  A polemic arose recently about the applicability of the $t$-expansion method
to the calculation of the ground state energy $E_0$ of the Rabi model. For
specific choices of the trial function and very large number of involved
connected moments, the $t$-expansion results are rather poor and exhibit
considerable oscillations. In this letter, we formulate the $t$-expansion
method for trial functions containing two free parameters which capture two
exactly solvable limits of the Rabi Hamiltonian. At each order of the
$t$-series, $E_0$ is assumed to be stationary with respect to the free
parameters. A high accuracy of $E_0$ estimates is achieved for small numbers (5
or 6) of involved connected moments, the relative error being smaller than
$10^{-4}$ (0.01%) within the whole parameter space of the Rabi Hamiltonian. A
special symmetrization of the trial function enables us to calculate also the
first excited energy $E_1$, with the relative error smaller than $10^{-2}$
(1%).
