Building energy simulation programs compute numerical approximations to physical phenomena that can be modeled by a system of differential algebraic equations (DAE). For a large class of building energy analysis problems, one can prove that the DAE system has a unique once continuously differentiable solution. Consequently, if building simulation programs are built on models that satisfy the smoothness assumptions required to prove existence of a unique smooth solution, and if their numerical solvers allow controlling the approximation error, one can use such programs with Generalized Pattern Search optimization algorithms that adaptively control the precision of the solutions of the DAE system. Those optimization algorithms construct sequences of iterates with stationary accumulation points and have been shown to yield a significant reduction in computation time compared to algorithms that use fixed precision cost function evaluations. In this paper, we state the required smoothness assumptions and present the theorems that state existence of a unique smooth solution of the DAE system. We present BuildOpt, a detailed thermal and daylighting building energy simulation program. We discuss examples that explain the smoothing techniques used in BuildOpt. We present numerical experiments that compare the computation time for an annual simulation with the smoothing techniques applied to different parts of the models. The experiments show that high precision approximate solutions can only be computed if smooth models are used. This is significant because today's building simulation programs do not use such smoothing techniques and their solvers frequently fail to obtain a numerical solution if the solver tolerances are tight. We also present how BuildOpt's approximate solutions converge to a smooth function as the precision parameter of the numerical solver is tightened.