It's called "Eugene's Trick Bag" and if you're gonna play it note for note...GOOD LUCK! Keep in mind that Steve Vai went through a 10 hour workout everyday for many years. To be honest, you can still hear a little bit of "slop" between the changes in the beginning part. This just goes to show that if Steve Vai can't drill it with his tremendous chops, it's hard for the average non-shredder to pull off.
My advice is to work it out slowly, measure by measure, and strive for accuracy, the speed will come in time. Also, towards the end there's a part where Steve jumps all over the neck between arppegios. This part is just a two string pattern shifted around quite a bit. If you can find an easy way to approaching this part...let me know. That part in particular discouraged me quite a bit and reminded me "Practice makes one almost perfect".
Good luck, and practice hard. Speed will come with time but accuracy and smoothness must be dealt with up front. If not you just end up with fast slop.