There is no double precision number between 1 and 
. Thus the following difference is zero despite its appearance.
. Thus the following difference is zero despite its appearance.( 1 + eps/2 ) - 1
However, 
is a double precision number, so it is represented exactly:
is a double precision number, so it is represented exactly:1 + ( eps/2 - 1 )
This is now the "correct'' result. But we have found a rather shocking breakdown of the associative law of addition!