math.square on complex, real part

Average Error: 0.3 → 0.1

Time: 14.0s

Precision: 64

Math

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

↓

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

C

double f(double re, double im) {
        double r653823 = re;
        double r653824 = r653823 * r653823;
        double r653825 = im;
        double r653826 = r653825 * r653825;
        double r653827 = r653824 - r653826;
        return r653827;
}

↓

double f(double re, double im) {
        double r653828 = re;
        double r653829 = im;
        double r653830 = r653828 - r653829;
        double r653831 = r653829 + r653828;
        double r653832 = r653830 * r653831;
        return r653832;
}

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

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

Reproduce

herbie shell --seed 2019168 
(FPCore (re im)
  :name "math.square on complex, real part"
  (-.p16 (*.p16 re re) (*.p16 im im)))