That is a pretty rook ending.
Instead of 37...Kf6 could not he have defended with 37...Rb8 intending 38...Rh8?
Why 38...a4? Was 38...Kg7 intending 39...Kh6 possible?
Instead of 45...Kxe5, would 45...Ke6 have gained a tempo? Here it is probably too late.
Yeah, it was certainly by no means better for white. I tried not to lose. :D
