math.square on complex, real part

Average Error: 0.3 → 0.1

Time: 15.3s

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 r1218543 = re;
        double r1218544 = r1218543 * r1218543;
        double r1218545 = im;
        double r1218546 = r1218545 * r1218545;
        double r1218547 = r1218544 - r1218546;
        return r1218547;
}

↓

double f(double re, double im) {
        double r1218548 = re;
        double r1218549 = im;
        double r1218550 = r1218548 - r1218549;
        double r1218551 = r1218549 + r1218548;
        double r1218552 = r1218550 * r1218551;
        return r1218552;
}

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 2019133 
(FPCore (re im)
  :name "math.square on complex, real part"
  (-.p16 (*.p16 re re) (*.p16 im im)))