Average Error: 30.8 → 0
Time: 5.5s
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 r2286221 = re;
        double r2286222 = r2286221 * r2286221;
        double r2286223 = im;
        double r2286224 = r2286223 * r2286223;
        double r2286225 = r2286222 + r2286224;
        double r2286226 = sqrt(r2286225);
        double r2286227 = log(r2286226);
        return r2286227;
}
↓
double f(double re, double im) {
        double r2286228 = re;
        double r2286229 = im;
        double r2286230 = hypot(r2286228, r2286229);
        double r2286231 = log(r2286230);
        return r2286231;
}

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 30.8

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

  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 2019168 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))