The game looks very drawish to me. If you traded rooks with, 26. Rxe6, then either ...Nxe6 or ...Kxe6 followed by 27.Ke3. I think black has no very big advantage. But why not just play Rd1 or Rd8, or even Rd2? It looks dead even to me. Fight for the draw!!!
As far as I can tell, and I never win against them, computers care about whether a given move makes their position immdiately worse ... I think that Rd1 is fine for you.
Keep fighting, the worst you should do is a draw. But it won't be easy :)
So this me playing a G/60/5 against the chess program that comes with my MacBook. I think it my record against it playing at 50% of its strength is like 1-101-0 (yeah to this day, I've never drawn against the program). So my one victory inspired me to play against it set to 80% (if you set it on 100%, it averages like 5-10 minutes to move).
The engine is near invincible at this level! Checking the engines moves in the database, it responds with the number one option practically every move until I went off book. This kind of makes me feel that this is sort of what it's like to play against a Master. I decided to open up its Philidor Defense and hammered away against it, threatening with tactical shots and gaining space. But the computer would continually parry all of my attacks, and pieces kept getting traded one by one, until I found myself staring at a weird position that I can only describe right now as an "opening endgame".
It's like we're opening a new game, but with only a Knight, Rook, and some pawns instead of a full army. After the 25th move, I not only had no idea what to do with the position, but I was late for an appointment, and I had to adjourn the game (D)