math.square on complex, real part

Average Error: 0.3 → 0.1

Time: 42.3s

Precision: 64

Math

\[\left(re \cdot re\right) - \left(im \cdot im\right)\]

↓

\[\left(re - im\right) \cdot \left(im + re\right)\]

C

double f(double re, double im) {
        double r312257 = re;
        double r312258 = r312257 * r312257;
        double r312259 = im;
        double r312260 = r312259 * r312259;
        double r312261 = r312258 - r312260;
        return r312261;
}

↓

double f(double re, double im) {
        double r312262 = re;
        double r312263 = im;
        double r312264 = r312262 - r312263;
        double r312265 = r312263 + r312262;
        double r312266 = r312264 * r312265;
        return r312266;
}

Error

Bits error versus re

Bits error versus im

Derivation

1. Initial program 0.3

   \[\left(re \cdot re\right) - \left(im \cdot im\right)\]

2. Simplified 0.1

   \[\leadsto \color{blue}{\left(re - im\right) \cdot \left(\frac{im}{re}\right)}\]

3. Final simplification 0.1

   \[\leadsto \left(re - im\right) \cdot \left(im + re\right)\]

Reproduce

herbie shell --seed 2019153 
(FPCore (re im)
  :name "math.square on complex, real part"
  (-.p16 (*.p16 re re) (*.p16 im im)))