Average Error: 32.1 → 0
Time: 952.0ms
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 r91988 = re;
        double r91989 = r91988 * r91988;
        double r91990 = im;
        double r91991 = r91990 * r91990;
        double r91992 = r91989 + r91991;
        double r91993 = sqrt(r91992);
        double r91994 = log(r91993);
        return r91994;
}
↓
double f(double re, double im) {
        double r91995 = re;
        double r91996 = im;
        double r91997 = hypot(r91995, r91996);
        double r91998 = log(r91997);
        return r91998;
}

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 32.1

    \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
  2. Using strategy rm

  3. Applied hypot-def0

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

  4. Final simplification0

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

Reproduce

herbie shell --seed 2020049 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))