math.square on complex, imaginary part

Average Error: 0.1 → 0.1

Time: 1.9m

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 r16683 = re;
        double r16684 = im;
        double r16685 = r16683 * r16684;
        double r16686 = r16684 * r16683;
        double r16687 = r16685 + r16686;
        return r16687;
}

↓

double f(double re, double im) {
        double r16688 = im;
        double r16689 = re;
        double r16690 = r16689 + r16689;
        double r16691 = r16688 * r16690;
        double r16692 = /*Error: no posit support in C */;
        double r16693 = /*Error: no posit support in C */;
        return r16693;
}

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 2019153 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+.p16 (*.p16 re im) (*.p16 im re)))