Plotting a function with singularities in TikZ/pfgplots [duplicate]

Question

Essentially I want to plot a function with singularities like

$\frac{1}{(x-0.5)^2+(y-0.5)^2}\cdot \frac{1}{(x+0.5)^2+(y+0.5)^2}$ 

at a higher sampling rate.

I tried to avoid the singularities by capping with some value ($20$):

\begin{tikzpicture}
\begin{axis}[view={55}{45}]
\addplot3[surf, colormap/jet, samples=50, domain=-1:1] {min(1/((x-0.5)^2+(y-0.5)^2)* 1/((x+0.5)^2+(y+0.5)^2),20)};
\end{axis}
\end{tikzpicture}

Which yields

But that really does not stop TikZ/pfgplots from having to evaluate the function near its singularities, so it gets quite slow at compiling. So here is my question:

Is there a better/faster way to plot functions that contain singularities? Or do i have to precompute the data and give it to TikZ/pfgplots manually?