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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 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 28, 45, 46, 47, 48, 53, 69, 74, 75, 76, 82, 84, 88, 91, 92, 93, 94, 98, 99, 100, 101, 104, 105, 106, 107, 111, 112, 113, 114, 115, 120, 128, 129, 130, 131, 133, 134, 135, 136, 137, 141, 142, 147, 148, 149, 150, 151, 152, 156, 157, 158, 161, 162, 163, 166, 167, 168, 169, 170 }

B grade: { 81, 83, 89, 90, 95, 96, 97, 102, 103, 108, 109, 110, 121, 126, 127, 140, 165, 171 }

C grade: { 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 77, 78, 79, 80, 85, 86, 87, 116, 117, 118, 119, 122, 123, 124, 125, 132, 138, 139, 143, 144, 145, 146, 153, 154, 155, 159, 160 }

F grade: { 49, 164}

2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 31, 32, 33, 38, 53 }

B grade: { 28, 29, 30, 34, 35, 36, 37, 39, 40, 41, 42, 43, 44, 50, 51, 52, 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 }

C grade: { }

F grade: { 45, 46, 47, 48, 49, 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 }

2.1.4 Maxima

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, 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, 77, 78, 79, 80, 81, 84, 85, 86, 87

B grade: { 76, 82, 83, 88, 89 }

C grade: { }

F grade: { 45, 46, 47, 48, 49, 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 }

2.1.5 FriCAS

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, 34, 35, 50, 51, 52, 53, 54, 57, 58, 59, 60, 61, 64, 65, 66, 67, 70, 71, 72, 73, 74, 79, 80 }

B grade: { 32, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 55, 56, 62, 63, 68, 69, 75, 76, 77, 78, 81, 82, 83, 84, 85, 86, 87, 88, 89 }

C grade: { }

F grade: { 45, 46, 47, 48, 49, 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 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 25, 26, 27, 28, 50, 51, 52, 53, 54, 57, 58, 59, 60, 61, 64, 65, 66, 67, 70, 71, 72, 73 }

B grade: { }

C grade: { }

F grade: { 23, 24, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 55, 56, 62, 63, 68, 69, 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 }

2.1.7 Giac

A grade: { 3, 4, 11, 12, 13, 18, 19, 20, 21, 25, 26, 27, 28, 29, 30, 31, 32, 33, 37, 38, 39, 44, 54, 61, 67, 70, 71, 72, 73, 74, 79 }

B grade: { 1, 2, 5, 6, 7, 8, 9, 10, 14, 15, 16, 17, 22, 23, 24, 34, 35, 36, 40, 41, 42, 43, 51, 52, 53, 55, 56, 59, 60, 62, 63, 66, 68, 69, 75, 76, 77, 78, 80, 81, 83, 84, 85, 86, 87, 88, 89 }

C grade: { }

F grade: { 45, 46, 47, 48, 49, 50, 57, 58, 64, 65, 82, 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 }

2.2 Detailed conclusion table per each integral for all CAS systems

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

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

Problem 1 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 87 87 86 135 116 208 139 1373
normalized size 1 1. 0.99 1.55 1.33 2.39 1.6 15.78
time (sec) N/A 0.134 0.55 0.013 1.61 1.372 1.525 2.509
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 66 66 67 105 89 161 105 832
normalized size 1 1. 1.02 1.59 1.35 2.44 1.59 12.61
time (sec) N/A 0.046 0.293 0.013 1.765 1.439 0.588 1.923
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 42 42 59 66 68 122 82 68
normalized size 1 1. 1.4 1.57 1.62 2.9 1.95 1.62
time (sec) N/A 0.06 0.054 0.061 1.752 1.351 2.891 1.421
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 37 37 44 51 70 146 85 72
normalized size 1 1. 1.19 1.38 1.89 3.95 2.3 1.95
time (sec) N/A 0.11 0.069 0.068 1.668 1.415 4.868 1.494
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 43 43 78 65 92 178 116 161
normalized size 1 1. 1.81 1.51 2.14 4.14 2.7 3.74
time (sec) N/A 0.124 0.162 0.059 1.734 1.338 15.03 1.538
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 66 66 77 96 116 234 143 242
normalized size 1 1. 1.17 1.45 1.76 3.55 2.17 3.67
time (sec) N/A 0.159 0.435 0.076 1.708 1.392 14.001 1.559
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 87 87 101 124 140 292 180 320
normalized size 1 1. 1.16 1.43 1.61 3.36 2.07 3.68
time (sec) N/A 0.193 0.996 0.076 1.639 1.267 28.298 1.621
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 108 108 100 150 165 340 211 404
normalized size 1 1. 0.93 1.39 1.53 3.15 1.95 3.74
time (sec) N/A 0.226 1.141 0.073 1.679 1.386 88.916 1.587
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 148 148 221 249 198 340 250 3008
normalized size 1 1. 1.49 1.68 1.34 2.3 1.69 20.32
time (sec) N/A 0.302 6.223 0.013 1.713 1.398 1.939 4.907
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 112 112 172 199 162 275 194 2037
normalized size 1 1. 1.54 1.78 1.45 2.46 1.73 18.19
time (sec) N/A 0.112 1.789 0.012 1.728 1.32 1.584 3.218
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 87 87 96 140 123 209 151 128
normalized size 1 1. 1.1 1.61 1.41 2.4 1.74 1.47
time (sec) N/A 0.135 0.45 0.079 1.749 1.368 5.89 1.744
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 70 70 91 109 115 217 136 116
normalized size 1 1. 1.3 1.56 1.64 3.1 1.94 1.66
time (sec) N/A 0.185 0.268 0.076 1.748 1.421 11.254 1.876
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 72 72 100 110 126 274 158 159
normalized size 1 1. 1.39 1.53 1.75 3.81 2.19 2.21
time (sec) N/A 0.207 0.247 0.076 1.756 1.404 18.927 1.836
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 88 88 123 141 162 285 206 320
normalized size 1 1. 1.4 1.6 1.84 3.24 2.34 3.64
time (sec) N/A 0.263 0.342 0.095 1.694 1.433 30.604 2.05
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 118 118 152 188 201 367 258 451
normalized size 1 1. 1.29 1.59 1.7 3.11 2.19 3.82
time (sec) N/A 0.311 1.146 0.093 1.688 1.506 47.642 2.085
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 151 151 180 238 236 446 311 587
normalized size 1 1. 1.19 1.58 1.56 2.95 2.06 3.89
time (sec) N/A 0.369 3.021 0.098 1.76 1.428 83.336 2.138
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 165 165 209 314 242 408 313 3875
normalized size 1 1. 1.27 1.9 1.47 2.47 1.9 23.48
time (sec) N/A 0.177 1.567 0.014 1.754 1.605 2.784 6.493
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 140 140 130 234 193 324 248 213
normalized size 1 1. 0.93 1.67 1.38 2.31 1.77 1.52
time (sec) N/A 0.208 1.058 0.089 1.769 1.641 10.421 2.371
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 117 117 113 183 167 305 211 174
normalized size 1 1. 0.97 1.56 1.43 2.61 1.8 1.49
time (sec) N/A 0.336 0.455 0.094 1.792 1.838 26.694 2.518
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 119 119 113 168 169 347 214 205
normalized size 1 1. 0.95 1.41 1.42 2.92 1.8 1.72
time (sec) N/A 0.331 0.469 0.082 1.763 1.752 35.377 2.515
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 127 127 126 186 192 383 253 261
normalized size 1 1. 0.99 1.46 1.51 3.02 1.99 2.06
time (sec) N/A 0.355 0.448 0.137 1.784 1.763 78.706 2.513
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 154 154 164 233 243 419 330 527
normalized size 1 1. 1.06 1.51 1.58 2.72 2.14 3.42
time (sec) N/A 0.427 1.273 0.087 1.697 1.097 142.243 2.659
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 191 191 199 302 290 518 0 713
normalized size 1 1. 1.04 1.58 1.52 2.71 0. 3.73
time (sec) N/A 0.514 0.746 0.101 1.72 1.145 0. 2.838
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 233 233 237 376 338 620 0 905
normalized size 1 1. 1.02 1.61 1.45 2.66 0. 3.88
time (sec) N/A 0.558 1.168 0.115 1.634 1.126 0. 3.013
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 127 127 138 211 176 412 1306 182
normalized size 1 1. 1.09 1.66 1.39 3.24 10.28 1.43
time (sec) N/A 0.468 1.366 0.037 1.759 1.264 21.148 1.808
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 101 101 118 179 147 333 1020 149
normalized size 1 1. 1.17 1.77 1.46 3.3 10.1 1.48
time (sec) N/A 0.243 0.571 0.034 1.775 1.206 16.672 1.551
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 85 85 98 159 127 251 711 128
normalized size 1 1. 1.15 1.87 1.49 2.95 8.36 1.51
time (sec) N/A 0.163 0.17 0.033 2.412 1.177 7.054 1.616
Problem 28 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 58 58 67 153 119 174 541 127
normalized size 1 1. 1.16 2.64 2.05 3. 9.33 2.19
time (sec) N/A 0.144 0.115 0.109 1.738 1.086 89.498 1.553
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 80 80 113 174 144 267 0 153
normalized size 1 1. 1.41 2.17 1.8 3.34 0. 1.91
time (sec) N/A 0.201 0.312 0.13 1.756 1.264 0. 1.663
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 103 103 138 214 177 404 0 212
normalized size 1 1. 1.34 2.08 1.72 3.92 0. 2.06
time (sec) N/A 0.342 0.833 0.119 1.787 1.237 0. 1.693
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 137 137 163 266 213 518 0 289
normalized size 1 1. 1.19 1.94 1.55 3.78 0. 2.11
time (sec) N/A 0.682 1.375 0.13 1.592 1.33 0. 1.77
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A B F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 208 208 444 364 297 936 0 392
normalized size 1 1. 2.13 1.75 1.43 4.5 0. 1.88
time (sec) N/A 0.532 4.039 0.043 1.717 1.462 0. 1.889
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A B F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 157 157 324 313 266 682 0 329
normalized size 1 1. 2.06 1.99 1.69 4.34 0. 2.1
time (sec) N/A 0.311 2.055 0.047 1.678 1.306 0. 1.634
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A A F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 115 115 140 305 250 490 0 325
normalized size 1 1. 1.22 2.65 2.17 4.26 0. 2.83
time (sec) N/A 0.147 2.027 0.042 1.726 1.131 0. 1.659
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A A F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 111 111 190 301 239 489 0 316
normalized size 1 1. 1.71 2.71 2.15 4.41 0. 2.85
time (sec) N/A 0.208 1.963 0.135 1.813 1.141 0. 1.631
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A B F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 137 137 159 325 281 701 0 377
normalized size 1 1. 1.16 2.37 2.05 5.12 0. 2.75
time (sec) N/A 0.403 2.361 0.148 1.636 1.352 0. 1.867
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 192 192 193 399 354 1017 0 489
normalized size 1 1. 1.01 2.08 1.84 5.3 0. 2.55
time (sec) N/A 0.608 3.434 0.137 1.716 1.531 0. 1.813
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 331 331 1146 619 525 1895 0 682
normalized size 1 1. 3.46 1.87 1.59 5.73 0. 2.06
time (sec) N/A 0.861 6.678 0.048 1.754 1.853 0. 2.075
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A B F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 250 250 462 566 494 1432 0 618
normalized size 1 1. 1.85 2.26 1.98 5.73 0. 2.47
time (sec) N/A 0.581 4.533 0.054 1.892 1.606 0. 1.932
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A B F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 189 189 288 495 450 1038 0 554
normalized size 1 1. 1.52 2.62 2.38 5.49 0. 2.93
time (sec) N/A 0.427 4.647 0.051 1.817 1.176 0. 1.625
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A B F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 179 179 188 488 446 1058 0 554
normalized size 1 1. 1.05 2.73 2.49 5.91 0. 3.09
time (sec) N/A 0.255 3.746 0.047 1.875 1.154 0. 1.533
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 175 175 243 483 433 1038 0 552
normalized size 1 1. 1.39 2.76 2.47 5.93 0. 3.15
time (sec) N/A 0.316 3.807 0.154 1.621 1.191 0. 1.503
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 215 215 223 540 502 1451 0 647
normalized size 1 1. 1.04 2.51 2.33 6.75 0. 3.01
time (sec) N/A 0.68 2.878 0.179 1.839 1.614 0. 1.583
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 287 287 288 651 613 1982 0 756
normalized size 1 1. 1. 2.27 2.14 6.91 0. 2.63
time (sec) N/A 0.941 6.402 0.174 1.804 1.823 0. 1.637
Problem 45 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 132 132 110 0 0 0 0 0
normalized size 1 1. 0.83 0. 0. 0. 0. 0.
time (sec) N/A 0.155 0.402 0.326 0. 0. 0. 0.
Problem 46 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 154 154 115 0 0 0 0 0
normalized size 1 1. 0.75 0. 0. 0. 0. 0.
time (sec) N/A 0.138 0.376 180. 0. 0. 0. 0.
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-1) F F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 170 170 133 0 0 0 0 0
normalized size 1 1. 0.78 0. 0. 0. 0. 0.
time (sec) N/A 0.144 0.513 0.435 0. 0. 0. 0.
Problem 48 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 170 170 133 0 0 0 0 0
normalized size 1 1. 0.78 0. 0. 0. 0. 0.
time (sec) N/A 0.137 0.504 0.411 0. 0. 0. 0.
Problem 49 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 328 328 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 1.561 27.173 0.6 0. 0. 0. 0.
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A A A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 353 353 300 994 562 915 1001 0
normalized size 1 1. 0.85 2.82 1.59 2.59 2.84 0.
time (sec) N/A 0.785 6.365 0.018 1.507 1.223 5.487 0.
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 248 248 243 631 370 608 617 8778
normalized size 1 1. 0.98 2.54 1.49 2.45 2.49 35.4
time (sec) N/A 0.451 3.175 0.017 1.491 1.21 1.889 8.418
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 161 161 161 334 204 348 326 3939
normalized size 1 1. 1. 2.07 1.27 2.16 2.02 24.47
time (sec) N/A 0.241 1.539 0.014 1.456 1.155 0.834 3.872
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 73 73 76 136 100 177 131 1239
normalized size 1 1. 1.04 1.86 1.37 2.42 1.79 16.97
time (sec) N/A 0.061 0.446 0.014 1.478 1.068 0.705 1.818
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 156 155 148 506 247 483 2387 251
normalized size 1 0.99 0.95 3.24 1.58 3.1 15.3 1.61
time (sec) N/A 0.349 1.111 0.041 1.466 1.966 23.099 1.401
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A B F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 265 265 589 948 456 1160 0 717
normalized size 1 1. 2.22 3.58 1.72 4.38 0. 2.71
time (sec) N/A 0.474 6.484 0.056 1.489 2.324 0. 1.397
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A B F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 320 320 331 1513 775 2072 0 1400
normalized size 1 1. 1.03 4.73 2.42 6.48 0. 4.38
time (sec) N/A 0.703 6.228 0.068 1.523 1.327 0. 1.496
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A A A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 661 661 573 1807 933 1490 1819 0
normalized size 1 1. 0.87 2.73 1.41 2.25 2.75 0.
time (sec) N/A 2.384 6.648 0.024 1.488 1.282 6.121 0.
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A A A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 443 443 383 1165 625 1007 1134 0
normalized size 1 1. 0.86 2.63 1.41 2.27 2.56 0.
time (sec) N/A 1.278 6.501 0.017 1.481 1.22 4.66 0.
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 266 264 241 631 351 583 617 8778
normalized size 1 0.99 0.91 2.37 1.32 2.19 2.32 33.
time (sec) N/A 0.472 2.647 0.016 1.474 1.128 3.395 9.247
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 131 131 176 262 182 308 241 2873
normalized size 1 1. 1.34 2. 1.39 2.35 1.84 21.93
time (sec) N/A 0.155 1.126 0.015 1.443 1.052 1.332 3.585
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 254 252 190 861 392 822 4444 456
normalized size 1 0.99 0.75 3.39 1.54 3.24 17.5 1.8
time (sec) N/A 0.827 3.035 0.048 1.521 2.917 36.782 1.739
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A B F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 415 415 2640 1554 670 1987 0 1231
normalized size 1 1. 6.36 3.74 1.61 4.79 0. 2.97
time (sec) N/A 1.053 7.783 0.061 1.529 3.562 0. 1.871
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A B F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 597 597 2499 2465 1133 3513 0 2314
normalized size 1 1. 4.19 4.13 1.9 5.88 0. 3.88
time (sec) N/A 1.29 7.905 0.077 1.596 4.656 0. 1.87
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A A A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 603 603 419 1807 918 1461 1819 0
normalized size 1 1. 0.69 3. 1.52 2.42 3.02 0.
time (sec) N/A 1.533 6.583 0.021 1.498 1.312 7.86 0.
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A A A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 389 387 297 994 522 861 1001 0
normalized size 1 0.99 0.76 2.56 1.34 2.21 2.57 0.
time (sec) N/A 0.705 6.342 0.017 1.56 1.236 5.768 0.
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 191 191 212 420 273 456 410 5805
normalized size 1 1. 1.11 2.2 1.43 2.39 2.15 30.39
time (sec) N/A 0.244 2.41 0.014 1.494 1.139 2.493 7.635
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 363 363 255 1304 589 1269 7096 774
normalized size 1 1. 0.7 3.59 1.62 3.5 19.55 2.13
time (sec) N/A 1.512 4.738 0.051 1.534 5.578 46.978 2.252
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A B F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 574 574 2467 2250 925 3131 0 1832
normalized size 1 1. 4.3 3.92 1.61 5.45 0. 3.19
time (sec) N/A 2.321 8.361 0.07 1.643 8.359 0. 2.423
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F(-1) B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 798 798 1451 3522 1511 5261 0 3382
normalized size 1 1. 1.82 4.41 1.89 6.59 0. 4.24
time (sec) N/A 2.839 15.051 0.079 1.771 10.924 0. 2.488
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 337 337 258 1304 601 1315 7096 774
normalized size 1 1. 0.77 3.87 1.78 3.9 21.06 2.3
time (sec) N/A 1.588 4.285 0.054 1.546 5.581 46.64 2.428
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 236 236 190 861 397 830 4444 456
normalized size 1 1. 0.81 3.65 1.68 3.52 18.83 1.93
time (sec) N/A 0.804 2.898 0.046 1.463 2.733 40.737 2.065
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 156 156 148 506 240 470 2387 251
normalized size 1 1. 0.95 3.24 1.54 3.01 15.3 1.61
time (sec) N/A 0.342 1.055 0.05 1.485 1.591 23.743 1.683
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 99 99 117 234 143 269 966 147
normalized size 1 1. 1.18 2.36 1.44 2.72 9.76 1.48
time (sec) N/A 0.098 0.213 0.037 1.456 1.222 14.003 1.621
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 165 164 313 647 328 633 0 367
normalized size 1 0.99 1.9 3.92 1.99 3.84 0. 2.22
time (sec) N/A 0.256 1.525 0.076 1.491 2.491 0. 1.721
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 281 281 543 1262 702 2738 0 1142
normalized size 1 1. 1.93 4.49 2.5 9.74 0. 4.06
time (sec) N/A 0.795 6.913 0.094 1.575 7.993 0. 1.742
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 477 477 898 2298 1480 7380 0 2871
normalized size 1 1. 1.88 4.82 3.1 15.47 0. 6.02
time (sec) N/A 1.786 8.879 0.111 1.804 26.386 0. 1.92
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A B F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 579 579 2463 2250 923 3141 0 1829
normalized size 1 1. 4.25 3.89 1.59 5.42 0. 3.16
time (sec) N/A 2.134 8.394 0.07 1.594 8.215 0. 2.439
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A B F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 417 417 2636 1554 666 1983 0 1231
normalized size 1 1. 6.32 3.73 1.6 4.76 0. 2.95
time (sec) N/A 1.113 7.763 0.072 1.574 3.755 0. 1.909
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 292 288 606 948 431 1095 0 713
normalized size 1 0.99 2.08 3.25 1.48 3.75 0. 2.44
time (sec) N/A 0.554 6.336 0.058 1.487 1.833 0. 1.628
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A A F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 140 140 207 438 277 566 0 404
normalized size 1 1. 1.48 3.13 1.98 4.04 0. 2.89
time (sec) N/A 0.209 2.241 0.042 1.462 1.132 0. 1.585
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B A B F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 293 293 592 1263 693 2620 0 1142
normalized size 1 1. 2.02 4.31 2.37 8.94 0. 3.9
time (sec) N/A 0.812 7.452 0.1 1.575 8.541 0. 1.81
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 509 508 984 2012 1600 8519 0 0
normalized size 1 1. 1.93 3.95 3.14 16.74 0. 0.
time (sec) N/A 2.151 8.905 0.144 1.812 35.291 0. 0.
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F(-1) B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 841 841 1758 3364 3401 19950 0 4288
normalized size 1 1. 2.09 4. 4.04 23.72 0. 5.1
time (sec) N/A 4.076 8.346 0.143 2.211 102.058 0. 3.14
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F(-1) B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 804 804 1445 3522 1499 5218 0 3382
normalized size 1 1. 1.8 4.38 1.86 6.49 0. 4.21
time (sec) N/A 2.747 14.923 0.085 1.742 13.21 0. 2.431
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 597 597 2499 2465 1116 3366 0 2307
normalized size 1 1. 4.19 4.13 1.87 5.64 0. 3.86
time (sec) N/A 1.385 7.863 0.085 1.636 5.451 0. 1.969
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A B F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 352 349 331 1513 733 1905 0 1400
normalized size 1 0.99 0.94 4.3 2.08 5.41 0. 3.98
time (sec) N/A 0.711 6.026 0.07 1.533 1.639 0. 1.822
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A B F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 209 209 261 713 495 1215 0 740
normalized size 1 1. 1.25 3.41 2.37 5.81 0. 3.54
time (sec) N/A 0.376 4.632 0.055 1.515 1.356 0. 1.966
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 487 487 912 2298 1455 7109 0 2869
normalized size 1 1. 1.87 4.72 2.99 14.6 0. 5.89
time (sec) N/A 1.83 8.882 0.117 1.84 38.508 0. 3.617
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F(-1) B
verified N/A Yes NO TBD TBD TBD TBD TBD
size 861 860 1732 3364 3425 20006 0 4288
normalized size 1 1. 2.01 3.91 3.98 23.24 0. 4.98
time (sec) N/A 4.276 8.2 0.14 2.273 98.95 0. 2.953
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-1) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 464 464 1232 6661 0 0 0 0
normalized size 1 1. 2.66 14.36 0. 0. 0. 0.
time (sec) N/A 2.089 6.426 0.227 0. 0. 0. 0.
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 325 325 314 4775 0 0 0 0
normalized size 1 1. 0.97 14.69 0. 0. 0. 0.
time (sec) N/A 1.306 4.771 0.172 0. 0. 0. 0.
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 224 224 220 3028 0 0 0 0
normalized size 1 1. 0.98 13.52 0. 0. 0. 0.
time (sec) N/A 0.628 1.96 0.148 0. 0. 0. 0.
Problem 93 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 155 155 150 1472 0 0 0 0
normalized size 1 1. 0.97 9.5 0. 0. 0. 0.
time (sec) N/A 0.306 0.552 0.128 0. 0. 0. 0.
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 234 234 233 3576 0 0 0 0
normalized size 1 1. 1. 15.28 0. 0. 0. 0.
time (sec) N/A 1.087 0.673 0.191 0. 0. 0. 0.
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 317 317 764 5778 0 0 0 0
normalized size 1 1. 2.41 18.23 0. 0. 0. 0.
time (sec) N/A 1.439 6.396 0.214 0. 0. 0. 0.
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 543 543 2819 9797 0 0 0 0
normalized size 1 1. 5.19 18.04 0. 0. 0. 0.
time (sec) N/A 4.037 6.413 0.241 0. 0. 0. 0.
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-1) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 550 550 1290 11056 0 0 0 0
normalized size 1 1. 2.35 20.1 0. 0. 0. 0.
time (sec) N/A 2.734 6.418 0.198 0. 0. 0. 0.
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 396 396 350 8031 0 0 0 0
normalized size 1 1. 0.88 20.28 0. 0. 0. 0.
time (sec) N/A 1.727 6.16 0.18 0. 0. 0. 0.
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 273 273 260 5149 0 0 0 0
normalized size 1 1. 0.95 18.86 0. 0. 0. 0.
time (sec) N/A 0.879 4.518 0.15 0. 0. 0. 0.
Problem 100 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 187 187 202 2517 0 0 0 0
normalized size 1 1. 1.08 13.46 0. 0. 0. 0.
time (sec) N/A 0.46 1.234 0.113 0. 0. 0. 0.
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 271 271 266 6055 0 0 0 0
normalized size 1 1. 0.98 22.34 0. 0. 0. 0.
time (sec) N/A 1.814 2.421 0.192 0. 0. 0. 0.
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 372 372 1732 9865 0 0 0 0
normalized size 1 1. 4.66 26.52 0. 0. 0. 0.
time (sec) N/A 2.547 6.225 0.235 0. 0. 0. 0.
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 532 532 7678 14441 0 0 0 0
normalized size 1 1. 14.43 27.14 0. 0. 0. 0.
time (sec) N/A 4.087 6.55 0.251 0. 0. 0. 0.
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 503 503 564 11478 0 0 0 0
normalized size 1 1. 1.12 22.82 0. 0. 0. 0.
time (sec) N/A 2.312 6.436 0.192 0. 0. 0. 0.
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 353 351 324 7402 0 0 0 0
normalized size 1 0.99 0.92 20.97 0. 0. 0. 0.
time (sec) N/A 1.212 4.999 0.164 0. 0. 0. 0.
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 229 229 262 3614 0 0 0 0
normalized size 1 1. 1.14 15.78 0. 0. 0. 0.
time (sec) N/A 0.629 2.031 0.123 0. 0. 0. 0.
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 336 336 322 8698 0 0 0 0
normalized size 1 1. 0.96 25.89 0. 0. 0. 0.
time (sec) N/A 2.812 5.328 0.214 0. 0. 0. 0.
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 473 473 6112 14119 0 0 0 0
normalized size 1 1. 12.92 29.85 0. 0. 0. 0.
time (sec) N/A 3.896 6.55 0.258 0. 0. 0. 0.
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 643 643 18214 20663 0 0 0 0
normalized size 1 1. 28.33 32.14 0. 0. 0. 0.
time (sec) N/A 6.065 6.898 0.282 0. 0. 0. 0.
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-1) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 407 407 1200 25426 0 0 0 0
normalized size 1 1. 2.95 62.47 0. 0. 0. 0.
time (sec) N/A 1.699 6.456 0.211 0. 0. 0. 0.
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 287 287 275 18289 0 0 0 0
normalized size 1 1. 0.96 63.72 0. 0. 0. 0.
time (sec) N/A 1.001 5.997 0.183 0. 0. 0. 0.
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 194 194 192 4132 0 0 0 0
normalized size 1 1. 0.99 21.3 0. 0. 0. 0.
time (sec) N/A 0.498 1.476 0.154 0. 0. 0. 0.
Problem 113 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 133 133 129 5570 0 0 0 0
normalized size 1 1. 0.97 41.88 0. 0. 0. 0.
time (sec) N/A 0.216 0.213 0.14 0. 0. 0. 0.
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 210 210 194 13474 0 0 0 0
normalized size 1 1. 0.92 64.16 0. 0. 0. 0.
time (sec) N/A 0.615 0.373 0.193 0. 0. 0. 0.
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 327 327 521 20870 0 0 0 0
normalized size 1 1. 1.59 63.82 0. 0. 0. 0.
time (sec) N/A 1.379 6.215 0.222 0. 0. 0. 0.
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 511 511 920 49725 0 0 0 0
normalized size 1 1. 1.8 97.31 0. 0. 0. 0.
time (sec) N/A 2.465 6.774 0.244 0. 0. 0. 0.
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 343 343 476 36710 0 0 0 0
normalized size 1 1. 1.39 107.03 0. 0. 0. 0.
time (sec) N/A 1.354 6.577 0.198 0. 0. 0. 0.
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 201 201 290 23472 0 0 0 0
normalized size 1 1. 1.44 116.78 0. 0. 0. 0.
time (sec) N/A 0.554 2.392 0.164 0. 0. 0. 0.
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 157 157 218 11427 0 0 0 0
normalized size 1 1. 1.39 72.78 0. 0. 0. 0.
time (sec) N/A 0.294 0.925 0.125 0. 0. 0. 0.
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 262 262 296 26343 0 0 0 0
normalized size 1 1. 1.13 100.55 0. 0. 0. 0.
time (sec) N/A 1.277 4.734 0.216 0. 0. 0. 0.
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 447 446 2078 40619 0 0 0 0
normalized size 1 1. 4.65 90.87 0. 0. 0. 0.
time (sec) N/A 2.881 6.252 0.263 0. 0. 0. 0.
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 585 585 670 85156 0 0 0 0
normalized size 1 1. 1.15 145.57 0. 0. 0. 0.
time (sec) N/A 2.968 6.832 0.284 0. 0. 0. 0.
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 358 358 502 61833 0 0 0 0
normalized size 1 1. 1.4 172.72 0. 0. 0. 0.
time (sec) N/A 1.551 6.477 0.247 0. 0. 0. 0.
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 273 271 300 40201 0 0 0 0
normalized size 1 0.99 1.1 147.26 0. 0. 0. 0.
time (sec) N/A 0.798 2.742 0.21 0. 0. 0. 0.
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-1) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 209 209 223 20647 0 0 0 0
normalized size 1 1. 1.07 98.79 0. 0. 0. 0.
time (sec) N/A 0.486 0.853 0.149 0. 0. 0. 0.
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 365 365 1948 45119 0 0 0 0
normalized size 1 1. 5.34 123.61 0. 0. 0. 0.
time (sec) N/A 2.466 6.264 0.25 0. 0. 0. 0.
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 679 678 6052 67570 0 0 0 0
normalized size 1 1. 8.91 99.51 0. 0. 0. 0.
time (sec) N/A 5.062 6.418 0.327 0. 0. 0. 0.
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-1) F(-1) F(-1) F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 679 679 1202 0 0 0 0 0
normalized size 1 1. 1.77 0. 0. 0. 0. 0.
time (sec) N/A 9.926 9.73 180. 0. 0. 0. 0.
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-1) F(-1) F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 505 505 835 0 0 0 0 0
normalized size 1 1. 1.65 0. 0. 0. 0. 0.
time (sec) N/A 7.338 8.815 180. 0. 0. 0. 0.
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 381 383 619 0 0 0 0 0
normalized size 1 1.01 1.62 0. 0. 0. 0. 0.
time (sec) N/A 4.973 7.708 180. 0. 0. 0. 0.
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 287 287 441 0 0 0 0 0
normalized size 1 1. 1.54 0. 0. 0. 0. 0.
time (sec) N/A 2.633 4.055 180. 0. 0. 0. 0.
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-1) F(-1) F F(-2)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 300 300 621058 0 0 0 0 0
normalized size 1 1. 2070.19 0. 0. 0. 0. 0.
time (sec) N/A 3.796 35.725 180. 0. 0. 0. 0.
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 370 370 603 0 0 0 0 0
normalized size 1 1. 1.63 0. 0. 0. 0. 0.
time (sec) N/A 2.052 6.959 180. 0. 0. 0. 0.
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-1) F(-1) F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 597 597 1108 0 0 0 0 0
normalized size 1 1. 1.86 0. 0. 0. 0. 0.
time (sec) N/A 3.589 7.154 180. 0. 0. 0. 0.
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-1) F(-1) F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 682 682 1316 0 0 0 0 0
normalized size 1 1. 1.93 0. 0. 0. 0. 0.
time (sec) N/A 11.896 8.172 180. 0. 0. 0. 0.
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-1) F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 508 508 867 0 0 0 0 0
normalized size 1 1. 1.71 0. 0. 0. 0. 0.
time (sec) N/A 7.488 8.795 180. 0. 0. 0. 0.
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-1) F(-1) F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 384 384 613 0 0 0 0 0
normalized size 1 1. 1.6 0. 0. 0. 0. 0.
time (sec) N/A 4.311 7.57 180. 0. 0. 0. 0.
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-1) F(-1) F F(-2)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 382 382 1073629 0 0 0 0 0
normalized size 1 1. 2810.55 0. 0. 0. 0. 0.
time (sec) N/A 5.739 39.48 180. 0. 0. 0. 0.
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-1) F(-1) F(-1) F(-2)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 402 402 1347065 0 0 0 0 0
normalized size 1 1. 3350.91 0. 0. 0. 0. 0.
time (sec) N/A 7.127 40.594 180. 0. 0. 0. 0.
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F(-2) F(-1) F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 586 586 3134 0 0 0 0 0
normalized size 1 1. 5.35 0. 0. 0. 0. 0.
time (sec) N/A 3.668 9.006 180. 0. 0. 0. 0.
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-1) F(-1) F(-1) F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 697 697 1261 0 0 0 0 0
normalized size 1 1. 1.81 0. 0. 0. 0. 0.
time (sec) N/A 10.416 9.266 180. 0. 0. 0. 0.
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-1) F(-1) F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 505 505 780 0 0 0 0 0
normalized size 1 1. 1.54 0. 0. 0. 0. 0.
time (sec) N/A 6.23 8.556 180. 0. 0. 0. 0.
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-1) F(-1) F(-1) F(-2)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 535 535 1654245 0 0 0 0 0
normalized size 1 1. 3092.05 0. 0. 0. 0. 0.
time (sec) N/A 8.314 44.009 180. 0. 0. 0. 0.
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-1) F(-1) F(-1) F(-2)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 545 545 2018669 0 0 0 0 0
normalized size 1 1. 3703.98 0. 0. 0. 0. 0.
time (sec) N/A 11.066 46.464 180. 0. 0. 0. 0.
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-1) F(-1) F(-1) F(-2)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 590 590 2345519 0 0 0 0 0
normalized size 1 1. 3975.46 0. 0. 0. 0. 0.
time (sec) N/A 14.02 48.323 180. 0. 0. 0. 0.
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-2) F(-1) F(-1) F(-2)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 946 946 2719441 0 0 0 0 0
normalized size 1 1. 2874.67 0. 0. 0. 0. 0.
time (sec) N/A 6.464 52.887 180. 0. 0. 0. 0.
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-1) F(-1) F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 505 505 785 0 0 0 0 0
normalized size 1 1. 1.55 0. 0. 0. 0. 0.
time (sec) N/A 5.953 8.342 180. 0. 0. 0. 0.
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-1) F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 383 383 607 0 0 0 0 0
normalized size 1 1. 1.58 0. 0. 0. 0. 0.
time (sec) N/A 4.077 7.453 180. 0. 0. 0. 0.
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 290 290 456 0 0 0 0 0
normalized size 1 1. 1.57 0. 0. 0. 0. 0.
time (sec) N/A 2.555 6.857 180. 0. 0. 0. 0.
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-1) F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 239 239 362 0 0 0 0 0
normalized size 1 1. 1.51 0. 0. 0. 0. 0.
time (sec) N/A 1.457 2.315 180. 0. 0. 0. 0.
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 251 251 264 0 0 0 0 0
normalized size 1 1. 1.05 0. 0. 0. 0. 0.
time (sec) N/A 0.969 2.482 180. 0. 0. 0. 0.
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-1) F(-1) F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 375 375 388 0 0 0 0 0
normalized size 1 1. 1.03 0. 0. 0. 0. 0.
time (sec) N/A 1.765 6.006 180. 0. 0. 0. 0.
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-1) F(-1) F(-1) F(-2)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 528 528 1653959 0 0 0 0 0
normalized size 1 1. 3132.5 0. 0. 0. 0. 0.
time (sec) N/A 8.188 44.227 180. 0. 0. 0. 0.
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-1) F(-1) F F(-2)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 380 380 1073499 0 0 0 0 0
normalized size 1 1. 2825. 0. 0. 0. 0. 0.
time (sec) N/A 5.627 39.369 180. 0. 0. 0. 0.
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-1) F(-1) F F(-2)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 299 299 621084 0 0 0 0 0
normalized size 1 1. 2077.2 0. 0. 0. 0. 0.
time (sec) N/A 3.333 35.438 180. 0. 0. 0. 0.
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 251 251 275 0 0 0 0 0
normalized size 1 1. 1.1 0. 0. 0. 0. 0.
time (sec) N/A 1.001 3.116 180. 0. 0. 0. 0.
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-1) F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 383 382 484 0 0 0 0 0
normalized size 1 1. 1.26 0. 0. 0. 0. 0.
time (sec) N/A 1.878 6.671 180. 0. 0. 0. 0.
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-1) F(-1) F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 598 598 902 0 0 0 0 0
normalized size 1 1. 1.51 0. 0. 0. 0. 0.
time (sec) N/A 3.435 6.849 180. 0. 0. 0. 0.
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-1) F(-1) F(-1) F(-2)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 549 549 2018643 0 0 0 0 0
normalized size 1 1. 3676.95 0. 0. 0. 0. 0.
time (sec) N/A 10.5 46.635 180. 0. 0. 0. 0.
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-1) F(-1) F(-1) F(-2)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 407 407 1347117 0 0 0 0 0
normalized size 1 1. 3309.87 0. 0. 0. 0. 0.
time (sec) N/A 7.163 40.789 180. 0. 0. 0. 0.
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F(-1) F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 373 373 609 0 0 0 0 0
normalized size 1 1. 1.63 0. 0. 0. 0. 0.
time (sec) N/A 1.922 6.91 180. 0. 0. 0. 0.
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-1) F(-1) F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 379 379 403 0 0 0 0 0
normalized size 1 1. 1.06 0. 0. 0. 0. 0.
time (sec) N/A 1.814 5.365 180. 0. 0. 0. 0.
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-1) F(-1) F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 651 650 903 0 0 0 0 0
normalized size 1 1. 1.39 0. 0. 0. 0. 0.
time (sec) N/A 3.431 6.875 180. 0. 0. 0. 0.
Problem 164 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 376 376 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.9 22.737 0.649 0. 0. 0. 0.
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F(-1) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 560 551 1390 0 0 0 0 0
normalized size 1 0.98 2.48 0. 0. 0. 0. 0.
time (sec) N/A 2.377 6.387 0.839 0. 0. 0. 0.
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-1) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 363 360 505 0 0 0 0 0
normalized size 1 0.99 1.39 0. 0. 0. 0. 0.
time (sec) N/A 1.152 6.332 0.591 0. 0. 0. 0.
Problem 167 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 247 247 202 0 0 0 0 0
normalized size 1 1. 0.82 0. 0. 0. 0. 0.
time (sec) N/A 0.528 2.711 0.492 0. 0. 0. 0.
Problem 168 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 178 178 135 0 0 0 0 0
normalized size 1 1. 0.76 0. 0. 0. 0. 0.
time (sec) N/A 0.184 0.209 0.39 0. 0. 0. 0.
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 258 258 204 0 0 0 0 0
normalized size 1 1. 0.79 0. 0. 0. 0. 0.
time (sec) N/A 0.482 0.998 0.543 0. 0. 0. 0.
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-1) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 403 402 563 0 0 0 0 0
normalized size 1 1. 1.4 0. 0. 0. 0. 0.
time (sec) N/A 1.215 6.184 0.641 0. 0. 0. 0.
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F(-1) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 702 702 2238 0 0 0 0 0
normalized size 1 1. 3.19 0. 0. 0. 0. 0.
time (sec) N/A 2.938 6.235 0.805 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 [38] had the largest ratio of [ 0.2 ]

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 5 1. 36 0.139
2 A 3 3 1. 30 0.1
3 A 3 3 1. 36 0.083
4 A 5 4 1. 38 0.105
5 A 4 4 1. 38 0.105
6 A 5 5 1. 38 0.132
7 A 6 5 1. 38 0.132
8 A 7 5 1. 38 0.132
9 A 6 6 1. 38 0.158
10 A 4 4 1. 32 0.125
11 A 4 4 1. 38 0.105
12 A 5 4 1. 40 0.1
13 A 5 4 1. 40 0.1
14 A 5 5 1. 40 0.125
15 A 6 6 1. 40 0.15
16 A 7 6 1. 40 0.15
17 A 5 4 1. 32 0.125
18 A 5 4 1. 38 0.105
19 A 6 5 1. 40 0.125
20 A 6 5 1. 40 0.125
21 A 6 5 1. 40 0.125
22 A 6 6 1. 40 0.15
23 A 7 7 1. 40 0.175
24 A 8 7 1. 40 0.175
25 A 7 7 1. 40 0.175
26 A 6 6 1. 38 0.158
27 A 6 4 1. 32 0.125
28 A 3 3 1. 38 0.079
29 A 4 4 1. 40 0.1
30 A 5 5 1. 40 0.125
31 A 6 6 1. 40 0.15
32 A 7 7 1. 40 0.175
33 A 6 6 1. 38 0.158
34 A 3 3 1. 32 0.094
35 A 4 4 1. 38 0.105
36 A 5 5 1. 40 0.125
37 A 6 6 1. 40 0.15
38 A 8 8 1. 40 0.2
39 A 7 7 1. 40 0.175
40 A 5 5 1. 38 0.132
41 A 4 4 1. 32 0.125
42 A 5 4 1. 38 0.105
43 A 6 6 1. 40 0.15
44 A 7 6 1. 40 0.15
45 A 7 5 1. 39 0.128
46 A 7 5 1. 39 0.128
47 A 7 5 1. 41 0.122
48 A 7 5 1. 41 0.122
49 A 13 7 1. 43 0.163
50 A 6 5 1. 43 0.116
51 A 5 5 1. 43 0.116
52 A 4 4 1. 41 0.098
53 A 3 3 1. 31 0.097
54 A 5 5 0.99 43 0.116
55 A 5 5 1. 43 0.116
56 A 4 4 1. 43 0.093
57 A 7 6 1. 45 0.133
58 A 6 6 1. 45 0.133
59 A 5 5 0.99 43 0.116
60 A 4 4 1. 33 0.121
61 A 6 6 0.99 45 0.133
62 A 6 6 1. 45 0.133
63 A 6 6 1. 45 0.133
64 A 7 6 1. 45 0.133
65 A 6 5 0.99 43 0.116
66 A 5 4 1. 33 0.121
67 A 7 6 1. 45 0.133
68 A 7 7 1. 45 0.156
69 A 7 6 1. 45 0.133
70 A 7 6 1. 45 0.133
71 A 6 6 1. 45 0.133
72 A 5 5 1. 43 0.116
73 A 4 4 1. 33 0.121
74 A 3 2 0.99 45 0.044
75 A 4 3 1. 45 0.067
76 A 5 3 1. 45 0.067
77 A 7 7 1. 45 0.156
78 A 6 6 1. 45 0.133
79 A 5 5 0.99 43 0.116
80 A 3 3 1. 33 0.091
81 A 4 3 1. 45 0.067
82 A 5 3 1. 45 0.067
83 A 6 3 1. 45 0.067
84 A 7 6 1. 45 0.133
85 A 6 6 1. 45 0.133
86 A 4 4 0.99 43 0.093
87 A 4 4 1. 33 0.121
88 A 5 3 1. 45 0.067
89 A 6 3 1. 45 0.067
90 A 12 8 1. 47 0.17
91 A 11 8 1. 47 0.17
92 A 10 7 1. 45 0.156
93 A 9 6 1. 35 0.171
94 A 12 7 1. 47 0.149
95 A 12 7 1. 47 0.149
96 A 13 8 1. 47 0.17
97 A 13 8 1. 47 0.17
98 A 12 8 1. 47 0.17
99 A 11 7 1. 45 0.156
100 A 10 6 1. 35 0.171
101 A 13 7 1. 47 0.149
102 A 13 8 1. 47 0.17
103 A 13 7 1. 47 0.149
104 A 13 8 1. 47 0.17
105 A 12 7 0.99 45 0.156
106 A 11 6 1. 35 0.171
107 A 14 7 1. 47 0.149
108 A 14 8 1. 47 0.17
109 A 14 8 1. 47 0.17
110 A 11 7 1. 47 0.149
111 A 10 7 1. 47 0.149
112 A 9 6 1. 45 0.133
113 A 8 5 1. 35 0.143
114 A 11 6 1. 47 0.128
115 A 12 7 1. 47 0.149
116 A 11 8 1. 47 0.17
117 A 10 7 1. 47 0.149
118 A 9 6 1. 45 0.133
119 A 8 5 1. 35 0.143
120 A 12 7 1. 47 0.149
121 A 13 7 1. 47 0.149
122 A 11 7 1. 47 0.149
123 A 10 7 1. 47 0.149
124 A 9 6 0.99 45 0.133
125 A 9 6 1. 35 0.171
126 A 13 7 1. 47 0.149
127 A 14 7 1. 47 0.149
128 A 16 8 1. 49 0.163
129 A 15 8 1. 49 0.163
130 A 14 8 1.01 49 0.163
131 A 13 8 1. 49 0.163
132 A 13 8 1. 49 0.163
133 A 9 6 1. 49 0.122
134 A 10 6 1. 49 0.122
135 A 16 8 1. 49 0.163
136 A 15 8 1. 49 0.163
137 A 14 8 1. 49 0.163
138 A 14 9 1. 49 0.184
139 A 14 8 1. 49 0.163
140 A 10 6 1. 49 0.122
141 A 16 8 1. 49 0.163
142 A 15 8 1. 49 0.163
143 A 15 9 1. 49 0.184
144 A 15 9 1. 49 0.184
145 A 15 8 1. 49 0.163
146 A 11 6 1. 49 0.122
147 A 15 8 1. 49 0.163
148 A 14 8 1. 49 0.163
149 A 13 8 1. 49 0.163
150 A 12 7 1. 49 0.143
151 A 8 5 1. 49 0.102
152 A 9 5 1. 49 0.102
153 A 15 9 1. 49 0.184
154 A 14 9 1. 49 0.184
155 A 13 8 1. 49 0.163
156 A 8 5 1. 49 0.102
157 A 9 5 1. 49 0.102
158 A 10 5 1. 49 0.102
159 A 15 9 1. 49 0.184
160 A 14 8 1. 49 0.163
161 A 9 6 1. 49 0.122
162 A 9 5 1. 49 0.102
163 A 10 5 1. 49 0.102
164 A 9 6 1. 45 0.133
165 A 9 6 0.98 45 0.133
166 A 8 6 0.99 45 0.133
167 A 7 5 1. 43 0.116
168 A 6 4 1. 33 0.121
169 A 8 5 1. 45 0.111
170 A 9 6 1. 45 0.133
171 A 10 6 1. 45 0.133

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