Fig. 4

Algorithm performance on a hard benchmark problem. We use the same problem as in Fig. 2. a Γ is the number of trajectories, \(\overline E\) the lowest energy found until that point, \(n\left( {\overline E } \right)\) is the number of times this energy has been found, E₀ is the parameter obtained from fitting of Eq. (5), \(E_{{\mathrm{min}}}^{{\mathrm{pred}}}\) and estimating \({\mathrm{\Gamma }}^{{\mathrm{pred}}}\left( {\overline E - 1} \right)\). The algorithm estimates the escape rate and performs a prediction at each Γ shown in the table and for the colored lines we show the fitting curves in (b). c The relevant parameter E₀ is shown as function of Γ. While it wildly fluctuates at the beginning when the statistics is small, it remains in the E₀ ∈ [4, 5) interval, convincingly predicting \(E_{{\mathrm{min}}}^{{\mathrm{pred}}} = 5\) already after Γ = 7000 up until the point that it finds this energy at Γ = 189,562. At this point it could be expected that we do not have a good estimate for κ(5) because it has been found only once (n(5) = 1), nevertheless the estimation \(E_{{\mathrm{min}}}^{{\mathrm{pred}}}\) remains consistently the same, convincing our algorithm to accept \(E_{{\mathrm{min}}}^{{\mathrm{dec}}} = 5\) and stop. d A zoom into the [0, 2 × 10⁴] interval of (c)