Average Error: 31.6 → 0.0
Time: 1.5s
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 r1204057 = re;
        double r1204058 = r1204057 * r1204057;
        double r1204059 = im;
        double r1204060 = r1204059 * r1204059;
        double r1204061 = r1204058 + r1204060;
        double r1204062 = sqrt(r1204061);
        double r1204063 = log(r1204062);
        return r1204063;
}
↓
double f(double re, double im) {
        double r1204064 = re;
        double r1204065 = im;
        double r1204066 = hypot(r1204064, r1204065);
        double r1204067 = log(r1204066);
        return r1204067;
}

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 2019192 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))