Average Error: 30.3 → 0
Time: 1.8s
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 r1338855 = re;
        double r1338856 = r1338855 * r1338855;
        double r1338857 = im;
        double r1338858 = r1338857 * r1338857;
        double r1338859 = r1338856 + r1338858;
        double r1338860 = sqrt(r1338859);
        double r1338861 = log(r1338860);
        return r1338861;
}
↓
double f(double re, double im) {
        double r1338862 = re;
        double r1338863 = im;
        double r1338864 = hypot(r1338862, r1338863);
        double r1338865 = log(r1338864);
        return r1338865;
}

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 30.3

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

  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 2019125 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))