Average Error: 31.9 → 0
Time: 759.0ms
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 r36582 = re;
        double r36583 = r36582 * r36582;
        double r36584 = im;
        double r36585 = r36584 * r36584;
        double r36586 = r36583 + r36585;
        double r36587 = sqrt(r36586);
        double r36588 = log(r36587);
        return r36588;
}
↓
double f(double re, double im) {
        double r36589 = re;
        double r36590 = im;
        double r36591 = hypot(r36589, r36590);
        double r36592 = log(r36591);
        return r36592;
}

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 31.9

    \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
  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 2020060 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))