[nestorD]

For the error free transform, the important part is the associativity and not the fusion (which would not degrade the operation).

As illustrated in the Wikipedia page, if move terms according to associativ rules you can show that one of the term is always zero and conclude that it is useless, dropping it from the computation.

However, in practice, floating-points are not associativ and that term contains the numerical error of the previous operation.