Average Error: 0.2 → 0.1
Time: 3.6s
Precision: 64
\[re \cdot im + im \cdot re\]
↓
\[im \cdot \left(re + re\right)\]
double f(double re, double im) {
        double r8829 = re;
        double r8830 = im;
        double r8831 = r8829 * r8830;
        double r8832 = r8830 * r8829;
        double r8833 = r8831 + r8832;
        return r8833;
}
↓
double f(double re, double im) {
        double r8834 = im;
        double r8835 = re;
        double r8836 = r8835 + r8835;
        double r8837 = r8834 * r8836;
        return r8837;
}


re \cdot im + im \cdot re
↓
im \cdot \left(re + re\right)

Error

Bits error versus re

Bits error versus im

Derivation

  1. Initial program 0.2

    \[\frac{\left(re \cdot im\right)}{\left(im \cdot re\right)}\]

  2. Simplified0.2

    \[\leadsto \color{blue}{\frac{\left(im \cdot re\right)}{\left(im \cdot re\right)}}\]
  3. Using strategy rm

  4. Applied p16-distribute-lft-out0.1

    \[\leadsto \color{blue}{im \cdot \left(\frac{re}{re}\right)}\]

  5. Final simplification0.1

    \[\leadsto im \cdot \left(re + re\right)\]

Reproduce

herbie shell --seed 2019102 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+.p16 (*.p16 re im) (*.p16 im re)))