Average Error: 31.3 → 0
Time: 3.5s
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 r26755 = re;
        double r26756 = r26755 * r26755;
        double r26757 = im;
        double r26758 = r26757 * r26757;
        double r26759 = r26756 + r26758;
        double r26760 = sqrt(r26759);
        double r26761 = log(r26760);
        return r26761;
}
↓
double f(double re, double im) {
        double r26762 = re;
        double r26763 = im;
        double r26764 = hypot(r26762, r26763);
        double r26765 = log(r26764);
        return r26765;
}

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 31.3

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

  2. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))