Average Error: 31.6 → 0.0
Time: 2.4s
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 r29460 = re;
        double r29461 = r29460 * r29460;
        double r29462 = im;
        double r29463 = r29462 * r29462;
        double r29464 = r29461 + r29463;
        double r29465 = sqrt(r29464);
        double r29466 = log(r29465);
        return r29466;
}
↓
double f(double re, double im) {
        double r29467 = re;
        double r29468 = im;
        double r29469 = hypot(r29467, r29468);
        double r29470 = log(r29469);
        return r29470;
}

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)))))