Before revision:  In contrast  we show that the situation with two additive inequalities is quite different, by showing that it is NP-hard to evaluate simple aggregation queries, with two additive inequalities, with any bounded relative error . We end by considering the problem of computing the gradient of the objective function in the Support Vector Machines (SVM) problem, a canonical machine learning problem. While computing the gradient for SVM can be reduced to the problem of computing an aggregation query with one additive inequality, our algorithm is not applicable due to what we call the ``subtraction problem''. However, we show how to circumvent this subtraction problem within the context of SVM to obtain a gradient-descent algorithm that will result in an approximately correct optimal solution, using an alternative notion of approximate correctness, which may be of independent interest .
After revision:  In contrast we show that the situation with two additive inequalities is quite different, by showing that it is NP-hard to evaluate simple aggregation queries, with two additive inequalities, with any bounded relative error .