Adder propagate P expression
Computing NAND and NOR functions is cheaper than computing XOR and XNOR.  While the best ways of computing X XOR Y and X XNOR Y are slightly cheaper than anything that could by synthesized out of NAND and NOR gates, it may be cheaper still to synthesize them out of other signals like X OR Y or X AND Y if those have also been computed for other reasons.  If one computes X OR Y for P, and X AND Y for G, then the combined cost of computing P==X OR Y, G=X AND Y, and S1=P AND NOT G will be cheaper than synthesizing P=X XOR Y, G=X and Y, and S1=P.

Note that I've slightly over-simplified things here; computing X AND Y in isolation would require computing X NAND Y and then inverting the result, but if complemented forms of X and Y are available it could instead be evaluated as X' NOR Y' for the same cost as a NAND.  Any real evaluation of the relative costs of different ways of writing out logic should take such issues into account.  Further, running wires for a significant distance on a chip can be expensive; if X and Y are needed in two places that are some distance apart, evaluating X nand Y in both places may be cheaper than evaluating it in one place and running a wire to feed that result to the other.