math.square on complex, imaginary part

Average Error: 0.2 → 0.1

Time: 4.5s

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 r10957 = re;
        double r10958 = im;
        double r10959 = r10957 * r10958;
        double r10960 = r10958 * r10957;
        double r10961 = r10959 + r10960;
        return r10961;
}

↓

double f(double re, double im) {
        double r10962 = im;
        double r10963 = r10962 + r10962;
        double r10964 = re;
        double r10965 = r10963 * r10964;
        return r10965;
}

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 2019158 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+.p16 (*.p16 re im) (*.p16 im re)))