Mathematical evaluation of the position remains a mystery to me :-) Indeed, sometimes to capture a particular cell chess field and not a pity to give two or three pawns.
I think that the estimate in pawn - this rough pattern. Elephant is 3.08 pawn, knight is 2.97 pawn. That is generally more profitable to save their elephant than horse. Although, of course, it all depends on the specific position. Often two pawns together hand in hand, winning the queen :-)
Recently, I was running again through this Kaufman/Heisman article on material value.
http://home.comcast.net/~danheisman/Articles/evaluation_of_material_imbalance.htm
Kaufman presents two tables: one for humans with constant values and one for computers with variable values depending on the number of pawns of the respective parties which affect the values of rooks and knights.
The rule of thumb is: exchange for 1 pawn is slightly not enough for a win, exchange for 2 pawns is slightly enough for the win.
This also is confirmed by the "human" values (rook - bishop/knight = 1,75)
When I take the "computer" values:
Rook =5 - 0.125*(pawns-5)
Knight = 3.25 + 0.0625*(pawns-5)
Bishop = 3.25
... I end up with confusion (see image below).
Example one:
Consider 0 pawns for the rook party = 5.625 units
Consider 2 pawns for the knight party = 5.0625 units (short of more than half a pawn)
Consider 2 pawns for the bishop party = 5.25 (almost 0.4 pawns less)
The crossing of all above values is at 3 vs. 5 pawns =5.25 for all combinations above.
I don't thinks that this is reflected at all in the reality on the board while it does for "human" values.
Where does this mismatch come from when on the other hand other rules of thumb (e.g. open position when bishop vs. knight and keep closed when knight vs. bishop) are reflected nicely?