math.square on complex, real part

Average Error: 0.3 → 0.1

Time: 14.7s

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 r572811 = re;
        double r572812 = r572811 * r572811;
        double r572813 = im;
        double r572814 = r572813 * r572813;
        double r572815 = r572812 - r572814;
        return r572815;
}

↓

double f(double re, double im) {
        double r572816 = re;
        double r572817 = im;
        double r572818 = r572816 - r572817;
        double r572819 = r572817 + r572816;
        double r572820 = r572818 * r572819;
        return r572820;
}

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 2019165 
(FPCore (re im)
  :name "math.square on complex, real part"
  (-.p16 (*.p16 re re) (*.p16 im im)))