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fix(simulation): correct exponential sampling and cache behavior logic

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- Fixed incorrect use of exponential sampling for `next_request` and `next_refresh` timings.
- Adjusted cache eviction logic to properly handle capacity checks.
- Improved simulation output and logging for least accessed objects.
- Corrected CSV export to include index labels for better data clarity.
- Reran experiments

Signed-off-by: Tuan-Dat Tran <tuan-dat.tran@tudattr.dev>
This commit is contained in:
Tuan-Dat Tran
2024-11-28 11:19:04 +01:00
parent dea6004160
commit 09b943e41d
41 changed files with 1828 additions and 1435 deletions
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200
experiments/No_Refresh_4_0s_ttl/details.csv
View File

@@ -1,100 +1,100 @@
,access_count,hits,misses,mu,lambda,hit_rate,avg_age
1,664,527,137,0,1,52.83,1.9316888045540797
2,212,112,100,0,3,79.79,2.080357142857143
3,673,537,136,0,1,80.87,2.0242085661080074
4,711,575,136,0,1,68.99,2.1339130434782607
5,345,238,107,0,2,79.35,2.168067226890756
6,649,515,134,0,1,43.8,1.9300970873786407
7,137,60,77,0,5,80.32,1.9333333333333333
8,681,547,134,0,1,79.97,2.03290676416819
9,689,551,138,0,1,79.31,1.9945553539019965
10,667,529,138,0,1,68.29,2.007561436672968
11,328,224,104,0,2,80.2,1.9866071428571428
12,692,555,137,0,1,80.09,1.936936936936937
13,683,547,136,0,1,80.6,2.113345521023766
14,696,561,135,0,1,67.15,1.9946524064171123
15,344,231,113,0,2,65.64,1.8874458874458875
16,326,214,112,0,2,80.12,2.046728971962617
17,689,552,137,0,1,80.32,1.9728260869565217
18,691,555,136,0,1,55.71,2.045045045045045
19,219,122,97,0,3,80.87,1.9344262295081966
20,732,592,140,0,1,81.33,2.0591216216216215
21,739,601,138,0,1,79.8,2.043261231281198
22,683,545,138,0,1,79.85,1.9064220183486238
23,670,535,135,0,1,67.07,1.97196261682243
24,331,222,109,0,2,80.66,2.1036036036036037
25,724,584,140,0,1,80.35,1.9777397260273972
26,692,556,136,0,1,80.85,2.1097122302158273
27,705,570,135,0,1,43.8,2.1070175438596492
28,137,60,77,0,5,79.76,2.1666666666666665
29,672,536,136,0,1,79.83,1.9011194029850746
30,694,554,140,0,1,79.82,1.96028880866426
31,674,538,136,0,1,47.92,2.0780669144981414
32,144,69,75,0,4,79.55,2.1594202898550723
33,670,533,137,0,1,43.26,1.8818011257035647
34,141,61,80,0,4,79.51,2.2131147540983607
35,659,524,135,0,1,80.03,2.068702290076336
36,691,553,138,0,1,80.73,1.9620253164556962
37,737,595,142,0,1,57.08,1.946218487394958
38,219,125,94,0,3,37.0,2.096
39,100,37,63,0,8,80.39,2.27027027027027
40,714,574,140,0,1,50.54,2.06794425087108
41,184,93,91,0,4,47.83,2.204301075268817
42,161,77,84,0,4,68.51,2.1948051948051948
43,362,248,114,0,2,80.6,1.8830645161290323
44,696,561,135,0,1,78.63,2.0089126559714794
45,627,493,134,0,1,79.63,1.997971602434077
46,648,516,132,0,1,24.53,2.0174418604651163
47,53,13,40,0,10,79.73,2.1538461538461537
48,676,539,137,0,1,78.68,1.9851576994434137
49,638,502,136,0,1,79.35,2.0358565737051793
50,673,534,139,0,1,42.97,1.9194756554307115
51,128,55,73,0,5,30.59,1.6363636363636365
52,85,26,59,0,9,81.12,1.8846153846153846
53,747,606,141,0,1,81.0,2.0132013201320134
54,700,567,133,0,1,80.2,2.0
55,687,551,136,0,1,81.25,1.9310344827586208
56,720,585,135,0,1,79.57,1.982905982905983
57,690,549,141,0,1,12.5,2.0491803278688523
58,40,5,35,0,17,65.72,2.2
59,318,209,109,0,2,79.82,1.9569377990430623
60,674,538,136,0,1,21.74,2.029739776951673
61,23,5,18,0,26,80.94,0.6
62,724,586,138,0,1,78.34,1.9112627986348123
63,628,492,136,0,1,66.96,1.8333333333333333
64,345,231,114,0,2,80.62,1.948051948051948
65,681,549,132,0,1,28.77,2.034608378870674
66,73,21,52,0,10,79.57,2.0952380952380953
67,651,518,133,0,1,0.0,2.0656370656370657
68,10,0,10,0,69,78.46,0.0
69,636,499,137,0,1,79.73,1.9799599198396793
70,656,523,133,0,1,67.74,2.0095602294455066
71,372,252,120,0,2,80.38,1.9722222222222223
72,678,545,133,0,1,79.31,1.891743119266055
73,638,506,132,0,1,79.85,1.8893280632411067
74,685,547,138,0,1,52.24,2.043875685557587
75,201,105,96,0,3,65.99,2.2095238095238097
76,344,227,117,0,2,68.41,1.9955947136563876
77,345,236,109,0,2,59.0,2.0254237288135593
78,261,154,107,0,3,14.89,2.0064935064935066
79,47,7,40,0,15,79.7,1.5714285714285714
80,660,526,134,0,1,79.02,2.0
81,634,501,133,0,1,43.07,2.0339321357285427
82,137,59,78,0,5,65.05,1.8644067796610169
83,309,201,108,0,2,80.47,2.2487562189054726
84,686,552,134,0,1,79.47,1.9909420289855073
85,682,542,140,0,1,64.91,1.985239852398524
86,322,209,113,0,2,79.14,1.8229665071770336
87,676,535,141,0,1,65.23,2.0261682242990653
88,325,212,113,0,2,80.41,1.9575471698113207
89,689,554,135,0,1,80.43,1.94043321299639
90,695,559,136,0,1,67.59,2.0697674418604652
91,324,219,105,0,2,67.36,1.9680365296803652
92,337,227,110,0,2,56.76,1.9162995594713657
93,222,126,96,0,3,79.74,1.9523809523809523
94,686,547,139,0,1,68.38,2.1316270566727606
95,351,240,111,0,2,80.61,2.0208333333333335
96,717,578,139,0,1,79.52,2.0328719723183393
97,664,528,136,0,1,17.39,1.9109848484848484
98,23,4,19,0,37,53.04,3.0
99,181,96,85,0,4,68.25,1.8854166666666667
obj_id,access_count,hits,misses,mu,lambda,hit_rate,avg_age
1,122,98,24,0,1,92.41,1.9081632653061225
2,382,353,29,0,3,79.53,2.0226628895184136
3,127,101,26,0,1,77.88,2.108910891089109
4,113,88,25,0,1,88.52,1.7840909090909092
5,244,216,28,0,2,77.59,2.199074074074074
6,116,90,26,0,1,95.43,1.9333333333333333
7,656,626,30,0,5,81.25,1.8801916932907348
8,128,104,24,0,1,78.07,2.125
9,114,89,25,0,1,79.13,2.1797752808988764
10,115,91,24,0,1,88.62,1.967032967032967
11,246,218,28,0,2,81.82,1.9311926605504588
12,132,108,24,0,1,80.58,2.0462962962962963
13,139,112,27,0,1,79.17,1.9107142857142858
14,120,95,25,0,1,89.27,1.8421052631578947
15,261,233,28,0,2,87.56,1.9871244635193133
16,225,197,28,0,2,79.17,1.9543147208121827
17,120,95,25,0,1,79.49,1.9157894736842105
18,117,93,24,0,1,91.67,2.129032258064516
19,360,330,30,0,3,79.49,2.1303030303030304
20,117,93,24,0,1,79.85,2.161290322580645
21,134,107,27,0,1,82.31,2.0186915887850465
22,147,121,26,0,1,81.69,2.206611570247934
23,142,116,26,0,1,89.39,2.146551724137931
24,264,236,28,0,2,78.86,1.978813559322034
25,123,97,26,0,1,81.56,1.8762886597938144
26,141,115,26,0,1,79.69,1.9130434782608696
27,128,102,26,0,1,94.68,1.8725490196078431
28,564,534,30,0,5,79.7,1.9887640449438202
29,133,106,27,0,1,79.2,1.849056603773585
30,125,99,26,0,1,78.26,1.8585858585858586
31,115,90,25,0,1,93.8,2.2888888888888888
32,468,439,29,0,4,78.45,2.0979498861047836
33,116,91,25,0,1,94.18,2.076923076923077
34,498,469,29,0,4,80.3,1.9829424307036247
35,132,106,26,0,1,74.0,1.990566037735849
36,100,74,26,0,1,81.88,1.864864864864865
37,149,122,27,0,1,91.83,2.0
38,355,326,29,0,3,96.78,1.9662576687116564
39,962,931,31,0,8,81.25,2.045112781954887
40,128,104,24,0,1,93.88,2.076923076923077
41,474,445,29,0,4,93.94,1.9235955056179774
42,495,465,30,0,4,87.79,2.163440860215054
43,213,187,26,0,2,76.79,1.9732620320855614
44,112,86,26,0,1,79.07,1.9069767441860466
45,129,102,27,0,1,81.95,2.127450980392157
46,133,109,24,0,1,97.54,2.2018348623853212
47,1262,1231,31,0,10,81.62,1.893582453290008
48,136,111,25,0,1,81.56,1.7747747747747749
49,141,115,26,0,1,78.15,1.791304347826087
50,119,93,26,0,1,95.16,1.989247311827957
51,599,570,29,0,5,97.29,1.9929824561403509
52,1106,1076,30,0,9,80.17,1.95817843866171
53,121,97,24,0,1,80.92,1.9484536082474226
54,131,106,25,0,1,81.45,2.0283018867924527
55,124,101,23,0,1,81.54,2.0693069306930694
56,130,106,24,0,1,79.03,1.971698113207547
57,124,98,26,0,1,98.54,2.010204081632653
58,2118,2087,31,0,17,86.83,1.9223766171538093
59,205,178,27,0,2,81.75,2.151685393258427
60,137,112,25,0,1,99.04,2.080357142857143
61,3216,3185,31,0,26,81.16,1.8982731554160126
62,138,112,26,0,1,78.63,2.232142857142857
63,117,92,25,0,1,89.39,2.0434782608695654
64,264,236,28,0,2,82.01,1.9957627118644068
65,139,114,25,0,1,97.52,1.8596491228070176
66,1248,1217,31,0,10,83.56,1.9079704190632703
67,146,122,24,0,1,99.63,1.9262295081967213
68,8414,8383,31,0,69,78.45,1.6843612072050578
69,116,91,25,0,1,79.17,1.9120879120879122
70,120,95,25,0,1,88.93,1.7473684210526317
71,244,217,27,0,2,79.49,2.013824884792627
72,117,93,24,0,1,80.92,1.989247311827957
73,131,106,25,0,1,82.39,1.9528301886792452
74,142,117,25,0,1,91.55,1.9145299145299146
75,343,314,29,0,3,88.4,1.9490445859872612
76,250,221,29,0,2,88.93,2.004524886877828
77,253,225,28,0,2,92.64,1.951111111111111
78,394,365,29,0,3,98.38,1.9534246575342467
79,1910,1879,31,0,15,79.17,1.8696114954763172
80,120,95,25,0,1,78.51,1.8526315789473684
81,121,95,26,0,1,95.36,2.0
82,647,617,30,0,5,88.71,1.8622366288492707
83,248,220,28,0,2,82.64,2.0045454545454544
84,144,119,25,0,1,77.78,2.033613445378151
85,108,84,24,0,1,87.2,2.1547619047619047
86,211,184,27,0,2,80.6,2.119565217391304
87,134,108,26,0,1,87.95,2.1296296296296298
88,224,197,27,0,2,82.22,2.1472081218274113
89,135,111,24,0,1,79.84,1.9189189189189189
90,124,99,25,0,1,88.33,2.2323232323232323
91,240,212,28,0,2,87.77,1.9622641509433962
92,229,201,28,0,2,92.62,1.935323383084577
93,393,364,29,0,3,78.4,2.1538461538461537
94,125,98,27,0,1,89.11,1.8673469387755102
95,257,229,28,0,2,81.29,1.8646288209606987
96,139,113,26,0,1,81.89,1.9823008849557522
97,127,104,23,0,1,99.32,2.1346153846153846
98,4578,4547,31,0,37,93.78,1.9736089729491972
99,482,452,30,0,4,88.76,2.1283185840707963
1 obj_id access_count hits misses mu lambda hit_rate avg_age
2 1 664 122 527 98 137 24 0 1 52.83 92.41 1.9316888045540797 1.9081632653061225
3 2 212 382 112 353 100 29 0 3 79.79 79.53 2.080357142857143 2.0226628895184136
4 3 673 127 537 101 136 26 0 1 80.87 77.88 2.0242085661080074 2.108910891089109
5 4 711 113 575 88 136 25 0 1 68.99 88.52 2.1339130434782607 1.7840909090909092
6 5 345 244 238 216 107 28 0 2 79.35 77.59 2.168067226890756 2.199074074074074
7 6 649 116 515 90 134 26 0 1 43.8 95.43 1.9300970873786407 1.9333333333333333
8 7 137 656 60 626 77 30 0 5 80.32 81.25 1.9333333333333333 1.8801916932907348
9 8 681 128 547 104 134 24 0 1 79.97 78.07 2.03290676416819 2.125
10 9 689 114 551 89 138 25 0 1 79.31 79.13 1.9945553539019965 2.1797752808988764
11 10 667 115 529 91 138 24 0 1 68.29 88.62 2.007561436672968 1.967032967032967
12 11 328 246 224 218 104 28 0 2 80.2 81.82 1.9866071428571428 1.9311926605504588
13 12 692 132 555 108 137 24 0 1 80.09 80.58 1.936936936936937 2.0462962962962963
14 13 683 139 547 112 136 27 0 1 80.6 79.17 2.113345521023766 1.9107142857142858
15 14 696 120 561 95 135 25 0 1 67.15 89.27 1.9946524064171123 1.8421052631578947
16 15 344 261 231 233 113 28 0 2 65.64 87.56 1.8874458874458875 1.9871244635193133
17 16 326 225 214 197 112 28 0 2 80.12 79.17 2.046728971962617 1.9543147208121827
18 17 689 120 552 95 137 25 0 1 80.32 79.49 1.9728260869565217 1.9157894736842105
19 18 691 117 555 93 136 24 0 1 55.71 91.67 2.045045045045045 2.129032258064516
20 19 219 360 122 330 97 30 0 3 80.87 79.49 1.9344262295081966 2.1303030303030304
21 20 732 117 592 93 140 24 0 1 81.33 79.85 2.0591216216216215 2.161290322580645
22 21 739 134 601 107 138 27 0 1 79.8 82.31 2.043261231281198 2.0186915887850465
23 22 683 147 545 121 138 26 0 1 79.85 81.69 1.9064220183486238 2.206611570247934
24 23 670 142 535 116 135 26 0 1 67.07 89.39 1.97196261682243 2.146551724137931
25 24 331 264 222 236 109 28 0 2 80.66 78.86 2.1036036036036037 1.978813559322034
26 25 724 123 584 97 140 26 0 1 80.35 81.56 1.9777397260273972 1.8762886597938144
27 26 692 141 556 115 136 26 0 1 80.85 79.69 2.1097122302158273 1.9130434782608696
28 27 705 128 570 102 135 26 0 1 43.8 94.68 2.1070175438596492 1.8725490196078431
29 28 137 564 60 534 77 30 0 5 79.76 79.7 2.1666666666666665 1.9887640449438202
30 29 672 133 536 106 136 27 0 1 79.83 79.2 1.9011194029850746 1.849056603773585
31 30 694 125 554 99 140 26 0 1 79.82 78.26 1.96028880866426 1.8585858585858586
32 31 674 115 538 90 136 25 0 1 47.92 93.8 2.0780669144981414 2.2888888888888888
33 32 144 468 69 439 75 29 0 4 79.55 78.45 2.1594202898550723 2.0979498861047836
34 33 670 116 533 91 137 25 0 1 43.26 94.18 1.8818011257035647 2.076923076923077
35 34 141 498 61 469 80 29 0 4 79.51 80.3 2.2131147540983607 1.9829424307036247
36 35 659 132 524 106 135 26 0 1 80.03 74.0 2.068702290076336 1.990566037735849
37 36 691 100 553 74 138 26 0 1 80.73 81.88 1.9620253164556962 1.864864864864865
38 37 737 149 595 122 142 27 0 1 57.08 91.83 1.946218487394958 2.0
39 38 219 355 125 326 94 29 0 3 37.0 96.78 2.096 1.9662576687116564
40 39 100 962 37 931 63 31 0 8 80.39 81.25 2.27027027027027 2.045112781954887
41 40 714 128 574 104 140 24 0 1 50.54 93.88 2.06794425087108 2.076923076923077
42 41 184 474 93 445 91 29 0 4 47.83 93.94 2.204301075268817 1.9235955056179774
43 42 161 495 77 465 84 30 0 4 68.51 87.79 2.1948051948051948 2.163440860215054
44 43 362 213 248 187 114 26 0 2 80.6 76.79 1.8830645161290323 1.9732620320855614
45 44 696 112 561 86 135 26 0 1 78.63 79.07 2.0089126559714794 1.9069767441860466
46 45 627 129 493 102 134 27 0 1 79.63 81.95 1.997971602434077 2.127450980392157
47 46 648 133 516 109 132 24 0 1 24.53 97.54 2.0174418604651163 2.2018348623853212
48 47 53 1262 13 1231 40 31 0 10 79.73 81.62 2.1538461538461537 1.893582453290008
49 48 676 136 539 111 137 25 0 1 78.68 81.56 1.9851576994434137 1.7747747747747749
50 49 638 141 502 115 136 26 0 1 79.35 78.15 2.0358565737051793 1.791304347826087
51 50 673 119 534 93 139 26 0 1 42.97 95.16 1.9194756554307115 1.989247311827957
52 51 128 599 55 570 73 29 0 5 30.59 97.29 1.6363636363636365 1.9929824561403509
53 52 85 1106 26 1076 59 30 0 9 81.12 80.17 1.8846153846153846 1.95817843866171
54 53 747 121 606 97 141 24 0 1 81.0 80.92 2.0132013201320134 1.9484536082474226
55 54 700 131 567 106 133 25 0 1 80.2 81.45 2.0 2.0283018867924527
56 55 687 124 551 101 136 23 0 1 81.25 81.54 1.9310344827586208 2.0693069306930694
57 56 720 130 585 106 135 24 0 1 79.57 79.03 1.982905982905983 1.971698113207547
58 57 690 124 549 98 141 26 0 1 12.5 98.54 2.0491803278688523 2.010204081632653
59 58 40 2118 5 2087 35 31 0 17 65.72 86.83 2.2 1.9223766171538093
60 59 318 205 209 178 109 27 0 2 79.82 81.75 1.9569377990430623 2.151685393258427
61 60 674 137 538 112 136 25 0 1 21.74 99.04 2.029739776951673 2.080357142857143
62 61 23 3216 5 3185 18 31 0 26 80.94 81.16 0.6 1.8982731554160126
63 62 724 138 586 112 138 26 0 1 78.34 78.63 1.9112627986348123 2.232142857142857
64 63 628 117 492 92 136 25 0 1 66.96 89.39 1.8333333333333333 2.0434782608695654
65 64 345 264 231 236 114 28 0 2 80.62 82.01 1.948051948051948 1.9957627118644068
66 65 681 139 549 114 132 25 0 1 28.77 97.52 2.034608378870674 1.8596491228070176
67 66 73 1248 21 1217 52 31 0 10 79.57 83.56 2.0952380952380953 1.9079704190632703
68 67 651 146 518 122 133 24 0 1 0.0 99.63 2.0656370656370657 1.9262295081967213
69 68 10 8414 0 8383 10 31 0 69 78.46 78.45 0.0 1.6843612072050578
70 69 636 116 499 91 137 25 0 1 79.73 79.17 1.9799599198396793 1.9120879120879122
71 70 656 120 523 95 133 25 0 1 67.74 88.93 2.0095602294455066 1.7473684210526317
72 71 372 244 252 217 120 27 0 2 80.38 79.49 1.9722222222222223 2.013824884792627
73 72 678 117 545 93 133 24 0 1 79.31 80.92 1.891743119266055 1.989247311827957
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200
experiments/No_Refresh_4_0s_ttl/hit_age.csv
View File

@@ -1,101 +1,101 @@
obj_id,hit_rate,avg_age
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73 72 0.803834808259587 0.7948717948717948 1.891743119266055 1.989247311827957
74 73 0.7931034482758621 0.8091603053435115 1.8893280632411067 1.9528301886792452
75 74 0.7985401459854015 0.823943661971831 2.043875685557587 1.9145299145299146
76 75 0.5223880597014925 0.9154518950437318 2.2095238095238097 1.9490445859872612
77 76 0.6598837209302325 0.884 1.9955947136563876 2.004524886877828
78 77 0.6840579710144927 0.8893280632411067 2.0254237288135593 1.951111111111111
79 78 0.5900383141762452 0.9263959390862944 2.0064935064935066 1.9534246575342467
80 79 0.14893617021276595 0.9837696335078534 1.5714285714285714 1.8696114954763172
81 80 0.796969696969697 0.7916666666666666 2.0 1.8526315789473684
82 81 0.7902208201892744 0.7851239669421488 2.0339321357285427 2.0
83 82 0.4306569343065693 0.9536321483771252 1.8644067796610169 1.8622366288492707
84 83 0.6504854368932039 0.8870967741935484 2.2487562189054726 2.0045454545454544
85 84 0.8046647230320699 0.8263888888888888 1.9909420289855073 2.033613445378151
86 85 0.7947214076246334 0.7777777777777778 1.985239852398524 2.1547619047619047
87 86 0.6490683229813664 0.8720379146919431 1.8229665071770336 2.119565217391304
88 87 0.7914201183431953 0.8059701492537313 2.0261682242990653 2.1296296296296298
89 88 0.6523076923076923 0.8794642857142857 1.9575471698113207 2.1472081218274113
90 89 0.8040638606676342 0.8222222222222222 1.94043321299639 1.9189189189189189
91 90 0.8043165467625899 0.7983870967741935 2.0697674418604652 2.2323232323232323
92 91 0.6759259259259259 0.8833333333333333 1.9680365296803652 1.9622641509433962
93 92 0.6735905044510386 0.8777292576419214 1.9162995594713657 1.935323383084577
94 93 0.5675675675675675 0.926208651399491 1.9523809523809523 2.1538461538461537
95 94 0.7973760932944607 0.784 2.1316270566727606 1.8673469387755102
96 95 0.6837606837606838 0.8910505836575876 2.0208333333333335 1.8646288209606987
97 96 0.806136680613668 0.8129496402877698 2.0328719723183393 1.9823008849557522
98 97 0.7951807228915663 0.8188976377952756 1.9109848484848484 2.1346153846153846
99 98 0.17391304347826086 0.9932284840541721 3.0 1.9736089729491972
100 99 0.5303867403314917 0.9377593360995851 1.8854166666666667 2.1283185840707963
101 100 0.6824925816023739 0.8875502008032129 1.8956521739130434 1.8461538461538463

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@@ -1,9 +1,9 @@
,hit_rate,avg_age
count,100.0,100.0
mean,0.6783420943812974,1.9802754170895376
std,0.18732473237217517,0.28636988978093675
min,0.0,0.0
25%,0.6501311584152445,1.9341530054644809
50%,0.7932827791156427,1.9989858012170385
75%,0.800949133741476,2.0662138619455694
max,0.8132611637347767,3.0
mean,0.8521008724556234,1.9920411130528226
std,0.06749178691284725,0.11936733193046596
min,0.74,1.6843612072050578
25%,0.7951746416313346,1.9117445054945055
50%,0.8188447920520002,1.9805572221388932
75%,0.8939393939393939,2.0777815934065935
max,0.996315664368909,2.2888888888888888
1 hit_rate avg_age
2 count 100.0 100.0
3 mean 0.6783420943812974 0.8521008724556234 1.9802754170895376 1.9920411130528226
4 std 0.18732473237217517 0.06749178691284725 0.28636988978093675 0.11936733193046596
5 min 0.0 0.74 0.0 1.6843612072050578
6 25% 0.6501311584152445 0.7951746416313346 1.9341530054644809 1.9117445054945055
7 50% 0.7932827791156427 0.8188447920520002 1.9989858012170385 1.9805572221388932
8 75% 0.800949133741476 0.8939393939393939 2.0662138619455694 2.0777815934065935
9 max 0.8132611637347767 0.996315664368909 3.0 2.2888888888888888