The answer to your question is that it takes a super computer to simulate 5 atoms interacting with each other. And the simulation won't be real time either.
So reality is not "simple" enough to be simulated accurately.
The simulations that do exist are gross simplifications called models and in no way accurate to what's really going on. Those models are usually application specific and are only relatively accurate within that scope.
You can make an argument that human intelligence can be simulated by a application specific model, however your statement of the universe being axiomatically premised in simple rules is categorically wrong.