This procedure converts a given rational function r into the continued-fraction form which minimizes the number of arithmetic operations required for evaluation.

If the second argument x is present then the first argument must be a rational expression in the variable x. If the second argument is omitted then either r is an operator such that  yields a rational expression in y, or else r is a rational expression with exactly one indeterminate (determined via indets).

Note that for the purpose of evaluating a rational function efficiently (i.e. minimizing the number of arithmetic operations), the rational function should be converted to continued-fraction form. In general, the cost of evaluating a rational function of degree  when each of numerator and denominator is expressed in Horner (nested multiplication) form, with the denominator made monic, is

whereas the same rational function can be evaluated in continued-fraction form with a cost not exceeding

The command with(numapprox,confracform) allows the use of the abbreviated form of this command.