math.square on complex, real part

Average Error: 0.3 → 0.1

Time: 6.2s

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 r59351 = re;
        double r59352 = r59351 * r59351;
        double r59353 = im;
        double r59354 = r59353 * r59353;
        double r59355 = r59352 - r59354;
        return r59355;
}

↓

double f(double re, double im) {
        double r59356 = re;
        double r59357 = im;
        double r59358 = r59356 - r59357;
        double r59359 = r59357 + r59356;
        double r59360 = r59358 * r59359;
        return r59360;
}

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 2019125 
(FPCore (re im)
  :name "math.square on complex, real part"
  (-.p16 (*.p16 re re) (*.p16 im im)))