Automatic Error Analysis for Determining Precision The problem considered is that of evaluating a rational expression to within any desired tolerance on a computer which performs variable-precision floating-point arithmetic operations. An automatic error analysis technique is given for determining, directly from the results of a trial low-precision interval arithmetic calculation, just how much precision and data accuracy are required to achieve a desired final accuracy. The technique given generalize easily to the evaluation of many nonrational expressions. CACM September, 1972 Richman, P. L. error analysis, interval arithmetic, precision control 5.11 CA720904 JB January 27, 1978 4:39 PM 2286 5 2286 2286 5 2286 2286 5 2286 2555 5 2286 2605 5 2286 1026 6 2286 2286 6 2286 2286 6 2286