Average Error: 31.6 → 0.0
Time: 2.9s
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 r2746365 = re;
        double r2746366 = r2746365 * r2746365;
        double r2746367 = im;
        double r2746368 = r2746367 * r2746367;
        double r2746369 = r2746366 + r2746368;
        double r2746370 = sqrt(r2746369);
        double r2746371 = log(r2746370);
        return r2746371;
}
↓
double f(double re, double im) {
        double r2746372 = re;
        double r2746373 = im;
        double r2746374 = hypot(r2746372, r2746373);
        double r2746375 = log(r2746374);
        return r2746375;
}

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 31.6

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

  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 2019179 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))