math.square on complex, real part

Average Error: 0.3 → 0.1

Time: 7.4s

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 r282595 = re;
        double r282596 = r282595 * r282595;
        double r282597 = im;
        double r282598 = r282597 * r282597;
        double r282599 = r282596 - r282598;
        return r282599;
}

↓

double f(double re, double im) {
        double r282600 = re;
        double r282601 = im;
        double r282602 = r282600 - r282601;
        double r282603 = r282601 + r282600;
        double r282604 = r282602 * r282603;
        return r282604;
}

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 2019112 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (-.p16 (*.p16 re re) (*.p16 im im)))