Average Error: 30.3 → 0.0
Time: 6.5s
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 r950077 = re;
        double r950078 = r950077 * r950077;
        double r950079 = im;
        double r950080 = r950079 * r950079;
        double r950081 = r950078 + r950080;
        double r950082 = sqrt(r950081);
        double r950083 = log(r950082);
        return r950083;
}
↓
double f(double re, double im) {
        double r950084 = re;
        double r950085 = im;
        double r950086 = hypot(r950084, r950085);
        double r950087 = log(r950086);
        return r950087;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019138 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))