  The fast flavor conversions (FFCs) of neutrinos generally exist in
core-collapse supernovae and binary neutron-star merger remnants, and can
significantly change the flavor composition and affect the dynamics and
nucleosynthesis processes. Several analytical prescriptions were proposed
recently to approximately explain or predict the asymptotic outcome of FFCs for
systems with different initial or boundary conditions, with the aim for
providing better understandings of FFCs and for practical implementation of
FFCs in hydrodynamic modeling. In this work, we obtain the asymptotic survival
probability distributions of FFCs in a survey over thousands of randomly
sampled initial angular distributions by means of numerical simulations in
one-dimensional boxes with the periodic boundary condition. We also propose
improved prescriptions that guarantee the continuity of the angular
distributions after FFCs. Detailed comparisons and evaluation of all these
prescriptions with our numerical survey results are performed. The survey
dataset is made publicly available to inspire the exploration and design for
more effective methods applicable to realistic hydrodynamic simulations.
