math.square on complex, real part

Average Error: 0.3 → 0.1

Time: 16.0s

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 r1051711 = re;
        double r1051712 = r1051711 * r1051711;
        double r1051713 = im;
        double r1051714 = r1051713 * r1051713;
        double r1051715 = r1051712 - r1051714;
        return r1051715;
}

↓

double f(double re, double im) {
        double r1051716 = re;
        double r1051717 = im;
        double r1051718 = r1051716 - r1051717;
        double r1051719 = r1051717 + r1051716;
        double r1051720 = r1051718 * r1051719;
        return r1051720;
}

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 2019130 
(FPCore (re im)
  :name "math.square on complex, real part"
  (-.p16 (*.p16 re re) (*.p16 im im)))