math.square on complex, imaginary part

Average Error: 0.1 → 0.1

Time: 4.6s

Precision: 64

Math

\[\frac{\left(re \cdot im\right)}{\left(im \cdot re\right)}\]

↓

\[\left(\left(im \cdot \left(re + re\right)\right)\right)\]

C

double f(double re, double im) {
        double r10711 = re;
        double r10712 = im;
        double r10713 = r10711 * r10712;
        double r10714 = r10712 * r10711;
        double r10715 = r10713 + r10714;
        return r10715;
}

↓

double f(double re, double im) {
        double r10716 = im;
        double r10717 = re;
        double r10718 = r10717 + r10717;
        double r10719 = r10716 * r10718;
        double r10720 = /*Error: no posit support in C */;
        double r10721 = /*Error: no posit support in C */;
        return r10721;
}

Error

Bits error versus re

Bits error versus im

Derivation

1. Initial program 0.1

   \[\frac{\left(re \cdot im\right)}{\left(im \cdot re\right)}\]
2. Using strategy rm

3. Applied introduce-quire 0.1

   \[\leadsto \color{blue}{\left(\left(\frac{\left(re \cdot im\right)}{\left(im \cdot re\right)}\right)\right)}\]

4. Simplified 0.1

   \[\leadsto \color{blue}{\left(\left(im \cdot \left(\frac{re}{re}\right)\right)\right)}\]

5. Final simplification 0.1

   \[\leadsto \left(\left(im \cdot \left(re + re\right)\right)\right)\]

Reproduce

herbie shell --seed 2019152 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+.p16 (*.p16 re im) (*.p16 im re)))