>>12483355Your last thing is equivalent to x^z (exclusive-or). This is what the second term in your original expression is equivalent to.
You could always try plugging in all your values to double-check. You have 3 variables so there are 8 potential combinations of true-false values.
You can ignore all cases when x=z since that will make the second term in your original expression false. So for x!=z, you just need to check 4 possible cases (including the y variable). 2 of those cases will have x as true which will make the first expression completely unnecessary. x=0,z=1,y=0 will make the zx' in the first term true. x=0,z=1,y=1 will also make the first term true because of the y. Therefore, the entire thing reduces to x xor z (at least from what I see).
tl;dr, looks good to me I think!
