math.square on complex, real part

Average Error: 0.3 → 0.1

Time: 34.4s

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 r444179 = re;
        double r444180 = r444179 * r444179;
        double r444181 = im;
        double r444182 = r444181 * r444181;
        double r444183 = r444180 - r444182;
        return r444183;
}

↓

double f(double re, double im) {
        double r444184 = re;
        double r444185 = im;
        double r444186 = r444184 - r444185;
        double r444187 = r444185 + r444184;
        double r444188 = r444186 * r444187;
        return r444188;
}

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 2019146 
(FPCore (re im)
  :name "math.square on complex, real part"
  (-.p16 (*.p16 re re) (*.p16 im im)))