Average Error: 31.8 → 0.0
Time: 8.7s
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 r2987168 = re;
        double r2987169 = r2987168 * r2987168;
        double r2987170 = im;
        double r2987171 = r2987170 * r2987170;
        double r2987172 = r2987169 + r2987171;
        double r2987173 = sqrt(r2987172);
        double r2987174 = log(r2987173);
        return r2987174;
}
↓
double f(double re, double im) {
        double r2987175 = re;
        double r2987176 = im;
        double r2987177 = hypot(r2987175, r2987176);
        double r2987178 = log(r2987177);
        return r2987178;
}

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 31.8

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

  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 2019200 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))