math.square on complex, real part

Average Error: 0.3 → 0.1

Time: 16.5s

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 r1038345 = re;
        double r1038346 = r1038345 * r1038345;
        double r1038347 = im;
        double r1038348 = r1038347 * r1038347;
        double r1038349 = r1038346 - r1038348;
        return r1038349;
}

↓

double f(double re, double im) {
        double r1038350 = re;
        double r1038351 = im;
        double r1038352 = r1038350 - r1038351;
        double r1038353 = r1038351 + r1038350;
        double r1038354 = r1038352 * r1038353;
        return r1038354;
}

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 2019134 
(FPCore (re im)
  :name "math.square on complex, real part"
  (-.p16 (*.p16 re re) (*.p16 im im)))