Average Error: 31.4 → 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 r26737 = re;
        double r26738 = r26737 * r26737;
        double r26739 = im;
        double r26740 = r26739 * r26739;
        double r26741 = r26738 + r26740;
        double r26742 = sqrt(r26741);
        double r26743 = log(r26742);
        return r26743;
}
↓
double f(double re, double im) {
        double r26744 = re;
        double r26745 = im;
        double r26746 = hypot(r26744, r26745);
        double r26747 = log(r26746);
        return r26747;
}

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 2019198 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))