% Runtimes for solver ve --elim random
% using query 2.1
times_ve_elim_random_2_1 = [ 284,  298,  329,  363,  372,  405,  431,  516,  523,  527,  580,  661,  670,  674,  678,  690,  702,  707,  738,  744,  748,  753,  769,  772,  793,  795,  796,  848,  857,  868,  881,  886,  909,  911,  929,  938,  940,  942,  950,  976,  979,  990,  1017,  1052,  1072,  1078,  1101,  1103,  1123,  1156,  1204,  1217,  1225,  1248,  1254,  1260,  1263,  1263,  1267,  1283,  1292,  1325,  1330,  1363,  1369,  1391,  1393,  1409,  1411,  1422,  1440,  1450,  1470,  1479,  1488,  1493,  1525,  1527,  1528,  1546,  1551,  1571,  1573,  1585,  1633,  1637,  1638,  1646,  1654,  1686,  1712,  1724,  1740,  1745,  1781,  1800,  1808,  1809,  1879,  1888,  1889,  1898,  1904,  1909,  1928,  1968,  1993,  1996,  2065,  2075,  2109,  2122,  2173,  2186,  2217,  2266,  2300,  2306,  2311,  2320,  2334,  2342,  2349,  2351,  2356,  2386,  2394,  2403,  2408,  2428,  2447,  2467,  2471,  2482,  2484,  2531,  2537,  2563,  2569,  2592,  2605,  2619,  2644,  2665,  2705,  2714,  2724,  2837,  2840,  2855,  2880,  2959,  2966,  2996,  3032,  3044,  3082,  3091,  3121,  3183,  3186,  3189,  3191,  3202,  3210,  3267,  3285,  3307,  3366,  3411,  3417,  3437,  3438,  3460,  3501,  3528,  3573,  3587,  3601,  3602,  3662,  3684,  3805,  3833,  3851,  3951,  3991,  4048,  4105,  4113,  4115,  4182,  4210,  4226,  4228,  4252,  4259,  4266,  4270,  4276,  4292,  4293,  4300,  4342,  4364,  4432,  4455,  4458,  4495,  4605,  4624,  4661,  4661,  4703,  4730,  4767,  4783,  4899,  4928,  4954,  4965,  5009,  5021,  5027,  5041,  5094,  5120,  5122,  5131,  5159,  5167,  5171,  5215,  5224,  5227,  5318,  5343,  5361,  5361,  5370,  5459,  5460,  5527,  5625,  5659,  5672,  5704,  5708,  5780,  5783,  5848,  5877,  5912,  5916,  5953,  6078,  6171,  6179,  6184,  6209,  6295,  6340,  6468,  6541,  6580,  6599,  6614,  6629,  6655,  6685,  6707,  6829,  6873,  6919,  7126,  7159,  7193,  7223,  7240,  7265,  7282,  7311,  7785,  7802,  7985,  8038,  8110,  8190,  8222,  8284,  8288,  8358,  8375,  8421,  8588,  8649,  8690,  8699,  8712,  8728,  8753,  8783,  8789,  8811,  8905,  9034,  9101,  9385,  9397,  9456,  9491,  9623,  9667,  10002,  10020,  10064,  10228,  10287,  10358,  10398,  10487,  10496,  10541,  10674,  10953,  11002,  11086,  11170,  11205,  11306,  11313,  11353,  11513,  11578,  11863,  11901,  11911,  12054,  12092,  12138,  12199,  12285,  12318,  12407,  12428,  12496,  12503,  12632,  12734,  12896,  13035,  13143,  13243,  13800,  14158,  14188,  14325,  14418,  14688,  15286,  15351,  15555,  15563,  15580,  15685,  16128,  16261,  16421,  16588,  16945,  17069,  17084,  17190,  17406,  17816,  18162,  18268,  18547,  18651,  19225,  19723,  19794,  20084,  20576,  20614,  20749,  20762,  20807,  21230,  21298,  21437,  21550,  21995,  22019,  22354,  22682,  22965,  23109,  23292,  23740,  24165,  24323,  24594,  24640,  24716,  24746,  24913,  25117,  25134,  25707,  26030,  26069,  26094,  26527,  26746,  26805,  27834,  29435,  29913,  29953,  30167,  33172,  33378,  33578,  33927,  34828,  34915,  35018,  35144,  35712,  35760,  36222,  37841,  39058,  39358,  40675,  45921,  46005,  46134,  46407,  46639,  46919,  47460,  49635,  49875,  49907,  50471,  50702,  51590,  51727,  52525,  52968,  53818,  54644,  56927,  60530,  60896,  65635,  69317,  74404,  75978,  76105,  81204,  82006,  82250,  89200,  90964,  91047,  92784,  102977,  107896,  113178,  126663,  135534,  136815,  220702,  271225,  278096,  333715,  333715 ];
hist(log10(times_ve_elim_random_2_1), 35);
xlabel('x = Log_{10}(milliseconds)');
ylabel('Number of trials of length 10^x milliseconds ');
print -deps2 ve_elim_random_2_1