math.square on complex, real part

Average Error: 0.3 → 0.1

Time: 8.2s

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 r323453 = re;
        double r323454 = r323453 * r323453;
        double r323455 = im;
        double r323456 = r323455 * r323455;
        double r323457 = r323454 - r323456;
        return r323457;
}

↓

double f(double re, double im) {
        double r323458 = re;
        double r323459 = im;
        double r323460 = r323458 - r323459;
        double r323461 = r323459 + r323458;
        double r323462 = r323460 * r323461;
        return r323462;
}

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 2019124 
(FPCore (re im)
  :name "math.square on complex, real part"
  (-.p16 (*.p16 re re) (*.p16 im im)))