820881;
        double r820883 = sqrt(r820882);
        double r820884 = log(r820883);
        return r820884;
}
↓
double f(double re, double im) {
        double r820885 = re;
        double r820886 = im;
        double r820887 = hypot(r820885, r820886);
        double r820888 = log(r820887);
        return r820888;
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 30.7

    \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]

  2. Simplified0

    \[\leadsto \color{blue}{\log \left(\mathsf{hypot}\left(re, im\right)\right)}\]

  3. Final simplification0

    \[\leadsto \log \left(\mathsf{hypot}\left(re, im\right)\right)\]

Reproduce

herbie shell --seed 2019134 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))