Average Error: 31.1 → 0
Time: 1.6s
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 r12287 = re;
        double r12288 = r12287 * r12287;
        double r12289 = im;
        double r12290 = r12289 * r12289;
        double r12291 = r12288 + r12290;
        double r12292 = sqrt(r12291);
        double r12293 = log(r12292);
        return r12293;
}
↓
double f(double re, double im) {
        double r12294 = re;
        double r12295 = im;
        double r12296 = hypot(r12294, r12295);
        double r12297 = log(r12296);
        return r12297;
}

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 31.1

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

  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 2019315 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))