math.square on complex, real part

Average Error: 0.3 → 0.1

Time: 25.0s

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 r735470 = re;
        double r735471 = r735470 * r735470;
        double r735472 = im;
        double r735473 = r735472 * r735472;
        double r735474 = r735471 - r735473;
        return r735474;
}

↓

double f(double re, double im) {
        double r735475 = re;
        double r735476 = im;
        double r735477 = r735475 - r735476;
        double r735478 = r735476 + r735475;
        double r735479 = r735477 * r735478;
        return r735479;
}

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 2019158 
(FPCore (re im)
  :name "math.square on complex, real part"
  (-.p16 (*.p16 re re) (*.p16 im im)))