Fig 2. Multimodal histogram of runtime distribution.

We used the Kaplan–Meier estimate to obtain the histogram of the runtime distribution of the instance UNSAT_ME_seq-sat_Thoughtful_p11_6_59-typed.pddl_43. We used the Expectation–maximization (EM) method to obtain the pdf of the fitted Weibull mixture model (see Definitions 6.1 and 6.2 for an introduction to this kind of distribution). The EM algorithm is an algorithm that allows cluster analysis by starting with a heuristically initialized model and alternating between two steps. First, in the expectation-step (E-step), the association of the data points to the different clusters gets changed. Then, in the maximization-step (M-step), the model’s parameters get improved by using this new association of the data points. We refer to the classic paper [51] for an introduction to the algorithm. The resulting fitted distribution that is seen in the plot is clearly multimodal. This is supported by a Hartigans’ dip test value of 0.015 > 0.005.