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.
