We test the gauge/gravity duality between the matrix model and type IIA string theory at low temperatures with unprecedented accuracy. To this end, we perform lattice Monte Carlo simulations of the Berenstein-Maldacena-Nastase (BMN) matrix model, which is the one-parameter deformation of the Banks-Fischler-Shenker-Susskind (BFSS) matrix model, taking both the large N and continuum limits. We leverage the fact that sufficiently small flux parameters in the BMN matrix model have a negligible impact on the energy of the system while stabilizing the flat directions so that simulations at smaller N than in the BFSS matrix model are possible. Hence, we can perform a precision measurement of the large N continuum energy at the lowest temperatures to date. The energy is in perfect agreement with supergravity predictions including estimations of alpha '-corrections from previous simulations. At the lowest temperature where we can simulate efficiently (T = 0.25 lambda(1/3), where lambda is the 't Hooft coupling), the difference in energy to the pure supergravity prediction is less than 10%. Furthermore, we can extract the coefficient of the 1/N-4 corrections at a fixed temperature with good accuracy, which was previously unknown.