Average Error: 0.4 → 0.3
Time: 33.0s
Precision: 64
\[\left(\left(\left(x.re \cdot x.re\right) - \left(x.im \cdot x.im\right)\right) \cdot x.re\right) - \left(\left(\frac{\left(x.re \cdot x.im\right)}{\left(x.im \cdot x.re\right)}\right) \cdot x.im\right)\]
↓
\[\left(\mathsf{qms}\left(\left(\left(x.re \cdot \left(\left(x.re - x.im\right) \cdot \left(x.im + x.re\right)\right)\right)\right), \left(\left(x.re + x.re\right) \cdot x.im\right), x.im\right)\right)\]
\left(\left(\left(x.re \cdot x.re\right) - \left(x.im \cdot x.im\right)\right) \cdot x.re\right) - \left(\left(\frac{\left(x.re \cdot x.im\right)}{\left(x.im \cdot x.re\right)}\right) \cdot x.im\right)
↓
\left(\mathsf{qms}\left(\left(\left(x.re \cdot \left(\left(x.re - x.im\right) \cdot \left(x.im + x.re\right)\right)\right)\right), \left(\left(x.re + x.re\right) \cdot x.im\right), x.im\right)\right)
double f(double x_re, double x_im) {
        double r2172637 = x_re;
        double r2172638 = r2172637 * r2172637;
        double r2172639 = x_im;
        double r2172640 = r2172639 * r2172639;
        double r2172641 = r2172638 - r2172640;
        double r2172642 = r2172641 * r2172637;
        double r2172643 = r2172637 * r2172639;
        double r2172644 = r2172639 * r2172637;
        double r2172645 = r2172643 + r2172644;
        double r2172646 = r2172645 * r2172639;
        double r2172647 = r2172642 - r2172646;
        return r2172647;
}
↓
double f(double x_re, double x_im) {
        double r2172648 = x_re;
        double r2172649 = x_im;
        double r2172650 = r2172648 - r2172649;
        double r2172651 = r2172649 + r2172648;
        double r2172652 = r2172650 * r2172651;
        double r2172653 = r2172648 * r2172652;
        double r2172654 = /*Error: no posit support in C */;
        double r2172655 = r2172648 + r2172648;
        double r2172656 = r2172655 * r2172649;
        double r2172657 = /*Error: no posit support in C */;
        double r2172658 = /*Error: no posit support in C */;
        return r2172658;
}

Error

Bits error versus x.re

Bits error versus x.im

Derivation

  1. Initial program 0.4

    \[\left(\left(\left(x.re \cdot x.re\right) - \left(x.im \cdot x.im\right)\right) \cdot x.re\right) - \left(\left(\frac{\left(x.re \cdot x.im\right)}{\left(x.im \cdot x.re\right)}\right) \cdot x.im\right)\]
  2. Using strategy rm

  3. Applied introduce-quire0.4

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

  4. Applied insert-quire-fdp-sub0.3

    \[\leadsto \color{blue}{\left(\mathsf{qms}\left(\left(\left(\left(\left(x.re \cdot x.re\right) - \left(x.im \cdot x.im\right)\right) \cdot x.re\right)\right), \left(\frac{\left(x.re \cdot x.im\right)}{\left(x.im \cdot x.re\right)}\right), x.im\right)\right)}\]

  5. Simplified0.3

    \[\leadsto \color{blue}{\left(\mathsf{qms}\left(\left(\left(\left(x.re \cdot \left(x.re - x.im\right)\right) \cdot \left(\frac{x.im}{x.re}\right)\right)\right), \left(\left(\frac{x.re}{x.re}\right) \cdot x.im\right), x.im\right)\right)}\]
  6. Using strategy rm

  7. Applied associate-*l*0.3

    \[\leadsto \left(\mathsf{qms}\left(\left(\color{blue}{\left(x.re \cdot \left(\left(x.re - x.im\right) \cdot \left(\frac{x.im}{x.re}\right)\right)\right)}\right), \left(\left(\frac{x.re}{x.re}\right) \cdot x.im\right), x.im\right)\right)\]

  8. Final simplification0.3

    \[\leadsto \left(\mathsf{qms}\left(\left(\left(x.re \cdot \left(\left(x.re - x.im\right) \cdot \left(x.im + x.re\right)\right)\right)\right), \left(\left(x.re + x.re\right) \cdot x.im\right), x.im\right)\right)\]

Reproduce

herbie shell --seed 2019144 
(FPCore (x.re x.im)
  :name "math.cube on complex, real part"
  (-.p16 (*.p16 (-.p16 (*.p16 x.re x.re) (*.p16 x.im x.im)) x.re) (*.p16 (+.p16 (*.p16 x.re x.im) (*.p16 x.im x.re)) x.im)))