Average Error: 30.7 → 0
Time: 1.2s
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 r701762 = re;
        double r701763 = r701762 * r701762;
        double r701764 = im;
        double r701765 = r701764 * r701764;
        double r701766 = r701763 + r701765;
        double r701767 = sqrt(r701766);
        double r701768 = log(r701767);
        return r701768;
}
↓
double f(double re, double im) {
        double r701769 = re;
        double r701770 = im;
        double r701771 = hypot(r701769, r701770);
        double r701772 = log(r701771);
        return r701772;
}

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 30.7

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

  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 2019154 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))