math.square on complex, imaginary part

Average Error: 0.1 → 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 r8525 = re;
        double r8526 = im;
        double r8527 = r8525 * r8526;
        double r8528 = r8526 * r8525;
        double r8529 = r8527 + r8528;
        return r8529;
}

↓

double f(double re, double im) {
        double r8530 = im;
        double r8531 = r8530 + r8530;
        double r8532 = re;
        double r8533 = r8531 * r8532;
        return r8533;
}

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 2019134 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+.p16 (*.p16 re im) (*.p16 im re)))