Average Error: 30.5 → 0.0
Time: 1.3s
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 r627356 = re;
        double r627357 = r627356 * r627356;
        double r627358 = im;
        double r627359 = r627358 * r627358;
        double r627360 = r627357 + r627359;
        double r627361 = sqrt(r627360);
        double r627362 = log(r627361);
        return r627362;
}
↓
double f(double re, double im) {
        double r627363 = re;
        double r627364 = im;
        double r627365 = hypot(r627363, r627364);
        double r627366 = log(r627365);
        return r627366;
}

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 30.5

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

  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 2019152 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))