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How is it winning to sacrifice my rook here?

I suck at chess but I'm trying to improve by looking at the computer enginge analysis instead of blindly starting new games after losing. I dont understand what is the point of sacrificing the rook in this position?
http://en.lichess.org/VMnmTLAa/white#20
It's putting a lot of pressure on black, by virtue of getting rid of the only developed piece, taking back would result in a horrid weakness, black is just losing.

As a tip, those lines are not the most important part in your chess knowledge right now. Don't just look at computer evaluations, before you leave the computer do the analysis do it yourself. Computer evaluations are in some way too precise, a for a human losing position can be evaluated to +-0 because of there being one line that would mean salvation.

Study openings, study endgames, middle game is hard to study, for those study your own games without a computer.
if he eats ur rook, u do nxe3, which opens the way for checkmate or extreme piece loss.
It's brutally hard to see the computer's suggested line, but generally it's a rook + piece + pawn + exposes the enemy's king. As you're so far ahead on development, it's worth it.

For the exact moves, you can play on the analysis board and wait for Stockfish to tell you exactly what it thinks is the best move.
in fact it is not that hard.
First of all, it is not the only move to play Rxe5. Be3 would also be a devastating advantage for example. And about Rxe5. You don't sacrifice a rook, but merely a quality. And afterwards you play Nxe6! with devastating effect. That's all about it ;)
I believe chess is more than exact mathematical moves.
Pawn structure strategies fit in middle game theory, like ...
Create and then exploit an isolated pawn during the middle game. Pawn structures are planned in the opening, executed in the middle game and pay-off in the endgame. Tactics alone can not create an isolani on purpose.
@Strategymaster: The hard line to see which I referred to was:

Rxe5 fxe5
Nxe6 Kf7
Nd8 Kg7
Nxb7 Qxb7
Qd6! Nc6
Bxc6 Qxc6
Qxe5+ winning the rook.

The line itself is hard to see, but other lines probably win as well.
It's a sacrifice exchange. If they take it then you win a bishop for your rook, and a pawn if it is accepted. You end up having a lot of relatively active pieces, and your opponents king is vulnerable. It's worth it to make this exchange. If they don't take the rook then they still are gonna lose castling rights... It matters very little what pieces are taken off the board when it comes to a game of chess. What matters is what pieces are left on the board, and how active they are.

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