math.square on complex, real part

Average Error: 0.3 → 0.1

Time: 14.9s

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 r592742 = re;
        double r592743 = r592742 * r592742;
        double r592744 = im;
        double r592745 = r592744 * r592744;
        double r592746 = r592743 - r592745;
        return r592746;
}

↓

double f(double re, double im) {
        double r592747 = re;
        double r592748 = im;
        double r592749 = r592747 - r592748;
        double r592750 = r592748 + r592747;
        double r592751 = r592749 * r592750;
        return r592751;
}

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 2019162 
(FPCore (re im)
  :name "math.square on complex, real part"
  (-.p16 (*.p16 re re) (*.p16 im im)))