Average Error: 31.3 → 0
Time: 918.0ms
Precision: 64
\[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
↓
\[\log \left(\sqrt{1} \cdot \mathsf{hypot}\left(re, im\right)\right)\]
\log \left(\sqrt{re \cdot re + im \cdot im}\right)
↓
\log \left(\sqrt{1} \cdot \mathsf{hypot}\left(re, im\right)\right)
double f(double re, double im) {
        double r44849 = re;
        double r44850 = r44849 * r44849;
        double r44851 = im;
        double r44852 = r44851 * r44851;
        double r44853 = r44850 + r44852;
        double r44854 = sqrt(r44853);
        double r44855 = log(r44854);
        return r44855;
}
↓
double f(double re, double im) {
        double r44856 = 1.0;
        double r44857 = sqrt(r44856);
        double r44858 = re;
        double r44859 = im;
        double r44860 = hypot(r44858, r44859);
        double r44861 = r44857 * r44860;
        double r44862 = log(r44861);
        return r44862;
}

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 31.3

    \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
  2. Using strategy rm

  3. Applied *-un-lft-identity31.3

    \[\leadsto \log \left(\sqrt{\color{blue}{1 \cdot \left(re \cdot re + im \cdot im\right)}}\right)\]

  4. Applied sqrt-prod31.3

    \[\leadsto \log \color{blue}{\left(\sqrt{1} \cdot \sqrt{re \cdot re + im \cdot im}\right)}\]

  5. Simplified0

    \[\leadsto \log \left(\sqrt{1} \cdot \color{blue}{\mathsf{hypot}\left(re, im\right)}\right)\]

  6. Final simplification0

    \[\leadsto \log \left(\sqrt{1} \cdot \mathsf{hypot}\left(re, im\right)\right)\]

Reproduce

herbie shell --seed 2019352 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))