# Borg-eps-1e-4 Brockhoff vs Borg-adaptive Brockhoff

## Empirical cumulative distribution functions (ECDFs) per function group

**1-separable 1-separable in 5-D**

**1-separable 2-moderate in 5-D**

**1-separable 3-ill-conditioned in 5-D**

**1-separable 4-multi-modal in 5-D**

**1-separable 5-weakly-structured in 5-D**

**2-moderate 2-moderate in 5-D**

**2-moderate 3-ill-conditioned in 5-D**

**2-moderate 4-multi-modal in 5-D**

**2-moderate 5-weakly-structured in 5-D**

**3-ill-conditioned 3-ill-conditioned in 5-D**

**3-ill-conditioned 4-multi-modal in 5-D**

**3-ill-conditioned 5-weakly-structured in 5-D**

**4-multi-modal 4-multi-modal in 5-D**

**4-multi-modal 5-weakly-structured in 5-D**

**5-weakly-structured 5-weakly-structured in 5-D**

**All functions in 5-D**

**1-separable 1-separable in 20-D**

**1-separable 2-moderate in 20-D**

**1-separable 3-ill-conditioned in 20-D**

**1-separable 4-multi-modal in 20-D**

**1-separable 5-weakly-structured in 20-D**

**2-moderate 2-moderate in 20-D**

**2-moderate 3-ill-conditioned in 20-D**

**2-moderate 4-multi-modal in 20-D**

**2-moderate 5-weakly-structured in 20-D**

**3-ill-conditioned 3-ill-conditioned in 20-D**

**3-ill-conditioned 4-multi-modal in 20-D**

**3-ill-conditioned 5-weakly-structured in 20-D**

**4-multi-modal 4-multi-modal in 20-D**

**4-multi-modal 5-weakly-structured in 20-D**

**5-weakly-structured 5-weakly-structured in 20-D**

**All functions in 20-D**

Empirical cumulative distributions (ECDF) of run lengths and speed-up ratios in 5-D (left) and 20-D (right). Left sub-columns: ECDF of the number of f-evaluations divided by dimension D (FEvals/D) to reach a target value I^{ref}+∆I with ∆I =10^{k}, where k is given by the first value in the legend, for algorithmA (°) and algorithmB (♦) . Right sub-columns: ECDF of FEvals ratios of algorithmA divided by algorithmB for fixed target precision values 10^{k} with k given in the legend; all trial pairs for each function. Pairs where both trials failed are disregarded, pairs where one trial failed are visible in the limits being > 0 or < 1. The legend also indicates, after the colon, the number of functions that were solved in at least one trial (algorithmA first).