Looping through all functions defined in Mathematica

Is there a way to loop through all the Functions (Elementary and Special functions) that exist in Mathematica?

I want to construct a table of some identities and maybe I can discover something surprising if I plug every function that there is into my formula.

I.e. I want to do something like:

for function in Mathematica print function[x]^2 

(Note this is not Mathematica syntax, but I hope you get the idea)

Thanks, MichaƂ