Average Error: 30.9 → 0
Time: 1.8s
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 r317729 = re;
        double r317730 = r317729 * r317729;
        double r317731 = im;
        double r317732 = r317731 * r317731;
        double r317733 = r317730 + r317732;
        double r317734 = sqrt(r317733);
        double r317735 = log(r317734);
        return r317735;
}
↓
double f(double re, double im) {
        double r317736 = re;
        double r317737 = im;
        double r317738 = hypot(r317736, r317737);
        double r317739 = log(r317738);
        return r317739;
}

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

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019112 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))