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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, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241 }

B grade: { }

C grade: { }

F grade: { 217}

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 8, 9, 10, 11, 12, 13, 14, 15, 19, 20, 24, 25, 26, 29, 30, 32, 33, 34, 35, 36, 41, 42, 43, 44, 45, 46, 50, 51, 52, 53, 54, 57, 58, 59, 60, 61, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 79, 80, 81, 82, 83, 84, 145, 146, 150, 154, 155, 156, 157, 160, 161, 162, 164, 168, 184, 185, 186, 187, 188, 189, 190, 191, 192, 194, 196, 199, 201, 203, 204, 208, 218, 221, 222, 223, 224, 225, 226, 227, 228, 229, 233, 236, 237, 238, 239 }

B grade: { 6, 16, 17, 21, 22, 23, 28, 31, 37, 39, 40, 144, 193, 195, 197, 200, 202, 209, 210, 211, 212, 213, 214, 215, 216, 220, 230, 240, 241 }

C grade: { 7, 18, 27, 38, 47, 48, 49, 55, 56, 62, 63, 64, 70, 71, 77, 78, 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, 143, 147, 148, 149, 151, 152, 153, 158, 159, 163, 165, 166, 167, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 198, 205, 206, 207, 217, 219 }

F grade: { 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 231, 232, 234, 235}

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, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 39, 40, 41, 44, 45, 46, 51, 60, 68, 69, 86, 87, 88, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 108, 109, 110, 111, 112, 113, 115, 116, 117, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 143, 144, 145, 146, 149, 189, 201, 203, 204, 207, 208, 217, 218, 219, 221, 222, 223, 224, 225, 226, 227, 228, 229, 236 }

B grade: { 42, 43, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 89, 90, 105, 106, 107, 114, 118, 147, 148, 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, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 202, 205, 206, 209, 210, 211, 212, 213, 214, 215, 216, 220 }

C grade: { }

F grade: { 27, 38, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 230, 231, 232, 233, 234, 235, 237, 238, 239, 240, 241 }

2.1.4 Maxima

A grade: { 1, 2, 4, 5, 13, 15, 26, 27, 28, 29, 30, 35, 36, 37, 38, 39, 40, 41, 89, 90, 97, 98, 106, 112, 113, 114, 119, 125, 221, 222, 223, 224, 225, 226, 227, 228, 229, 236

B grade: { 3, 6, 7, 8, 9, 10, 11, 12, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 31, 32, 33, 34, 45, 52, 59, 86, 87, 88, 91, 92, 93, 94, 95, 96, 99, 100, 101, 102, 103, 107, 108, 115, 116, 117, 120, 121, 122, 123, 126, 127, 128, 129, 130, 150, 156, 162 }

C grade: { }

F grade: { 42, 43, 44, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 104, 105, 109, 110, 111, 118, 124, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 151, 152, 153, 154, 155, 157, 158, 159, 160, 161, 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, 230, 231, 232, 233, 234, 235, 237, 238, 239, 240, 241 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 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, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 77, 78, 79, 80, 81, 82, 86, 87, 88, 94, 95, 96, 101, 102, 103, 130, 143, 147, 148, 149, 150, 151, 152, 154, 155, 156, 157, 158, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 175, 178, 179, 184, 185, 187, 188, 189, 236 }

B grade: { 5, 22, 23, 61, 62, 63, 74, 75, 83, 89, 105, 114, 118, 122, 153, 159, 174, 180, 186, 190, 191, 192, 193, 194, 195, 196, 197 }

C grade: { }

F grade: { 76, 84, 85, 90, 91, 92, 93, 97, 98, 99, 100, 104, 106, 107, 108, 109, 110, 111, 112, 113, 115, 116, 117, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 144, 145, 146, 176, 177, 181, 182, 183, 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, 228, 229, 230, 231, 232, 233, 234, 235, 237, 238, 239, 240, 241 }

2.1.6 Sympy

A grade: { 221, 224, 236 }

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, 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, 222, 223, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 237, 238, 239, 240, 241 }

2.1.7 Giac

A grade: { 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 39, 40, 41, 113, 118, 119, 120, 125, 126, 127, 189, 190, 192, 221, 222, 223, 224, 225, 226, 227, 228, 229, 236 }

B grade: { 5, 27, 38, 191, 193, 194, 195, 196, 197 }

C grade: { }

F grade: { 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, 114, 115, 116, 117, 121, 122, 123, 124, 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, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 230, 231, 232, 233, 234, 235, 237, 238, 239, 240, 241 }

2.2 Detailed conclusion table per each integral for all CAS systems

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

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

Problem 1 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 196 196 165 186 451 452 0 271
normalized size 1 1. 0.84 0.95 2.3 2.31 0. 1.38
time (sec) N/A 0.302 2.003 0.033 1.032 1.171 0. 1.519
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 140 140 146 161 324 404 0 244
normalized size 1 1. 1.04 1.15 2.31 2.89 0. 1.74
time (sec) N/A 0.199 1.152 0.028 1.038 1.135 0. 1.446
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 97 97 122 136 274 359 0 217
normalized size 1 1. 1.26 1.4 2.82 3.7 0. 2.24
time (sec) N/A 0.118 0.738 0.025 1.029 1.164 0. 1.52
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 47 47 45 58 77 144 0 69
normalized size 1 1. 0.96 1.23 1.64 3.06 0. 1.47
time (sec) N/A 0.065 0.034 0.021 1.014 1.077 0. 1.434
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 72 76 128 259 0 147
normalized size 1 1. 1.31 1.38 2.33 4.71 0. 2.67
time (sec) N/A 0.063 0.291 0.02 1.07 1.076 0. 1.361
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 56 56 169 90 207 217 0 109
normalized size 1 1. 3.02 1.61 3.7 3.88 0. 1.95
time (sec) N/A 0.164 0.286 0.079 1.599 1.096 0. 1.384
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 71 71 53 67 235 204 0 81
normalized size 1 1. 0.75 0.94 3.31 2.87 0. 1.14
time (sec) N/A 0.236 0.057 0.091 1.633 1.034 0. 1.342
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 102 102 171 89 290 313 0 103
normalized size 1 1. 1.68 0.87 2.84 3.07 0. 1.01
time (sec) N/A 0.329 0.62 0.1 1.78 1.027 0. 1.366
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 133 133 227 111 397 424 0 126
normalized size 1 1. 1.71 0.83 2.98 3.19 0. 0.95
time (sec) N/A 0.427 0.616 0.109 1.602 1.054 0. 1.365
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 164 164 283 133 452 535 0 149
normalized size 1 1. 1.73 0.81 2.76 3.26 0. 0.91
time (sec) N/A 0.543 0.886 0.119 1.635 1.05 0. 1.652
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 188 188 189 211 481 498 0 298
normalized size 1 1. 1.01 1.12 2.56 2.65 0. 1.59
time (sec) N/A 0.237 2.219 0.035 1.01 1.219 0. 1.429
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 132 132 165 186 451 448 0 271
normalized size 1 1. 1.25 1.41 3.42 3.39 0. 2.05
time (sec) N/A 0.151 1.834 0.028 1.02 1.188 0. 1.361
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 68 68 61 93 127 189 0 93
normalized size 1 1. 0.9 1.37 1.87 2.78 0. 1.37
time (sec) N/A 0.074 0.04 0.023 1.035 1.066 0. 1.475
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 97 97 122 136 274 359 0 217
normalized size 1 1. 1.26 1.4 2.82 3.7 0. 2.24
time (sec) N/A 0.114 0.791 0.025 1.019 1.147 0. 1.345
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 77 77 101 98 144 298 0 149
normalized size 1 1. 1.31 1.27 1.87 3.87 0. 1.94
time (sec) N/A 0.147 0.44 0.023 1.018 1.109 0. 1.392
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 78 78 240 137 370 313 0 158
normalized size 1 1. 3.08 1.76 4.74 4.01 0. 2.03
time (sec) N/A 0.209 2.369 0.083 1.553 1.097 0. 1.35
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 88 88 177 90 370 379 0 113
normalized size 1 1. 2.01 1.02 4.2 4.31 0. 1.28
time (sec) N/A 0.361 1.17 0.087 1.533 1.125 0. 1.346
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 102 102 53 89 381 312 0 104
normalized size 1 1. 0.52 0.87 3.74 3.06 0. 1.02
time (sec) N/A 0.452 0.085 0.104 1.587 1.073 0. 1.441
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 133 133 227 111 517 424 0 126
normalized size 1 1. 1.71 0.83 3.89 3.19 0. 0.95
time (sec) N/A 0.579 0.611 0.114 1.563 1.046 0. 1.377
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 164 164 283 133 544 535 0 149
normalized size 1 1. 1.73 0.81 3.32 3.26 0. 0.91
time (sec) N/A 0.733 0.88 0.128 1.664 1.115 0. 1.509
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 136 153 384 207 814 601 0 217
normalized size 1 1.12 2.82 1.52 5.99 4.42 0. 1.6
time (sec) N/A 0.402 3.019 0.105 1.591 1.15 0. 1.466
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 102 102 448 159 558 541 0 190
normalized size 1 1. 4.39 1.56 5.47 5.3 0. 1.86
time (sec) N/A 0.309 6.016 0.088 1.543 1.132 0. 1.328
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 85 85 216 90 362 425 0 113
normalized size 1 1. 2.54 1.06 4.26 5. 0. 1.33
time (sec) N/A 0.331 1.092 0.086 1.581 1.076 0. 1.338
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 67 67 67 65 230 225 0 85
normalized size 1 1. 1. 0.97 3.43 3.36 0. 1.27
time (sec) N/A 0.228 0.052 0.08 1.559 1.044 0. 1.236
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 61 61 113 59 161 212 0 76
normalized size 1 1. 1.85 0.97 2.64 3.48 0. 1.25
time (sec) N/A 0.145 0.314 0.08 1.548 1.025 0. 1.424
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 69 69 135 87 138 180 0 115
normalized size 1 1. 1.96 1.26 2. 2.61 0. 1.67
time (sec) N/A 0.114 0.543 0.056 1.516 1.042 0. 1.343
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 39 0 62 188 0 135
normalized size 1 1. 0.85 0. 1.35 4.09 0. 2.93
time (sec) N/A 0.071 0.05 180. 1.525 1.058 0. 1.411
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 98 98 257 130 198 374 0 157
normalized size 1 1. 2.62 1.33 2.02 3.82 0. 1.6
time (sec) N/A 0.145 1.314 0.065 1.546 1.034 0. 1.478
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 166 166 315 153 225 424 0 174
normalized size 1 1. 1.9 0.92 1.36 2.55 0. 1.05
time (sec) N/A 0.211 1.257 0.071 1.529 1.085 0. 1.433
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 210 210 383 175 251 598 0 193
normalized size 1 1. 1.82 0.83 1.2 2.85 0. 0.92
time (sec) N/A 0.286 1.235 0.074 1.555 1.104 0. 1.406
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 162 162 557 179 759 721 0 219
normalized size 1 1. 3.44 1.1 4.69 4.45 0. 1.35
time (sec) N/A 0.443 5.623 0.099 1.586 1.19 0. 1.549
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 148 148 231 110 535 601 0 144
normalized size 1 1. 1.56 0.74 3.61 4.06 0. 0.97
time (sec) N/A 0.606 1.175 0.103 1.596 1.132 0. 1.456
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 96 96 90 87 374 340 0 113
normalized size 1 1. 0.94 0.91 3.9 3.54 0. 1.18
time (sec) N/A 0.421 0.079 0.102 1.646 1.024 0. 1.481
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 96 96 171 87 285 338 0 113
normalized size 1 1. 1.78 0.91 2.97 3.52 0. 1.18
time (sec) N/A 0.304 0.461 0.091 1.572 1.002 0. 1.376
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 88 88 169 79 215 313 0 101
normalized size 1 1. 1.92 0.9 2.44 3.56 0. 1.15
time (sec) N/A 0.202 0.457 0.086 1.574 0.995 0. 1.377
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 126 126 197 109 165 284 0 144
normalized size 1 1. 1.56 0.87 1.31 2.25 0. 1.14
time (sec) N/A 0.193 0.929 0.061 1.553 1.039 0. 1.332
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 100 100 257 131 197 374 0 165
normalized size 1 1. 2.57 1.31 1.97 3.74 0. 1.65
time (sec) N/A 0.143 0.917 0.063 1.546 1.08 0. 1.392
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 67 67 39 0 76 290 0 184
normalized size 1 1. 0.58 0. 1.13 4.33 0. 2.75
time (sec) N/A 0.081 0.074 180. 1.575 1.119 0. 1.456
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 129 129 362 174 252 581 0 203
normalized size 1 1. 2.81 1.35 1.95 4.5 0. 1.57
time (sec) N/A 0.173 1.371 0.069 1.564 1.062 0. 1.511
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 210 210 441 197 277 687 0 220
normalized size 1 1. 2.1 0.94 1.32 3.27 0. 1.05
time (sec) N/A 0.236 1.729 0.075 1.549 1.163 0. 1.44
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 252 252 499 219 306 799 0 242
normalized size 1 1. 1.98 0.87 1.21 3.17 0. 0.96
time (sec) N/A 0.3 2.216 0.076 1.606 1.16 0. 1.3
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 175 175 121 391 0 960 0 0
normalized size 1 1. 0.69 2.23 0. 5.49 0. 0.
time (sec) N/A 0.176 1.012 0.319 0. 1.262 0. 0.
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 140 140 111 302 0 882 0 0
normalized size 1 1. 0.79 2.16 0. 6.3 0. 0.
time (sec) N/A 0.168 1.206 0.291 0. 1.21 0. 0.
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-1) A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 105 105 97 142 0 792 0 0
normalized size 1 1. 0.92 1.35 0. 7.54 0. 0.
time (sec) N/A 0.158 0.772 0.263 0. 1.172 0. 0.
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 66 66 70 115 198 620 0 0
normalized size 1 1. 1.06 1.74 3. 9.39 0. 0.
time (sec) N/A 0.109 0.32 0.212 1.713 1.146 0. 0.
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 69 69 90 116 0 680 0 0
normalized size 1 1. 1.3 1.68 0. 9.86 0. 0.
time (sec) N/A 0.148 0.58 0.251 0. 1.465 0. 0.
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 104 104 78 214 0 872 0 0
normalized size 1 1. 0.75 2.06 0. 8.38 0. 0.
time (sec) N/A 0.157 0.241 0.289 0. 1.449 0. 0.
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 139 139 78 311 0 1056 0 0
normalized size 1 1. 0.56 2.24 0. 7.6 0. 0.
time (sec) N/A 0.167 0.26 0.329 0. 1.566 0. 0.
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 174 174 78 402 0 1245 0 0
normalized size 1 1. 0.45 2.31 0. 7.16 0. 0.
time (sec) N/A 0.177 0.25 0.37 0. 1.646 0. 0.
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 177 177 122 392 0 990 0 0
normalized size 1 1. 0.69 2.21 0. 5.59 0. 0.
time (sec) N/A 0.184 0.959 0.272 0. 1.275 0. 0.
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-1) A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 142 142 112 232 0 900 0 0
normalized size 1 1. 0.79 1.63 0. 6.34 0. 0.
time (sec) N/A 0.17 0.842 0.247 0. 1.196 0. 0.
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 101 101 96 212 1347 792 0 0
normalized size 1 1. 0.95 2.1 13.34 7.84 0. 0.
time (sec) N/A 0.123 0.67 0.222 1.912 1.173 0. 0.
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 70 70 93 194 0 689 0 0
normalized size 1 1. 1.33 2.77 0. 9.84 0. 0.
time (sec) N/A 0.156 0.577 0.191 0. 1.409 0. 0.
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 102 102 113 215 0 888 0 0
normalized size 1 1. 1.11 2.11 0. 8.71 0. 0.
time (sec) N/A 0.162 0.653 0.255 0. 1.517 0. 0.
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 137 137 102 304 0 1083 0 0
normalized size 1 1. 0.74 2.22 0. 7.91 0. 0.
time (sec) N/A 0.178 0.77 0.276 0. 1.577 0. 0.
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 172 172 102 401 0 1283 0 0
normalized size 1 1. 0.59 2.33 0. 7.46 0. 0.
time (sec) N/A 0.187 1.327 0.314 0. 1.625 0. 0.
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 212 212 134 483 0 1098 0 0
normalized size 1 1. 0.63 2.28 0. 5.18 0. 0.
time (sec) N/A 0.191 1.214 0.28 0. 1.307 0. 0.
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 177 177 124 323 0 1019 0 0
normalized size 1 1. 0.7 1.82 0. 5.76 0. 0.
time (sec) N/A 0.174 0.921 0.26 0. 1.237 0. 0.
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 132 132 110 303 1885 887 0 0
normalized size 1 1. 0.83 2.3 14.28 6.72 0. 0.
time (sec) N/A 0.141 0.803 0.229 2.032 1.245 0. 0.
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 103 103 96 120 0 724 0 0
normalized size 1 1. 0.93 1.17 0. 7.03 0. 0.
time (sec) N/A 0.172 0.68 0.227 0. 1.471 0. 0.
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) B F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 102 351 0 844 0 0
normalized size 1 1. 1.38 4.74 0. 11.41 0. 0.
time (sec) N/A 0.168 4.226 0.24 0. 1.491 0. 0.
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) B F(-1) F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 104 104 196 306 0 1106 0 0
normalized size 1 1. 1.88 2.94 0. 10.63 0. 0.
time (sec) N/A 0.177 5.409 0.27 0. 1.55 0. 0.
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) B F(-1) F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 140 140 361 395 0 1310 0 0
normalized size 1 1. 2.58 2.82 0. 9.36 0. 0.
time (sec) N/A 0.184 7.938 0.295 0. 1.611 0. 0.
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) A F(-1) F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 172 172 205 492 0 1512 0 0
normalized size 1 1. 1.19 2.86 0. 8.79 0. 0.
time (sec) N/A 0.198 3.477 0.357 0. 1.67 0. 0.
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 185 185 153 544 0 1420 0 0
normalized size 1 1. 0.83 2.94 0. 7.68 0. 0.
time (sec) N/A 0.276 1.424 0.321 0. 5.261 0. 0.
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 152 152 166 372 0 1342 0 0
normalized size 1 1. 1.09 2.45 0. 8.83 0. 0.
time (sec) N/A 0.228 1.316 0.299 0. 4.499 0. 0.
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 119 119 124 330 0 1138 0 0
normalized size 1 1. 1.04 2.77 0. 9.56 0. 0.
time (sec) N/A 0.188 0.475 0.277 0. 2.759 0. 0.
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 87 87 82 144 0 787 0 0
normalized size 1 1. 0.94 1.66 0. 9.05 0. 0.
time (sec) N/A 0.138 0.276 0.219 0. 2.119 0. 0.
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 121 121 101 194 0 1143 0 0
normalized size 1 1. 0.83 1.6 0. 9.45 0. 0.
time (sec) N/A 0.192 0.553 0.267 0. 2.359 0. 0.
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F A F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 161 161 5586 377 0 1395 0 0
normalized size 1 1. 34.7 2.34 0. 8.66 0. 0.
time (sec) N/A 0.235 23.791 0.303 0. 2.321 0. 0.
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F A F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 196 196 5602 545 0 1627 0 0
normalized size 1 1. 28.58 2.78 0. 8.3 0. 0.
time (sec) N/A 0.284 23.501 0.359 0. 2.623 0. 0.
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 203 203 196 552 0 1616 0 0
normalized size 1 1. 0.97 2.72 0. 7.96 0. 0.
time (sec) N/A 0.286 1.53 0.28 0. 10.802 0. 0.
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 169 169 132 376 0 1405 0 0
normalized size 1 1. 0.78 2.22 0. 8.31 0. 0.
time (sec) N/A 0.24 1.739 0.257 0. 5.021 0. 0.
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 119 134 128 369 0 1389 0 0
normalized size 1 1.13 1.08 3.1 0. 11.67 0. 0.
time (sec) N/A 0.192 1.068 0.189 0. 3.802 0. 0.
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 113 130 130 371 0 1347 0 0
normalized size 1 1.15 1.15 3.28 0. 11.92 0. 0.
time (sec) N/A 0.166 0.993 0.181 0. 4.327 0. 0.
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F(-2) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 177 177 154 377 0 0 0 0
normalized size 1 1. 0.87 2.13 0. 0. 0. 0.
time (sec) N/A 0.244 1.174 0.254 0. 0. 0. 0.
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F A F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 214 214 5622 387 0 1478 0 0
normalized size 1 1. 26.27 1.81 0. 6.91 0. 0.
time (sec) N/A 0.278 23.793 0.293 0. 2.008 0. 0.
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F A F(-1) F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 249 249 5639 725 0 1867 0 0
normalized size 1 1. 22.65 2.91 0. 7.5 0. 0.
time (sec) N/A 0.34 23.795 0.362 0. 2.18 0. 0.
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 260 260 180 726 0 1879 0 0
normalized size 1 1. 0.69 2.79 0. 7.23 0. 0.
time (sec) N/A 0.341 3.485 0.308 0. 14.54 0. 0.
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 229 229 164 550 0 1673 0 0
normalized size 1 1. 0.72 2.4 0. 7.31 0. 0.
time (sec) N/A 0.296 2.599 0.272 0. 11.877 0. 0.
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 191 191 136 553 0 1643 0 0
normalized size 1 1. 0.71 2.9 0. 8.6 0. 0.
time (sec) N/A 0.252 1.537 0.252 0. 9.106 0. 0.
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 189 189 136 545 0 1655 0 0
normalized size 1 1. 0.72 2.88 0. 8.76 0. 0.
time (sec) N/A 0.23 1.482 0.194 0. 6.558 0. 0.
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 148 181 134 543 0 1605 0 0
normalized size 1 1.22 0.91 3.67 0. 10.84 0. 0.
time (sec) N/A 0.192 1.458 0.179 0. 3.964 0. 0.
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F(-2) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 230 230 158 545 0 0 0 0
normalized size 1 1. 0.69 2.37 0. 0. 0. 0.
time (sec) N/A 0.306 1.443 0.265 0. 0. 0. 0.
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) F(-2) F(-1) F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 269 269 5660 725 0 0 0 0
normalized size 1 1. 21.04 2.7 0. 0. 0. 0.
time (sec) N/A 0.335 24.052 0.326 0. 0. 0. 0.
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 185 185 149 194 1740 1135 0 0
normalized size 1 1. 0.81 1.05 9.41 6.14 0. 0.
time (sec) N/A 0.372 5.818 0.356 2.141 1.696 0. 0.
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 139 139 162 184 959 1052 0 0
normalized size 1 1. 1.17 1.32 6.9 7.57 0. 0.
time (sec) N/A 0.273 2.16 0.309 1.882 1.69 0. 0.
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 93 93 99 164 328 887 0 0
normalized size 1 1. 1.06 1.76 3.53 9.54 0. 0.
time (sec) N/A 0.178 1.226 0.297 1.796 1.657 0. 0.
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A B F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 48 48 102 127 53 506 0 0
normalized size 1 1. 2.12 2.65 1.1 10.54 0. 0.
time (sec) N/A 0.084 0.573 0.308 1.838 1.62 0. 0.
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 51 51 86 97 88 0 0 0
normalized size 1 1. 1.69 1.9 1.73 0. 0. 0.
time (sec) N/A 0.086 0.878 0.276 1.52 0. 0. 0.
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 96 96 107 164 539 0 0 0
normalized size 1 1. 1.11 1.71 5.61 0. 0. 0.
time (sec) N/A 0.179 1.001 0.293 1.803 0. 0. 0.
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 142 142 152 226 1584 0 0 0
normalized size 1 1. 1.07 1.59 11.15 0. 0. 0.
time (sec) N/A 0.271 1.231 0.303 2.415 0. 0. 0.
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 188 188 198 288 3299 0 0 0
normalized size 1 1. 1.05 1.53 17.55 0. 0. 0.
time (sec) N/A 0.366 1.784 0.306 11.007 0. 0. 0.
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 190 190 157 187 1831 1154 0 0
normalized size 1 1. 0.83 0.98 9.64 6.07 0. 0.
time (sec) N/A 0.364 1.253 0.29 2.173 1.697 0. 0.
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 103 103 159 171 644 873 0 0
normalized size 1 1. 1.54 1.66 6.25 8.48 0. 0.
time (sec) N/A 0.11 1.371 0.276 1.824 1.688 0. 0.
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 93 93 128 151 328 884 0 0
normalized size 1 1. 1.38 1.62 3.53 9.51 0. 0.
time (sec) N/A 0.169 0.727 0.309 1.781 1.66 0. 0.
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 104 104 105 149 81 0 0 0
normalized size 1 1. 1.01 1.43 0.78 0. 0. 0.
time (sec) N/A 0.103 1.185 0.262 1.846 0. 0. 0.
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 100 100 115 163 128 0 0 0
normalized size 1 1. 1.15 1.63 1.28 0. 0. 0.
time (sec) N/A 0.186 0.671 0.268 1.535 0. 0. 0.
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 146 146 153 227 2411 0 0 0
normalized size 1 1. 1.05 1.55 16.51 0. 0. 0.
time (sec) N/A 0.283 1.21 0.265 2.512 0. 0. 0.
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 196 196 199 289 4698 0 0 0
normalized size 1 1. 1.02 1.47 23.97 0. 0. 0.
time (sec) N/A 0.382 2.096 0.275 11.301 0. 0. 0.
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 153 153 164 191 2186 987 0 0
normalized size 1 1. 1.07 1.25 14.29 6.45 0. 0.
time (sec) N/A 0.12 1.492 0.299 2.432 1.742 0. 0.
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 190 190 149 199 1831 1152 0 0
normalized size 1 1. 0.78 1.05 9.64 6.06 0. 0.
time (sec) N/A 0.363 1.166 0.281 2.19 1.727 0. 0.
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 139 139 164 179 959 1049 0 0
normalized size 1 1. 1.18 1.29 6.9 7.55 0. 0.
time (sec) N/A 0.263 1.259 0.307 1.843 1.641 0. 0.
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 152 152 292 183 0 0 0 0
normalized size 1 1. 1.92 1.2 0. 0. 0. 0.
time (sec) N/A 0.114 6.767 0.319 0. 0. 0. 0.
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-2) B F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 96 96 111 237 0 1062 0 0
normalized size 1 1. 1.16 2.47 0. 11.06 0. 0.
time (sec) N/A 0.179 1.22 0.27 0. 1.412 0. 0.
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 100 100 155 229 188 0 0 0
normalized size 1 1. 1.55 2.29 1.88 0. 0. 0.
time (sec) N/A 0.181 1.37 0.266 1.514 0. 0. 0.
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B B F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 148 148 202 281 5046 0 0 0
normalized size 1 1. 1.36 1.9 34.09 0. 0. 0.
time (sec) N/A 0.278 2.615 0.277 11.149 0. 0. 0.
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 194 194 285 353 8281 0 0 0
normalized size 1 1. 1.47 1.82 42.69 0. 0. 0.
time (sec) N/A 0.376 5.435 0.282 76.433 0. 0. 0.
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 244 244 299 415 0 0 0 0
normalized size 1 1. 1.23 1.7 0. 0. 0. 0.
time (sec) N/A 0.474 5.949 0.292 0. 0. 0. 0.
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 204 204 153 189 0 0 0 0
normalized size 1 1. 0.75 0.93 0. 0. 0. 0.
time (sec) N/A 0.124 15.341 0.309 0. 0. 0. 0.
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 151 151 181 169 0 0 0 0
normalized size 1 1. 1.2 1.12 0. 0. 0. 0.
time (sec) N/A 0.113 3.886 0.3 0. 0. 0. 0.
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A F F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 102 102 103 93 81 0 0 0
normalized size 1 1. 1.01 0.91 0.79 0. 0. 0.
time (sec) N/A 0.107 9.154 0.287 1.811 0. 0. 0.
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 127 75 46 0 0 92
normalized size 1 1. 2.59 1.53 0.94 0. 0. 1.88
time (sec) N/A 0.084 0.911 0.302 1.576 0. 0. 1.796
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A B F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 104 100 53 682 0 0
normalized size 1 1. 2.26 2.17 1.15 14.83 0. 0.
time (sec) N/A 0.09 1.069 0.26 1.772 1.876 0. 0.
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 168 217 143 167 1104 0 0 0
normalized size 1 1.29 0.85 0.99 6.57 0. 0. 0.
time (sec) N/A 0.137 8.145 0.294 1.941 0. 0. 0.
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 274 274 194 229 2978 0 0 0
normalized size 1 1. 0.71 0.84 10.87 0. 0. 0.
time (sec) N/A 0.161 1.879 0.303 2.55 0. 0. 0.
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B F F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 215 215 204 276 3231 0 0 0
normalized size 1 1. 0.95 1.28 15.03 0. 0. 0.
time (sec) N/A 0.145 2.082 0.276 2.719 0. 0. 0.
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-2) B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 96 96 116 236 0 1098 0 185
normalized size 1 1. 1.21 2.46 0. 11.44 0. 1.93
time (sec) N/A 0.193 0.731 0.27 0. 1.353 0. 3.058
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A F F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 98 98 114 106 95 0 0 170
normalized size 1 1. 1.16 1.08 0.97 0. 0. 1.73
time (sec) N/A 0.196 1.113 0.256 1.493 0. 0. 2.348
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 94 94 106 119 533 0 0 158
normalized size 1 1. 1.13 1.27 5.67 0. 0. 1.68
time (sec) N/A 0.189 0.561 0.291 1.789 0. 0. 1.9
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 215 215 141 161 1104 0 0 0
normalized size 1 1. 0.66 0.75 5.13 0. 0. 0.
time (sec) N/A 0.146 1.384 0.3 1.916 0. 0. 0.
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B B F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 101 101 121 175 656 1242 0 0
normalized size 1 1. 1.2 1.73 6.5 12.3 0. 0.
time (sec) N/A 0.121 1.478 0.264 1.837 2.438 0. 0.
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 347 347 275 291 5767 0 0 0
normalized size 1 1. 0.79 0.84 16.62 0. 0. 0.
time (sec) N/A 0.184 2.553 0.273 11.272 0. 0. 0.
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 220 220 157 335 0 0 0 0
normalized size 1 1. 0.71 1.52 0. 0. 0. 0.
time (sec) N/A 0.144 2.395 0.26 0. 0. 0. 0.
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A F F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 98 98 154 144 138 0 0 170
normalized size 1 1. 1.57 1.47 1.41 0. 0. 1.73
time (sec) N/A 0.187 1.52 0.252 1.511 0. 0. 7.161
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B F F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 144 144 152 152 2411 0 0 316
normalized size 1 1. 1.06 1.06 16.74 0. 0. 2.19
time (sec) N/A 0.288 0.839 0.253 2.546 0. 0. 4.428
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B F F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 140 140 151 152 1573 0 0 215
normalized size 1 1. 1.08 1.09 11.24 0. 0. 1.54
time (sec) N/A 0.282 0.641 0.291 2.434 0. 0. 2.403
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 270 270 195 223 2978 0 0 0
normalized size 1 1. 0.72 0.83 11.03 0. 0. 0.
time (sec) N/A 0.154 1.605 0.298 2.602 0. 0. 0.
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 345 345 275 286 5767 0 0 0
normalized size 1 1. 0.8 0.83 16.72 0. 0. 0.
time (sec) N/A 0.181 2.263 0.268 11.514 0. 0. 0.
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 151 151 149 237 1871 1446 0 0
normalized size 1 1. 0.99 1.57 12.39 9.58 0. 0.
time (sec) N/A 0.131 2.105 0.276 2.487 3.188 0. 0.
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 92 92 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.094 1.042 0.407 0. 0. 0. 0.
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 109 109 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.122 0.429 0.392 0. 0. 0. 0.
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 101 101 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.1 3.217 0.427 0. 0. 0. 0.
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 101 101 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.099 1.443 0.389 0. 0. 0. 0.
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 99 99 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.075 1.577 0.391 0. 0. 0. 0.
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 99 99 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.1 0.97 0.396 0. 0. 0. 0.
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 101 101 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.1 1.574 0.287 0. 0. 0. 0.
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F(-1) F(-1)
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 172 172 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.145 8.511 0.282 0. 0. 0. 0.
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F(-1) F(-1)
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 119 119 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.162 11.806 0.302 0. 0. 0. 0.
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F F(-1)
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 68 68 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.083 0.147 0.302 0. 0. 0. 0.
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F F(-1)
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 139 139 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.112 1.369 0.295 0. 0. 0. 0.
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F(-1) F(-1)
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 205 205 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.168 1.653 0.264 0. 0. 0. 0.
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 91 91 133 141 0 782 0 0
normalized size 1 1. 1.46 1.55 0. 8.59 0. 0.
time (sec) N/A 0.082 0.706 0.227 0. 1.584 0. 0.
Problem 144 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 231 231 814 295 0 0 0 0
normalized size 1 1. 3.52 1.28 0. 0. 0. 0.
time (sec) N/A 0.257 17.997 0.398 0. 0. 0. 0.
Problem 145 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 225 225 180 285 0 0 0 0
normalized size 1 1. 0.8 1.27 0. 0. 0. 0.
time (sec) N/A 0.211 8.52 0.414 0. 0. 0. 0.
Problem 146 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 319 319 193 327 0 0 0 0
normalized size 1 1. 0.61 1.03 0. 0. 0. 0.
time (sec) N/A 0.37 5.374 0.351 0. 0. 0. 0.
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) A F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 271 271 589 546 0 1181 0 0
normalized size 1 1. 2.17 2.01 0. 4.36 0. 0.
time (sec) N/A 0.173 14.618 0.413 0. 1.699 0. 0.
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) A F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 205 205 519 389 0 976 0 0
normalized size 1 1. 2.53 1.9 0. 4.76 0. 0.
time (sec) N/A 0.141 14.566 0.307 0. 1.592 0. 0.
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-1) A F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 144 144 444 248 0 819 0 0
normalized size 1 1. 3.08 1.72 0. 5.69 0. 0.
time (sec) N/A 0.116 6.591 0.272 0. 1.301 0. 0.
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 66 66 76 118 198 620 0 0
normalized size 1 1. 1.15 1.79 3. 9.39 0. 0.
time (sec) N/A 0.087 0.316 0.214 1.678 1.155 0. 0.
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F A F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 105 105 2686 501 0 1704 0 0
normalized size 1 1. 25.58 4.77 0. 16.23 0. 0.
time (sec) N/A 0.23 24.991 0.288 0. 2.954 0. 0.
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) A F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 219 219 2943 97143 0 3494 0 0
normalized size 1 1. 13.44 443.58 0. 15.95 0. 0.
time (sec) N/A 0.222 28.425 1.534 0. 13.778 0. 0.
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) B F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 287 287 3106 330372 0 5542 0 0
normalized size 1 1. 10.82 1151.12 0. 19.31 0. 0.
time (sec) N/A 0.307 24.137 14.995 0. 27.238 0. 0.
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 241 241 219 539 0 1230 0 0
normalized size 1 1. 0.91 2.24 0. 5.1 0. 0.
time (sec) N/A 0.2 3.869 0.316 0. 1.345 0. 0.
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 176 176 145 382 0 1006 0 0
normalized size 1 1. 0.82 2.17 0. 5.72 0. 0.
time (sec) N/A 0.144 1.336 0.271 0. 1.217 0. 0.
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 105 105 102 237 1347 819 0 0
normalized size 1 1. 0.97 2.26 12.83 7.8 0. 0.
time (sec) N/A 0.15 0.562 0.229 1.903 1.204 0. 0.
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 110 110 135 864 0 1804 0 0
normalized size 1 1. 1.23 7.85 0. 16.4 0. 0.
time (sec) N/A 0.241 0.478 0.217 0. 8.844 0. 0.
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) A F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 229 229 2886 62283 0 4466 0 0
normalized size 1 1. 12.6 271.98 0. 19.5 0. 0.
time (sec) N/A 0.249 24.763 1.636 0. 30.339 0. 0.
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) B F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 310 310 3190 234091 0 6322 0 0
normalized size 1 1. 10.29 755.13 0. 20.39 0. 0.
time (sec) N/A 0.342 24.581 10.07 0. 79.148 0. 0.
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 336 336 286 677 0 1513 0 0
normalized size 1 1. 0.85 2.01 0. 4.5 0. 0.
time (sec) N/A 0.209 6.189 0.343 0. 1.095 0. 0.
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 258 258 191 504 0 1233 0 0
normalized size 1 1. 0.74 1.95 0. 4.78 0. 0.
time (sec) N/A 0.177 2.684 0.283 0. 1.103 0. 0.
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 142 142 128 341 1885 976 0 0
normalized size 1 1. 0.9 2.4 13.27 6.87 0. 0.
time (sec) N/A 0.232 0.922 0.241 1.97 1.025 0. 0.
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F A F(-1) F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 203 203 343 1487 0 2773 0 0
normalized size 1 1. 1.69 7.33 0. 13.66 0. 0.
time (sec) N/A 0.232 6.489 0.237 0. 19.611 0. 0.
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) A F(-1) F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 329 329 280 46082 0 4579 0 0
normalized size 1 1. 0.85 140.07 0. 13.92 0. 0.
time (sec) N/A 0.337 3.725 0.848 0. 89.091 0. 0.
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) A F(-1) F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 536 536 3368 209489 0 7337 0 0
normalized size 1 1. 6.28 390.84 0. 13.69 0. 0.
time (sec) N/A 0.492 25.668 6.465 0. 172.515 0. 0.
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-2) A F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 258 258 787 907 0 1553 0 0
normalized size 1 1. 3.05 3.52 0. 6.02 0. 0.
time (sec) N/A 0.207 8.115 0.307 0. 72.664 0. 0.
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-2) A F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 183 183 295 358 0 1246 0 0
normalized size 1 1. 1.61 1.96 0. 6.81 0. 0.
time (sec) N/A 0.158 2.468 0.24 0. 16.946 0. 0.
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 91 91 92 194 0 824 0 0
normalized size 1 1. 1.01 2.13 0. 9.05 0. 0.
time (sec) N/A 0.11 0.287 0.217 0. 5.146 0. 0.
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F A F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 166 166 431238 662 0 2695 0 0
normalized size 1 1. 2597.82 3.99 0. 16.23 0. 0.
time (sec) N/A 0.372 38.708 0.249 0. 100.191 0. 0.
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F A F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 416 416 472069 117715 0 6564 0 0
normalized size 1 1. 1134.78 282.97 0. 15.78 0. 0.
time (sec) N/A 0.422 35.861 2.335 0. 96.091 0. 0.
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) A F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 653 653 652560 402966 0 10966 0 0
normalized size 1 1. 999.33 617.1 0. 16.79 0. 0.
time (sec) N/A 0.646 38.679 20.612 0. 132.514 0. 0.
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) A F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 324 324 856 957 0 1740 0 0
normalized size 1 1. 2.64 2.95 0. 5.37 0. 0.
time (sec) N/A 0.237 6.507 0.268 0. 66.132 0. 0.
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F A F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 290 290 16163 756 0 1578 0 0
normalized size 1 1. 55.73 2.61 0. 5.44 0. 0.
time (sec) N/A 0.217 27.706 0.19 0. 29.978 0. 0.
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 127 127 10115 554 0 1416 0 0
normalized size 1 1. 79.65 4.36 0. 11.15 0. 0.
time (sec) N/A 0.183 26.611 0.174 0. 7.86 0. 0.
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F A F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 394 394 377837 2076 0 5720 0 0
normalized size 1 1. 958.98 5.27 0. 14.52 0. 0.
time (sec) N/A 0.335 35.08 0.294 0. 54.434 0. 0.
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) F(-1) F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 560 560 581056 164796 0 0 0 0
normalized size 1 1. 1037.6 294.28 0. 0. 0. 0.
time (sec) N/A 0.511 37.741 3.779 0. 0. 0. 0.
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) F(-1) F(-1) F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 802 802 774154 480553 0 0 0 0
normalized size 1 1. 965.28 599.19 0. 0. 0. 0.
time (sec) N/A 0.797 40.873 28.445 0. 0. 0. 0.
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) A F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 480 480 21204 1444 0 2188 0 0
normalized size 1 1. 44.18 3.01 0. 4.56 0. 0.
time (sec) N/A 0.316 29.311 0.278 0. 145.17 0. 0.
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) A F(-1) F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 468 468 16259 1133 0 1967 0 0
normalized size 1 1. 34.74 2.42 0. 4.2 0. 0.
time (sec) N/A 0.295 27.949 0.208 0. 65.139 0. 0.
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F(-1) F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 164 164 10177 824 0 1754 0 0
normalized size 1 1. 62.05 5.02 0. 10.7 0. 0.
time (sec) N/A 0.265 26.881 0.185 0. 16.705 0. 0.
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) F(-1) F F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 592 592 484869 3860 0 0 0 0
normalized size 1 1. 819.04 6.52 0. 0. 0. 0.
time (sec) N/A 0.457 36.987 0.29 0. 0. 0. 0.
Problem 182 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) F(-1) F(-1) F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 756 756 686248 197500 0 0 0 0
normalized size 1 1. 907.74 261.24 0. 0. 0. 0.
time (sec) N/A 0.634 39.996 5.676 0. 0. 0. 0.
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) F(-1) F(-1) F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 999 999 891356 556423 0 0 0 0
normalized size 1 1. 892.25 556.98 0. 0. 0. 0.
time (sec) N/A 0.914 43.595 37.042 0. 0. 0. 0.
Problem 184 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 123 123 240 1563 0 2034 0 0
normalized size 1 1. 1.95 12.71 0. 16.54 0. 0.
time (sec) N/A 0.339 18.159 0.42 0. 1.403 0. 0.
Problem 185 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 61 61 102 189 0 502 0 0
normalized size 1 1. 1.67 3.1 0. 8.23 0. 0.
time (sec) N/A 0.097 0.214 0.318 0. 0.798 0. 0.
Problem 186 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 111 111 135 377 0 1262 0 0
normalized size 1 1. 1.22 3.4 0. 11.37 0. 0.
time (sec) N/A 0.357 0.956 0.338 0. 0.92 0. 0.
Problem 187 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 141 141 184 494 0 2190 0 0
normalized size 1 1. 1.3 3.5 0. 15.53 0. 0.
time (sec) N/A 0.369 14.504 0.33 0. 1.892 0. 0.
Problem 188 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 141 141 171 424 0 2290 0 0
normalized size 1 1. 1.21 3.01 0. 16.24 0. 0.
time (sec) N/A 0.339 0.343 0.332 0. 3.868 0. 0.
Problem 189 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 67 67 68 113 0 540 0 142
normalized size 1 1. 1.01 1.69 0. 8.06 0. 2.12
time (sec) N/A 0.126 0.151 0.066 0. 0.593 0. 1.477
Problem 190 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 123 123 155 328 0 1226 0 282
normalized size 1 1. 1.26 2.67 0. 9.97 0. 2.29
time (sec) N/A 0.247 0.643 0.086 0. 0.602 0. 1.46
Problem 191 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 204 204 267 1063 0 2479 0 644
normalized size 1 1. 1.31 5.21 0. 12.15 0. 3.16
time (sec) N/A 0.51 1.311 0.091 0. 0.747 0. 1.552
Problem 192 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 133 133 136 462 0 1426 0 332
normalized size 1 1. 1.02 3.47 0. 10.72 0. 2.5
time (sec) N/A 0.285 0.643 0.085 0. 0.621 0. 1.46
Problem 193 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 237 237 493 1593 0 2946 0 926
normalized size 1 1. 2.08 6.72 0. 12.43 0. 3.91
time (sec) N/A 0.796 2.019 0.098 0. 0.821 0. 1.579
Problem 194 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 377 377 438 3293 0 5010 0 1692
normalized size 1 1. 1.16 8.73 0. 13.29 0. 4.49
time (sec) N/A 1.999 3.322 0.113 0. 1.109 0. 1.632
Problem 195 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 254 254 517 2031 0 3343 0 1150
normalized size 1 1. 2.04 8. 0. 13.16 0. 4.53
time (sec) N/A 1.132 2.252 0.111 0. 0.928 0. 1.565
Problem 196 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 412 412 459 4330 0 5782 0 2213
normalized size 1 1. 1.11 10.51 0. 14.03 0. 5.37
time (sec) N/A 1.062 3.805 0.167 0. 1.273 0. 1.79
Problem 197 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 622 622 1285 8573 0 9385 0 4470
normalized size 1 1. 2.07 13.78 0. 15.09 0. 7.19
time (sec) N/A 1.769 6.842 0.159 0. 1.999 0. 2.036
Problem 198 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 320 320 913 1372 0 0 0 0
normalized size 1 1. 2.85 4.29 0. 0. 0. 0.
time (sec) N/A 0.283 17.81 0.38 0. 0. 0. 0.
Problem 199 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 220 220 229 443 0 0 0 0
normalized size 1 1. 1.04 2.01 0. 0. 0. 0.
time (sec) N/A 0.244 4.205 0.335 0. 0. 0. 0.
Problem 200 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 380 380 6093 2337 0 0 0 0
normalized size 1 1. 16.03 6.15 0. 0. 0. 0.
time (sec) N/A 0.433 24.346 0.424 0. 0. 0. 0.
Problem 201 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 326 326 233 581 0 0 0 0
normalized size 1 1. 0.71 1.78 0. 0. 0. 0.
time (sec) N/A 0.361 5.627 0.305 0. 0. 0. 0.
Problem 202 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 442 442 7168 3285 0 0 0 0
normalized size 1 1. 16.22 7.43 0. 0. 0. 0.
time (sec) N/A 0.629 25.286 0.687 0. 0. 0. 0.
Problem 203 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 208 208 147 215 0 0 0 0
normalized size 1 1. 0.71 1.03 0. 0. 0. 0.
time (sec) N/A 0.117 2.483 0.325 0. 0. 0. 0.
Problem 204 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 216 216 254 318 0 0 0 0
normalized size 1 1. 1.18 1.47 0. 0. 0. 0.
time (sec) N/A 0.238 9.955 0.31 0. 0. 0. 0.
Problem 205 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 376 376 1491 2009 0 0 0 0
normalized size 1 1. 3.97 5.34 0. 0. 0. 0.
time (sec) N/A 0.428 14.561 0.327 0. 0. 0. 0.
Problem 206 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 495 495 2083 5712 0 0 0 0
normalized size 1 1. 4.21 11.54 0. 0. 0. 0.
time (sec) N/A 0.778 17.104 0.368 0. 0. 0. 0.
Problem 207 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 389 389 39925 543 0 0 0 0
normalized size 1 1. 102.63 1.4 0. 0. 0. 0.
time (sec) N/A 0.447 32.517 0.434 0. 0. 0. 0.
Problem 208 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 198 198 336 352 0 0 0 0
normalized size 1 1. 1.7 1.78 0. 0. 0. 0.
time (sec) N/A 0.106 5.191 0.376 0. 0. 0. 0.
Problem 209 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 598 598 1678 2847 0 0 0 0
normalized size 1 1. 2.81 4.76 0. 0. 0. 0.
time (sec) N/A 0.902 9.258 0.484 0. 0. 0. 0.
Problem 210 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 899 899 1960 15728 0 0 0 0
normalized size 1 1. 2.18 17.49 0. 0. 0. 0.
time (sec) N/A 2.258 6.719 0.621 0. 0. 0. 0.
Problem 211 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 744 744 1720 4298 0 0 0 0
normalized size 1 1. 2.31 5.78 0. 0. 0. 0.
time (sec) N/A 1.106 9.454 0.442 0. 0. 0. 0.
Problem 212 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 919 919 1930 13060 0 0 0 0
normalized size 1 1. 2.1 14.21 0. 0. 0. 0.
time (sec) N/A 2.132 6.635 0.536 0. 0. 0. 0.
Problem 213 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 1122 1122 2355 39418 0 0 0 0
normalized size 1 1. 2.1 35.13 0. 0. 0. 0.
time (sec) N/A 3.163 7.319 1.249 0. 0. 0. 0.
Problem 214 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 891 891 1996 15912 0 0 0 0
normalized size 1 1. 2.24 17.86 0. 0. 0. 0.
time (sec) N/A 2.009 6.695 0.607 0. 0. 0. 0.
Problem 215 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 1150 1150 2314 32283 0 0 0 0
normalized size 1 1. 2.01 28.07 0. 0. 0. 0.
time (sec) N/A 3.435 7.167 1.121 0. 0. 0. 0.
Problem 216 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 1428 1428 2949 75468 0 0 0 0
normalized size 1 1. 2.07 52.85 0. 0. 0. 0.
time (sec) N/A 5.438 8.174 2.485 0. 0. 0. 0.
Problem 217 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F C A F F(-1) F(-1) F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 652 0 49385 491 0 0 0 0
normalized size 1 0. 75.74 0.75 0. 0. 0. 0.
time (sec) N/A 0.093 32.658 0.386 0. 0. 0. 0.
Problem 218 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 198 198 325 352 0 0 0 0
normalized size 1 1. 1.64 1.78 0. 0. 0. 0.
time (sec) N/A 0.111 5.25 0.372 0. 0. 0. 0.
Problem 219 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 398 398 249 292 0 0 0 0
normalized size 1 1. 0.63 0.73 0. 0. 0. 0.
time (sec) N/A 0.437 1.983 0.372 0. 0. 0. 0.
Problem 220 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 622 763 1731 3451 0 0 0 0
normalized size 1 1.23 2.78 5.55 0. 0. 0. 0.
time (sec) N/A 1.316 9.535 0.463 0. 0. 0. 0.
Problem 221 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 88 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.191 2.16 0.257 0. 0. 0. 0.
Problem 222 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-1) F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 31 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.092 46.951 0.143 0. 0. 0. 0.
Problem 223 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-1) F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 31 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.091 77.687 0.18 0. 0. 0. 0.
Problem 224 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 88 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.22 2.171 0.227 0. 0. 0. 0.
Problem 225 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-1) F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 31 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.097 47.852 0.16 0. 0. 0. 0.
Problem 226 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-1) F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 31 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.096 82.067 0.172 0. 0. 0. 0.
Problem 227 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-1) F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 88 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.218 57.332 0.143 0. 0. 0. 0.
Problem 228 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-1) F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 31 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.097 92.543 0.158 0. 0. 0. 0.
Problem 229 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-1) F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 31 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.097 132.591 0.168 0. 0. 0. 0.
Problem 230 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 106 106 2425 0 0 0 0 0
normalized size 1 1. 22.88 0. 0. 0. 0. 0.
time (sec) N/A 0.189 14.44 0.349 0. 0. 0. 0.
Problem 231 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F(-1) F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 275 275 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.437 2.398 0.173 0. 0. 0. 0.
Problem 232 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 205 205 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.249 1. 0.161 0. 0. 0. 0.
Problem 233 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 156 156 124 0 0 0 0 0
normalized size 1 1. 0.79 0. 0. 0. 0. 0.
time (sec) N/A 0.146 0.202 0.148 0. 0. 0. 0.
Problem 234 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 208 208 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.271 1.205 0.15 0. 0. 0. 0.
Problem 235 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F(-1) F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 248 248 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.451 1.797 0.161 0. 0. 0. 0.
Problem 236 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 55 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.116 2.421 0.251 0. 0. 0. 0.
Problem 237 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 296 296 278 0 0 0 0 0
normalized size 1 1. 0.94 0. 0. 0. 0. 0.
time (sec) N/A 0.515 1.052 0.163 0. 0. 0. 0.
Problem 238 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 211 211 200 0 0 0 0 0
normalized size 1 1. 0.95 0. 0. 0. 0. 0.
time (sec) N/A 0.242 0.493 0.15 0. 0. 0. 0.
Problem 239 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 156 156 125 0 0 0 0 0
normalized size 1 1. 0.8 0. 0. 0. 0. 0.
time (sec) N/A 0.144 0.222 0.133 0. 0. 0. 0.
Problem 240 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 206 206 5411 0 0 0 0 0
normalized size 1 1. 26.27 0. 0. 0. 0. 0.
time (sec) N/A 0.402 25.592 0.147 0. 0. 0. 0.
Problem 241 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F(-1) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 322 322 10678 0 0 0 0 0
normalized size 1 1. 33.16 0. 0. 0. 0. 0.
time (sec) N/A 0.559 32.853 0.154 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 [31] had the largest ratio of [ 0.5769 ]

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 15 9 1. 26 0.346
2 A 11 8 1. 26 0.308
3 A 5 3 1. 26 0.115
4 A 4 3 1. 26 0.115
5 A 4 3 1. 24 0.125
6 A 8 6 1. 26 0.231
7 A 9 6 1. 26 0.231
8 A 12 7 1. 26 0.269
9 A 15 7 1. 26 0.269
10 A 18 7 1. 26 0.269
11 A 13 8 1. 26 0.308
12 A 6 3 1. 26 0.115
13 A 5 3 1. 26 0.115
14 A 5 3 1. 26 0.115
15 A 9 8 1. 24 0.333
16 A 15 11 1. 26 0.423
17 A 13 9 1. 26 0.346
18 A 15 9 1. 26 0.346
19 A 19 9 1. 26 0.346
20 A 23 9 1. 26 0.346
21 A 26 14 1.12 26 0.538
22 A 21 13 1. 26 0.5
23 A 13 9 1. 26 0.346
24 A 9 6 1. 26 0.231
25 A 7 5 1. 24 0.208
26 A 4 3 1. 26 0.115
27 A 4 3 1. 26 0.115
28 A 5 3 1. 26 0.115
29 A 13 8 1. 26 0.308
30 A 17 9 1. 26 0.346
31 A 29 15 1. 26 0.577
32 A 20 13 1. 26 0.5
33 A 15 9 1. 26 0.346
34 A 12 7 1. 26 0.269
35 A 9 6 1. 24 0.25
36 A 12 8 1. 26 0.308
37 A 5 3 1. 26 0.115
38 A 5 3 1. 26 0.115
39 A 6 3 1. 26 0.115
40 A 14 8 1. 26 0.308
41 A 18 9 1. 26 0.346
42 A 5 4 1. 28 0.143
43 A 5 4 1. 28 0.143
44 A 5 4 1. 28 0.143
45 A 4 4 1. 26 0.154
46 A 4 4 1. 28 0.143
47 A 5 4 1. 28 0.143
48 A 6 4 1. 28 0.143
49 A 7 4 1. 28 0.143
50 A 6 5 1. 28 0.179
51 A 6 5 1. 28 0.179
52 A 5 5 1. 26 0.192
53 A 4 4 1. 28 0.143
54 A 5 5 1. 28 0.179
55 A 6 5 1. 28 0.179
56 A 7 5 1. 28 0.179
57 A 5 4 1. 28 0.143
58 A 5 4 1. 28 0.143
59 A 5 4 1. 26 0.154
60 A 5 4 1. 28 0.143
61 A 5 4 1. 28 0.143
62 A 5 4 1. 28 0.143
63 A 5 4 1. 28 0.143
64 A 5 4 1. 28 0.143
65 A 8 6 1. 28 0.214
66 A 7 6 1. 28 0.214
67 A 6 5 1. 28 0.179
68 A 5 4 1. 26 0.154
69 A 6 5 1. 28 0.179
70 A 7 6 1. 28 0.214
71 A 8 6 1. 28 0.214
72 A 8 6 1. 28 0.214
73 A 7 6 1. 28 0.214
74 A 7 6 1.13 28 0.214
75 A 6 5 1.15 26 0.192
76 A 7 6 1. 28 0.214
77 A 8 6 1. 28 0.214
78 A 9 6 1. 28 0.214
79 A 9 7 1. 28 0.25
80 A 8 7 1. 28 0.25
81 A 7 6 1. 28 0.214
82 A 7 6 1. 28 0.214
83 A 7 6 1.22 26 0.231
84 A 8 7 1. 28 0.25
85 A 9 7 1. 28 0.25
86 A 5 3 1. 30 0.1
87 A 4 3 1. 30 0.1
88 A 3 3 1. 30 0.1
89 A 2 2 1. 30 0.067
90 A 2 2 1. 30 0.067
91 A 3 3 1. 30 0.1
92 A 4 3 1. 30 0.1
93 A 5 3 1. 30 0.1
94 A 5 4 1. 30 0.133
95 A 3 3 1. 30 0.1
96 A 3 3 1. 30 0.1
97 A 3 2 1. 30 0.067
98 A 3 3 1. 30 0.1
99 A 4 4 1. 30 0.133
100 A 5 4 1. 30 0.133
101 A 4 3 1. 30 0.1
102 A 5 4 1. 30 0.133
103 A 4 3 1. 30 0.1
104 A 3 2 1. 30 0.067
105 A 3 3 1. 30 0.1
106 A 3 3 1. 30 0.1
107 A 4 4 1. 30 0.133
108 A 5 4 1. 30 0.133
109 A 6 4 1. 30 0.133
110 A 3 2 1. 30 0.067
111 A 3 2 1. 30 0.067
112 A 3 2 1. 30 0.067
113 A 2 2 1. 30 0.067
114 A 2 2 1. 30 0.067
115 A 3 2 1.29 30 0.067
116 A 3 2 1. 30 0.067
117 A 3 2 1. 30 0.067
118 A 3 3 1. 30 0.1
119 A 3 3 1. 30 0.1
120 A 3 3 1. 30 0.1
121 A 3 2 1. 30 0.067
122 A 3 3 1. 30 0.1
123 A 3 2 1. 30 0.067
124 A 3 2 1. 30 0.067
125 A 3 3 1. 30 0.1
126 A 4 4 1. 30 0.133
127 A 4 3 1. 30 0.1
128 A 3 2 1. 30 0.067
129 A 3 2 1. 30 0.067
130 A 4 3 1. 30 0.1
131 A 2 2 1. 24 0.083
132 A 3 3 1. 26 0.115
133 A 3 3 1. 26 0.115
134 A 3 3 1. 26 0.115
135 A 3 3 1. 24 0.125
136 A 3 3 1. 26 0.115
137 A 3 3 1. 26 0.115
138 A 4 3 1. 28 0.107
139 A 3 3 1. 28 0.107
140 A 2 2 1. 28 0.071
141 A 4 4 1. 28 0.143
142 A 5 5 1. 28 0.179
143 A 6 5 1. 27 0.185
144 A 3 3 1. 27 0.111
145 A 3 3 1. 27 0.111
146 A 5 5 1. 27 0.185
147 A 5 4 1. 27 0.148
148 A 5 4 1. 27 0.148
149 A 5 4 1. 27 0.148
150 A 4 4 1. 25 0.16
151 A 5 5 1. 27 0.185
152 A 7 6 1. 27 0.222
153 A 8 7 1. 27 0.259
154 A 6 5 1. 27 0.185
155 A 5 5 1. 27 0.185
156 A 5 5 1. 25 0.2
157 A 5 5 1. 27 0.185
158 A 7 6 1. 27 0.222
159 A 8 6 1. 27 0.222
160 A 5 4 1. 27 0.148
161 A 5 4 1. 27 0.148
162 A 6 5 1. 25 0.2
163 A 7 5 1. 27 0.185
164 A 10 6 1. 27 0.222
165 A 14 6 1. 27 0.222
166 A 9 5 1. 27 0.185
167 A 7 4 1. 27 0.148
168 A 5 4 1. 25 0.16
169 A 8 7 1. 27 0.259
170 A 12 6 1. 27 0.222
171 A 16 6 1. 27 0.222
172 A 10 5 1. 27 0.185
173 A 10 5 1. 27 0.185
174 A 6 5 1. 25 0.2
175 A 12 6 1. 27 0.222
176 A 15 6 1. 27 0.222
177 A 19 6 1. 27 0.222
178 A 14 5 1. 27 0.185
179 A 14 5 1. 27 0.185
180 A 7 5 1. 25 0.2
181 A 16 6 1. 27 0.222
182 A 19 6 1. 27 0.222
183 A 23 6 1. 27 0.222
184 A 5 5 1. 29 0.172
185 A 2 2 1. 29 0.069
186 A 5 5 1. 29 0.172
187 A 5 4 1. 29 0.138
188 A 5 4 1. 29 0.138
189 A 4 4 1. 23 0.174
190 A 5 5 1. 23 0.217
191 A 6 6 1. 23 0.261
192 A 5 5 1. 25 0.2
193 A 6 6 1. 25 0.24
194 A 7 7 1. 25 0.28
195 A 6 6 1. 25 0.24
196 A 7 7 1. 25 0.28
197 A 8 8 1. 25 0.32
198 A 5 5 1. 25 0.2
199 A 3 3 1. 27 0.111
200 A 6 6 1. 25 0.24
201 A 5 5 1. 27 0.185
202 A 7 7 1. 25 0.28
203 A 3 3 1. 25 0.12
204 A 3 3 1. 27 0.111
205 A 6 6 1. 25 0.24
206 A 7 7 1. 25 0.28
207 A 3 3 1. 29 0.103
208 A 1 1 1. 29 0.034
209 A 5 5 1. 29 0.172
210 A 7 7 1. 29 0.241
211 A 6 6 1. 29 0.207
212 A 7 7 1. 29 0.241
213 A 8 8 1. 29 0.276
214 A 7 7 1. 29 0.241
215 A 8 8 1. 29 0.276
216 A 9 8 1. 29 0.276
217 F 0 0 N/A 0 N/A
218 A 1 1 1. 29 0.034
219 A 3 3 1. 29 0.103
220 A 6 6 1.23 29 0.207
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.
228 A 0 0 0. 0 0.
229 A 0 0 0. 0 0.
230 A 4 4 1. 27 0.148
231 A 8 6 1. 27 0.222
232 A 7 5 1. 27 0.185
233 A 6 4 1. 25 0.16
234 A 7 5 1. 27 0.185
235 A 8 6 1. 27 0.222
236 A 0 0 0. 0 0.
237 A 8 6 1. 27 0.222
238 A 7 5 1. 27 0.185
239 A 6 4 1. 25 0.16
240 A 7 5 1. 27 0.185
241 A 10 5 1. 27 0.185

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