Average Error: 32.6 → 0
Time: 972.0ms
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 r31482 = re;
        double r31483 = r31482 * r31482;
        double r31484 = im;
        double r31485 = r31484 * r31484;
        double r31486 = r31483 + r31485;
        double r31487 = sqrt(r31486);
        double r31488 = log(r31487);
        return r31488;
}
↓
double f(double re, double im) {
        double r31489 = re;
        double r31490 = im;
        double r31491 = hypot(r31489, r31490);
        double r31492 = log(r31491);
        return r31492;
}

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 32.6

    \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
  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 2020002 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))