Signed-symmetric function approximation in affine arithmetic

One major cause of the error explosion is the overestimation of a non-affine function introducing a new noise symbol term with non-minimum coefficient. This paper proposes theorems and its proofs to construct the best univariate affine approximation to a non-affine function in the exception case, Signed-symmetric function, that the existing theorem is not sufficient to determine the optimum one. And, as the result, it shows the use by evaluating the power function and approximating sine function.