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 r17189 = re;
        double r17190 = im;
        double r17191 = r17189 * r17190;
        double r17192 = r17190 * r17189;
        double r17193 = r17191 + r17192;
        return r17193;
}

↓

double f(double re, double im) {
        double r17194 = im;
        double r17195 = re;
        double r17196 = r17195 + r17195;
        double r17197 = r17194 * r17196;
        double r17198 = /*Error: no posit support in C */;
        double r17199 = /*Error: no posit support in C */;
        return r17199;
}

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