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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 }

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, 29, 30, 31, 33, 34, 35, 36, 37, 38, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 55, 56, 57, 58, 59, 61, 63, 64, 65, 66, 67, 68, 69, 70, 72, 73, 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, 113, 114, 115, 116, 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, 175, 176, 177, 178, 179, 180, 181, 182, 183 }

B grade: { 28, 52, 54, 60, 62, 71, 173, 174 }

C grade: { 32, 74, 112, 117 }

F grade: { 39, 40}

2.1.3 Maple

A grade: { 4, 5, 6, 12, 13, 19, 20, 21, 25, 29, 30, 33, 34, 35, 39, 40, 68, 69, 70, 75, 79, 80, 102, 103, 107, 108, 109, 113, 114, 115, 117, 118, 119, 120, 121, 122, 123, 127, 128, 129, 142, 143, 147, 148, 150, 154, 155, 159, 164, 165, 166, 171, 172, 176, 177, 178, 182, 183 }

B grade: { 1, 2, 3, 7, 8, 9, 10, 11, 14, 15, 16, 17, 18, 22, 23, 24, 28, 31, 32, 38, 99, 100, 101, 104, 105, 106, 110, 111, 112, 116, 156, 157, 158, 161, 163, 167, 170, 175 }

C grade: { 63, 64, 65, 66, 67, 81, 82, 83, 84, 85, 86, 87 }

F grade: { 26, 27, 36, 37, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 71, 72, 73, 74, 76, 77, 78, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 124, 125, 126, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 144, 145, 146, 149, 151, 152, 153, 160, 162, 168, 169, 173, 174, 179, 180, 181 }

2.1.4 Maxima

A grade: { 5, 6, 7, 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 24, 25, 29, 30, 34, 35, 39, 40, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 66, 67, 68, 69, 70, 75, 76, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 101, 102, 103, 104, 107, 108, 109, 110, 113, 114, 115, 119, 120, 121, 122, 123, 127, 128, 129, 133, 134, 135, 142, 143, 147, 148, 149, 150, 154, 155, 158, 159, 160, 161, 163, 164, 165, 166, 167, 171, 172, 176, 177, 178, 182, 183

B grade: { 1, 2, 3, 4, 8, 9, 16, 17, 18, 19, 31, 33, 41, 42, 43, 44, 63, 64, 65, 99, 100, 105, 106, 111, 116, 118, 156, 157, 162 }

C grade: { }

F grade: { 26, 27, 28, 32, 36, 37, 38, 71, 72, 73, 74, 77, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 112, 117, 124, 125, 126, 130, 131, 132, 136, 137, 138, 139, 140, 141, 144, 145, 146, 151, 152, 153, 168, 169, 170, 173, 174, 175, 179, 180, 181 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 9, 10, 11, 12, 18, 19, 20, 23, 24, 25, 29, 30, 34, 35, 39, 40, 44, 51, 59, 65, 68, 69, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 99, 100, 101, 102, 103, 105, 106, 107, 108, 114, 115, 119, 120, 142, 143, 147, 148, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 162, 163, 164, 165, 166, 171, 172, 176, 177, 178, 179, 180, 181, 182, 183 }

B grade: { 6, 7, 8, 13, 14, 15, 16, 17, 21, 22, 28, 33, 38, 41, 42, 43, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 66, 67, 72, 104, 109, 110, 112, 113, 117, 118, 161, 167, 170, 175 }

C grade: { 26, 27, 31, 32, 36, 37, 111, 116, 168, 169, 173, 174 }

F grade: { 70, 71, 73, 74, 95, 96, 97, 98, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 144, 145, 146, 149 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 8, 9, 10, 11, 16, 17, 18, 19, 23, 24, 25, 29, 30, 34, 35, 39, 68, 69, 75, 79, 80, 99, 100, 101, 105, 106, 107, 113, 114, 115, 118, 119, 142, 143, 149, 154, 155, 156, 157, 158, 162, 163, 164, 182, 183 }

B grade: { }

C grade: { 63, 64, 65, 66 }

F grade: { 5, 6, 7, 12, 13, 14, 15, 20, 21, 22, 26, 27, 28, 31, 32, 33, 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, 67, 70, 71, 72, 73, 74, 76, 77, 78, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 102, 103, 104, 108, 109, 110, 111, 112, 116, 117, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 144, 145, 146, 147, 148, 150, 151, 152, 153, 159, 160, 161, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181 }

2.1.7 Giac

A grade: { 4, 5, 10, 11, 12, 19, 20, 23, 24, 25, 29, 30, 34, 35, 39, 40, 41, 42, 43, 44, 63, 64, 65, 68, 69, 70, 75, 79, 80, 101, 102, 103, 107, 108, 113, 114, 115, 119, 120, 121, 122, 123, 124, 125, 126, 133, 134, 135, 136, 137, 138, 142, 143, 147, 148, 149, 150, 154, 155, 158, 159, 160, 164, 165, 166, 171, 172, 176, 177, 178, 182, 183 }

B grade: { 1, 2, 3, 6, 7, 8, 9, 14, 15, 16, 17, 18, 21, 22, 33, 99, 100, 104, 105, 106, 109, 110, 118, 156, 157, 161, 162, 163, 167 }

C grade: { }

F grade: { 13, 26, 27, 28, 31, 32, 36, 37, 38, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 66, 67, 71, 72, 73, 74, 76, 77, 78, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 111, 112, 116, 117, 127, 128, 129, 130, 131, 132, 139, 140, 141, 144, 145, 146, 151, 152, 153, 168, 169, 170, 173, 174, 175, 179, 180, 181 }

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 B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 91 91 76 547 440 351 311 437
normalized size 1 1. 0.84 6.01 4.84 3.86 3.42 4.8
time (sec) N/A 0.119 0.303 0.013 1.241 1.72 3.25 1.456
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 70 70 61 308 300 232 202 275
normalized size 1 1. 0.87 4.4 4.29 3.31 2.89 3.93
time (sec) N/A 0.079 0.193 0.006 1.289 1.979 1.564 1.39
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 44 147 182 140 112 151
normalized size 1 1. 0.9 3. 3.71 2.86 2.29 3.08
time (sec) N/A 0.047 0.14 0.007 1.194 1.906 0.754 1.32
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 28 28 27 53 92 73 46 62
normalized size 1 1. 0.96 1.89 3.29 2.61 1.64 2.21
time (sec) N/A 0.02 0.053 0.007 1.11 1.766 0.276 1.27
Problem 5 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 51 51 49 82 77 193 0 76
normalized size 1 1. 0.96 1.61 1.51 3.78 0. 1.49
time (sec) N/A 0.101 0.073 0.024 1.204 1.716 0. 1.218
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 71 71 65 133 109 316 0 201
normalized size 1 1. 0.92 1.87 1.54 4.45 0. 2.83
time (sec) N/A 0.119 0.243 0.033 1.359 1.769 0. 1.231
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 104 104 88 277 128 518 0 402
normalized size 1 1. 0.85 2.66 1.23 4.98 0. 3.87
time (sec) N/A 0.163 0.525 0.039 1.215 1.849 0. 1.256
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 162 162 132 910 516 662 660 502
normalized size 1 1. 0.81 5.62 3.19 4.09 4.07 3.1
time (sec) N/A 0.101 0.616 0.01 1.125 1.876 6.526 1.178
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 134 134 104 523 355 458 456 328
normalized size 1 1. 0.78 3.9 2.65 3.42 3.4 2.45
time (sec) N/A 0.073 0.41 0.01 1.105 1.795 3.506 1.373
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 95 95 75 262 223 286 264 184
normalized size 1 1. 0.79 2.76 2.35 3.01 2.78 1.94
time (sec) N/A 0.053 0.278 0.008 1.143 1.81 1.625 1.333
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 51 103 119 163 126 85
normalized size 1 1. 0.93 1.87 2.16 2.96 2.29 1.55
time (sec) N/A 0.025 0.155 0.008 1.065 1.83 0.674 1.254
Problem 12 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 78 78 64 97 97 232 0 92
normalized size 1 1. 0.82 1.24 1.24 2.97 0. 1.18
time (sec) N/A 0.154 0.114 0.071 1.345 1.783 0. 1.294
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 81 81 75 152 119 365 0 0
normalized size 1 1. 0.93 1.88 1.47 4.51 0. 0.
time (sec) N/A 0.146 0.402 0.076 1.237 1.785 0. 0.
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 112 112 102 299 134 597 0 446
normalized size 1 1. 0.91 2.67 1.2 5.33 0. 3.98
time (sec) N/A 0.187 0.88 0.081 1.288 1.85 0. 1.408
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 162 162 121 555 149 859 0 725
normalized size 1 1. 0.75 3.43 0.92 5.3 0. 4.48
time (sec) N/A 0.181 0.834 0.092 1.298 1.892 0. 1.33
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 225 225 385 1217 869 1149 772 883
normalized size 1 1. 1.71 5.41 3.86 5.11 3.43 3.92
time (sec) N/A 0.282 0.934 0.013 1.165 2.042 11.293 1.398
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 175 175 122 676 593 757 495 559
normalized size 1 1. 0.7 3.86 3.39 4.33 2.83 3.19
time (sec) N/A 0.176 0.926 0.01 1.101 2.111 5.883 1.368
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 123 123 93 320 367 474 284 311
normalized size 1 1. 0.76 2.6 2.98 3.85 2.31 2.53
time (sec) N/A 0.103 0.536 0.01 1.104 2.018 2.934 1.329
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 75 75 52 115 193 257 126 132
normalized size 1 1. 0.69 1.53 2.57 3.43 1.68 1.76
time (sec) N/A 0.044 0.227 0.009 1.072 1.961 1.334 1.304
Problem 20 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 121 121 102 166 158 398 0 151
normalized size 1 1. 0.84 1.37 1.31 3.29 0. 1.25
time (sec) N/A 0.24 0.227 0.088 1.278 1.984 0. 1.332
Problem 21 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 145 145 196 271 196 680 0 401
normalized size 1 1. 1.35 1.87 1.35 4.69 0. 2.77
time (sec) N/A 0.237 0.534 0.102 1.335 1.947 0. 1.395
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 184 184 218 562 196 1122 0 813
normalized size 1 1. 1.18 3.05 1.07 6.1 0. 4.42
time (sec) N/A 0.34 0.9 0.106 1.356 2.041 0. 1.308
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 172 172 100 432 238 486 262 203
normalized size 1 1. 0.58 2.51 1.38 2.83 1.52 1.18
time (sec) N/A 0.146 0.405 0.011 1.043 2.05 8.106 1.237
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 134 134 90 253 178 373 209 159
normalized size 1 1. 0.67 1.89 1.33 2.78 1.56 1.19
time (sec) N/A 0.107 0.157 0.007 1.048 1.986 4.356 1.302
Problem 25 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 80 80 53 120 130 306 144 116
normalized size 1 1. 0.66 1.5 1.62 3.82 1.8 1.45
time (sec) N/A 0.044 0.175 0.007 1.08 2.021 2.379 1.274
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 179 179 343 0 0 1300 0 0
normalized size 1 1. 1.92 0. 0. 7.26 0. 0.
time (sec) N/A 0.123 2.556 0.216 0. 2.251 0. 0.
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 119 119 199 0 0 845 0 0
normalized size 1 1. 1.67 0. 0. 7.1 0. 0.
time (sec) N/A 0.081 1.459 0.128 0. 2.229 0. 0.
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 61 61 129 449 0 463 0 0
normalized size 1 1. 2.11 7.36 0. 7.59 0. 0.
time (sec) N/A 0.037 0.079 0.007 0. 2.146 0. 0.
Problem 29 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 0.021 3.538 0.053 0. 0. 0. 0.
Problem 30 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 0.02 7.201 0.046 0. 0. 0. 0.
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 103 103 145 298 321 3131 0 0
normalized size 1 1. 1.41 2.89 3.12 30.4 0. 0.
time (sec) N/A 0.206 2.039 0.067 1.694 2.426 0. 0.
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F C F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 73 73 277 159 0 1777 0 0
normalized size 1 1. 3.79 2.18 0. 24.34 0. 0.
time (sec) N/A 0.133 6.281 0.031 0. 2.232 0. 0.
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 51 57 97 429 0 105
normalized size 1 1. 1.76 1.97 3.34 14.79 0. 3.62
time (sec) N/A 0.029 0.09 0.023 1.012 2.07 0. 1.315
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.037 17.409 0.073 0. 0. 0. 0.
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.035 17.628 0.085 0. 0. 0. 0.
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 296 296 455 0 0 11732 0 0
normalized size 1 1. 1.54 0. 0. 39.64 0. 0.
time (sec) N/A 0.217 27.244 0.193 0. 3.435 0. 0.
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 175 175 270 0 0 6791 0 0
normalized size 1 1. 1.54 0. 0. 38.81 0. 0.
time (sec) N/A 0.133 5.31 0.164 0. 2.832 0. 0.
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 102 102 180 216 0 3492 0 0
normalized size 1 1. 1.76 2.12 0. 34.24 0. 0.
time (sec) N/A 0.063 2.858 0.053 0. 2.521 0. 0.
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A F A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.037 180.016 0.3 0. 0. 0. 0.
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A F A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.034 180.015 0.422 0. 0. 0. 0.
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F B B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 171 171 107 0 416 1177 0 313
normalized size 1 1. 0.63 0. 2.43 6.88 0. 1.83
time (sec) N/A 0.33 0.052 0.046 1.083 2.128 0. 1.479
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 146 146 107 0 362 892 0 273
normalized size 1 1. 0.73 0. 2.48 6.11 0. 1.87
time (sec) N/A 0.243 0.101 0.045 1.086 2.166 0. 1.466
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 123 123 105 0 311 717 0 228
normalized size 1 1. 0.85 0. 2.53 5.83 0. 1.85
time (sec) N/A 0.178 0.092 0.043 1.117 2.083 0. 1.442
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F B A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 104 104 105 0 243 271 0 123
normalized size 1 1. 1.01 0. 2.34 2.61 0. 1.18
time (sec) N/A 0.13 0.043 0.046 1.084 2.096 0. 1.396
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 119 119 118 0 140 815 0 0
normalized size 1 1. 0.99 0. 1.18 6.85 0. 0.
time (sec) N/A 0.183 0.35 0.044 1.051 2.101 0. 0.
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 149 149 150 0 155 1224 0 0
normalized size 1 1. 1.01 0. 1.04 8.21 0. 0.
time (sec) N/A 0.248 0.709 0.043 1.206 2.157 0. 0.
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 174 174 191 0 155 1821 0 0
normalized size 1 1. 1.1 0. 0.89 10.47 0. 0.
time (sec) N/A 0.312 0.395 0.046 1.187 2.293 0. 0.
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A B F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 239 239 189 0 379 2319 0 0
normalized size 1 1. 0.79 0. 1.59 9.7 0. 0.
time (sec) N/A 0.4 1.156 0.085 1.59 2.256 0. 0.
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 211 211 163 0 323 1789 0 0
normalized size 1 1. 0.77 0. 1.53 8.48 0. 0.
time (sec) N/A 0.303 0.583 0.08 1.57 2.218 0. 0.
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 166 166 129 0 255 1438 0 0
normalized size 1 1. 0.78 0. 1.54 8.66 0. 0.
time (sec) N/A 0.269 0.44 0.08 1.549 2.215 0. 0.
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 138 138 141 0 144 369 0 0
normalized size 1 1. 1.02 0. 1.04 2.67 0. 0.
time (sec) N/A 0.214 0.118 0.088 1.568 2.211 0. 0.
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 142 142 570 0 157 1442 0 0
normalized size 1 1. 4.01 0. 1.11 10.15 0. 0.
time (sec) N/A 0.23 2.847 0.092 1.269 2.226 0. 0.
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 174 174 156 0 159 2053 0 0
normalized size 1 1. 0.9 0. 0.91 11.8 0. 0.
time (sec) N/A 0.309 1.35 0.102 1.206 2.328 0. 0.
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F A B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 220 220 825 0 157 2974 0 0
normalized size 1 1. 3.75 0. 0.71 13.52 0. 0.
time (sec) N/A 0.311 3.034 0.095 1.201 2.388 0. 0.
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 251 251 222 0 157 3951 0 0
normalized size 1 1. 0.88 0. 0.63 15.74 0. 0.
time (sec) N/A 0.379 0.828 0.104 1.213 2.29 0. 0.
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 381 381 243 0 693 4815 0 0
normalized size 1 1. 0.64 0. 1.82 12.64 0. 0.
time (sec) N/A 0.906 3.736 0.125 1.666 2.246 0. 0.
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 326 326 243 0 579 3621 0 0
normalized size 1 1. 0.75 0. 1.78 11.11 0. 0.
time (sec) N/A 0.712 1.929 0.119 1.86 2.018 0. 0.
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 275 275 210 0 451 2965 0 0
normalized size 1 1. 0.76 0. 1.64 10.78 0. 0.
time (sec) N/A 0.484 0.287 0.122 1.704 1.872 0. 0.
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 228 228 192 0 239 594 0 0
normalized size 1 1. 0.84 0. 1.05 2.61 0. 0.
time (sec) N/A 0.374 0.206 0.123 1.62 2.087 0. 0.
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 246 246 717 0 265 3313 0 0
normalized size 1 1. 2.91 0. 1.08 13.47 0. 0.
time (sec) N/A 0.421 2.736 0.155 1.363 2.376 0. 0.
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 277 277 253 0 262 4825 0 0
normalized size 1 1. 0.91 0. 0.95 17.42 0. 0.
time (sec) N/A 0.605 2.907 0.141 1.36 2.365 0. 0.
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F A B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 331 331 3211 0 265 7121 0 0
normalized size 1 1. 9.7 0. 0.8 21.51 0. 0.
time (sec) N/A 0.68 6.325 0.131 1.341 2.48 0. 0.
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C B B C A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 111 111 51 133 235 466 131 194
normalized size 1 1. 0.46 1.2 2.12 4.2 1.18 1.75
time (sec) N/A 0.155 0.013 0.027 1.062 1.839 142.406 1.232
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C B B C A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 92 92 48 121 200 355 100 138
normalized size 1 1. 0.52 1.32 2.17 3.86 1.09 1.5
time (sec) N/A 0.106 0.011 0.019 1.124 1.85 3.545 1.216
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C B A C A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 77 77 48 72 158 136 66 81
normalized size 1 1. 0.62 0.94 2.05 1.77 0.86 1.05
time (sec) N/A 0.077 0.008 0.022 1.057 1.833 1.643 1.292
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A B C F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 88 88 67 115 103 356 99 0
normalized size 1 1. 0.76 1.31 1.17 4.05 1.12 0.
time (sec) N/A 0.113 0.034 0.022 1.043 1.792 7.426 0.
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 114 114 78 126 78 452 0 0
normalized size 1 1. 0.68 1.11 0.68 3.96 0. 0.
time (sec) N/A 0.148 0.093 0.027 1.261 1.855 0. 0.
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.028 11.162 0.068 0. 0. 0. 0.
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.03 9.845 0.064 0. 0. 0. 0.
Problem 70 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 61 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.085 3.849 0.026 0. 0. 0. 0.
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 20 20 46 0 0 0 0 0
normalized size 1 1. 2.3 0. 0. 0. 0. 0.
time (sec) N/A 0.048 0.372 0.074 0. 0. 0. 0.
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 24 24 16 0 0 374 0 0
normalized size 1 1. 0.67 0. 0. 15.58 0. 0.
time (sec) N/A 0.05 0.074 0.079 0. 1.76 0. 0.
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 47 47 64 0 0 0 0 0
normalized size 1 1. 1.36 0. 0. 0. 0. 0.
time (sec) N/A 0.066 0.616 0.1 0. 0. 0. 0.
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 36 36 76 0 0 0 0 0
normalized size 1 1. 2.11 0. 0. 0. 0. 0.
time (sec) N/A 0.092 0.947 0.07 0. 0. 0. 0.
Problem 75 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 0.046 2.79 0.072 0. 0. 0. 0.
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 237 237 205 0 217 801 0 0
normalized size 1 1. 0.86 0. 0.92 3.38 0. 0.
time (sec) N/A 0.284 0.188 0.135 1.28 1.948 0. 0.
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 144 144 132 0 0 597 0 0
normalized size 1 1. 0.92 0. 0. 4.15 0. 0.
time (sec) N/A 0.184 0.202 0.091 0. 1.796 0. 0.
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 110 110 102 0 107 378 0 0
normalized size 1 1. 0.93 0. 0.97 3.44 0. 0.
time (sec) N/A 0.091 0.056 0.06 1.244 1.905 0. 0.
Problem 79 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 0.02 5.654 0.046 0. 0. 0. 0.
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.036 3.295 0.052 0. 0. 0. 0.
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 59 59 54 73 74 259 0 0
normalized size 1 1. 0.92 1.24 1.25 4.39 0. 0.
time (sec) N/A 0.074 0.038 0.033 1.26 1.818 0. 0.
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 59 59 54 73 74 259 0 0
normalized size 1 1. 0.92 1.24 1.25 4.39 0. 0.
time (sec) N/A 0.072 0.019 0.055 1.144 1.898 0. 0.
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 59 59 54 73 74 259 0 0
normalized size 1 1. 0.92 1.24 1.25 4.39 0. 0.
time (sec) N/A 0.071 0.032 0.048 1.153 1.748 0. 0.
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 59 59 54 73 74 227 0 0
normalized size 1 1. 0.92 1.24 1.25 3.85 0. 0.
time (sec) N/A 0.069 0.018 0.039 1.153 1.928 0. 0.
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 49 67 58 238 0 0
normalized size 1 1. 1. 1.37 1.18 4.86 0. 0.
time (sec) N/A 0.069 0.02 0.046 1.17 1.974 0. 0.
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 52 67 74 259 0 0
normalized size 1 1. 0.95 1.22 1.35 4.71 0. 0.
time (sec) N/A 0.069 0.019 0.055 1.155 1.849 0. 0.
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 59 59 55 71 74 259 0 0
normalized size 1 1. 0.93 1.2 1.25 4.39 0. 0.
time (sec) N/A 0.07 0.022 0.032 1.161 1.891 0. 0.
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 86 86 79 0 0 425 0 0
normalized size 1 1. 0.92 0. 0. 4.94 0. 0.
time (sec) N/A 0.15 0.106 0.048 0. 1.878 0. 0.
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 85 85 78 0 0 425 0 0
normalized size 1 1. 0.92 0. 0. 5. 0. 0.
time (sec) N/A 0.133 0.095 0.052 0. 1.803 0. 0.
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 86 86 79 0 0 425 0 0
normalized size 1 1. 0.92 0. 0. 4.94 0. 0.
time (sec) N/A 0.133 0.106 0.08 0. 1.741 0. 0.
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 85 85 76 0 0 374 0 0
normalized size 1 1. 0.89 0. 0. 4.4 0. 0.
time (sec) N/A 0.127 0.085 0.054 0. 1.861 0. 0.
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 72 72 64 0 0 363 0 0
normalized size 1 1. 0.89 0. 0. 5.04 0. 0.
time (sec) N/A 0.125 0.056 0.078 0. 1.981 0. 0.
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 83 83 73 0 0 423 0 0
normalized size 1 1. 0.88 0. 0. 5.1 0. 0.
time (sec) N/A 0.13 0.098 0.049 0. 2.092 0. 0.
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 84 84 84 0 0 425 0 0
normalized size 1 1. 1. 0. 0. 5.06 0. 0.
time (sec) N/A 0.14 0.102 0.049 0. 2.198 0. 0.
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 24 24 17 0 0 0 0 0
normalized size 1 1. 0.71 0. 0. 0. 0. 0.
time (sec) N/A 0.091 0.087 0.079 0. 0. 0. 0.
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 24 24 17 0 0 0 0 0
normalized size 1 1. 0.71 0. 0. 0. 0. 0.
time (sec) N/A 0.088 0.139 0.077 0. 0. 0. 0.
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 47 47 45 0 0 0 0 0
normalized size 1 1. 0.96 0. 0. 0. 0. 0.
time (sec) N/A 0.104 0.104 0.082 0. 0. 0. 0.
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 66 66 55 0 0 0 0 0
normalized size 1 1. 0.83 0. 0. 0. 0. 0.
time (sec) N/A 0.169 0.101 0.074 0. 0. 0. 0.
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 89 89 122 482 320 365 264 351
normalized size 1 1. 1.37 5.42 3.6 4.1 2.97 3.94
time (sec) N/A 0.132 0.541 0.016 1.121 2.012 2.418 1.255
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 67 67 80 240 190 231 151 200
normalized size 1 1. 1.19 3.58 2.84 3.45 2.25 2.99
time (sec) N/A 0.091 0.314 0.012 1.091 1.972 0.946 1.293
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 52 91 89 128 68 89
normalized size 1 1. 1.16 2.02 1.98 2.84 1.51 1.98
time (sec) N/A 0.045 0.218 0.012 1.06 1.983 0.402 1.253
Problem 102 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 64 64 54 94 95 230 0 93
normalized size 1 1. 0.84 1.47 1.48 3.59 0. 1.45
time (sec) N/A 0.138 0.108 0.042 1.262 2.046 0. 1.294
Problem 103 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 87 87 68 149 117 351 0 227
normalized size 1 1. 0.78 1.71 1.34 4.03 0. 2.61
time (sec) N/A 0.172 0.298 0.052 1.231 2.005 0. 1.271
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 123 123 90 296 132 572 0 443
normalized size 1 1. 0.73 2.41 1.07 4.65 0. 3.6
time (sec) N/A 0.216 0.456 0.053 1.226 2.072 0. 1.197
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 237 237 217 1071 711 828 779 784
normalized size 1 1. 0.92 4.52 3. 3.49 3.29 3.31
time (sec) N/A 0.265 1.408 0.016 1.281 2.158 6.985 1.256
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 168 168 192 541 441 491 456 450
normalized size 1 1. 1.14 3.22 2.62 2.92 2.71 2.68
time (sec) N/A 0.188 0.521 0.014 1.249 2.118 3.247 1.237
Problem 107 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 118 118 81 211 225 269 219 209
normalized size 1 1. 0.69 1.79 1.91 2.28 1.86 1.77
time (sec) N/A 0.099 0.478 0.013 1.08 2.023 1.398 1.33
Problem 108 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 145 145 113 191 201 470 0 188
normalized size 1 1. 0.78 1.32 1.39 3.24 0. 1.3
time (sec) N/A 0.342 0.197 0.105 1.303 2.141 0. 1.28
Problem 109 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 157 157 207 308 246 767 0 485
normalized size 1 1. 1.32 1.96 1.57 4.89 0. 3.09
time (sec) N/A 0.333 0.63 0.123 1.32 2.17 0. 2.314
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 207 207 353 618 273 1223 0 953
normalized size 1 1. 1.71 2.99 1.32 5.91 0. 4.6
time (sec) N/A 0.505 1.082 0.134 1.41 2.196 0. 1.276
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 117 117 154 325 308 1008 0 0
normalized size 1 1. 1.32 2.78 2.63 8.62 0. 0.
time (sec) N/A 0.273 2.059 0.119 1.615 2.06 0. 0.
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 88 88 472 174 0 590 0 0
normalized size 1 1. 5.36 1.98 0. 6.7 0. 0.
time (sec) N/A 0.201 6.346 0.045 0. 2.103 0. 0.
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 70 63 96 251 76 96
normalized size 1 1. 1.43 1.29 1.96 5.12 1.55 1.96
time (sec) N/A 0.068 0.258 0.039 1.036 2.108 2.011 1.31
Problem 114 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 22 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.06 8.873 0.07 0. 0. 0. 0.
Problem 115 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 22 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.057 9.314 0.083 0. 0. 0. 0.
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 255 255 462 600 824 4103 0 0
normalized size 1 1. 1.81 2.35 3.23 16.09 0. 0.
time (sec) N/A 0.364 3.434 0.116 1.895 2.327 0. 0.
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 200 200 637 313 0 2267 0 0
normalized size 1 1. 3.18 1.56 0. 11.34 0. 0.
time (sec) N/A 0.252 6.457 0.065 0. 2.194 0. 0.
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 123 123 114 108 323 1002 156 279
normalized size 1 1. 0.93 0.88 2.63 8.15 1.27 2.27
time (sec) N/A 0.096 0.437 0.06 1.11 2.119 2.872 1.257
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 22 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.054 30.104 0.347 0. 0. 0. 0.
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 22 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.052 31.286 0.465 0. 0. 0. 0.
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A F(-2) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 110 110 53 108 162 0 0 198
normalized size 1 1. 0.48 0.98 1.47 0. 0. 1.8
time (sec) N/A 0.148 0.197 0.106 1.71 0. 0. 1.305
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A F(-2) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 88 88 44 86 122 0 0 144
normalized size 1 1. 0.5 0.98 1.39 0. 0. 1.64
time (sec) N/A 0.113 0.149 0.056 1.659 0. 0. 1.333
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A F(-2) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 53 53 34 64 81 0 0 90
normalized size 1 1. 0.64 1.21 1.53 0. 0. 1.7
time (sec) N/A 0.062 0.12 0.055 1.766 0. 0. 1.294
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 83 83 54 0 0 0 0 43
normalized size 1 1. 0.65 0. 0. 0. 0. 0.52
time (sec) N/A 0.132 0.075 0.069 0. 0. 0. 1.3
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 110 110 75 0 0 0 0 92
normalized size 1 1. 0.68 0. 0. 0. 0. 0.84
time (sec) N/A 0.14 0.136 0.052 0. 0. 0. 1.216
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 151 151 97 0 0 0 0 144
normalized size 1 1. 0.64 0. 0. 0. 0. 0.95
time (sec) N/A 0.17 0.205 0.053 0. 0. 0. 1.198
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 68 68 33 62 119 0 0 0
normalized size 1 1. 0.49 0.91 1.75 0. 0. 0.
time (sec) N/A 0.117 0.052 0.051 1.74 0. 0. 0.
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 53 53 31 50 89 0 0 0
normalized size 1 1. 0.58 0.94 1.68 0. 0. 0.
time (sec) N/A 0.097 0.044 0.038 1.695 0. 0. 0.
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 32 32 22 38 59 0 0 0
normalized size 1 1. 0.69 1.19 1.84 0. 0. 0.
time (sec) N/A 0.051 0.02 0.036 1.687 0. 0. 0.
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 23 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.083 0.007 0.049 0. 0. 0. 0.
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 42 42 33 0 0 0 0 0
normalized size 1 1. 0.79 0. 0. 0. 0. 0.
time (sec) N/A 0.09 0.053 0.039 0. 0. 0. 0.
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 67 67 44 0 0 0 0 0
normalized size 1 1. 0.66 0. 0. 0. 0. 0.
time (sec) N/A 0.106 0.07 0.043 0. 0. 0. 0.
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F(-2) F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 185 185 70 0 243 0 0 240
normalized size 1 1. 0.38 0. 1.31 0. 0. 1.3
time (sec) N/A 0.195 0.279 0.023 1.67 0. 0. 1.188
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F(-2) F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 145 145 54 0 184 0 0 176
normalized size 1 1. 0.37 0. 1.27 0. 0. 1.21
time (sec) N/A 0.149 0.215 0.024 1.683 0. 0. 1.202
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F(-2) F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 89 89 56 0 124 0 0 111
normalized size 1 1. 0.63 0. 1.39 0. 0. 1.25
time (sec) N/A 0.075 0.084 0.023 1.743 0. 0. 1.211
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 36 0 0 0 0 54
normalized size 1 1. 0.65 0. 0. 0. 0. 0.98
time (sec) N/A 0.128 0.02 0.023 0. 0. 0. 1.179
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 79 79 53 0 0 0 0 115
normalized size 1 1. 0.67 0. 0. 0. 0. 1.46
time (sec) N/A 0.131 0.084 0.023 0. 0. 0. 1.268
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 109 109 69 0 0 0 0 180
normalized size 1 1. 0.63 0. 0. 0. 0. 1.65
time (sec) N/A 0.173 0.065 0.023 0. 0. 0. 1.309
Problem 139 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 383 383 213 0 0 0 0 0
normalized size 1 1. 0.56 0. 0. 0. 0. 0.
time (sec) N/A 0.208 1.724 0.041 0. 0. 0. 0.
Problem 140 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 269 269 163 0 0 0 0 0
normalized size 1 1. 0.61 0. 0. 0. 0. 0.
time (sec) N/A 0.163 1.707 0.039 0. 0. 0. 0.
Problem 141 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 157 157 117 0 0 0 0 0
normalized size 1 1. 0.75 0. 0. 0. 0. 0.
time (sec) N/A 0.082 0.665 180. 0. 0. 0. 0.
Problem 142 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 0.068 2.664 0.043 0. 0. 0. 0.
Problem 143 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 0.066 1.646 0.042 0. 0. 0. 0.
Problem 144 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 402 402 716 0 0 0 0 0
normalized size 1 1. 1.78 0. 0. 0. 0. 0.
time (sec) N/A 0.257 2.923 0.024 0. 0. 0. 0.
Problem 145 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 248 248 214 0 0 0 0 0
normalized size 1 1. 0.86 0. 0. 0. 0. 0.
time (sec) N/A 0.191 0.879 0.023 0. 0. 0. 0.
Problem 146 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 140 140 137 0 0 0 0 0
normalized size 1 1. 0.98 0. 0. 0. 0. 0.
time (sec) N/A 0.101 0.102 0.026 0. 0. 0. 0.
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 16 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.077 8.373 0.026 0. 0. 0. 0.
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 16 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.074 10.178 0.023 0. 0. 0. 0.
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A F A F(-2) 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 0.063 2.513 180. 0. 0. 0. 0.
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 22 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.045 5.875 0.082 0. 0. 0. 0.
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 402 402 429 0 0 1665 0 0
normalized size 1 1. 1.07 0. 0. 4.14 0. 0.
time (sec) N/A 0.553 2.289 0.15 0. 2.403 0. 0.
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 263 263 302 0 0 1139 0 0
normalized size 1 1. 1.15 0. 0. 4.33 0. 0.
time (sec) N/A 0.342 1.045 0.113 0. 2.297 0. 0.
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 131 131 189 0 0 586 0 0
normalized size 1 1. 1.44 0. 0. 4.47 0. 0.
time (sec) N/A 0.147 0.312 0.069 0. 2.214 0. 0.
Problem 154 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 22 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.054 4.925 0.055 0. 0. 0. 0.
Problem 155 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 22 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.052 8.884 0.082 0. 0. 0. 0.
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 89 89 123 482 320 365 264 351
normalized size 1 1. 1.38 5.42 3.6 4.1 2.97 3.94
time (sec) N/A 0.132 0.461 0.014 1.203 2.121 2.231 1.281
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 67 67 83 240 190 231 151 200
normalized size 1 1. 1.24 3.58 2.84 3.45 2.25 2.99
time (sec) N/A 0.09 0.317 0.01 1.192 2.011 1.157 1.237
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 46 91 89 128 68 89
normalized size 1 1. 1.02 2.02 1.98 2.84 1.51 1.98
time (sec) N/A 0.046 0.096 0.012 1.142 2.006 0.715 1.171
Problem 159 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 64 64 57 94 95 230 0 93
normalized size 1 1. 0.89 1.47 1.48 3.59 0. 1.45
time (sec) N/A 0.121 0.137 0.028 1.307 2.169 0. 1.187
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 87 87 71 0 117 351 0 227
normalized size 1 1. 0.82 0. 1.34 4.03 0. 2.61
time (sec) N/A 0.152 0.4 180. 1.399 2.35 0. 1.202
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 123 123 95 296 132 572 0 443
normalized size 1 1. 0.77 2.41 1.07 4.65 0. 3.6
time (sec) N/A 0.197 0.602 0.029 1.331 2.368 0. 1.149
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 250 250 232 0 706 879 779 814
normalized size 1 1. 0.93 0. 2.82 3.52 3.12 3.26
time (sec) N/A 0.285 1.394 180. 1.252 2.114 5.54 1.224
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 182 182 252 535 437 541 456 471
normalized size 1 1. 1.38 2.94 2.4 2.97 2.51 2.59
time (sec) N/A 0.194 0.95 0.015 1.221 2.035 2.352 1.194
Problem 164 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 116 116 96 208 223 294 219 221
normalized size 1 1. 0.83 1.79 1.92 2.53 1.89 1.91
time (sec) N/A 0.101 0.846 0.013 1.179 2.043 0.929 1.202
Problem 165 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 156 156 133 202 200 483 0 200
normalized size 1 1. 0.85 1.29 1.28 3.1 0. 1.28
time (sec) N/A 0.31 0.282 0.102 1.447 2.133 0. 1.254
Problem 166 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 183 183 233 319 244 778 0 485
normalized size 1 1. 1.27 1.74 1.33 4.25 0. 2.65
time (sec) N/A 0.345 0.76 0.12 1.386 2.156 0. 1.924
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 242 242 394 626 271 1234 0 948
normalized size 1 1. 1.63 2.59 1.12 5.1 0. 3.92
time (sec) N/A 0.428 1.234 0.133 1.49 2.242 0. 1.265
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 436 436 384 0 0 2418 0 0
normalized size 1 1. 0.88 0. 0. 5.55 0. 0.
time (sec) N/A 0.821 1.469 0.226 0. 2.311 0. 0.
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) C F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 320 320 247 0 0 1736 0 0
normalized size 1 1. 0.77 0. 0. 5.42 0. 0.
time (sec) N/A 0.67 0.963 0.151 0. 2.261 0. 0.
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 203 203 152 437 0 1127 0 0
normalized size 1 1. 0.75 2.15 0. 5.55 0. 0.
time (sec) N/A 0.376 0.887 0.063 0. 2.129 0. 0.
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 22 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.061 0.893 0.05 0. 0. 0. 0.
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 22 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.059 0.961 0.05 0. 0. 0. 0.
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F(-2) C F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 823 823 11178 0 0 14923 0 0
normalized size 1 1. 13.58 0. 0. 18.13 0. 0.
time (sec) N/A 1.353 26.463 0.289 0. 3.715 0. 0.
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F(-2) C F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 593 593 6018 0 0 8911 0 0
normalized size 1 1. 10.15 0. 0. 15.03 0. 0.
time (sec) N/A 1.025 22.266 0.243 0. 3.01 0. 0.
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 274 274 509 585 0 4074 0 0
normalized size 1 1. 1.86 2.14 0. 14.87 0. 0.
time (sec) N/A 0.457 4.978 0.096 0. 2.323 0. 0.
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 22 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.056 49.026 0.292 0. 0. 0. 0.
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 22 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.054 51.967 0.461 0. 0. 0. 0.
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 22 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.05 4.125 0.063 0. 0. 0. 0.
Problem 179 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 543 543 447 0 0 1886 0 0
normalized size 1 1. 0.82 0. 0. 3.47 0. 0.
time (sec) N/A 0.743 1.68 0.138 0. 2.454 0. 0.
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 282 282 254 0 0 1191 0 0
normalized size 1 1. 0.9 0. 0. 4.22 0. 0.
time (sec) N/A 0.363 0.721 0.112 0. 2.302 0. 0.
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 131 131 119 0 0 586 0 0
normalized size 1 1. 0.91 0. 0. 4.47 0. 0.
time (sec) N/A 0.145 0.172 0.068 0. 2.159 0. 0.
Problem 182 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 22 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.056 1.122 0.049 0. 0. 0. 0.
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 22 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.055 5.085 0.076 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 [144] had the largest ratio of [ 0.6429 ]

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 5 2 1. 14 0.143
2 A 4 2 1. 14 0.143
3 A 3 2 1. 14 0.143
4 A 2 2 1. 12 0.167
5 A 3 3 1. 14 0.214
6 A 4 4 1. 14 0.286
7 A 5 4 1. 14 0.286
8 A 6 4 1. 16 0.25
9 A 4 3 1. 16 0.188
10 A 4 4 1. 16 0.25
11 A 2 1 1. 14 0.071
12 A 5 4 1. 16 0.25
13 A 5 5 1. 16 0.312
14 A 7 6 1. 16 0.375
15 A 7 7 1. 16 0.438
16 A 12 4 1. 16 0.25
17 A 8 4 1. 16 0.25
18 A 6 4 1. 16 0.25
19 A 3 3 1. 14 0.214
20 A 8 4 1. 16 0.25
21 A 8 4 1. 16 0.25
22 A 12 5 1. 16 0.312
23 A 8 3 1. 12 0.25
24 A 8 4 1. 12 0.333
25 A 3 2 1. 10 0.2
26 A 9 5 1. 14 0.357
27 A 7 4 1. 14 0.286
28 A 5 3 1. 12 0.25
29 A 0 0 0. 0 0.
30 A 0 0 0. 0 0.
31 A 6 6 1. 16 0.375
32 A 5 5 1. 16 0.312
33 A 2 2 1. 14 0.143
34 A 0 0 0. 0 0.
35 A 0 0 0. 0 0.
36 A 15 8 1. 16 0.5
37 A 9 6 1. 16 0.375
38 A 6 4 1. 14 0.286
39 A 0 0 0. 0 0.
40 A 0 0 0. 0 0.
41 A 8 5 1. 16 0.312
42 A 7 5 1. 16 0.312
43 A 6 5 1. 16 0.312
44 A 5 4 1. 16 0.25
45 A 6 5 1. 16 0.312
46 A 7 5 1. 16 0.312
47 A 8 5 1. 16 0.312
48 A 10 8 1. 18 0.444
49 A 9 7 1. 18 0.389
50 A 8 6 1. 18 0.333
51 A 7 5 1. 18 0.278
52 A 7 6 1. 18 0.333
53 A 9 7 1. 18 0.389
54 A 9 8 1. 18 0.444
55 A 11 7 1. 18 0.389
56 A 23 7 1. 18 0.389
57 A 20 7 1. 18 0.389
58 A 14 6 1. 18 0.333
59 A 12 5 1. 18 0.278
60 A 12 5 1. 18 0.278
61 A 18 6 1. 18 0.333
62 A 19 7 1. 18 0.389
63 A 7 5 1. 12 0.417
64 A 6 5 1. 12 0.417
65 A 5 4 1. 12 0.333
66 A 6 5 1. 12 0.417
67 A 7 5 1. 12 0.417
68 A 0 0 0. 0 0.
69 A 0 0 0. 0 0.
70 A 0 0 0. 0 0.
71 A 2 1 1. 17 0.059
72 A 2 1 1. 20 0.05
73 A 3 1 1. 20 0.05
74 A 3 2 1. 21 0.095
75 A 0 0 0. 0 0.
76 A 8 3 1. 16 0.188
77 A 5 3 1. 16 0.188
78 A 3 2 1. 14 0.143
79 A 0 0 0. 0 0.
80 A 0 0 0. 0 0.
81 A 3 2 1. 12 0.167
82 A 3 2 1. 12 0.167
83 A 3 2 1. 12 0.167
84 A 3 2 1. 10 0.2
85 A 3 2 1. 12 0.167
86 A 3 2 1. 12 0.167
87 A 3 2 1. 12 0.167
88 A 5 3 1. 14 0.214
89 A 5 3 1. 14 0.214
90 A 5 3 1. 14 0.214
91 A 5 3 1. 12 0.25
92 A 5 3 1. 14 0.214
93 A 5 3 1. 14 0.214
94 A 5 3 1. 14 0.214
95 A 4 2 1. 20 0.1
96 A 4 2 1. 20 0.1
97 A 5 2 1. 20 0.1
98 A 7 5 1. 24 0.208
99 A 6 3 1. 18 0.167
100 A 5 3 1. 18 0.167
101 A 4 3 1. 16 0.188
102 A 5 4 1. 18 0.222
103 A 6 5 1. 18 0.278
104 A 7 5 1. 18 0.278
105 A 10 6 1. 20 0.3
106 A 9 7 1. 20 0.35
107 A 6 4 1. 18 0.222
108 A 9 5 1. 20 0.25
109 A 9 5 1. 20 0.25
110 A 15 6 1. 20 0.3
111 A 7 7 1. 20 0.35
112 A 6 6 1. 20 0.3
113 A 3 3 1. 18 0.167
114 A 0 0 0. 0 0.
115 A 0 0 0. 0 0.
116 A 10 9 1. 20 0.45
117 A 9 9 1. 20 0.45
118 A 4 4 1. 18 0.222
119 A 0 0 0. 0 0.
120 A 0 0 0. 0 0.
121 A 5 3 1. 18 0.167
122 A 4 3 1. 18 0.167
123 A 3 3 1. 16 0.188
124 A 4 4 1. 18 0.222
125 A 5 5 1. 18 0.278
126 A 6 5 1. 18 0.278
127 A 5 3 1. 14 0.214
128 A 4 3 1. 14 0.214
129 A 3 3 1. 12 0.25
130 A 2 2 1. 14 0.143
131 A 3 3 1. 14 0.214
132 A 4 3 1. 14 0.214
133 A 9 5 1. 14 0.357
134 A 7 5 1. 14 0.357
135 A 4 4 1. 12 0.333
136 A 5 3 1. 14 0.214
137 A 5 3 1. 14 0.214
138 A 7 4 1. 14 0.286
139 A 10 6 1. 18 0.333
140 A 8 5 1. 18 0.278
141 A 6 4 1. 16 0.25
142 A 0 0 0. 0 0.
143 A 0 0 0. 0 0.
144 A 16 9 1. 14 0.643
145 A 10 7 1. 14 0.5
146 A 7 5 1. 12 0.417
147 A 0 0 0. 0 0.
148 A 0 0 0. 0 0.
149 A 0 0 0. 0 0.
150 A 0 0 0. 0 0.
151 A 12 4 1. 20 0.2
152 A 9 4 1. 20 0.2
153 A 5 3 1. 18 0.167
154 A 0 0 0. 0 0.
155 A 0 0 0. 0 0.
156 A 6 3 1. 18 0.167
157 A 5 3 1. 18 0.167
158 A 4 3 1. 16 0.188
159 A 5 4 1. 18 0.222
160 A 6 5 1. 18 0.278
161 A 7 5 1. 18 0.278
162 A 10 6 1. 20 0.3
163 A 9 7 1. 20 0.35
164 A 6 4 1. 18 0.222
165 A 10 5 1. 20 0.25
166 A 11 7 1. 20 0.35
167 A 14 8 1. 20 0.4
168 A 12 7 1. 20 0.35
169 A 10 6 1. 20 0.3
170 A 8 5 1. 18 0.278
171 A 0 0 0. 0 0.
172 A 0 0 0. 0 0.
173 A 22 9 1. 20 0.45
174 A 18 10 1. 20 0.5
175 A 11 8 1. 18 0.444
176 A 0 0 0. 0 0.
177 A 0 0 0. 0 0.
178 A 0 0 0. 0 0.
179 A 18 4 1. 20 0.2
180 A 10 4 1. 20 0.2
181 A 5 3 1. 18 0.167
182 A 0 0 0. 0 0.
183 A 0 0 0. 0 0.

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