math.square on complex, real part

Average Error: 0.3 → 0.1

Time: 34.3s

Precision: 64

Math

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

↓

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

C

double f(double re, double im) {
        double r443690 = re;
        double r443691 = r443690 * r443690;
        double r443692 = im;
        double r443693 = r443692 * r443692;
        double r443694 = r443691 - r443693;
        return r443694;
}

↓

double f(double re, double im) {
        double r443695 = re;
        double r443696 = im;
        double r443697 = r443695 - r443696;
        double r443698 = r443696 + r443695;
        double r443699 = r443697 * r443698;
        return r443699;
}

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. Simplified 0.1

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

3. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019151 
(FPCore (re im)
  :name "math.square on complex, real part"
  (-.p16 (*.p16 re re) (*.p16 im im)))