_multiplyComplex, imaginary part

Average Error: 0.3 → 0.2

Time: 6.1s

Precision: 64

Math

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

↓

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

C

double f(double x_re, double x_im, double y_re, double y_im) {
        double r1966752 = x_re;
        double r1966753 = y_im;
        double r1966754 = r1966752 * r1966753;
        double r1966755 = x_im;
        double r1966756 = y_re;
        double r1966757 = r1966755 * r1966756;
        double r1966758 = r1966754 + r1966757;
        return r1966758;
}

↓

double f(double x_re, double x_im, double y_re, double y_im) {
        double r1966759 = x_re;
        double r1966760 = y_im;
        double r1966761 = r1966759 * r1966760;
        double r1966762 = /*Error: no posit support in C */;
        double r1966763 = x_im;
        double r1966764 = y_re;
        double r1966765 = /*Error: no posit support in C */;
        double r1966766 = /*Error: no posit support in C */;
        return r1966766;
}

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-quire 0.3

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

4. Applied insert-quire-fdp-add 0.2

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

5. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019168 +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)))