All three reviewers participated in the discussion, and found the approach appealing. Two of the reviewers feel it is critical that the content which was added by, or promised in, the author response, makes it into the final camera-ready version of the paper. In particular, in addition to all the clarifications included in the author rebuttal, this includes: * Experiments comparing against SINDY * Experiments on Hamiltonians that cannot be captured by the given basis (e.g. finding Taylor expansions with polynomials) * Whether the symplectic integrator is indeed essential (and whether RK4 would work) Additionally, I found it necessary to check the source code for some details — it would be good to explicitly describe the integrator itself (perhaps in an appendix), and explain how it is used in conjunction with automatic differentiation.