  Using a large sample of fast radio bursts (FRBs) from the first CHIME/FRB
catalog, we apply the Lynden-Bell's c$^-$ method to study their energy function
and formation rate evolutions with redshift. It is found with the
non-parametric Kendell's $\tau$ statistics that the FRB energy strongly evolves
with the cosmological redshift as $E(z)\propto(1 + z)^{5.23}$. After removing
the redshift dependence, the local energy distribution can be described by a
broken power-law form of $\Psi(E_{0})\propto E_{0}^{-0.38}$ for the low-energy
segment and $\Psi(E_{0})\propto E_{0}^{-2.01}$ for the high-energy segment with
a dividing line of $\sim2.1\times10^{40} \rm erg$. Interestingly, we find that
the formation rate of CHIME FRBs also evolves with redshift as
$\rho(z)\propto(1+z)^{-4.73\pm0.08}$. The local formation rate $\rho(0)$ of the
CHIME FRBs is constrained to be about $ 1.25\times 10^4\rm{\,Gpc^{-3}yr^{-1}}$
that is comparable with some previous estimations. In addition, we notice the
formation rate not only exceeds the star formation rate at the lower redshifts
but also always declines with the increase of redshift, which does not match
the star formation history at all. Consequently, we suggest that most FRBs
could originate from the older stellar populations.
