math.square on complex, real part

Average Error: 0.3 → 0.1

Time: 7.2s

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 r282613 = re;
        double r282614 = r282613 * r282613;
        double r282615 = im;
        double r282616 = r282615 * r282615;
        double r282617 = r282614 - r282616;
        return r282617;
}

↓

double f(double re, double im) {
        double r282618 = re;
        double r282619 = im;
        double r282620 = r282618 - r282619;
        double r282621 = r282619 + r282618;
        double r282622 = r282620 * r282621;
        return r282622;
}

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 2019119 
(FPCore (re im)
  :name "math.square on complex, real part"
  (-.p16 (*.p16 re re) (*.p16 im im)))