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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 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 36, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 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, 133, 134, 135, 136, 137, 138, 139, 140, 141 }

B grade: { 35 }

C grade: { 11, 12, 31, 32, 33, 34, 37, 38, 62, 63, 75, 76, 93, 126, 127, 128, 129, 130, 131, 132, 142 }

F grade: { 143}

2.1.3 Maple

A grade: { 1, 2, 3, 10, 22, 28, 31, 32, 33, 34, 36, 38, 39, 92, 94, 95, 96, 99, 100, 101, 126, 127, 128, 129, 130, 131, 132, 133, 134, 138, 139, 140, 141 }

B grade: { 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 29, 30, 35, 37, 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, 93, 97, 98, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 135, 136, 137 }

C grade: { 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51 }

F grade: { 142, 143 }

2.1.4 Maxima

A grade: { 10, 92, 133, 134, 138, 139

B grade: { 25, 26, 27, 28, 29, 30 }

C grade: { }

F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 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, 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, 135, 136, 137, 140, 141, 142, 143 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 10, 13, 14, 33, 36, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 92, 126, 127, 128, 129, 130, 131, 132, 133, 134, 136, 137, 138, 139, 140, 141 }

B grade: { 11, 17, 18, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 37, 66, 67, 81, 82, 93, 97, 98, 116, 117, 135 }

C grade: { }

F grade: { 4, 5, 6, 7, 8, 9, 12, 15, 16, 19, 20, 21, 22, 23, 35, 39, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 83, 84, 85, 86, 87, 88, 89, 90, 91, 94, 95, 96, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 118, 119, 120, 121, 122, 123, 124, 125, 142, 143 }

2.1.6 Sympy

A grade: { 33, 139 }

B grade: { 1, 2, 3, 13, 17, 18, 31, 138 }

C grade: { }

F grade: { 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 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, 140, 141, 142, 143 }

2.1.7 Giac

A grade: { 1, 2, 3, 4, 10, 13, 14, 17, 18, 36, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 92, 126, 127, 129, 131, 133, 134, 137, 138, 139 }

B grade: { 5, 16, 31, 32, 33, 37, 38, 51, 128, 130, 132, 135, 136 }

C grade: { 11, 24, 34, 93 }

F grade: { 6, 7, 8, 9, 12, 15, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 35, 39, 49, 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, 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, 140, 141, 142, 143 }

2.2 Detailed conclusion table per each integral for all CAS systems

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

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

Problem 1 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 94 94 86 133 0 452 332 117
normalized size 1 1. 0.91 1.41 0. 4.81 3.53 1.24
time (sec) N/A 0.113 0.078 0.053 0. 1.88 2.537 1.212
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 228 228 204 373 0 1088 928 355
normalized size 1 1. 0.89 1.64 0. 4.77 4.07 1.56
time (sec) N/A 0.33 0.222 0.052 0. 1.913 8.991 1.402
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 441 441 422 822 0 2164 1940 841
normalized size 1 1. 0.96 1.86 0. 4.91 4.4 1.91
time (sec) N/A 0.621 0.493 0.053 0. 2.217 25.993 1.335
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 274 274 212 745 0 0 0 359
normalized size 1 1. 0.77 2.72 0. 0. 0. 1.31
time (sec) N/A 0.282 0.404 0.199 0. 0. 0. 1.237
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 596 596 523 9311 0 0 0 1773
normalized size 1 1. 0.88 15.62 0. 0. 0. 2.97
time (sec) N/A 1.772 2.17 0.204 0. 0. 0. 1.233
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 331 331 322 3358 0 0 0 0
normalized size 1 1. 0.97 10.15 0. 0. 0. 0.
time (sec) N/A 0.601 0.805 0.45 0. 0. 0. 0.
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 249 249 249 714 0 0 0 0
normalized size 1 1. 1. 2.87 0. 0. 0. 0.
time (sec) N/A 0.204 0.255 0.334 0. 0. 0. 0.
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 381 380 440 2758 0 0 0 0
normalized size 1 1. 1.15 7.24 0. 0. 0. 0.
time (sec) N/A 0.798 0.812 0.306 0. 0. 0. 0.
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 797 796 674 6422 0 0 0 0
normalized size 1 1. 0.85 8.06 0. 0. 0. 0.
time (sec) N/A 1.87 5.165 0.256 0. 0. 0. 0.
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 47 47 49 46 88 146 0 65
normalized size 1 1. 1.04 0.98 1.87 3.11 0. 1.38
time (sec) N/A 0.034 0.008 0.05 1.536 1.526 0. 1.218
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 117 117 78 637 0 2379 0 336
normalized size 1 1. 0.67 5.44 0. 20.33 0. 2.87
time (sec) N/A 0.169 0.034 0.161 0. 1.206 0. 1.298
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 484 484 136 6871419 0 0 0 0
normalized size 1 1. 0.28 14197.2 0. 0. 0. 0.
time (sec) N/A 23.581 0.087 0.901 0. 0. 0. 0.
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 184 182 175 510 0 1280 1260 258
normalized size 1 0.99 0.95 2.77 0. 6.96 6.85 1.4
time (sec) N/A 0.346 0.203 0.175 0. 1.799 25.275 1.149
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 542 542 535 1672 0 3933 0 996
normalized size 1 1. 0.99 3.08 0. 7.26 0. 1.84
time (sec) N/A 1.102 0.626 0.167 0. 2.74 0. 1.155
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 406 398 267 1698 0 0 0 0
normalized size 1 0.98 0.66 4.18 0. 0. 0. 0.
time (sec) N/A 0.478 0.54 0.314 0. 0. 0. 0.
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 1075 1067 1376 51470 0 0 0 4355
normalized size 1 0.99 1.28 47.88 0. 0. 0. 4.05
time (sec) N/A 4.177 7.641 0.312 0. 0. 0. 1.578
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 140 140 131 340 0 2399 709 296
normalized size 1 1. 0.94 2.43 0. 17.14 5.06 2.11
time (sec) N/A 0.131 0.153 0.161 0. 1.931 3.775 1.208
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 140 140 131 340 0 2372 680 279
normalized size 1 1. 0.94 2.43 0. 16.94 4.86 1.99
time (sec) N/A 0.104 0.028 0.167 0. 1.936 3.192 1.159
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 617 615 517 16209 0 0 0 0
normalized size 1 1. 0.84 26.27 0. 0. 0. 0.
time (sec) N/A 8.998 2.152 0.309 0. 0. 0. 0.
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 1092 1092 1627 59465 0 0 0 0
normalized size 1 1. 1.49 54.46 0. 0. 0. 0.
time (sec) N/A 18.867 6.536 0.306 0. 0. 0. 0.
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 416 416 393 2269 0 0 0 0
normalized size 1 1. 0.94 5.45 0. 0. 0. 0.
time (sec) N/A 2.702 4.235 0.431 0. 0. 0. 0.
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 780 780 254 784 0 0 0 0
normalized size 1 1. 0.33 1.01 0. 0. 0. 0.
time (sec) N/A 5.162 0.438 0.355 0. 0. 0. 0.
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 302 302 283 1771 0 0 0 0
normalized size 1 1. 0.94 5.86 0. 0. 0. 0.
time (sec) N/A 0.843 0.49 0.344 0. 0. 0. 0.
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 101 101 154 608 0 2943 0 11297
normalized size 1 1. 1.52 6.02 0. 29.14 0. 111.85
time (sec) N/A 0.127 0.177 0.326 0. 2.497 0. 3.821
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F F(-2)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 139 139 140 324 487 948 0 0
normalized size 1 1. 1.01 2.33 3.5 6.82 0. 0.
time (sec) N/A 0.22 0.296 0.135 1.56 1.649 0. 0.
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 166 166 167 760 915 1029 0 0
normalized size 1 1. 1.01 4.58 5.51 6.2 0. 0.
time (sec) N/A 0.221 0.38 0.106 1.584 1.451 0. 0.
Problem 27 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 193 193 185 1560 1723 1304 0 0
normalized size 1 1. 0.96 8.08 8.93 6.76 0. 0.
time (sec) N/A 0.266 0.609 0.107 1.733 1.491 0. 0.
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F F(-2)
verified N/A Yes NO TBD TBD TBD TBD TBD
size 151 151 148 186 490 709 0 0
normalized size 1 1. 0.98 1.23 3.25 4.7 0. 0.
time (sec) N/A 0.229 0.354 0.125 1.538 1.284 0. 0.
Problem 29 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 174 174 172 466 902 1131 0 0
normalized size 1 1. 0.99 2.68 5.18 6.5 0. 0.
time (sec) N/A 0.255 0.576 0.11 1.565 1.477 0. 0.
Problem 30 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 197 197 190 878 1723 1422 0 0
normalized size 1 1. 0.96 4.46 8.75 7.22 0. 0.
time (sec) N/A 0.303 0.722 0.101 1.762 1.457 0. 0.
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 15 15 79 14 0 136 36 78
normalized size 1 1. 5.27 0.93 0. 9.07 2.4 5.2
time (sec) N/A 0.017 0.044 0.046 0. 1.323 3.443 1.158
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 44 44 101 40 0 327 0 146
normalized size 1 1. 2.3 0.91 0. 7.43 0. 3.32
time (sec) N/A 0.052 0.054 0.046 0. 1.283 0. 1.129
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 24 24 90 20 0 103 68 127
normalized size 1 1. 3.75 0.83 0. 4.29 2.83 5.29
time (sec) N/A 0.019 0.063 0.099 0. 1.262 3.175 1.259
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F B F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 56 56 114 45 0 1018 0 217
normalized size 1 1. 2.04 0.8 0. 18.18 0. 3.88
time (sec) N/A 0.05 0.063 0.049 0. 1.474 0. 1.244
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F F(-1) F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 249 249 767 3606 0 0 0 0
normalized size 1 1. 3.08 14.48 0. 0. 0. 0.
time (sec) N/A 0.91 1.654 0.325 0. 0. 0. 0.
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 48 48 46 48 0 181 0 109
normalized size 1 1. 0.96 1. 0. 3.77 0. 2.27
time (sec) N/A 0.05 0.198 0.044 0. 3.785 0. 1.17
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 17 17 165 94 0 142 0 132
normalized size 1 1. 9.71 5.53 0. 8.35 0. 7.76
time (sec) N/A 0.022 0.298 0.091 0. 1.795 0. 1.165
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 86 86 150 123 0 360 0 220
normalized size 1 1. 1.74 1.43 0. 4.19 0. 2.56
time (sec) N/A 0.185 0.113 0.092 0. 1.645 0. 1.176
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 136 136 108 122 0 0 0 0
normalized size 1 1. 0.79 0.9 0. 0. 0. 0.
time (sec) N/A 0.114 0.095 0.234 0. 0. 0. 0.
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 212 212 129 103 0 435 0 158
normalized size 1 1. 0.61 0.49 0. 2.05 0. 0.75
time (sec) N/A 0.116 0.157 0.211 0. 1.966 0. 1.172
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 161 161 117 83 0 381 0 132
normalized size 1 1. 0.73 0.52 0. 2.37 0. 0.82
time (sec) N/A 0.067 0.119 0.223 0. 1.904 0. 1.149
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 148 148 85 65 0 316 0 107
normalized size 1 1. 0.57 0.44 0. 2.14 0. 0.72
time (sec) N/A 0.057 0.059 0.216 0. 1.873 0. 1.201
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 160 160 139 94 0 859 0 138
normalized size 1 1. 0.87 0.59 0. 5.37 0. 0.86
time (sec) N/A 0.119 0.147 0.205 0. 1.853 0. 1.206
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 156 156 118 120 0 821 0 170
normalized size 1 1. 0.76 0.77 0. 5.26 0. 1.09
time (sec) N/A 0.113 0.283 0.228 0. 1.72 0. 1.181
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 161 161 126 141 0 934 0 269
normalized size 1 1. 0.78 0.88 0. 5.8 0. 1.67
time (sec) N/A 0.116 0.117 0.24 0. 1.723 0. 1.147
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 317 317 198 530 0 1250 0 497
normalized size 1 1. 0.62 1.67 0. 3.94 0. 1.57
time (sec) N/A 0.333 0.282 0.214 0. 1.845 0. 1.185
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 227 227 147 381 0 930 0 362
normalized size 1 1. 0.65 1.68 0. 4.1 0. 1.59
time (sec) N/A 0.127 0.137 0.213 0. 1.782 0. 1.192
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 198 198 134 257 0 683 0 250
normalized size 1 1. 0.68 1.3 0. 3.45 0. 1.26
time (sec) N/A 0.101 0.128 0.202 0. 1.711 0. 1.211
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 211 211 149 214 0 1581 0 0
normalized size 1 1. 0.71 1.01 0. 7.49 0. 0.
time (sec) N/A 0.221 0.202 0.244 0. 6.149 0. 0.
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 202 202 155 249 0 1562 0 284
normalized size 1 1. 0.77 1.23 0. 7.73 0. 1.41
time (sec) N/A 0.194 0.195 0.216 0. 3.455 0. 1.212
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 215 215 161 358 0 1670 0 608
normalized size 1 1. 0.75 1.67 0. 7.77 0. 2.83
time (sec) N/A 0.183 0.232 0.206 0. 4.573 0. 1.271
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 452 452 516 7739 0 0 0 0
normalized size 1 1. 1.14 17.12 0. 0. 0. 0.
time (sec) N/A 1.967 2.596 0.319 0. 0. 0. 0.
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 395 395 422 5581 0 0 0 0
normalized size 1 1. 1.07 14.13 0. 0. 0. 0.
time (sec) N/A 0.931 1.585 0.258 0. 0. 0. 0.
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 298 298 282 3249 0 0 0 0
normalized size 1 1. 0.95 10.9 0. 0. 0. 0.
time (sec) N/A 0.376 0.414 0.256 0. 0. 0. 0.
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 358 358 314 3544 0 0 0 0
normalized size 1 1. 0.88 9.9 0. 0. 0. 0.
time (sec) N/A 1.314 0.734 0.266 0. 0. 0. 0.
Problem 56 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 382 382 569 3703 0 0 0 0
normalized size 1 1. 1.49 9.69 0. 0. 0. 0.
time (sec) N/A 1.417 3.202 0.311 0. 0. 0. 0.
Problem 57 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 507 507 642 3993 0 0 0 0
normalized size 1 1. 1.27 7.88 0. 0. 0. 0.
time (sec) N/A 1.88 2.751 0.268 0. 0. 0. 0.
Problem 58 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 795 795 793 19148 0 0 0 0
normalized size 1 1. 1. 24.09 0. 0. 0. 0.
time (sec) N/A 4.264 3.761 0.275 0. 0. 0. 0.
Problem 59 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 553 553 755 14709 0 0 0 0
normalized size 1 1. 1.37 26.6 0. 0. 0. 0.
time (sec) N/A 2.431 2.168 0.26 0. 0. 0. 0.
Problem 60 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 484 482 603 8954 0 0 0 0
normalized size 1 1. 1.25 18.5 0. 0. 0. 0.
time (sec) N/A 4.24 1.158 0.269 0. 0. 0. 0.
Problem 61 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 496 496 746 9728 0 0 0 0
normalized size 1 1. 1.5 19.61 0. 0. 0. 0.
time (sec) N/A 2.569 1.627 0.262 0. 0. 0. 0.
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 604 604 885 9912 0 0 0 0
normalized size 1 1. 1.47 16.41 0. 0. 0. 0.
time (sec) N/A 2.809 4.639 0.288 0. 0. 0. 0.
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 668 668 904 10298 0 0 0 0
normalized size 1 1. 1.35 15.42 0. 0. 0. 0.
time (sec) N/A 3.465 3.547 0.312 0. 0. 0. 0.
Problem 64 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 380 380 378 2397 0 0 0 0
normalized size 1 1. 0.99 6.31 0. 0. 0. 0.
time (sec) N/A 1.17 1.377 0.291 0. 0. 0. 0.
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 344 344 334 1796 0 0 0 0
normalized size 1 1. 0.97 5.22 0. 0. 0. 0.
time (sec) N/A 0.541 0.732 0.269 0. 0. 0. 0.
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 294 294 275 1172 0 10211 0 0
normalized size 1 1. 0.94 3.99 0. 34.73 0. 0.
time (sec) N/A 0.235 0.385 0.261 0. 8.071 0. 0.
Problem 67 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 266 266 247 589 0 10168 0 0
normalized size 1 1. 0.93 2.21 0. 38.23 0. 0.
time (sec) N/A 0.151 0.336 0.263 0. 6.903 0. 0.
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 330 330 319 681 0 0 0 0
normalized size 1 1. 0.97 2.06 0. 0. 0. 0.
time (sec) N/A 0.825 0.788 0.319 0. 0. 0. 0.
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 367 367 356 736 0 0 0 0
normalized size 1 1. 0.97 2.01 0. 0. 0. 0.
time (sec) N/A 1.199 0.903 0.273 0. 0. 0. 0.
Problem 70 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 457 457 460 911 0 0 0 0
normalized size 1 1. 1.01 1.99 0. 0. 0. 0.
time (sec) N/A 1.863 1.679 0.278 0. 0. 0. 0.
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 499 499 577 6124 0 0 0 0
normalized size 1 1. 1.16 12.27 0. 0. 0. 0.
time (sec) N/A 2.107 2.91 0.276 0. 0. 0. 0.
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 410 410 509 4752 0 0 0 0
normalized size 1 1. 1.24 11.59 0. 0. 0. 0.
time (sec) N/A 0.709 2.494 0.296 0. 0. 0. 0.
Problem 73 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 411 411 457 3000 0 0 0 0
normalized size 1 1. 1.11 7.3 0. 0. 0. 0.
time (sec) N/A 0.826 0.912 0.29 0. 0. 0. 0.
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 416 416 320 1713 0 0 0 0
normalized size 1 1. 0.77 4.12 0. 0. 0. 0.
time (sec) N/A 0.617 2.335 0.304 0. 0. 0. 0.
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 526 526 497 1945 0 0 0 0
normalized size 1 1. 0.94 3.7 0. 0. 0. 0.
time (sec) N/A 2.183 4.021 0.273 0. 0. 0. 0.
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 618 618 557 2046 0 0 0 0
normalized size 1 1. 0.9 3.31 0. 0. 0. 0.
time (sec) N/A 2.28 4.924 0.273 0. 0. 0. 0.
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 392 392 327 1817 0 0 0 0
normalized size 1 1. 0.83 4.64 0. 0. 0. 0.
time (sec) N/A 0.952 1.03 0.266 0. 0. 0. 0.
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 316 316 302 1810 0 0 0 0
normalized size 1 1. 0.96 5.73 0. 0. 0. 0.
time (sec) N/A 0.489 0.523 0.263 0. 0. 0. 0.
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 282 282 272 1667 0 0 0 0
normalized size 1 1. 0.96 5.91 0. 0. 0. 0.
time (sec) N/A 0.295 0.333 0.258 0. 0. 0. 0.
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 266 266 253 1669 0 0 0 0
normalized size 1 1. 0.95 6.27 0. 0. 0. 0.
time (sec) N/A 0.226 0.186 0.255 0. 0. 0. 0.
Problem 81 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 267 267 255 1764 0 2695 0 0
normalized size 1 1. 0.96 6.61 0. 10.09 0. 0.
time (sec) N/A 0.778 0.313 0.253 0. 116.964 0. 0.
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 286 286 275 1819 0 2422 0 0
normalized size 1 1. 0.96 6.36 0. 8.47 0. 0.
time (sec) N/A 0.706 0.456 0.293 0. 141.882 0. 0.
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 353 353 316 1953 0 0 0 0
normalized size 1 1. 0.9 5.53 0. 0. 0. 0.
time (sec) N/A 0.879 0.549 0.299 0. 0. 0. 0.
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 501 501 447 4884 0 0 0 0
normalized size 1 1. 0.89 9.75 0. 0. 0. 0.
time (sec) N/A 1.412 1.563 0.273 0. 0. 0. 0.
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 417 417 395 4900 0 0 0 0
normalized size 1 1. 0.95 11.75 0. 0. 0. 0.
time (sec) N/A 1.015 1.082 0.269 0. 0. 0. 0.
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 349 349 330 4567 0 0 0 0
normalized size 1 1. 0.95 13.09 0. 0. 0. 0.
time (sec) N/A 0.522 0.875 0.263 0. 0. 0. 0.
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 315 315 298 4574 0 0 0 0
normalized size 1 1. 0.95 14.52 0. 0. 0. 0.
time (sec) N/A 0.517 0.842 0.263 0. 0. 0. 0.
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 469 469 755 4765 0 0 0 0
normalized size 1 1. 1.61 10.16 0. 0. 0. 0.
time (sec) N/A 1.274 0.532 0.278 0. 0. 0. 0.
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 463 463 765 4799 0 0 0 0
normalized size 1 1. 1.65 10.37 0. 0. 0. 0.
time (sec) N/A 1.201 0.669 0.268 0. 0. 0. 0.
Problem 90 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 614 614 303 5056 0 0 0 0
normalized size 1 1. 0.49 8.23 0. 0. 0. 0.
time (sec) N/A 1.436 1.011 0.276 0. 0. 0. 0.
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 189 189 181 1346 0 0 0 0
normalized size 1 1. 0.96 7.12 0. 0. 0. 0.
time (sec) N/A 0.285 0.621 0.2 0. 0. 0. 0.
Problem 92 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 75 75 75 102 112 197 0 99
normalized size 1 1. 1. 1.36 1.49 2.63 0. 1.32
time (sec) N/A 0.058 0.039 0.055 1.718 1.802 0. 1.276
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 130 130 120 789 0 2356 0 369
normalized size 1 1. 0.92 6.07 0. 18.12 0. 2.84
time (sec) N/A 0.16 0.172 0.127 0. 2.039 0. 1.418
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 369 369 300 516 0 0 0 0
normalized size 1 1. 0.81 1.4 0. 0. 0. 0.
time (sec) N/A 0.809 1.923 0.28 0. 0. 0. 0.
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 287 287 325 410 0 0 0 0
normalized size 1 1. 1.13 1.43 0. 0. 0. 0.
time (sec) N/A 0.633 1.202 0.265 0. 0. 0. 0.
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 266 266 250 399 0 0 0 0
normalized size 1 1. 0.94 1.5 0. 0. 0. 0.
time (sec) N/A 0.216 0.456 0.279 0. 0. 0. 0.
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 220 220 211 354 0 5501 0 0
normalized size 1 1. 0.96 1.61 0. 25. 0. 0.
time (sec) N/A 0.13 0.184 0.265 0. 5.229 0. 0.
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 220 220 209 358 0 5328 0 0
normalized size 1 1. 0.95 1.63 0. 24.22 0. 0.
time (sec) N/A 0.118 0.097 0.26 0. 4.682 0. 0.
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 267 267 252 391 0 0 0 0
normalized size 1 1. 0.94 1.46 0. 0. 0. 0.
time (sec) N/A 0.663 0.472 0.28 0. 0. 0. 0.
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 291 291 325 427 0 0 0 0
normalized size 1 1. 1.12 1.47 0. 0. 0. 0.
time (sec) N/A 0.657 1.067 0.265 0. 0. 0. 0.
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 376 376 314 519 0 0 0 0
normalized size 1 1. 0.84 1.38 0. 0. 0. 0.
time (sec) N/A 0.734 2.155 0.279 0. 0. 0. 0.
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F(-1) F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 466 466 562 1648 0 0 0 0
normalized size 1 1. 1.21 3.54 0. 0. 0. 0.
time (sec) N/A 1.347 1.64 0.283 0. 0. 0. 0.
Problem 103 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 341 341 414 1480 0 0 0 0
normalized size 1 1. 1.21 4.34 0. 0. 0. 0.
time (sec) N/A 1.041 1.379 0.287 0. 0. 0. 0.
Problem 104 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 297 297 352 1427 0 0 0 0
normalized size 1 1. 1.19 4.8 0. 0. 0. 0.
time (sec) N/A 0.454 0.468 0.309 0. 0. 0. 0.
Problem 105 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 299 299 356 1360 0 0 0 0
normalized size 1 1. 1.19 4.55 0. 0. 0. 0.
time (sec) N/A 0.4 0.415 0.298 0. 0. 0. 0.
Problem 106 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 310 310 360 1376 0 0 0 0
normalized size 1 1. 1.16 4.44 0. 0. 0. 0.
time (sec) N/A 0.411 0.447 0.292 0. 0. 0. 0.
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 394 394 436 1518 0 0 0 0
normalized size 1 1. 1.11 3.85 0. 0. 0. 0.
time (sec) N/A 1.182 1. 0.26 0. 0. 0. 0.
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 454 454 488 1656 0 0 0 0
normalized size 1 1. 1.07 3.65 0. 0. 0. 0.
time (sec) N/A 1.193 1.342 0.25 0. 0. 0. 0.
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 761 761 552 14815 0 0 0 0
normalized size 1 1. 0.73 19.47 0. 0. 0. 0.
time (sec) N/A 3.135 2.394 0.312 0. 0. 0. 0.
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 549 549 496 10138 0 0 0 0
normalized size 1 1. 0.9 18.47 0. 0. 0. 0.
time (sec) N/A 7.028 1.942 0.321 0. 0. 0. 0.
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 431 431 417 6019 0 0 0 0
normalized size 1 1. 0.97 13.97 0. 0. 0. 0.
time (sec) N/A 0.65 0.764 0.32 0. 0. 0. 0.
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 523 521 454 6460 0 0 0 0
normalized size 1 1. 0.87 12.35 0. 0. 0. 0.
time (sec) N/A 3.701 1.389 0.303 0. 0. 0. 0.
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 736 736 520 6765 0 0 0 0
normalized size 1 1. 0.71 9.19 0. 0. 0. 0.
time (sec) N/A 3.476 1.839 0.313 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(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 545 545 550 3131 0 0 0 0
normalized size 1 1. 1.01 5.74 0. 0. 0. 0.
time (sec) N/A 3.722 2.473 0.321 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(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 463 463 468 2321 0 0 0 0
normalized size 1 1. 1.01 5.01 0. 0. 0. 0.
time (sec) N/A 3.436 1.211 0.342 0. 0. 0. 0.
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 402 402 407 1516 0 23019 0 0
normalized size 1 1. 1.01 3.77 0. 57.26 0. 0.
time (sec) N/A 0.963 1.014 0.326 0. 48.067 0. 0.
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 374 374 376 761 0 22873 0 0
normalized size 1 1. 1.01 2.03 0. 61.16 0. 0.
time (sec) N/A 0.314 0.805 0.319 0. 51.604 0. 0.
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 451 451 450 859 0 0 0 0
normalized size 1 1. 1. 1.9 0. 0. 0. 0.
time (sec) N/A 2.632 2.61 0.374 0. 0. 0. 0.
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F(-1) F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 543 543 533 983 0 0 0 0
normalized size 1 1. 0.98 1.81 0. 0. 0. 0.
time (sec) N/A 4.592 1.598 0.344 0. 0. 0. 0.
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 679 679 669 1296 0 0 0 0
normalized size 1 1. 0.99 1.91 0. 0. 0. 0.
time (sec) N/A 11.226 2.534 0.342 0. 0. 0. 0.
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 779 779 1066 14651 0 0 0 0
normalized size 1 1. 1.37 18.81 0. 0. 0. 0.
time (sec) N/A 14.17 2.914 0.359 0. 0. 0. 0.
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 609 609 1097 11341 0 0 0 0
normalized size 1 1. 1.8 18.62 0. 0. 0. 0.
time (sec) N/A 5.842 6.611 0.348 0. 0. 0. 0.
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 609 609 983 7163 0 0 0 0
normalized size 1 1. 1.61 11.76 0. 0. 0. 0.
time (sec) N/A 5.643 6.333 0.352 0. 0. 0. 0.
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 666 666 700 4099 0 0 0 0
normalized size 1 1. 1.05 6.15 0. 0. 0. 0.
time (sec) N/A 1.746 6.573 0.333 0. 0. 0. 0.
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F(-1) F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 816 814 1121 4594 0 0 0 0
normalized size 1 1. 1.37 5.63 0. 0. 0. 0.
time (sec) N/A 15.916 6.642 0.325 0. 0. 0. 0.
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 140 140 210 159 0 494 0 254
normalized size 1 1. 1.5 1.14 0. 3.53 0. 1.81
time (sec) N/A 0.501 0.549 0.1 0. 2.197 0. 1.273
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 115 115 192 144 0 474 0 250
normalized size 1 1. 1.67 1.25 0. 4.12 0. 2.17
time (sec) N/A 0.42 0.437 0.135 0. 2.2 0. 1.293
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 98 98 159 130 0 441 0 231
normalized size 1 1. 1.62 1.33 0. 4.5 0. 2.36
time (sec) N/A 0.198 0.199 0.1 0. 1.857 0. 1.247
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 68 69 174 92 0 138 0 92
normalized size 1 1.01 2.56 1.35 0. 2.03 0. 1.35
time (sec) N/A 0.062 0.18 0.098 0. 1.553 0. 1.216
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 95 95 150 121 0 365 0 223
normalized size 1 1. 1.58 1.27 0. 3.84 0. 2.35
time (sec) N/A 0.111 0.109 0.1 0. 1.608 0. 1.256
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 130 130 200 152 0 473 0 269
normalized size 1 1. 1.54 1.17 0. 3.64 0. 2.07
time (sec) N/A 0.417 0.453 0.102 0. 1.633 0. 1.307
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 151 151 225 169 0 518 0 363
normalized size 1 1. 1.49 1.12 0. 3.43 0. 2.4
time (sec) N/A 0.454 0.456 0.111 0. 1.632 0. 1.279
Problem 133 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 149 149 87 147 209 398 0 115
normalized size 1 1. 0.58 0.99 1.4 2.67 0. 0.77
time (sec) N/A 0.093 0.225 0.057 1.534 1.576 0. 1.161
Problem 134 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 103 103 72 96 140 263 0 95
normalized size 1 1. 0.7 0.93 1.36 2.55 0. 0.92
time (sec) N/A 0.042 0.035 0.05 1.471 1.56 0. 1.156
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 28 28 37 163 0 153 0 85
normalized size 1 1. 1.32 5.82 0. 5.46 0. 3.04
time (sec) N/A 0.048 0.11 0.058 0. 1.544 0. 1.173
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 84 84 114 245 0 370 0 215
normalized size 1 1. 1.36 2.92 0. 4.4 0. 2.56
time (sec) N/A 0.078 0.244 0.064 0. 1.586 0. 1.227
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 139 139 131 306 0 674 0 313
normalized size 1 1. 0.94 2.2 0. 4.85 0. 2.25
time (sec) N/A 0.117 0.38 0.071 0. 1.69 0. 1.216
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 15 15 13 16 15 31 31 15
normalized size 1 1. 0.87 1.07 1. 2.07 2.07 1.
time (sec) N/A 0.004 0.007 0.046 0.988 1.494 0.449 1.155
Problem 139 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 16 16 13 14 12 31 10 15
normalized size 1 1. 0.81 0.88 0.75 1.94 0.62 0.94
time (sec) N/A 0.006 0.003 0.045 1.015 1.661 10.071 1.183
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 15 15 13 20 0 31 0 0
normalized size 1 1. 0.87 1.33 0. 2.07 0. 0.
time (sec) N/A 0.028 0.006 0.046 0. 1.478 0. 0.
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 15 15 13 18 0 31 0 0
normalized size 1 1. 0.87 1.2 0. 2.07 0. 0.
time (sec) N/A 0.058 0.004 0.046 0. 1.458 0. 0.
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 242 242 268 0 0 0 0 0
normalized size 1 1. 1.11 0. 0. 0. 0. 0.
time (sec) N/A 0.093 0.582 0.803 0. 0. 0. 0.
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F(-1) F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 488 488 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.36 0.549 3.165 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 [63] had the largest ratio of [ 0.5556 ]

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 4 1. 25 0.16
2 A 5 4 1. 27 0.148
3 A 5 4 1. 27 0.148
4 A 8 8 1. 27 0.296
5 A 9 9 1. 27 0.333
6 A 9 6 1. 30 0.2
7 A 5 3 1. 30 0.1
8 A 6 4 1. 30 0.133
9 A 7 5 1. 30 0.167
10 A 5 4 1. 23 0.174
11 A 5 4 1. 23 0.174
12 A 5 4 1. 30 0.133
13 A 6 5 0.99 28 0.179
14 A 6 5 1. 30 0.167
15 A 9 5 0.98 30 0.167
16 A 10 6 0.99 30 0.2
17 A 5 5 1. 34 0.147
18 A 5 5 1. 34 0.147
19 A 9 6 1. 32 0.188
20 A 10 7 1. 32 0.219
21 A 5 3 1. 32 0.094
22 A 5 3 1. 29 0.103
23 A 5 3 1. 29 0.103
24 A 6 6 1. 26 0.231
25 A 5 4 1. 30 0.133
26 A 7 6 1. 30 0.2
27 A 7 6 1. 30 0.2
28 A 5 3 1. 30 0.1
29 A 6 4 1. 30 0.133
30 A 7 5 1. 30 0.167
31 A 2 2 1. 26 0.077
32 A 5 5 1. 26 0.192
33 A 2 2 1. 24 0.083
34 A 5 5 1. 20 0.25
35 A 6 5 1. 36 0.139
36 A 2 2 1. 36 0.056
37 A 2 2 1. 32 0.062
38 A 13 9 1. 32 0.281
39 A 5 5 1. 38 0.132
40 A 6 6 1. 35 0.171
41 A 5 5 1. 33 0.152
42 A 5 5 1. 32 0.156
43 A 8 8 1. 35 0.229
44 A 8 8 1. 35 0.229
45 A 8 8 1. 35 0.229
46 A 6 6 1. 38 0.158
47 A 5 5 1. 36 0.139
48 A 5 5 1. 35 0.143
49 A 7 6 1. 38 0.158
50 A 7 6 1. 38 0.158
51 A 7 6 1. 38 0.158
52 A 9 6 1. 27 0.222
53 A 9 6 1. 25 0.24
54 A 8 5 1. 24 0.208
55 A 12 9 1. 27 0.333
56 A 18 12 1. 27 0.444
57 A 22 13 1. 27 0.482
58 A 10 7 1. 27 0.259
59 A 10 7 1. 25 0.28
60 A 9 6 1. 24 0.25
61 A 17 11 1. 27 0.407
62 A 21 14 1. 27 0.518
63 A 26 15 1. 27 0.556
64 A 10 6 1. 27 0.222
65 A 8 5 1. 27 0.185
66 A 5 3 1. 25 0.12
67 A 5 3 1. 24 0.125
68 A 10 7 1. 27 0.259
69 A 11 8 1. 27 0.296
70 A 15 9 1. 27 0.333
71 A 10 7 1. 27 0.259
72 A 6 4 1. 27 0.148
73 A 6 4 1. 25 0.16
74 A 6 4 1. 24 0.167
75 A 12 9 1. 27 0.333
76 A 14 11 1. 27 0.407
77 A 15 9 1. 28 0.321
78 A 9 6 1. 28 0.214
79 A 9 6 1. 26 0.231
80 A 8 5 1. 25 0.2
81 A 17 9 1. 28 0.321
82 A 16 8 1. 28 0.286
83 A 20 10 1. 28 0.357
84 A 17 10 1. 28 0.357
85 A 10 7 1. 28 0.25
86 A 10 7 1. 26 0.269
87 A 9 6 1. 25 0.24
88 A 19 11 1. 28 0.393
89 A 18 10 1. 28 0.357
90 A 26 13 1. 28 0.464
91 A 9 6 1. 24 0.25
92 A 8 6 1. 22 0.273
93 A 10 9 1. 17 0.529
94 A 13 7 1. 28 0.25
95 A 10 6 1. 28 0.214
96 A 8 5 1. 28 0.179
97 A 5 3 1. 26 0.115
98 A 5 3 1. 25 0.12
99 A 9 4 1. 28 0.143
100 A 10 5 1. 28 0.179
101 A 13 6 1. 28 0.214
102 A 13 9 1. 28 0.321
103 A 9 6 1. 28 0.214
104 A 6 4 1. 28 0.143
105 A 6 4 1. 26 0.154
106 A 6 4 1. 25 0.16
107 A 12 7 1. 28 0.25
108 A 12 7 1. 28 0.25
109 A 9 6 1. 30 0.2
110 A 9 6 1. 28 0.214
111 A 8 5 1. 27 0.185
112 A 17 9 1. 30 0.3
113 A 23 10 1. 30 0.333
114 A 12 6 1. 30 0.2
115 A 8 5 1. 30 0.167
116 A 5 3 1. 28 0.107
117 A 5 3 1. 27 0.111
118 A 9 4 1. 30 0.133
119 A 12 5 1. 30 0.167
120 A 16 7 1. 30 0.233
121 A 10 7 1. 30 0.233
122 A 6 4 1. 30 0.133
123 A 6 4 1. 28 0.143
124 A 6 4 1. 27 0.148
125 A 12 7 1. 30 0.233
126 A 24 14 1. 30 0.467
127 A 20 13 1. 30 0.433
128 A 16 12 1. 30 0.4
129 A 6 4 1.01 28 0.143
130 A 10 8 1. 27 0.296
131 A 17 11 1. 30 0.367
132 A 20 12 1. 30 0.4
133 A 8 6 1. 34 0.176
134 A 6 5 1. 30 0.167
135 A 3 3 1. 34 0.088
136 A 5 5 1. 34 0.147
137 A 7 7 1. 34 0.206
138 A 1 1 1. 17 0.059
139 A 1 1 1. 15 0.067
140 A 2 2 1. 23 0.087
141 A 3 3 1. 21 0.143
142 A 2 2 1. 40 0.05
143 A 2 2 1. 104 0.019

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