math.square on complex, imaginary part

Average Error: 0.2 → 0.1

Time: 3.9s

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 r8508 = re;
        double r8509 = im;
        double r8510 = r8508 * r8509;
        double r8511 = r8509 * r8508;
        double r8512 = r8510 + r8511;
        return r8512;
}

↓

double f(double re, double im) {
        double r8513 = im;
        double r8514 = r8513 + r8513;
        double r8515 = re;
        double r8516 = r8514 * r8515;
        return r8516;
}

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 2019130 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+.p16 (*.p16 re im) (*.p16 im re)))