math.square on complex, imaginary part

Average Error: 0.2 → 0.1

Time: 3.8s

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 r10109 = re;
        double r10110 = im;
        double r10111 = r10109 * r10110;
        double r10112 = r10110 * r10109;
        double r10113 = r10111 + r10112;
        return r10113;
}

↓

double f(double re, double im) {
        double r10114 = im;
        double r10115 = r10114 + r10114;
        double r10116 = re;
        double r10117 = r10115 * r10116;
        return r10117;
}

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 2019163 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+.p16 (*.p16 re im) (*.p16 im re)))