Let x and y be real numbers that are not machine numbers for a 32-bit word-length computer and have to be rounded to get them into the machine. Assume that there is no overflow or under flow in getting their (rounded) values into the machine. (Thus, the numbers are within the range of a 32-bit word-length computer, although they are not machine numbers.) Find a rough upper bound on the relative error in computing x2 y3.
Hint: We say rough upper bound because you may use (1 + δ1)(1 + δ2) ≈ 1 + δ1 + δ2 and similar approximations. Be sure to include errors involved in getting the numbers into the machine as well as errors that arise from the arithmetic operations.
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