math.square on complex, imaginary part

Average Error: 0.2 → 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 r17201 = re;
        double r17202 = im;
        double r17203 = r17201 * r17202;
        double r17204 = r17202 * r17201;
        double r17205 = r17203 + r17204;
        return r17205;
}

↓

double f(double re, double im) {
        double r17206 = im;
        double r17207 = re;
        double r17208 = r17207 + r17207;
        double r17209 = r17206 * r17208;
        double r17210 = /*Error: no posit support in C */;
        double r17211 = /*Error: no posit support in C */;
        return r17211;
}

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 2019151 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+.p16 (*.p16 re im) (*.p16 im re)))