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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, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 77, 79, 83, 85, 89, 91, 95, 97, 98, 104, 106, 110, 112, 116, 118, 119, 120, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 174, 176, 177, 179, 181, 182, 184, 186, 187, 189, 191, 192, 194, 196, 197, 199, 201, 202, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227 }

B grade: { 39, 41, 157, 209 }

C grade: { 74, 75, 76, 78, 80, 81, 82, 84, 86, 87, 88, 90, 92, 93, 94, 96, 99, 100, 101, 102, 103, 105, 107, 108, 109, 111, 113, 114, 115, 117, 121, 173, 175, 178, 180, 183, 185, 188, 190, 193, 195, 198, 200, 203, 204, 205, 206, 207, 208 }

F grade: { }

2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 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, 123, 124, 125, 126, 127, 128, 129, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 179, 181, 182, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 201, 202, 203, 204, 205, 206, 207, 208, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227 }

B grade: { 156, 178, 180, 183, 184, 185, 198, 199, 200 }

C grade: { 130, 132, 133 }

F grade: { 28, 39, 121, 122, 131, 157, 209, 210, 211, 212, 213, 214 }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 14, 16, 19, 21, 22, 24, 26, 33, 35, 37, 49, 50, 58, 65, 66, 72, 73, 123, 140, 141, 142, 143, 145, 146, 147, 148, 150, 153, 155, 161, 162, 171, 172, 176, 177, 181, 182, 186, 187, 191, 192, 196, 197, 201, 202, 220, 221, 222, 223, 224, 225, 226, 227

B grade: { }

C grade: { }

F grade: { 6, 13, 15, 17, 18, 20, 23, 25, 27, 28, 29, 30, 31, 32, 34, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 67, 68, 69, 70, 71, 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, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 144, 149, 151, 152, 154, 156, 157, 158, 159, 160, 163, 164, 165, 166, 167, 168, 169, 170, 173, 174, 175, 178, 179, 180, 183, 184, 185, 188, 189, 190, 193, 194, 195, 198, 199, 200, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 8, 10, 11, 12, 13, 14, 15, 16, 19, 21, 22, 23, 24, 25, 26, 32, 33, 34, 35, 36, 37, 49, 50, 58, 59, 65, 66, 72, 73, 119, 120, 123, 124, 129, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 146, 148, 149, 150, 153, 154, 155, 161, 162, 166, 167, 171, 172, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227 }

B grade: { 7, 9, 145, 147 }

C grade: { }

F grade: { 6, 17, 18, 20, 27, 28, 29, 30, 31, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 63, 64, 67, 68, 69, 70, 71, 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, 121, 122, 125, 126, 127, 128, 130, 131, 132, 133, 144, 151, 152, 156, 157, 158, 159, 160, 163, 164, 165, 168, 169, 170, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 12, 13, 14, 15, 16, 22, 23, 24, 25, 26, 32, 33, 34, 35, 36, 37, 49, 50, 58, 59, 65, 66, 72, 73, 79, 85, 97, 98, 106, 112, 119, 120, 123, 124, 126, 127, 128, 129, 134, 135, 137, 138, 139, 140, 141, 142, 143, 145, 146, 147, 148, 149, 150, 153, 154, 155, 161, 162, 166, 167, 171, 172, 176, 177, 181, 182, 191, 192, 196, 197, 201, 204, 205, 216, 220, 221, 222, 223, 224, 225, 226, 227 }

B grade: { }

C grade: { 7, 8, 9, 10, 11 }

F grade: { 6, 17, 18, 19, 20, 21, 27, 28, 29, 30, 31, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 63, 64, 67, 68, 69, 70, 71, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 99, 100, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 118, 121, 122, 125, 130, 131, 132, 133, 136, 144, 151, 152, 156, 157, 158, 159, 160, 163, 164, 165, 168, 169, 170, 173, 174, 175, 178, 179, 180, 183, 184, 185, 186, 187, 188, 189, 190, 193, 194, 195, 198, 199, 200, 202, 203, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 217, 218, 219 }

2.1.7 Giac

A grade: { 1, 2, 3, 4, 5, 7, 9, 11, 12, 13, 14, 15, 16, 22, 23, 24, 25, 26, 32, 33, 34, 35, 36, 37, 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, 79, 83, 85, 89, 91, 97, 98, 106, 112, 118, 119, 120, 123, 124, 125, 126, 127, 128, 129, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 148, 149, 150, 153, 155, 158, 159, 160, 161, 162, 166, 167, 171, 172, 174, 176, 177, 181, 182, 186, 187, 188, 189, 190, 191, 192, 196, 197, 201, 202, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227 }

B grade: { 8, 10, 19, 21, 74, 75, 76, 77, 78, 80, 81, 82, 84, 86, 87, 88, 90, 92, 93, 94, 95, 96, 145, 146, 147, 154, 163, 164, 165, 168, 169, 170, 173, 175, 178, 179, 180, 183, 184, 185 }

C grade: { }

F grade: { 6, 17, 18, 20, 27, 28, 29, 30, 31, 38, 39, 40, 41, 99, 100, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 121, 122, 130, 131, 132, 133, 144, 151, 152, 156, 157, 193, 194, 195, 198, 199, 200, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214 }

2.2 Detailed conclusion table per each integral for all CAS systems

Detailed conclusion table per each integral is given by table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given just an F.

In this table,the column normalized size is defined as \(\frac{\text{antiderivative leaf size}}{\text{optimal antiderivative leaf size}}\)

Problem 1 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 75 75 51 72 96 113 75 90
normalized size 1 1. 0.68 0.96 1.28 1.51 1. 1.2
time (sec) N/A 0.048 0.031 0.003 1.486 2.012 2.185 1.147
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 69 69 54 60 99 109 66 77
normalized size 1 1. 0.78 0.87 1.43 1.58 0.96 1.12
time (sec) N/A 0.031 0.032 0.004 1.462 1.958 1.087 1.177
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 54 54 42 52 68 92 53 63
normalized size 1 1. 0.78 0.96 1.26 1.7 0.98 1.17
time (sec) N/A 0.035 0.025 0.003 1.457 1.896 0.587 1.163
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 42 40 70 88 42 50
normalized size 1 1. 0.93 0.89 1.56 1.96 0.93 1.11
time (sec) N/A 0.016 0.016 0.002 1.456 1.966 0.241 1.138
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 26 26 26 27 35 57 24 35
normalized size 1 1. 1. 1.04 1.35 2.19 0.92 1.35
time (sec) N/A 0.008 0.007 0.002 1.441 1.916 0.15 1.16
Problem 6 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 51 51 51 68 0 0 0 0
normalized size 1 1. 1. 1.33 0. 0. 0. 0.
time (sec) N/A 0.057 0.017 0.063 0. 0. 0. 0.
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B C A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 34 29 51 203 34 65
normalized size 1 1. 1.26 1.07 1.89 7.52 1.26 2.41
time (sec) N/A 0.022 0.011 0.003 1.455 2.478 1.615 1.132
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A C B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 34 34 31 38 38 65 53 92
normalized size 1 1. 0.91 1.12 1.12 1.91 1.56 2.71
time (sec) N/A 0.016 0.014 0.003 1.463 2.333 1.388 1.114
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B C A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 56 56 67 53 81 259 110 95
normalized size 1 1. 1.2 0.95 1.45 4.62 1.96 1.7
time (sec) N/A 0.035 0.024 0.004 1.453 2.491 3.007 1.138
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A C B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 58 58 41 58 68 88 102 176
normalized size 1 1. 0.71 1. 1.17 1.52 1.76 3.03
time (sec) N/A 0.022 0.022 0.003 1.439 2.029 2.673 1.136
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A C A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 80 80 72 73 111 289 184 120
normalized size 1 1. 0.9 0.91 1.39 3.61 2.3 1.5
time (sec) N/A 0.047 0.062 0.003 1.451 2.197 6.438 1.157
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 120 120 82 76 138 189 121 135
normalized size 1 1. 0.68 0.63 1.15 1.58 1.01 1.12
time (sec) N/A 0.196 0.056 0.05 1.496 2.002 4.149 1.173
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 98 98 74 93 0 162 97 117
normalized size 1 1. 0.76 0.95 0. 1.65 0.99 1.19
time (sec) N/A 0.17 0.038 0.054 0. 1.954 2.381 1.18
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 82 82 63 59 97 143 83 92
normalized size 1 1. 0.77 0.72 1.18 1.74 1.01 1.12
time (sec) N/A 0.126 0.046 0.048 1.466 1.976 1.16 1.166
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 57 63 0 123 58 74
normalized size 1 1. 0.95 1.05 0. 2.05 0.97 1.23
time (sec) N/A 0.097 0.025 0.048 0. 1.927 0.59 1.137
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 35 35 35 37 45 89 37 45
normalized size 1 1. 1. 1.06 1.29 2.54 1.06 1.29
time (sec) N/A 0.047 0.016 0.046 1.434 1.874 0.239 1.139
Problem 17 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 73 73 73 101 0 0 0 0
normalized size 1 1. 1. 1.38 0. 0. 0. 0.
time (sec) N/A 0.093 0.02 0.054 0. 0. 0. 0.
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 74 74 98 135 0 0 0 0
normalized size 1 1. 1.32 1.82 0. 0. 0. 0.
time (sec) N/A 0.107 0.132 0.105 0. 0. 0. 0.
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 43 43 43 42 53 112 0 117
normalized size 1 1. 1. 0.98 1.23 2.6 0. 2.72
time (sec) N/A 0.078 0.028 0.051 1.524 2.396 0. 1.19
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 124 124 152 173 0 0 0 0
normalized size 1 1. 1.23 1.4 0. 0. 0. 0.
time (sec) N/A 0.177 0.571 0.19 0. 0. 0. 0.
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 87 87 69 76 100 149 0 223
normalized size 1 1. 0.79 0.87 1.15 1.71 0. 2.56
time (sec) N/A 0.152 0.041 0.053 1.496 2.382 0. 1.318
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 201 201 122 159 231 265 202 236
normalized size 1 1. 0.61 0.79 1.15 1.32 1. 1.17
time (sec) N/A 0.403 0.068 0.056 1.501 2.373 7.922 1.144
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 167 167 115 151 0 234 167 190
normalized size 1 1. 0.69 0.9 0. 1.4 1. 1.14
time (sec) N/A 0.315 0.076 0.056 0. 2.432 4.587 1.219
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 136 136 95 106 162 189 134 158
normalized size 1 1. 0.7 0.78 1.19 1.39 0.99 1.16
time (sec) N/A 0.241 0.05 0.051 1.514 2.256 2.458 1.156
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 99 99 85 90 0 170 99 112
normalized size 1 1. 0.86 0.91 0. 1.72 1. 1.13
time (sec) N/A 0.156 0.041 0.05 0. 2.426 1.196 1.141
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 60 57 80 116 60 76
normalized size 1 1. 1. 0.95 1.33 1.93 1. 1.27
time (sec) N/A 0.081 0.019 0.049 1.449 2.268 0.573 1.119
Problem 27 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 101 101 101 135 0 0 0 0
normalized size 1 1. 1. 1.34 0. 0. 0. 0.
time (sec) N/A 0.111 0.02 0.07 0. 0. 0. 0.
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 122 122 139 0 0 0 0 0
normalized size 1 1. 1.14 0. 0. 0. 0. 0.
time (sec) N/A 0.175 0.11 0.207 0. 0. 0. 0.
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 102 102 92 113 0 0 0 0
normalized size 1 1. 0.9 1.11 0. 0. 0. 0.
time (sec) N/A 0.175 0.192 0.139 0. 0. 0. 0.
Problem 30 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 192 192 165 272 0 0 0 0
normalized size 1 1. 0.86 1.42 0. 0. 0. 0.
time (sec) N/A 0.304 0.739 0.175 0. 0. 0. 0.
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 169 169 149 176 0 0 0 0
normalized size 1 1. 0.88 1.04 0. 0. 0. 0.
time (sec) N/A 0.29 0.471 0.188 0. 0. 0. 0.
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 282 282 167 318 0 383 275 331
normalized size 1 1. 0.59 1.13 0. 1.36 0.98 1.17
time (sec) N/A 0.874 0.088 0.09 0. 2.456 24.165 1.188
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 250 250 150 197 278 352 248 286
normalized size 1 1. 0.6 0.79 1.11 1.41 0.99 1.14
time (sec) N/A 0.669 0.084 0.058 1.525 2.337 13.673 1.169
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 198 198 135 207 0 292 197 234
normalized size 1 1. 0.68 1.05 0. 1.47 0.99 1.18
time (sec) N/A 0.52 0.067 0.06 0. 2.329 8.284 1.205
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 166 166 114 130 197 247 165 189
normalized size 1 1. 0.69 0.78 1.19 1.49 0.99 1.14
time (sec) N/A 0.366 0.072 0.052 1.529 2.427 4.373 1.178
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 112 112 96 113 0 205 110 136
normalized size 1 1. 0.86 1.01 0. 1.83 0.98 1.21
time (sec) N/A 0.237 0.038 0.053 0. 2.328 2.343 1.161
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 69 69 69 67 100 149 70 88
normalized size 1 1. 1. 0.97 1.45 2.16 1.01 1.28
time (sec) N/A 0.12 0.022 0.047 1.485 2.382 1.104 1.142
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 119 119 119 168 0 0 0 0
normalized size 1 1. 1. 1.41 0. 0. 0. 0.
time (sec) N/A 0.125 0.021 0.069 0. 0. 0. 0.
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 176 176 549 0 0 0 0 0
normalized size 1 1. 3.12 0. 0. 0. 0. 0.
time (sec) N/A 0.204 1.081 0.206 0. 0. 0. 0.
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 121 121 115 149 0 0 0 0
normalized size 1 1. 0.95 1.23 0. 0. 0. 0.
time (sec) N/A 0.213 0.358 0.124 0. 0. 0. 0.
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 304 304 1475 451 0 0 0 0
normalized size 1 1. 4.85 1.48 0. 0. 0. 0.
time (sec) N/A 0.421 12.067 0.184 0. 0. 0. 0.
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 40 40 0 0 0 63
normalized size 1 1. 0.73 0.73 0. 0. 0. 1.15
time (sec) N/A 0.091 0.103 0.058 0. 0. 0. 1.159
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 43 43 33 33 0 0 0 50
normalized size 1 1. 0.77 0.77 0. 0. 0. 1.16
time (sec) N/A 0.079 0.087 0.055 0. 0. 0. 1.156
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 41 41 31 31 0 0 0 47
normalized size 1 1. 0.76 0.76 0. 0. 0. 1.15
time (sec) N/A 0.075 0.074 0.047 0. 0. 0. 1.122
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 24 24 0 0 0 34
normalized size 1 1. 0.83 0.83 0. 0. 0. 1.17
time (sec) N/A 0.064 0.062 0.046 0. 0. 0. 1.177
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 20 22 0 0 0 31
normalized size 1 1. 0.74 0.81 0. 0. 0. 1.15
time (sec) N/A 0.06 0.053 0.045 0. 0. 0. 1.172
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 14 14 14 13 0 0 0 16
normalized size 1 1. 1. 0.93 0. 0. 0. 1.14
time (sec) N/A 0.035 0.019 0.043 0. 0. 0. 1.161
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 10 10 10 11 0 0 0 14
normalized size 1 1. 1. 1.1 0. 0. 0. 1.4
time (sec) N/A 0.015 0.024 0.041 0. 0. 0. 1.118
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 0.23 0.145 0. 0. 0. 0.
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.014 0.855 0.188 0. 0. 0. 0.
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-1) F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 82 82 86 105 0 0 0 97
normalized size 1 1. 1.05 1.28 0. 0. 0. 1.18
time (sec) N/A 0.079 0.158 0.062 0. 0. 0. 1.186
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-1) F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 70 70 63 78 0 0 0 84
normalized size 1 1. 0.9 1.11 0. 0. 0. 1.2
time (sec) N/A 0.064 0.163 0.056 0. 0. 0. 1.168
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-1) F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 68 68 61 81 0 0 0 81
normalized size 1 1. 0.9 1.19 0. 0. 0. 1.19
time (sec) N/A 0.063 0.16 0.05 0. 0. 0. 1.175
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-1) F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 56 56 50 54 0 0 0 68
normalized size 1 1. 0.89 0.96 0. 0. 0. 1.21
time (sec) N/A 0.05 0.139 0.045 0. 0. 0. 1.188
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-1) F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 54 54 50 57 0 0 0 65
normalized size 1 1. 0.93 1.06 0. 0. 0. 1.2
time (sec) N/A 0.046 0.123 0.047 0. 0. 0. 1.176
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-1) F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 38 38 37 30 0 0 0 49
normalized size 1 1. 0.97 0.79 0. 0. 0. 1.29
time (sec) N/A 0.024 0.085 0.045 0. 0. 0. 1.219
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 35 35 35 32 0 0 0 45
normalized size 1 1. 1. 0.91 0. 0. 0. 1.29
time (sec) N/A 0.081 0.041 0.046 0. 0. 0. 1.142
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 0.012 0.96 0.146 0. 0. 0. 0.
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-1) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 16.643 0.206 0. 0. 0. 0.
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 98 98 103 121 0 0 0 116
normalized size 1 1. 1.05 1.23 0. 0. 0. 1.18
time (sec) N/A 0.344 0.13 0.059 0. 0. 0. 1.231
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 83 83 70 82 0 0 0 101
normalized size 1 1. 0.84 0.99 0. 0. 0. 1.22
time (sec) N/A 0.305 0.152 0.055 0. 0. 0. 1.201
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 82 82 65 82 0 0 0 97
normalized size 1 1. 0.79 1. 0. 0. 0. 1.18
time (sec) N/A 0.243 0.132 0.051 0. 0. 0. 1.219
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 63 63 63 43 0 0 0 77
normalized size 1 1. 1. 0.68 0. 0. 0. 1.22
time (sec) N/A 0.165 0.039 0.044 0. 0. 0. 1.175
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 51 51 47 43 0 0 0 58
normalized size 1 1. 0.92 0.84 0. 0. 0. 1.14
time (sec) N/A 0.083 0.031 0.045 0. 0. 0. 1.158
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 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.012 0.708 0.149 0. 0. 0. 0.
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 9.133 0.207 0. 0. 0. 0.
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 158 158 159 171 0 0 0 186
normalized size 1 1. 1.01 1.08 0. 0. 0. 1.18
time (sec) N/A 0.338 0.17 0.059 0. 0. 0. 1.237
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 143 143 107 114 0 0 0 169
normalized size 1 1. 0.75 0.8 0. 0. 0. 1.18
time (sec) N/A 0.291 0.255 0.056 0. 0. 0. 1.202
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 141 141 129 117 0 0 0 163
normalized size 1 1. 0.91 0.83 0. 0. 0. 1.16
time (sec) N/A 0.312 0.12 0.056 0. 0. 0. 1.193
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 97 97 86 60 0 0 0 112
normalized size 1 1. 0.89 0.62 0. 0. 0. 1.15
time (sec) N/A 0.166 0.103 0.046 0. 0. 0. 1.156
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 78 78 71 63 0 0 0 89
normalized size 1 1. 0.91 0.81 0. 0. 0. 1.14
time (sec) N/A 0.156 0.044 0.045 0. 0. 0. 1.152
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 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.026 2.79 0.153 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 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.016 27.256 0.214 0. 0. 0. 0.
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 121 121 212 143 0 0 0 425
normalized size 1 1. 1.75 1.18 0. 0. 0. 3.51
time (sec) N/A 0.281 0.266 0.096 0. 0. 0. 1.329
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 95 95 125 91 0 0 0 255
normalized size 1 1. 1.32 0.96 0. 0. 0. 2.68
time (sec) N/A 0.195 0.11 0.08 0. 0. 0. 1.288
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 86 86 122 96 0 0 0 284
normalized size 1 1. 1.42 1.12 0. 0. 0. 3.3
time (sec) N/A 0.184 0.185 0.079 0. 0. 0. 1.274
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 59 59 49 42 0 0 0 120
normalized size 1 1. 0.83 0.71 0. 0. 0. 2.03
time (sec) N/A 0.151 0.036 0.066 0. 0. 0. 1.248
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 44 44 76 49 0 0 0 142
normalized size 1 1. 1.73 1.11 0. 0. 0. 3.23
time (sec) N/A 0.09 0.034 0.065 0. 0. 0. 1.245
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.012 0.388 0.096 0. 0. 0. 0.
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F(-1) B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 282 282 185 193 0 0 0 586
normalized size 1 1. 0.66 0.68 0. 0. 0. 2.08
time (sec) N/A 0.515 0.124 0.104 0. 0. 0. 1.348
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 157 157 128 121 0 0 0 363
normalized size 1 1. 0.82 0.77 0. 0. 0. 2.31
time (sec) N/A 0.368 0.072 0.089 0. 0. 0. 1.327
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 147 147 125 130 0 0 0 390
normalized size 1 1. 0.85 0.88 0. 0. 0. 2.65
time (sec) N/A 0.302 0.086 0.087 0. 0. 0. 1.297
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 89 89 64 64 0 0 0 174
normalized size 1 1. 0.72 0.72 0. 0. 0. 1.96
time (sec) N/A 0.179 0.066 0.076 0. 0. 0. 1.281
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 75 75 66 72 0 0 0 194
normalized size 1 1. 0.88 0.96 0. 0. 0. 2.59
time (sec) N/A 0.101 0.026 0.071 0. 0. 0. 1.295
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 0.399 0.095 0. 0. 0. 0.
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F(-1) B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 298 298 212 233 0 0 0 738
normalized size 1 1. 0.71 0.78 0. 0. 0. 2.48
time (sec) N/A 0.79 0.192 0.109 0. 0. 0. 1.453
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F(-1) B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 205 205 140 154 0 0 0 466
normalized size 1 1. 0.68 0.75 0. 0. 0. 2.27
time (sec) N/A 0.589 0.127 0.094 0. 0. 0. 1.323
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F(-1) B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 178 178 122 156 0 0 0 491
normalized size 1 1. 0.69 0.88 0. 0. 0. 2.76
time (sec) N/A 0.457 0.119 0.09 0. 0. 0. 1.315
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 119 119 73 79 0 0 0 225
normalized size 1 1. 0.61 0.66 0. 0. 0. 1.89
time (sec) N/A 0.287 0.089 0.078 0. 0. 0. 1.234
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F(-1) B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 88 88 76 88 0 0 0 244
normalized size 1 1. 0.86 1. 0. 0. 0. 2.77
time (sec) N/A 0.16 0.037 0.073 0. 0. 0. 1.32
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) F(-2) F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.012 0.391 0.097 0. 0. 0. 0.
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 106 106 192 72 0 0 0 273
normalized size 1 1. 1.81 0.68 0. 0. 0. 2.58
time (sec) N/A 0.105 0.1 0.078 0. 0. 0. 1.411
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 65 65 130 43 0 0 0 153
normalized size 1 1. 2. 0.66 0. 0. 0. 2.35
time (sec) N/A 0.078 0.068 0.07 0. 0. 0. 1.358
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 71 71 126 50 0 0 0 182
normalized size 1 1. 1.77 0.7 0. 0. 0. 2.56
time (sec) N/A 0.079 0.082 0.069 0. 0. 0. 1.351
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 28 28 28 21 0 0 0 69
normalized size 1 1. 1. 0.75 0. 0. 0. 2.46
time (sec) N/A 0.04 0.023 0.054 0. 0. 0. 1.312
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 31 31 68 26 0 0 0 92
normalized size 1 1. 2.19 0.84 0. 0. 0. 2.97
time (sec) N/A 0.023 0.024 0.049 0. 0. 0. 1.246
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 0.309 0.08 0. 0. 0. 0.
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 3.469 0.154 0. 0. 0. 0.
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 171 171 306 182 0 0 0 0
normalized size 1 1. 1.79 1.06 0. 0. 0. 0.
time (sec) N/A 0.146 0.287 0.109 0. 0. 0. 0.
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 127 127 226 121 0 0 0 0
normalized size 1 1. 1.78 0.95 0. 0. 0. 0.
time (sec) N/A 0.104 0.483 0.092 0. 0. 0. 0.
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 136 136 233 140 0 0 0 0
normalized size 1 1. 1.71 1.03 0. 0. 0. 0.
time (sec) N/A 0.095 0.2 0.089 0. 0. 0. 0.
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 91 91 154 81 0 0 0 0
normalized size 1 1. 1.69 0.89 0. 0. 0. 0.
time (sec) N/A 0.065 0.396 0.074 0. 0. 0. 0.
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 97 97 159 96 0 0 0 0
normalized size 1 1. 1.64 0.99 0. 0. 0. 0.
time (sec) N/A 0.069 0.109 0.079 0. 0. 0. 0.
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 44 42 0 0 0 0
normalized size 1 1. 0.8 0.76 0. 0. 0. 0.
time (sec) N/A 0.031 0.048 0.066 0. 0. 0. 0.
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 59 59 86 66 0 0 0 0
normalized size 1 1. 1.46 1.12 0. 0. 0. 0.
time (sec) N/A 0.087 0.035 0.07 0. 0. 0. 0.
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.012 0.446 0.095 0. 0. 0. 0.
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 235 235 322 173 0 0 0 0
normalized size 1 1. 1.37 0.74 0. 0. 0. 0.
time (sec) N/A 0.41 1.634 0.102 0. 0. 0. 0.
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 126 126 203 107 0 0 0 0
normalized size 1 1. 1.61 0.85 0. 0. 0. 0.
time (sec) N/A 0.325 0.891 0.085 0. 0. 0. 0.
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 125 125 220 115 0 0 0 0
normalized size 1 1. 1.76 0.92 0. 0. 0. 0.
time (sec) N/A 0.286 0.821 0.085 0. 0. 0. 0.
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 89 89 61 56 0 0 0 0
normalized size 1 1. 0.69 0.63 0. 0. 0. 0.
time (sec) N/A 0.173 0.083 0.069 0. 0. 0. 0.
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 76 76 122 83 0 0 0 0
normalized size 1 1. 1.61 1.09 0. 0. 0. 0.
time (sec) N/A 0.093 0.239 0.072 0. 0. 0. 0.
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 0.466 0.098 0. 0. 0. 0.
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 264 264 418 225 0 0 0 0
normalized size 1 1. 1.58 0.85 0. 0. 0. 0.
time (sec) N/A 0.383 7.733 0.11 0. 0. 0. 0.
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 190 190 264 139 0 0 0 0
normalized size 1 1. 1.39 0.73 0. 0. 0. 0.
time (sec) N/A 0.323 4.24 0.091 0. 0. 0. 0.
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 191 191 281 154 0 0 0 0
normalized size 1 1. 1.47 0.81 0. 0. 0. 0.
time (sec) N/A 0.341 2.726 0.091 0. 0. 0. 0.
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 119 119 75 73 0 0 0 0
normalized size 1 1. 0.63 0.61 0. 0. 0. 0.
time (sec) N/A 0.172 0.099 0.075 0. 0. 0. 0.
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 105 105 151 110 0 0 0 0
normalized size 1 1. 1.44 1.05 0. 0. 0. 0.
time (sec) N/A 0.166 1.045 0.075 0. 0. 0. 0.
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) F(-2) F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 0.461 0.102 0. 0. 0. 0.
Problem 119 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 64 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.117 1.179 0.842 0. 0. 0. 0.
Problem 120 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 64 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.114 1.063 0.614 0. 0. 0. 0.
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 150 150 132 0 0 0 0 0
normalized size 1 1. 0.88 0. 0. 0. 0. 0.
time (sec) N/A 0.107 2.18 0.808 0. 0. 0. 0.
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 68 68 54 0 0 0 0 0
normalized size 1 1. 0.79 0. 0. 0. 0. 0.
time (sec) N/A 0.026 0.035 0.866 0. 0. 0. 0.
Problem 123 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 0.65 0.536 0. 0. 0. 0.
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-1) 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 0.662 0.693 0. 0. 0. 0.
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) F(-2) F(-1) 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 0.015 5.825 0.108 0. 0. 0. 0.
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) F(-2) 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 0.016 6.052 0.1 0. 0. 0. 0.
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) F(-2) 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 0.016 5.737 0.099 0. 0. 0. 0.
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) F(-2) 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 0.015 3.402 0.098 0. 0. 0. 0.
Problem 129 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 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.016 0.987 0.839 0. 0. 0. 0.
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 165 165 130 287 0 0 0 0
normalized size 1 1. 0.79 1.74 0. 0. 0. 0.
time (sec) N/A 0.176 0.101 0.215 0. 0. 0. 0.
Problem 131 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 163 163 152 0 0 0 0 0
normalized size 1 1. 0.93 0. 0. 0. 0. 0.
time (sec) N/A 0.149 0.194 0.152 0. 0. 0. 0.
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 83 83 74 138 0 0 0 0
normalized size 1 1. 0.89 1.66 0. 0. 0. 0.
time (sec) N/A 0.083 0.055 0.117 0. 0. 0. 0.
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 75 75 70 148 0 0 0 0
normalized size 1 1. 0.93 1.97 0. 0. 0. 0.
time (sec) N/A 0.049 0.03 0.095 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 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.015 0.328 0.121 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 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.015 0.609 0.102 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 16 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.021 4.308 0.169 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 16 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.018 5.454 0.162 0. 0. 0. 0.
Problem 138 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 16 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.019 1.744 0.153 0. 0. 0. 0.
Problem 139 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 16 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.022 1.808 0.148 0. 0. 0. 0.
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 76 76 68 72 112 139 85 90
normalized size 1 1. 0.89 0.95 1.47 1.83 1.12 1.18
time (sec) N/A 0.036 0.047 0.006 1.448 2.454 1.289 1.133
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 55 64 81 119 70 76
normalized size 1 1. 0.92 1.07 1.35 1.98 1.17 1.27
time (sec) N/A 0.042 0.042 0.005 1.443 2.597 0.643 1.133
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 51 51 56 52 84 111 60 62
normalized size 1 1. 1.1 1.02 1.65 2.18 1.18 1.22
time (sec) N/A 0.019 0.036 0.005 1.439 2.578 0.331 1.155
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 31 32 42 73 29 42
normalized size 1 1. 1. 1.03 1.35 2.35 0.94 1.35
time (sec) N/A 0.019 0.012 0.002 1.436 2.495 0.154 1.123
Problem 144 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 58 77 0 0 0 0
normalized size 1 1. 0.92 1.22 0. 0. 0. 0.
time (sec) N/A 0.072 0.018 0.06 0. 0. 0. 0.
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 32 32 43 41 63 221 41 468
normalized size 1 1. 1.34 1.28 1.97 6.91 1.28 14.62
time (sec) N/A 0.028 0.012 0.006 1.424 2.743 1.955 1.52
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 39 39 44 50 50 86 63 664
normalized size 1 1. 1.13 1.28 1.28 2.21 1.62 17.03
time (sec) N/A 0.019 0.021 0.005 1.456 2.848 1.563 1.181
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 62 62 79 65 93 281 121 2206
normalized size 1 1. 1.27 1.05 1.5 4.53 1.95 35.58
time (sec) N/A 0.037 0.025 0.004 1.435 3.187 3.263 2.428
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 102 102 121 126 192 255 175 193
normalized size 1 1. 1.19 1.24 1.88 2.5 1.72 1.89
time (sec) N/A 0.152 0.137 0.052 1.451 2.8 1.487 1.162
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 76 76 104 118 0 221 131 161
normalized size 1 1. 1.37 1.55 0. 2.91 1.72 2.12
time (sec) N/A 0.118 0.111 0.051 0. 2.643 0.756 1.175
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 47 47 76 74 99 159 87 101
normalized size 1 1. 1.62 1.57 2.11 3.38 1.85 2.15
time (sec) N/A 0.058 0.062 0.046 1.438 2.419 0.332 1.145
Problem 151 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 92 92 128 194 0 0 0 0
normalized size 1 1. 1.39 2.11 0. 0. 0. 0.
time (sec) N/A 0.118 0.117 0.058 0. 0. 0. 0.
Problem 152 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 89 89 134 187 0 0 0 0
normalized size 1 1. 1.51 2.1 0. 0. 0. 0.
time (sec) N/A 0.128 0.207 0.053 0. 0. 0. 0.
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 178 178 218 235 369 441 333 390
normalized size 1 1. 1.22 1.32 2.07 2.48 1.87 2.19
time (sec) N/A 0.295 0.198 0.05 1.492 2.424 3.298 1.213
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 125 125 185 211 0 378 269 312
normalized size 1 1. 1.48 1.69 0. 3.02 2.15 2.5
time (sec) N/A 0.208 0.168 0.052 0. 2.293 1.627 1.208
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 82 82 128 134 194 262 165 203
normalized size 1 1. 1.56 1.63 2.37 3.2 2.01 2.48
time (sec) N/A 0.108 0.114 0.047 1.441 2.294 0.77 1.148
Problem 156 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 127 127 204 353 0 0 0 0
normalized size 1 1. 1.61 2.78 0. 0. 0. 0.
time (sec) N/A 0.141 0.171 0.063 0. 0. 0. 0.
Problem 157 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 151 151 308 0 0 0 0 0
normalized size 1 1. 2.04 0. 0. 0. 0. 0.
time (sec) N/A 0.214 0.292 0.161 0. 0. 0. 0.
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 121 117 91 102 0 0 0 232
normalized size 1 0.97 0.75 0.84 0. 0. 0. 1.92
time (sec) N/A 0.216 0.161 0.05 0. 0. 0. 1.207
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 63 63 56 58 0 0 0 116
normalized size 1 1. 0.89 0.92 0. 0. 0. 1.84
time (sec) N/A 0.121 0.068 0.046 0. 0. 0. 1.173
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 54 54 46 49 0 0 0 68
normalized size 1 1. 0.85 0.91 0. 0. 0. 1.26
time (sec) N/A 0.062 0.062 0.049 0. 0. 0. 1.147
Problem 161 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 0.023 0.302 0.263 0. 0. 0. 0.
Problem 162 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 3.59 0.18 0. 0. 0. 0.
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-1) F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 155 151 124 147 0 0 0 830
normalized size 1 0.97 0.8 0.95 0. 0. 0. 5.35
time (sec) N/A 0.183 0.565 0.056 0. 0. 0. 1.311
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-1) F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 91 91 80 78 0 0 0 436
normalized size 1 1. 0.88 0.86 0. 0. 0. 4.79
time (sec) N/A 0.097 0.258 0.052 0. 0. 0. 1.216
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-1) F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 86 82 72 74 0 0 0 261
normalized size 1 0.95 0.84 0.86 0. 0. 0. 3.03
time (sec) N/A 0.168 0.142 0.052 0. 0. 0. 1.17
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-1) 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 0.021 6.415 0.247 0. 0. 0. 0.
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-1) 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 0.022 51.281 0.198 0. 0. 0. 0.
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 197 246 169 291 0 0 0 1997
normalized size 1 1.25 0.86 1.48 0. 0. 0. 10.14
time (sec) N/A 0.535 0.455 0.06 0. 0. 0. 1.45
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 130 130 107 157 0 0 0 1161
normalized size 1 1. 0.82 1.21 0. 0. 0. 8.93
time (sec) N/A 0.311 0.278 0.053 0. 0. 0. 1.336
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 111 111 89 139 0 0 0 649
normalized size 1 1. 0.8 1.25 0. 0. 0. 5.85
time (sec) N/A 0.166 0.233 0.058 0. 0. 0. 1.177
Problem 171 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 0.023 3.374 0.317 0. 0. 0. 0.
Problem 172 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 31.544 0.51 0. 0. 0. 0.
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F(-2) F B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 242 242 243 357 0 0 0 549
normalized size 1 1. 1. 1.48 0. 0. 0. 2.27
time (sec) N/A 0.702 0.516 0.134 0. 0. 0. 2.007
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 137 137 123 173 0 0 0 243
normalized size 1 1. 0.9 1.26 0. 0. 0. 1.77
time (sec) N/A 0.4 0.201 0.102 0. 0. 0. 1.576
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F(-2) F B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 121 121 120 179 0 0 0 274
normalized size 1 1. 0.99 1.48 0. 0. 0. 2.26
time (sec) N/A 0.278 0.183 0.099 0. 0. 0. 1.407
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.034 3.589 0.209 0. 0. 0. 0.
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.034 9.94 0.274 0. 0. 0. 0.
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-2) F B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 313 313 589 541 0 0 0 1800
normalized size 1 1. 1.88 1.73 0. 0. 0. 5.75
time (sec) N/A 0.949 9.595 0.148 0. 0. 0. 3.148
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 172 172 155 267 0 0 0 791
normalized size 1 1. 0.9 1.55 0. 0. 0. 4.6
time (sec) N/A 0.461 0.825 0.114 0. 0. 0. 1.971
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-2) F B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 159 159 295 270 0 0 0 905
normalized size 1 1. 1.86 1.7 0. 0. 0. 5.69
time (sec) N/A 0.237 2.371 0.11 0. 0. 0. 2.237
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.039 3.198 0.221 0. 0. 0. 0.
Problem 182 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.039 9.76 0.286 0. 0. 0. 0.
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-2) F(-1) B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 358 358 1002 792 0 0 0 3471
normalized size 1 1. 2.8 2.21 0. 0. 0. 9.7
time (sec) N/A 1.316 16.464 0.171 0. 0. 0. 4.669
Problem 184 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F(-2) F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 216 216 201 366 0 0 0 1638
normalized size 1 1. 0.93 1.69 0. 0. 0. 7.58
time (sec) N/A 0.703 1.932 0.132 0. 0. 0. 2.401
Problem 185 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-2) F(-1) B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 179 179 383 393 0 0 0 1621
normalized size 1 1. 2.14 2.2 0. 0. 0. 9.06
time (sec) N/A 0.428 4.106 0.123 0. 0. 0. 2.906
Problem 186 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.041 3.336 0.217 0. 0. 0. 0.
Problem 187 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.04 9.763 0.283 0. 0. 0. 0.
Problem 188 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F(-2) F A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 223 223 225 167 0 0 0 446
normalized size 1 1. 1.01 0.75 0. 0. 0. 2.
time (sec) N/A 0.371 0.421 0.085 0. 0. 0. 2.086
Problem 189 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 99 99 91 80 0 0 0 188
normalized size 1 1. 0.92 0.81 0. 0. 0. 1.9
time (sec) N/A 0.171 0.16 0.06 0. 0. 0. 1.821
Problem 190 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F(-2) F A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 102 102 118 85 0 0 0 220
normalized size 1 1. 1.16 0.83 0. 0. 0. 2.16
time (sec) N/A 0.09 0.082 0.056 0. 0. 0. 1.691
Problem 191 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.036 3.261 0.199 0. 0. 0. 0.
Problem 192 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.035 11.961 0.253 0. 0. 0. 0.
Problem 193 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 252 252 273 295 0 0 0 0
normalized size 1 1. 1.08 1.17 0. 0. 0. 0.
time (sec) N/A 0.388 0.499 0.118 0. 0. 0. 0.
Problem 194 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 130 130 124 142 0 0 0 0
normalized size 1 1. 0.95 1.09 0. 0. 0. 0.
time (sec) N/A 0.154 0.33 0.102 0. 0. 0. 0.
Problem 195 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 137 137 150 150 0 0 0 0
normalized size 1 1. 1.09 1.09 0. 0. 0. 0.
time (sec) N/A 0.266 0.167 0.092 0. 0. 0. 0.
Problem 196 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.043 4.118 0.159 0. 0. 0. 0.
Problem 197 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.041 12.275 0.277 0. 0. 0. 0.
Problem 198 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 292 292 322 659 0 0 0 0
normalized size 1 1. 1.1 2.26 0. 0. 0. 0.
time (sec) N/A 0.945 2.576 0.148 0. 0. 0. 0.
Problem 199 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 180 180 176 311 0 0 0 0
normalized size 1 1. 0.98 1.73 0. 0. 0. 0.
time (sec) N/A 0.487 0.668 0.114 0. 0. 0. 0.
Problem 200 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 163 163 194 324 0 0 0 0
normalized size 1 1. 1.19 1.99 0. 0. 0. 0.
time (sec) N/A 0.259 1.621 0.111 0. 0. 0. 0.
Problem 201 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.041 4.212 0.16 0. 0. 0. 0.
Problem 202 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.041 12.702 0.272 0. 0. 0. 0.
Problem 203 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 120 120 158 144 0 0 0 0
normalized size 1 1. 1.32 1.2 0. 0. 0. 0.
time (sec) N/A 0.067 0.254 0.024 0. 0. 0. 0.
Problem 204 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 124 124 66 138 0 0 82 0
normalized size 1 1. 0.53 1.11 0. 0. 0.66 0.
time (sec) N/A 0.091 0.067 0.007 0. 0. 117.363 0.
Problem 205 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 88 88 113 119 0 0 76 0
normalized size 1 1. 1.28 1.35 0. 0. 0.86 0.
time (sec) N/A 0.046 0.188 0.006 0. 0. 3.349 0.
Problem 206 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 89 89 45 98 0 0 0 0
normalized size 1 1. 0.51 1.1 0. 0. 0. 0.
time (sec) N/A 0.074 0.034 0.008 0. 0. 0. 0.
Problem 207 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 93 85 0 0 0 0
normalized size 1 1. 1.69 1.55 0. 0. 0. 0.
time (sec) N/A 0.034 0.151 0.006 0. 0. 0. 0.
Problem 208 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 125 125 68 129 0 0 0 0
normalized size 1 1. 0.54 1.03 0. 0. 0. 0.
time (sec) N/A 0.092 0.067 0.007 0. 0. 0. 0.
Problem 209 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F(-2) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 109 109 234 0 0 0 0 0
normalized size 1 1. 2.15 0. 0. 0. 0. 0.
time (sec) N/A 0.139 1.261 0.358 0. 0. 0. 0.
Problem 210 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 109 109 176 0 0 0 0 0
normalized size 1 1. 1.61 0. 0. 0. 0. 0.
time (sec) N/A 0.14 7.42 0.335 0. 0. 0. 0.
Problem 211 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 109 109 202 0 0 0 0 0
normalized size 1 1. 1.85 0. 0. 0. 0. 0.
time (sec) N/A 0.134 0.532 0.352 0. 0. 0. 0.
Problem 212 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 107 107 142 0 0 0 0 0
normalized size 1 1. 1.33 0. 0. 0. 0. 0.
time (sec) N/A 0.125 1.272 0.518 0. 0. 0. 0.
Problem 213 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 105 105 129 0 0 0 0 0
normalized size 1 1. 1.23 0. 0. 0. 0. 0.
time (sec) N/A 0.13 0.433 0.339 0. 0. 0. 0.
Problem 214 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 109 109 198 0 0 0 0 0
normalized size 1 1. 1.82 0. 0. 0. 0. 0.
time (sec) N/A 0.142 0.786 0.342 0. 0. 0. 0.
Problem 215 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 68 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.164 30.752 0.335 0. 0. 0. 0.
Problem 216 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 66 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.167 135.147 0.349 0. 0. 0. 0.
Problem 217 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-2) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 64 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.147 10.427 0.356 0. 0. 0. 0.
Problem 218 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-2) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 64 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.158 7.313 0.334 0. 0. 0. 0.
Problem 219 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-2) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 66 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.167 11.473 0.341 0. 0. 0. 0.
Problem 220 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 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.028 3.473 0.238 0. 0. 0. 0.
Problem 221 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 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.025 2.271 0.245 0. 0. 0. 0.
Problem 222 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 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.026 0.854 0.24 0. 0. 0. 0.
Problem 223 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 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.029 2.946 0.229 0. 0. 0. 0.
Problem 224 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 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.027 6.461 0.228 0. 0. 0. 0.
Problem 225 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 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.023 4.953 0.246 0. 0. 0. 0.
Problem 226 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 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.024 9.581 0.244 0. 0. 0. 0.
Problem 227 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 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.029 13.925 0.233 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 [30] 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 4 3 1. 8 0.375
2 A 4 3 1. 8 0.375
3 A 4 3 1. 8 0.375
4 A 3 3 1. 6 0.5
5 A 2 2 1. 4 0.5
6 A 5 5 1. 8 0.625
7 A 4 4 1. 8 0.5
8 A 2 2 1. 8 0.25
9 A 5 5 1. 8 0.625
10 A 3 3 1. 8 0.375
11 A 6 5 1. 8 0.625
12 A 7 5 1. 10 0.5
13 A 6 4 1. 10 0.4
14 A 5 5 1. 10 0.5
15 A 4 4 1. 8 0.5
16 A 3 3 1. 6 0.5
17 A 6 6 1. 10 0.6
18 A 7 5 1. 10 0.5
19 A 3 3 1. 10 0.3
20 A 9 7 1. 10 0.7
21 A 5 5 1. 10 0.5
22 A 14 7 1. 10 0.7
23 A 11 5 1. 10 0.5
24 A 9 7 1. 10 0.7
25 A 6 5 1. 8 0.625
26 A 4 3 1. 6 0.5
27 A 7 7 1. 10 0.7
28 A 9 6 1. 10 0.6
29 A 7 7 1. 10 0.7
30 A 14 10 1. 10 1.
31 A 10 9 1. 10 0.9
32 A 23 4 1. 10 0.4
33 A 19 6 1. 10 0.6
34 A 14 4 1. 10 0.4
35 A 11 6 1. 10 0.6
36 A 7 4 1. 8 0.5
37 A 5 3 1. 6 0.5
38 A 8 7 1. 10 0.7
39 A 11 7 1. 10 0.7
40 A 8 8 1. 10 0.8
41 A 19 10 1. 10 1.
42 A 7 3 1. 10 0.3
43 A 6 3 1. 10 0.3
44 A 6 3 1. 10 0.3
45 A 5 3 1. 10 0.3
46 A 5 3 1. 10 0.3
47 A 4 4 1. 8 0.5
48 A 2 2 1. 6 0.333
49 A 0 0 0. 0 0.
50 A 0 0 0. 0 0.
51 A 6 2 1. 10 0.2
52 A 5 2 1. 10 0.2
53 A 5 2 1. 10 0.2
54 A 4 2 1. 10 0.2
55 A 4 2 1. 10 0.2
56 A 2 2 1. 8 0.25
57 A 3 3 1. 6 0.5
58 A 0 0 0. 0 0.
59 A 0 0 0. 0 0.
60 A 14 5 1. 10 0.5
61 A 12 6 1. 10 0.6
62 A 10 6 1. 10 0.6
63 A 7 7 1. 8 0.875
64 A 4 4 1. 6 0.667
65 A 0 0 0. 0 0.
66 A 0 0 0. 0 0.
67 A 12 4 1. 10 0.4
68 A 9 4 1. 10 0.4
69 A 10 6 1. 10 0.6
70 A 5 5 1. 8 0.625
71 A 5 4 1. 6 0.667
72 A 0 0 0. 0 0.
73 A 0 0 0. 0 0.
74 A 10 5 1. 12 0.417
75 A 8 5 1. 12 0.417
76 A 8 5 1. 12 0.417
77 A 6 5 1. 10 0.5
78 A 4 4 1. 8 0.5
79 A 0 0 0. 0 0.
80 A 23 8 1. 12 0.667
81 A 16 8 1. 12 0.667
82 A 13 8 1. 12 0.667
83 A 8 8 1. 10 0.8
84 A 5 5 1. 8 0.625
85 A 0 0 0. 0 0.
86 A 26 8 1. 12 0.667
87 A 18 7 1. 12 0.583
88 A 15 8 1. 12 0.667
89 A 9 7 1. 10 0.7
90 A 6 5 1. 8 0.625
91 A 0 0 0. 0 0.
92 A 9 4 1. 12 0.333
93 A 7 4 1. 12 0.333
94 A 7 4 1. 12 0.333
95 A 5 5 1. 10 0.5
96 A 3 3 1. 8 0.375
97 A 0 0 0. 0 0.
98 A 0 0 0. 0 0.
99 A 10 3 1. 12 0.25
100 A 8 3 1. 12 0.25
101 A 8 3 1. 12 0.25
102 A 6 3 1. 12 0.25
103 A 6 3 1. 12 0.25
104 A 3 3 1. 10 0.3
105 A 4 4 1. 8 0.5
106 A 0 0 0. 0 0.
107 A 19 6 1. 12 0.5
108 A 15 7 1. 12 0.583
109 A 13 7 1. 12 0.583
110 A 8 8 1. 10 0.8
111 A 5 5 1. 8 0.625
112 A 0 0 0. 0 0.
113 A 17 5 1. 12 0.417
114 A 12 5 1. 12 0.417
115 A 13 7 1. 12 0.583
116 A 6 6 1. 10 0.6
117 A 6 5 1. 8 0.625
118 A 0 0 0. 0 0.
119 A 0 0 0. 0 0.
120 A 0 0 0. 0 0.
121 A 2 2 1. 12 0.167
122 A 2 2 1. 10 0.2
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 0 0 0. 0 0.
130 A 9 4 1. 10 0.4
131 A 9 4 1. 10 0.4
132 A 6 5 1. 8 0.625
133 A 4 3 1. 6 0.5
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 0 0 0. 0 0.
139 A 0 0 0. 0 0.
140 A 4 3 1. 12 0.25
141 A 4 3 1. 12 0.25
142 A 3 3 1. 10 0.3
143 A 3 2 1. 8 0.25
144 A 5 5 1. 12 0.417
145 A 4 4 1. 12 0.333
146 A 2 2 1. 12 0.167
147 A 5 5 1. 12 0.417
148 A 5 5 1. 14 0.357
149 A 4 4 1. 12 0.333
150 A 3 3 1. 10 0.3
151 A 6 6 1. 14 0.429
152 A 7 5 1. 14 0.357
153 A 10 7 1. 14 0.5
154 A 6 5 1. 12 0.417
155 A 5 3 1. 10 0.3
156 A 7 7 1. 14 0.5
157 A 9 6 1. 14 0.429
158 A 9 5 0.97 14 0.357
159 A 6 6 1. 12 0.5
160 A 4 4 1. 10 0.4
161 A 0 0 0. 0 0.
162 A 0 0 0. 0 0.
163 A 8 4 0.97 14 0.286
164 A 4 4 1. 12 0.333
165 A 5 5 0.95 10 0.5
166 A 0 0 0. 0 0.
167 A 0 0 0. 0 0.
168 A 16 8 1.25 14 0.571
169 A 9 9 1. 12 0.75
170 A 6 6 1. 10 0.6
171 A 0 0 0. 0 0.
172 A 0 0 0. 0 0.
173 A 14 8 1. 16 0.5
174 A 9 8 1. 14 0.571
175 A 7 7 1. 12 0.583
176 A 0 0 0. 0 0.
177 A 0 0 0. 0 0.
178 A 22 11 1. 16 0.688
179 A 11 11 1. 14 0.786
180 A 8 8 1. 12 0.667
181 A 0 0 0. 0 0.
182 A 0 0 0. 0 0.
183 A 24 11 1. 16 0.688
184 A 12 10 1. 14 0.714
185 A 9 8 1. 12 0.667
186 A 0 0 0. 0 0.
187 A 0 0 0. 0 0.
188 A 13 7 1. 16 0.438
189 A 8 8 1. 14 0.571
190 A 6 6 1. 12 0.5
191 A 0 0 0. 0 0.
192 A 0 0 0. 0 0.
193 A 12 6 1. 16 0.375
194 A 6 6 1. 14 0.429
195 A 7 7 1. 12 0.583
196 A 0 0 0. 0 0.
197 A 0 0 0. 0 0.
198 A 22 10 1. 16 0.625
199 A 11 11 1. 14 0.786
200 A 8 8 1. 12 0.667
201 A 0 0 0. 0 0.
202 A 0 0 0. 0 0.
203 A 5 4 1. 16 0.25
204 A 7 7 1. 16 0.438
205 A 4 4 1. 16 0.25
206 A 6 6 1. 16 0.375
207 A 3 3 1. 16 0.188
208 A 7 7 1. 16 0.438
209 A 2 2 1. 18 0.111
210 A 2 2 1. 18 0.111
211 A 2 2 1. 18 0.111
212 A 2 2 1. 18 0.111
213 A 2 2 1. 18 0.111
214 A 2 2 1. 18 0.111
215 A 0 0 0. 0 0.
216 A 0 0 0. 0 0.
217 A 0 0 0. 0 0.
218 A 0 0 0. 0 0.
219 A 0 0 0. 0 0.
220 A 0 0 0. 0 0.
221 A 0 0 0. 0 0.
222 A 0 0 0. 0 0.
223 A 0 0 0. 0 0.
224 A 0 0 0. 0 0.
225 A 0 0 0. 0 0.
226 A 0 0 0. 0 0.
227 A 0 0 0. 0 0.

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