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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
 2.2 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, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 21, 22, 32, 44, 46, 53, 55, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 86, 87, 88, 89, 96, 100, 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, 141, 144, 149, 152, 153, 154, 155, 156 }

B grade: { 93, 94, 95, 97, 98, 99, 101, 102, 103, 142, 143 }

C grade: { 12, 13, 14, 15, 16, 17, 18, 19, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 54, 56, 57, 58, 59, 60, 79, 80, 81, 82, 83, 84, 85, 138, 139, 140 }

F grade: { 90, 91, 92, 145, 146, 147, 148, 150, 151}

2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 7, 8, 10, 11, 12, 13, 20, 21, 22, 23, 24, 32, 33, 34, 44, 48, 53, 55, 57, 59, 64, 65, 66, 67, 74, 86, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 144, 155, 156 }

B grade: { 6, 9, 35, 36, 37, 38, 39, 40, 41, 42, 46, 50, 61, 62, 63, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 125, 126, 127, 128 }

C grade: { 14, 15, 16, 17, 18, 19, 25, 26, 27, 28, 29, 30, 31, 43, 45, 47, 49, 51, 52, 54, 56, 58, 60, 140 }

F grade: { 87, 88, 89, 90, 91, 92, 141, 142, 143, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154 }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 20, 21, 22, 23, 24, 32, 33, 53, 57, 86, 93, 97, 101, 105, 106, 107, 108, 109, 113, 114, 115, 116, 117, 121, 122, 123, 125, 130, 131, 132, 134, 135, 136, 138, 139, 140, 144, 155, 156

B grade: { 94, 95, 98, 99, 102, 103, 110, 111, 112, 118, 119, 120, 124, 126, 127, 128 }

C grade: { }

F grade: { 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 25, 26, 27, 28, 29, 30, 31, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 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, 87, 88, 89, 90, 91, 92, 96, 100, 104, 129, 133, 137, 141, 142, 143, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 20, 21, 22, 23, 24, 32, 33, 34, 44, 48, 52, 53, 55, 57, 58, 61, 62, 63, 64, 65, 66, 86, 105, 106, 107, 108, 113, 114, 115, 116, 121, 122, 123, 124, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 144, 155, 156 }

B grade: { 8, 17, 25, 26, 27, 28, 29, 30, 31, 45, 46, 47, 50, 54, 56, 59, 60, 72, 73, 74, 75, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 109, 110, 111, 112, 117, 118, 119, 120, 125, 126, 127, 128 }

C grade: { }

F grade: { 14, 15, 16, 18, 19, 35, 36, 37, 38, 39, 40, 41, 42, 43, 49, 51, 67, 68, 69, 70, 71, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 87, 88, 89, 90, 91, 92, 141, 142, 143, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 16, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 52, 53, 54, 55, 56, 57, 58, 59, 60, 105, 106, 107, 113, 114, 115, 121, 122, 123, 124, 137 }

B grade: { 9, 10, 11, 44, 93, 94, 95, 97, 98, 99, 101, 102, 103, 109, 117, 125, 129, 133, 138 }

C grade: { 144 }

F grade: { 12, 13, 14, 15, 17, 18, 19, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 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, 96, 100, 104, 108, 110, 111, 112, 116, 118, 119, 120, 126, 127, 128, 130, 131, 132, 134, 135, 136, 139, 140, 141, 142, 143, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156 }

2.1.7 Giac

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 20, 21, 22, 23, 24, 32, 33, 34, 44, 48, 52, 53, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 86, 105, 106, 107, 108, 109, 110, 112, 113, 114, 115, 116, 117, 118, 120, 121, 122, 123, 124, 125, 126, 127, 128, 132, 136, 137, 138, 139, 140, 144, 155, 156 }

B grade: { 25, 26, 27, 28, 29, 30, 31, 59, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 129, 130, 131, 133, 134, 135 }

C grade: { 46, 50 }

F grade: { 14, 15, 16, 17, 18, 19, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 47, 49, 51, 79, 80, 81, 82, 83, 84, 85, 87, 88, 89, 90, 91, 92, 111, 119, 141, 142, 143, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154 }

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
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 163 163 164 169 224 448 187 234
normalized size 1 1. 1.01 1.04 1.37 2.75 1.15 1.44
time (sec) N/A 0.185 0.048 0.001 1.006 1.139 0.096 1.133
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 135 135 135 136 182 360 151 190
normalized size 1 1. 1. 1.01 1.35 2.67 1.12 1.41
time (sec) N/A 0.125 0.036 0.001 0.983 1.164 0.089 1.114
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 103 103 104 103 138 282 117 147
normalized size 1 1. 1.01 1. 1.34 2.74 1.14 1.43
time (sec) N/A 0.097 0.029 0.002 1.053 1.157 0.082 1.077
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 73 73 73 70 93 192 75 103
normalized size 1 1. 1. 0.96 1.27 2.63 1.03 1.41
time (sec) N/A 0.062 0.022 0. 0.962 1.097 0.075 1.162
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 42 42 42 37 49 107 39 58
normalized size 1 1. 1. 0.88 1.17 2.55 0.93 1.38
time (sec) N/A 0.028 0.009 0. 1.058 1.128 0.063 1.099
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 188 188 176 313 0 1096 175 279
normalized size 1 1. 0.94 1.66 0. 5.83 0.93 1.48
time (sec) N/A 0.211 0.155 0.004 0. 1.433 1.07 1.103
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 213 213 199 345 0 1548 206 306
normalized size 1 1. 0.93 1.62 0. 7.27 0.97 1.44
time (sec) N/A 0.226 0.199 0.008 0. 1.389 1.984 1.122
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 242 242 209 362 0 2067 246 340
normalized size 1 1. 0.86 1.5 0. 8.54 1.02 1.4
time (sec) N/A 0.262 0.271 0.01 0. 1.398 7.551 1.145
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 132 132 126 260 0 902 619 177
normalized size 1 1. 0.95 1.97 0. 6.83 4.69 1.34
time (sec) N/A 0.218 0.065 0.004 0. 3.254 15.002 1.361
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 97 97 93 175 0 664 434 128
normalized size 1 1. 0.96 1.8 0. 6.85 4.47 1.32
time (sec) N/A 0.12 0.07 0.003 0. 1.928 9.096 1.35
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 72 72 71 99 0 481 287 95
normalized size 1 1. 0.99 1.38 0. 6.68 3.99 1.32
time (sec) N/A 0.073 0.05 0.002 0. 1.445 4.389 1.375
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 78 78 80 106 0 556 0 103
normalized size 1 1. 1.03 1.36 0. 7.13 0. 1.32
time (sec) N/A 0.128 0.034 0.006 0. 2.198 0. 1.384
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 112 112 130 191 0 845 0 173
normalized size 1 1. 1.16 1.71 0. 7.54 0. 1.54
time (sec) N/A 0.197 0.052 0.009 0. 4.111 0. 1.366
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F(-1) F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 723 723 88 70 0 0 0 0
normalized size 1 1. 0.12 0.1 0. 0. 0. 0.
time (sec) N/A 1.813 0.049 0.007 0. 0. 0. 0.
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F(-1) F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 718 718 88 67 0 0 0 0
normalized size 1 1. 0.12 0.09 0. 0. 0. 0.
time (sec) N/A 1.457 0.052 0.006 0. 0. 0. 0.
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 634 634 59 49 0 0 920 0
normalized size 1 1. 0.09 0.08 0. 0. 1.45 0.
time (sec) N/A 0.728 0.031 0.002 0. 0. 133.311 0.
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 634 634 61 47 0 28045 0 0
normalized size 1 1. 0.1 0.07 0. 44.24 0. 0.
time (sec) N/A 0.654 0.031 0.003 0. 108.462 0. 0.
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F(-1) F(-1) F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 653 653 85 70 0 0 0 0
normalized size 1 1. 0.13 0.11 0. 0. 0. 0.
time (sec) N/A 1.175 0.049 0.006 0. 0. 0. 0.
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F(-1) F(-1) F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 655 655 89 68 0 0 0 0
normalized size 1 1. 0.14 0.1 0. 0. 0. 0.
time (sec) N/A 1.11 0.048 0.006 0. 0. 0. 0.
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 46 38 50 109 42 50
normalized size 1 1. 1. 0.83 1.09 2.37 0.91 1.09
time (sec) N/A 0.058 0.016 0.003 1.491 1.778 0.15 1.11
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 31 25 32 76 32 32
normalized size 1 1. 1. 0.81 1.03 2.45 1.03 1.03
time (sec) N/A 0.035 0.008 0.003 1.457 1.8 0.126 1.167
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 39 39 39 33 43 95 37 43
normalized size 1 1. 1. 0.85 1.1 2.44 0.95 1.1
time (sec) N/A 0.04 0.009 0.002 1.507 1.681 0.14 1.146
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 41 41 44 35 51 108 41 47
normalized size 1 1. 1.07 0.85 1.24 2.63 1. 1.15
time (sec) N/A 0.055 0.013 0.005 1.458 1.766 0.154 1.11
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 45 25 32 84 36 32
normalized size 1 1. 1.45 0.81 1.03 2.71 1.16 1.03
time (sec) N/A 0.045 0.013 0.004 1.526 1.352 0.158 1.106
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 418 418 47 46 0 3918 31 867
normalized size 1 1. 0.11 0.11 0. 9.37 0.07 2.07
time (sec) N/A 0.538 0.011 0.006 0. 1.607 0.177 1.168
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 382 382 48 44 0 5949 32 1103
normalized size 1 1. 0.13 0.12 0. 15.57 0.08 2.89
time (sec) N/A 0.328 0.014 0.004 0. 1.942 0.193 1.16
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 378 378 46 41 0 3906 24 853
normalized size 1 1. 0.12 0.11 0. 10.33 0.06 2.26
time (sec) N/A 0.259 0.013 0.004 0. 1.673 0.179 1.178
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 411 411 55 44 0 5936 22 1108
normalized size 1 1. 0.13 0.11 0. 14.44 0.05 2.7
time (sec) N/A 0.276 0.012 0.006 0. 2.013 0.183 1.196
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 411 411 57 44 0 3903 26 860
normalized size 1 1. 0.14 0.11 0. 9.5 0.06 2.09
time (sec) N/A 0.277 0.012 0.004 0. 1.639 0.185 1.195
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 416 416 47 46 0 5952 31 1119
normalized size 1 1. 0.11 0.11 0. 14.31 0.07 2.69
time (sec) N/A 0.275 0.014 0.006 0. 1.937 0.19 1.157
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 418 418 47 46 0 3945 32 867
normalized size 1 1. 0.11 0.11 0. 9.44 0.08 2.07
time (sec) N/A 0.359 0.012 0.006 0. 1.626 0.2 1.164
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 36 36 37 33 43 96 37 43
normalized size 1 1. 1.03 0.92 1.19 2.67 1.03 1.19
time (sec) N/A 0.039 0.01 0.003 1.5 1.276 0.136 1.171
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 39 39 55 35 51 107 41 47
normalized size 1 1. 1.41 0.9 1.31 2.74 1.05 1.21
time (sec) N/A 0.056 0.014 0.006 1.486 1.476 0.143 1.128
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 39 39 55 35 0 107 41 47
normalized size 1 1. 1.41 0.9 0. 2.74 1.05 1.21
time (sec) N/A 0.063 0.01 0.004 0. 1.498 0.148 1.094
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 396 396 103 1070 0 0 400 0
normalized size 1 1. 0.26 2.7 0. 0. 1.01 0.
time (sec) N/A 0.416 0.179 0.161 0. 0. 10.083 0.
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 356 356 101 1010 0 0 257 0
normalized size 1 1. 0.28 2.84 0. 0. 0.72 0.
time (sec) N/A 0.311 0.153 0.029 0. 0. 5.848 0.
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 316 316 98 956 0 0 124 0
normalized size 1 1. 0.31 3.03 0. 0. 0.39 0.
time (sec) N/A 0.246 0.134 0.027 0. 0. 3.115 0.
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 278 278 98 907 0 0 119 0
normalized size 1 1. 0.35 3.26 0. 0. 0.43 0.
time (sec) N/A 0.182 0.091 0.028 0. 0. 2.629 0.
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 289 289 102 934 0 0 119 0
normalized size 1 1. 0.35 3.23 0. 0. 0.41 0.
time (sec) N/A 0.189 0.106 0.038 0. 0. 18.698 0.
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 309 309 129 1005 0 0 0 0
normalized size 1 1. 0.42 3.25 0. 0. 0. 0.
time (sec) N/A 0.211 0.139 0.042 0. 0. 0. 0.
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 349 349 166 1095 0 0 0 0
normalized size 1 1. 0.48 3.14 0. 0. 0. 0.
time (sec) N/A 0.324 0.191 0.043 0. 0. 0. 0.
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 389 389 200 1182 0 0 0 0
normalized size 1 1. 0.51 3.04 0. 0. 0. 0.
time (sec) N/A 0.395 0.243 0.048 0. 0. 0. 0.
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F(-1) F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 433 433 88 67 0 0 0 0
normalized size 1 1. 0.2 0.15 0. 0. 0. 0.
time (sec) N/A 1.132 0.075 0.004 0. 0. 0. 0.
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 72 72 71 99 0 481 287 95
normalized size 1 1. 0.99 1.38 0. 6.68 3.99 1.32
time (sec) N/A 0.072 0.056 0.003 0. 2.224 7.519 6.167
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F B F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 375 375 59 51 0 26996 0 0
normalized size 1 1. 0.16 0.14 0. 71.99 0. 0.
time (sec) N/A 0.456 0.047 0.003 0. 97.806 0. 0.
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 184 184 179 340 0 3077 0 6484
normalized size 1 1. 0.97 1.85 0. 16.72 0. 35.24
time (sec) N/A 0.213 0.156 0.022 0. 2.278 0. 7.939
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F B F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 375 375 61 47 0 26437 0 0
normalized size 1 1. 0.16 0.13 0. 70.5 0. 0.
time (sec) N/A 0.351 0.048 0.003 0. 20.939 0. 0.
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 78 78 80 106 0 556 0 105
normalized size 1 1. 1.03 1.36 0. 7.13 0. 1.35
time (sec) N/A 0.126 0.034 0.007 0. 4.899 0. 6.592
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F(-1) F(-1) F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 392 392 85 72 0 0 0 0
normalized size 1 1. 0.22 0.18 0. 0. 0. 0.
time (sec) N/A 0.683 0.065 0.006 0. 0. 0. 0.
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F(-1) C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 199 199 89 365 0 5485 0 2365
normalized size 1 1. 0.45 1.83 0. 27.56 0. 11.88
time (sec) N/A 0.311 0.049 0.02 0. 5.412 0. 7.081
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F(-1) F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 394 394 86 68 0 0 0 0
normalized size 1 1. 0.22 0.17 0. 0. 0. 0.
time (sec) N/A 0.625 0.074 0.007 0. 0. 0. 0.
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 278 278 46 34 0 613 170 281
normalized size 1 1. 0.17 0.12 0. 2.21 0.61 1.01
time (sec) N/A 0.3 0.016 0.006 0. 1.832 0.328 1.151
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 39 39 39 33 43 96 37 43
normalized size 1 1. 1. 0.85 1.1 2.46 0.95 1.1
time (sec) N/A 0.042 0.013 0.004 1.487 1.752 0.182 1.119
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 355 355 55 46 0 2313 27 342
normalized size 1 1. 0.15 0.13 0. 6.52 0.08 0.96
time (sec) N/A 0.289 0.016 0.007 0. 2.07 1.35 1.14
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 50 50 44 39 0 104 42 42
normalized size 1 1. 0.88 0.78 0. 2.08 0.84 0.84
time (sec) N/A 0.04 0.016 0.012 0. 1.726 0.162 1.112
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 355 355 57 44 0 2313 26 342
normalized size 1 1. 0.16 0.12 0. 6.52 0.07 0.96
time (sec) N/A 0.216 0.013 0. 0. 1.868 1.542 1.127
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 41 41 44 35 51 109 41 51
normalized size 1 1. 1.07 0.85 1.24 2.66 1. 1.24
time (sec) N/A 0.053 0.013 0.006 1.545 1.466 0.201 1.108
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 280 280 47 38 0 617 168 284
normalized size 1 1. 0.17 0.14 0. 2.2 0.6 1.01
time (sec) N/A 0.208 0.016 0.007 0. 1.629 0.306 1.135
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 89 89 49 70 0 566 76 348
normalized size 1 1. 0.55 0.79 0. 6.36 0.85 3.91
time (sec) N/A 0.09 0.016 0.01 0. 1.569 0.263 1.263
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 370 370 47 46 0 1962 32 348
normalized size 1 1. 0.13 0.12 0. 5.3 0.09 0.94
time (sec) N/A 0.269 0.015 0.01 0. 1.798 1.599 1.17
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 280 280 283 662 0 2079 0 398
normalized size 1 1. 1.01 2.36 0. 7.42 0. 1.42
time (sec) N/A 0.597 0.241 0.014 0. 137.062 0. 1.108
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 218 218 218 512 0 1623 0 302
normalized size 1 1. 1. 2.35 0. 7.44 0. 1.39
time (sec) N/A 0.395 0.181 0.006 0. 84.083 0. 1.115
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 176 176 178 388 0 1237 0 250
normalized size 1 1. 1.01 2.2 0. 7.03 0. 1.42
time (sec) N/A 0.285 0.187 0.007 0. 30.694 0. 1.096
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 149 149 132 275 0 872 0 201
normalized size 1 1. 0.89 1.85 0. 5.85 0. 1.35
time (sec) N/A 0.21 0.128 0.007 0. 9.367 0. 1.117
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 124 124 107 169 0 694 0 171
normalized size 1 1. 0.86 1.36 0. 5.6 0. 1.38
time (sec) N/A 0.145 0.079 0.003 0. 3.256 0. 1.109
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 123 123 105 168 0 697 0 170
normalized size 1 1. 0.85 1.37 0. 5.67 0. 1.38
time (sec) N/A 0.107 0.077 0.006 0. 3.293 0. 1.096
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-1) F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 158 159 152 285 0 0 0 221
normalized size 1 1.01 0.96 1.8 0. 0. 0. 1.4
time (sec) N/A 0.271 0.189 0.008 0. 0. 0. 1.104
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 193 193 194 412 0 0 0 284
normalized size 1 1. 1.01 2.13 0. 0. 0. 1.47
time (sec) N/A 0.343 0.178 0.011 0. 0. 0. 1.108
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 252 252 252 562 0 0 0 377
normalized size 1 1. 1. 2.23 0. 0. 0. 1.5
time (sec) N/A 0.428 0.234 0.012 0. 0. 0. 1.099
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 343 343 338 943 0 0 0 763
normalized size 1 1. 0.99 2.75 0. 0. 0. 2.22
time (sec) N/A 0.907 0.38 0.012 0. 0. 0. 1.134
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 274 274 269 765 0 0 0 643
normalized size 1 1. 0.98 2.79 0. 0. 0. 2.35
time (sec) N/A 0.563 0.316 0.012 0. 0. 0. 1.131
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 246 246 207 580 0 3005 0 556
normalized size 1 1. 0.84 2.36 0. 12.22 0. 2.26
time (sec) N/A 0.395 0.248 0.007 0. 110.084 0. 1.117
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 194 194 159 389 0 2365 0 455
normalized size 1 1. 0.82 2.01 0. 12.19 0. 2.35
time (sec) N/A 0.306 0.24 0.008 0. 36.977 0. 1.122
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 183 183 148 328 0 2217 0 441
normalized size 1 1. 0.81 1.79 0. 12.11 0. 2.41
time (sec) N/A 0.236 0.262 0.007 0. 31.559 0. 1.136
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 189 189 151 386 0 2295 0 447
normalized size 1 1. 0.8 2.04 0. 12.14 0. 2.37
time (sec) N/A 0.305 0.226 0.009 0. 17.499 0. 1.112
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 248 249 246 589 0 0 0 528
normalized size 1 1. 0.99 2.38 0. 0. 0. 2.13
time (sec) N/A 0.409 0.285 0.013 0. 0. 0. 1.136
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 291 291 287 791 0 0 0 657
normalized size 1 1. 0.99 2.72 0. 0. 0. 2.26
time (sec) N/A 0.563 0.381 0.016 0. 0. 0. 1.109
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 372 372 370 993 0 0 0 792
normalized size 1 1. 0.99 2.67 0. 0. 0. 2.13
time (sec) N/A 0.851 0.468 0.019 0. 0. 0. 1.119
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F F(-1) F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 981 981 10904 11938 0 0 0 0
normalized size 1 1. 11.12 12.17 0. 0. 0. 0.
time (sec) N/A 6.172 14.328 0.148 0. 0. 0. 0.
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F F(-1) F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 778 778 7531 9182 0 0 0 0
normalized size 1 1. 9.68 11.8 0. 0. 0. 0.
time (sec) N/A 2.349 13.756 0.062 0. 0. 0. 0.
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F F(-1) F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 636 636 5350 6302 0 0 0 0
normalized size 1 1. 8.41 9.91 0. 0. 0. 0.
time (sec) N/A 0.993 13.094 0.049 0. 0. 0. 0.
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 550 550 693 4361 0 0 0 0
normalized size 1 1. 1.26 7.93 0. 0. 0. 0.
time (sec) N/A 0.655 12.161 0.045 0. 0. 0. 0.
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-1) F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 955 955 1258 3023 0 0 0 0
normalized size 1 1. 1.32 3.17 0. 0. 0. 0.
time (sec) N/A 3.313 10.681 0.048 0. 0. 0. 0.
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 929 929 1372 3553 0 0 0 0
normalized size 1 1. 1.48 3.82 0. 0. 0. 0.
time (sec) N/A 2.725 11.486 0.045 0. 0. 0. 0.
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-1) F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 1287 1287 811 4957 0 0 0 0
normalized size 1 1. 0.63 3.85 0. 0. 0. 0.
time (sec) N/A 5.302 12.653 0.051 0. 0. 0. 0.
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 28 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.019 0.191 0.424 0. 0. 0. 0.
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 358 358 249 0 0 0 0 0
normalized size 1 1. 0.7 0. 0. 0. 0. 0.
time (sec) N/A 0.237 0.314 0.074 0. 0. 0. 0.
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 262 262 189 0 0 0 0 0
normalized size 1 1. 0.72 0. 0. 0. 0. 0.
time (sec) N/A 0.16 0.168 0.075 0. 0. 0. 0.
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 166 166 136 0 0 0 0 0
normalized size 1 1. 0.82 0. 0. 0. 0. 0.
time (sec) N/A 0.095 0.076 0.073 0. 0. 0. 0.
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 194 194 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.224 0.116 0.094 0. 0. 0. 0.
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 302 302 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.333 0.163 0.094 0. 0. 0. 0.
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 412 412 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.449 0.607 0.092 0. 0. 0. 0.
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 201 46548 19 3474 1326 1952
normalized size 1 1. 12.56 2909.25 1.19 217.12 82.88 122.
time (sec) N/A 0.06 0.169 0.004 1.036 0.936 0.305 1.113
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 18 18 233 46552 1674 3578 1384 1963
normalized size 1 1. 12.94 2586.22 93. 198.78 76.89 109.06
time (sec) N/A 0.329 0.174 0.003 1.037 0.893 0.307 1.15
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 18 18 233 46552 1674 3594 1394 1963
normalized size 1 1. 12.94 2586.22 93. 199.67 77.44 109.06
time (sec) N/A 0.302 0.179 0.003 1.07 0.927 0.305 1.147
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 22 2042 0 2969 0 2286
normalized size 1 1. 0.96 88.78 0. 129.09 0. 99.39
time (sec) N/A 0.056 0.068 0.062 0. 1.298 0. 1.291
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 18 18 201 47685 22 3474 1326 1958
normalized size 1 1. 11.17 2649.17 1.22 193. 73.67 108.78
time (sec) N/A 0.069 0.173 0.006 1.23 0.808 0.313 1.11
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 20 20 233 47688 1677 3578 1384 1963
normalized size 1 1. 11.65 2384.4 83.85 178.9 69.2 98.15
time (sec) N/A 0.322 0.168 0.002 1.054 0.86 0.311 1.146
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 20 20 233 47688 1677 3594 1394 1963
normalized size 1 1. 11.65 2384.4 83.85 179.7 69.7 98.15
time (sec) N/A 0.31 0.165 0.001 1.062 0.968 0.321 1.14
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 25 25 24 2046 0 2969 0 2286
normalized size 1 1. 0.96 81.84 0. 118.76 0. 91.44
time (sec) N/A 0.06 0.056 0.06 0. 1.358 0. 1.287
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 15 15 172 155 18 387 175 208
normalized size 1 1. 11.47 10.33 1.2 25.8 11.67 13.87
time (sec) N/A 0.014 0.005 0.003 1.002 0.937 0.118 1.088
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 182 157 211 402 182 211
normalized size 1 1. 11.38 9.81 13.19 25.12 11.38 13.19
time (sec) N/A 0.054 0.006 0.004 1.134 0.897 0.157 1.089
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 186 157 211 408 185 211
normalized size 1 1. 11.62 9.81 13.19 25.5 11.56 13.19
time (sec) N/A 0.056 0.006 0.004 1.17 0.818 0.121 1.094
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 21 21 21 230 0 467 0 255
normalized size 1 1. 1. 10.95 0. 22.24 0. 12.14
time (sec) N/A 0.033 0.118 0.033 0. 1.103 0. 1.132
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 11 11 10 12 15 30 10 15
normalized size 1 1. 0.91 1.09 1.36 2.73 0.91 1.36
time (sec) N/A 0.004 0.003 0.001 1.138 0.979 0.297 1.096
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 17 17 17 16 20 38 14 20
normalized size 1 1. 1. 0.94 1.18 2.24 0.82 1.18
time (sec) N/A 0.019 0.006 0. 1.139 0.995 0.418 1.137
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 17 17 17 16 20 38 14 20
normalized size 1 1. 1. 0.94 1.18 2.24 0.82 1.18
time (sec) N/A 0.024 0.007 0.002 1.03 0.988 0.53 1.368
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 19 19 19 24 31 41 0 26
normalized size 1 1. 1. 1.26 1.63 2.16 0. 1.37
time (sec) N/A 0.027 0.109 0.019 1.161 1.109 0. 1.082
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 15 15 19 737 359 19
normalized size 1 1. 0.94 0.94 1.19 46.06 22.44 1.19
time (sec) N/A 0.005 0.011 0. 1.031 1.236 51.451 1.141
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 18 18 18 17 475 748 0 22
normalized size 1 1. 1. 0.94 26.39 41.56 0. 1.22
time (sec) N/A 0.02 0.014 0.002 1.673 1.244 0. 50.318
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 18 18 18 17 475 749 0 0
normalized size 1 1. 1. 0.94 26.39 41.61 0. 0.
time (sec) N/A 0.023 0.013 0.001 1.705 1.268 0. 0.
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 22 22 562 851 0 28
normalized size 1 1. 0.96 0.96 24.43 37. 0. 1.22
time (sec) N/A 0.027 0.062 0.059 3.203 1.356 0. 1.183
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 13 13 12 14 18 30 10 18
normalized size 1 1. 0.92 1.08 1.38 2.31 0.77 1.38
time (sec) N/A 0.005 0.005 0. 1.186 0.95 0.393 1.121
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 19 19 19 18 23 38 14 23
normalized size 1 1. 1. 0.95 1.21 2. 0.74 1.21
time (sec) N/A 0.019 0.007 0.003 1.014 1.038 0.418 1.158
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 19 19 19 18 23 38 14 23
normalized size 1 1. 1. 0.95 1.21 2. 0.74 1.21
time (sec) N/A 0.024 0.006 0. 0.979 1.016 0.512 1.332
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 21 21 21 26 34 41 0 28
normalized size 1 1. 1. 1.24 1.62 1.95 0. 1.33
time (sec) N/A 0.029 0.114 0.02 1.148 1.208 0. 1.095
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 18 18 16 17 22 737 359 22
normalized size 1 1. 0.89 0.94 1.22 40.94 19.94 1.22
time (sec) N/A 0.004 0.013 0.002 1.006 1.318 55.204 1.109
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 20 20 20 19 481 748 0 24
normalized size 1 1. 1. 0.95 24.05 37.4 0. 1.2
time (sec) N/A 0.02 0.017 0.001 1.481 1.324 0. 55.488
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 20 20 20 19 481 749 0 0
normalized size 1 1. 1. 0.95 24.05 37.45 0. 0.
time (sec) N/A 0.024 0.017 0. 1.531 1.327 0. 0.
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 25 25 23 24 566 851 0 31
normalized size 1 1. 0.92 0.96 22.64 34.04 0. 1.24
time (sec) N/A 0.029 0.068 0.059 2.891 1.513 0. 1.238
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 10 10 9 9 14 24 8 15
normalized size 1 1. 0.9 0.9 1.4 2.4 0.8 1.5
time (sec) N/A 0.004 0.004 0.002 1.026 1.096 0.353 1.096
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 15 15 14 23 39 12 20
normalized size 1 0.94 0.94 0.88 1.44 2.44 0.75 1.25
time (sec) N/A 0.024 0.006 0.004 0.997 1.021 0.324 1.097
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 15 15 14 23 39 12 20
normalized size 1 0.94 0.94 0.88 1.44 2.44 0.75 1.25
time (sec) N/A 0.03 0.007 0.006 1.202 1.168 0.348 1.121
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 15 15 15 18 63 42 48 23
normalized size 1 1. 1. 1.2 4.2 2.8 3.2 1.53
time (sec) N/A 0.035 0.012 0.018 1.028 1.086 134.943 1.091
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 15 15 14 177 18 171 87 18
normalized size 1 1. 0.93 11.8 1.2 11.4 5.8 1.2
time (sec) N/A 0.004 0.02 0.017 0.981 1.189 4.082 1.112
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 16 197 109 177 0 20
normalized size 1 1. 1. 12.31 6.81 11.06 0. 1.25
time (sec) N/A 0.021 0.028 0.019 1.038 1.05 0. 1.125
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 16 197 109 177 0 20
normalized size 1 1. 1. 12.31 6.81 11.06 0. 1.25
time (sec) N/A 0.025 0.035 0.013 1.086 1.138 0. 1.121
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 21 21 21 203 826 236 0 27
normalized size 1 1. 1. 9.67 39.33 11.24 0. 1.29
time (sec) N/A 0.032 0.181 0.05 1.215 1.315 0. 1.139
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 20 20 19 21 0 63 104 72
normalized size 1 1. 0.95 1.05 0. 3.15 5.2 3.6
time (sec) N/A 0.005 0.008 0.004 0. 1.078 51.315 1.118
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 25 25 25 24 45 74 0 84
normalized size 1 1. 1. 0.96 1.8 2.96 0. 3.36
time (sec) N/A 0.019 0.011 0.003 1.163 1.188 0. 1.143
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 25 25 25 24 45 74 0 84
normalized size 1 1. 1. 0.96 1.8 2.96 0. 3.36
time (sec) N/A 0.024 0.012 0.006 1.191 1.089 0. 1.158
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 26 40 53 82 0 36
normalized size 1 1. 0.96 1.48 1.96 3.04 0. 1.33
time (sec) N/A 0.028 0.034 0.055 1.29 1.18 0. 1.152
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 22 22 21 23 0 63 104 81
normalized size 1 1. 0.95 1.05 0. 2.86 4.73 3.68
time (sec) N/A 0.005 0.011 0.003 0. 1.08 51.531 1.083
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 27 26 50 74 0 93
normalized size 1 1. 1. 0.96 1.85 2.74 0. 3.44
time (sec) N/A 0.02 0.014 0.003 1.168 1.079 0. 1.151
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 27 26 50 74 0 93
normalized size 1 1. 1. 0.96 1.85 2.74 0. 3.44
time (sec) N/A 0.025 0.016 0.004 1.215 1.062 0. 1.148
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 28 45 58 82 0 39
normalized size 1 1. 0.97 1.55 2. 2.83 0. 1.34
time (sec) N/A 0.028 0.035 0.057 1.253 1.054 0. 1.189
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 19 19 17 24 0 53 46 50
normalized size 1 1. 0.89 1.26 0. 2.79 2.42 2.63
time (sec) N/A 0.004 0.01 0.004 0. 1.005 0.577 1.112
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 24 24 97 31 47 63 85 59
normalized size 1 1. 4.04 1.29 1.96 2.62 3.54 2.46
time (sec) N/A 0.014 0.074 0.005 1.156 1.084 20.152 1.146
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 24 24 97 31 47 63 0 59
normalized size 1 1. 4.04 1.29 1.96 2.62 0. 2.46
time (sec) N/A 0.02 0.076 0.004 1.181 1.299 0. 1.125
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 26 26 111 155 54 72 0 35
normalized size 1 1. 4.27 5.96 2.08 2.77 0. 1.35
time (sec) N/A 0.079 0.13 0.098 1.322 1.29 0. 1.145
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 196 196 158 0 0 0 0 0
normalized size 1 1. 0.81 0. 0. 0. 0. 0.
time (sec) N/A 0.289 0.308 0.031 0. 0. 0. 0.
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 374 374 2305 0 0 0 0 0
normalized size 1 1. 6.16 0. 0. 0. 0. 0.
time (sec) N/A 1.38 4.304 0.039 0. 0. 0. 0.
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 816 816 13117 0 0 0 0 0
normalized size 1 1. 16.07 0. 0. 0. 0. 0.
time (sec) N/A 4.552 7.357 0.055 0. 0. 0. 0.
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A C A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 47 47 47 36 46 109 126 46
normalized size 1 1. 1. 0.77 0.98 2.32 2.68 0.98
time (sec) N/A 0.062 0.02 0.003 1.063 1.385 7.148 1.161
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 245 245 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.54 0.175 0.076 0. 0. 0. 0.
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 210 210 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.501 0.187 0.054 0. 0. 0. 0.
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 206 206 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.376 0.138 0.055 0. 0. 0. 0.
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 194 194 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.3 0.084 0.052 0. 0. 0. 0.
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 263 263 218 0 0 0 0 0
normalized size 1 1. 0.83 0. 0. 0. 0. 0.
time (sec) N/A 0.734 0.728 0.079 0. 0. 0. 0.
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 212 212 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.489 0.142 0.053 0. 0. 0. 0.
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 210 210 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.476 0.128 0.053 0. 0. 0. 0.
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F(-2)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 498 498 391 0 0 0 0 0
normalized size 1 1. 0.79 0. 0. 0. 0. 0.
time (sec) N/A 0.609 1.167 0.054 0. 0. 0. 0.
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 323 323 273 0 0 0 0 0
normalized size 1 1. 0.85 0. 0. 0. 0. 0.
time (sec) N/A 0.371 0.633 0.049 0. 0. 0. 0.
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 158 158 181 0 0 0 0 0
normalized size 1 1. 1.15 0. 0. 0. 0. 0.
time (sec) N/A 0.124 0.331 0.05 0. 0. 0. 0.
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 33 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.026 0.208 0.073 0. 0. 0. 0.
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 33 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.025 0.285 0.074 0. 0. 0. 0.

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 [83] had the largest ratio of [ 0.4231 ]

Table 2.1Rubi 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. 22 0.045
2 A 2 1 1. 22 0.045
3 A 2 1 1. 22 0.045
4 A 2 1 1. 22 0.045
5 A 2 1 1. 20 0.05
6 A 8 8 1. 22 0.364
7 A 8 8 1. 22 0.364
8 A 8 8 1. 22 0.364
9 A 7 6 1. 25 0.24
10 A 6 6 1. 25 0.24
11 A 5 5 1. 25 0.2
12 A 7 6 1. 25 0.24
13 A 7 6 1. 25 0.24
14 A 14 8 1. 25 0.32
15 A 14 8 1. 25 0.32
16 A 13 7 1. 23 0.304
17 A 13 7 1. 22 0.318
18 A 14 8 1. 25 0.32
19 A 14 8 1. 25 0.32
20 A 7 6 1. 23 0.261
21 A 4 4 1. 23 0.174
22 A 5 5 1. 23 0.217
23 A 7 6 1. 23 0.261
24 A 5 4 1. 23 0.174
25 A 15 9 1. 23 0.391
26 A 15 9 1. 23 0.391
27 A 14 8 1. 23 0.348
28 A 13 7 1. 21 0.333
29 A 13 7 1. 20 0.35
30 A 14 8 1. 23 0.348
31 A 15 9 1. 23 0.391
32 A 5 5 1. 21 0.238
33 A 7 6 1. 21 0.286
34 A 8 7 1. 18 0.389
35 A 6 4 1. 24 0.167
36 A 5 4 1. 24 0.167
37 A 4 4 1. 24 0.167
38 A 3 3 1. 24 0.125
39 A 3 3 1. 24 0.125
40 A 3 3 1. 24 0.125
41 A 4 4 1. 24 0.167
42 A 5 4 1. 24 0.167
43 A 8 5 1. 25 0.2
44 A 5 5 1. 25 0.2
45 A 7 4 1. 25 0.16
46 A 4 3 1. 23 0.13
47 A 7 4 1. 22 0.182
48 A 7 6 1. 25 0.24
49 A 8 5 1. 25 0.2
50 A 5 4 1. 25 0.16
51 A 8 5 1. 25 0.2
52 A 20 7 1. 23 0.304
53 A 5 5 1. 23 0.217
54 A 21 7 1. 23 0.304
55 A 4 3 1. 21 0.143
56 A 19 6 1. 20 0.3
57 A 7 6 1. 23 0.261
58 A 20 7 1. 23 0.304
59 A 11 8 1. 23 0.348
60 A 21 9 1. 23 0.391
61 A 7 6 1. 25 0.24
62 A 7 6 1. 25 0.24
63 A 7 6 1. 23 0.261
64 A 7 6 1. 22 0.273
65 A 7 6 1. 25 0.24
66 A 7 7 1. 25 0.28
67 A 7 6 1.01 25 0.24
68 A 7 6 1. 25 0.24
69 A 7 6 1. 25 0.24
70 A 7 6 1. 25 0.24
71 A 7 6 1. 25 0.24
72 A 7 6 1. 23 0.261
73 A 7 6 1. 22 0.273
74 A 7 6 1. 25 0.24
75 A 8 7 1. 25 0.28
76 A 7 6 1. 25 0.24
77 A 7 6 1. 25 0.24
78 A 7 6 1. 25 0.24
79 A 11 7 1. 29 0.241
80 A 10 7 1. 29 0.241
81 A 8 7 1. 29 0.241
82 A 8 7 1. 27 0.259
83 A 16 11 1. 26 0.423
84 A 16 11 1. 29 0.379
85 A 24 12 1. 29 0.414
86 A 0 0 0. 0 0.
87 A 13 4 1. 26 0.154
88 A 10 4 1. 26 0.154
89 A 7 4 1. 24 0.167
90 A 6 3 1. 26 0.115
91 A 8 3 1. 26 0.115
92 A 10 3 1. 26 0.115
93 A 1 1 1. 19 0.053
94 A 2 2 1. 24 0.083
95 A 2 2 1. 26 0.077
96 A 2 2 1. 30 0.067
97 A 1 1 1. 21 0.048
98 A 2 2 1. 26 0.077
99 A 2 2 1. 28 0.071
100 A 2 2 1. 32 0.062
101 A 1 1 1. 18 0.056
102 A 3 3 1. 23 0.13
103 A 3 3 1. 25 0.12
104 A 3 3 1. 29 0.103
105 A 1 1 1. 19 0.053
106 A 2 2 1. 24 0.083
107 A 2 2 1. 26 0.077
108 A 2 2 1. 30 0.067
109 A 1 1 1. 19 0.053
110 A 2 2 1. 24 0.083
111 A 2 2 1. 26 0.077
112 A 2 2 1. 30 0.067
113 A 1 1 1. 21 0.048
114 A 2 2 1. 26 0.077
115 A 2 2 1. 28 0.071
116 A 2 2 1. 32 0.062
117 A 1 1 1. 21 0.048
118 A 2 2 1. 26 0.077
119 A 2 2 1. 28 0.071
120 A 2 2 1. 32 0.062
121 A 1 1 1. 18 0.056
122 A 4 3 0.94 23 0.13
123 A 4 3 0.94 25 0.12
124 A 4 3 1. 29 0.103
125 A 1 1 1. 18 0.056
126 A 3 3 1. 23 0.13
127 A 3 3 1. 25 0.12
128 A 3 3 1. 29 0.103
129 A 1 1 1. 19 0.053
130 A 2 2 1. 24 0.083
131 A 2 2 1. 26 0.077
132 A 2 2 1. 30 0.067
133 A 1 1 1. 21 0.048
134 A 2 2 1. 26 0.077
135 A 2 2 1. 28 0.071
136 A 2 2 1. 32 0.062
137 A 1 1 1. 18 0.056
138 A 1 1 1. 23 0.043
139 A 1 1 1. 25 0.04
140 A 2 2 1. 29 0.069
141 A 4 2 1. 29 0.069
142 A 5 3 1. 29 0.103
143 A 6 3 1. 29 0.103
144 A 3 3 1. 59 0.051
145 A 5 3 1. 31 0.097
146 A 5 3 1. 29 0.103
147 A 5 3 1. 27 0.111
148 A 5 3 1. 26 0.115
149 A 8 5 1. 29 0.172
150 A 5 3 1. 29 0.103
151 A 5 3 1. 29 0.103
152 A 10 4 1. 31 0.129
153 A 7 4 1. 29 0.138
154 A 2 2 1. 22 0.091
155 A 0 0 0. 0 0.
156 A 0 0 0. 0 0.

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