## 6 Results and Discussion
### RQ2: Does MPPEngine Produce More Patches for Bugs Compared to jGenProg?
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Bug** & **Approach** & **No. of Patches** & **TC Count** & **Patch Diff. Count** & **Better?** \\ \hline Chart 1 & jGenProg & 226 & 1,129,624 & 4 & MPPEngine \\  & MPPEngine & 230 & 1,158,113 & & \\ \hline Chart 3 & jGenProg & 9 & 192,418 & 23 & MPPEngine \\  & MPPEngine & 32 & 1,387,003 & & \\ \hline Chart 5 & jGenProg & 2 & 144,165 & 0 & Same \\  & MPPEngine & 2 & 649,313 & 0 & Same \\ \hline Chart 7 & jGenProg & 6 & 387,157 & 0 & Same \\  & MPPEngine & 6 & 379,745 & 0 & Same \\ \hline Chart 12 & jGenProg & x & x & \\  & MPPEngine & 1 & 21,118 & 1 & MPPEngine \\ \hline Chart 13 & jGenProg & 550 & 2,078,382 & & \\  & MPPEngine & 490 & 1,751,298 & 60 & jGenProg \\ \hline Chart 14 & jGenProg & 7 & 182,591 & & \\  & MPPEngine & x & 459,574 & 7 & jGenProg \\ \hline Chart 15 & jGenProg & 36 & 169,752 & & \\  & MPPEngine & 23 & 133,133 & 13 & jGenProg \\ \hline Chart 25 & jGenProg & 51 & 1,073,187 & & \\  & MPPEngine & 79 & 323,300 & 28 & MPPEngine \\ \hline Chart 26 & jGenProg & 38 & 1,682,156 & & \\  & MPPEngine & 49 & 792,467 & 11 & MPPEngine \\ \hline Math 20 & jGenProg & x & x & & \\  & MPPEngine & 34 & 67,160 & & \\ \hline Math 28 & jGenProg & x & x & & \\  & MPPEngine & 142 & 129,675 & & \\ \hline Math 32 & jGenProg & x & x & & \\  & MPPEngine & 6 & 16,351 & 6 & MPPEngine \\ \hline Math 49 & jGenProg & x & x & & \\  & MPPEngine & 26 & 40,314 & 26 & MPPEngine \\ \hline Math 50 & jGenProg & x & x & & \\  & MPPEngine & 112 & 121,654 & 112 & MPPEngine \\ \hline Math 60 & jGenProg & 2 & 27,794 & & \\  & MPPEngine & 2 & 25,492 & 0 & Same \\ \hline Math 64 & jGenProg & 1 & 118,020 & & \\  & MPPEngine & 1 & 118,304 & 0 & Same \\ \hline Math 70 & jGenProg & 2 & 153,420 & & \\  & MPPEngine & 2 & 154,858 & 0 & Same \\ \hline Math 71 & jGenProg & 1 & 26,482 & & \\  & MPPEngine & 3 & 36,320 & 2 & MPPEngine \\ \hline Math 73 & jGenProg & 17 & 112,824 & & \\  & MPPEngine & 17 & 108,728 & 0 & Same \\ \hline Math 78 & jGenProg & 1 & 389,952 & & \\  & MPPEngine & 12 & 121,657 & 11 & MPPEngine \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experiment results of jGenProg and MPPEngine on Defects4j benchmark. Therefore, MPPEngine produced equal or more patches than jGenProg except for 4 bugs (14.82%): Chart 13, Chart 14, Chart 15, and Math 15 bugs for which jGenProg produced more patches. However, it is clear that the repair efficiency of MPPEngine is at least good as jGenProg for 10 bugs (37.04%) and better than jGenProg for 12 bugs (44.5%). To prove the overall performance of our MPPEngine, we performed a statistical data analysis on both approaches in terms of the number of patches generated. From Table 4, we can observe the sample statistics for the number of patches generated by jGenProg and MPPEngine. As per the statistics, there was a significant difference in the scores of jGenProg (Mean = 44.52, Standard Deviation = 111.43) and MPPEngine (Mean = 56.44, Standard Deviation = 102.02). This data analysis has been conducted on 27 observations (data) in total with p value = 0.05 and obtained t (27) = 1.65. The Mean value suggests that jGenProg does produce less patches compared to MPPEngine. Also, the standard error of MPPEngine (19.63) is lesser than jGenProg (21.45). This also means that the smaller the standard error, the less the spread and the more likely it is that any sample mean is close to the population mean. So, when a buggy program is processed through MPPEngine, the number of patches generated is increased. Therefore, it is evidence that, on average, our module MPPEngine does lead to improvements. RQ3: Is There Any New Patch Generated for Bugs by MPPEngine for Which jGenProg Does Not Produce Any Solution? In this section, we investigate whether our proposed approach produced any new patch to the buggy programs in the given time limit and within maximum generation. Figure 3 compares the patches generated by both jGenProg and MPPEngine. There are patches generated for 27 bugs in which 20 bugs (20/27) were repaired in the same way by both approaches.