math.square on complex, real part

Average Error: 0.3 → 0.1

Time: 11.8s

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 r252199 = re;
        double r252200 = r252199 * r252199;
        double r252201 = im;
        double r252202 = r252201 * r252201;
        double r252203 = r252200 - r252202;
        return r252203;
}

↓

double f(double re, double im) {
        double r252204 = re;
        double r252205 = im;
        double r252206 = r252204 - r252205;
        double r252207 = r252205 + r252204;
        double r252208 = r252206 * r252207;
        return r252208;
}

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 2019155 
(FPCore (re im)
  :name "math.square on complex, real part"
  (-.p16 (*.p16 re re) (*.p16 im im)))