Average Error: 31.5 → 0
Time: 1.2s
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 r2918113 = re;
        double r2918114 = r2918113 * r2918113;
        double r2918115 = im;
        double r2918116 = r2918115 * r2918115;
        double r2918117 = r2918114 + r2918116;
        double r2918118 = sqrt(r2918117);
        double r2918119 = log(r2918118);
        return r2918119;
}
↓
double f(double re, double im) {
        double r2918120 = re;
        double r2918121 = im;
        double r2918122 = hypot(r2918120, r2918121);
        double r2918123 = log(r2918122);
        return r2918123;
}

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

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019173 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))