math.square on complex, imaginary part

Average Error: 0.1 → 0.1

Time: 4.6s

Precision: 64

Math

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

↓

\[re \cdot \left(im + im\right)\]

C

double f(double re, double im) {
        double r124186 = re;
        double r124187 = im;
        double r124188 = r124186 * r124187;
        double r124189 = r124187 * r124186;
        double r124190 = r124188 + r124189;
        return r124190;
}

↓

double f(double re, double im) {
        double r124191 = re;
        double r124192 = im;
        double r124193 = r124192 + r124192;
        double r124194 = r124191 * r124193;
        return r124194;
}

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. Simplified 0.1

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

3. Final simplification 0.1

   \[\leadsto re \cdot \left(im + im\right)\]

Reproduce

herbie shell --seed 2019165 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+.p16 (*.p16 re im) (*.p16 im re)))