  We give a fully polynomial-time approximation scheme (FPTAS) to count the
number of independent sets on almost every $\Delta$-regular bipartite graph if
$\Delta\ge 53$. In the weighted case, for all sufficiently large integers
$\Delta$ and weight parameters
$\lambda=\tilde\Omega\left(\frac{1}{\Delta}\right)$, we also obtain an FPTAS on
almost every $\Delta$-regular bipartite graph. Our technique is based on the
recent work of Jenssen, Keevash and Perkins (SODA, 2019) and we also apply it
to confirm an open question raised there: For all $q\ge 3$ and sufficiently
large integers $\Delta=\Delta(q)$, there is an FPTAS to count the number of
$q$-colorings on almost every $\Delta$-regular bipartite graph.
