math.square on complex, imaginary part

Average Error: 0.2 → 0.1

Time: 5.9s

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 r11217 = re;
        double r11218 = im;
        double r11219 = r11217 * r11218;
        double r11220 = r11218 * r11217;
        double r11221 = r11219 + r11220;
        return r11221;
}

↓

double f(double re, double im) {
        double r11222 = im;
        double r11223 = re;
        double r11224 = r11223 + r11223;
        double r11225 = r11222 * r11224;
        double r11226 = /*Error: no posit support in C */;
        double r11227 = /*Error: no posit support in C */;
        return r11227;
}

Error

Bits error versus re

Bits error versus im

Derivation

1. Initial program 0.2

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

3. Applied introduce-quire 0.2

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

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 2019144 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+.p16 (*.p16 re im) (*.p16 im re)))