_multiplyComplex, imaginary part

Average Error: 0.3 → 0.2

Time: 6.0s

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 r1454580 = x_re;
        double r1454581 = y_im;
        double r1454582 = r1454580 * r1454581;
        double r1454583 = x_im;
        double r1454584 = y_re;
        double r1454585 = r1454583 * r1454584;
        double r1454586 = r1454582 + r1454585;
        return r1454586;
}

↓

double f(double x_re, double x_im, double y_re, double y_im) {
        double r1454587 = x_re;
        double r1454588 = y_im;
        double r1454589 = r1454587 * r1454588;
        double r1454590 = /*Error: no posit support in C */;
        double r1454591 = x_im;
        double r1454592 = y_re;
        double r1454593 = /*Error: no posit support in C */;
        double r1454594 = /*Error: no posit support in C */;
        return r1454594;
}

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 2019162 +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)))