Commit 7724b549 authored by ehebrard's avatar ehebrard
Browse files

cactuses

parent 1cfd31cb
......@@ -1404,6 +1404,15 @@ for low values of \numfeat\ and $\mdepth$.
% \numfeat) is low, and for small values of $\mdepth$.
When $\numfeat$ grows, however, it often exceeds the memory limit of 50GB (whereas \budalg does not require more memory than the size of the data set). Finally, \binoct does not produce a single optimality proof and very often exceeds the memory limit.%\footnote{In the experiments in \cite{verwer2019learning} not all datapoints were used.}
\begin{figure}
% \subfloat[depth=3]{\input{src/tables/xscopt3.tex}}
\subfloat[depth=4]{\input{src/tables/xscopt4.tex}}
% \subfloat[depth=5]{\input{src/tables/xscopt5.tex}}
\subfloat[depth=7]{\input{src/tables/xscopt7.tex}}
\subfloat[depth=10]{\input{src/tables/xscopt10.tex}}
\caption{\label{fig:cactus}Proof ratio over time, averaged across all data sets}
\end{figure}
% \clearpage
......@@ -1458,12 +1467,11 @@ We can see in those graphs that \murtree finds an initial tree extremely quickly
\begin{figure}
\subfloat[depth=3]{\input{src/tables/xscerror3.tex}}
% \subfloat[depth=3]{\input{src/tables/xscerror3.tex}}
\subfloat[depth=4]{\input{src/tables/xscerror4.tex}}
% \subfloat[depth=5]{\input{src/tables/xscerror5.tex}}
\subfloat[depth=7]{\input{src/tables/xscerror7.tex}}
\subfloat[depth=10]{\input{src/tables/xscerror10.tex}}
% \subfloat[depth=8]{\input{src/tables/xscerror8.tex}}
% \subfloat[depth=9]{\input{src/tables/xscerror9.tex}}
% \subfloat[depth=10]{\input{src/tables/xscerror10.tex}}
\caption{\label{fig:cactus}Accuracy over time, averaged across all data sets}
\end{figure}
......
This diff is collapsed.
\begin{tabular}{lrrrrrrrrrrrr}
\toprule
\multirow{2}{*}{$\mdepth$}& \multicolumn{3}{c}{\budalg} & \multicolumn{3}{c}{\noheuristic} & \multicolumn{3}{c}{\nopreprocessing} & \multicolumn{3}{c}{\nolb}\\
\cmidrule(rr){2-4}\cmidrule(rr){5-7}\cmidrule(rr){8-10}\cmidrule(rr){11-13}
& \multicolumn{1}{c}{acc.} & \multicolumn{1}{c}{opt.} & \multicolumn{1}{c}{cpu} & \multicolumn{1}{c}{acc.} & \multicolumn{1}{c}{opt.} & \multicolumn{1}{c}{cpu$^*$} & \multicolumn{1}{c}{acc.} & \multicolumn{1}{c}{opt.} & \multicolumn{1}{c}{cpu$^*$} & \multicolumn{1}{c}{acc.} & \multicolumn{1}{c}{opt.} & \multicolumn{1}{c}{cpu$^*$} \\
\midrule
\texttt{3} & 0.8875 & 0.93 & 67 & 0.8871 & 0.93 & -1.6 & 0.8875 & 0.93 & $\mathsmaller{+}$4.3 & 0.8875 & 0.93 & -2.8\\
\texttt{4} & 0.9095 & 0.78 & 388 & 0.9081 & 0.79 & -61 & 0.9093 & 0.72 & $\mathsmaller{+}$47 & 0.9095 & 0.78 & $\mathsmaller{+}$13\\
\texttt{5} & 0.9275 & 0.64 & 479 & 0.9257 & 0.67 & -30 & 0.9272 & 0.55 & $\mathsmaller{+}$276 & 0.9275 & 0.64 & $\mathsmaller{+}$39\\
\texttt{7} & 0.9517 & 0.48 & 1045 & 0.9455 & 0.48 & $\mathsmaller{+}$17 & 0.9512 & 0.43 & $\mathsmaller{+}$163 & 0.9512 & 0.48 & $\mathsmaller{+}$30\\
\texttt{10} & 0.9667 & 0.62 & 570 & 0.9583 & 0.53 & $\mathsmaller{+}$66 & 0.9656 & 0.43 & $\mathsmaller{+}$63 & 0.9665 & 0.60 & $\mathsmaller{+}$8.0\\
\bottomrule
\end{tabular}
\begin{tabular}{lrrr}
\toprule
\multirow{2}{*}{}& \multicolumn{3}{c}{\gosdtmed}\\
\cmidrule(rr){2-4}
& \multicolumn{1}{c}{error} & \multicolumn{1}{c}{size} & \multicolumn{1}{c}{depth} \\
\midrule
\texttt{pendigits} & - & - & -\\
\texttt{vote} & - & - & -\\
\texttt{zoo-1} & - & - & -\\
\texttt{audiology} & 11.0 & 5.0 & 2.0\\
\texttt{german-credit} & 275.0 & 9.0 & 3.0\\
\texttt{weather-aus-un} & - & - & -\\
\texttt{adult\_discretized} & - & - & -\\
\texttt{soybean} & 92.0 & 1.0 & 0.0\\
\texttt{mnist\_4} & - & - & -\\
\texttt{ionosphere} & - & - & -\\
\texttt{hypothyroid} & 70.0 & 5.0 & 2.0\\
\texttt{heart-cleveland} & 60.0 & 7.0 & 2.0\\
\texttt{taiwan\_binarised} & - & - & -\\
\texttt{breast-cancer-un} & 35.0 & 7.0 & 2.0\\
\texttt{wine2-un} & - & - & -\\
\texttt{hepatitis} & 17.0 & 5.0 & 2.0\\
\texttt{tic-tac-toe} & - & - & -\\
\texttt{vehicle} & - & - & -\\
\texttt{anneal} & 119.0 & 13.0 & 5.0\\
\texttt{titanic-un} & - & - & -\\
\texttt{mushroom} & - & - & -\\
\texttt{yeast} & 440.0 & 5.0 & 2.0\\
\texttt{car-un} & 178.0 & 9.0 & 4.0\\
\texttt{letter} & - & - & -\\
\texttt{lymph} & 22.0 & 7.0 & 2.0\\
\texttt{surgical-deepnet-un} & - & - & -\\
\texttt{segment} & 5.0 & 7.0 & 3.0\\
\texttt{wine3-un} & - & - & -\\
\texttt{diabetes} & - & - & -\\
\texttt{compas\_discretized} & 2045.0 & 9.0 & 4.0\\
\texttt{primary-tumor} & - & - & -\\
\texttt{kr-vs-kp} & 494.0 & 7.0 & 2.0\\
\texttt{forest-fires-un} & - & - & -\\
\texttt{splice-1} & - & - & -\\
\texttt{bank-un} & - & - & -\\
\texttt{wine1-un} & - & - & -\\
\texttt{australian-credit} & - & - & -\\
\texttt{mnist\_9} & - & - & -\\
\texttt{mnist\_8} & - & - & -\\
\texttt{mnist\_5} & - & - & -\\
\texttt{breast-wisconsin} & 31.0 & 5.0 & 2.0\\
\texttt{mnist\_7} & - & - & -\\
\texttt{mnist\_6} & - & - & -\\
\texttt{mnist\_1} & - & - & -\\
\texttt{mnist\_0} & - & - & -\\
\texttt{mnist\_3} & - & - & -\\
\texttt{mnist\_2} & - & - & -\\
\bottomrule
\end{tabular}
\alt<2->{\newcolumntype{R}{>{\columncolor{red!30}}r}}{\newcolumntype{R}{r}}
\alt<3->{\newcolumntype{B}{>{\columncolor{blue!30}}r}}{\newcolumntype{B}{r}}
\tabcolsep=9pt
\begin{tabular}{lRBrrrrRB
% rrrrrr
}
\toprule
\multirow{2}{*}{$\mdepth$}& \multicolumn{6}{c}{\budalg}
% & \multicolumn{6}{c}{\murtree}
& \multicolumn{2}{c}{\cart}\\
\cmidrule(rr){2-7}
% \cmidrule(rr){8-13}\cmidrule(rr){14-15}
\cmidrule(rr){8-9}
& \multicolumn{1}{c}{cpu} & \multicolumn{1}{c}{first} & \multicolumn{1}{c}{$\leq$3s} & \multicolumn{1}{c}{$\leq$10s} & \multicolumn{1}{c}{$\leq$1m} & \multicolumn{1}{c}{$\leq$5m}
%& \multicolumn{1}{c}{cpu} & \multicolumn{1}{c}{first} & \multicolumn{1}{c}{$\leq$3s} & \multicolumn{1}{c}{$\leq$10s} & \multicolumn{1}{c}{$\leq$1m} & \multicolumn{1}{c}{$\leq$5m}
& \multicolumn{1}{c}{cpu} & \multicolumn{1}{c}{first} \\
\midrule
\texttt{3} & 0.03 & 858 & 808 & 798 & 793 & 793
% & 0.04 & 2156 & 1060 & 974 & 967 & 967
& 1.48 & 871\\
\texttt{4} & 0.03 & 751 & 725 & 714 & 706 & 698
% & 0.04 & 2156 & 1396 & 860 & 853 & 843
& 1.60 & 758\\
\texttt{5} & 0.03 & 670 & 641 & 638 & 632 & 626
% & 0.04 & 2156 & 803 & 788 & 775 & 762
& 2.30 & 674\\
\texttt{7} & 0.04 & 559 & 537 & 531 & 528 & 522
% & 0.05 & 2156 & 872 & 634 & 628 & 618
& 3.55 & 568\\
\texttt{10} & 0.04 & 456 & 437 & 431 & 423 & 418
% & 0.04 & 2156 & 802 & 511 & 507 & 497
& 4.33 & 462\\
\bottomrule
\end{tabular}
This diff is collapsed.
\begin{tabular}{lrrrrrrrrrrrrr}
\toprule
\multirow{2}{*}{$\mdepth$}& \multicolumn{6}{c}{\budalg} & \multicolumn{6}{c}{\murtree} & \multicolumn{1}{c}{\cart}\\
\cmidrule(rr){2-7}\cmidrule(rr){8-13}\cmidrule(rr){14-14}
& \multicolumn{1}{c}{cpu} & \multicolumn{1}{c}{first} & \multicolumn{1}{c}{$\leq$3s} & \multicolumn{1}{c}{$\leq$10s} & \multicolumn{1}{c}{$\leq$1m} & \multicolumn{1}{c}{$\leq$5m} & \multicolumn{1}{c}{cpu} & \multicolumn{1}{c}{first} & \multicolumn{1}{c}{$\leq$3s} & \multicolumn{1}{c}{$\leq$10s} & \multicolumn{1}{c}{$\leq$1m} & \multicolumn{1}{c}{$\leq$5m} & \multicolumn{1}{c}{first} \\
\midrule
\texttt{3} & 0.03 & 0.8743 & 0.8867 & 0.8871 & 0.8874 & 0.8875 & 0.04 & 0.7089 & 0.8821 & 0.8841 & 0.8845 & 0.8845 & 0.8719\\
\texttt{4} & 0.03 & 0.8918 & 0.9069 & 0.9078 & 0.9090 & 0.9092 & 0.04 & 0.7089 & 0.8972 & 0.9046 & 0.9060 & 0.9069 & 0.8909\\
\texttt{5} & 0.03 & 0.9062 & 0.9231 & 0.9249 & 0.9262 & 0.9269 & 0.04 & 0.7089 & 0.9121 & 0.9163 & 0.9205 & 0.9223 & 0.9053\\
\texttt{7} & 0.04 & 0.9299 & 0.9431 & 0.9455 & 0.9471 & 0.9491 & 0.05 & 0.7089 & 0.9270 & 0.9328 & 0.9357 & 0.9414 & 0.9286\\
\texttt{10} & 0.04 & 0.9527 & 0.9613 & 0.9626 & 0.9637 & 0.9647 & 0.04 & 0.7089 & 0.9429 & 0.9509 & 0.9527 & 0.9555 & 0.9521\\
\bottomrule
\end{tabular}
\begin{tabular}{lrrrrrrrrrrrrrrr}
\toprule
\multirow{2}{*}{$\mdepth$}& \multicolumn{3}{c}{\budalg} & \multicolumn{3}{c}{\murtree} & \multicolumn{3}{c}{\cp} & \multicolumn{4}{c}{\dleight} & \multicolumn{2}{c}{\binoct}\\
\cmidrule(rr){2-4}\cmidrule(rr){5-7}\cmidrule(rr){8-10}\cmidrule(rr){11-14}\cmidrule(rr){15-16}
& \multicolumn{1}{c}{opt.} & \multicolumn{1}{c}{error} & \multicolumn{1}{c}{cpu} & \multicolumn{1}{c}{opt.} & \multicolumn{1}{c}{error} & \multicolumn{1}{c}{cpu$^*$} & \multicolumn{1}{c}{opt.} & \multicolumn{1}{c}{error} & \multicolumn{1}{c}{cpu$^*$} & \multicolumn{1}{c}{sol.} & \multicolumn{1}{c}{opt.} & \multicolumn{1}{c}{error$^*$} & \multicolumn{1}{c}{cpu$^*$} & \multicolumn{1}{c}{sol.} & \multicolumn{1}{c}{error$^*$} \\
\midrule
&\multicolumn{15}{c}{$\numfeat < 100$ (29 data sets)}\\
\midrule
\texttt{3} & 1.00 & 458 & 0.23 & 1.00 & 458 & $\mathsmaller{+}$0.31 & 1.00 & 458 & $\mathsmaller{+}$3.2 & 1.00 & 1.00 & 0 & $\mathsmaller{+}$2.5 & 0.52 & $\mathsmaller{+}$57\\
\texttt{4} & 1.00 & 412 & 14 & 1.00 & 412 & $\mathsmaller{+}$8.0 & 1.00 & 412 & $\mathsmaller{+}$115 & 1.00 & 1.00 & 0 & $\mathsmaller{+}$105 & 0.52 & $\mathsmaller{+}$89\\
\texttt{5} & 0.93 & 379 & 187 & 0.97 & 379 & -12 & 0.62 & 380 & $\mathsmaller{+}$121 & 0.76 & 0.66 & $\mathsmaller{+}$2.5 & $\mathsmaller{+}$2.0 & 0.52 & $\mathsmaller{+}$211\\
\texttt{7} & 0.66 & 329 & 81 & 0.69 & 348 & $\mathsmaller{+}$90 & 0.45 & 682 & $\mathsmaller{+}$193 & 0.66 & 0.55 & $\mathsmaller{+}$93 & $\mathsmaller{+}$6.7 & 0.52 & $\mathsmaller{+}$350\\
\texttt{10} & 0.79 & 270 & 85 & 0.52 & 320 & $\mathsmaller{+}$83 & 0.45 & 766 & $\mathsmaller{+}$2.6 & 0.62 & 0.52 & $\mathsmaller{+}$278 & $\mathsmaller{+}$49 & 0.41 & $\mathsmaller{+}$292\\
\midrule
&\multicolumn{15}{c}{$\numfeat \geq 100$ (29 data sets)}\\
\midrule
\texttt{3} & 0.86 & 1127 & 100 & 0.86 & 1156 & -42 & 0.72 & 1155 & $\mathsmaller{+}$256 & 0.76 & 0.66 & $\mathsmaller{+}$165 & $\mathsmaller{+}$247 & 0.62 & $\mathsmaller{+}$148\\
\texttt{4} & 0.55 & 979 & 662 & 0.72 & 1023 & $\mathsmaller{+}$64 & 0.28 & 1585 & $\mathsmaller{+}$576 & 0.48 & 0.24 & $\mathsmaller{+}$565 & $\mathsmaller{+}$258 & 0.62 & $\mathsmaller{+}$189\\
\texttt{5} & 0.34 & 870 & 452 & 0.34 & 947 & $\mathsmaller{+}$99 & 0.14 & 1870 & $\mathsmaller{+}$11 & 0.34 & 0.10 & $\mathsmaller{+}$1136 & $\mathsmaller{+}$12 & 0.62 & $\mathsmaller{+}$329\\
\texttt{7} & 0.31 & 688 & 11 & 0.31 & 791 & $\mathsmaller{+}$7.4 & 0.28 & 1857 & $\mathsmaller{+}$571 & 0.34 & 0.14 & $\mathsmaller{+}$1805 & $\mathsmaller{+}$793 & 0.55 & $\mathsmaller{+}$510\\
\texttt{10} & 0.45 & 550 & 101 & 0.41 & 659 & $\mathsmaller{+}$19 & 0.38 & 1827 & $\mathsmaller{+}$85 & 0.45 & 0.28 & $\mathsmaller{+}$1612 & $\mathsmaller{+}$183 & 0.21 & $\mathsmaller{+}$375\\
\bottomrule
\end{tabular}
\begin{tabular}{lrrrrrrrrrrrrrrr}
\toprule
\multirow{2}{*}{$\mdepth$}& \multicolumn{3}{c}{\budalg} & \multicolumn{3}{c}{\murtree} & \multicolumn{3}{c}{\cp} & \multicolumn{4}{c}{\dleight} & \multicolumn{2}{c}{\binoct}\\
\cmidrule(rr){2-4}\cmidrule(rr){5-7}\cmidrule(rr){8-10}\cmidrule(rr){11-14}\cmidrule(rr){15-16}
& \multicolumn{1}{c}{opt.} & \multicolumn{1}{c}{acc.} & \multicolumn{1}{c}{cpu} & \multicolumn{1}{c}{opt.} & \multicolumn{1}{c}{acc.} & \multicolumn{1}{c}{cpu$^*$} & \multicolumn{1}{c}{opt.} & \multicolumn{1}{c}{acc.} & \multicolumn{1}{c}{cpu$^*$} & \multicolumn{1}{c}{sol.} & \multicolumn{1}{c}{opt.} & \multicolumn{1}{c}{acc.$^*$} & \multicolumn{1}{c}{cpu$^*$} & \multicolumn{1}{c}{sol.} & \multicolumn{1}{c}{acc.$^*$} \\
\midrule
&\multicolumn{15}{c}{$\numfeat < 100$ (29 data sets)}\\
\midrule
\texttt{3} & 1.00 & 0.8871 & 0.23 & 1.00 & 0.8871 & $\mathsmaller{+}$0.31 & 1.00 & 0.8871 & $\mathsmaller{+}$3.2 & 1.00 & 1.00 & -0.00\% & $\mathsmaller{+}$2.5 & 0.52 & -1.21\%\\
\texttt{4} & 1.00 & 0.9130 & 14 & 1.00 & 0.9130 & $\mathsmaller{+}$8.0 & 1.00 & 0.9130 & $\mathsmaller{+}$115 & 1.00 & 1.00 & $\mathsmaller{+}$0.00\% & $\mathsmaller{+}$105 & 0.52 & -2.62\%\\
\texttt{5} & 0.93 & 0.9344 & 187 & 0.97 & 0.9344 & -12 & 0.62 & 0.9337 & $\mathsmaller{+}$121 & 0.76 & 0.66 & -0.01\% & $\mathsmaller{+}$2.0 & 0.52 & -3.81\%\\
\texttt{7} & 0.66 & 0.9596 & 81 & 0.69 & 0.9564 & $\mathsmaller{+}$90 & 0.45 & 0.9075 & $\mathsmaller{+}$193 & 0.66 & 0.55 & -0.46\% & $\mathsmaller{+}$6.7 & 0.52 & -7.30\%\\
\texttt{10} & 0.79 & 0.9733 & 85 & 0.52 & 0.9623 & $\mathsmaller{+}$83 & 0.45 & 0.8691 & $\mathsmaller{+}$2.6 & 0.62 & 0.52 & -1.34\% & $\mathsmaller{+}$49 & 0.41 & -29.46\%\\
\midrule
&\multicolumn{15}{c}{$\numfeat \geq 100$ (29 data sets)}\\
\midrule
\texttt{3} & 0.86 & 0.8879 & 100 & 0.86 & 0.8873 & -42 & 0.72 & 0.8875 & $\mathsmaller{+}$256 & 0.76 & 0.66 & -0.25\% & $\mathsmaller{+}$247 & 0.62 & -2.36\%\\
\texttt{4} & 0.55 & 0.9060 & 662 & 0.72 & 0.9050 & $\mathsmaller{+}$64 & 0.28 & 0.8926 & $\mathsmaller{+}$576 & 0.48 & 0.24 & -0.87\% & $\mathsmaller{+}$258 & 0.62 & -4.78\%\\
\texttt{5} & 0.34 & 0.9206 & 452 & 0.34 & 0.9197 & $\mathsmaller{+}$99 & 0.14 & 0.8344 & $\mathsmaller{+}$11 & 0.34 & 0.10 & -1.81\% & $\mathsmaller{+}$12 & 0.62 & -8.55\%\\
\texttt{7} & 0.31 & 0.9439 & 11 & 0.31 & 0.9327 & $\mathsmaller{+}$7.4 & 0.28 & 0.8193 & $\mathsmaller{+}$571 & 0.34 & 0.14 & -2.95\% & $\mathsmaller{+}$793 & 0.55 & -22.33\%\\
\texttt{10} & 0.45 & 0.9602 & 101 & 0.41 & 0.9529 & $\mathsmaller{+}$19 & 0.38 & 0.8612 & $\mathsmaller{+}$85 & 0.45 & 0.28 & -2.68\% & $\mathsmaller{+}$183 & 0.21 & -55.08\%\\
\bottomrule
\end{tabular}
This diff is collapsed.
\cactus{Average Accuracy}{CPU time}{\budalg, \murtree, \cart}{{{(0.8662064701436945, 0) [a]
(0.8700043377060156, 0.001) [a]
(0.8702714609936868, 0.002) [a]
(0.8765154118753802, 0.003) [a]
(0.8767551379027775, 0.006) [a]
(0.8767811653000378, 0.008) [a]
(0.8767976036562022, 0.009) [a]
(0.8831415798503431, 0.01) [a]
(0.8831813058777404, 0.011) [a]
(0.8837758264256855, 0.012) [a]
(0.8867170325349597, 0.015) [a]
(0.8867184023979734, 0.017) [a]
(0.8867197722609871, 0.019) [a]
(0.8879462562792519, 0.02) [a]
(0.8879489960052793, 0.021) [a]
(0.8879613247724026, 0.025) [a]
(0.8880092699778821, 0.026) [a]
(0.8880311877861012, 0.027) [a]
(0.8880846124436355, 0.028) [a]
(0.8884740644984299, 0.03) [a]
(0.8885261192929504, 0.033) [a]
(0.8885617357313066, 0.034) [a]
(0.8885740644984299, 0.035) [a]
(0.8887761192929505, 0.04) [a]
(0.8888939275121286, 0.043) [a]
(0.8889720097039094, 0.044) [a]
(0.8889774891559642, 0.048) [a]
(0.8890822836765121, 0.05) [a]
(0.8890850234025395, 0.058) [a]
(0.8891639275121286, 0.06) [a]
(0.8892317357313066, 0.08) [a]
(0.889264475457334, 0.09) [a]
(0.8892740644984299, 0.096) [a]
(0.8892768042244573, 0.098) [a]
(0.8893884480600738, 0.11) [a]
(0.8894048864162382, 0.138) [a]
(0.8894499549093888, 0.14) [a]
(0.8894526946354162, 0.155) [a]
(0.8894787220326765, 0.157) [a]
(0.8895557083340464, 0.16) [a]
(0.8895598179230875, 0.167) [a]
(0.8895625576491148, 0.168) [a]
(0.8895639275121285, 0.174) [a]
(0.8895652973751422, 0.176) [a]
(0.8895689960052792, 0.2) [a]
(0.8904115342533334, 0.22) [a]
(0.8904653698697718, 0.23) [a]
(0.8904749589108677, 0.239) [a]
(0.89049619178758, 0.24) [a]
(0.8905057808286759, 0.248) [a]
(0.8905113972670321, 0.25) [a]
(0.8905144109656622, 0.26) [a]
(0.890519890417717, 0.305) [a]
(0.8919044380401684, 0.311) [a]
(0.8919427942045519, 0.32) [a]
(0.8919681366703054, 0.33) [a]
(0.8920037531086615, 0.339) [a]
(0.8920112873552368, 0.34) [a]
(0.8920126572182505, 0.359) [a]
(0.892029506533319, 0.36) [a]
(0.8920541640675655, 0.403) [a]
(0.8920671777661957, 0.41) [a]
(0.8920740270812642, 0.492) [a]
(0.8920767668072915, 0.493) [a]
(0.8921537531086614, 0.51) [a]
(0.8922153969442779, 0.539) [a]
(0.8951170574714661, 0.54) [a]
(0.8951204821290003, 0.55) [a]
(0.8951276054166716, 0.56) [a]
(0.8951307561016031, 0.57) [a]
(0.8951362355536578, 0.62) [a]
(0.8952143177454387, 0.64) [a]
(0.8953047287043429, 0.739) [a]
(0.895557123287671, 0.83) [a]
(0.8955573972602737, 0.86) [a]
(0.8955628767123285, 0.907) [a]
(0.8955630136986299, 0.96) [a]
(0.8955709589041093, 1.17) [a]
(0.8955750684931504, 1.213) [a]
(0.8955764383561641, 1.219) [a]
(0.8955765753424655, 1.24) [a]
(0.8955771232876709, 1.25) [a]
(0.8955780821917805, 1.26) [a]
(0.8955808219178079, 1.39) [a]
(0.8956130136986298, 1.43) [a]
(0.8956131506849312, 1.44) [a]
(0.8956143835616435, 1.65) [a]
(0.8956145205479449, 1.78) [a]
(0.8956150684931503, 1.8) [a]
(0.895615342465753, 2.07) [a]
(0.895617534246575, 2.37) [a]
(0.8956631506849312, 2.39) [a]
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}}}{legend pos=north west}
\ No newline at end of file
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