  We propose a polynomial approximation of the global Lense-Thirring rigid
precession frequency to study low frequency quasi-periodic oscillations around
spinning black holes. This high-performing approximation allows to determine
the expected frequencies of a precessing thick accretion disc with fixed inner
radius and variable outer radius around a black hole with given mass and spin.
We discuss the accuracy and the applicability regions of our polynomial
approximation, showing that the computational times are reduced by a factor of
$\approx70$ in the range of minutes.
