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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, 167, 168, 169, 170, 171, 172, 173, 174 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 66, 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, 100, 101, 102, 103, 108, 109, 110, 112, 113, 114, 115, 116, 117, 118, 122, 123, 124, 125, 126, 127, 128, 131, 132, 133, 134, 135, 136, 137, 138, 141, 142, 143, 144, 145, 146, 147, 148, 151, 152, 153, 154, 155, 156, 157, 158, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174 }

B grade: { 96, 97, 104 }

C grade: { 63, 64, 65, 67, 68, 98, 105, 106, 111, 119, 120, 121, 129, 130, 139, 140, 149, 150, 159, 160 }

F grade: { 99, 107, 161, 162, 163}

2.1.3 Maple

A grade: { 1, 2, 3, 4, 6, 7, 8, 9, 11, 13, 14, 18, 19, 22, 26, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 58, 59, 60, 64, 65, 66, 69, 72, 73, 74, 75, 76, 77, 78, 79, 80, 83, 84, 85, 86, 87, 88, 89, 90, 114, 115, 116, 117, 118, 123, 124, 125, 126, 127, 128, 134, 135, 136, 137, 144, 145, 146, 147, 154, 155, 156, 157, 164, 165, 166, 167, 168, 169, 173, 174 }

B grade: { 5, 10, 12, 15, 16, 17, 20, 21, 23, 24, 25, 28, 29, 30, 31, 32, 56, 57, 61, 62, 63, 67, 68, 70, 71, 81, 82, 98, 105, 106 }

C grade: { 91, 92, 93, 94, 95, 96, 97, 99, 100, 101, 102, 103, 104, 107, 108, 109, 110 }

F grade: { 27, 53, 111, 112, 113, 119, 120, 121, 122, 129, 130, 131, 132, 133, 138, 139, 140, 141, 142, 143, 148, 149, 150, 151, 152, 153, 158, 159, 160, 161, 162, 163, 170, 171, 172 }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 20, 22, 29, 33, 34, 35, 39, 40, 41, 45, 46, 47, 54, 55, 56, 57, 58, 59, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 81, 82, 83, 84, 85, 86, 87, 88, 164, 165, 166, 167, 168, 169, 173, 174

B grade: { 31 }

C grade: { }

F grade: { 8, 16, 18, 19, 21, 23, 24, 25, 26, 27, 28, 30, 32, 36, 37, 38, 42, 43, 44, 48, 49, 50, 51, 52, 53, 60, 61, 62, 63, 64, 65, 66, 67, 68, 79, 80, 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, 170, 171, 172 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 29, 30, 31, 32, 33, 34, 35, 39, 40, 41, 45, 46, 47, 51, 52, 54, 55, 56, 57, 58, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 81, 82, 83, 84, 85, 86, 87, 88, 98, 111, 112, 113, 114, 115, 116, 117, 118, 121, 122, 123, 124, 125, 126, 127, 128, 131, 132, 133, 134, 135, 136, 137, 141, 142, 143, 144, 145, 146, 147, 154, 155, 156, 157, 164, 165, 166, 167, 168, 169, 173, 174 }

B grade: { 7, 17, 59, 61, 62, 105, 106, 151, 152, 153 }

C grade: { }

F grade: { 8, 16, 18, 19, 24, 25, 26, 27, 28, 36, 37, 38, 42, 43, 44, 48, 49, 50, 53, 60, 63, 64, 65, 66, 67, 68, 79, 80, 89, 90, 91, 92, 93, 94, 95, 96, 97, 99, 100, 101, 102, 103, 104, 107, 108, 109, 110, 119, 120, 129, 130, 138, 139, 140, 148, 149, 150, 158, 159, 160, 161, 162, 163, 170, 171, 172 }

2.1.6 Sympy

A grade: { 9, 33, 34, 35, 39, 40, 41, 45, 46, 47, 52, 54, 55, 114, 117, 118, 134, 137, 173 }

B grade: { }

C grade: { }

F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 36, 37, 38, 42, 43, 44, 48, 49, 50, 51, 53, 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, 115, 116, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 135, 136, 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, 167, 168, 169, 170, 171, 172, 174 }

2.1.7 Giac

A grade: { 7, 33, 34, 35, 39, 40, 41, 45, 46, 47, 51, 52, 54, 55, 59, 114, 115, 116, 117, 118, 123, 124, 125, 126, 127, 128, 134, 135, 136, 137, 144, 145, 146, 147, 154, 155, 156, 157, 164, 165, 166, 167, 168, 169, 173, 174 }

B grade: { }

C grade: { }

F grade: { 1, 2, 3, 4, 5, 6, 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, 36, 37, 38, 42, 43, 44, 48, 49, 50, 53, 56, 57, 58, 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, 119, 120, 121, 122, 129, 130, 131, 132, 133, 138, 139, 140, 141, 142, 143, 148, 149, 150, 151, 152, 153, 158, 159, 160, 161, 162, 163, 170, 171, 172 }

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 F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 114 114 107 177 219 275 0 0
normalized size 1 1. 0.94 1.55 1.92 2.41 0. 0.
time (sec) N/A 0.061 0.133 0.19 0.987 3.107 0. 0.
Problem 2 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 89 89 72 83 109 143 0 0
normalized size 1 1. 0.81 0.93 1.22 1.61 0. 0.
time (sec) N/A 0.041 0.081 0.16 0.987 2.78 0. 0.
Problem 3 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 89 89 97 150 177 248 0 0
normalized size 1 1. 1.09 1.69 1.99 2.79 0. 0.
time (sec) N/A 0.046 0.069 0.19 1.007 2.79 0. 0.
Problem 4 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 64 64 62 74 81 119 0 0
normalized size 1 1. 0.97 1.16 1.27 1.86 0. 0.
time (sec) N/A 0.027 0.1 0.162 0.977 2.665 0. 0.
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 64 64 85 123 132 219 0 0
normalized size 1 1. 1.33 1.92 2.06 3.42 0. 0.
time (sec) N/A 0.035 0.05 0.162 1.028 2.67 0. 0.
Problem 6 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 39 39 50 65 50 90 0 0
normalized size 1 1. 1.28 1.67 1.28 2.31 0. 0.
time (sec) N/A 0.012 0.021 0.161 0.995 2.686 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 59 38 72 154 0 62
normalized size 1 1. 1.84 1.19 2.25 4.81 0. 1.94
time (sec) N/A 0.02 0.063 0.155 0.962 2.641 0. 1.132
Problem 8 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 64 64 59 86 0 0 0 0
normalized size 1 1. 0.92 1.34 0. 0. 0. 0.
time (sec) N/A 0.084 0.016 0.281 0. 0. 0. 0.
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 40 62 45 62 36 0
normalized size 1 1. 1.29 2. 1.45 2. 1.16 0.
time (sec) N/A 0.02 0.028 0.164 0.982 2.441 2.787 0.
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 51 51 66 118 112 93 0 0
normalized size 1 1. 1.29 2.31 2.2 1.82 0. 0.
time (sec) N/A 0.033 0.033 0.163 1.445 2.852 0. 0.
Problem 11 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 60 60 59 75 78 97 0 0
normalized size 1 1. 0.98 1.25 1.3 1.62 0. 0.
time (sec) N/A 0.039 0.045 0.161 0.97 2.655 0. 0.
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 76 76 78 147 169 122 0 0
normalized size 1 1. 1.03 1.93 2.22 1.61 0. 0.
time (sec) N/A 0.045 0.059 0.16 1.497 2.685 0. 0.
Problem 13 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 82 82 69 83 103 123 0 0
normalized size 1 1. 0.84 1.01 1.26 1.5 0. 0.
time (sec) N/A 0.049 0.066 0.165 0.977 2.722 0. 0.
Problem 14 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 101 101 88 174 223 150 0 0
normalized size 1 1. 0.87 1.72 2.21 1.49 0. 0.
time (sec) N/A 0.059 0.071 0.16 1.464 2.489 0. 0.
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 107 107 124 208 220 339 0 0
normalized size 1 1. 1.16 1.94 2.06 3.17 0. 0.
time (sec) N/A 0.107 0.21 0.248 2.094 2.845 0. 0.
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 147 147 225 343 0 0 0 0
normalized size 1 1. 1.53 2.33 0. 0. 0. 0.
time (sec) N/A 0.123 1.197 0.392 0. 0. 0. 0.
Problem 17 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 56 56 90 134 117 266 0 0
normalized size 1 1. 1.61 2.39 2.09 4.75 0. 0.
time (sec) N/A 0.068 0.149 0.249 1.02 2.757 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 Yes TBD TBD TBD TBD TBD
size 92 92 163 212 0 0 0 0
normalized size 1 1. 1.77 2.3 0. 0. 0. 0.
time (sec) N/A 0.072 0.166 0.294 0. 0. 0. 0.
Problem 19 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 93 93 129 215 0 0 0 0
normalized size 1 1. 1.39 2.31 0. 0. 0. 0.
time (sec) N/A 0.119 0.12 0.358 0. 0. 0. 0.
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 50 50 75 117 105 140 0 0
normalized size 1 1. 1.5 2.34 2.1 2.8 0. 0.
time (sec) N/A 0.059 0.123 0.24 1.022 2.666 0. 0.
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 94 94 102 199 0 196 0 0
normalized size 1 1. 1.09 2.12 0. 2.09 0. 0.
time (sec) N/A 0.079 0.114 0.244 0. 2.389 0. 0.
Problem 22 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 102 102 108 154 221 224 0 0
normalized size 1 1. 1.06 1.51 2.17 2.2 0. 0.
time (sec) N/A 0.094 0.184 0.243 2.186 2.226 0. 0.
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 134 134 148 265 0 275 0 0
normalized size 1 1. 1.1 1.98 0. 2.05 0. 0.
time (sec) N/A 0.111 0.174 0.253 0. 2.211 0. 0.
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 207 207 288 447 0 0 0 0
normalized size 1 1. 1.39 2.16 0. 0. 0. 0.
time (sec) N/A 0.211 0.836 0.472 0. 0. 0. 0.
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 236 236 403 687 0 0 0 0
normalized size 1 1. 1.71 2.91 0. 0. 0. 0.
time (sec) N/A 0.192 1.322 0.52 0. 0. 0. 0.
Problem 26 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 126 126 184 285 0 0 0 0
normalized size 1 1. 1.46 2.26 0. 0. 0. 0.
time (sec) N/A 0.142 0.46 0.401 0. 0. 0. 0.
Problem 27 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 158 158 289 0 0 0 0 0
normalized size 1 1. 1.83 0. 0. 0. 0. 0.
time (sec) N/A 0.118 0.236 0.508 0. 0. 0. 0.
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 128 128 204 390 0 0 0 0
normalized size 1 1. 1.59 3.05 0. 0. 0. 0.
time (sec) N/A 0.141 0.17 0.431 0. 0. 0. 0.
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 80 80 141 198 197 238 0 0
normalized size 1 1. 1.76 2.48 2.46 2.98 0. 0.
time (sec) N/A 0.083 0.161 0.319 1.044 2.221 0. 0.
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 137 137 185 324 0 342 0 0
normalized size 1 1. 1.35 2.36 0. 2.5 0. 0.
time (sec) N/A 0.105 0.202 0.323 0. 2.219 0. 0.
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 170 170 204 299 787 401 0 0
normalized size 1 1. 1.2 1.76 4.63 2.36 0. 0.
time (sec) N/A 0.147 0.28 0.319 3.223 2.244 0. 0.
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 208 208 283 472 0 512 0 0
normalized size 1 1. 1.36 2.27 0. 2.46 0. 0.
time (sec) N/A 0.173 0.336 0.342 0. 2.344 0. 0.
Problem 33 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 0.014 2.556 0.973 0. 0. 0. 0.
Problem 34 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 0.006 2.187 0.447 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 16 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.025 0.269 0.74 0. 0. 0. 0.
Problem 36 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 46 46 43 47 0 0 0 0
normalized size 1 1. 0.93 1.02 0. 0. 0. 0.
time (sec) N/A 0.105 0.074 0.247 0. 0. 0. 0.
Problem 37 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 63 63 56 58 0 0 0 0
normalized size 1 1. 0.89 0.92 0. 0. 0. 0.
time (sec) N/A 0.136 0.072 0.24 0. 0. 0. 0.
Problem 38 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 117 117 91 102 0 0 0 0
normalized size 1 1. 0.78 0.87 0. 0. 0. 0.
time (sec) N/A 0.225 0.165 0.246 0. 0. 0. 0.
Problem 39 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 0.015 9.877 1.09 0. 0. 0. 0.
Problem 40 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 0.006 21.574 0.461 0. 0. 0. 0.
Problem 41 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 16 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.024 3.249 0.75 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 75 75 69 78 0 0 0 0
normalized size 1 1. 0.92 1.04 0. 0. 0. 0.
time (sec) N/A 0.129 0.256 0.241 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 84 84 80 77 0 0 0 0
normalized size 1 1. 0.95 0.92 0. 0. 0. 0.
time (sec) N/A 0.149 0.351 0.243 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 178 178 223 153 0 0 0 0
normalized size 1 1. 1.25 0.86 0. 0. 0. 0.
time (sec) N/A 0.267 0.446 0.247 0. 0. 0. 0.
Problem 45 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 0.014 3.353 1.274 0. 0. 0. 0.
Problem 46 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 0.006 11.262 0.545 0. 0. 0. 0.
Problem 47 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 16 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.025 1.688 0.799 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 103 103 88 154 0 0 0 0
normalized size 1 1. 0.85 1.5 0. 0. 0. 0.
time (sec) N/A 0.147 0.372 0.27 0. 0. 0. 0.
Problem 49 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 112 112 114 157 0 0 0 0
normalized size 1 1. 1.02 1.4 0. 0. 0. 0.
time (sec) N/A 0.18 0.401 0.248 0. 0. 0. 0.
Problem 50 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 228 228 169 307 0 0 0 0
normalized size 1 1. 0.74 1.35 0. 0. 0. 0.
time (sec) N/A 0.313 0.445 0.25 0. 0. 0. 0.
Problem 51 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 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.022 4.393 1.964 0. 0. 0. 0.
Problem 52 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 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.022 2.863 1.876 0. 0. 0. 0.
Problem 53 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 67 67 82 0 0 0 0 0
normalized size 1 1. 1.22 0. 0. 0. 0. 0.
time (sec) N/A 0.043 0.24 1.828 0. 0. 0. 0.
Problem 54 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 0.026 0.245 1.791 0. 0. 0. 0.
Problem 55 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 0.024 0.5 1.411 0. 0. 0. 0.
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 167 167 166 486 367 633 0 0
normalized size 1 1. 0.99 2.91 2.2 3.79 0. 0.
time (sec) N/A 0.401 0.279 0.135 0.976 4.563 0. 0.
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 124 124 124 362 270 462 0 0
normalized size 1 1. 1. 2.92 2.18 3.73 0. 0.
time (sec) N/A 0.266 0.177 0.129 1.01 3.902 0. 0.
Problem 58 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 84 84 114 141 126 302 0 0
normalized size 1 1. 1.36 1.68 1.5 3.6 0. 0.
time (sec) N/A 0.167 0.208 0.163 0.995 2.829 0. 0.
Problem 59 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 59 38 72 154 0 62
normalized size 1 1. 1.84 1.19 2.25 4.81 0. 1.94
time (sec) N/A 0.022 0.051 0.158 0.982 2.824 0. 1.118
Problem 60 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 247 247 333 456 0 0 0 0
normalized size 1 1. 1.35 1.85 0. 0. 0. 0.
time (sec) N/A 0.373 0.588 0.374 0. 0. 0. 0.
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 104 104 142 214 0 960 0 0
normalized size 1 1. 1.37 2.06 0. 9.23 0. 0.
time (sec) N/A 0.156 0.223 0.25 0. 3.283 0. 0.
Problem 62 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 172 172 247 1005 0 2223 0 0
normalized size 1 1. 1.44 5.84 0. 12.92 0. 0.
time (sec) N/A 0.292 0.48 0.28 0. 7.152 0. 0.
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-2) F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 372 372 333 812 0 0 0 0
normalized size 1 1. 0.9 2.18 0. 0. 0. 0.
time (sec) N/A 0.759 1.406 0.371 0. 0. 0. 0.
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 315 315 277 388 0 0 0 0
normalized size 1 1. 0.88 1.23 0. 0. 0. 0.
time (sec) N/A 0.463 6.018 0.255 0. 0. 0. 0.
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 212 212 212 254 0 0 0 0
normalized size 1 1. 1. 1.2 0. 0. 0. 0.
time (sec) N/A 0.304 2.658 0.257 0. 0. 0. 0.
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 119 119 124 217 0 0 0 0
normalized size 1 1. 1.04 1.82 0. 0. 0. 0.
time (sec) N/A 0.219 0.267 0.247 0. 0. 0. 0.
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 298 298 326 886 0 0 0 0
normalized size 1 1. 1.09 2.97 0. 0. 0. 0.
time (sec) N/A 0.406 6.175 0.267 0. 0. 0. 0.
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-2) F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 540 637 407 1640 0 0 0 0
normalized size 1 1.18 0.75 3.04 0. 0. 0. 0.
time (sec) N/A 0.711 8.302 0.276 0. 0. 0. 0.
Problem 69 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 206 206 141 338 400 459 0 0
normalized size 1 1. 0.68 1.64 1.94 2.23 0. 0.
time (sec) N/A 0.128 0.223 0.167 0.974 4.522 0. 0.
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 161 161 123 282 313 398 0 0
normalized size 1 1. 0.76 1.75 1.94 2.47 0. 0.
time (sec) N/A 0.103 0.166 0.179 0.98 3.411 0. 0.
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 109 109 150 195 208 327 0 0
normalized size 1 1. 1.38 1.79 1.91 3. 0. 0.
time (sec) N/A 0.051 0.264 0.171 0.965 2.541 0. 0.
Problem 72 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 87 87 104 137 120 286 0 0
normalized size 1 1. 1.2 1.57 1.38 3.29 0. 0.
time (sec) N/A 0.063 0.118 0.172 0.981 2.321 0. 0.
Problem 73 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 105 105 69 121 127 157 0 0
normalized size 1 1. 0.66 1.15 1.21 1.5 0. 0.
time (sec) N/A 0.075 0.079 0.171 0.983 1.999 0. 0.
Problem 74 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 152 152 94 140 185 217 0 0
normalized size 1 1. 0.62 0.92 1.22 1.43 0. 0.
time (sec) N/A 0.094 0.125 0.172 0.985 1.835 0. 0.
Problem 75 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 197 197 110 158 232 273 0 0
normalized size 1 1. 0.56 0.8 1.18 1.39 0. 0.
time (sec) N/A 0.117 0.144 0.184 0.991 2.058 0. 0.
Problem 76 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 196 196 118 152 250 304 0 0
normalized size 1 1. 0.6 0.78 1.28 1.55 0. 0.
time (sec) N/A 0.147 0.224 0.181 0.963 2.411 0. 0.
Problem 77 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 153 153 98 134 194 247 0 0
normalized size 1 1. 0.64 0.88 1.27 1.61 0. 0.
time (sec) N/A 0.122 0.253 0.171 0.968 2.182 0. 0.
Problem 78 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 138 138 79 115 135 192 0 0
normalized size 1 1. 0.57 0.83 0.98 1.39 0. 0.
time (sec) N/A 0.093 0.099 0.171 0.979 2.05 0. 0.
Problem 79 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 124 124 104 142 0 0 0 0
normalized size 1 1. 0.84 1.15 0. 0. 0. 0.
time (sec) N/A 0.284 0.122 0.531 0. 0. 0. 0.
Problem 80 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 137 137 136 145 0 0 0 0
normalized size 1 1. 0.99 1.06 0. 0. 0. 0.
time (sec) N/A 0.291 0.442 0.386 0. 0. 0. 0.
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 252 252 186 494 547 641 0 0
normalized size 1 1. 0.74 1.96 2.17 2.54 0. 0.
time (sec) N/A 0.236 0.355 0.167 1.022 4.634 0. 0.
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 191 191 153 372 400 547 0 0
normalized size 1 1. 0.8 1.95 2.09 2.86 0. 0.
time (sec) N/A 0.115 0.229 0.168 0.999 3.529 0. 0.
Problem 83 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 162 162 136 286 267 502 0 0
normalized size 1 1. 0.84 1.77 1.65 3.1 0. 0.
time (sec) N/A 0.127 0.195 0.174 0.993 2.58 0. 0.
Problem 84 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 158 158 127 255 215 501 0 0
normalized size 1 1. 0.8 1.61 1.36 3.17 0. 0.
time (sec) N/A 0.131 0.213 0.179 0.973 2.227 0. 0.
Problem 85 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 183 183 127 191 244 302 0 0
normalized size 1 1. 0.69 1.04 1.33 1.65 0. 0.
time (sec) N/A 0.157 0.211 0.177 0.974 1.67 0. 0.
Problem 86 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 241 241 153 223 325 401 0 0
normalized size 1 1. 0.63 0.93 1.35 1.66 0. 0.
time (sec) N/A 0.193 0.229 0.175 1.001 1.658 0. 0.
Problem 87 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 242 242 162 214 346 431 0 0
normalized size 1 1. 0.67 0.88 1.43 1.78 0. 0.
time (sec) N/A 0.224 0.275 0.171 0.986 2.189 0. 0.
Problem 88 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 195 195 125 182 259 336 0 0
normalized size 1 1. 0.64 0.93 1.33 1.72 0. 0.
time (sec) N/A 0.148 0.286 0.166 0.974 1.934 0. 0.
Problem 89 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 186 186 160 242 0 0 0 0
normalized size 1 1. 0.86 1.3 0. 0. 0. 0.
time (sec) N/A 0.412 0.333 0.714 0. 0. 0. 0.
Problem 90 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 189 189 187 218 0 0 0 0
normalized size 1 1. 0.99 1.15 0. 0. 0. 0.
time (sec) N/A 0.417 0.638 0.608 0. 0. 0. 0.
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 546 546 1023 374 0 0 0 0
normalized size 1 1. 1.87 0.68 0. 0. 0. 0.
time (sec) N/A 1.294 1.362 1.723 0. 0. 0. 0.
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 487 487 891 453 0 0 0 0
normalized size 1 1. 1.83 0.93 0. 0. 0. 0.
time (sec) N/A 1.152 0.376 0.5 0. 0. 0. 0.
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 509 509 871 272 0 0 0 0
normalized size 1 1. 1.71 0.53 0. 0. 0. 0.
time (sec) N/A 0.869 0.326 0.961 0. 0. 0. 0.
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 459 459 402 2933 0 0 0 0
normalized size 1 1. 0.88 6.39 0. 0. 0. 0.
time (sec) N/A 0.896 0.828 0.605 0. 0. 0. 0.
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 551 551 997 331 0 0 0 0
normalized size 1 1. 1.81 0.6 0. 0. 0. 0.
time (sec) N/A 1.096 1.291 1.541 0. 0. 0. 0.
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B C F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 608 608 1255 783 0 0 0 0
normalized size 1 1. 2.06 1.29 0. 0. 0. 0.
time (sec) N/A 1.306 3.904 0.695 0. 0. 0. 0.
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B C F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 570 570 1213 594 0 0 0 0
normalized size 1 1. 2.13 1.04 0. 0. 0. 0.
time (sec) N/A 1.216 1.113 0.647 0. 0. 0. 0.
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 131 131 286 354 0 833 0 0
normalized size 1 1. 2.18 2.7 0. 6.36 0. 0.
time (sec) N/A 0.121 0.575 0.256 0. 1.943 0. 0.
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F C F F F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 546 546 0 3095 0 0 0 0
normalized size 1 1. 0. 5.67 0. 0. 0. 0.
time (sec) N/A 1.14 35.01 0.879 0. 0. 0. 0.
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 784 784 1331 1887 0 0 0 0
normalized size 1 1. 1.7 2.41 0. 0. 0. 0.
time (sec) N/A 2.354 2.257 9.726 0. 0. 0. 0.
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 745 745 1245 1756 0 0 0 0
normalized size 1 1. 1.67 2.36 0. 0. 0. 0.
time (sec) N/A 1.217 1.532 1.681 0. 0. 0. 0.
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 739 739 1239 1748 0 0 0 0
normalized size 1 1. 1.68 2.37 0. 0. 0. 0.
time (sec) N/A 2.211 1.97 1.806 0. 0. 0. 0.
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 785 785 1291 1817 0 0 0 0
normalized size 1 1. 1.64 2.31 0. 0. 0. 0.
time (sec) N/A 2.307 1.952 8.437 0. 0. 0. 0.
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B C F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 707 707 1805 1626 0 0 0 0
normalized size 1 1. 2.55 2.3 0. 0. 0. 0.
time (sec) N/A 1.404 7.807 0.819 0. 0. 0. 0.
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 157 157 389 1870 0 2093 0 0
normalized size 1 1. 2.48 11.91 0. 13.33 0. 0.
time (sec) N/A 0.175 1.311 0.277 0. 4.356 0. 0.
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 193 193 386 1840 0 1839 0 0
normalized size 1 1. 2. 9.53 0. 9.53 0. 0.
time (sec) N/A 0.19 0.877 0.262 0. 5.009 0. 0.
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F C F F F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 685 685 0 5373 0 0 0 0
normalized size 1 1. 0. 7.84 0. 0. 0. 0.
time (sec) N/A 1.291 50.101 1.949 0. 0. 0. 0.
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 1124 1124 1819 3223 0 0 0 0
normalized size 1 1. 1.62 2.87 0. 0. 0. 0.
time (sec) N/A 1.583 6.177 2.084 0. 0. 0. 0.
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 1124 1124 1827 2357 0 0 0 0
normalized size 1 1. 1.63 2.1 0. 0. 0. 0.
time (sec) N/A 3.022 6.113 2.354 0. 0. 0. 0.
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 1114 1114 1812 3214 0 0 0 0
normalized size 1 1. 1.63 2.89 0. 0. 0. 0.
time (sec) N/A 3.791 6.055 2.15 0. 0. 0. 0.
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-2) A F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 403 403 366 0 0 3776 0 0
normalized size 1 1. 0.91 0. 0. 9.37 0. 0.
time (sec) N/A 1.275 0.647 1.842 0. 33.813 0. 0.
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 294 294 327 0 0 3039 0 0
normalized size 1 1. 1.11 0. 0. 10.34 0. 0.
time (sec) N/A 0.398 0.737 1.681 0. 15.325 0. 0.
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 195 195 266 0 0 2425 0 0
normalized size 1 1. 1.36 0. 0. 12.44 0. 0.
time (sec) N/A 0.19 0.457 1.386 0. 6.691 0. 0.
Problem 114 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 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.098 4.094 1.288 0. 0. 0. 0.
Problem 115 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 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.101 4.428 1.26 0. 0. 0. 0.
Problem 116 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 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.094 8.824 1.629 0. 0. 0. 0.
Problem 117 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 22 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.034 4.207 1.29 0. 0. 0. 0.
Problem 118 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 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.086 1.408 1.257 0. 0. 0. 0.
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 328 328 247 0 0 0 0 0
normalized size 1 1. 0.75 0. 0. 0. 0. 0.
time (sec) N/A 0.424 0.613 1.7 0. 0. 0. 0.
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 453 453 325 0 0 0 0 0
normalized size 1 1. 0.72 0. 0. 0. 0. 0.
time (sec) N/A 0.601 0.667 2.864 0. 0. 0. 0.
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-2) A F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 374 374 339 0 0 3771 0 0
normalized size 1 1. 0.91 0. 0. 10.08 0. 0.
time (sec) N/A 0.508 0.595 1.519 0. 31.276 0. 0.
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 262 262 305 0 0 3004 0 0
normalized size 1 1. 1.16 0. 0. 11.47 0. 0.
time (sec) N/A 0.27 0.714 1.191 0. 10.902 0. 0.
Problem 123 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 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.115 4.984 1.133 0. 0. 0. 0.
Problem 124 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 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.119 5.339 1.036 0. 0. 0. 0.
Problem 125 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 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.112 8.753 1.458 0. 0. 0. 0.
Problem 126 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 22 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.042 4.864 1.105 0. 0. 0. 0.
Problem 127 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 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.103 8.089 1.031 0. 0. 0. 0.
Problem 128 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 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.104 10.674 1.447 0. 0. 0. 0.
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 416 416 303 0 0 0 0 0
normalized size 1 1. 0.73 0. 0. 0. 0. 0.
time (sec) N/A 0.539 0.642 1.676 0. 0. 0. 0.
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 554 554 383 0 0 0 0 0
normalized size 1 1. 0.69 0. 0. 0. 0. 0.
time (sec) N/A 0.778 0.835 2.136 0. 0. 0. 0.
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 321 321 328 0 0 3060 0 0
normalized size 1 1. 1.02 0. 0. 9.53 0. 0.
time (sec) N/A 1.012 0.718 2.826 0. 11.84 0. 0.
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 225 225 272 0 0 2452 0 0
normalized size 1 1. 1.21 0. 0. 10.9 0. 0.
time (sec) N/A 0.308 0.507 2.027 0. 5.059 0. 0.
Problem 133 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 132 132 211 0 0 1925 0 0
normalized size 1 1. 1.6 0. 0. 14.58 0. 0.
time (sec) N/A 0.146 0.22 1.591 0. 2.6 0. 0.
Problem 134 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 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.097 1.422 1.52 0. 0. 0. 0.
Problem 135 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 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.108 11.006 1.239 0. 0. 0. 0.
Problem 136 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 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.091 8.703 1.276 0. 0. 0. 0.
Problem 137 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 22 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.03 0.795 1.261 0. 0. 0. 0.
Problem 138 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 246 246 143 0 0 0 0 0
normalized size 1 1. 0.58 0. 0. 0. 0. 0.
time (sec) N/A 0.255 0.194 1.273 0. 0. 0. 0.
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 362 362 249 0 0 0 0 0
normalized size 1 1. 0.69 0. 0. 0. 0. 0.
time (sec) N/A 0.447 0.635 1.717 0. 0. 0. 0.
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 1006 1006 329 0 0 0 0 0
normalized size 1 1. 0.33 0. 0. 0. 0. 0.
time (sec) N/A 1.78 0.806 1.97 0. 0. 0. 0.
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 252 252 303 0 0 3171 0 0
normalized size 1 1. 1.2 0. 0. 12.58 0. 0.
time (sec) N/A 1.006 0.65 1.828 0. 4.994 0. 0.
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 157 157 221 0 0 2360 0 0
normalized size 1 1. 1.41 0. 0. 15.03 0. 0.
time (sec) N/A 0.259 0.352 1.589 0. 3.339 0. 0.
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 80 80 95 0 0 626 0 0
normalized size 1 1. 1.19 0. 0. 7.82 0. 0.
time (sec) N/A 0.102 0.145 1.233 0. 2.355 0. 0.
Problem 144 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 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.11 15.089 1.081 0. 0. 0. 0.
Problem 145 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 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.123 21.066 1.079 0. 0. 0. 0.
Problem 146 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 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.106 7.663 1.148 0. 0. 0. 0.
Problem 147 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 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.099 3.641 1.159 0. 0. 0. 0.
Problem 148 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 109 109 113 0 0 0 0 0
normalized size 1 1. 1.04 0. 0. 0. 0. 0.
time (sec) N/A 0.088 0.188 1.088 0. 0. 0. 0.
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 274 274 212 0 0 0 0 0
normalized size 1 1. 0.77 0. 0. 0. 0. 0.
time (sec) N/A 0.31 0.475 1.032 0. 0. 0. 0.
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 701 701 292 0 0 0 0 0
normalized size 1 1. 0.42 0. 0. 0. 0. 0.
time (sec) N/A 1.392 0.717 1.481 0. 0. 0. 0.
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 244 244 312 0 0 4483 0 0
normalized size 1 1. 1.28 0. 0. 18.37 0. 0.
time (sec) N/A 1.063 0.522 1.862 0. 5.146 0. 0.
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 163 163 172 0 0 1380 0 0
normalized size 1 1. 1.06 0. 0. 8.47 0. 0.
time (sec) N/A 0.243 0.256 1.631 0. 3.348 0. 0.
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 138 138 158 0 0 1189 0 0
normalized size 1 1. 1.14 0. 0. 8.62 0. 0.
time (sec) N/A 0.131 0.205 1.233 0. 3.091 0. 0.
Problem 154 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 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.12 25.452 1.078 0. 0. 0. 0.
Problem 155 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 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.138 31.587 1.08 0. 0. 0. 0.
Problem 156 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 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.116 9.905 1.224 0. 0. 0. 0.
Problem 157 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 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.106 9.378 1.169 0. 0. 0. 0.
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 276 276 186 0 0 0 0 0
normalized size 1 1. 0.67 0. 0. 0. 0. 0.
time (sec) N/A 0.276 0.285 1.157 0. 0. 0. 0.
Problem 159 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 296 296 248 0 0 0 0 0
normalized size 1 1. 0.84 0. 0. 0. 0. 0.
time (sec) N/A 0.235 0.556 1.08 0. 0. 0. 0.
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 631 631 323 0 0 0 0 0
normalized size 1 1. 0.51 0. 0. 0. 0. 0.
time (sec) N/A 1.396 0.791 1.022 0. 0. 0. 0.
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F(-2) F F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 589 570 0 0 0 0 0 0
normalized size 1 0.97 0. 0. 0. 0. 0. 0.
time (sec) N/A 2.415 0.212 4.007 0. 0. 0. 0.
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F(-2) F F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 374 355 0 0 0 0 0 0
normalized size 1 0.95 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.432 0.141 3.049 0. 0. 0. 0.
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F(-2) F F(-1) F
verified N/A NO N/A TBD TBD TBD TBD TBD
size 178 204 0 0 0 0 0 0
normalized size 1 1.15 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.187 0.101 2.319 0. 0. 0. 0.
Problem 164 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 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.071 1.937 1.646 0. 0. 0. 0.
Problem 165 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 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.071 1.916 1.95 0. 0. 0. 0.
Problem 166 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 27 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.105 0.885 1.532 0. 0. 0. 0.
Problem 167 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 27 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.094 0.108 1.655 0. 0. 0. 0.
Problem 168 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 27 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.096 1.108 2.517 0. 0. 0. 0.
Problem 169 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 27 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.105 1.365 1.757 0. 0. 0. 0.
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-1) F(-2) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 401 401 194 0 0 0 0 0
normalized size 1 1. 0.48 0. 0. 0. 0. 0.
time (sec) N/A 2.484 0.249 17.217 0. 0. 0. 0.
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-1) F(-2) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 268 268 159 0 0 0 0 0
normalized size 1 1. 0.59 0. 0. 0. 0. 0.
time (sec) N/A 2.018 0.316 4.461 0. 0. 0. 0.
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-1) F(-2) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 126 135 118 0 0 0 0 0
normalized size 1 1.07 0.94 0. 0. 0. 0. 0.
time (sec) N/A 0.208 0.213 1.641 0. 0. 0. 0.
Problem 173 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 28 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.088 0.333 1.9 0. 0. 0. 0.
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 28 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.099 6.369 1.836 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 [160] had the largest ratio of [ 0.7826 ]

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 7 5 1. 12 0.417
2 A 4 3 1. 12 0.25
3 A 6 5 1. 12 0.417
4 A 3 3 1. 12 0.25
5 A 5 5 1. 12 0.417
6 A 2 2 1. 10 0.2
7 A 5 4 1. 8 0.5
8 A 6 6 1. 12 0.5
9 A 2 2 1. 12 0.167
10 A 4 4 1. 12 0.333
11 A 4 3 1. 12 0.25
12 A 5 4 1. 12 0.333
13 A 4 3 1. 12 0.25
14 A 6 4 1. 12 0.333
15 A 5 5 1. 14 0.357
16 A 8 6 1. 14 0.429
17 A 4 4 1. 12 0.333
18 A 7 5 1. 10 0.5
19 A 6 6 1. 14 0.429
20 A 4 3 1. 14 0.214
21 A 4 3 1. 14 0.214
22 A 5 5 1. 14 0.357
23 A 5 3 1. 14 0.214
24 A 10 10 1. 14 0.714
25 A 11 8 1. 14 0.571
26 A 7 7 1. 12 0.583
27 A 9 6 1. 10 0.6
28 A 7 7 1. 14 0.5
29 A 5 3 1. 14 0.214
30 A 6 6 1. 14 0.429
31 A 8 6 1. 14 0.429
32 A 10 6 1. 14 0.429
33 A 0 0 0. 0 0.
34 A 0 0 0. 0 0.
35 A 0 0 0. 0 0.
36 A 4 4 1. 14 0.286
37 A 6 6 1. 14 0.429
38 A 9 5 1. 14 0.357
39 A 0 0 0. 0 0.
40 A 0 0 0. 0 0.
41 A 0 0 0. 0 0.
42 A 5 5 1. 14 0.357
43 A 7 7 1. 14 0.5
44 A 11 6 1. 14 0.429
45 A 0 0 0. 0 0.
46 A 0 0 0. 0 0.
47 A 0 0 0. 0 0.
48 A 6 5 1. 14 0.357
49 A 8 7 1. 14 0.5
50 A 13 6 1. 14 0.429
51 A 0 0 0. 0 0.
52 A 0 0 0. 0 0.
53 A 3 3 1. 14 0.214
54 A 0 0 0. 0 0.
55 A 0 0 0. 0 0.
56 A 11 9 1. 16 0.562
57 A 10 9 1. 16 0.562
58 A 9 9 1. 14 0.643
59 A 5 4 1. 8 0.5
60 A 4 2 1. 16 0.125
61 A 7 7 1. 16 0.438
62 A 8 8 1. 16 0.5
63 A 22 13 1. 18 0.722
64 A 15 11 1. 18 0.611
65 A 9 9 1. 18 0.5
66 A 6 6 1. 18 0.333
67 A 12 11 1. 18 0.611
68 A 19 14 1.18 18 0.778
69 A 7 7 1. 19 0.368
70 A 6 7 1. 19 0.368
71 A 5 5 1. 16 0.312
72 A 4 5 1. 19 0.263
73 A 4 5 1. 19 0.263
74 A 5 6 1. 19 0.316
75 A 6 6 1. 19 0.316
76 A 5 5 1. 19 0.263
77 A 5 5 1. 19 0.263
78 A 6 5 1. 17 0.294
79 A 11 11 1. 19 0.579
80 A 13 13 1. 19 0.684
81 A 7 8 1. 21 0.381
82 A 6 7 1. 18 0.389
83 A 6 7 1. 21 0.333
84 A 6 7 1. 21 0.333
85 A 5 6 1. 21 0.286
86 A 6 7 1. 21 0.333
87 A 5 6 1. 21 0.286
88 A 6 5 1. 19 0.263
89 A 12 13 1. 21 0.619
90 A 14 15 1. 21 0.714
91 A 25 12 1. 21 0.571
92 A 26 9 1. 19 0.474
93 A 19 7 1. 18 0.389
94 A 19 7 1. 21 0.333
95 A 24 10 1. 21 0.476
96 A 31 14 1. 21 0.667
97 A 29 12 1. 21 0.571
98 A 7 5 1. 19 0.263
99 A 24 10 1. 21 0.476
100 A 51 15 1. 21 0.714
101 A 27 10 1. 21 0.476
102 A 47 11 1. 18 0.611
103 A 50 13 1. 21 0.619
104 A 33 13 1. 21 0.619
105 A 6 7 1. 21 0.333
106 A 8 6 1. 19 0.316
107 A 28 11 1. 21 0.524
108 A 35 11 1. 21 0.524
109 A 63 12 1. 21 0.571
110 A 81 12 1. 18 0.667
111 A 12 12 1. 23 0.522
112 A 11 12 1. 23 0.522
113 A 9 9 1. 21 0.429
114 A 0 0 0. 0 0.
115 A 0 0 0. 0 0.
116 A 0 0 0. 0 0.
117 A 0 0 0. 0 0.
118 A 0 0 0. 0 0.
119 A 11 11 1. 23 0.478
120 A 12 12 1. 23 0.522
121 A 12 12 1. 23 0.522
122 A 10 10 1. 21 0.476
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 0 0 0. 0 0.
128 A 0 0 0. 0 0.
129 A 12 12 1. 23 0.522
130 A 13 12 1. 23 0.522
131 A 11 12 1. 23 0.522
132 A 10 12 1. 23 0.522
133 A 8 8 1. 21 0.381
134 A 0 0 0. 0 0.
135 A 0 0 0. 0 0.
136 A 0 0 0. 0 0.
137 A 0 0 0. 0 0.
138 A 11 11 1. 23 0.478
139 A 11 12 1. 23 0.522
140 A 32 15 1. 23 0.652
141 A 10 11 1. 23 0.478
142 A 9 11 1. 23 0.478
143 A 4 4 1. 21 0.19
144 A 0 0 0. 0 0.
145 A 0 0 0. 0 0.
146 A 0 0 0. 0 0.
147 A 0 0 0. 0 0.
148 A 5 5 1. 20 0.25
149 A 10 11 1. 23 0.478
150 A 25 14 1. 23 0.609
151 A 10 11 1. 23 0.478
152 A 7 8 1. 23 0.348
153 A 5 5 1. 21 0.238
154 A 0 0 0. 0 0.
155 A 0 0 0. 0 0.
156 A 0 0 0. 0 0.
157 A 0 0 0. 0 0.
158 A 10 10 1. 23 0.435
159 A 10 11 1. 20 0.55
160 A 26 18 1. 23 0.783
161 A 6 7 0.97 23 0.304
162 A 6 7 0.95 23 0.304
163 A 5 6 1.15 21 0.286
164 A 0 0 0. 0 0.
165 A 0 0 0. 0 0.
166 A 0 0 0. 0 0.
167 A 0 0 0. 0 0.
168 A 0 0 0. 0 0.
169 A 0 0 0. 0 0.
170 A 16 11 1. 26 0.423
171 A 13 11 1. 26 0.423
172 A 8 9 1.07 26 0.346
173 A 0 0 0. 0 0.
174 A 0 0 0. 0 0.

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