math.square on complex, real part

Average Error: 0.3 → 0.1

Time: 5.9s

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 r74428 = re;
        double r74429 = r74428 * r74428;
        double r74430 = im;
        double r74431 = r74430 * r74430;
        double r74432 = r74429 - r74431;
        return r74432;
}

↓

double f(double re, double im) {
        double r74433 = re;
        double r74434 = im;
        double r74435 = r74433 - r74434;
        double r74436 = r74434 + r74433;
        double r74437 = r74435 * r74436;
        return r74437;
}

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 2019104 
(FPCore (re im)
  :name "math.square on complex, real part"
  (-.p16 (*.p16 re re) (*.p16 im im)))