math.square on complex, imaginary part

Average Error: 0.2 → 0.1

Time: 4.5s

Precision: 64

Math

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

↓

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

C

double f(double re, double im) {
        double r10139 = re;
        double r10140 = im;
        double r10141 = r10139 * r10140;
        double r10142 = r10140 * r10139;
        double r10143 = r10141 + r10142;
        return r10143;
}

↓

double f(double re, double im) {
        double r10144 = im;
        double r10145 = r10144 + r10144;
        double r10146 = re;
        double r10147 = r10145 * r10146;
        return r10147;
}

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

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

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)))