Average Error: 31.0 → 0.0
Time: 1.6s
Precision: 64
\[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
↓
\[\log \left(\sqrt{re^2 + im^2}^*\right)\]
\log \left(\sqrt{re \cdot re + im \cdot im}\right)
↓
\log \left(\sqrt{re^2 + im^2}^*\right)
double f(double re, double im) {
        double r1221718 = re;
        double r1221719 = r1221718 * r1221718;
        double r1221720 = im;
        double r1221721 = r1221720 * r1221720;
        double r1221722 = r1221719 + r1221721;
        double r1221723 = sqrt(r1221722);
        double r1221724 = log(r1221723);
        return r1221724;
}
↓
double f(double re, double im) {
        double r1221725 = re;
        double r1221726 = im;
        double r1221727 = hypot(r1221725, r1221726);
        double r1221728 = log(r1221727);
        return r1221728;
}

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. Simplified0.0

    \[\leadsto \color{blue}{\log \left(\sqrt{re^2 + im^2}^*\right)}\]

  3. Final simplification0.0

    \[\leadsto \log \left(\sqrt{re^2 + im^2}^*\right)\]

Reproduce

herbie shell --seed 2019104 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))