Average Error: 0.3 → 0.2
Time: 5.7s
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 r447026 = x_re;
        double r447027 = y_im;
        double r447028 = r447026 * r447027;
        double r447029 = x_im;
        double r447030 = y_re;
        double r447031 = r447029 * r447030;
        double r447032 = r447028 + r447031;
        return r447032;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r447033 = x_re;
        double r447034 = y_im;
        double r447035 = r447033 * r447034;
        double r447036 = /*Error: no posit support in C */;
        double r447037 = x_im;
        double r447038 = y_re;
        double r447039 = /*Error: no posit support in C */;
        double r447040 = /*Error: no posit support in C */;
        return r447040;
}

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 2019153 +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)))