Suppose there is some function with the property
f[x,y] f[y,x^2] / f[x^3,y] == f[2x,y]
How can I simplify an arbitrary expression that contains the lhs of the above equation in a somewhat obscured way? Say as in
a f[x^3,y] b / (c f[y,x^2] d f[x,y] e)
I tried Simplify with TransformationFunctions but I only seem to be able to replace the three f when they're literally next to each other in the syntax tree. Any ideas on how to proceed?