math.square on complex, real part

Average Error: 0.3 → 0.1

Time: 48.3s

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 r312318 = re;
        double r312319 = r312318 * r312318;
        double r312320 = im;
        double r312321 = r312320 * r312320;
        double r312322 = r312319 - r312321;
        return r312322;
}

↓

double f(double re, double im) {
        double r312323 = re;
        double r312324 = im;
        double r312325 = r312323 - r312324;
        double r312326 = r312324 + r312323;
        double r312327 = r312325 * r312326;
        return r312327;
}

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 2019151 
(FPCore (re im)
  :name "math.square on complex, real part"
  (-.p16 (*.p16 re re) (*.p16 im im)))