It is possible not to have to work out the triangles.


Subdiv Surfaces > Collapse Hierarchy
this will give you higher mesh. BUT you can keep your triangle count down in renders, buy lowering the Tessellation, sample count of 2 should get you close to the original count.

There will be a Higher mesh to deal with. could slow down interactivity for animation. But this is something that would be done right before renders anyway.