Average Error: 31.8 → 0
Time: 900.0ms
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 r46879 = re;
        double r46880 = r46879 * r46879;
        double r46881 = im;
        double r46882 = r46881 * r46881;
        double r46883 = r46880 + r46882;
        double r46884 = sqrt(r46883);
        double r46885 = log(r46884);
        return r46885;
}
↓
double f(double re, double im) {
        double r46886 = re;
        double r46887 = im;
        double r46888 = hypot(r46886, r46887);
        double r46889 = log(r46888);
        return r46889;
}

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 31.8

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

  3. Applied hypot-def0

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

  4. Final simplification0

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

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))