math.square on complex, real part

Average Error: 0.3 → 0.1

Time: 17.4s

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 r627063 = re;
        double r627064 = r627063 * r627063;
        double r627065 = im;
        double r627066 = r627065 * r627065;
        double r627067 = r627064 - r627066;
        return r627067;
}

↓

double f(double re, double im) {
        double r627068 = re;
        double r627069 = im;
        double r627070 = r627068 - r627069;
        double r627071 = r627069 + r627068;
        double r627072 = r627070 * r627071;
        return r627072;
}

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 2019158 
(FPCore (re im)
  :name "math.square on complex, real part"
  (-.p16 (*.p16 re re) (*.p16 im im)))