  We explore anomalous high-harmonic generation in a model that realizes a
transition from a broken time-reversal symmetry Weyl-semimetal to a semi-Dirac
regime, i.e. a gapless semimetal with dispersion that is parabolic in one
direction and conical in the other two. We point out the intensity of the
induced anomalous high harmonics is high in the semi-Dirac regime. For Weyl
semimetals, we reveal anomalous high harmonics are due to excitations at
momenta where the dispersion is not strictly linear and that in the linearized
low-energy theory the anomalous response is harmonic only. Our findings aid
experimental characterization of Weyl, Dirac, and semi-Dirac semimetals.
