So every time we store an number and do a operation, we introduce an error bounded by machine epsilon e, so for example, the computed sum of two number is fl($x_1+x_2$)=$[x_1(1+d_1)+x_2(1+d_2)](1+d_3)$, where $|d_i|<=e$. A complete example of subtraction is like this: Hope this can express my question.
I reckon, as the inequality we want has (n+3)u, and all higher terms are included in $O(u^2)$, I think we need only count how many first order terms left in the final multiplication result. However, the calculation already gets complicated and I am not sure whether I am on the right track, even if I am, it is easy to make mistake in this way, is there an easier and smart way to attack this question?
Any suggestion would be appreciated! Thanks in advance!