  In the long-time pursuit of the solution to calculate the partition function
(or free energy) of condensed matter, Monte-Carlo-based nested sampling should
be the state-of-the-art method, and very recently, we established a direct
integral approach that works at least four orders faster. In present work, the
above two methods were applied to solid argon at temperatures up to $300$K, and
the derived internal energy and pressure were compared with the molecular
dynamics simulation as well as experimental measurements, showing that the
calculation precision of our approach is about 10 times higher than that of the
nested sampling method.
