  A large number of fast radio bursts (FRBs) detected with the CHIME telescope
have enabled investigations of their energy distributions in different redshift
intervals, incorporating the consideration of the selection effects of CHIME.
As a result, we obtained a non-evolving energy function (EF) for the
high-energy FRBs (HEFRBs) of energies $E\gtrsim2\times0^{38}$ erg, which takes
the form of a power law with a low-energy exponential cutoff. On the contrary,
the energy distribution of the low-energy FRBs (LEFRBs) obviously cannot be
described by the same EF. Including the lowest dispersion measure (DM) samples,
the LEFRBs are concentrated towards the Galactic plane and their latitude
distribution is similar to that of Galactic rotational radio transients
(RRATs). These indications hint that LEFRBs might compose a special type of
RRATs, with relatively higher DMs and energies (i.e., $\sim10^{28-31}$ erg for
a reference distance of $\sim10$ kpc if they belong to the Milky Way). Finally,
we revisit the redshift-dependent event rate of HEFRBs and confirm that they
could be produced by the remnants of cosmological compact binary mergers.
