math.square on complex, real part

Average Error: 0.3 → 0.1

Time: 34.5s

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 r443612 = re;
        double r443613 = r443612 * r443612;
        double r443614 = im;
        double r443615 = r443614 * r443614;
        double r443616 = r443613 - r443615;
        return r443616;
}

↓

double f(double re, double im) {
        double r443617 = re;
        double r443618 = im;
        double r443619 = r443617 - r443618;
        double r443620 = r443618 + r443617;
        double r443621 = r443619 * r443620;
        return r443621;
}

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 2019141 
(FPCore (re im)
  :name "math.square on complex, real part"
  (-.p16 (*.p16 re re) (*.p16 im im)))