Is Hamlet Actually Insane?

 There is debate on whether or not Hamlet is actually pretending to be mad or if he has actually lost his mind. I firmly believe that Hamlet started out as sane and only pretending to be insane, but eventually his act caught up with him and he became obsessed with unveiling what his uncle did that he lost his mind. In the beginning of the movie, Hamlet had periods of time that his sanity would shine through, however, as the movie continued forward those periods become less and less frequent. He also acts unstable when others are not around, unlike he did in the beginning of the movie. I also believe that Horatio now believes that Hamlet is actually insane now too. When Hamlet speaks to him it is in haste and not always coherent thoughts, which lead him to believe that Hamlet has gone mad for real. Throughout the movie there are little hints that show to me that Hamlet has stopped pretending to be mad, but is now legitimately insane. Do you believe that Hamlet is pretending or that he has actually lost it?