Average Error: 31.7 → 0.0
Time: 3.1s
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 r23172 = re;
        double r23173 = r23172 * r23172;
        double r23174 = im;
        double r23175 = r23174 * r23174;
        double r23176 = r23173 + r23175;
        double r23177 = sqrt(r23176);
        double r23178 = log(r23177);
        return r23178;
}
↓
double f(double re, double im) {
        double r23179 = re;
        double r23180 = im;
        double r23181 = hypot(r23179, r23180);
        double r23182 = log(r23181);
        return r23182;
}

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 31.7

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

  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 2019306 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))