math.square on complex, imaginary part

Average Error: 0.2 → 0.1

Time: 5.6s

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 r11093 = re;
        double r11094 = im;
        double r11095 = r11093 * r11094;
        double r11096 = r11094 * r11093;
        double r11097 = r11095 + r11096;
        return r11097;
}

↓

double f(double re, double im) {
        double r11098 = im;
        double r11099 = r11098 + r11098;
        double r11100 = re;
        double r11101 = r11099 * r11100;
        return r11101;
}

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 2019139 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+.p16 (*.p16 re im) (*.p16 im re)))