Average Error: 30.8 → 0.0
Time: 1.7s
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 r464518 = re;
        double r464519 = r464518 * r464518;
        double r464520 = im;
        double r464521 = r464520 * r464520;
        double r464522 = r464519 + r464521;
        double r464523 = sqrt(r464522);
        double r464524 = log(r464523);
        return r464524;
}
↓
double f(double re, double im) {
        double r464525 = re;
        double r464526 = im;
        double r464527 = hypot(r464525, r464526);
        double r464528 = log(r464527);
        return r464528;
}

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 30.8

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

  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 2019119 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))