Average Error: 0.3 → 0.2
Time: 18.3s
Precision: 64
\[\left(x.re \cdot y.re\right) - \left(x.im \cdot y.im\right)\]
↓
\[\left(\mathsf{qms}\left(\left(\left(x.re \cdot y.re\right)\right), x.im, y.im\right)\right)\]
\left(x.re \cdot y.re\right) - \left(x.im \cdot y.im\right)
↓
\left(\mathsf{qms}\left(\left(\left(x.re \cdot y.re\right)\right), x.im, y.im\right)\right)
double f(double x_re, double x_im, double y_re, double y_im) {
        double r736046 = x_re;
        double r736047 = y_re;
        double r736048 = r736046 * r736047;
        double r736049 = x_im;
        double r736050 = y_im;
        double r736051 = r736049 * r736050;
        double r736052 = r736048 - r736051;
        return r736052;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r736053 = x_re;
        double r736054 = y_re;
        double r736055 = r736053 * r736054;
        double r736056 = /*Error: no posit support in C */;
        double r736057 = x_im;
        double r736058 = y_im;
        double r736059 = /*Error: no posit support in C */;
        double r736060 = /*Error: no posit support in C */;
        return r736060;
}

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

    \[\left(x.re \cdot y.re\right) - \left(x.im \cdot y.im\right)\]
  2. Using strategy rm

  3. Applied introduce-quire0.3

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

  4. Applied insert-quire-fdp-sub0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019153 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (-.p16 (*.p16 x.re y.re) (*.p16 x.im y.im)))