  We present a high-precision mass model of galaxy cluster Abell 2744, based on
a strong-gravitational-lensing analysis of the \emph{Hubble Space Telescope
Frontier Fields} (HFF) imaging data, which now include both \emph{Advanced
Camera for Surveys} and \emph{Wide-Field Camera 3} observations to the final
depth. Taking advantage of the unprecedented depth of the visible and
near-infrared data, we identify 34 new multiply imaged galaxies, bringing the
total to 61, comprising 181 individual lensed images. In the process, we
correct previous erroneous identifications and positions of multiple systems in
the northern part of the cluster core. With the \textsc{Lenstool} software and
the new sets of multiple images, we model the cluster using two cluster-scale
dark matter halos plus galaxy-scale halos for the cluster members. Our best-fit
model predicts image positions with an \emph{RMS} error of 0.69$\arcsec$, which
constitutes an improvement by almost a factor of two over previous parametric
models of this cluster. We measure the total projected mass inside a 200~kpc
aperture as ($2.162\pm 0.005$)$\times 10^{14}M_{\odot}$, thus reaching 1\%
level precision for the second time, following the recent HFF measurement of
MACSJ0416.1-2403. Importantly, the higher quality of the mass model translates
into an overall improvement by a factor of 4 of the derived magnification
factor. % for the high-redshift lensed background galaxies. Together with our
previous HFF gravitational lensing analysis, this work demonstrates that the
HFF data enables high-precision mass measurements for massive galaxy clusters
and the derivation of robust magnification maps to probe the early Universe.
