2. Two Types of databases:

We have decided to use two different databases to study the effect of different databases: one is biased, i.e. towards large size polyhedra, and the other is periodically sampled since it contains many polyhedra. We have considered two types of POLYBENCH databases, for each operator. For instance, with the satisfiability test in 6_tab:satisfiability_databases:

• Sampled Database: constraint systems are periodically selected with probability at intervals of $100$, i.e., for every hundred constraint systems, we take only one, which means we use only $1\%$ to speed-up experiments and obtain average results. We have chosen $1\%$ for the sampling adapting to our experimentation: $1\%$ is still quite large for satisfiability databases that relatively assures accurate measurements. And even with only $1\%$, the execution of the satisfiability test databases still last a week: while the input/output, database compression/decompression, computations of polyhedral characteristics, e.g. number of vertices, for each input using the Chernikova algorithm, output comparisons and timeout exception cases, which are not counted in our displayed total execution time as explained in 6_polybench_implementation, already require important execution times, our implementation of head-to-head comparisons sometimes requires several executions of the same implementation on the same databases, which adds up to the total execution times. For example, JANUS versus Simplex and JANUS versus Fourier-Motzkin need two executions of JANUS on our satisfiability databases. Since other databases are smaller, we use no sampling when possible;

• Filtered Database: only large size constraint systems, large according to some size criteria, are selected to analyze better the impact of exceptions. Thus this database is biased on purpose. We have used the following criterion: $((dimensions > 80) \lor (nb\_constraints > 50) \lor (density > 200) \lor (magnitude>800))$. It presents the case where the ``size'' of constraint systems is relatively large, which might lead to large run times according to our experimentation on some extracted examples. We notice here that, for some cases, these databases are very small or even empty, thus they are only used for statistical purposes.