math.square on complex, imaginary part

Average Error: 0.2 → 0.1

Time: 3.2s

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 r8556 = re;
        double r8557 = im;
        double r8558 = r8556 * r8557;
        double r8559 = r8557 * r8556;
        double r8560 = r8558 + r8559;
        return r8560;
}

↓

double f(double re, double im) {
        double r8561 = im;
        double r8562 = r8561 + r8561;
        double r8563 = re;
        double r8564 = r8562 * r8563;
        return r8564;
}

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 2019128 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+.p16 (*.p16 re im) (*.p16 im re)))