Average Error: 0.3 → 0.1
Time: 6.6s
Precision: 64
\[re \cdot re - im \cdot im\]
↓
\[\left(re - im\right) \cdot \left(im + re\right)\]
double f(double re, double im) {
        double r22734 = re;
        double r22735 = r22734 * r22734;
        double r22736 = im;
        double r22737 = r22736 * r22736;
        double r22738 = r22735 - r22737;
        return r22738;
}
↓
double f(double re, double im) {
        double r22739 = re;
        double r22740 = im;
        double r22741 = r22739 - r22740;
        double r22742 = r22740 + r22739;
        double r22743 = r22741 * r22742;
        return r22743;
}


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

Error

Bits error versus re

Bits error versus im

Derivation

  1. Initial program 0.3

    \[\left(re \cdot re\right) - \left(im \cdot im\right)\]

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019101 
(FPCore (re im)
  :name "math.square on complex, real part"
  (-.p16 (*.p16 re re) (*.p16 im im)))