math.square on complex, imaginary part

Average Error: 0.2 → 0.1

Time: 6.1s

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 r11139 = re;
        double r11140 = im;
        double r11141 = r11139 * r11140;
        double r11142 = r11140 * r11139;
        double r11143 = r11141 + r11142;
        return r11143;
}

↓

double f(double re, double im) {
        double r11144 = im;
        double r11145 = re;
        double r11146 = r11145 + r11145;
        double r11147 = r11144 * r11146;
        double r11148 = /*Error: no posit support in C */;
        double r11149 = /*Error: no posit support in C */;
        return r11149;
}

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 2019138 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+.p16 (*.p16 re im) (*.p16 im re)))