  In this paper, we first use the "complexity equals action" conjecture to
discuss the complexity growth rate in both perturbation Einsteinian cubic
gravity and non-perturbation Einstein-Weyl gravity. We find that the CA
complexity rate in these cases is divergent. To avoid this divergence, we
modify the original conjecture, where we assume that the complexity of the
boundary state equals the boundary actions contributed by the null segments as
well as the joints of the Wheeler-DeWitt patch. Then, the late time growth rate
of this modified holographic complexity is given by entropy $S$ times
temperature $T$, which is quite in agreement with the circuit analysis.
Finally, to test its rationality, we also investigate the switchback effect by
evaluating it in a Vaidya geometry and analyze the results in circuit models.
