Average Error: 31.5 → 0.0
Time: 2.7s
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 r86860 = re;
        double r86861 = r86860 * r86860;
        double r86862 = im;
        double r86863 = r86862 * r86862;
        double r86864 = r86861 + r86863;
        double r86865 = sqrt(r86864);
        double r86866 = log(r86865);
        return r86866;
}
↓
double f(double re, double im) {
        double r86867 = re;
        double r86868 = im;
        double r86869 = hypot(r86867, r86868);
        double r86870 = log(r86869);
        return r86870;
}

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)))))