Average Error: 31.3 → 0
Time: 597.0ms
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 r87492 = re;
        double r87493 = r87492 * r87492;
        double r87494 = im;
        double r87495 = r87494 * r87494;
        double r87496 = r87493 + r87495;
        double r87497 = sqrt(r87496);
        double r87498 = log(r87497);
        return r87498;
}
↓
double f(double re, double im) {
        double r87499 = re;
        double r87500 = im;
        double r87501 = hypot(r87499, r87500);
        double r87502 = log(r87501);
        return r87502;
}

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 31.3

    \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]

  2. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019350 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))