Two Bishops vs. Two Rooks

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Here's the situation. I messed up take a look at the comments on moves 22 ... Bxf2 and 23. Rf1 

So here's the question. Has anyone looked at these types of endgames? Or are they typically deemed losing? Did I make the right call here after realizing my mistake?
I'm not asking for a full game analysis, just at the end where I drew. I still have my own full analysis to accomplish.
Thanks in advance.
Cheers.