http://gyazo.com/2941ef9ba952de70447cc431ccb69cc0

Once I figure out the circuit expression I can find the karnuagh map easily, however figuring out the circuit expression is where I am finding difficulty.

The answer that I am reaching is not the same as the one in the back of the book.

I get (((A+B)' +(A'+C)')'+(A+D)')', which of course has to be simplified but it does not come out to the one in the back of the book which is (A'B'+AC')(A+D)

Am I reading the circuit wrong or did I get that right and im just messing up on the simplification?