It is known that if a and b have exact representation in a given t-bit arith-...

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It is known that if a and b have exact representation in a given t-bit arith- metic, then fl(a+b) = (a+b)(1+6), where fl(.) denotes the result of an operation performed by a computer, and [8] ≤ u (u = 2-t-¹ denotes the unit round-off error). Assume that four numbers a, b, c, d = R, |a| < |b| < |c| < |d|, have exact computer representation. Which of the two algorithms: fl(a+b+c+d) or fl(d+c+b+a), computes more accurate result (with smaller absolute error)? Justify the answer! A note: the conclusion in this problem is independent on the fact that the numbers have exact representation. This assumption only makes the calculation easier. It is known that if a and b have exact representation in a given t-bit arith- metic, then fl(a+b) = (a+b)(1+6), where fl(.) denotes the result of an operation performed by a computer, and [8] ≤ u (u = 2-t-¹ denotes the unit round-off error). Assume that four numbers a, b, c, d = R, |a| < |b| < |c| < |d|, have exact computer representation. Which of the two algorithms: fl(a+b+c+d) or fl(d+c+b+a), computes more accurate result (with smaller absolute error)? Justify the answer! A note: the conclusion in this problem is independent on the fact that the numbers have exact representation. This assumption only makes the calculation easier.