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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, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190 }

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, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 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, 76, 77, 79, 87, 91, 92, 93, 94, 95, 96, 97, 98, 99, 104, 105, 106, 107, 108, 109, 130, 131, 132, 133, 134, 135, 136, 137, 140, 141, 142, 143, 144, 145, 146, 147, 150, 151, 152, 153, 154, 155, 156, 159, 160, 161, 162, 163, 164, 165, 168, 169, 170, 171, 172, 173, 174, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190 }

B grade: { 45 }

C grade: { 19, 21, 23, 74, 75, 78, 80, 81, 82, 83, 84, 85, 86, 88, 89, 90, 100, 101, 102, 103, 110, 111, 112, 113, 114, 115, 116, 117, 119, 120, 121, 122, 123, 124, 125, 127, 128, 129, 138, 139, 148, 149, 157, 158, 166, 167, 175, 176 }

F grade: { 118, 126, 177, 178, 179}

2.1.3 Maple

A grade: { 1, 2, 3, 5, 6, 7, 8, 9, 11, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 36, 37, 39, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 63, 64, 65, 69, 70, 72, 73, 74, 75, 76, 77, 79, 82, 83, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 133, 134, 135, 136, 137, 142, 143, 144, 145, 146, 147, 153, 154, 155, 156, 162, 163, 164, 165, 171, 172, 173, 174, 180, 181, 182, 183, 184, 185, 189, 190 }

B grade: { 4, 33, 35, 38, 40, 41, 42, 44, 46, 47, 48, 49, 50, 61, 62, 66, 67, 68, 80, 81, 84, 85, 86, 117, 124, 125 }

C grade: { 78, 110, 111, 112, 113, 114, 115, 116, 118, 119, 120, 121, 122, 123, 126, 127, 128, 129 }

F grade: { 10, 12, 14, 43, 45, 71, 130, 131, 132, 138, 139, 140, 141, 148, 149, 150, 151, 152, 157, 158, 159, 160, 161, 166, 167, 168, 169, 170, 175, 176, 177, 178, 179, 186, 187, 188 }

2.1.4 Maxima

A grade: { 4, 7, 16, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 35, 38, 47, 51, 52, 53, 57, 58, 59, 63, 64, 65, 72, 73, 74, 75, 76, 77, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 100, 101, 102, 103, 104, 105, 106, 107, 180, 181, 182, 183, 184, 185, 189, 190

B grade: { }

C grade: { }

F grade: { 1, 2, 3, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 26, 33, 34, 36, 37, 39, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 54, 55, 56, 60, 61, 62, 66, 67, 68, 69, 70, 71, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 98, 99, 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, 175, 176, 177, 178, 179, 186, 187, 188 }

2.1.5 FriCAS

A grade: { 2, 8, 9, 16, 17, 18, 19, 20, 22, 27, 28, 29, 30, 31, 32, 39, 40, 41, 48, 49, 50, 51, 52, 53, 57, 58, 59, 63, 64, 65, 69, 70, 72, 73, 87, 88, 92, 93, 94, 95, 96, 97, 100, 104, 105, 106, 107, 130, 131, 133, 134, 135, 136, 137, 140, 142, 143, 144, 145, 146, 147, 150, 153, 154, 155, 156, 162, 163, 164, 165, 171, 172, 173, 174, 180, 181, 182, 183, 184, 185, 186, 187, 189, 190 }

B grade: { 4, 7, 21, 23, 24, 25, 33, 35, 38, 47, 74, 75, 76, 77, 79, 80, 89, 90, 91, 101, 102, 103, 117, 124, 125, 132, 141, 151, 152, 159, 160, 161, 168, 169, 170, 188 }

C grade: { }

F grade: { 1, 3, 5, 6, 10, 11, 12, 13, 14, 15, 26, 34, 36, 37, 42, 43, 44, 45, 46, 54, 55, 56, 60, 61, 62, 66, 67, 68, 71, 78, 81, 82, 83, 84, 85, 86, 98, 99, 108, 109, 110, 111, 112, 113, 114, 115, 116, 118, 119, 120, 121, 122, 123, 126, 127, 128, 129, 138, 139, 148, 149, 157, 158, 166, 167, 175, 176, 177, 178, 179 }

2.1.6 Sympy

A grade: { 4, 20, 22, 24, 35, 51, 52, 53, 57, 58, 59, 63, 64, 65, 69, 70, 72, 73, 87, 95, 96, 97, 106, 107, 133, 134, 135, 136, 137, 153, 154, 155, 156, 165, 180, 183, 184, 189 }

B grade: { }

C grade: { }

F grade: { 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 54, 55, 56, 60, 61, 62, 66, 67, 68, 71, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 88, 89, 90, 91, 92, 93, 94, 98, 99, 100, 101, 102, 103, 104, 105, 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, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 157, 158, 159, 160, 161, 162, 163, 164, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 181, 182, 185, 186, 187, 188, 190 }

2.1.7 Giac

A grade: { 51, 52, 53, 57, 58, 59, 63, 64, 65, 69, 70, 72, 73, 87, 133, 134, 135, 136, 137, 142, 143, 144, 145, 146, 147, 153, 154, 155, 156, 162, 163, 164, 165, 171, 172, 173, 174, 180, 181, 182, 183, 184, 185, 189, 190 }

B grade: { }

C grade: { }

F 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, 54, 55, 56, 60, 61, 62, 66, 67, 68, 71, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 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, 138, 139, 140, 141, 148, 149, 150, 151, 152, 157, 158, 159, 160, 161, 166, 167, 168, 169, 170, 175, 176, 177, 178, 179, 186, 187, 188 }

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 F(-1) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 164 164 182 289 0 0 0 0
normalized size 1 1. 1.11 1.76 0. 0. 0. 0.
time (sec) N/A 0.124 0.362 0.404 0. 0. 0. 0.
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 104 104 77 151 0 273 0 0
normalized size 1 1. 0.74 1.45 0. 2.62 0. 0.
time (sec) N/A 0.088 0.101 0.328 0. 1.699 0. 0.
Problem 3 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 117 117 138 240 0 0 0 0
normalized size 1 1. 1.18 2.05 0. 0. 0. 0.
time (sec) N/A 0.097 0.231 0.325 0. 0. 0. 0.
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 53 53 53 101 54 236 42 0
normalized size 1 1. 1. 1.91 1.02 4.45 0.79 0.
time (sec) N/A 0.057 0.06 0.258 1.048 1.636 3.11 0.
Problem 5 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 63 63 90 190 0 0 0 0
normalized size 1 1. 1.43 3.02 0. 0. 0. 0.
time (sec) N/A 0.055 0.185 0.272 0. 0. 0. 0.
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 64 64 63 136 0 0 0 0
normalized size 1 1. 0.98 2.12 0. 0. 0. 0.
time (sec) N/A 0.092 0.031 0.241 0. 0. 0. 0.
Problem 7 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 49 49 42 61 47 208 0 0
normalized size 1 1. 0.86 1.24 0.96 4.24 0. 0.
time (sec) N/A 0.048 0.087 0.213 1.016 1.709 0. 0.
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 90 90 54 77 0 235 0 0
normalized size 1 1. 0.6 0.86 0. 2.61 0. 0.
time (sec) N/A 0.059 0.041 0.213 0. 1.631 0. 0.
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 102 102 73 146 0 258 0 0
normalized size 1 1. 0.72 1.43 0. 2.53 0. 0.
time (sec) N/A 0.084 0.095 0.237 0. 1.696 0. 0.
Problem 10 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 297 297 281 0 0 0 0 0
normalized size 1 1. 0.95 0. 0. 0. 0. 0.
time (sec) N/A 0.203 0.554 0.651 0. 0. 0. 0.
Problem 11 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 184 184 188 246 0 0 0 0
normalized size 1 1. 1.02 1.34 0. 0. 0. 0.
time (sec) N/A 0.177 0.576 0.349 0. 0. 0. 0.
Problem 12 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 198 198 199 0 0 0 0 0
normalized size 1 1. 1.01 0. 0. 0. 0. 0.
time (sec) N/A 0.141 0.46 0.434 0. 0. 0. 0.
Problem 13 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 102 102 101 152 0 0 0 0
normalized size 1 1. 0.99 1.49 0. 0. 0. 0.
time (sec) N/A 0.122 0.36 0.267 0. 0. 0. 0.
Problem 14 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 111 111 128 0 0 0 0 0
normalized size 1 1. 1.15 0. 0. 0. 0. 0.
time (sec) N/A 0.088 0.116 0.304 0. 0. 0. 0.
Problem 15 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 88 88 84 181 0 0 0 0
normalized size 1 1. 0.95 2.06 0. 0. 0. 0.
time (sec) N/A 0.108 0.049 0.244 0. 0. 0. 0.
Problem 16 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 83 83 75 98 74 333 0 0
normalized size 1 1. 0.9 1.18 0.89 4.01 0. 0.
time (sec) N/A 0.071 0.072 0.211 1.034 1.937 0. 0.
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 137 137 147 126 0 382 0 0
normalized size 1 1. 1.07 0.92 0. 2.79 0. 0.
time (sec) N/A 0.086 0.133 0.217 0. 2.035 0. 0.
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 179 179 120 226 0 406 0 0
normalized size 1 1. 0.67 1.26 0. 2.27 0. 0.
time (sec) N/A 0.125 0.113 0.229 0. 1.975 0. 0.
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 142 142 143 138 182 406 0 0
normalized size 1 1. 1.01 0.97 1.28 2.86 0. 0.
time (sec) N/A 0.061 0.188 0.217 1.492 2.331 0. 0.
Problem 20 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 109 109 97 81 105 217 94 0
normalized size 1 1. 0.89 0.74 0.96 1.99 0.86 0.
time (sec) N/A 0.047 0.084 0.193 0.99 1.984 16.626 0.
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 110 110 123 118 143 378 0 0
normalized size 1 1. 1.12 1.07 1.3 3.44 0. 0.
time (sec) N/A 0.04 0.118 0.225 1.515 2.011 0. 0.
Problem 22 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 77 77 77 72 77 193 68 0
normalized size 1 1. 1. 0.94 1. 2.51 0.88 0.
time (sec) N/A 0.031 0.077 0.187 1.008 1.987 5.803 0.
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 78 78 103 96 99 352 0 0
normalized size 1 1. 1.32 1.23 1.27 4.51 0. 0.
time (sec) N/A 0.027 0.087 0.192 1.53 2.12 0. 0.
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 57 63 49 157 46 0
normalized size 1 1. 1.27 1.4 1.09 3.49 1.02 0.
time (sec) N/A 0.014 0.052 0.178 0.979 1.91 1.319 0.
Problem 25 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 40 40 60 42 42 262 0 0
normalized size 1 1. 1.5 1.05 1.05 6.55 0. 0.
time (sec) N/A 0.015 0.099 0.159 0.973 2. 0. 0.
Problem 26 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 56 56 47 100 0 0 0 0
normalized size 1 1. 0.84 1.79 0. 0. 0. 0.
time (sec) N/A 0.088 0.044 0.256 0. 0. 0. 0.
Problem 27 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 40 40 42 58 43 138 0 0
normalized size 1 1. 1.05 1.45 1.08 3.45 0. 0.
time (sec) N/A 0.02 0.054 0.178 0.982 1.965 0. 0.
Problem 28 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 94 94 117 112 142 170 0 0
normalized size 1 1. 1.24 1.19 1.51 1.81 0. 0.
time (sec) N/A 0.04 0.068 0.183 0.989 1.858 0. 0.
Problem 29 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 77 77 74 77 76 174 0 0
normalized size 1 1. 0.96 1. 0.99 2.26 0. 0.
time (sec) N/A 0.033 0.063 0.181 0.979 1.89 0. 0.
Problem 30 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 126 126 137 135 198 198 0 0
normalized size 1 1. 1.09 1.07 1.57 1.57 0. 0.
time (sec) N/A 0.055 0.095 0.182 0.988 1.901 0. 0.
Problem 31 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 109 109 94 85 99 200 0 0
normalized size 1 1. 0.86 0.78 0.91 1.83 0. 0.
time (sec) N/A 0.05 0.086 0.18 0.996 1.873 0. 0.
Problem 32 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 158 158 157 155 250 227 0 0
normalized size 1 1. 0.99 0.98 1.58 1.44 0. 0.
time (sec) N/A 0.073 0.142 0.189 1.015 1.833 0. 0.
Problem 33 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 124 124 212 264 0 525 0 0
normalized size 1 1. 1.71 2.13 0. 4.23 0. 0.
time (sec) N/A 0.119 0.33 0.29 0. 2.161 0. 0.
Problem 34 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 140 140 224 372 0 0 0 0
normalized size 1 1. 1.6 2.66 0. 0. 0. 0.
time (sec) N/A 0.123 1.154 0.278 0. 0. 0. 0.
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 65 65 112 168 113 446 99 0
normalized size 1 1. 1.72 2.58 1.74 6.86 1.52 0.
time (sec) N/A 0.075 0.209 0.253 1.02 2.066 3.947 0.
Problem 36 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 78 78 126 250 0 0 0 0
normalized size 1 1. 1.62 3.21 0. 0. 0. 0.
time (sec) N/A 0.07 0.224 0.221 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 NO TBD TBD TBD TBD TBD
size 83 83 116 250 0 0 0 0
normalized size 1 1. 1.4 3.01 0. 0. 0. 0.
time (sec) N/A 0.125 0.157 0.237 0. 0. 0. 0.
Problem 38 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 61 61 87 124 105 301 0 0
normalized size 1 1. 1.43 2.03 1.72 4.93 0. 0.
time (sec) N/A 0.07 0.229 0.217 1.029 1.66 0. 0.
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 118 118 183 192 0 355 0 0
normalized size 1 1. 1.55 1.63 0. 3.01 0. 0.
time (sec) N/A 0.085 0.163 0.236 0. 1.618 0. 0.
Problem 40 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 122 122 134 226 0 392 0 0
normalized size 1 1. 1.1 1.85 0. 3.21 0. 0.
time (sec) N/A 0.102 0.25 0.225 0. 1.654 0. 0.
Problem 41 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 151 151 268 298 0 439 0 0
normalized size 1 1. 1.77 1.97 0. 2.91 0. 0.
time (sec) N/A 0.12 0.259 0.233 0. 1.67 0. 0.
Problem 42 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 223 223 315 546 0 0 0 0
normalized size 1 1. 1.41 2.45 0. 0. 0. 0.
time (sec) N/A 0.239 1.558 0.385 0. 0. 0. 0.
Problem 43 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 242 242 440 0 0 0 0 0
normalized size 1 1. 1.82 0. 0. 0. 0. 0.
time (sec) N/A 0.195 1.018 0.49 0. 0. 0. 0.
Problem 44 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 126 126 219 343 0 0 0 0
normalized size 1 1. 1.74 2.72 0. 0. 0. 0.
time (sec) N/A 0.157 0.868 0.302 0. 0. 0. 0.
Problem 45 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 140 140 282 0 0 0 0 0
normalized size 1 1. 2.01 0. 0. 0. 0. 0.
time (sec) N/A 0.111 0.409 0.329 0. 0. 0. 0.
Problem 46 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 114 114 182 454 0 0 0 0
normalized size 1 1. 1.6 3.98 0. 0. 0. 0.
time (sec) N/A 0.145 0.229 0.272 0. 0. 0. 0.
Problem 47 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 102 102 165 227 194 485 0 0
normalized size 1 1. 1.62 2.23 1.9 4.75 0. 0.
time (sec) N/A 0.103 0.322 0.252 1.035 1.689 0. 0.
Problem 48 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 163 163 245 321 0 583 0 0
normalized size 1 1. 1.5 1.97 0. 3.58 0. 0.
time (sec) N/A 0.116 0.461 0.274 0. 1.642 0. 0.
Problem 49 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 213 213 256 455 0 649 0 0
normalized size 1 1. 1.2 2.14 0. 3.05 0. 0.
time (sec) N/A 0.166 0.383 0.274 0. 1.785 0. 0.
Problem 50 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 242 242 332 553 0 756 0 0
normalized size 1 1. 1.37 2.29 0. 3.12 0. 0.
time (sec) N/A 0.196 0.714 0.277 0. 1.639 0. 0.
Problem 51 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 0.017 2.21 0.736 0. 0. 0. 0.
Problem 52 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 0.007 0.033 0.367 0. 0. 0. 0.
Problem 53 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 0.027 0.294 0.298 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 Yes TBD TBD TBD TBD TBD
size 46 46 43 54 0 0 0 0
normalized size 1 1. 0.93 1.17 0. 0. 0. 0.
time (sec) N/A 0.11 0.075 0.211 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 Yes TBD TBD TBD TBD TBD
size 63 63 56 60 0 0 0 0
normalized size 1 1. 0.89 0.95 0. 0. 0. 0.
time (sec) N/A 0.142 0.076 0.207 0. 0. 0. 0.
Problem 56 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 91 110 0 0 0 0
normalized size 1 1. 0.78 0.94 0. 0. 0. 0.
time (sec) N/A 0.236 0.156 0.234 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 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.016 16.38 0.677 0. 0. 0. 0.
Problem 58 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 0.007 8.593 0.3 0. 0. 0. 0.
Problem 59 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 4.993 0.286 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 86 86 82 164 0 0 0 0
normalized size 1 1. 0.95 1.91 0. 0. 0. 0.
time (sec) N/A 0.145 0.334 0.258 0. 0. 0. 0.
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 85 85 92 186 0 0 0 0
normalized size 1 1. 1.08 2.19 0. 0. 0. 0.
time (sec) N/A 0.165 0.335 0.237 0. 0. 0. 0.
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 190 190 170 420 0 0 0 0
normalized size 1 1. 0.89 2.21 0. 0. 0. 0.
time (sec) N/A 0.295 0.623 0.273 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 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.016 5.791 0.67 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 0.006 3.587 0.589 0. 0. 0. 0.
Problem 65 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 2.499 0.276 0. 0. 0. 0.
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 114 114 103 244 0 0 0 0
normalized size 1 1. 0.9 2.14 0. 0. 0. 0.
time (sec) N/A 0.176 0.288 0.231 0. 0. 0. 0.
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 112 112 122 277 0 0 0 0
normalized size 1 1. 1.09 2.47 0. 0. 0. 0.
time (sec) N/A 0.206 0.405 0.293 0. 0. 0. 0.
Problem 68 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 240 240 204 628 0 0 0 0
normalized size 1 1. 0.85 2.62 0. 0. 0. 0.
time (sec) N/A 0.371 0.555 0.329 0. 0. 0. 0.
Problem 69 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 0.024 5.077 1.97 0. 0. 0. 0.
Problem 70 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 0.026 3.336 1.681 0. 0. 0. 0.
Problem 71 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 87 87 97 0 0 0 0 0
normalized size 1 1. 1.11 0. 0. 0. 0. 0.
time (sec) N/A 0.037 0.147 1.601 0. 0. 0. 0.
Problem 72 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 0.394 1.291 0. 0. 0. 0.
Problem 73 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 0.027 0.806 1.267 0. 0. 0. 0.
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 264 264 190 283 298 764 0 0
normalized size 1 1. 0.72 1.07 1.13 2.89 0. 0.
time (sec) N/A 0.362 0.397 0.196 1.516 2.417 0. 0.
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 201 201 147 215 205 601 0 0
normalized size 1 1. 0.73 1.07 1.02 2.99 0. 0.
time (sec) N/A 0.217 0.214 0.213 1.507 2.13 0. 0.
Problem 76 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 142 142 122 125 95 401 0 0
normalized size 1 1. 0.86 0.88 0.67 2.82 0. 0.
time (sec) N/A 0.118 0.344 0.193 0.99 1.852 0. 0.
Problem 77 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 40 40 60 42 42 262 0 0
normalized size 1 1. 1.5 1.05 1.05 6.55 0. 0.
time (sec) N/A 0.015 0.087 0.165 0.971 1.694 0. 0.
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 229 229 393 514 0 0 0 0
normalized size 1 1. 1.72 2.24 0. 0. 0. 0.
time (sec) N/A 0.933 0.523 0.271 0. 0. 0. 0.
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 147 147 222 231 0 1162 0 0
normalized size 1 1. 1.51 1.57 0. 7.9 0. 0.
time (sec) N/A 0.119 0.226 0.29 0. 1.824 0. 0.
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-2) B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 306 306 342 1090 0 2423 0 0
normalized size 1 1. 1.12 3.56 0. 7.92 0. 0.
time (sec) N/A 0.193 0.629 0.274 0. 2.689 0. 0.
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-2) F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 343 343 2653 830 0 0 0 0
normalized size 1 1. 7.73 2.42 0. 0. 0. 0.
time (sec) N/A 0.621 9.876 0.395 0. 0. 0. 0.
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 279 279 2938 415 0 0 0 0
normalized size 1 1. 10.53 1.49 0. 0. 0. 0.
time (sec) N/A 0.372 12.983 0.324 0. 0. 0. 0.
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 187 187 1707 288 0 0 0 0
normalized size 1 1. 9.13 1.54 0. 0. 0. 0.
time (sec) N/A 0.247 10.784 0.275 0. 0. 0. 0.
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 105 105 1675 253 0 0 0 0
normalized size 1 1. 15.95 2.41 0. 0. 0. 0.
time (sec) N/A 0.178 10.398 0.271 0. 0. 0. 0.
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-2) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 278 278 4527 902 0 0 0 0
normalized size 1 1. 16.28 3.24 0. 0. 0. 0.
time (sec) N/A 0.313 12.662 0.335 0. 0. 0. 0.
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-2) F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 609 609 8675 1632 0 0 0 0
normalized size 1 1. 14.24 2.68 0. 0. 0. 0.
time (sec) N/A 0.594 12.924 0.352 0. 0. 0. 0.
Problem 87 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 86 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.048 1.836 1.454 0. 0. 0. 0.
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 229 229 162 224 329 590 0 0
normalized size 1 1. 0.71 0.98 1.44 2.58 0. 0.
time (sec) N/A 0.127 0.318 0.185 1.48 2.984 0. 0.
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 174 174 144 182 246 531 0 0
normalized size 1 1. 0.83 1.05 1.41 3.05 0. 0.
time (sec) N/A 0.103 0.208 0.185 1.506 2.732 0. 0.
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 112 112 169 135 144 460 0 0
normalized size 1 1. 1.51 1.21 1.29 4.11 0. 0.
time (sec) N/A 0.051 0.356 0.175 1.491 2.526 0. 0.
Problem 91 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 96 96 107 114 89 401 0 0
normalized size 1 1. 1.11 1.19 0.93 4.18 0. 0.
time (sec) N/A 0.066 0.239 0.21 1.007 2.085 0. 0.
Problem 92 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 126 126 76 123 123 236 0 0
normalized size 1 1. 0.6 0.98 0.98 1.87 0. 0.
time (sec) N/A 0.079 0.104 0.184 0.996 1.755 0. 0.
Problem 93 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 183 183 101 142 178 297 0 0
normalized size 1 1. 0.55 0.78 0.97 1.62 0. 0.
time (sec) N/A 0.099 0.165 0.184 1.001 1.894 0. 0.
Problem 94 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 238 238 117 160 223 352 0 0
normalized size 1 1. 0.49 0.67 0.94 1.48 0. 0.
time (sec) N/A 0.122 0.201 0.191 1.027 1.955 0. 0.
Problem 95 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 232 232 126 150 239 381 228 0
normalized size 1 1. 0.54 0.65 1.03 1.64 0.98 0.
time (sec) N/A 0.164 0.21 0.185 1.001 2.054 69.773 0.
Problem 96 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 180 180 106 132 186 325 177 0
normalized size 1 1. 0.59 0.73 1.03 1.81 0.98 0.
time (sec) N/A 0.135 0.178 0.183 1.009 1.973 14.968 0.
Problem 97 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 164 164 85 113 130 269 126 0
normalized size 1 1. 0.52 0.69 0.79 1.64 0.77 0.
time (sec) N/A 0.193 0.126 0.178 0.998 2.044 4.156 0.
Problem 98 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 296 296 98 166 0 0 0 0
normalized size 1 1. 0.33 0.56 0. 0. 0. 0.
time (sec) N/A 0.875 0.292 0.365 0. 0. 0. 0.
Problem 99 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 309 309 149 170 0 0 0 0
normalized size 1 1. 0.48 0.55 0. 0. 0. 0.
time (sec) N/A 0.78 0.591 0.334 0. 0. 0. 0.
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 275 275 207 300 443 775 0 0
normalized size 1 1. 0.75 1.09 1.61 2.82 0. 0.
time (sec) N/A 0.235 0.457 0.212 1.515 3.602 0. 0.
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 204 204 174 228 302 679 0 0
normalized size 1 1. 0.85 1.12 1.48 3.33 0. 0.
time (sec) N/A 0.127 0.279 0.178 1.499 3.004 0. 0.
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 177 177 158 197 205 614 0 0
normalized size 1 1. 0.89 1.11 1.16 3.47 0. 0.
time (sec) N/A 0.132 0.242 0.187 1.524 2.452 0. 0.
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 176 176 149 205 181 590 0 0
normalized size 1 1. 0.85 1.16 1.03 3.35 0. 0.
time (sec) N/A 0.139 0.269 0.185 0.979 2.235 0. 0.
Problem 104 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 213 213 134 193 236 385 0 0
normalized size 1 1. 0.63 0.91 1.11 1.81 0. 0.
time (sec) N/A 0.167 0.266 0.185 0.987 1.794 0. 0.
Problem 105 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 281 281 160 225 313 483 0 0
normalized size 1 1. 0.57 0.8 1.11 1.72 0. 0.
time (sec) N/A 0.201 0.333 0.189 1.018 1.871 0. 0.
Problem 106 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 278 278 168 212 331 509 332 0
normalized size 1 1. 0.6 0.76 1.19 1.83 1.19 0.
time (sec) N/A 0.237 0.287 0.181 0.994 2.088 51.106 0.
Problem 107 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 230 230 139 180 250 413 252 0
normalized size 1 1. 0.6 0.78 1.09 1.8 1.1 0.
time (sec) N/A 0.252 0.257 0.175 0.992 2.014 22.678 0.
Problem 108 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 370 370 176 286 0 0 0 0
normalized size 1 1. 0.48 0.77 0. 0. 0. 0.
time (sec) N/A 1.098 0.421 0.485 0. 0. 0. 0.
Problem 109 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 373 373 212 252 0 0 0 0
normalized size 1 1. 0.57 0.68 0. 0. 0. 0.
time (sec) N/A 1.047 0.808 0.417 0. 0. 0. 0.
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 519 519 921 411 0 0 0 0
normalized size 1 1. 1.77 0.79 0. 0. 0. 0.
time (sec) N/A 1.273 1.42 2.277 0. 0. 0. 0.
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F F
verified N/A NO NO TBD TBD TBD TBD TBD
size 459 441 860 513 0 0 0 0
normalized size 1 0.96 1.87 1.12 0. 0. 0. 0.
time (sec) N/A 1.229 0.317 0.454 0. 0. 0. 0.
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 469 469 849 302 0 0 0 0
normalized size 1 1. 1.81 0.64 0. 0. 0. 0.
time (sec) N/A 0.966 0.37 1.344 0. 0. 0. 0.
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 417 417 386 3157 0 0 0 0
normalized size 1 1. 0.93 7.57 0. 0. 0. 0.
time (sec) N/A 0.989 0.885 0.605 0. 0. 0. 0.
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 523 523 933 372 0 0 0 0
normalized size 1 1. 1.78 0.71 0. 0. 0. 0.
time (sec) N/A 1.261 1.739 2.456 0. 0. 0. 0.
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F(-1) F
verified N/A NO NO TBD TBD TBD TBD TBD
size 631 611 1278 870 0 0 0 0
normalized size 1 0.97 2.03 1.38 0. 0. 0. 0.
time (sec) N/A 1.548 4.816 0.779 0. 0. 0. 0.
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F(-1) F
verified N/A NO NO TBD TBD TBD TBD TBD
size 580 562 1208 661 0 0 0 0
normalized size 1 0.97 2.08 1.14 0. 0. 0. 0.
time (sec) N/A 1.463 1.216 0.461 0. 0. 0. 0.
Problem 117 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 147 147 345 844 0 1265 0 0
normalized size 1 1. 2.35 5.74 0. 8.61 0. 0.
time (sec) N/A 0.245 0.963 0.283 0. 1.975 0. 0.
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F C F(-2) F F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 542 542 0 3326 0 0 0 0
normalized size 1 1. 0. 6.14 0. 0. 0. 0.
time (sec) N/A 1.363 40.277 0.757 0. 0. 0. 0.
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F(-2) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 840 840 1270 2016 0 0 0 0
normalized size 1 1. 1.51 2.4 0. 0. 0. 0.
time (sec) N/A 3.088 1.49 17.249 0. 0. 0. 0.
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F(-2) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 786 786 1226 1880 0 0 0 0
normalized size 1 1. 1.56 2.39 0. 0. 0. 0.
time (sec) N/A 1.574 1.57 2.401 0. 0. 0. 0.
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F(-2) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 786 786 1216 1870 0 0 0 0
normalized size 1 1. 1.55 2.38 0. 0. 0. 0.
time (sec) N/A 2.836 1.543 1.619 0. 0. 0. 0.
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F(-2) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 844 844 1305 1952 0 0 0 0
normalized size 1 1. 1.55 2.31 0. 0. 0. 0.
time (sec) N/A 2.953 1.087 11.697 0. 0. 0. 0.
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F F F(-1) F
verified N/A NO NO TBD TBD TBD TBD TBD
size 778 760 2000 1779 0 0 0 0
normalized size 1 0.98 2.57 2.29 0. 0. 0. 0.
time (sec) N/A 1.709 7.487 0.846 0. 0. 0. 0.
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-2) B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 173 173 486 3343 0 2743 0 0
normalized size 1 1. 2.81 19.32 0. 15.86 0. 0.
time (sec) N/A 0.189 1.486 0.362 0. 2.978 0. 0.
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-2) B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 217 217 486 3301 0 2538 0 0
normalized size 1 1. 2.24 15.21 0. 11.7 0. 0.
time (sec) N/A 0.293 1.022 0.354 0. 2.895 0. 0.
Problem 126 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 741 741 0 5713 0 0 0 0
normalized size 1 1. 0. 7.71 0. 0. 0. 0.
time (sec) N/A 1.542 62.378 1.322 0. 0. 0. 0.
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F(-2) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 1272 1272 2022 3455 0 0 0 0
normalized size 1 1. 1.59 2.72 0. 0. 0. 0.
time (sec) N/A 2.263 6.201 3.527 0. 0. 0. 0.
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F(-2) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 1276 1276 2030 2537 0 0 0 0
normalized size 1 1. 1.59 1.99 0. 0. 0. 0.
time (sec) N/A 4.04 6.157 2.858 0. 0. 0. 0.
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C C F(-2) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 1272 1272 2015 3446 0 0 0 0
normalized size 1 1. 1.58 2.71 0. 0. 0. 0.
time (sec) N/A 4.91 6.063 6.369 0. 0. 0. 0.
Problem 130 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 447 447 409 0 0 4373 0 0
normalized size 1 1. 0.91 0. 0. 9.78 0. 0.
time (sec) N/A 1.395 3.014 1.95 0. 15.839 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 329 329 365 0 0 3636 0 0
normalized size 1 1. 1.11 0. 0. 11.05 0. 0.
time (sec) N/A 0.427 1.452 1.626 0. 7.637 0. 0.
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 221 221 307 0 0 3011 0 0
normalized size 1 1. 1.39 0. 0. 13.62 0. 0.
time (sec) N/A 0.357 1.287 1.395 0. 4.037 0. 0.
Problem 133 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 0.099 5.545 1.325 0. 0. 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 0.104 6.152 1.473 0. 0. 0. 0.
Problem 135 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 12.809 1.685 0. 0. 0. 0.
Problem 136 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 0.036 2.936 1.279 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 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.087 1.841 1.034 0. 0. 0. 0.
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 312 312 576 0 0 0 0 0
normalized size 1 1. 1.85 0. 0. 0. 0. 0.
time (sec) N/A 0.38 3.969 1.318 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 446 446 641 0 0 0 0 0
normalized size 1 1. 1.44 0. 0. 0. 0. 0.
time (sec) N/A 0.561 6.121 1.605 0. 0. 0. 0.
Problem 140 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 418 418 382 0 0 4365 0 0
normalized size 1 1. 0.91 0. 0. 10.44 0. 0.
time (sec) N/A 0.53 2.856 1.135 0. 17.743 0. 0.
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 297 297 342 0 0 3606 0 0
normalized size 1 1. 1.15 0. 0. 12.14 0. 0.
time (sec) N/A 0.432 1.48 0.888 0. 8.491 0. 0.
Problem 142 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 6.205 0.828 0. 0. 0. 0.
Problem 143 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 0.125 6.563 0.937 0. 0. 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 0.122 14.233 1.113 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 22 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.044 4.293 0.824 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 0.104 6.724 0.806 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 0.128 16.079 1.039 0. 0. 0. 0.
Problem 148 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 409 409 620 0 0 0 0 0
normalized size 1 1. 1.52 0. 0. 0. 0. 0.
time (sec) N/A 0.533 6.274 1.224 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 556 556 728 0 0 0 0 0
normalized size 1 1. 1.31 0. 0. 0. 0. 0.
time (sec) N/A 0.758 7.763 1.421 0. 0. 0. 0.
Problem 150 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 356 356 366 0 0 3663 0 0
normalized size 1 1. 1.03 0. 0. 10.29 0. 0.
time (sec) N/A 1.16 1.564 1.832 0. 9.047 0. 0.
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 251 251 406 0 0 3032 0 0
normalized size 1 1. 1.62 0. 0. 12.08 0. 0.
time (sec) N/A 0.33 1.266 1.794 0. 5.226 0. 0.
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 153 153 239 0 0 2419 0 0
normalized size 1 1. 1.56 0. 0. 15.81 0. 0.
time (sec) N/A 0.295 0.536 1.265 0. 3.582 0. 0.
Problem 153 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 0.095 3.1 1.22 0. 0. 0. 0.
Problem 154 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 0.111 22.189 1.105 0. 0. 0. 0.
Problem 155 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 6.828 1.578 0. 0. 0. 0.
Problem 156 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 0.035 1.012 1.223 0. 0. 0. 0.
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 221 221 501 0 0 0 0 0
normalized size 1 1. 2.27 0. 0. 0. 0. 0.
time (sec) N/A 0.258 4.01 1.015 0. 0. 0. 0.
Problem 158 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 346 346 612 0 0 0 0 0
normalized size 1 1. 1.77 0. 0. 0. 0. 0.
time (sec) N/A 0.485 4.64 1.263 0. 0. 0. 0.
Problem 159 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 278 278 436 0 0 3760 0 0
normalized size 1 1. 1.57 0. 0. 13.53 0. 0.
time (sec) N/A 1.117 1.423 1.541 0. 4.15 0. 0.
Problem 160 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 177 177 249 0 0 2867 0 0
normalized size 1 1. 1.41 0. 0. 16.2 0. 0.
time (sec) N/A 0.272 1.666 1.487 0. 2.889 0. 0.
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 87 87 135 0 0 829 0 0
normalized size 1 1. 1.55 0. 0. 9.53 0. 0.
time (sec) N/A 0.245 0.591 0.918 0. 2.396 0. 0.
Problem 162 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 30.269 0.841 0. 0. 0. 0.
Problem 163 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 0.133 36.645 0.939 0. 0. 0. 0.
Problem 164 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 0.111 9.462 1.534 0. 0. 0. 0.
Problem 165 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 0.106 4.674 1.47 0. 0. 0. 0.
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 92 92 334 0 0 0 0 0
normalized size 1 1. 3.63 0. 0. 0. 0. 0.
time (sec) N/A 0.079 1.324 1.067 0. 0. 0. 0.
Problem 167 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 249 249 501 0 0 0 0 0
normalized size 1 1. 2.01 0. 0. 0. 0. 0.
time (sec) N/A 0.287 4.461 0.809 0. 0. 0. 0.
Problem 168 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 272 272 348 0 0 5094 0 0
normalized size 1 1. 1.28 0. 0. 18.73 0. 0.
time (sec) N/A 1.281 1.955 1.441 0. 4.44 0. 0.
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 179 179 218 0 0 1635 0 0
normalized size 1 1. 1.22 0. 0. 9.13 0. 0.
time (sec) N/A 0.264 0.369 1.405 0. 3.22 0. 0.
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 154 154 204 0 0 1447 0 0
normalized size 1 1. 1.32 0. 0. 9.4 0. 0.
time (sec) N/A 0.291 0.31 0.935 0. 3.175 0. 0.
Problem 171 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 42.658 0.829 0. 0. 0. 0.
Problem 172 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 0.142 52.642 0.951 0. 0. 0. 0.
Problem 173 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 0.122 13.681 1.511 0. 0. 0. 0.
Problem 174 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 0.111 13.229 1.481 0. 0. 0. 0.
Problem 175 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 246 246 488 0 0 0 0 0
normalized size 1 1. 1.98 0. 0. 0. 0. 0.
time (sec) N/A 0.246 2.474 1.457 0. 0. 0. 0.
Problem 176 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 266 266 517 0 0 0 0 0
normalized size 1 1. 1.94 0. 0. 0. 0. 0.
time (sec) N/A 0.206 5.085 1.012 0. 0. 0. 0.
Problem 177 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 596 576 0 0 0 0 0 0
normalized size 1 0.97 0. 0. 0. 0. 0. 0.
time (sec) N/A 2.545 0.241 2.759 0. 0. 0. 0.
Problem 178 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 372 352 0 0 0 0 0 0
normalized size 1 0.95 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.432 0.153 2.111 0. 0. 0. 0.
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F(-2) F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 206 192 0 0 0 0 0 0
normalized size 1 0.93 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.179 0.117 1.873 0. 0. 0. 0.
Problem 180 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 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.076 2.357 1.319 0. 0. 0. 0.
Problem 181 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 0.075 2.632 1.441 0. 0. 0. 0.
Problem 182 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 0.11 1.051 0.862 0. 0. 0. 0.
Problem 183 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 27 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.099 0.118 1.079 0. 0. 0. 0.
Problem 184 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 27 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.1 1.344 1.279 0. 0. 0. 0.
Problem 185 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 0.11 1.752 1.191 0. 0. 0. 0.
Problem 186 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 473 473 213 0 0 852 0 0
normalized size 1 1. 0.45 0. 0. 1.8 0. 0.
time (sec) N/A 1.579 0.419 1.938 0. 2.176 0. 0.
Problem 187 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 316 316 178 0 0 705 0 0
normalized size 1 1. 0.56 0. 0. 2.23 0. 0.
time (sec) N/A 1.383 0.36 2.082 0. 1.902 0. 0.
Problem 188 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 159 159 140 0 0 575 0 0
normalized size 1 1. 0.88 0. 0. 3.62 0. 0.
time (sec) N/A 0.164 0.336 1.24 0. 2.112 0. 0.
Problem 189 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 0.091 0.391 1.691 0. 0. 0. 0.
Problem 190 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 0.102 3.373 1.526 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 [11] 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 9 6 1. 10 0.6
2 A 5 5 1. 10 0.5
3 A 8 6 1. 10 0.6
4 A 4 4 1. 8 0.5
5 A 7 5 1. 6 0.833
6 A 6 6 1. 10 0.6
7 A 4 3 1. 10 0.3
8 A 4 4 1. 10 0.4
9 A 5 5 1. 10 0.5
10 A 14 9 1. 10 0.9
11 A 10 10 1. 10 1.
12 A 11 8 1. 10 0.8
13 A 7 7 1. 8 0.875
14 A 9 6 1. 6 1.
15 A 7 7 1. 10 0.7
16 A 5 3 1. 10 0.3
17 A 6 6 1. 10 0.6
18 A 8 6 1. 10 0.6
19 A 8 6 1. 12 0.5
20 A 6 4 1. 12 0.333
21 A 6 6 1. 12 0.5
22 A 4 4 1. 12 0.333
23 A 4 4 1. 12 0.333
24 A 2 2 1. 10 0.2
25 A 3 2 1. 8 0.25
26 A 6 6 1. 12 0.5
27 A 2 2 1. 12 0.167
28 A 5 5 1. 12 0.417
29 A 4 4 1. 12 0.333
30 A 7 5 1. 12 0.417
31 A 6 4 1. 12 0.333
32 A 9 5 1. 12 0.417
33 A 5 5 1. 14 0.357
34 A 8 6 1. 14 0.429
35 A 4 4 1. 12 0.333
36 A 7 5 1. 10 0.5
37 A 6 6 1. 14 0.429
38 A 4 3 1. 14 0.214
39 A 4 3 1. 14 0.214
40 A 5 5 1. 14 0.357
41 A 5 3 1. 14 0.214
42 A 10 10 1. 14 0.714
43 A 11 8 1. 14 0.571
44 A 7 7 1. 12 0.583
45 A 9 6 1. 10 0.6
46 A 7 7 1. 14 0.5
47 A 5 3 1. 14 0.214
48 A 6 6 1. 14 0.429
49 A 8 6 1. 14 0.429
50 A 10 6 1. 14 0.429
51 A 0 0 0. 0 0.
52 A 0 0 0. 0 0.
53 A 0 0 0. 0 0.
54 A 4 4 1. 14 0.286
55 A 6 6 1. 14 0.429
56 A 9 5 1. 14 0.357
57 A 0 0 0. 0 0.
58 A 0 0 0. 0 0.
59 A 0 0 0. 0 0.
60 A 5 5 1. 14 0.357
61 A 7 7 1. 14 0.5
62 A 11 6 1. 14 0.429
63 A 0 0 0. 0 0.
64 A 0 0 0. 0 0.
65 A 0 0 0. 0 0.
66 A 6 5 1. 14 0.357
67 A 8 7 1. 14 0.5
68 A 13 6 1. 14 0.429
69 A 0 0 0. 0 0.
70 A 0 0 0. 0 0.
71 A 3 3 1. 14 0.214
72 A 0 0 0. 0 0.
73 A 0 0 0. 0 0.
74 A 9 7 1. 16 0.438
75 A 8 7 1. 16 0.438
76 A 7 7 1. 14 0.5
77 A 3 2 1. 8 0.25
78 A 4 2 1. 16 0.125
79 A 8 7 1. 16 0.438
80 A 11 8 1. 16 0.5
81 A 21 12 1. 18 0.667
82 A 14 10 1. 18 0.556
83 A 8 8 1. 18 0.444
84 A 5 5 1. 18 0.278
85 A 11 10 1. 18 0.556
86 A 18 13 1. 18 0.722
87 A 0 0 0. 0 0.
88 A 6 6 1. 19 0.316
89 A 5 6 1. 19 0.316
90 A 4 4 1. 16 0.25
91 A 3 4 1. 19 0.21
92 A 4 5 1. 19 0.263
93 A 5 6 1. 19 0.316
94 A 6 6 1. 19 0.316
95 A 5 5 1. 19 0.263
96 A 5 5 1. 19 0.263
97 A 7 6 1. 17 0.353
98 A 12 12 1. 19 0.632
99 A 14 14 1. 19 0.737
100 A 6 7 1. 21 0.333
101 A 5 6 1. 18 0.333
102 A 5 6 1. 21 0.286
103 A 5 6 1. 21 0.286
104 A 5 6 1. 21 0.286
105 A 6 7 1. 21 0.333
106 A 5 6 1. 21 0.286
107 A 7 6 1. 19 0.316
108 A 13 14 1. 21 0.667
109 A 15 16 1. 21 0.762
110 A 24 11 1. 21 0.524
111 A 26 9 0.96 19 0.474
112 A 19 7 1. 18 0.389
113 A 19 7 1. 21 0.333
114 A 24 10 1. 21 0.476
115 A 32 15 0.97 21 0.714
116 A 30 13 0.97 21 0.619
117 A 8 6 1. 19 0.316
118 A 25 11 1. 21 0.524
119 A 50 13 1. 21 0.619
120 A 27 10 1. 21 0.476
121 A 47 11 1. 18 0.611
122 A 50 13 1. 21 0.619
123 A 35 14 0.98 21 0.667
124 A 6 7 1. 21 0.333
125 A 9 7 1. 19 0.368
126 A 30 12 1. 21 0.571
127 A 35 11 1. 21 0.524
128 A 63 12 1. 21 0.571
129 A 81 12 1. 18 0.667
130 A 12 12 1. 23 0.522
131 A 11 12 1. 23 0.522
132 A 10 10 1. 21 0.476
133 A 0 0 0. 0 0.
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 9 10 1. 23 0.435
139 A 10 11 1. 23 0.478
140 A 12 12 1. 23 0.522
141 A 11 11 1. 21 0.524
142 A 0 0 0. 0 0.
143 A 0 0 0. 0 0.
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 10 11 1. 23 0.478
149 A 11 11 1. 23 0.478
150 A 11 12 1. 23 0.522
151 A 10 12 1. 23 0.522
152 A 9 9 1. 21 0.429
153 A 0 0 0. 0 0.
154 A 0 0 0. 0 0.
155 A 0 0 0. 0 0.
156 A 0 0 0. 0 0.
157 A 9 10 1. 23 0.435
158 A 9 11 1. 23 0.478
159 A 10 11 1. 23 0.478
160 A 9 11 1. 23 0.478
161 A 5 5 1. 21 0.238
162 A 0 0 0. 0 0.
163 A 0 0 0. 0 0.
164 A 0 0 0. 0 0.
165 A 0 0 0. 0 0.
166 A 4 5 1. 20 0.25
167 A 8 10 1. 23 0.435
168 A 10 11 1. 23 0.478
169 A 7 8 1. 23 0.348
170 A 6 6 1. 21 0.286
171 A 0 0 0. 0 0.
172 A 0 0 0. 0 0.
173 A 0 0 0. 0 0.
174 A 0 0 0. 0 0.
175 A 8 9 1. 23 0.391
176 A 8 10 1. 20 0.5
177 A 5 6 0.97 23 0.261
178 A 5 6 0.95 23 0.261
179 A 4 5 0.93 21 0.238
180 A 0 0 0. 0 0.
181 A 0 0 0. 0 0.
182 A 0 0 0. 0 0.
183 A 0 0 0. 0 0.
184 A 0 0 0. 0 0.
185 A 0 0 0. 0 0.
186 A 15 10 1. 26 0.385
187 A 12 10 1. 26 0.385
188 A 7 8 1. 26 0.308
189 A 0 0 0. 0 0.
190 A 0 0 0. 0 0.

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