math.square on complex, real part

Average Error: 0.3 → 0.1

Time: 10.6s

Precision: 64

Math

\[\left(re \cdot re\right) - \left(im \cdot im\right)\]

↓

\[\left(re - im\right) \cdot \left(\frac{im}{re}\right)\]

C

double f(double re, double im) {
        double r513426 = re;
        double r513427 = r513426 * r513426;
        double r513428 = im;
        double r513429 = r513428 * r513428;
        double r513430 = r513427 - r513429;
        return r513430;
}

↓

double f(double re, double im) {
        double r513431 = re;
        double r513432 = im;
        double r513433 = r513431 - r513432;
        double r513434 = r513432 + r513431;
        double r513435 = r513433 * r513434;
        return r513435;
}

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

   \[\leadsto \left(re - im\right) \cdot \left(\frac{im}{re}\right)\]

Reproduce

herbie shell --seed 2019164 
(FPCore (re im)
  :name "math.square on complex, real part"
  (-.p16 (*.p16 re re) (*.p16 im im)))