Average Error: 32.1 → 0.0
Time: 1.0s
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 r24629 = re;
        double r24630 = r24629 * r24629;
        double r24631 = im;
        double r24632 = r24631 * r24631;
        double r24633 = r24630 + r24632;
        double r24634 = sqrt(r24633);
        double r24635 = log(r24634);
        return r24635;
}
↓
double f(double re, double im) {
        double r24636 = re;
        double r24637 = im;
        double r24638 = hypot(r24636, r24637);
        double r24639 = log(r24638);
        return r24639;
}

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 32.1

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019212 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))