math.square on complex, real part

Average Error: 0.3 → 0.1

Time: 9.7s

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 r252231 = re;
        double r252232 = r252231 * r252231;
        double r252233 = im;
        double r252234 = r252233 * r252233;
        double r252235 = r252232 - r252234;
        return r252235;
}

↓

double f(double re, double im) {
        double r252236 = re;
        double r252237 = im;
        double r252238 = r252236 - r252237;
        double r252239 = r252237 + r252236;
        double r252240 = r252238 * r252239;
        return r252240;
}

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 2019154 
(FPCore (re im)
  :name "math.square on complex, real part"
  (-.p16 (*.p16 re re) (*.p16 im im)))