Average Error: 31.3 → 0.0
Time: 8.1s
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 r914865 = re;
        double r914866 = r914865 * r914865;
        double r914867 = im;
        double r914868 = r914867 * r914867;
        double r914869 = r914866 + r914868;
        double r914870 = sqrt(r914869);
        double r914871 = log(r914870);
        return r914871;
}
↓
double f(double re, double im) {
        double r914872 = re;
        double r914873 = im;
        double r914874 = hypot(r914872, r914873);
        double r914875 = log(r914874);
        return r914875;
}

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 31.3

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

  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 2019142 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))