math.square on complex, imaginary part

Average Error: 0.1 → 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 r8515 = re;
        double r8516 = im;
        double r8517 = r8515 * r8516;
        double r8518 = r8516 * r8515;
        double r8519 = r8517 + r8518;
        return r8519;
}

↓

double f(double re, double im) {
        double r8520 = im;
        double r8521 = r8520 + r8520;
        double r8522 = re;
        double r8523 = r8521 * r8522;
        return r8523;
}

Error

Bits error versus re

Bits error versus im

Derivation

1. Initial program 0.1

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

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 2019133 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+.p16 (*.p16 re im) (*.p16 im re)))