> It fails for x-y when x and y are close. Subtraction is the easiest way to get big floating point errors.

And note: addition might be subtraction, while subtraction might be addition.

Consider x=1.0 and y=-0.99999.

x + y = 0.00001

You did addition, but you got cancellation error. The only solution is to sort the numbers from largest to smallest dynamically during runtime.