  Perturbation theory of large-scale structures of the Universe at
next-to-leading order and next-to-next-to-leading order provides us with
predictions of cosmological statistics at sub-percent level in the mildly
non-linear regime. Its use to infer cosmological parameters from spectroscopic
surveys, however, is hampered by the computational cost of making predictions
for a large number of parameters. In order to reduce the running time of the
codes, we present a fast scheme in the context of the regularized perturbation
theory approach and applied it to power spectra at 2-loop level and bispectra
at 1-loop level, including the impact of binning. This method utilizes a Taylor
expansion of the power spectrum as a functional of the linear power spectrum
around fiducial points at which costly direct evaluation of perturbative
diagrams is performed and tabulated. The computation of the predicted spectra
for arbitrary cosmological parameters then requires only one-dimensional
integrals that can be done within a few minutes. It makes this method suitable
for Markov chain Monte-Carlo analyses for cosmological parameter inference.
