math.square on complex, imaginary part

Average Error: 0.2 → 0.1

Time: 4.2s

Precision: 64

Math

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

↓

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

C

double f(double re, double im) {
        double r10029 = re;
        double r10030 = im;
        double r10031 = r10029 * r10030;
        double r10032 = r10030 * r10029;
        double r10033 = r10031 + r10032;
        return r10033;
}

↓

double f(double re, double im) {
        double r10034 = im;
        double r10035 = r10034 + r10034;
        double r10036 = re;
        double r10037 = r10035 * r10036;
        return r10037;
}

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. Simplified 0.1

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

3. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019155 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+.p16 (*.p16 re im) (*.p16 im re)))