Average Error: 31.8 → 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 r26752 = re;
        double r26753 = r26752 * r26752;
        double r26754 = im;
        double r26755 = r26754 * r26754;
        double r26756 = r26753 + r26755;
        double r26757 = sqrt(r26756);
        double r26758 = log(r26757);
        return r26758;
}
↓
double f(double re, double im) {
        double r26759 = re;
        double r26760 = im;
        double r26761 = hypot(r26759, r26760);
        double r26762 = log(r26761);
        return r26762;
}

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 31.8

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

  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 2019323 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))