  In this paper the observed Dirac semimetals Na$_3$Bi and Cd$_3$As$_2$ are
studied within lattice simulation. We formulate lattice field theory with
rooted staggered fermions on anisotropic lattice. It is shown that in the limit
of zero temporal lattice spacing this theory reproduces low energy effective
theory of Dirac semimetals. Using this lattice theory we study the phase
diagram of Dirac semimetals in the plane effective coupling constant--Fermi
velocity anisotropy. Within the formulated theory the results are practically
volume independent in contrast with our previous study. Our results confirm our
previous finding that within the Dirac model with bare Coulomb interaction both
Na$_3$Bi and Cd$_3$As$_2$ lie deep in the insulator phase.
