Average Error: 30.9 → 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 r850767 = re;
        double r850768 = r850767 * r850767;
        double r850769 = im;
        double r850770 = r850769 * r850769;
        double r850771 = r850768 + r850770;
        double r850772 = sqrt(r850771);
        double r850773 = log(r850772);
        return r850773;
}
↓
double f(double re, double im) {
        double r850774 = re;
        double r850775 = im;
        double r850776 = hypot(r850774, r850775);
        double r850777 = log(r850776);
        return r850777;
}

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 30.9

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

  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 2019146 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))