  Existing theoretical works differ on whether three-dimensional Dirac and Weyl
semimetals are stable to a short-range-correlated random potential. Numerical
evidence suggests the semimetal to be unstable, while some field-theoretic
instanton calculations have found it to be stable. The differences go beyond
method: the continuum field-theoretic works use a single, perfectly linear Weyl
cone, while numerical works use tight-binding lattice models which inherently
have band curvature and multiple Weyl cones. In this work, we bridge this gap
by performing exact numerics on the same model used in analytic treatments, and
we find that all phenomena associated with rare regions near the Weyl node
energy found in lattice models persist in the continuum theory: The density of
states is non-zero and exhibits an avoided transition. In addition to
characterizing this transition, we find rare states and show that they have the
expected behavior. The simulations utilize sparse matrix techniques with
formally dense matrices; doing so allows us to reach Hilbert space sizes
upwards of $10^7$ states, substantially larger than anything achieved before.
