The paper has been considered reasonable, even though there have been some concerns with the clarity/exaggeration of some claims that were made (as also acknowledged in the response). This should definitely be properly addressed by the authors. There were also concerns about completeness of literature and experiments, and again the authors have proposed fixes to that (admittedly we cannot check if they are implemented, but we may choose to trust it). Since those are implementable changes, authors are expected to achieve them in great part. One related paper which was not mentioned (besides those mentioned in the reviews) is Nico Piatkowski, Katharina Morik: Stochastic Discrete Clenshaw-Curtis Quadrature. ICML 2016: 3000-3009, where they derive bounds on the approximation error for the partition function. It seems highly relevant for this paper. It is also expected that the authors will fix any sloppy situation as pointed out.