Output Statistics

One way to study the info on the rendering would be the use of Output Statistic.

To enable this feature, go to Render Settings, under Advance tab, Statistics, check Output Statistics to turn it ON. Insert a path into Statistics XML File field:

C:/myProj/mystatistics.xml

After each render, you should get mystatistics.xml file. Drag and drop it into Firefox browser.
Look under Memory tab, search for Radiosity Cache and you can see how much memory was used in the render. Renderman default 102400 kilobytes (100mb) for Radiosity Cache. If the renders use up more than 100 mb, then it would be better to raise the default to match the memory used, else the rendering will get slowdown.

Another info to look up for is the Bounds in the xml file, This is where you will find if your displacement bound has been set too low or too high.

Other interesting stats to look out for is Texture. Here you will find how many hits are at what resolution if the textures and the memory used.