Average Error: 30.7 → 0.0
Time: 1.3s
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 r151418 = re;
        double r151419 = r151418 * r151418;
        double r151420 = im;
        double r151421 = r151420 * r151420;
        double r151422 = r151419 + r151421;
        double r151423 = sqrt(r151422);
        double r151424 = log(r151423);
        return r151424;
}
↓
double f(double re, double im) {
        double r151425 = re;
        double r151426 = im;
        double r151427 = hypot(r151425, r151426);
        double r151428 = log(r151427);
        return r151428;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))