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\begin{itemize}
\item classification accuracy of each rule must exceed 90\%, because we deem a 10\% false-positive error as acceptable;
\item each term in the condition of a rule must be significant according to the likelihood test, meaning that each pattern in the condition part is indeed relevant (we set the significance threshold to p=0.05);
\item a condition can have at most 3 patterns; and
\item each rule must cover at least 5 distinct programs -- to avoid learning redundant rules representing the same error.
\end{itemize}
\begin{table}[t]
\caption{Solving statistics, classification accuracy, and coverage of rules for several introductory Python problems. The second column shows the number of users attempting the problem. Columns 3 and 4 show the number of all / correct submissions. The next two columns show the classification accuracy for the majority and random-forest classifiers. The last three columns show percentages of covered examples: columns $n_p$ and $n$ give covered incorrect programs (n-rules with presence of patterns and all n-rules), and column $p$ gives the percentage of correct programs covered by p-rules.}
\centering
\begin{tabular}{l|c|cc|cc|ccc}
& & \multicolumn{2}{c|}{\textbf{Submissions}} & \multicolumn{2}{c|}{\textbf{CA}} & \multicolumn{3}{c}{\textbf{Coverage}} \\
\textbf{Problem} & \textbf{Users} & Total & Correct & Maj & RF & $n_p$ & $n$ & $p$ \\
\hline
\textsf{fahrenheit\_to\_celsius}& 521 & 1177 & 495 & 0.579 & 0.933 & 0.708 & 0.935 & 0.867 \\
%\textsf{pythagorean\_theorem}& 349 & 669 & 317 & 0.499 & 0.809 \\
\textsf{ballistics}& 248 & 873 & 209 & 0.761 & 0.802 & 0.551 & 0.666 & 0.478 \\
\textsf{average}& 209 & 482 & 186 & 0.614 & 0.830 & 0.230 & 0.338 & 0.618 \\
\hline
\textsf{buy\_five}& 294 & 476 & 292 & 0.613 & 0.828 & 0.234 & 0.489 & 0.719 \\
\textsf{competition}& 227 & 327 & 230 & 0.703 & 0.847 & 0.361 & 0.515 & 0.896 \\
\textsf{top\_shop}& 142 & 476 & 133 & 0.721 & 0.758 & 0.399 & 0.802 & 0.444 \\
\textsf{minimax}& 74 & 163 & 57 & 0.650 & 0.644 & 0.462 & 0.745 & 0.298 \\
\textsf{checking\_account}& 132 & 234 & 112 & 0.521 & 0.744 & 0.143 & 0.491 & 0.115\\
\textsf{consumers\_anon}& 65 & 170 & 53 & 0.688 & 0.800 & 0.376 & 0.880 & 0.623 \\
\hline
\textsf{greatest}& 70 & 142 & 83 & 0.585 & 0.859 & 0.492 & 0.746 & 0.880\\
\textsf{greatest\_abs}& 58 & 155 & 57 & 0.632 & 0.845 & 0.612 & 0.878 & 0.789 \\
\textsf{greatest\_neg}& 62 & 195 & 71 & 0.636 & 0.815 & 0.621 & 0.960 & 0.718 \\
\hline
Total / average & 2102 & 4811 & 1978 & 0.642 & 0.809 & 0.432 & 0.704 & 0.620 \\
\end{tabular}
\label{tab:stats}
\end{table}
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