Average Error: 31.0 → 0
Time: 3.1s
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 r30773 = re;
        double r30774 = r30773 * r30773;
        double r30775 = im;
        double r30776 = r30775 * r30775;
        double r30777 = r30774 + r30776;
        double r30778 = sqrt(r30777);
        double r30779 = log(r30778);
        return r30779;
}
↓
double f(double re, double im) {
        double r30780 = re;
        double r30781 = im;
        double r30782 = hypot(r30780, r30781);
        double r30783 = log(r30782);
        return r30783;
}

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 31.0

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

  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 2019194 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))