If $f(x)=\cos (\log x)$, then $f({{x}^{2}})f({{y}^{2}})-\frac{1}{2}\left[ f\,\left( \frac{{{x}^{2}}}{2} \right)+f\left( \frac{{{x}^{2}}}{{{y}^{2}}} \right) \right]$ has the value