Average Error: 31.6 → 0.0
Time: 3.1s
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 r42621 = re;
        double r42622 = r42621 * r42621;
        double r42623 = im;
        double r42624 = r42623 * r42623;
        double r42625 = r42622 + r42624;
        double r42626 = sqrt(r42625);
        double r42627 = log(r42626);
        return r42627;
}
↓
double f(double re, double im) {
        double r42628 = re;
        double r42629 = im;
        double r42630 = hypot(r42628, r42629);
        double r42631 = log(r42630);
        return r42631;
}

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 2020042 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))