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 r296960 = x_re;
        double r296961 = y_im;
        double r296962 = r296960 * r296961;
        double r296963 = x_im;
        double r296964 = y_re;
        double r296965 = r296963 * r296964;
        double r296966 = r296962 + r296965;
        return r296966;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r296967 = x_re;
        double r296968 = y_im;
        double r296969 = r296967 * r296968;
        double r296970 = /*Error: no posit support in C */;
        double r296971 = x_im;
        double r296972 = y_re;
        double r296973 = /*Error: no posit support in C */;
        double r296974 = /*Error: no posit support in C */;
        return r296974;
}

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 2019163 +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)))