Average Error: 31.5 → 0.0
Time: 3.1s
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 r3718927 = re;
        double r3718928 = r3718927 * r3718927;
        double r3718929 = im;
        double r3718930 = r3718929 * r3718929;
        double r3718931 = r3718928 + r3718930;
        double r3718932 = sqrt(r3718931);
        double r3718933 = log(r3718932);
        return r3718933;
}
↓
double f(double re, double im) {
        double r3718934 = re;
        double r3718935 = im;
        double r3718936 = hypot(r3718934, r3718935);
        double r3718937 = log(r3718936);
        return r3718937;
}

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 31.5

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))