math.square on complex, real part

Average Error: 0.3 → 0.1

Time: 8.3s

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 r287126 = re;
        double r287127 = r287126 * r287126;
        double r287128 = im;
        double r287129 = r287128 * r287128;
        double r287130 = r287127 - r287129;
        return r287130;
}

↓

double f(double re, double im) {
        double r287131 = re;
        double r287132 = im;
        double r287133 = r287131 - r287132;
        double r287134 = r287132 + r287131;
        double r287135 = r287133 * r287134;
        return r287135;
}

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 2019156 
(FPCore (re im)
  :name "math.square on complex, real part"
  (-.p16 (*.p16 re re) (*.p16 im im)))