Average Error: 31.5 → 0.0
Time: 14.5s
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 r1192010 = re;
        double r1192011 = r1192010 * r1192010;
        double r1192012 = im;
        double r1192013 = r1192012 * r1192012;
        double r1192014 = r1192011 + r1192013;
        double r1192015 = sqrt(r1192014);
        double r1192016 = log(r1192015);
        return r1192016;
}
↓
double f(double re, double im) {
        double r1192017 = re;
        double r1192018 = im;
        double r1192019 = hypot(r1192017, r1192018);
        double r1192020 = log(r1192019);
        return r1192020;
}

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 31.5

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

  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 2019165 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))