math.square on complex, real part

Average Error: 0.3 → 0.1

Time: 10.0s

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 r252180 = re;
        double r252181 = r252180 * r252180;
        double r252182 = im;
        double r252183 = r252182 * r252182;
        double r252184 = r252181 - r252183;
        return r252184;
}

↓

double f(double re, double im) {
        double r252185 = re;
        double r252186 = im;
        double r252187 = r252185 - r252186;
        double r252188 = r252186 + r252185;
        double r252189 = r252187 * r252188;
        return r252189;
}

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 2019153 
(FPCore (re im)
  :name "math.square on complex, real part"
  (-.p16 (*.p16 re re) (*.p16 im im)))