Average Error: 0.3 → 0.2
Time: 6.3s
Precision: 64
\[\frac{\left(x.re \cdot y.im\right)}{\left(x.im \cdot y.re\right)}\]
↓
\[\left(\mathsf{qma}\left(\left(\left(x.re \cdot y.im\right)\right), x.im, y.re\right)\right)\]
\frac{\left(x.re \cdot y.im\right)}{\left(x.im \cdot y.re\right)}
↓
\left(\mathsf{qma}\left(\left(\left(x.re \cdot y.im\right)\right), x.im, y.re\right)\right)
double f(double x_re, double x_im, double y_re, double y_im) {
        double r669844 = x_re;
        double r669845 = y_im;
        double r669846 = r669844 * r669845;
        double r669847 = x_im;
        double r669848 = y_re;
        double r669849 = r669847 * r669848;
        double r669850 = r669846 + r669849;
        return r669850;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r669851 = x_re;
        double r669852 = y_im;
        double r669853 = r669851 * r669852;
        double r669854 = /*Error: no posit support in C */;
        double r669855 = x_im;
        double r669856 = y_re;
        double r669857 = /*Error: no posit support in C */;
        double r669858 = /*Error: no posit support in C */;
        return r669858;
}

Error

Bits error versus x.re

Bits error versus x.im

Bits error versus y.re

Bits error versus y.im

Derivation

  1. Initial program 0.3

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

  3. Applied introduce-quire0.3

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

  4. Applied insert-quire-fdp-add0.2

    \[\leadsto \color{blue}{\left(\mathsf{qma}\left(\left(\left(x.re \cdot y.im\right)\right), x.im, y.re\right)\right)}\]

  5. Final simplification0.2

    \[\leadsto \left(\mathsf{qma}\left(\left(\left(x.re \cdot y.im\right)\right), x.im, y.re\right)\right)\]

Reproduce

herbie shell --seed 2019152 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+.p16 (*.p16 x.re y.im) (*.p16 x.im y.re)))