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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, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 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, 149, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166 }

B grade: { 39, 41, 148, 150 }

C grade: { }

F grade: { }

2.1.3 Maple

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, 29, 31, 32, 33, 34, 35, 36, 37, 38, 40, 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, 75, 76, 77, 81, 82, 83, 87, 88, 89, 93, 94, 95, 96, 100, 101, 102, 106, 107, 108, 112, 113, 114, 115, 116, 119, 120, 121, 122, 123, 124, 125, 126, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 166 }

B grade: { }

C grade: { 130, 131 }

F grade: { 28, 30, 39, 41, 72, 73, 74, 78, 79, 80, 84, 85, 86, 90, 91, 92, 97, 98, 99, 103, 104, 105, 109, 110, 111, 117, 118, 127, 128, 129, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165 }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 14, 16, 19, 21, 22, 24, 26, 33, 35, 37, 49, 50, 56, 57, 63, 64, 70, 71, 77, 83, 89, 95, 96, 102, 108, 114, 119, 120, 121, 122, 123, 124, 125, 126, 132, 133, 134, 135, 136, 138, 139, 140, 141, 166

B grade: { }

C grade: { }

F grade: { 6, 13, 15, 17, 18, 20, 23, 25, 27, 28, 29, 30, 31, 32, 34, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 97, 98, 99, 100, 101, 103, 104, 105, 106, 107, 109, 110, 111, 112, 113, 115, 116, 117, 118, 127, 128, 129, 130, 131, 137, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 19, 21, 22, 23, 24, 25, 26, 32, 33, 34, 35, 36, 37, 49, 50, 56, 57, 63, 64, 70, 71, 115, 116, 119, 120, 121, 126, 132, 133, 134, 135, 136, 139, 140, 141, 166 }

B grade: { 7, 138 }

C grade: { }

F grade: { 6, 17, 18, 20, 27, 28, 29, 30, 31, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 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, 117, 118, 122, 123, 124, 125, 127, 128, 129, 130, 131, 137, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 12, 13, 14, 15, 16, 22, 23, 24, 25, 26, 32, 33, 34, 35, 36, 37, 49, 50, 56, 57, 63, 64, 70, 71, 77, 83, 95, 96, 102, 108, 115, 116, 119, 120, 121, 123, 124, 125, 126, 132, 133, 134, 135, 136, 166 }

B grade: { }

C grade: { }

F grade: { 6, 7, 8, 9, 10, 11, 17, 18, 19, 20, 21, 27, 28, 29, 30, 31, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 97, 98, 99, 100, 101, 103, 104, 105, 106, 107, 109, 110, 111, 112, 113, 114, 117, 118, 122, 127, 128, 129, 130, 131, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165 }

2.1.7 Giac

A grade: { 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 14, 16, 21, 22, 24, 26, 33, 35, 37, 49, 50, 56, 57, 63, 64, 70, 71, 77, 83, 89, 95, 96, 102, 108, 114, 115, 116, 119, 120, 121, 122, 123, 124, 125, 126, 132, 133, 134, 135, 136, 166 }

B grade: { 19 }

C grade: { }

F grade: { 6, 13, 15, 17, 18, 20, 23, 25, 27, 28, 29, 30, 31, 32, 34, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 97, 98, 99, 100, 101, 103, 104, 105, 106, 107, 109, 110, 111, 112, 113, 117, 118, 127, 128, 129, 130, 131, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165 }

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 93 93 55 52 92 135 76 90
normalized size 1 1. 0.59 0.56 0.99 1.45 0.82 0.97
time (sec) N/A 0.037 0.033 0.014 1.092 2.505 2.482 1.23
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 77 77 71 99 116 131 68 109
normalized size 1 1. 0.92 1.29 1.51 1.7 0.88 1.42
time (sec) N/A 0.03 0.062 0.017 1.144 2.274 1.346 1.353
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 65 65 46 43 65 113 54 70
normalized size 1 1. 0.71 0.66 1. 1.74 0.83 1.08
time (sec) N/A 0.023 0.023 0.009 1.111 2.402 0.619 1.244
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 49 49 61 77 88 109 44 95
normalized size 1 1. 1.24 1.57 1.8 2.22 0.9 1.94
time (sec) N/A 0.015 0.025 0.011 1.132 2.346 0.265 1.277
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 30 30 30 29 34 78 26 47
normalized size 1 1. 1. 0.97 1.13 2.6 0.87 1.57
time (sec) N/A 0.006 0.016 0.001 1.159 2.363 0.208 1.373
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 43 43 42 66 0 0 0 0
normalized size 1 1. 0.98 1.53 0. 0. 0. 0.
time (sec) N/A 0.059 0.034 0.034 0. 0. 0. 0.
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 32 32 57 51 32 158 0 49
normalized size 1 1. 1.78 1.59 1. 4.94 0. 1.53
time (sec) N/A 0.017 0.025 0.013 1.781 2.403 0. 1.396
Problem 8 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 38 38 35 40 36 86 0 68
normalized size 1 1. 0.92 1.05 0.95 2.26 0. 1.79
time (sec) N/A 0.013 0.007 0.012 1.728 2.419 0. 1.209
Problem 9 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 65 65 78 73 61 215 0 78
normalized size 1 1. 1.2 1.12 0.94 3.31 0. 1.2
time (sec) N/A 0.027 0.075 0.013 1.827 2.451 0. 1.335
Problem 10 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 66 66 45 50 65 109 0 104
normalized size 1 1. 0.68 0.76 0.98 1.65 0. 1.58
time (sec) N/A 0.024 0.023 0.012 1.772 2.466 0. 1.345
Problem 11 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 93 93 104 95 88 238 0 103
normalized size 1 1. 1.12 1.02 0.95 2.56 0. 1.11
time (sec) N/A 0.041 0.044 0.016 1.766 2.519 0. 1.349
Problem 12 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 132 132 80 168 134 234 122 153
normalized size 1 1. 0.61 1.27 1.02 1.77 0.92 1.16
time (sec) N/A 0.49 0.107 0.04 1.282 2.53 4.914 1.332
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 106 106 77 126 0 205 99 0
normalized size 1 1. 0.73 1.19 0. 1.93 0.93 0.
time (sec) N/A 0.44 0.072 0.035 0. 2.367 2.876 0.
Problem 14 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 90 90 64 100 95 188 85 120
normalized size 1 1. 0.71 1.11 1.06 2.09 0.94 1.33
time (sec) N/A 0.311 0.095 0.031 1.181 2.257 1.295 1.323
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 64 64 58 58 0 166 60 0
normalized size 1 1. 0.91 0.91 0. 2.59 0.94 0.
time (sec) N/A 0.251 0.05 0.029 0. 2.193 0.639 0.
Problem 16 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 39 43 134 39 84
normalized size 1 1. 1. 1. 1.1 3.44 1. 2.15
time (sec) N/A 0.127 0.02 0.026 1.137 2.325 0.244 1.353
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 62 62 63 98 0 0 0 0
normalized size 1 1. 1.02 1.58 0. 0. 0. 0.
time (sec) N/A 0.093 0.028 0.029 0. 0. 0. 0.
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 60 60 92 137 0 0 0 0
normalized size 1 1. 1.53 2.28 0. 0. 0. 0.
time (sec) N/A 0.209 0.251 0.061 0. 0. 0. 0.
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 48 48 48 73 53 158 0 149
normalized size 1 1. 1. 1.52 1.1 3.29 0. 3.1
time (sec) N/A 0.192 0.019 0.063 1.733 2.515 0. 1.425
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 114 114 144 177 0 0 0 0
normalized size 1 1. 1.26 1.55 0. 0. 0. 0.
time (sec) N/A 0.392 0.243 0.106 0. 0. 0. 0.
Problem 21 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 95 95 69 109 97 194 0 198
normalized size 1 1. 0.73 1.15 1.02 2.04 0. 2.08
time (sec) N/A 0.365 0.078 0.107 1.555 2.545 0. 1.626
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 231 231 130 246 223 359 206 243
normalized size 1 1. 0.56 1.06 0.97 1.55 0.89 1.05
time (sec) N/A 0.771 0.117 0.048 1.198 2.419 8.787 1.607
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 183 183 143 184 0 327 170 0
normalized size 1 1. 0.78 1.01 0. 1.79 0.93 0.
time (sec) N/A 0.666 0.131 0.042 0. 2.528 5.034 0.
Problem 24 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 155 155 103 150 157 281 138 190
normalized size 1 1. 0.66 0.97 1.01 1.81 0.89 1.23
time (sec) N/A 0.474 0.093 0.037 1.252 2.509 2.599 1.583
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 107 107 113 88 0 261 102 0
normalized size 1 1. 1.06 0.82 0. 2.44 0.95 0.
time (sec) N/A 0.381 0.082 0.03 0. 2.45 1.258 0.
Problem 26 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 68 68 68 61 77 205 63 132
normalized size 1 1. 1. 0.9 1.13 3.01 0.93 1.94
time (sec) N/A 0.183 0.025 0.031 1.21 2.476 0.57 1.362
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 87 87 82 132 0 0 0 0
normalized size 1 1. 0.94 1.52 0. 0. 0. 0.
time (sec) N/A 0.105 0.05 0.037 0. 0. 0. 0.
Problem 28 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 104 104 128 0 0 0 0 0
normalized size 1 1. 1.23 0. 0. 0. 0. 0.
time (sec) N/A 0.31 0.168 0.099 0. 0. 0. 0.
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 98 98 92 113 0 0 0 0
normalized size 1 1. 0.94 1.15 0. 0. 0. 0.
time (sec) N/A 0.317 0.794 0.082 0. 0. 0. 0.
Problem 30 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 183 183 201 0 0 0 0 0
normalized size 1 1. 1.1 0. 0. 0. 0. 0.
time (sec) N/A 0.577 0.546 0.169 0. 0. 0. 0.
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 174 174 220 180 0 0 0 0
normalized size 1 1. 1.26 1.03 0. 0. 0. 0.
time (sec) N/A 0.578 0.598 0.122 0. 0. 0. 0.
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 306 306 175 344 0 497 275 0
normalized size 1 1. 0.57 1.12 0. 1.62 0.9 0.
time (sec) N/A 2.193 0.153 0.052 0. 2.398 25.086 0.
Problem 33 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 274 274 158 300 271 466 248 293
normalized size 1 1. 0.58 1.09 0.99 1.7 0.91 1.07
time (sec) N/A 1.628 0.127 0.05 1.231 2.615 14.652 1.85
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 214 214 143 224 0 402 197 0
normalized size 1 1. 0.67 1.05 0. 1.88 0.92 0.
time (sec) N/A 1.314 0.109 0.045 0. 2.477 8.668 0.
Problem 35 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 182 182 122 180 193 358 165 230
normalized size 1 1. 0.67 0.99 1.06 1.97 0.91 1.26
time (sec) N/A 0.881 0.112 0.04 1.205 2.358 5.032 1.779
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 120 120 104 104 0 316 110 0
normalized size 1 1. 0.87 0.87 0. 2.63 0.92 0.
time (sec) N/A 0.603 0.07 0.033 0. 2.606 2.612 0.
Problem 37 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 77 77 77 71 99 262 70 169
normalized size 1 1. 1. 0.92 1.29 3.4 0.91 2.19
time (sec) N/A 0.298 0.028 0.033 1.157 2.312 1.181 1.467
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 103 103 103 165 0 0 0 0
normalized size 1 1. 1. 1.6 0. 0. 0. 0.
time (sec) N/A 0.12 0.029 0.037 0. 0. 0. 0.
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 150 150 478 0 0 0 0 0
normalized size 1 1. 3.19 0. 0. 0. 0. 0.
time (sec) N/A 0.335 0.648 0.086 0. 0. 0. 0.
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 115 115 112 149 0 0 0 0
normalized size 1 1. 0.97 1.3 0. 0. 0. 0.
time (sec) N/A 0.358 1.073 0.071 0. 0. 0. 0.
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 268 268 595 0 0 0 0 0
normalized size 1 1. 2.22 0. 0. 0. 0. 0.
time (sec) N/A 0.802 3.075 0.181 0. 0. 0. 0.
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 40 40 0 0 0 0
normalized size 1 1. 0.73 0.73 0. 0. 0. 0.
time (sec) N/A 0.096 0.095 0.039 0. 0. 0. 0.
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 43 43 33 33 0 0 0 0
normalized size 1 1. 0.77 0.77 0. 0. 0. 0.
time (sec) N/A 0.084 0.083 0.033 0. 0. 0. 0.
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 41 41 31 31 0 0 0 0
normalized size 1 1. 0.76 0.76 0. 0. 0. 0.
time (sec) N/A 0.08 0.071 0.026 0. 0. 0. 0.
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 24 24 0 0 0 0
normalized size 1 1. 0.83 0.83 0. 0. 0. 0.
time (sec) N/A 0.066 0.061 0.027 0. 0. 0. 0.
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 20 22 0 0 0 0
normalized size 1 1. 0.74 0.81 0. 0. 0. 0.
time (sec) N/A 0.064 0.052 0.03 0. 0. 0. 0.
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 14 14 14 13 0 0 0 0
normalized size 1 1. 1. 0.93 0. 0. 0. 0.
time (sec) N/A 0.037 0.022 0.024 0. 0. 0. 0.
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 9 9 9 10 0 0 0 0
normalized size 1 1. 1. 1.11 0. 0. 0. 0.
time (sec) N/A 0.017 0.022 0.021 0. 0. 0. 0.
Problem 49 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 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.014 0.194 0.065 0. 0. 0. 0.
Problem 50 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 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.014 0.421 0.089 0. 0. 0. 0.
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 73 73 101 83 0 0 0 0
normalized size 1 1. 1.38 1.14 0. 0. 0. 0.
time (sec) N/A 0.064 0.209 0.037 0. 0. 0. 0.
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 61 61 58 54 0 0 0 0
normalized size 1 1. 0.95 0.89 0. 0. 0. 0.
time (sec) N/A 0.05 0.231 0.033 0. 0. 0. 0.
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 59 59 58 59 0 0 0 0
normalized size 1 1. 0.98 1. 0. 0. 0. 0.
time (sec) N/A 0.047 0.226 0.03 0. 0. 0. 0.
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 42 42 44 28 0 0 0 0
normalized size 1 1. 1.05 0.67 0. 0. 0. 0.
time (sec) N/A 0.025 0.241 0.026 0. 0. 0. 0.
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 39 39 60 33 0 0 0 0
normalized size 1 1. 1.54 0.85 0. 0. 0. 0.
time (sec) N/A 0.184 0.1 0.026 0. 0. 0. 0.
Problem 56 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 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 4.35 0.05 0. 0. 0. 0.
Problem 57 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 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.014 7.917 0.091 0. 0. 0. 0.
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 102 102 107 123 0 0 0 0
normalized size 1 1. 1.05 1.21 0. 0. 0. 0.
time (sec) N/A 0.645 0.135 0.042 0. 0. 0. 0.
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 87 87 75 82 0 0 0 0
normalized size 1 1. 0.86 0.94 0. 0. 0. 0.
time (sec) N/A 0.598 0.166 0.036 0. 0. 0. 0.
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 85 85 69 84 0 0 0 0
normalized size 1 1. 0.81 0.99 0. 0. 0. 0.
time (sec) N/A 0.504 0.146 0.029 0. 0. 0. 0.
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 68 68 67 43 0 0 0 0
normalized size 1 1. 0.99 0.63 0. 0. 0. 0.
time (sec) N/A 0.393 0.049 0.026 0. 0. 0. 0.
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 55 45 0 0 0 0
normalized size 1 1. 1. 0.82 0. 0. 0. 0.
time (sec) N/A 0.188 0.042 0.027 0. 0. 0. 0.
Problem 63 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 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.014 0.659 0.065 0. 0. 0. 0.
Problem 64 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 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.015 2.194 0.089 0. 0. 0. 0.
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 170 170 126 175 0 0 0 0
normalized size 1 1. 0.74 1.03 0. 0. 0. 0.
time (sec) N/A 0.617 0.609 0.043 0. 0. 0. 0.
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 155 155 188 114 0 0 0 0
normalized size 1 1. 1.21 0.74 0. 0. 0. 0.
time (sec) N/A 0.588 0.373 0.043 0. 0. 0. 0.
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 153 153 183 121 0 0 0 0
normalized size 1 1. 1.2 0.79 0. 0. 0. 0.
time (sec) N/A 0.676 0.365 0.035 0. 0. 0. 0.
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 105 105 131 60 0 0 0 0
normalized size 1 1. 1.25 0.57 0. 0. 0. 0.
time (sec) N/A 0.396 0.294 0.026 0. 0. 0. 0.
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 86 86 116 67 0 0 0 0
normalized size 1 1. 1.35 0.78 0. 0. 0. 0.
time (sec) N/A 0.378 0.179 0.027 0. 0. 0. 0.
Problem 70 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 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.014 9.826 0.069 0. 0. 0. 0.
Problem 71 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 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.015 11.941 0.093 0. 0. 0. 0.
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 182 182 162 0 0 0 0 0
normalized size 1 1. 0.89 0. 0. 0. 0. 0.
time (sec) N/A 0.475 0.095 0.183 0. 0. 0. 0.
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 139 139 101 0 0 0 0 0
normalized size 1 1. 0.73 0. 0. 0. 0. 0.
time (sec) N/A 0.403 0.084 0.103 0. 0. 0. 0.
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 120 120 100 0 0 0 0 0
normalized size 1 1. 0.83 0. 0. 0. 0. 0.
time (sec) N/A 0.397 0.083 0.089 0. 0. 0. 0.
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 93 93 65 73 0 0 0 0
normalized size 1 1. 0.7 0.78 0. 0. 0. 0.
time (sec) N/A 0.35 0.075 0.089 0. 0. 0. 0.
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 53 53 45 41 0 0 0 0
normalized size 1 1. 0.85 0.77 0. 0. 0. 0.
time (sec) N/A 0.219 0.036 0.074 0. 0. 0. 0.
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 0.283 0.07 0. 0. 0. 0.
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 345 345 152 0 0 0 0 0
normalized size 1 1. 0.44 0. 0. 0. 0. 0.
time (sec) N/A 1.115 0.112 0.187 0. 0. 0. 0.
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 209 209 101 0 0 0 0 0
normalized size 1 1. 0.48 0. 0. 0. 0. 0.
time (sec) N/A 0.874 0.085 0.097 0. 0. 0. 0.
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 189 189 100 0 0 0 0 0
normalized size 1 1. 0.53 0. 0. 0. 0. 0.
time (sec) N/A 0.64 0.087 0.091 0. 0. 0. 0.
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 127 127 84 105 0 0 0 0
normalized size 1 1. 0.66 0.83 0. 0. 0. 0.
time (sec) N/A 0.438 0.125 0.112 0. 0. 0. 0.
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 86 86 45 68 0 0 0 0
normalized size 1 1. 0.52 0.79 0. 0. 0. 0.
time (sec) N/A 0.22 0.029 0.095 0. 0. 0. 0.
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 0.289 0.069 0. 0. 0. 0.
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 394 394 162 0 0 0 0 0
normalized size 1 1. 0.41 0. 0. 0. 0. 0.
time (sec) N/A 1.822 0.097 0.191 0. 0. 0. 0.
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 257 257 101 0 0 0 0 0
normalized size 1 1. 0.39 0. 0. 0. 0. 0.
time (sec) N/A 1.375 0.083 0.109 0. 0. 0. 0.
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 220 220 100 0 0 0 0 0
normalized size 1 1. 0.45 0. 0. 0. 0. 0.
time (sec) N/A 1.055 0.082 0.088 0. 0. 0. 0.
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 157 157 92 139 0 0 0 0
normalized size 1 1. 0.59 0.89 0. 0. 0. 0.
time (sec) N/A 0.709 0.165 0.115 0. 0. 0. 0.
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 99 99 45 81 0 0 0 0
normalized size 1 1. 0.45 0.82 0. 0. 0. 0.
time (sec) N/A 0.395 0.035 0.098 0. 0. 0. 0.
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.014 0.294 0.071 0. 0. 0. 0.
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 163 163 150 0 0 0 0 0
normalized size 1 1. 0.92 0. 0. 0. 0. 0.
time (sec) N/A 0.199 0.11 0.203 0. 0. 0. 0.
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 109 109 101 0 0 0 0 0
normalized size 1 1. 0.93 0. 0. 0. 0. 0.
time (sec) N/A 0.146 0.086 0.113 0. 0. 0. 0.
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 105 105 100 0 0 0 0 0
normalized size 1 1. 0.95 0. 0. 0. 0. 0.
time (sec) N/A 0.14 0.083 0.101 0. 0. 0. 0.
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 63 63 49 37 0 0 0 0
normalized size 1 1. 0.78 0.59 0. 0. 0. 0.
time (sec) N/A 0.077 0.036 0.053 0. 0. 0. 0.
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 43 43 45 26 0 0 0 0
normalized size 1 1. 1.05 0.6 0. 0. 0. 0.
time (sec) N/A 0.047 0.028 0.043 0. 0. 0. 0.
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.014 0.228 0.071 0. 0. 0. 0.
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.014 0.617 0.102 0. 0. 0. 0.
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 193 193 201 0 0 0 0 0
normalized size 1 1. 1.04 0. 0. 0. 0. 0.
time (sec) N/A 0.184 0.292 0.183 0. 0. 0. 0.
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 143 143 124 0 0 0 0 0
normalized size 1 1. 0.87 0. 0. 0. 0. 0.
time (sec) N/A 0.128 0.159 0.092 0. 0. 0. 0.
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 135 135 139 0 0 0 0 0
normalized size 1 1. 1.03 0. 0. 0. 0. 0.
time (sec) N/A 0.124 0.166 0.086 0. 0. 0. 0.
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 89 89 63 83 0 0 0 0
normalized size 1 1. 0.71 0.93 0. 0. 0. 0.
time (sec) N/A 0.066 0.1 0.111 0. 0. 0. 0.
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 68 68 76 66 0 0 0 0
normalized size 1 1. 1.12 0.97 0. 0. 0. 0.
time (sec) N/A 0.218 0.06 0.095 0. 0. 0. 0.
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.014 0.341 0.066 0. 0. 0. 0.
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 228 228 278 0 0 0 0 0
normalized size 1 1. 1.22 0. 0. 0. 0. 0.
time (sec) N/A 0.864 1.542 0.174 0. 0. 0. 0.
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 172 172 175 0 0 0 0 0
normalized size 1 1. 1.02 0. 0. 0. 0. 0.
time (sec) N/A 0.755 0.759 0.102 0. 0. 0. 0.
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 166 166 194 0 0 0 0 0
normalized size 1 1. 1.17 0. 0. 0. 0. 0.
time (sec) N/A 0.627 0.66 0.086 0. 0. 0. 0.
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 123 123 83 122 0 0 0 0
normalized size 1 1. 0.67 0.99 0. 0. 0. 0.
time (sec) N/A 0.483 0.255 0.113 0. 0. 0. 0.
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 89 89 121 84 0 0 0 0
normalized size 1 1. 1.36 0.94 0. 0. 0. 0.
time (sec) N/A 0.234 0.151 0.106 0. 0. 0. 0.
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.015 0.343 0.067 0. 0. 0. 0.
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 300 300 374 0 0 0 0 0
normalized size 1 1. 1.25 0. 0. 0. 0. 0.
time (sec) N/A 0.932 1.988 0.172 0. 0. 0. 0.
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 244 244 291 0 0 0 0 0
normalized size 1 1. 1.19 0. 0. 0. 0. 0.
time (sec) N/A 0.757 0.556 0.098 0. 0. 0. 0.
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 237 237 286 0 0 0 0 0
normalized size 1 1. 1.21 0. 0. 0. 0. 0.
time (sec) N/A 0.848 0.796 0.086 0. 0. 0. 0.
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 157 157 91 153 0 0 0 0
normalized size 1 1. 0.58 0.97 0. 0. 0. 0.
time (sec) N/A 0.495 0.286 0.118 0. 0. 0. 0.
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 122 122 147 111 0 0 0 0
normalized size 1 1. 1.2 0.91 0. 0. 0. 0.
time (sec) N/A 0.444 0.181 0.101 0. 0. 0. 0.
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.017 0.345 0.066 0. 0. 0. 0.
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 58 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.277 1.809 0.646 0. 0. 0. 0.
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 58 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.298 1.735 0.569 0. 0. 0. 0.
Problem 117 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 154 167 143 0 0 0 0 0
normalized size 1 1.08 0.93 0. 0. 0. 0. 0.
time (sec) N/A 0.238 0.355 0.693 0. 0. 0. 0.
Problem 118 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 91 91 82 0 0 0 0 0
normalized size 1 1. 0.9 0. 0. 0. 0. 0.
time (sec) N/A 0.055 0.095 0.676 0. 0. 0. 0.
Problem 119 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 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.023 1.301 0.485 0. 0. 0. 0.
Problem 120 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 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.023 1.319 0.576 0. 0. 0. 0.
Problem 121 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 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.02 1.326 0.457 0. 0. 0. 0.
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.019 1.871 0.07 0. 0. 0. 0.
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.016 2.169 0.067 0. 0. 0. 0.
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.016 2.011 0.071 0. 0. 0. 0.
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.016 1.932 0.069 0. 0. 0. 0.
Problem 126 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 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.019 1.396 0.082 0. 0. 0. 0.
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 173 173 144 0 0 0 0 0
normalized size 1 1. 0.83 0. 0. 0. 0. 0.
time (sec) N/A 0.247 0.194 0.155 0. 0. 0. 0.
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 117 117 97 0 0 0 0 0
normalized size 1 1. 0.83 0. 0. 0. 0. 0.
time (sec) N/A 0.191 0.095 0.08 0. 0. 0. 0.
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 113 113 95 0 0 0 0 0
normalized size 1 1. 0.84 0. 0. 0. 0. 0.
time (sec) N/A 0.182 0.111 0.092 0. 0. 0. 0.
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 59 59 58 38 0 0 0 0
normalized size 1 1. 0.98 0.64 0. 0. 0. 0.
time (sec) N/A 0.087 0.045 0.031 0. 0. 0. 0.
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 43 40 0 0 0 0
normalized size 1 1. 0.88 0.82 0. 0. 0. 0.
time (sec) N/A 0.049 0.024 0.041 0. 0. 0. 0.
Problem 132 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 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.017 0.327 0.053 0. 0. 0. 0.
Problem 133 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 84 84 105 109 130 161 87 123
normalized size 1 1. 1.25 1.3 1.55 1.92 1.04 1.46
time (sec) N/A 0.039 0.037 0.012 1.17 2.459 1.459 1.469
Problem 134 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 71 71 54 55 78 140 71 84
normalized size 1 1. 0.76 0.77 1.1 1.97 1. 1.18
time (sec) N/A 0.03 0.044 0.004 1.172 2.429 0.677 1.453
Problem 135 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 55 55 76 86 101 132 61 108
normalized size 1 1. 1.38 1.56 1.84 2.4 1.11 1.96
time (sec) N/A 0.02 0.035 0.004 1.15 2.5 0.373 1.433
Problem 136 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 35 35 35 34 41 95 31 55
normalized size 1 1. 1. 0.97 1.17 2.71 0.89 1.57
time (sec) N/A 0.014 0.021 0.003 1.106 2.493 0.167 1.296
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A NO NO TBD TBD TBD TBD TBD
size 55 55 48 75 0 0 0 0
normalized size 1 1. 0.87 1.36 0. 0. 0. 0.
time (sec) N/A 0.077 0.04 0.03 0. 0. 0. 0.
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 37 37 65 59 43 171 0 0
normalized size 1 1. 1.76 1.59 1.16 4.62 0. 0.
time (sec) N/A 0.024 0.072 0.004 1.676 2.596 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 43 43 48 52 49 108 0 0
normalized size 1 1. 1.12 1.21 1.14 2.51 0. 0.
time (sec) N/A 0.02 0.018 0.004 1.74 2.319 0. 0.
Problem 140 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 71 71 101 82 73 234 0 0
normalized size 1 1. 1.42 1.15 1.03 3.3 0. 0.
time (sec) N/A 0.033 0.101 0.006 1.7 2.642 0. 0.
Problem 141 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 72 72 50 62 77 139 0 0
normalized size 1 1. 0.69 0.86 1.07 1.93 0. 0.
time (sec) N/A 0.032 0.029 0.004 1.645 2.512 0. 0.
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 213 213 214 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.788 0.481 0.109 0. 0. 0. 0.
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 145 145 136 0 0 0 0 0
normalized size 1 1. 0.94 0. 0. 0. 0. 0.
time (sec) N/A 0.649 0.38 0.108 0. 0. 0. 0.
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 102 102 100 0 0 0 0 0
normalized size 1 1. 0.98 0. 0. 0. 0. 0.
time (sec) N/A 0.412 0.222 0.092 0. 0. 0. 0.
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 292 292 540 0 0 0 0 0
normalized size 1 1. 1.85 0. 0. 0. 0. 0.
time (sec) N/A 1.251 2.255 0.099 0. 0. 0. 0.
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 184 184 165 0 0 0 0 0
normalized size 1 1. 0.9 0. 0. 0. 0. 0.
time (sec) N/A 0.816 1.008 0.106 0. 0. 0. 0.
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 140 140 269 0 0 0 0 0
normalized size 1 1. 1.92 0. 0. 0. 0. 0.
time (sec) N/A 0.428 0.625 0.094 0. 0. 0. 0.
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 337 337 924 0 0 0 0 0
normalized size 1 1. 2.74 0. 0. 0. 0. 0.
time (sec) N/A 2.09 10.694 0.102 0. 0. 0. 0.
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 228 228 207 0 0 0 0 0
normalized size 1 1. 0.91 0. 0. 0. 0. 0.
time (sec) N/A 1.328 1.88 0.124 0. 0. 0. 0.
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 160 160 452 0 0 0 0 0
normalized size 1 1. 2.82 0. 0. 0. 0. 0.
time (sec) N/A 0.751 2.351 0.095 0. 0. 0. 0.
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 194 194 195 0 0 0 0 0
normalized size 1 1. 1.01 0. 0. 0. 0. 0.
time (sec) N/A 0.36 0.346 0.108 0. 0. 0. 0.
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 107 107 104 0 0 0 0 0
normalized size 1 1. 0.97 0. 0. 0. 0. 0.
time (sec) N/A 0.185 0.22 0.115 0. 0. 0. 0.
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 88 88 100 0 0 0 0 0
normalized size 1 1. 1.14 0. 0. 0. 0. 0.
time (sec) N/A 0.105 0.1 0.094 0. 0. 0. 0.
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 231 231 247 0 0 0 0 0
normalized size 1 1. 1.07 0. 0. 0. 0. 0.
time (sec) N/A 0.31 0.658 0.105 0. 0. 0. 0.
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 140 140 135 0 0 0 0 0
normalized size 1 1. 0.96 0. 0. 0. 0. 0.
time (sec) N/A 0.155 1.202 0.105 0. 0. 0. 0.
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 120 120 132 0 0 0 0 0
normalized size 1 1. 1.1 0. 0. 0. 0. 0.
time (sec) N/A 0.41 0.237 0.099 0. 0. 0. 0.
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 276 276 340 0 0 0 0 0
normalized size 1 1. 1.23 0. 0. 0. 0. 0.
time (sec) N/A 1.33 2.04 0.095 0. 0. 0. 0.
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 188 188 157 0 0 0 0 0
normalized size 1 1. 0.84 0. 0. 0. 0. 0.
time (sec) N/A 0.893 1.517 0.118 0. 0. 0. 0.
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 148 148 192 0 0 0 0 0
normalized size 1 1. 1.3 0. 0. 0. 0. 0.
time (sec) N/A 0.456 1.015 0.094 0. 0. 0. 0.
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 361 361 394 0 0 0 0 0
normalized size 1 1. 1.09 0. 0. 0. 0. 0.
time (sec) N/A 1.627 2.461 0.099 0. 0. 0. 0.
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 229 229 175 0 0 0 0 0
normalized size 1 1. 0.76 0. 0. 0. 0. 0.
time (sec) N/A 0.87 1.61 0.111 0. 0. 0. 0.
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 188 188 214 0 0 0 0 0
normalized size 1 1. 1.14 0. 0. 0. 0. 0.
time (sec) N/A 0.772 0.698 0.109 0. 0. 0. 0.
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 128 141 118 0 0 0 0 0
normalized size 1 1.1 0.92 0. 0. 0. 0. 0.
time (sec) N/A 0.285 0.397 0.29 0. 0. 0. 0.
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 181 194 164 0 0 0 0 0
normalized size 1 1.07 0.91 0. 0. 0. 0. 0.
time (sec) N/A 0.31 0.246 2.246 0. 0. 0. 0.
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 106 106 87 0 0 0 0 0
normalized size 1 1. 0.82 0. 0. 0. 0. 0.
time (sec) N/A 0.053 0.137 2.023 0. 0. 0. 0.
Problem 166 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 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.028 0.457 0.811 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 [41] had the largest ratio of [ 1. ]

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 6 4 1. 8 0.5
2 A 5 5 1. 8 0.625
3 A 4 4 1. 8 0.5
4 A 3 3 1. 6 0.5
5 A 2 2 1. 4 0.5
6 A 5 5 1. 8 0.625
7 A 3 3 1. 8 0.375
8 A 2 2 1. 8 0.25
9 A 5 5 1. 8 0.625
10 A 4 4 1. 8 0.5
11 A 7 5 1. 8 0.625
12 A 7 5 1. 10 0.5
13 A 6 4 1. 10 0.4
14 A 5 5 1. 10 0.5
15 A 4 4 1. 8 0.5
16 A 3 3 1. 6 0.5
17 A 6 6 1. 10 0.6
18 A 7 5 1. 10 0.5
19 A 3 3 1. 10 0.3
20 A 9 7 1. 10 0.7
21 A 5 5 1. 10 0.5
22 A 16 7 1. 10 0.7
23 A 12 7 1. 10 0.7
24 A 9 7 1. 10 0.7
25 A 6 5 1. 8 0.625
26 A 4 3 1. 6 0.5
27 A 7 7 1. 10 0.7
28 A 9 6 1. 10 0.6
29 A 7 7 1. 10 0.7
30 A 13 9 1. 10 0.9
31 A 10 9 1. 10 0.9
32 A 23 4 1. 10 0.4
33 A 19 6 1. 10 0.6
34 A 14 4 1. 10 0.4
35 A 11 6 1. 10 0.6
36 A 7 4 1. 8 0.5
37 A 5 3 1. 6 0.5
38 A 8 7 1. 10 0.7
39 A 11 7 1. 10 0.7
40 A 8 8 1. 10 0.8
41 A 19 10 1. 10 1.
42 A 7 3 1. 10 0.3
43 A 6 3 1. 10 0.3
44 A 6 3 1. 10 0.3
45 A 5 3 1. 10 0.3
46 A 5 3 1. 10 0.3
47 A 4 4 1. 8 0.5
48 A 2 2 1. 6 0.333
49 A 0 0 0. 0 0.
50 A 0 0 0. 0 0.
51 A 5 2 1. 10 0.2
52 A 4 2 1. 10 0.2
53 A 4 2 1. 10 0.2
54 A 2 2 1. 8 0.25
55 A 3 3 1. 6 0.5
56 A 0 0 0. 0 0.
57 A 0 0 0. 0 0.
58 A 14 5 1. 10 0.5
59 A 12 6 1. 10 0.6
60 A 10 6 1. 10 0.6
61 A 7 7 1. 8 0.875
62 A 4 4 1. 6 0.667
63 A 0 0 0. 0 0.
64 A 0 0 0. 0 0.
65 A 12 4 1. 10 0.4
66 A 9 4 1. 10 0.4
67 A 10 6 1. 10 0.6
68 A 5 5 1. 8 0.625
69 A 5 4 1. 6 0.667
70 A 0 0 0. 0 0.
71 A 0 0 0. 0 0.
72 A 19 7 1. 12 0.583
73 A 14 7 1. 12 0.583
74 A 14 7 1. 12 0.583
75 A 9 7 1. 10 0.7
76 A 7 6 1. 8 0.75
77 A 0 0 0. 0 0.
78 A 41 10 1. 12 0.833
79 A 25 10 1. 12 0.833
80 A 22 10 1. 12 0.833
81 A 11 10 1. 10 1.
82 A 8 7 1. 8 0.875
83 A 0 0 0. 0 0.
84 A 44 10 1. 12 0.833
85 A 27 9 1. 12 0.75
86 A 24 10 1. 12 0.833
87 A 12 9 1. 10 0.9
88 A 9 7 1. 8 0.875
89 A 0 0 0. 0 0.
90 A 18 6 1. 12 0.5
91 A 13 6 1. 12 0.5
92 A 13 6 1. 12 0.5
93 A 8 7 1. 10 0.7
94 A 6 5 1. 8 0.625
95 A 0 0 0. 0 0.
96 A 0 0 0. 0 0.
97 A 17 5 1. 12 0.417
98 A 12 5 1. 12 0.417
99 A 12 5 1. 12 0.417
100 A 6 5 1. 10 0.5
101 A 7 6 1. 8 0.75
102 A 0 0 0. 0 0.
103 A 34 8 1. 12 0.667
104 A 24 9 1. 12 0.75
105 A 22 9 1. 12 0.75
106 A 11 10 1. 10 1.
107 A 8 7 1. 8 0.875
108 A 0 0 0. 0 0.
109 A 32 7 1. 12 0.583
110 A 21 7 1. 12 0.583
111 A 22 9 1. 12 0.75
112 A 9 8 1. 10 0.8
113 A 9 7 1. 8 0.875
114 A 0 0 0. 0 0.
115 A 0 0 0. 0 0.
116 A 0 0 0. 0 0.
117 A 2 2 1.08 10 0.2
118 A 4 4 1. 8 0.5
119 A 0 0 0. 0 0.
120 A 0 0 0. 0 0.
121 A 0 0 0. 0 0.
122 A 0 0 0. 0 0.
123 A 0 0 0. 0 0.
124 A 0 0 0. 0 0.
125 A 0 0 0. 0 0.
126 A 0 0 0. 0 0.
127 A 12 4 1. 10 0.4
128 A 9 4 1. 10 0.4
129 A 9 4 1. 10 0.4
130 A 6 5 1. 8 0.625
131 A 4 3 1. 6 0.5
132 A 0 0 0. 0 0.
133 A 5 5 1. 12 0.417
134 A 4 4 1. 12 0.333
135 A 3 3 1. 10 0.3
136 A 3 2 1. 8 0.25
137 A 5 5 1. 12 0.417
138 A 3 3 1. 12 0.25
139 A 2 2 1. 12 0.167
140 A 5 5 1. 12 0.417
141 A 4 4 1. 12 0.333
142 A 14 7 1. 16 0.438
143 A 9 7 1. 14 0.5
144 A 7 6 1. 12 0.5
145 A 22 10 1. 16 0.625
146 A 11 10 1. 14 0.714
147 A 8 7 1. 12 0.583
148 A 24 10 1. 16 0.625
149 A 12 9 1. 14 0.643
150 A 9 7 1. 12 0.583
151 A 13 6 1. 16 0.375
152 A 8 7 1. 14 0.5
153 A 6 5 1. 12 0.417
154 A 12 5 1. 16 0.312
155 A 6 5 1. 14 0.357
156 A 7 6 1. 12 0.5
157 A 22 9 1. 16 0.562
158 A 11 10 1. 14 0.714
159 A 8 7 1. 12 0.583
160 A 22 9 1. 16 0.562
161 A 9 8 1. 14 0.571
162 A 9 7 1. 12 0.583
163 A 2 2 1.1 18 0.111
164 A 2 2 1.07 16 0.125
165 A 4 4 1. 14 0.286
166 A 0 0 0. 0 0.

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