_multiplyComplex, imaginary part

Average Error: 0.3 → 0.2

Time: 5.9s

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 r1574153 = x_re;
        double r1574154 = y_im;
        double r1574155 = r1574153 * r1574154;
        double r1574156 = x_im;
        double r1574157 = y_re;
        double r1574158 = r1574156 * r1574157;
        double r1574159 = r1574155 + r1574158;
        return r1574159;
}

↓

double f(double x_re, double x_im, double y_re, double y_im) {
        double r1574160 = x_re;
        double r1574161 = y_im;
        double r1574162 = r1574160 * r1574161;
        double r1574163 = /*Error: no posit support in C */;
        double r1574164 = x_im;
        double r1574165 = y_re;
        double r1574166 = /*Error: no posit support in C */;
        double r1574167 = /*Error: no posit support in C */;
        return r1574167;
}

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 2019144 +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)))