We present three-dimensional simulations of the dynamics of binary neutron star mergers from the late stage of the inspiral process up to ∼20 ms after the system has merged, either to form a hypermassive neutron star or a rotating black hole. We investigate five equal mass models of total gravitational mass 2.207, 2.373, 2.537, 2.697, and 2.854 M☉, respectively, and four unequal mass models with MADM≃2.53 M☉ and q ≃0.94 , 0.88, 0.83, and 0.77 (where q =M(1 )/M(2 ) is the mass ratio). We use a semirealistic equation of state, namely, the seven-segment piecewise polytropic SLyPP with a thermal component given by Γth=1.8 . We have also compared the resulting dynamics (for one model) using both the BSSN-NOK and CCZ4 methods for the evolution of the gravitational sector and also different reconstruction methods for the matter sector, namely, PPM, WENO, and MP5. Our results show agreement at high resolution, but superiority of BSSN-NOK supplemented by WENO reconstruction at lower resolutions. One of the important characteristics of the present investigation is that for the first time it has been done using only publicly available open source software: the Einstein Toolkit code, deployed for the dynamical evolution, and the LORENE code, for the generation of the initial models. All of the source code and parameters used for the simulations have been made publicly available. This not only makes it possible to rerun and reanalyze our data but also enables others to directly build upon this work for future research.