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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 }

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, 16, 17, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 55, 56, 57, 59, 60, 61, 62, 64, 65, 66, 68, 69, 70, 72, 73, 74, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 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, 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, 152 }

B grade: { 50, 54, 58, 63, 67, 71, 75, 76, 93 }

C grade: { 15, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 121, 148, 149, 150, 151, 153 }

F grade: { }

2.1.3 Maple

A grade: { 1, 3, 4, 5, 7, 8, 9, 10, 15, 16, 17, 30, 31, 35, 36, 37, 38, 39, 40, 41, 42, 46, 47, 51, 55, 59, 64, 68, 72, 80, 84, 88, 92, 97, 101, 105, 109, 111, 112, 116, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 132, 133, 134, 135, 136, 137, 138, 139 }

B grade: { 11, 12, 13, 14, 32, 33, 34, 43, 44, 45, 50, 54, 58, 60, 63, 67, 71, 73, 79, 83, 87, 91, 96, 100, 104, 108, 110, 113, 114, 115, 117, 118, 130, 131 }

C grade: { 2, 48, 49, 52, 53, 56, 57, 61, 62, 65, 66, 69, 70, 74, 75, 76, 77, 78, 81, 82, 85, 86, 89, 90, 93, 94, 95, 98, 99, 102, 103, 106, 107, 147, 148, 149, 150, 151, 152, 153 }

F grade: { 6, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 140, 141, 142, 143, 144, 145, 146 }

2.1.4 Maxima

A grade: { 1, 2, 7, 8, 9, 10, 11, 12, 13, 30, 31, 35, 36, 40, 43, 44, 45, 46, 47, 60, 80, 84, 85, 86, 87, 88, 89, 90, 91, 92, 97, 101, 102, 103, 104, 105, 106, 107, 108, 109, 116, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 138, 139, 144, 145, 147, 148, 149, 150, 151, 152

B grade: { 14, 38, 39, 41, 50, 52, 53, 54, 56, 57, 58, 63, 65, 66, 67, 69, 70, 71, 110, 113 }

C grade: { }

F grade: { 3, 4, 5, 6, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 32, 33, 34, 37, 42, 48, 49, 51, 55, 59, 61, 62, 64, 68, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 93, 94, 95, 96, 98, 99, 100, 111, 112, 114, 115, 117, 118, 134, 135, 136, 137, 140, 141, 142, 143, 146, 153 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 30, 31, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 51, 55, 59, 60, 64, 67, 68, 71, 72, 80, 84, 88, 92, 97, 101, 105, 109, 116, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 131, 132, 133, 137, 138, 139, 140, 143, 144, 145, 147 }

B grade: { 50, 54, 58, 63, 73, 79, 83, 87, 91, 96, 100, 104, 108, 110, 113, 134, 148, 149, 150, 151, 152 }

C grade: { 48, 49, 52, 53, 56, 57, 61, 62, 65, 66, 69, 70, 74, 75, 76, 77, 78, 81, 82, 85, 86, 89, 90, 93, 94, 95, 98, 99, 102, 103, 106, 107, 111, 112, 114, 115, 117, 118, 153 }

F grade: { 6, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 32, 33, 34, 130, 135, 136, 141, 142, 146 }

2.1.6 Sympy

A grade: { 1, 3, 4, 5, 7, 8, 11, 12, 13, 14, 15, 16, 17, 30, 31, 35, 36, 38, 39, 40, 41, 43, 44, 45, 47, 60, 80, 119, 122, 123, 124, 129 }

B grade: { 9, 10, 120, 121, 125 }

C grade: { 20, 21, 26, 27, 28 }

F grade: { 2, 6, 18, 19, 22, 23, 24, 25, 29, 32, 33, 34, 37, 42, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 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, 126, 127, 128, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153 }

2.1.7 Giac

A grade: { 1, 2, 3, 4, 5, 11, 12, 13, 14, 15, 16, 17, 20, 30, 31, 35, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 51, 55, 59, 60, 64, 68, 72, 80, 84, 88, 92, 97, 101, 105, 109, 119, 120, 121, 122, 123, 124, 126, 127, 128, 129, 131, 132, 133, 147, 148, 149, 150, 151, 152 }

B grade: { 7, 8, 9, 10, 37, 125 }

C grade: { }

F grade: { 6, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 32, 33, 34, 48, 49, 50, 52, 53, 54, 56, 57, 58, 61, 62, 63, 65, 66, 67, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 85, 86, 87, 89, 90, 91, 93, 94, 95, 96, 98, 99, 100, 102, 103, 104, 106, 107, 108, 110, 111, 112, 113, 114, 115, 116, 117, 118, 130, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 153 }

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 42 42 37 46 50 105 60 50
normalized size 1 1. 0.88 1.1 1.19 2.5 1.43 1.19
time (sec) N/A 0.041 0.015 0.035 0.991 2.365 6.029 1.133
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 40 140 54 140 0 54
normalized size 1 1. 0.89 3.11 1.2 3.11 0. 1.2
time (sec) N/A 0.042 0.036 0.115 0.975 2.338 0. 1.1
Problem 3 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 144 144 86 211 0 182 129 119
normalized size 1 1. 0.6 1.47 0. 1.26 0.9 0.83
time (sec) N/A 0.08 0.075 0.043 0. 2.23 8.857 1.22
Problem 4 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 116 116 74 163 0 153 102 101
normalized size 1 1. 0.64 1.41 0. 1.32 0.88 0.87
time (sec) N/A 0.042 0.053 0.041 0. 2.279 2.479 1.17
Problem 5 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 88 88 59 116 0 119 71 84
normalized size 1 1. 0.67 1.32 0. 1.35 0.81 0.95
time (sec) N/A 0.029 0.04 0.04 0. 2.355 0.833 1.183
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 288 288 171 0 0 0 0 0
normalized size 1 1. 0.59 0. 0. 0. 0. 0.
time (sec) N/A 0.167 2.462 0.316 0. 0. 0. 0.
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 57 57 54 67 78 111 53 142
normalized size 1 1. 0.95 1.18 1.37 1.95 0.93 2.49
time (sec) N/A 0.019 0.036 0.039 1.143 2.355 3.246 1.236
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 85 85 67 69 92 139 83 267
normalized size 1 1. 0.79 0.81 1.08 1.64 0.98 3.14
time (sec) N/A 0.028 0.044 0.039 1.012 2.524 5.535 1.206
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 113 113 78 117 147 165 352 381
normalized size 1 1. 0.69 1.04 1.3 1.46 3.12 3.37
time (sec) N/A 0.039 0.057 0.042 1.018 2.689 12.426 1.212
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 141 141 89 167 178 189 575 487
normalized size 1 1. 0.63 1.18 1.26 1.34 4.08 3.45
time (sec) N/A 0.05 0.068 0.043 1.002 3.186 31.126 1.213
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 124 124 83 230 225 182 124 185
normalized size 1 1. 0.67 1.85 1.81 1.47 1. 1.49
time (sec) N/A 0.067 0.104 0.046 1.007 2.33 15.824 1.19
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 99 99 72 180 188 158 97 138
normalized size 1 1. 0.73 1.82 1.9 1.6 0.98 1.39
time (sec) N/A 0.051 0.089 0.043 0.999 2.218 4.501 1.203
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 60 132 150 131 70 88
normalized size 1 1. 0.81 1.78 2.03 1.77 0.95 1.19
time (sec) N/A 0.036 0.083 0.042 1.01 2.364 1.327 1.162
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 43 43 43 84 104 96 39 55
normalized size 1 1. 1. 1.95 2.42 2.23 0.91 1.28
time (sec) N/A 0.01 0.02 0.038 1.002 2.361 0.768 1.139
Problem 15 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 59 59 86 57 0 339 60 73
normalized size 1 1. 1.46 0.97 0. 5.75 1.02 1.24
time (sec) N/A 0.033 0.06 0.039 0. 2.607 4.084 1.209
Problem 16 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 91 91 101 100 0 460 82 112
normalized size 1 1. 1.11 1.1 0. 5.05 0.9 1.23
time (sec) N/A 0.046 0.111 0.039 0. 2.711 8.67 1.239
Problem 17 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 119 119 114 150 0 529 148 143
normalized size 1 1. 0.96 1.26 0. 4.45 1.24 1.2
time (sec) N/A 0.06 0.141 0.04 0. 2.849 17.144 1.184
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 211 211 170 0 0 0 0 0
normalized size 1 1. 0.81 0. 0. 0. 0. 0.
time (sec) N/A 0.12 0.588 0.297 0. 0. 0. 0.
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 181 181 158 0 0 0 0 0
normalized size 1 1. 0.87 0. 0. 0. 0. 0.
time (sec) N/A 0.088 0.416 0.401 0. 0. 0. 0.
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F C A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 153 153 147 0 0 0 75 1
normalized size 1 1. 0.96 0. 0. 0. 0.49 0.01
time (sec) N/A 0.074 0.285 0.289 0. 0. 3.615 1.268
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 122 122 115 0 0 0 71 0
normalized size 1 1. 0.94 0. 0. 0. 0.58 0.
time (sec) N/A 0.061 0.122 0.293 0. 0. 5.202 0.
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 156 156 150 0 0 0 0 0
normalized size 1 1. 0.96 0. 0. 0. 0. 0.
time (sec) N/A 0.075 0.267 0.29 0. 0. 0. 0.
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 186 186 162 0 0 0 0 0
normalized size 1 1. 0.87 0. 0. 0. 0. 0.
time (sec) N/A 0.09 0.366 0.29 0. 0. 0. 0.
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 216 216 171 0 0 0 0 0
normalized size 1 1. 0.79 0. 0. 0. 0. 0.
time (sec) N/A 0.108 0.578 0.285 0. 0. 0. 0.
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 326 326 139 0 0 0 0 0
normalized size 1 1. 0.43 0. 0. 0. 0. 0.
time (sec) N/A 0.192 0.138 0.29 0. 0. 0. 0.
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 296 296 119 0 0 0 75 0
normalized size 1 1. 0.4 0. 0. 0. 0.25 0.
time (sec) N/A 0.161 0.109 0.296 0. 0. 40.537 0.
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 260 260 89 0 0 0 71 0
normalized size 1 1. 0.34 0. 0. 0. 0.27 0.
time (sec) N/A 0.139 0.106 0.283 0. 0. 7.209 0.
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 298 298 121 0 0 0 78 0
normalized size 1 1. 0.41 0. 0. 0. 0.26 0.
time (sec) N/A 0.166 0.133 0.296 0. 0. 37.529 0.
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 331 331 137 0 0 0 0 0
normalized size 1 1. 0.41 0. 0. 0. 0. 0.
time (sec) N/A 0.194 0.118 0.313 0. 0. 0. 0.
Problem 30 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 50 50 50 43 57 143 41 58
normalized size 1 1. 1. 0.86 1.14 2.86 0.82 1.16
time (sec) N/A 0.146 0.015 0.043 1.48 2.032 1.077 1.126
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 42 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.046 0.089 1.224 0. 0. 0. 0.
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 431 431 530 1745 0 0 0 0
normalized size 1 1. 1.23 4.05 0. 0. 0. 0.
time (sec) N/A 0.485 0.177 2.559 0. 0. 0. 0.
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 283 283 354 947 0 0 0 0
normalized size 1 1. 1.25 3.35 0. 0. 0. 0.
time (sec) N/A 0.295 0.107 1.218 0. 0. 0. 0.
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 98 98 93 371 0 0 0 0
normalized size 1 1. 0.95 3.79 0. 0. 0. 0.
time (sec) N/A 0.067 0.028 0.717 0. 0. 0. 0.
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 42 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.044 0.087 1.135 0. 0. 0. 0.
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 42 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.041 0.778 1.051 0. 0. 0. 0.
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 37 37 34 41 0 72 0 108
normalized size 1 1. 0.92 1.11 0. 1.95 0. 2.92
time (sec) N/A 0.024 0.056 0.056 0. 1.726 0. 1.126
Problem 38 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 23 23 20 20 109 31 109 36
normalized size 1 1. 0.87 0.87 4.74 1.35 4.74 1.57
time (sec) N/A 0.009 0.016 0.041 0.989 1.708 0.775 1.152
Problem 39 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 23 23 20 20 77 31 32 36
normalized size 1 1. 0.87 0.87 3.35 1.35 1.39 1.57
time (sec) N/A 0.007 0.015 0.048 1.001 1.749 0.241 1.117
Problem 40 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 16 18 15 16 23 42 35
normalized size 1 1. 1.12 0.94 1. 1.44 2.62 2.19
time (sec) N/A 0.003 0.007 0.034 0.972 1.751 0.173 1.079
Problem 41 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 21 21 19 21 57 22 34 31
normalized size 1 1. 0.9 1. 2.71 1.05 1.62 1.48
time (sec) N/A 0.031 0.014 0.045 1.468 1.804 0.893 1.108
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 36 36 31 56 0 101 0 84
normalized size 1 1. 0.86 1.56 0. 2.81 0. 2.33
time (sec) N/A 0.021 0.048 0.052 0. 2.072 0. 1.094
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 20 65 23 45 68 26
normalized size 1 1. 0.87 2.83 1. 1.96 2.96 1.13
time (sec) N/A 0.008 0.015 0.061 0.964 2.074 0.782 1.151
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 20 54 23 45 65 26
normalized size 1 1. 0.87 2.35 1. 1.96 2.83 1.13
time (sec) N/A 0.007 0.014 0.057 0.992 2.048 0.382 1.11
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 18 51 20 42 24 20
normalized size 1 1. 1.12 3.19 1.25 2.62 1.5 1.25
time (sec) N/A 0.003 0.007 0.056 0.951 1.978 0.151 1.085
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 19 19 19 35 19 41 0 20
normalized size 1 1. 1. 1.84 1. 2.16 0. 1.05
time (sec) N/A 0.033 0.015 0.059 0.95 2.021 0. 1.111
Problem 47 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 16 18 15 16 23 42 35
normalized size 1 1. 1.12 0.94 1. 1.44 2.62 2.19
time (sec) N/A 0.003 0. 0.034 0.964 1.933 0.168 1.102
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 403 403 363 8076 0 5146 0 0
normalized size 1 1. 0.9 20.04 0. 12.77 0. 0.
time (sec) N/A 0.517 0.91 8.128 0. 2.952 0. 0.
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 305 305 272 7660 0 4035 0 0
normalized size 1 1. 0.89 25.11 0. 13.23 0. 0.
time (sec) N/A 0.405 0.569 24.112 0. 2.728 0. 0.
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 198 198 555 1002 585 2894 0 0
normalized size 1 1. 2.8 5.06 2.95 14.62 0. 0.
time (sec) N/A 0.234 6.765 0.384 1.881 2.707 0. 0.
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-1) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 17 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.132 4.666 0.354 0. 0. 0. 0.
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C B C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 154 154 140 1532 417 907 0 0
normalized size 1 1. 0.91 9.95 2.71 5.89 0. 0.
time (sec) N/A 0.238 0.424 17.733 1.149 2.2 0. 0.
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C B C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 123 123 110 1497 294 755 0 0
normalized size 1 1. 0.89 12.17 2.39 6.14 0. 0.
time (sec) N/A 0.206 0.311 9.421 1.076 2.217 0. 0.
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 85 85 967 1489 605 547 0 0
normalized size 1 1. 11.38 17.52 7.12 6.44 0. 0.
time (sec) N/A 0.125 14.265 0.132 1.59 2.304 0. 0.
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.12 0.59 0.408 0. 0. 0. 0.
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C B C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 155 155 137 1533 419 915 0 0
normalized size 1 1. 0.88 9.89 2.7 5.9 0. 0.
time (sec) N/A 0.244 0.44 19.335 1.135 1.985 0. 0.
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C B C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 124 124 111 1498 296 760 0 0
normalized size 1 1. 0.9 12.08 2.39 6.13 0. 0.
time (sec) N/A 0.208 0.306 8.505 1.065 1.943 0. 0.
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 86 86 847 1681 605 549 0 0
normalized size 1 1. 9.85 19.55 7.03 6.38 0. 0.
time (sec) N/A 0.129 13.618 0.143 1.581 1.729 0. 0.
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.136 0.932 0.428 0. 0. 0. 0.
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 18 51 20 42 24 20
normalized size 1 1. 1.12 3.19 1.25 2.62 1.5 1.25
time (sec) N/A 0.003 0.007 0.043 0.986 1.692 0.165 1.085
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 399 399 359 7924 0 4058 0 0
normalized size 1 1. 0.9 19.86 0. 10.17 0. 0.
time (sec) N/A 0.511 0.856 6.152 0. 3.217 0. 0.
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 303 303 270 7556 0 3298 0 0
normalized size 1 1. 0.89 24.94 0. 10.88 0. 0.
time (sec) N/A 0.4 0.538 24.825 0. 2.883 0. 0.
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 198 198 1648 1159 710 2508 0 0
normalized size 1 1. 8.32 5.85 3.59 12.67 0. 0.
time (sec) N/A 0.25 21.684 0.38 1.912 2.967 0. 0.
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-1) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 17 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.134 4.493 0.405 0. 0. 0. 0.
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C B C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 154 154 136 1532 417 459 0 0
normalized size 1 1. 0.88 9.95 2.71 2.98 0. 0.
time (sec) N/A 0.256 0.326 18.458 1.136 1.944 0. 0.
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C B C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 123 123 110 1497 294 394 0 0
normalized size 1 1. 0.89 12.17 2.39 3.2 0. 0.
time (sec) N/A 0.222 0.206 9.3 1.086 1.905 0. 0.
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B A F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 85 85 929 1495 616 309 0 0
normalized size 1 1. 10.93 17.59 7.25 3.64 0. 0.
time (sec) N/A 0.131 15.84 0.137 1.573 1.968 0. 0.
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.121 0.629 0.408 0. 0. 0. 0.
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C B C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 155 155 140 1533 419 466 0 0
normalized size 1 1. 0.9 9.89 2.7 3.01 0. 0.
time (sec) N/A 0.261 0.321 18.921 1.126 1.933 0. 0.
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C B C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 124 124 110 1498 296 400 0 0
normalized size 1 1. 0.89 12.08 2.39 3.23 0. 0.
time (sec) N/A 0.224 0.196 9.099 1.077 1.93 0. 0.
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B A F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 86 86 872 1753 616 313 0 0
normalized size 1 1. 10.14 20.38 7.16 3.64 0. 0.
time (sec) N/A 0.134 12.737 0.136 1.595 1.984 0. 0.
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.119 0.645 0.431 0. 0. 0. 0.
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 39 39 64 142 0 217 0 0
normalized size 1 1. 1.64 3.64 0. 5.56 0. 0.
time (sec) N/A 0.032 0.031 0.051 0. 1.96 0. 0.
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 105 732 0 351 0 0
normalized size 1 1. 1.42 9.89 0. 4.74 0. 0.
time (sec) N/A 0.061 0.025 0.388 0. 1.979 0. 0.
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B C F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 108 108 356 758 0 477 0 0
normalized size 1 1. 3.3 7.02 0. 4.42 0. 0.
time (sec) N/A 0.088 0.107 0.227 0. 1.886 0. 0.
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B C F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 299 299 600 7275 0 4070 0 0
normalized size 1 1. 2.01 24.33 0. 13.61 0. 0.
time (sec) N/A 0.209 4.936 6.493 0. 3.1 0. 0.
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 229 229 375 5425 0 2903 0 0
normalized size 1 1. 1.64 23.69 0. 12.68 0. 0.
time (sec) N/A 0.152 2.622 8.241 0. 2.675 0. 0.
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 159 159 278 2414 0 1894 0 0
normalized size 1 1. 1.75 15.18 0. 11.91 0. 0.
time (sec) N/A 0.097 1.706 7.638 0. 2.322 0. 0.
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 132 440 0 1098 0 0
normalized size 1 1. 1.78 5.95 0. 14.84 0. 0.
time (sec) N/A 0.042 0.062 0.121 0. 2.102 0. 0.
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 17 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.038 6.441 0.606 0. 0. 0. 0.
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 355 355 305 6981 0 3641 0 0
normalized size 1 1. 0.86 19.66 0. 10.26 0. 0.
time (sec) N/A 0.461 5.225 6.736 0. 2.924 0. 0.
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 267 267 229 6640 0 2985 0 0
normalized size 1 1. 0.86 24.87 0. 11.18 0. 0.
time (sec) N/A 0.373 3.992 16.382 0. 2.637 0. 0.
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 174 174 288 350 0 2288 0 0
normalized size 1 1. 1.66 2.01 0. 13.15 0. 0.
time (sec) N/A 0.231 3.907 0.085 0. 5.626 0. 0.
Problem 84 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 17 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.126 8.14 0.358 0. 0. 0. 0.
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 142 142 128 1555 174 868 0 0
normalized size 1 1. 0.9 10.95 1.23 6.11 0. 0.
time (sec) N/A 0.228 5.128 11.773 5.932 1.99 0. 0.
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 113 113 102 1519 143 718 0 0
normalized size 1 1. 0.9 13.44 1.27 6.35 0. 0.
time (sec) N/A 0.195 5.235 6.903 5.797 1.885 0. 0.
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 79 79 71 1381 108 518 0 0
normalized size 1 1. 0.9 17.48 1.37 6.56 0. 0.
time (sec) N/A 0.118 1.701 0.145 5.864 1.905 0. 0.
Problem 88 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 21 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.112 3.598 0.428 0. 0. 0. 0.
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 145 145 128 1570 174 857 0 0
normalized size 1 1. 0.88 10.83 1.2 5.91 0. 0.
time (sec) N/A 0.22 5.103 10.954 5.898 2.017 0. 0.
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 116 116 102 1534 144 710 0 0
normalized size 1 1. 0.88 13.22 1.24 6.12 0. 0.
time (sec) N/A 0.197 4.981 3.744 5.922 1.958 0. 0.
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 82 82 71 1351 108 513 0 0
normalized size 1 1. 0.87 16.48 1.32 6.26 0. 0.
time (sec) N/A 0.119 1.665 0.143 5.946 1.985 0. 0.
Problem 92 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 24 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.116 3.602 0.439 0. 0. 0. 0.
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B C F C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 299 299 600 7275 0 4072 0 0
normalized size 1 1. 2.01 24.33 0. 13.62 0. 0.
time (sec) N/A 0.209 4.815 4.787 0. 2.998 0. 0.
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 229 229 375 5425 0 2901 0 0
normalized size 1 1. 1.64 23.69 0. 12.67 0. 0.
time (sec) N/A 0.153 2.656 7.741 0. 2.621 0. 0.
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 159 159 278 2415 0 1894 0 0
normalized size 1 1. 1.75 15.19 0. 11.91 0. 0.
time (sec) N/A 0.1 1.773 7.496 0. 2.618 0. 0.
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 73 73 132 440 0 1098 0 0
normalized size 1 1. 1.81 6.03 0. 15.04 0. 0.
time (sec) N/A 0.043 0.055 0.118 0. 2.446 0. 0.
Problem 97 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 17 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.043 4.329 0.872 0. 0. 0. 0.
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 351 351 299 6909 0 3614 0 0
normalized size 1 1. 0.85 19.68 0. 10.3 0. 0.
time (sec) N/A 0.465 5.477 5.885 0. 3.268 0. 0.
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 265 265 225 6529 0 2963 0 0
normalized size 1 1. 0.85 24.64 0. 11.18 0. 0.
time (sec) N/A 0.37 4.073 16.575 0. 3.021 0. 0.
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 174 174 287 350 0 2272 0 0
normalized size 1 1. 1.65 2.01 0. 13.06 0. 0.
time (sec) N/A 0.228 3.703 0.091 0. 6.505 0. 0.
Problem 101 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 17 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.121 8.399 0.387 0. 0. 0. 0.
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 142 142 128 1554 174 855 0 0
normalized size 1 1. 0.9 10.94 1.23 6.02 0. 0.
time (sec) N/A 0.236 1.572 12.993 5.847 2.292 0. 0.
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 113 113 102 1518 143 707 0 0
normalized size 1 1. 0.9 13.43 1.27 6.26 0. 0.
time (sec) N/A 0.206 1.475 4.582 5.892 2.264 0. 0.
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 79 79 71 1381 108 510 0 0
normalized size 1 1. 0.9 17.48 1.37 6.46 0. 0.
time (sec) N/A 0.122 0.661 0.152 5.924 2.247 0. 0.
Problem 105 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 21 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.11 3.594 0.438 0. 0. 0. 0.
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 145 145 128 1571 174 871 0 0
normalized size 1 1. 0.88 10.83 1.2 6.01 0. 0.
time (sec) N/A 0.231 1.575 12.849 5.856 2.263 0. 0.
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 116 116 102 1535 144 721 0 0
normalized size 1 1. 0.88 13.23 1.24 6.22 0. 0.
time (sec) N/A 0.201 1.495 7.276 5.759 2.235 0. 0.
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 82 82 71 1351 108 521 0 0
normalized size 1 1. 0.87 16.48 1.32 6.35 0. 0.
time (sec) N/A 0.121 0.662 0.144 5.829 2.239 0. 0.
Problem 109 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 24 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.112 3.629 0.447 0. 0. 0. 0.
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 59 59 46 147 0 0
normalized size 1 1. 1.9 1.9 1.48 4.74 0. 0.
time (sec) N/A 0.026 0.044 0.049 1.51 2.168 0. 0.
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 63 63 50 44 0 238 0 0
normalized size 1 1. 0.79 0.7 0. 3.78 0. 0.
time (sec) N/A 0.043 0.009 0.089 0. 2.163 0. 0.
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 91 91 91 70 0 298 0 0
normalized size 1 1. 1. 0.77 0. 3.27 0. 0.
time (sec) N/A 0.066 0.008 0.079 0. 2.282 0. 0.
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 83 106 85 297 0 0
normalized size 1 1. 1.84 2.36 1.89 6.6 0. 0.
time (sec) N/A 0.028 0.101 0.049 1.499 2.232 0. 0.
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 91 91 71 349 0 431 0 0
normalized size 1 1. 0.78 3.84 0. 4.74 0. 0.
time (sec) N/A 0.058 0.013 0.171 0. 2.336 0. 0.
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 133 133 133 407 0 540 0 0
normalized size 1 1. 1. 3.06 0. 4.06 0. 0.
time (sec) N/A 0.09 0.01 0.182 0. 2.351 0. 0.
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 196 196 167 186 302 554 0 0
normalized size 1 1. 0.85 0.95 1.54 2.83 0. 0.
time (sec) N/A 0.148 0.181 0.053 1.7 2.413 0. 0.
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) C F(-1) F
verified N/A NO NO TBD TBD TBD TBD TBD
size 232 250 236 672 0 778 0 0
normalized size 1 1.08 1.02 2.9 0. 3.35 0. 0.
time (sec) N/A 0.151 0.087 0.242 0. 2.476 0. 0.
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) C F(-1) F
verified N/A NO NO TBD TBD TBD TBD TBD
size 302 313 334 758 0 967 0 0
normalized size 1 1.04 1.11 2.51 0. 3.2 0. 0.
time (sec) N/A 0.201 0.014 0.217 0. 2.473 0. 0.
Problem 119 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 25 25 25 23 26 82 19 27
normalized size 1 1. 1. 0.92 1.04 3.28 0.76 1.08
time (sec) N/A 0.021 0.017 0.04 0.946 2.148 11.452 1.099
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 35 32 42 144 153 43
normalized size 1 1. 0.78 0.71 0.93 3.2 3.4 0.96
time (sec) N/A 0.032 0.033 0.043 1.442 2.392 0.652 1.104
Problem 121 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 64 64 81 54 73 219 223 74
normalized size 1 1. 1.27 0.84 1.14 3.42 3.48 1.16
time (sec) N/A 0.067 0.044 0.044 1.448 2.421 0.78 1.102
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 30 30 22 25 32 58 26 32
normalized size 1 1. 0.73 0.83 1.07 1.93 0.87 1.07
time (sec) N/A 0.011 0.01 0.038 1.438 2.395 0.256 1.112
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 5 5 5 6 7 27 5 7
normalized size 1 1. 1. 1.2 1.4 5.4 1. 1.4
time (sec) N/A 0.025 0.029 0.036 0.954 1.985 0.35 1.109
Problem 124 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 19 22 45 14 22
normalized size 1 1. 1. 1.12 1.29 2.65 0.82 1.29
time (sec) N/A 0.039 0.045 0.073 0.969 1.796 0.705 1.095
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 18 18 18 17 22 84 53 45
normalized size 1 1. 1. 0.94 1.22 4.67 2.94 2.5
time (sec) N/A 0.151 0.031 0.045 1.912 1.804 0.856 1.131
Problem 126 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 68 68 58 45 59 124 0 59
normalized size 1 1. 0.85 0.66 0.87 1.82 0. 0.87
time (sec) N/A 0.028 0.059 0.056 1.589 1.968 0. 1.129
Problem 127 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 59 59 53 40 53 107 0 53
normalized size 1 1. 0.9 0.68 0.9 1.81 0. 0.9
time (sec) N/A 0.026 0.032 0.051 1.595 1.967 0. 1.132
Problem 128 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 50 50 48 35 46 92 0 46
normalized size 1 1. 0.96 0.7 0.92 1.84 0. 0.92
time (sec) N/A 0.018 0.029 0.054 1.57 1.877 0. 1.113
Problem 129 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 37 37 39 28 35 72 29 36
normalized size 1 1. 1.05 0.76 0.95 1.95 0.78 0.97
time (sec) N/A 0.01 0.397 0.054 1.596 1.915 77.464 1.111
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 42 42 84 374 58 0 0 0
normalized size 1 1. 2. 8.9 1.38 0. 0. 0.
time (sec) N/A 0.042 0.185 1.115 1.55 0. 0. 0.
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 41 41 40 57 39 81 0 38
normalized size 1 1. 0.98 1.39 0.95 1.98 0. 0.93
time (sec) N/A 0.022 0.032 0.055 1.621 2.025 0. 1.115
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 50 50 48 35 46 100 0 46
normalized size 1 1. 0.96 0.7 0.92 2. 0. 0.92
time (sec) N/A 0.024 0.029 0.07 1.607 1.961 0. 1.108
Problem 133 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 59 59 51 40 53 115 0 53
normalized size 1 1. 0.86 0.68 0.9 1.95 0. 0.9
time (sec) N/A 0.025 0.041 0.048 1.625 2.069 0. 1.131
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 63 63 63 73 0 252 0 0
normalized size 1 1. 1. 1.16 0. 4. 0. 0.
time (sec) N/A 0.107 0.06 0.756 0. 2.432 0. 0.
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 59 59 59 72 0 0 0 0
normalized size 1 1. 1. 1.22 0. 0. 0. 0.
time (sec) N/A 0.098 0.03 0.68 0. 0. 0. 0.
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 59 59 59 72 0 0 0 0
normalized size 1 1. 1. 1.22 0. 0. 0. 0.
time (sec) N/A 0.062 0.023 0.675 0. 0. 0. 0.
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 55 71 0 165 0 0
normalized size 1 1. 1. 1.29 0. 3. 0. 0.
time (sec) N/A 0.108 0.055 1.108 0. 1.808 0. 0.
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 57 57 57 71 39 158 0 0
normalized size 1 1. 1. 1.25 0.68 2.77 0. 0.
time (sec) N/A 0.099 0.026 0.672 1.538 1.851 0. 0.
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 59 59 59 72 39 165 0 0
normalized size 1 1. 1. 1.22 0.66 2.8 0. 0.
time (sec) N/A 0.101 0.026 0.675 1.693 1.881 0. 0.
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 72 72 66 0 0 270 0 0
normalized size 1 1. 0.92 0. 0. 3.75 0. 0.
time (sec) N/A 0.108 0.222 0.9 0. 2.138 0. 0.
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 68 68 62 0 0 0 0 0
normalized size 1 1. 0.91 0. 0. 0. 0. 0.
time (sec) N/A 0.098 0.125 0.722 0. 0. 0. 0.
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 68 68 62 0 0 0 0 0
normalized size 1 1. 0.91 0. 0. 0. 0. 0.
time (sec) N/A 0.062 0.06 0.717 0. 0. 0. 0.
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 64 64 58 0 0 170 0 0
normalized size 1 1. 0.91 0. 0. 2.66 0. 0.
time (sec) N/A 0.108 0.104 0.715 0. 1.765 0. 0.
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 66 66 60 0 62 163 0 0
normalized size 1 1. 0.91 0. 0.94 2.47 0. 0.
time (sec) N/A 0.101 0.091 0.728 1.516 1.845 0. 0.
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 68 68 62 0 80 173 0 0
normalized size 1 1. 0.91 0. 1.18 2.54 0. 0.
time (sec) N/A 0.1 0.088 0.711 1.711 1.919 0. 0.
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 101 101 79 0 0 0 0 0
normalized size 1 1. 0.78 0. 0. 0. 0. 0.
time (sec) N/A 0.266 0.137 1.936 0. 0. 0. 0.
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A F(-1) A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 48 48 61 1299 65 192 0 88
normalized size 1 1. 1.27 27.06 1.35 4. 0. 1.83
time (sec) N/A 0.075 0.103 0.671 1.516 1.927 0. 1.116
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C A B F(-1) A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 103 103 146 1375 177 591 0 208
normalized size 1 1. 1.42 13.35 1.72 5.74 0. 2.02
time (sec) N/A 0.155 0.144 0.801 1.532 1.997 0. 1.125
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C A B F(-1) A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 180 180 89 1355 225 1152 0 344
normalized size 1 1. 0.49 7.53 1.25 6.4 0. 1.91
time (sec) N/A 0.182 0.117 0.73 1.523 2.236 0. 1.418
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C A B F(-1) A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 180 180 89 1355 225 1153 0 344
normalized size 1 1. 0.49 7.53 1.25 6.41 0. 1.91
time (sec) N/A 0.179 0.111 0.591 1.546 2.232 0. 1.364
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C A B F(-1) A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 103 103 145 842 228 741 0 208
normalized size 1 1. 1.41 8.17 2.21 7.19 0. 2.02
time (sec) N/A 0.145 0.148 0.609 1.575 2.068 0. 1.13
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A B F A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 47 47 57 885 63 343 0 89
normalized size 1 1. 1.21 18.83 1.34 7.3 0. 1.89
time (sec) N/A 0.079 0.107 0.513 1.519 1.905 0. 1.151
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F C F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 163 163 116 896 0 711 0 0
normalized size 1 1. 0.71 5.5 0. 4.36 0. 0.
time (sec) N/A 0.572 0.324 0.422 0. 2.174 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 [73] had the largest ratio of [ 1.333 ]

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 4 4 1. 12 0.333
2 A 4 4 1. 14 0.286
3 A 6 4 1. 25 0.16
4 A 5 4 1. 25 0.16
5 A 4 4 1. 23 0.174
6 A 8 8 1. 25 0.32
7 A 2 2 1. 25 0.08
8 A 3 3 1. 25 0.12
9 A 4 3 1. 25 0.12
10 A 5 3 1. 25 0.12
11 A 4 3 1. 25 0.12
12 A 4 3 1. 25 0.12
13 A 4 3 1. 25 0.12
14 A 2 2 1. 21 0.095
15 A 4 4 1. 25 0.16
16 A 5 5 1. 25 0.2
17 A 6 5 1. 25 0.2
18 A 6 4 1. 27 0.148
19 A 5 4 1. 27 0.148
20 A 4 4 1. 27 0.148
21 A 3 3 1. 27 0.111
22 A 4 4 1. 27 0.148
23 A 5 4 1. 27 0.148
24 A 6 4 1. 27 0.148
25 A 7 6 1. 27 0.222
26 A 6 6 1. 27 0.222
27 A 5 5 1. 27 0.185
28 A 6 6 1. 27 0.222
29 A 7 6 1. 27 0.222
30 A 8 7 1. 11 0.636
31 A 0 0 0. 0 0.
32 A 9 7 1. 40 0.175
33 A 7 6 1. 40 0.15
34 A 4 4 1. 38 0.105
35 A 0 0 0. 0 0.
36 A 0 0 0. 0 0.
37 A 2 2 1. 11 0.182
38 A 2 2 1. 11 0.182
39 A 2 2 1. 9 0.222
40 A 2 2 1. 7 0.286
41 A 2 2 1. 11 0.182
42 A 2 2 1. 11 0.182
43 A 2 2 1. 11 0.182
44 A 2 2 1. 9 0.222
45 A 2 2 1. 7 0.286
46 A 2 2 1. 11 0.182
47 A 2 2 1. 7 0.286
48 A 11 6 1. 15 0.4
49 A 9 5 1. 13 0.385
50 A 7 4 1. 11 0.364
51 A 0 0 0. 0 0.
52 A 7 7 1. 21 0.333
53 A 6 6 1. 19 0.316
54 A 5 5 1. 17 0.294
55 A 0 0 0. 0 0.
56 A 7 7 1. 21 0.333
57 A 6 6 1. 19 0.316
58 A 5 5 1. 17 0.294
59 A 0 0 0. 0 0.
60 A 2 2 1. 7 0.286
61 A 11 6 1. 15 0.4
62 A 9 5 1. 13 0.385
63 A 7 4 1. 11 0.364
64 A 0 0 0. 0 0.
65 A 7 7 1. 21 0.333
66 A 6 6 1. 19 0.316
67 A 5 5 1. 17 0.294
68 A 0 0 0. 0 0.
69 A 7 7 1. 21 0.333
70 A 6 6 1. 19 0.316
71 A 5 5 1. 17 0.294
72 A 0 0 0. 0 0.
73 A 6 4 1. 3 1.333
74 A 8 5 1. 5 1.
75 A 10 6 1. 7 0.857
76 A 12 6 1. 15 0.4
77 A 10 6 1. 15 0.4
78 A 8 5 1. 13 0.385
79 A 6 4 1. 7 0.571
80 A 0 0 0. 0 0.
81 A 11 6 1. 15 0.4
82 A 9 5 1. 13 0.385
83 A 7 4 1. 11 0.364
84 A 0 0 0. 0 0.
85 A 7 7 1. 19 0.368
86 A 6 6 1. 17 0.353
87 A 5 5 1. 15 0.333
88 A 0 0 0. 0 0.
89 A 7 7 1. 22 0.318
90 A 6 6 1. 20 0.3
91 A 5 5 1. 18 0.278
92 A 0 0 0. 0 0.
93 A 12 6 1. 15 0.4
94 A 10 6 1. 15 0.4
95 A 8 5 1. 13 0.385
96 A 6 4 1. 7 0.571
97 A 0 0 0. 0 0.
98 A 11 6 1. 15 0.4
99 A 9 5 1. 13 0.385
100 A 7 4 1. 11 0.364
101 A 0 0 0. 0 0.
102 A 7 7 1. 19 0.368
103 A 6 6 1. 17 0.353
104 A 5 5 1. 15 0.333
105 A 0 0 0. 0 0.
106 A 7 7 1. 22 0.318
107 A 6 6 1. 20 0.3
108 A 5 5 1. 18 0.278
109 A 0 0 0. 0 0.
110 A 4 3 1. 4 0.75
111 A 7 4 1. 6 0.667
112 A 9 5 1. 8 0.625
113 A 4 3 1. 8 0.375
114 A 7 4 1. 10 0.4
115 A 9 5 1. 12 0.417
116 A 6 6 1. 12 0.5
117 A 9 5 1.08 14 0.357
118 A 11 6 1.04 16 0.375
119 A 5 6 1. 10 0.6
120 A 5 4 1. 8 0.5
121 A 9 8 1. 14 0.571
122 A 4 4 1. 8 0.5
123 A 1 1 1. 14 0.071
124 A 1 1 1. 19 0.053
125 A 5 3 1. 26 0.115
126 A 9 6 1. 21 0.286
127 A 8 6 1. 21 0.286
128 A 7 6 1. 19 0.316
129 A 6 6 1. 18 0.333
130 A 6 5 1. 21 0.238
131 A 6 6 1. 21 0.286
132 A 7 6 1. 21 0.286
133 A 8 6 1. 21 0.286
134 A 2 2 1. 39 0.051
135 A 2 2 1. 39 0.051
136 A 2 2 1. 37 0.054
137 A 2 2 1. 39 0.051
138 A 2 2 1. 39 0.051
139 A 2 2 1. 39 0.051
140 A 2 2 1. 40 0.05
141 A 2 2 1. 40 0.05
142 A 2 2 1. 38 0.053
143 A 2 2 1. 40 0.05
144 A 2 2 1. 40 0.05
145 A 2 2 1. 40 0.05
146 A 9 7 1. 24 0.292
147 A 5 5 1. 20 0.25
148 A 8 7 1. 20 0.35
149 A 13 10 1. 20 0.5
150 A 13 10 1. 20 0.5
151 A 8 7 1. 20 0.35
152 A 5 5 1. 20 0.25
153 A 13 9 1. 24 0.375

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