Average Error: 31.4 → 0.0
Time: 3.2s
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 r19703 = re;
        double r19704 = r19703 * r19703;
        double r19705 = im;
        double r19706 = r19705 * r19705;
        double r19707 = r19704 + r19706;
        double r19708 = sqrt(r19707);
        double r19709 = log(r19708);
        return r19709;
}
↓
double f(double re, double im) {
        double r19710 = re;
        double r19711 = im;
        double r19712 = hypot(r19710, r19711);
        double r19713 = log(r19712);
        return r19713;
}

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 31.4

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

  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 2019195 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))