math.square on complex, real part

Average Error: 0.3 → 0.1

Time: 6.0s

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 r81322 = re;
        double r81323 = r81322 * r81322;
        double r81324 = im;
        double r81325 = r81324 * r81324;
        double r81326 = r81323 - r81325;
        return r81326;
}

↓

double f(double re, double im) {
        double r81327 = re;
        double r81328 = im;
        double r81329 = r81327 - r81328;
        double r81330 = r81328 + r81327;
        double r81331 = r81329 * r81330;
        return r81331;
}

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 2019120 
(FPCore (re im)
  :name "math.square on complex, real part"
  (-.p16 (*.p16 re re) (*.p16 im im)))