A symbolic-numeric interface, approximation-freeness, and differentiability are three main features of SymBoltz that form a synergy. Differentiability computes the ODE Jacobian J accurately and efficiently; which implicit solvers use to integrate stiff ODEs without approximations; which makes it easy to write equations in simple symbolic form; which provide the exact sparsity pattern of J; in turn speeding up J and the solver. This loop creates a self-reinforcing design.