Is there a classification that exists for a surface of the following form?
$${\frac {{x}^{2}}{ \left( {x}^{2}+1 \right) ^{2}}}+{\frac {{y}^{2}}{ \left( {y}^{2}+1 \right) ^{2}}}={\frac {{z}^{2}}{ \left( {z}^{2}+1 \right) ^{2}}}$$
The expression seems simple enough, but wolfram alpha's website chokes on it, and refused to plot it for me online.
Maple gave me this, when plotting on the interval -1..1 for each of x,y,and z:
Although that didn't help me figure out what the name of the surface was, or if it even has a name.