Average Error: 0.3 → 0.1
Time: 5.7s
Precision: 64
\[\left(re \cdot re\right) - \left(im \cdot im\right)\]
↓
\[\left(re - im\right) \cdot \left(im + re\right)\]
\left(re \cdot re\right) - \left(im \cdot im\right)
↓
\left(re - im\right) \cdot \left(im + re\right)
double f(double re, double im) {
        double r88696 = re;
        double r88697 = r88696 * r88696;
        double r88698 = im;
        double r88699 = r88698 * r88698;
        double r88700 = r88697 - r88699;
        return r88700;
}
↓
double f(double re, double im) {
        double r88701 = re;
        double r88702 = im;
        double r88703 = r88701 - r88702;
        double r88704 = r88702 + r88701;
        double r88705 = r88703 * r88704;
        return r88705;
}

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. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019120 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (-.p16 (*.p16 re re) (*.p16 im im)))