Help comparing relative error for different parenthesizations of addition
With nothing but an upper bound for the relative error: Consider that the final sums are almost the same, so bounds for relative error will be almost the same. What’s significantly different is the absolute error of the first addition, and that will be smallest if the first sum has the smallest possible absolute value. 

In the first case 0 &lt; x+y &lt; y+z, so the first function has the smaller error. 

In the second case it depends whether x+y or y+z is closer to zero, which we don’t know. And exactly the same in the third case.