  Two important parameters inferred from the gravitational wave signals of
binaries of precessing black holes are the spin tilt angles, i.e., the angles
at which the black holes' spin axes are inclined with respect to the binary's
orbital angular momentum. The LIGO-Virgo parameter estimation analyses
currently provide spin tilts at a fiducial reference frequency, often the
lowest frequency used in the data analysis. However, the most astrophysically
interesting quantities are the spin tilts when the binary was formed, which can
be significantly different from those at the reference frequency for strongly
precessing binaries. The spin tilts at formally infinite separation are a good
approximation to the tilts at formation in many formation channels and can be
computed efficiently for binary black holes using precession-averaged
evolution. Here, we present a new code for computing the tilts at infinity that
combines the precession-averaged evolution with orbit-averaged evolution at
high frequencies and illustrate its application to GW190521 and other binary
black hole detections from O3a. We have empirically determined the transition
frequency between the orbit-averaged and precession-averaged evolution to
produce tilts at infinity with a given accuracy. We also have regularized the
precession-averaged equations in order to obtain good accuracy for the very
close-to-equal-mass binary parameters encountered in practice. This
additionally allows us to investigate the singular equal-mass limit of the
precession-averaged expressions, where we find an approximate scaling of $1/(1
- q)$ with the mass ratio $q$.

High Energy Astrophysical Phenomena;General Relativity and Quantum Cosmology