Average Error: 0.1 → 0.1
Time: 3.7s
Precision: 64
\[\frac{\left(re \cdot im\right)}{\left(im \cdot re\right)}\]
↓
\[im \cdot \left(re + re\right)\]
\frac{\left(re \cdot im\right)}{\left(im \cdot re\right)}
↓
im \cdot \left(re + re\right)
double f(double re, double im) {
        double r8813 = re;
        double r8814 = im;
        double r8815 = r8813 * r8814;
        double r8816 = r8814 * r8813;
        double r8817 = r8815 + r8816;
        return r8817;
}
↓
double f(double re, double im) {
        double r8818 = im;
        double r8819 = re;
        double r8820 = r8819 + r8819;
        double r8821 = r8818 * r8820;
        return r8821;
}

Error

Bits error versus re

Bits error versus im

Derivation

  1. Initial program 0.1

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

  2. Simplified0.1

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

  4. Applied 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 2019120 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+.p16 (*.p16 re im) (*.p16 im re)))