Average Error: 31.5 → 0.0
Time: 695.0ms
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 r85775 = re;
        double r85776 = r85775 * r85775;
        double r85777 = im;
        double r85778 = r85777 * r85777;
        double r85779 = r85776 + r85778;
        double r85780 = sqrt(r85779);
        double r85781 = log(r85780);
        return r85781;
}
↓
double f(double re, double im) {
        double r85782 = re;
        double r85783 = im;
        double r85784 = hypot(r85782, r85783);
        double r85785 = log(r85784);
        return r85785;
}

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 31.5

    \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
  2. Using strategy rm

  3. Applied hypot-def0.0

    \[\leadsto \log \color{blue}{\left(\mathsf{hypot}\left(re, im\right)\right)}\]

  4. Final simplification0.0

    \[\leadsto \log \left(\mathsf{hypot}\left(re, im\right)\right)\]

Reproduce

herbie shell --seed 2020059 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))