math.square on complex, imaginary part

Average Error: 0.2 → 0.1

Time: 5.5s

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 r10889 = re;
        double r10890 = im;
        double r10891 = r10889 * r10890;
        double r10892 = r10890 * r10889;
        double r10893 = r10891 + r10892;
        return r10893;
}

↓

double f(double re, double im) {
        double r10894 = im;
        double r10895 = r10894 + r10894;
        double r10896 = re;
        double r10897 = r10895 * r10896;
        return r10897;
}

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 2019139 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+.p16 (*.p16 re im) (*.p16 im re)))