math.square on complex, imaginary part

Average Error: 0.1 → 0.1

Time: 2.0m

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 r17186 = re;
        double r17187 = im;
        double r17188 = r17186 * r17187;
        double r17189 = r17187 * r17186;
        double r17190 = r17188 + r17189;
        return r17190;
}

↓

double f(double re, double im) {
        double r17191 = im;
        double r17192 = re;
        double r17193 = r17192 + r17192;
        double r17194 = r17191 * r17193;
        double r17195 = /*Error: no posit support in C */;
        double r17196 = /*Error: no posit support in C */;
        return r17196;
}

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)))