This paper presents new methods for evaluating differentiable functions. These function evaluation methods use look-up tables, but need no explicit multiplication operations. These methods produce interpolatory correction values of first, second, and higher order, with respective quantities of associated table entries growing proportional to 2n/2, 2n/3, and so on, for n-bit inputs, to yield outputs of about n-3 bits of precision. Production of such integer-order correction values are contrasted with that of half-order correction values of two-table semi-direct table look-up where the quantity of entries in each of the two tables grows as 2(2/3)n for n-bit inputs.