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Chapter 2
detailed summary tables of results

 2.1 List of integrals sorted by grade for each CAS
  2.1.1 Rubi
  2.1.2 Mathematica
  2.1.3 Maple
  2.1.4 Maxima
  2.1.5 FriCAS
  2.1.6 Sympy
  2.1.7 Giac
  2.1.8 Mupad
 2.2 Detailed conclusion table per each integral for all CAS systems
 2.3 Detailed conclusion table specific for Rubi results

2.1 List of integrals sorted by grade for each CAS

2.1.1 Rubi

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 106, 108, 109, 111, 113, 115, 118, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139 }

B grade: { }

C grade: { 105, 107, 110, 112, 114, 116, 117, 119 }

F grade: { 140 }

2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 29, 30, 31, 32, 33, 34, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 80, 82, 83, 84, 85, 86, 87, 88, 91, 93, 95, 96, 97, 106, 107, 108, 109, 111, 113, 114, 115, 116, 117, 120, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139 }

B grade: { 19, 24, 25, 26, 27, 28, 35, 37, 47, 48, 65, 72, 79, 81, 89, 90, 92, 94, 98, 99, 100, 101, 102, 103, 105, 110, 112, 118, 119 }

C grade: { }

F grade: { 104, 121, 122, 140 }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 137 }

B grade: { }

C grade: { }

F grade: { 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 138, 139, 140 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 80, 82, 84, 86, 88, 106, 108, 109, 111, 113, 115, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139 }

B grade: { 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 60, 72, 79, 81, 83, 85, 87, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 118 }

C grade: { }

F grade: { 104, 105, 107, 110, 112, 114, 116, 117, 119, 122, 140 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 79, 81, 83, 85, 87, 92, 94, 96, 98 }

B grade: { 11, 12, 13, 14, 15, 19, 20, 21, 22, 23, 78, 80, 82, 84, 86, 88, 89, 91, 93, 95, 97 }

C grade: { }

F grade: { 16, 17, 18, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 90, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140 }

2.1.7 Giac

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 38, 39, 40, 41, 42, 50, 51, 52, 56, 57, 58, 59, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 80, 82, 84, 86, 88, 89, 91, 93, 95, 97, 99, 101, 103, 106, 113, 115, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139 }

B grade: { 65, 72, 79, 81, 83, 85, 87, 90, 92, 94, 96, 98, 100, 102, 109, 111, 118 }

C grade: { }

F grade: { 33, 34, 35, 36, 37, 43, 44, 45, 46, 47, 48, 49, 53, 54, 55, 60, 61, 62, 63, 64, 104, 105, 107, 108, 110, 112, 114, 116, 117, 119, 120, 121, 122, 140 }

2.1.8 Mupad

A grade: { }

B grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 58, 59, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 129, 133, 137 }

C grade: { }

F grade: { 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 63, 64, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 130, 131, 132, 134, 135, 136, 138, 139, 140 }

2.2 Detailed conclusion table per each integral for all CAS systems

Detailed conclusion table per each integral is given by table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given just an F.

In this table,the column normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\)

Problem 1 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 25 20 19 19 19 19 19
normalized size 1 1.00 1.00 0.80 0.76 0.76 0.76 0.76 0.76
time (sec) N/A 0.007 0.002 0.000 0.440 0.563 0.062 0.542 0.032
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 25 20 19 19 19 19 19
normalized size 1 1.00 1.00 0.80 0.76 0.76 0.76 0.76 0.76
time (sec) N/A 0.007 0.002 0.000 0.436 0.469 0.062 0.454 0.032
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 25 20 19 19 19 19 19
normalized size 1 1.00 1.00 0.80 0.76 0.76 0.76 0.76 0.76
time (sec) N/A 0.004 0.000 0.002 0.429 0.628 0.061 0.536 0.032
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 25 20 19 19 19 19 19
normalized size 1 1.00 1.00 0.80 0.76 0.76 0.76 0.76 0.76
time (sec) N/A 0.006 0.001 0.001 0.445 0.760 0.064 0.361 0.031
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 20 20 20 17 16 16 15 16 16
normalized size 1 1.00 1.00 0.85 0.80 0.80 0.75 0.80 0.80
time (sec) N/A 0.006 0.001 0.001 0.426 0.580 0.061 0.490 0.025
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 54 45 44 46 48 46 45
normalized size 1 1.00 1.00 0.83 0.81 0.85 0.89 0.85 0.83
time (sec) N/A 0.054 0.008 0.000 0.427 0.428 0.075 0.576 0.034
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 54 45 44 46 49 46 45
normalized size 1 1.00 1.00 0.83 0.81 0.85 0.91 0.85 0.83
time (sec) N/A 0.029 0.007 0.001 0.436 0.593 0.075 0.484 0.024
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 54 45 48 46 48 46 45
normalized size 1 1.00 1.00 0.83 0.89 0.85 0.89 0.85 0.83
time (sec) N/A 0.027 0.006 0.000 0.447 0.476 0.072 0.396 0.022
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 54 45 44 44 49 46 45
normalized size 1 1.00 1.00 0.83 0.81 0.81 0.91 0.85 0.83
time (sec) N/A 0.032 0.007 0.002 0.428 0.674 0.076 0.493 0.025
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 54 45 44 44 48 46 45
normalized size 1 1.00 1.00 0.83 0.81 0.81 0.89 0.85 0.83
time (sec) N/A 0.032 0.009 0.002 0.425 0.581 0.078 0.482 0.024
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 89 89 84 132 0 297 381 86 112
normalized size 1 1.00 0.94 1.48 0.00 3.34 4.28 0.97 1.26
time (sec) N/A 0.094 0.109 0.005 0.000 0.772 0.841 0.453 0.141
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 70 70 73 101 0 235 306 67 172
normalized size 1 1.00 1.04 1.44 0.00 3.36 4.37 0.96 2.46
time (sec) N/A 0.059 0.063 0.003 0.000 0.885 0.623 0.548 2.033
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 56 56 57 56 0 185 216 55 112
normalized size 1 1.00 1.02 1.00 0.00 3.30 3.86 0.98 2.00
time (sec) N/A 0.040 0.030 0.003 0.000 0.926 0.326 0.421 0.133
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 34 34 38 35 0 120 124 34 46
normalized size 1 1.00 1.12 1.03 0.00 3.53 3.65 1.00 1.35
time (sec) N/A 0.026 0.006 0.001 0.000 0.755 0.222 0.497 0.035
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 62 62 61 62 0 211 564 62 213
normalized size 1 1.00 0.98 1.00 0.00 3.40 9.10 1.00 3.44
time (sec) N/A 0.047 0.065 0.007 0.000 0.946 4.358 0.505 2.298
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 81 81 77 112 0 269 0 79 339
normalized size 1 1.00 0.95 1.38 0.00 3.32 0.00 0.98 4.19
time (sec) N/A 0.098 0.081 0.007 0.000 0.918 0.000 0.325 2.504
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 104 104 102 150 0 358 0 105 447
normalized size 1 1.00 0.98 1.44 0.00 3.44 0.00 1.01 4.30
time (sec) N/A 0.146 0.136 0.007 0.000 0.977 0.000 0.508 0.587
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 137 137 131 214 0 445 0 136 524
normalized size 1 1.00 0.96 1.56 0.00 3.25 0.00 0.99 3.82
time (sec) N/A 0.203 0.104 0.010 0.000 0.874 0.000 0.457 2.596
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 150 150 132 352 0 837 842 161 261
normalized size 1 1.00 0.88 2.35 0.00 5.58 5.61 1.07 1.74
time (sec) N/A 0.159 0.196 0.010 0.000 0.694 1.792 0.567 2.456
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 114 114 109 209 0 635 729 125 279
normalized size 1 1.00 0.96 1.83 0.00 5.57 6.39 1.10 2.45
time (sec) N/A 0.103 0.146 0.009 0.000 0.619 1.366 0.595 2.491
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 81 97 0 387 280 88 135
normalized size 1 1.00 1.21 1.45 0.00 5.78 4.18 1.31 2.01
time (sec) N/A 0.039 0.091 0.007 0.000 0.675 0.600 0.493 2.129
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 66 66 69 70 0 338 253 76 110
normalized size 1 1.00 1.05 1.06 0.00 5.12 3.83 1.15 1.67
time (sec) N/A 0.038 0.067 0.003 0.000 0.586 0.564 0.383 2.183
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 66 66 70 68 0 341 265 76 119
normalized size 1 1.00 1.06 1.03 0.00 5.17 4.02 1.15 1.80
time (sec) N/A 0.035 0.071 0.004 0.000 0.593 0.588 0.459 0.084
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 108 108 107 237 0 781 0 126 620
normalized size 1 1.00 0.99 2.19 0.00 7.23 0.00 1.17 5.74
time (sec) N/A 0.148 0.184 0.014 0.000 0.545 0.000 0.505 2.871
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 148 148 131 328 0 975 0 171 775
normalized size 1 1.00 0.89 2.22 0.00 6.59 0.00 1.16 5.24
time (sec) N/A 0.198 0.264 0.015 0.000 0.859 0.000 0.454 2.833
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 202 202 175 418 0 1226 0 229 914
normalized size 1 1.00 0.87 2.07 0.00 6.07 0.00 1.13 4.52
time (sec) N/A 0.250 0.343 0.016 0.000 1.030 0.000 0.441 2.956
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 252 252 218 515 0 1407 0 282 1120
normalized size 1 1.00 0.87 2.04 0.00 5.58 0.00 1.12 4.44
time (sec) N/A 0.323 0.318 0.017 0.000 1.320 0.000 0.550 3.064
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 318 318 272 619 0 1640 0 347 1260
normalized size 1 1.00 0.86 1.95 0.00 5.16 0.00 1.09 3.96
time (sec) N/A 0.392 0.378 0.020 0.000 2.067 0.000 0.439 3.143
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 257 257 180 310 0 390 0 283 -1
normalized size 1 1.00 0.70 1.21 0.00 1.52 0.00 1.10 -0.00
time (sec) N/A 0.588 0.237 0.009 0.000 0.848 0.000 0.873 0.000
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 205 205 150 265 0 326 0 230 -1
normalized size 1 1.00 0.73 1.29 0.00 1.59 0.00 1.12 -0.00
time (sec) N/A 0.370 0.161 0.009 0.000 0.825 0.000 0.746 0.000
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 163 163 119 167 0 260 0 166 -1
normalized size 1 1.00 0.73 1.02 0.00 1.60 0.00 1.02 -0.01
time (sec) N/A 0.058 0.213 0.008 0.000 0.712 0.000 0.881 0.000
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 119 119 100 146 0 220 0 125 -1
normalized size 1 1.00 0.84 1.23 0.00 1.85 0.00 1.05 -0.01
time (sec) N/A 0.078 0.133 0.005 0.000 0.607 0.000 0.946 0.000
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 173 173 134 126 0 638 0 0 -1
normalized size 1 1.00 0.77 0.73 0.00 3.69 0.00 0.00 -0.01
time (sec) N/A 0.126 0.095 0.006 0.000 0.672 0.000 0.000 0.000
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 173 173 131 173 0 653 0 0 -1
normalized size 1 1.00 0.76 1.00 0.00 3.77 0.00 0.00 -0.01
time (sec) N/A 0.124 0.117 0.006 0.000 0.788 0.000 0.000 0.000
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 114 114 112 207 0 226 0 0 -1
normalized size 1 1.00 0.98 1.82 0.00 1.98 0.00 0.00 -0.01
time (sec) N/A 0.148 0.096 0.006 0.000 0.772 0.000 0.000 0.000
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 155 155 131 234 0 272 0 0 -1
normalized size 1 1.00 0.85 1.51 0.00 1.75 0.00 0.00 -0.01
time (sec) N/A 0.256 0.123 0.008 0.000 0.742 0.000 0.000 0.000
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 205 205 160 387 0 336 0 0 -1
normalized size 1 1.00 0.78 1.89 0.00 1.64 0.00 0.00 -0.00
time (sec) N/A 0.386 0.168 0.011 0.000 0.994 0.000 0.000 0.000
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 422 422 236 649 0 664 0 521 -1
normalized size 1 1.00 0.56 1.54 0.00 1.57 0.00 1.23 -0.00
time (sec) N/A 1.203 0.384 0.010 0.000 0.948 0.000 1.461 0.000
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 364 364 197 479 0 558 0 429 -1
normalized size 1 1.00 0.54 1.32 0.00 1.53 0.00 1.18 -0.00
time (sec) N/A 1.039 0.246 0.010 0.000 0.734 0.000 1.351 0.000
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 288 288 180 431 0 474 0 365 -1
normalized size 1 1.00 0.62 1.50 0.00 1.65 0.00 1.27 -0.00
time (sec) N/A 0.519 0.219 0.009 0.000 0.682 0.000 0.994 0.000
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 198 198 163 289 0 384 0 284 -1
normalized size 1 1.00 0.82 1.46 0.00 1.94 0.00 1.43 -0.01
time (sec) N/A 0.178 0.173 0.007 0.000 0.832 0.000 0.925 0.000
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 165 165 132 265 0 320 0 232 -1
normalized size 1 1.00 0.80 1.61 0.00 1.94 0.00 1.41 -0.01
time (sec) N/A 0.128 0.060 0.005 0.000 0.742 0.000 1.013 0.000
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 227 227 166 222 0 791 0 0 -1
normalized size 1 1.00 0.73 0.98 0.00 3.48 0.00 0.00 -0.00
time (sec) N/A 0.255 0.224 0.006 0.000 0.898 0.000 0.000 0.000
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 219 219 158 254 0 757 0 0 -1
normalized size 1 1.00 0.72 1.16 0.00 3.46 0.00 0.00 -0.00
time (sec) N/A 0.242 0.180 0.006 0.000 0.710 0.000 0.000 0.000
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 219 219 162 338 0 757 0 0 -1
normalized size 1 1.00 0.74 1.54 0.00 3.46 0.00 0.00 -0.00
time (sec) N/A 0.238 0.190 0.007 0.000 0.904 0.000 0.000 0.000
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 257 257 175 435 0 815 0 0 -1
normalized size 1 1.00 0.68 1.69 0.00 3.17 0.00 0.00 -0.00
time (sec) N/A 0.351 0.289 0.009 0.000 0.811 0.000 0.000 0.000
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 197 197 141 501 0 332 0 0 -1
normalized size 1 1.00 0.72 2.54 0.00 1.69 0.00 0.00 -0.01
time (sec) N/A 0.363 0.115 0.007 0.000 0.997 0.000 0.000 0.000
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 249 249 177 534 0 394 0 0 -1
normalized size 1 1.00 0.71 2.14 0.00 1.58 0.00 0.00 -0.00
time (sec) N/A 0.504 0.166 0.010 0.000 0.989 0.000 0.000 0.000
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 143 143 105 144 0 226 0 0 -1
normalized size 1 1.00 0.73 1.01 0.00 1.58 0.00 0.00 -0.01
time (sec) N/A 0.174 0.093 0.009 0.000 0.499 0.000 0.000 0.000
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 103 103 89 88 0 188 0 108 -1
normalized size 1 1.00 0.86 0.85 0.00 1.83 0.00 1.05 -0.01
time (sec) N/A 0.078 0.052 0.006 0.000 0.782 0.000 0.915 0.000
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 66 65 0 129 0 37 -1
normalized size 1 1.00 0.93 0.92 0.00 1.82 0.00 0.52 -0.01
time (sec) N/A 0.037 0.035 0.006 0.000 0.665 0.000 0.912 0.000
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 70 66 0 130 0 59 -1
normalized size 1 1.00 1.56 1.47 0.00 2.89 0.00 1.31 -0.02
time (sec) N/A 0.016 0.019 0.005 0.000 0.789 0.000 0.919 0.000
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 89 88 0 194 0 0 -1
normalized size 1 1.00 1.16 1.14 0.00 2.52 0.00 0.00 -0.01
time (sec) N/A 0.054 0.051 0.007 0.000 0.681 0.000 0.000 0.000
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 119 119 112 152 0 232 0 0 -1
normalized size 1 1.00 0.94 1.28 0.00 1.95 0.00 0.00 -0.01
time (sec) N/A 0.149 0.084 0.007 0.000 0.763 0.000 0.000 0.000
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 262 262 183 283 0 616 0 0 -1
normalized size 1 1.00 0.70 1.08 0.00 2.35 0.00 0.00 -0.00
time (sec) N/A 0.506 0.230 0.009 0.000 0.816 0.000 0.000 0.000
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 201 201 141 199 0 486 0 195 -1
normalized size 1 1.00 0.70 0.99 0.00 2.42 0.00 0.97 -0.00
time (sec) N/A 0.305 0.152 0.009 0.000 0.881 0.000 0.888 0.000
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 153 153 112 166 0 414 0 110 -1
normalized size 1 1.00 0.73 1.08 0.00 2.71 0.00 0.72 -0.01
time (sec) N/A 0.175 0.119 0.007 0.000 0.768 0.000 0.983 0.000
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 37 53 0 73 0 45 75
normalized size 1 1.00 0.92 1.32 0.00 1.82 0.00 1.12 1.88
time (sec) N/A 0.040 0.075 0.004 0.000 0.620 0.000 0.916 2.122
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 39 39 36 52 0 72 0 45 75
normalized size 1 1.00 0.92 1.33 0.00 1.85 0.00 1.15 1.92
time (sec) N/A 0.040 0.024 0.003 0.000 0.659 0.000 0.765 2.034
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 94 94 109 166 0 411 0 0 -1
normalized size 1 1.00 1.16 1.77 0.00 4.37 0.00 0.00 -0.01
time (sec) N/A 0.068 0.128 0.008 0.000 0.926 0.000 0.000 0.000
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 144 144 138 201 0 496 0 0 -1
normalized size 1 1.00 0.96 1.40 0.00 3.44 0.00 0.00 -0.01
time (sec) N/A 0.163 0.100 0.009 0.000 0.622 0.000 0.000 0.000
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 209 209 181 292 0 630 0 0 -1
normalized size 1 1.00 0.87 1.40 0.00 3.01 0.00 0.00 -0.00
time (sec) N/A 0.287 0.157 0.009 0.000 0.917 0.000 0.000 0.000
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 271 271 225 340 0 716 0 0 -1
normalized size 1 1.00 0.83 1.25 0.00 2.64 0.00 0.00 -0.00
time (sec) N/A 0.452 0.203 0.010 0.000 1.016 0.000 0.000 0.000
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 343 343 272 446 0 866 0 0 -1
normalized size 1 1.00 0.79 1.30 0.00 2.52 0.00 0.00 -0.00
time (sec) N/A 0.621 0.249 0.011 0.000 1.306 0.000 0.000 0.000
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 34 77 37 71 280 107 89
normalized size 1 1.00 0.92 2.08 1.00 1.92 7.57 2.89 2.41
time (sec) N/A 0.013 0.026 0.003 0.446 0.663 1.176 0.485 2.084
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 25 20 19 19 19 19 19
normalized size 1 1.00 1.00 0.80 0.76 0.76 0.76 0.76 0.76
time (sec) N/A 0.008 0.002 0.002 0.428 0.456 0.061 0.382 0.029
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 25 20 19 19 19 19 19
normalized size 1 1.00 1.00 0.80 0.76 0.76 0.76 0.76 0.76
time (sec) N/A 0.007 0.002 0.002 0.428 0.519 0.061 0.391 0.031
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 25 20 19 19 19 19 19
normalized size 1 1.00 1.00 0.80 0.76 0.76 0.76 0.76 0.76
time (sec) N/A 0.004 0.000 0.002 0.423 0.613 0.061 0.378 0.028
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 20 20 20 17 16 16 15 16 16
normalized size 1 1.00 1.00 0.85 0.80 0.80 0.75 0.80 0.80
time (sec) N/A 0.006 0.001 0.000 0.425 0.557 0.066 0.363 0.027
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 21 21 21 18 17 17 17 20 17
normalized size 1 1.00 1.00 0.86 0.81 0.81 0.81 0.95 0.81
time (sec) N/A 0.008 0.002 0.001 0.426 0.599 0.095 0.415 0.025
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 18 18 18 17 16 20 12 16 16
normalized size 1 1.00 1.00 0.94 0.89 1.11 0.67 0.89 0.89
time (sec) N/A 0.007 0.002 0.003 0.428 0.606 0.095 0.585 0.030
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 76 76 69 300 85 241 1377 399 271
normalized size 1 1.00 0.91 3.95 1.12 3.17 18.12 5.25 3.57
time (sec) N/A 0.046 0.071 0.005 0.436 0.673 4.287 0.516 2.195
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 54 45 44 46 51 46 45
normalized size 1 1.00 1.00 0.83 0.81 0.85 0.94 0.85 0.83
time (sec) N/A 0.036 0.007 0.002 0.424 0.410 0.079 0.405 0.034
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 48 45 44 46 46 46 45
normalized size 1 1.00 0.89 0.83 0.81 0.85 0.85 0.85 0.83
time (sec) N/A 0.054 0.008 0.000 0.446 0.502 0.076 0.384 0.024
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 54 45 48 46 51 46 45
normalized size 1 1.00 1.00 0.83 0.89 0.85 0.94 0.85 0.83
time (sec) N/A 0.026 0.007 0.001 0.430 0.554 0.074 0.357 0.024
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 48 45 44 44 46 46 45
normalized size 1 1.00 0.89 0.83 0.81 0.81 0.85 0.85 0.83
time (sec) N/A 0.046 0.008 0.001 0.429 0.613 0.077 0.524 0.024
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 49 42 41 41 48 43 42
normalized size 1 1.00 1.00 0.86 0.84 0.84 0.98 0.88 0.86
time (sec) N/A 0.027 0.005 0.001 0.430 0.595 0.080 0.507 0.023
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 100 100 93 142 0 313 391 92 842
normalized size 1 1.00 0.93 1.42 0.00 3.13 3.91 0.92 8.42
time (sec) N/A 0.122 0.085 0.004 0.000 0.586 2.946 0.467 2.203
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 203 203 250 467 0 1564 194 2457 4127
normalized size 1 1.00 1.23 2.30 0.00 7.70 0.96 12.10 20.33
time (sec) N/A 0.602 0.155 0.025 0.000 0.652 4.254 2.037 2.718
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 81 81 78 111 0 254 316 75 655
normalized size 1 1.00 0.96 1.37 0.00 3.14 3.90 0.93 8.09
time (sec) N/A 0.087 0.044 0.004 0.000 0.677 1.950 0.633 2.438
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 179 179 202 343 0 1059 129 2109 3026
normalized size 1 1.00 1.13 1.92 0.00 5.92 0.72 11.78 16.91
time (sec) N/A 0.227 0.108 0.014 0.000 0.653 2.177 1.500 2.584
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 63 63 62 60 0 197 223 59 118
normalized size 1 1.00 0.98 0.95 0.00 3.13 3.54 0.94 1.87
time (sec) N/A 0.067 0.023 0.003 0.000 0.791 0.919 0.423 0.166
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 150 150 165 208 0 559 75 503 416
normalized size 1 1.00 1.10 1.39 0.00 3.73 0.50 3.35 2.77
time (sec) N/A 0.094 0.082 0.011 0.000 0.758 0.819 1.805 2.209
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 36 36 39 36 0 129 131 35 41
normalized size 1 1.00 1.08 1.00 0.00 3.58 3.64 0.97 1.14
time (sec) N/A 0.043 0.008 0.003 0.000 0.624 0.495 0.489 2.040
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 150 150 129 116 0 613 87 1026 763
normalized size 1 1.00 0.86 0.77 0.00 4.09 0.58 6.84 5.09
time (sec) N/A 0.080 0.079 0.013 0.000 0.765 1.185 1.863 2.479
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 69 69 113 66 0 223 253 68 1014
normalized size 1 1.00 1.64 0.96 0.00 3.23 3.67 0.99 14.70
time (sec) N/A 0.072 0.061 0.007 0.000 0.583 4.284 0.428 2.701
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 174 174 191 232 0 1116 148 1839 2997
normalized size 1 1.00 1.10 1.33 0.00 6.41 0.85 10.57 17.22
time (sec) N/A 0.195 0.401 0.018 0.000 1.192 2.623 1.883 2.859
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 89 89 135 119 0 293 345 94 2033
normalized size 1 1.00 1.52 1.34 0.00 3.29 3.88 1.06 22.84
time (sec) N/A 0.133 0.120 0.007 0.000 1.048 123.748 0.432 3.910
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 166 166 151 383 0 868 877 161 1473
normalized size 1 1.00 0.91 2.31 0.00 5.23 5.28 0.97 8.87
time (sec) N/A 0.223 0.186 0.013 0.000 0.732 112.278 1.985 0.528
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 331 331 327 844 0 2856 0 3339 7599
normalized size 1 1.00 0.99 2.55 0.00 8.63 0.00 10.09 22.96
time (sec) N/A 0.703 0.663 0.036 0.000 0.907 0.000 3.707 3.756
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 132 132 121 222 0 663 745 152 1336
normalized size 1 1.00 0.92 1.68 0.00 5.02 5.64 1.15 10.12
time (sec) N/A 0.152 0.168 0.012 0.000 0.647 19.764 1.951 2.943
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 271 271 282 602 0 2257 379 2736 6293
normalized size 1 1.00 1.04 2.22 0.00 8.33 1.40 10.10 23.22
time (sec) N/A 0.526 0.513 0.029 0.000 1.059 33.307 4.025 3.858
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 78 78 93 104 0 407 282 96 187
normalized size 1 1.00 1.19 1.33 0.00 5.22 3.62 1.23 2.40
time (sec) N/A 0.072 0.086 0.010 0.000 0.866 1.517 2.000 2.197
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 237 237 235 452 0 1668 296 2132 4973
normalized size 1 1.00 0.99 1.91 0.00 7.04 1.25 9.00 20.98
time (sec) N/A 0.358 0.407 0.026 0.000 0.955 4.547 3.389 3.635
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 75 75 79 77 0 360 269 82 178
normalized size 1 1.00 1.05 1.03 0.00 4.80 3.59 1.09 2.37
time (sec) N/A 0.069 0.066 0.006 0.000 0.867 1.360 2.053 0.144
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 221 221 222 342 0 1680 298 1970 4854
normalized size 1 1.00 1.00 1.55 0.00 7.60 1.35 8.91 21.96
time (sec) N/A 0.240 0.434 0.069 0.000 0.904 13.168 3.080 3.363
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 79 75 0 361 267 82 172
normalized size 1 1.00 1.07 1.01 0.00 4.88 3.61 1.11 2.32
time (sec) N/A 0.065 0.080 0.006 0.000 0.802 1.277 2.132 2.160
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 252 252 243 733 0 2309 394 2682 6404
normalized size 1 1.00 0.96 2.91 0.00 9.16 1.56 10.64 25.41
time (sec) N/A 0.461 0.418 0.057 0.000 1.058 165.893 3.818 3.847
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 122 122 207 253 0 813 0 166 5048
normalized size 1 1.00 1.70 2.07 0.00 6.66 0.00 1.36 41.38
time (sec) N/A 0.188 0.331 0.017 0.000 1.016 0.000 2.322 6.312
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 308 308 302 712 0 2912 0 3087 7555
normalized size 1 1.00 0.98 2.31 0.00 9.45 0.00 10.02 24.53
time (sec) N/A 1.352 0.616 0.034 0.000 1.239 0.000 2.433 2.639
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 162 162 248 352 0 1007 0 182 5491
normalized size 1 1.00 1.53 2.17 0.00 6.22 0.00 1.12 33.90
time (sec) N/A 0.250 0.264 0.020 0.000 1.229 0.000 2.407 6.766
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 361 361 344 913 0 3435 0 3651 8739
normalized size 1 1.00 0.95 2.53 0.00 9.52 0.00 10.11 24.21
time (sec) N/A 3.077 0.715 0.038 0.000 1.501 0.000 3.916 4.907
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 219 219 328 443 0 1242 0 274 5999
normalized size 1 1.00 1.50 2.02 0.00 5.67 0.00 1.25 27.39
time (sec) N/A 0.312 0.375 0.023 0.000 1.408 0.000 2.040 7.473
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 142 142 170 0 0 0 0 0 -1
normalized size 1 1.00 1.20 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.171 0.090 0.040 0.000 0.882 0.000 0.000 0.000
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 380 380 486 1042 0 0 0 0 -1
normalized size 1 1.00 1.28 2.74 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.287 1.481 0.053 0.000 0.883 0.000 0.000 0.000
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 129 129 126 157 0 232 0 127 -1
normalized size 1 1.00 0.98 1.22 0.00 1.80 0.00 0.98 -0.01
time (sec) N/A 0.093 0.077 0.010 0.000 0.823 0.000 0.971 0.000
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 347 347 452 508 0 0 0 0 -1
normalized size 1 1.00 1.30 1.46 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.224 0.989 0.016 0.000 0.922 0.000 0.000 0.000
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 194 194 155 136 0 666 0 0 -1
normalized size 1 1.00 0.80 0.70 0.00 3.43 0.00 0.00 -0.01
time (sec) N/A 0.209 0.060 0.013 0.000 0.957 0.000 0.000 0.000
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F(-1) B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 244 244 192 369 0 396 0 662 -1
normalized size 1 1.00 0.79 1.51 0.00 1.62 0.00 2.71 -0.00
time (sec) N/A 0.357 0.204 0.014 0.000 0.712 0.000 2.112 0.000
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 487 487 609 1878 0 0 0 0 -1
normalized size 1 1.00 1.25 3.86 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.457 2.291 0.020 0.000 0.890 0.000 0.000 0.000
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 177 177 152 295 0 332 0 518 -1
normalized size 1 1.00 0.86 1.67 0.00 1.88 0.00 2.93 -0.01
time (sec) N/A 0.138 0.111 0.023 0.000 0.835 0.000 1.583 0.000
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 425 425 540 1394 0 0 0 0 -1
normalized size 1 1.00 1.27 3.28 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.449 1.736 0.020 0.000 0.880 0.000 0.000 0.000
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 82 72 0 135 0 60 -1
normalized size 1 1.00 1.00 0.88 0.00 1.65 0.00 0.73 -0.01
time (sec) N/A 0.062 0.018 0.011 0.000 0.933 0.000 0.625 0.000
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 121 121 193 177 0 0 0 0 -1
normalized size 1 1.00 1.60 1.46 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.046 0.118 0.015 0.000 0.892 0.000 0.000 0.000
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 83 72 0 137 0 56 -1
normalized size 1 1.00 1.63 1.41 0.00 2.69 0.00 1.10 -0.02
time (sec) N/A 0.029 0.019 0.018 0.000 0.830 0.000 0.545 0.000
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 330 330 303 508 0 0 0 0 -1
normalized size 1 1.00 0.92 1.54 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.184 0.471 0.018 0.000 0.906 0.000 0.000 0.000
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 391 391 463 533 0 0 0 0 -1
normalized size 1 1.00 1.18 1.36 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.248 1.027 0.019 0.000 0.861 0.000 0.000 0.000
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 103 103 126 179 0 424 0 193 -1
normalized size 1 1.00 1.22 1.74 0.00 4.12 0.00 1.87 -0.01
time (sec) N/A 0.073 0.079 0.015 0.000 0.802 0.000 0.662 0.000
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 468 468 519 1136 0 0 0 0 -1
normalized size 1 1.00 1.11 2.43 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.409 1.347 0.045 0.000 1.039 0.000 0.000 0.000
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 154 154 160 220 0 508 0 0 -1
normalized size 1 1.00 1.04 1.43 0.00 3.30 0.00 0.00 -0.01
time (sec) N/A 0.175 0.074 0.023 0.000 0.948 0.000 0.000 0.000
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 46 0 0 83 0 0 -1
normalized size 1 1.00 0.90 0.00 0.00 1.63 0.00 0.00 -0.02
time (sec) N/A 0.050 0.086 0.079 0.000 0.704 0.000 0.000 0.000
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 287 287 239 0 0 0 0 0 -1
normalized size 1 1.00 0.83 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.399 5.125 0.038 0.000 0.800 0.000 0.000 0.000
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 73 58 0 55 0 60 -1
normalized size 1 1.00 1.62 1.29 0.00 1.22 0.00 1.33 -0.02
time (sec) N/A 0.009 0.020 0.011 0.000 0.865 0.000 0.437 0.000
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 73 58 0 55 0 60 -1
normalized size 1 1.00 1.62 1.29 0.00 1.22 0.00 1.33 -0.02
time (sec) N/A 0.012 0.003 0.007 0.000 0.800 0.000 0.725 0.000
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 73 58 0 55 0 60 -1
normalized size 1 1.00 1.62 1.29 0.00 1.22 0.00 1.33 -0.02
time (sec) N/A 0.012 0.004 0.004 0.000 0.872 0.000 0.492 0.000
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 86 86 70 81 0 70 0 69 -1
normalized size 1 1.00 0.81 0.94 0.00 0.81 0.00 0.80 -0.01
time (sec) N/A 0.041 0.033 0.010 0.000 0.849 0.000 0.393 0.000
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 86 86 70 81 0 70 0 69 -1
normalized size 1 1.00 0.81 0.94 0.00 0.81 0.00 0.80 -0.01
time (sec) N/A 0.042 0.010 0.006 0.000 0.867 0.000 0.511 0.000
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 86 86 70 81 0 70 0 69 -1
normalized size 1 1.00 0.81 0.94 0.00 0.81 0.00 0.80 -0.01
time (sec) N/A 0.041 0.003 0.004 0.000 0.592 0.000 0.381 0.000
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 38 38 37 35 0 111 0 35 34
normalized size 1 1.00 0.97 0.92 0.00 2.92 0.00 0.92 0.89
time (sec) N/A 0.016 0.020 0.003 0.000 0.909 0.000 0.386 0.080
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 70 64 0 130 0 59 -1
normalized size 1 1.00 1.56 1.42 0.00 2.89 0.00 1.31 -0.02
time (sec) N/A 0.022 0.024 0.009 0.000 0.897 0.000 0.466 0.000
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 47 47 72 64 0 131 0 53 -1
normalized size 1 1.00 1.53 1.36 0.00 2.79 0.00 1.13 -0.02
time (sec) N/A 0.076 0.034 0.014 0.000 1.052 0.000 0.493 0.000
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 74 66 0 139 0 53 -1
normalized size 1 1.00 1.51 1.35 0.00 2.84 0.00 1.08 -0.02
time (sec) N/A 0.090 0.028 0.008 0.000 0.984 0.000 0.490 0.000
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 44 44 44 39 0 124 0 38 44
normalized size 1 1.00 1.00 0.89 0.00 2.82 0.00 0.86 1.00
time (sec) N/A 0.036 0.007 0.006 0.000 0.858 0.000 0.449 2.226
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 81 72 0 135 0 62 -1
normalized size 1 1.00 1.65 1.47 0.00 2.76 0.00 1.27 -0.02
time (sec) N/A 0.015 0.017 0.007 0.000 0.946 0.000 0.436 0.000
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 83 72 0 137 0 56 -1
normalized size 1 1.00 1.63 1.41 0.00 2.69 0.00 1.10 -0.02
time (sec) N/A 0.067 0.018 0.011 0.000 0.926 0.000 0.399 0.000
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 85 74 0 145 0 56 -1
normalized size 1 1.00 1.60 1.40 0.00 2.74 0.00 1.06 -0.02
time (sec) N/A 0.077 0.019 0.010 0.000 0.925 0.000 0.551 0.000
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 40 31 20 47 0 55 33
normalized size 1 1.00 1.00 0.78 0.50 1.18 0.00 1.38 0.82
time (sec) N/A 0.027 0.008 0.004 0.945 0.795 0.000 0.472 0.427
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 73 58 0 55 0 60 -1
normalized size 1 1.00 1.62 1.29 0.00 1.22 0.00 1.33 -0.02
time (sec) N/A 0.012 0.008 0.000 0.000 0.709 0.000 0.427 0.000
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F A F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 62 50 0 49 0 47 -1
normalized size 1 1.00 1.44 1.16 0.00 1.14 0.00 1.09 -0.02
time (sec) N/A 0.047 0.020 0.013 0.000 0.815 0.000 0.331 0.000
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F(-2) F(-1) F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 70 70 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.067 0.395 0.138 0.000 0.000 0.000 0.000 0.000

2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. It gives additional statistics for each integral. the column steps is the number of steps used by Rubi to obtain the antiderivative. The rules column is the number of unique rules used. The integrand size column is the leaf size of the integrand. Finally the ratio \(\frac {\text {number of rules}}{\text {integrand size}}\) is given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [86] had the largest ratio of [.5000]

Table 2.1:Rubi specific breakdown of results for each integral
# grade
number of
steps
used
number of
unique
rules
normalized
antiderivative
leaf size
integrand
leaf size
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\)
1 A 2 1 1.00 20 0.050
2 A 2 1 1.00 18 0.056
3 A 1 0 1.00 16 0.000
4 A 2 1 1.00 20 0.050
5 A 2 1 1.00 20 0.050
6 A 3 2 1.00 22 0.091
7 A 3 2 1.00 20 0.100
8 A 3 2 1.00 18 0.111
9 A 3 2 1.00 22 0.091
10 A 3 2 1.00 22 0.091
11 A 7 6 1.00 22 0.273
12 A 6 6 1.00 22 0.273
13 A 5 5 1.00 22 0.227
14 A 3 3 1.00 22 0.136
15 A 7 7 1.00 20 0.350
16 A 8 7 1.00 18 0.389
17 A 8 7 1.00 22 0.318
18 A 8 7 1.00 22 0.318
19 A 8 7 1.00 22 0.318
20 A 7 7 1.00 22 0.318
21 A 4 4 1.00 22 0.182
22 A 4 4 1.00 22 0.182
23 A 4 4 1.00 22 0.182
24 A 8 7 1.00 22 0.318
25 A 8 7 1.00 22 0.318
26 A 8 7 1.00 20 0.350
27 A 8 7 1.00 18 0.389
28 A 8 7 1.00 22 0.318
29 A 8 6 1.00 24 0.250
30 A 7 6 1.00 22 0.273
31 A 5 5 1.00 20 0.250
32 A 4 4 1.00 24 0.167
33 A 7 6 1.00 24 0.250
34 A 7 6 1.00 24 0.250
35 A 5 5 1.00 24 0.208
36 A 6 5 1.00 24 0.208
37 A 7 5 1.00 24 0.208
38 A 10 7 1.00 22 0.318
39 A 10 7 1.00 20 0.350
40 A 8 7 1.00 24 0.292
41 A 6 5 1.00 24 0.208
42 A 5 4 1.00 24 0.167
43 A 8 7 1.00 24 0.292
44 A 8 7 1.00 24 0.292
45 A 8 7 1.00 24 0.292
46 A 9 8 1.00 24 0.333
47 A 7 6 1.00 24 0.250
48 A 8 6 1.00 24 0.250
49 A 6 6 1.00 24 0.250
50 A 4 4 1.00 24 0.167
51 A 3 3 1.00 22 0.136
52 A 2 2 1.00 20 0.100
53 A 3 3 1.00 24 0.125
54 A 5 5 1.00 24 0.208
55 A 8 6 1.00 24 0.250
56 A 7 6 1.00 24 0.250
57 A 6 6 1.00 24 0.250
58 A 1 1 1.00 24 0.042
59 A 1 1 1.00 24 0.042
60 A 3 3 1.00 24 0.125
61 A 5 5 1.00 22 0.227
62 A 6 5 1.00 20 0.250
63 A 7 5 1.00 24 0.208
64 A 8 5 1.00 24 0.208
65 A 2 1 1.00 18 0.056
66 A 2 1 1.00 18 0.056
67 A 2 1 1.00 16 0.062
68 A 1 0 1.00 14 0.000
69 A 2 1 1.00 18 0.056
70 A 2 1 1.00 18 0.056
71 A 2 1 1.00 18 0.056
72 A 3 2 1.00 20 0.100
73 A 3 2 1.00 20 0.100
74 A 4 3 1.00 18 0.167
75 A 3 2 1.00 16 0.125
76 A 4 3 1.00 20 0.150
77 A 3 2 1.00 20 0.100
78 A 8 7 1.00 20 0.350
79 A 6 5 1.00 20 0.250
80 A 7 7 1.00 20 0.350
81 A 5 4 1.00 20 0.200
82 A 6 6 1.00 20 0.300
83 A 4 3 1.00 20 0.150
84 A 4 4 1.00 20 0.200
85 A 4 3 1.00 18 0.167
86 A 8 8 1.00 16 0.500
87 A 5 4 1.00 20 0.200
88 A 9 8 1.00 20 0.400
89 A 9 8 1.00 20 0.400
90 A 7 5 1.00 20 0.250
91 A 8 8 1.00 20 0.400
92 A 6 5 1.00 20 0.250
93 A 5 5 1.00 20 0.250
94 A 5 4 1.00 20 0.200
95 A 5 5 1.00 20 0.250
96 A 5 4 1.00 20 0.200
97 A 5 5 1.00 20 0.250
98 A 5 4 1.00 20 0.200
99 A 9 8 1.00 18 0.444
100 A 6 5 1.00 16 0.312
101 A 9 8 1.00 20 0.400
102 A 7 5 1.00 20 0.250
103 A 9 8 1.00 20 0.400
104 A 3 3 1.00 20 0.150
105 A 5 5 1.00 24 0.208
106 A 5 5 1.00 24 0.208
107 A 5 5 1.00 24 0.208
108 A 8 7 1.00 24 0.292
109 A 8 8 1.00 24 0.333
110 A 6 6 1.00 24 0.250
111 A 6 5 1.00 24 0.208
112 A 6 6 1.00 24 0.250
113 A 4 4 1.00 24 0.167
114 A 2 2 1.00 24 0.083
115 A 2 2 1.00 24 0.083
116 A 6 6 1.00 24 0.250
117 A 5 5 1.00 24 0.208
118 A 3 3 1.00 24 0.125
119 A 6 6 1.00 24 0.250
120 A 5 5 1.00 24 0.208
121 A 1 1 1.00 34 0.029
122 A 7 4 1.00 27 0.148
123 A 2 2 1.00 18 0.111
124 A 3 3 1.00 18 0.167
125 A 3 3 1.00 17 0.176
126 A 5 5 1.00 18 0.278
127 A 6 6 1.00 18 0.333
128 A 6 6 1.00 17 0.353
129 A 2 2 1.00 18 0.111
130 A 3 3 1.00 18 0.167
131 A 3 3 1.00 22 0.136
132 A 3 3 1.00 24 0.125
133 A 3 3 1.00 20 0.150
134 A 3 3 1.00 20 0.150
135 A 3 3 1.00 24 0.125
136 A 3 3 1.00 26 0.115
137 A 3 3 1.00 18 0.167
138 A 3 3 1.00 18 0.167
139 A 3 3 1.00 20 0.150
140 A 2 2 1.00 36 0.056

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