Average Error: 31.2 → 0
Time: 987.0ms
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 r80922 = re;
        double r80923 = r80922 * r80922;
        double r80924 = im;
        double r80925 = r80924 * r80924;
        double r80926 = r80923 + r80925;
        double r80927 = sqrt(r80926);
        double r80928 = log(r80927);
        return r80928;
}
↓
double f(double re, double im) {
        double r80929 = re;
        double r80930 = im;
        double r80931 = hypot(r80929, r80930);
        double r80932 = log(r80931);
        return r80932;
}

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 31.2

    \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
  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 2020001 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))