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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, 78, 81, 82, 83, 84, 85, 88, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 117, 124, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 144, 151, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166 }

B grade: { 75, 77, 79, 86, 87, 114, 116, 118, 120, 121, 122, 123, 141, 143, 145, 152 }

C grade: { 74, 76, 80, 113, 115, 119, 140, 142, 146 }

F grade: { 89, 90, 125, 126, 147, 148, 149, 150, 153}

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 10, 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, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 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, 160, 161, 162, 163, 164, 165, 166 }

B grade: { 83 }

C grade: { 9, 11, 66, 82, 102, 158, 159 }

F grade: { 81, 84, 85}

2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 17, 18, 21, 23, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 80, 91, 92, 94, 95, 96, 97, 98, 99, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 115, 116, 119, 127, 128, 130, 131, 132, 133, 134, 135, 137, 138, 139, 140, 142, 145, 146, 154, 155, 156, 158, 159, 160, 161, 162, 163, 164 }

B grade: { 7, 14, 16, 20, 22, 24, 26, 28, 29, 32, 34, 87, 123, 136, 141, 143, 147, 149, 152, 153, 157, 166 }

C grade: { 19, 25, 27, 30, 31, 33, 64, 86, 100, 122, 144, 148, 150, 151, 165 }

F grade: { 56, 75, 78, 79, 81, 82, 83, 84, 85, 88, 89, 90, 93, 114, 117, 118, 120, 121, 124, 125, 126, 129 }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 17, 21, 23, 35, 36, 37, 38, 39, 40, 53, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 74, 76, 80, 94, 95, 96, 97, 98, 99, 101, 102, 103, 105, 107, 109, 111, 113, 115, 119, 130, 131, 132, 133, 134, 135, 137, 138, 139, 140, 142, 146, 154, 155, 156, 158, 159, 160, 161, 162, 163, 164

B grade: { 68, 69, 70, 71, 72, 73, 104, 106, 108, 110, 112, 157, 165 }

C grade: { }

F grade: { 7, 14, 16, 18, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 64, 75, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 100, 114, 116, 117, 118, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 136, 141, 143, 144, 145, 147, 148, 149, 150, 151, 152, 153, 166 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 17, 21, 23, 35, 36, 37, 38, 39, 40, 53, 54, 55, 57, 58, 60, 61, 62, 63, 65, 66, 67, 74, 76, 80, 91, 92, 94, 95, 96, 97, 98, 99, 101, 102, 103, 105, 107, 109, 111, 113, 115, 119, 127, 128, 130, 131, 132, 133, 134, 135, 137, 138, 139, 140, 142, 146, 154, 155, 156, 158, 159, 160, 161, 162, 163, 164 }

B grade: { 68, 69, 70, 71, 72, 73, 104, 106, 108, 110, 112, 166 }

C grade: { }

F grade: { 7, 14, 16, 18, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 56, 59, 64, 75, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 93, 100, 114, 116, 117, 118, 120, 121, 122, 123, 124, 125, 126, 129, 136, 141, 143, 144, 145, 147, 148, 149, 150, 151, 152, 153, 157, 165 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 17, 21, 23, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 76, 80, 98, 99, 101, 102, 104, 105, 106, 109, 110, 111, 132, 133, 134, 135, 137, 138, 139, 140, 142, 146, 154, 155, 156, 161, 162, 163 }

B grade: { 158, 159, 160, 164 }

C grade: { }

F grade: { 7, 14, 16, 18, 19, 20, 22, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 56, 59, 64, 74, 75, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 100, 103, 107, 108, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 136, 141, 143, 144, 145, 147, 148, 149, 150, 151, 152, 153, 157, 165, 166 }

2.1.7 Giac

A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 17, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 65, 67, 68, 69, 70, 71, 72, 73, 74, 76, 91, 92, 94, 95, 96, 97, 98, 99, 101, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 115, 127, 128, 130, 131, 132, 133, 134, 135, 137, 138, 139, 140, 142, 154, 155, 156, 158, 159, 160, 161, 162, 163, 164 }

B grade: { 66, 102 }

C grade: { }

F grade: { 7, 14, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 56, 64, 75, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 93, 100, 114, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 129, 136, 141, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 157, 165, 166 }

2.2 Detailed conclusion table per each integral for all CAS systems

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

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

Problem 1 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 59 59 64 53 77 131 63 89
normalized size 1 1. 1.08 0.9 1.31 2.22 1.07 1.51
time (sec) N/A 0.032 0.003 0.006 1.46 2.364 2.023 1.223
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 56 56 61 52 76 134 60 80
normalized size 1 1. 1.09 0.93 1.36 2.39 1.07 1.43
time (sec) N/A 0.042 0.013 0.006 0.977 2.29 1.446 1.249
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 48 48 53 44 65 105 53 66
normalized size 1 1. 1.1 0.92 1.35 2.19 1.1 1.38
time (sec) N/A 0.027 0.003 0.005 1.443 2.442 1.108 1.353
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 50 43 62 111 49 66
normalized size 1 1. 1.11 0.96 1.38 2.47 1.09 1.47
time (sec) N/A 0.032 0.008 0.006 0.982 2.306 0.765 1.203
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 37 37 42 35 50 80 42 61
normalized size 1 1. 1.14 0.95 1.35 2.16 1.14 1.65
time (sec) N/A 0.016 0.002 0.004 1.484 2.22 0.561 1.194
Problem 6 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 29 29 29 28 42 81 26 42
normalized size 1 1. 1. 0.97 1.45 2.79 0.9 1.45
time (sec) N/A 0.011 0.003 0.003 0.985 2.232 0.253 1.335
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 35 35 35 74 0 0 0 0
normalized size 1 1. 1. 2.11 0. 0. 0. 0.
time (sec) N/A 0.029 0.002 0.015 0. 0. 0. 0.
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 35 35 38 39 53 100 37 50
normalized size 1 1. 1.09 1.11 1.51 2.86 1.06 1.43
time (sec) N/A 0.023 0.003 0.006 0.969 2.492 0.889 1.323
Problem 9 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 37 37 46 35 42 70 37 74
normalized size 1 1. 1.24 0.95 1.14 1.89 1. 2.
time (sec) N/A 0.02 0.003 0.007 1.468 2.565 0.744 1.298
Problem 10 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 53 53 54 51 69 123 61 68
normalized size 1 1. 1.02 0.96 1.3 2.32 1.15 1.28
time (sec) N/A 0.033 0.016 0.007 0.969 2.481 1.536 1.807
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 48 48 46 44 62 95 46 88
normalized size 1 1. 0.96 0.92 1.29 1.98 0.96 1.83
time (sec) N/A 0.025 0.003 0.009 1.459 2.376 1.205 1.735
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 64 64 64 60 84 147 71 80
normalized size 1 1. 1. 0.94 1.31 2.3 1.11 1.25
time (sec) N/A 0.038 0.017 0.01 0.975 2.528 2.591 1.406
Problem 13 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 144 144 138 171 220 351 199 243
normalized size 1 1. 0.96 1.19 1.53 2.44 1.38 1.69
time (sec) N/A 0.31 0.13 0.013 1.509 2.543 3.607 1.203
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 170 170 169 334 0 0 0 0
normalized size 1 1. 0.99 1.96 0. 0. 0. 0.
time (sec) N/A 0.289 0.485 0.044 0. 0. 0. 0.
Problem 15 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 112 112 111 135 184 266 155 181
normalized size 1 1. 0.99 1.21 1.64 2.38 1.38 1.62
time (sec) N/A 0.209 0.079 0.016 1.52 2.407 2.089 1.187
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 138 138 131 298 0 0 0 0
normalized size 1 1. 0.95 2.16 0. 0. 0. 0.
time (sec) N/A 0.194 0.28 0.014 0. 0. 0. 0.
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 76 76 75 97 140 189 107 140
normalized size 1 1. 0.99 1.28 1.84 2.49 1.41 1.84
time (sec) N/A 0.106 0.065 0.012 1.531 2.441 0.935 1.197
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 83 83 90 128 0 0 0 0
normalized size 1 1. 1.08 1.54 0. 0. 0. 0.
time (sec) N/A 0.098 0.076 0.071 0. 0. 0. 0.
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 132 132 144 1128 0 0 0 0
normalized size 1 1. 1.09 8.55 0. 0. 0. 0.
time (sec) N/A 0.25 0.072 0.394 0. 0. 0. 0.
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 82 82 102 323 0 0 0 0
normalized size 1 1. 1.24 3.94 0. 0. 0. 0.
time (sec) N/A 0.147 0.141 0.013 0. 0. 0. 0.
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 79 79 90 110 132 221 119 0
normalized size 1 1. 1.14 1.39 1.67 2.8 1.51 0.
time (sec) N/A 0.128 0.065 0.011 1.497 2.54 1.452 0.
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 140 140 153 399 0 0 0 0
normalized size 1 1. 1.09 2.85 0. 0. 0. 0.
time (sec) N/A 0.23 0.364 0.014 0. 0. 0. 0.
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 116 116 128 147 205 297 170 0
normalized size 1 1. 1.1 1.27 1.77 2.56 1.47 0.
time (sec) N/A 0.219 0.088 0.017 1.538 2.75 2.615 0.
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 255 255 291 528 0 0 0 0
normalized size 1 1. 1.14 2.07 0. 0. 0. 0.
time (sec) N/A 0.948 0.764 0.017 0. 0. 0. 0.
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 271 271 396 3053 0 0 0 0
normalized size 1 1. 1.46 11.27 0. 0. 0. 0.
time (sec) N/A 0.756 0.83 3.677 0. 0. 0. 0.
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 194 194 225 445 0 0 0 0
normalized size 1 1. 1.16 2.29 0. 0. 0. 0.
time (sec) N/A 0.545 0.524 0.019 0. 0. 0. 0.
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 206 206 269 2020 0 0 0 0
normalized size 1 1. 1.31 9.81 0. 0. 0. 0.
time (sec) N/A 0.434 0.566 1.106 0. 0. 0. 0.
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 131 131 152 352 0 0 0 0
normalized size 1 1. 1.16 2.69 0. 0. 0. 0.
time (sec) N/A 0.239 0.284 0.089 0. 0. 0. 0.
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 119 119 192 270 0 0 0 0
normalized size 1 1. 1.61 2.27 0. 0. 0. 0.
time (sec) N/A 0.209 0.092 0.134 0. 0. 0. 0.
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 206 206 212 2309 0 0 0 0
normalized size 1 1. 1.03 11.21 0. 0. 0. 0.
time (sec) N/A 0.427 0.136 0.301 0. 0. 0. 0.
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-1) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 116 116 214 2159 0 0 0 0
normalized size 1 1. 1.84 18.61 0. 0. 0. 0.
time (sec) N/A 0.267 0.369 0.341 0. 0. 0. 0.
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 133 133 176 457 0 0 0 0
normalized size 1 1. 1.32 3.44 0. 0. 0. 0.
time (sec) N/A 0.285 0.323 0.043 0. 0. 0. 0.
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-1) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 213 213 321 5974 0 0 0 0
normalized size 1 1. 1.51 28.05 0. 0. 0. 0.
time (sec) N/A 0.476 0.812 1.735 0. 0. 0. 0.
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 198 198 265 550 0 0 0 0
normalized size 1 1. 1.34 2.78 0. 0. 0. 0.
time (sec) N/A 0.601 0.656 0.1 0. 0. 0. 0.
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 10 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.008 0.611 0.189 0. 0. 0. 0.
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 8 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.003 0.011 0.148 0. 0. 0. 0.
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.015 0.425 0.12 0. 0. 0. 0.
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 10 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.008 0.591 0.368 0. 0. 0. 0.
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 8 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.003 0.881 0.149 0. 0. 0. 0.
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 1.01 0.135 0. 0. 0. 0.
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.007 1.959 0.246 0. 0. 0. 0.
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 10 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.003 1.741 0.131 0. 0. 0. 0.
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 1.246 0.26 0. 0. 0. 0.
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.007 0.948 0.206 0. 0. 0. 0.
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 10 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.003 2.149 0.135 0. 0. 0. 0.
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 1.069 0.25 0. 0. 0. 0.
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.007 1.232 0.225 0. 0. 0. 0.
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 10 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.003 0.02 0.132 0. 0. 0. 0.
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.014 1.13 0.223 0. 0. 0. 0.
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.007 1.477 0.239 0. 0. 0. 0.
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 10 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.003 2.531 0.135 0. 0. 0. 0.
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 2.72 0.183 0. 0. 0. 0.
Problem 53 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 117 117 108 74 116 404 104 116
normalized size 1 1. 0.92 0.63 0.99 3.45 0.89 0.99
time (sec) N/A 0.067 0.025 0.023 1.485 2.794 8.17 1.212
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.022 3.731 1.937 0. 0. 0. 0.
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.021 2.433 1.633 0. 0. 0. 0.
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 73 73 60 0 0 0 0 0
normalized size 1 1. 0.82 0. 0. 0. 0. 0.
time (sec) N/A 0.031 0.031 1.434 0. 0. 0. 0.
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.024 0.253 0.824 0. 0. 0. 0.
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.005 0.437 0.41 0. 0. 0. 0.
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.021 0.328 0.986 0. 0. 0. 0.
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 54 54 59 50 73 111 58 81
normalized size 1 1. 1.09 0.93 1.35 2.06 1.07 1.5
time (sec) N/A 0.035 0.008 0.024 1.458 2.628 128.876 1.097
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 47 47 52 45 65 115 80 63
normalized size 1 1. 1.11 0.96 1.38 2.45 1.7 1.34
time (sec) N/A 0.031 0.013 0.024 0.984 2.582 76.17 1.125
Problem 62 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 43 43 48 41 58 85 48 58
normalized size 1 1. 1.12 0.95 1.35 1.98 1.12 1.35
time (sec) N/A 0.027 0.005 0.025 1.519 2.605 40.632 1.154
Problem 63 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 36 36 41 36 51 89 70 54
normalized size 1 1. 1.14 1. 1.42 2.47 1.94 1.5
time (sec) N/A 0.014 0.006 0.019 1.027 2.932 20.899 1.154
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 39 39 39 63 0 0 0 0
normalized size 1 1. 1. 1.62 0. 0. 0. 0.
time (sec) N/A 0.045 0.005 0.082 0. 0. 0. 0.
Problem 65 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 39 39 44 39 55 111 593 81
normalized size 1 1. 1.13 1. 1.41 2.85 15.21 2.08
time (sec) N/A 0.024 0.006 0.027 0.998 2.749 45.408 1.226
Problem 66 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 41 41 48 39 47 76 42 100
normalized size 1 1. 1.17 0.95 1.15 1.85 1.02 2.44
time (sec) N/A 0.025 0.007 0.024 1.501 2.681 36.268 1.201
Problem 67 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 55 55 60 51 72 130 784 93
normalized size 1 1. 1.09 0.93 1.31 2.36 14.25 1.69
time (sec) N/A 0.032 0.014 0.029 1.002 2.822 140.139 1.142
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 161 161 179 140 375 894 184 228
normalized size 1 1. 1.11 0.87 2.33 5.55 1.14 1.42
time (sec) N/A 0.113 0.048 0.037 1.527 2.852 55.237 1.305
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 159 159 177 138 354 807 1207 223
normalized size 1 1. 1.11 0.87 2.23 5.08 7.59 1.4
time (sec) N/A 0.101 0.033 0.026 1.532 2.803 28.332 1.239
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 140 140 107 125 348 768 146 201
normalized size 1 1. 0.76 0.89 2.49 5.49 1.04 1.44
time (sec) N/A 0.105 0.042 0.023 1.519 2.826 15.067 1.144
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 143 143 158 125 339 790 1105 186
normalized size 1 1. 1.1 0.87 2.37 5.52 7.73 1.3
time (sec) N/A 0.086 0.042 0.025 1.529 2.757 32.019 1.228
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 159 159 177 132 369 900 704 215
normalized size 1 1. 1.11 0.83 2.32 5.66 4.43 1.35
time (sec) N/A 0.104 0.052 0.029 1.525 2.858 55.576 1.268
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 159 159 177 138 366 873 1265 203
normalized size 1 1. 1.11 0.87 2.3 5.49 7.96 1.28
time (sec) N/A 0.103 0.05 0.03 1.52 2.831 107.518 1.364
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A C A A A A F(-1) A
verified N/A NO Yes TBD TBD TBD TBD TBD
size 124 731 121 151 228 301 0 196
normalized size 1 5.9 0.98 1.22 1.84 2.43 0. 1.58
time (sec) N/A 1.627 0.091 0.036 1.779 2.993 0. 1.196
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A F F(-2) F F F
verified N/A NO NO TBD TBD TBD TBD TBD
size 154 647 141 0 0 0 0 0
normalized size 1 4.2 0.92 0. 0. 0. 0. 0.
time (sec) N/A 1.366 0.289 180. 0. 0. 0. 0.
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A C A A A A A A
verified N/A NO Yes TBD TBD TBD TBD TBD
size 90 612 85 113 170 227 529 135
normalized size 1 6.8 0.94 1.26 1.89 2.52 5.88 1.5
time (sec) N/A 1.042 0.064 0.033 1.752 2.773 63.552 1.197
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A A F F F F
verified N/A NO NO TBD TBD TBD TBD TBD
size 101 255 107 146 0 0 0 0
normalized size 1 2.52 1.06 1.45 0. 0. 0. 0.
time (sec) N/A 0.554 0.087 0.087 0. 0. 0. 0.
Problem 78 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 151 151 165 0 0 0 0 0
normalized size 1 1. 1.09 0. 0. 0. 0. 0.
time (sec) N/A 0.321 0.1 0.167 0. 0. 0. 0.
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A F F(-2) F F F
verified N/A NO NO TBD TBD TBD TBD TBD
size 97 290 127 0 0 0 0 0
normalized size 1 2.99 1.31 0. 0. 0. 0. 0.
time (sec) N/A 0.653 0.149 0.337 0. 0. 0. 0.
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A C A A A A A F
verified N/A NO Yes TBD TBD TBD TBD TBD
size 87 419 98 118 149 258 1187 0
normalized size 1 4.82 1.13 1.36 1.71 2.97 13.64 0.
time (sec) N/A 1.136 0.077 0.037 1.837 2.732 86.816 0.
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F(-2) F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 1393 1393 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 2.602 4.849 0.207 0. 0. 0. 0.
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 1191 1191 5466 0 0 0 0 0
normalized size 1 1. 4.59 0. 0. 0. 0. 0.
time (sec) N/A 1.778 31.777 0.188 0. 0. 0. 0.
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 1164 1164 5434 0 0 0 0 0
normalized size 1 1. 4.67 0. 0. 0. 0. 0.
time (sec) N/A 1.622 31.403 0.191 0. 0. 0. 0.
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F(-2) F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 1360 1360 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 2.227 2.674 0.2 0. 0. 0. 0.
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F(-2) F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 1444 1444 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 2.427 2.7 0.208 0. 0. 0. 0.
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A C F F F F
verified N/A NO NO TBD TBD TBD TBD TBD
size 149 951 170 690 0 0 0 0
normalized size 1 6.38 1.14 4.63 0. 0. 0. 0.
time (sec) N/A 4.736 0.311 0.733 0. 0. 0. 0.
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A B F F F F
verified N/A NO NO TBD TBD TBD TBD TBD
size 144 545 224 306 0 0 0 0
normalized size 1 3.78 1.56 2.12 0. 0. 0. 0.
time (sec) N/A 2.545 0.102 0.125 0. 0. 0. 0.
Problem 88 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 229 229 245 0 0 0 0 0
normalized size 1 1. 1.07 0. 0. 0. 0. 0.
time (sec) N/A 0.529 0.195 0.199 0. 0. 0. 0.
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A F F(-2) F F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 138 0 239 0 0 0 0 0
normalized size 1 0. 1.73 0. 0. 0. 0. 0.
time (sec) N/A 0.831 0.43 0.332 0. 0. 0. 0.
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A F F(-2) F F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 149 0 196 0 0 0 0 0
normalized size 1 0. 1.32 0. 0. 0. 0. 0.
time (sec) N/A 1.659 0.334 0.661 0. 0. 0. 0.
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.023 1.788 0.237 0. 0. 0. 0.
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.024 1.175 0.213 0. 0. 0. 0.
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 75 75 65 0 0 0 0 0
normalized size 1 1. 0.87 0. 0. 0. 0. 0.
time (sec) N/A 0.041 0.059 0.209 0. 0. 0. 0.
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.027 0.312 0.145 0. 0. 0. 0.
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.026 0.329 0.171 0. 0. 0. 0.
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 54 54 59 50 73 113 0 81
normalized size 1 1. 1.09 0.93 1.35 2.09 0. 1.5
time (sec) N/A 0.039 0.008 0.026 1.502 2.619 0. 1.117
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 47 47 52 45 65 115 0 63
normalized size 1 1. 1.11 0.96 1.38 2.45 0. 1.34
time (sec) N/A 0.036 0.013 0.023 1.052 2.656 0. 1.137
Problem 98 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 43 43 48 41 58 85 48 58
normalized size 1 1. 1.12 0.95 1.35 1.98 1.12 1.35
time (sec) N/A 0.029 0.005 0.023 1.483 2.587 166.108 1.105
Problem 99 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 36 36 41 36 51 89 808 54
normalized size 1 1. 1.14 1. 1.42 2.47 22.44 1.5
time (sec) N/A 0.021 0.007 0.021 1.003 2.661 83.144 1.161
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 39 39 39 63 0 0 0 0
normalized size 1 1. 1. 1.62 0. 0. 0. 0.
time (sec) N/A 0.05 0.005 0.086 0. 0. 0. 0.
Problem 101 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 39 39 44 39 55 111 505 81
normalized size 1 1. 1.13 1. 1.41 2.85 12.95 2.08
time (sec) N/A 0.025 0.007 0.026 0.993 3.279 155.503 1.111
Problem 102 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 41 41 48 39 47 76 42 100
normalized size 1 1. 1.17 0.95 1.15 1.85 1.02 2.44
time (sec) N/A 0.027 0.006 0.028 1.505 3.132 153.635 1.166
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 60 51 72 130 0 93
normalized size 1 1. 1.09 0.93 1.31 2.36 0. 1.69
time (sec) N/A 0.035 0.014 0.027 1.021 3.325 0. 1.113
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 174 174 179 165 396 948 1287 225
normalized size 1 1. 1.03 0.95 2.28 5.45 7.4 1.29
time (sec) N/A 0.325 0.043 0.092 1.532 3.141 111.885 1.235
Problem 105 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 101 101 131 98 143 632 1703 128
normalized size 1 1. 1.3 0.97 1.42 6.26 16.86 1.27
time (sec) N/A 0.098 0.04 0.023 1.494 3.306 55.892 1.152
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 165 165 170 148 381 1224 311 185
normalized size 1 1. 1.03 0.9 2.31 7.42 1.88 1.12
time (sec) N/A 0.294 0.048 0.056 1.521 3.584 124.381 1.244
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 115 115 183 105 144 336 0 146
normalized size 1 1. 1.59 0.91 1.25 2.92 0. 1.27
time (sec) N/A 0.091 0.045 0.03 1.541 2.738 0. 1.205
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 176 176 181 170 432 1069 0 231
normalized size 1 1. 1.03 0.97 2.45 6.07 0. 1.31
time (sec) N/A 0.431 0.075 0.069 1.503 3.25 0. 1.394
Problem 109 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 117 117 185 113 162 362 1640 161
normalized size 1 1. 1.58 0.97 1.38 3.09 14.02 1.38
time (sec) N/A 0.096 0.027 0.028 1.521 3.246 160.661 1.22
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 165 165 170 154 412 971 1620 212
normalized size 1 1. 1.03 0.93 2.5 5.88 9.82 1.28
time (sec) N/A 0.393 0.025 0.056 1.557 2.54 67.111 1.307
Problem 111 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 104 104 170 104 151 258 1975 123
normalized size 1 1. 1.63 1. 1.45 2.48 18.99 1.18
time (sec) N/A 0.085 0.037 0.026 1.54 2.66 92.538 1.23
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 174 174 179 159 425 1385 0 217
normalized size 1 1. 1.03 0.91 2.44 7.96 0. 1.25
time (sec) N/A 0.413 0.05 0.059 1.535 2.963 0. 1.714
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A C A A A A F(-1) A
verified N/A NO Yes TBD TBD TBD TBD TBD
size 124 731 121 151 228 281 0 196
normalized size 1 5.9 0.98 1.22 1.84 2.27 0. 1.58
time (sec) N/A 1.655 0.095 0.037 1.928 2.711 0. 1.14
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A F F F F(-1) F
verified N/A NO NO TBD TBD TBD TBD TBD
size 154 647 141 0 0 0 0 0
normalized size 1 4.2 0.92 0. 0. 0. 0. 0.
time (sec) N/A 1.394 0.293 180. 0. 0. 0. 0.
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A C A A A A F(-1) A
verified N/A NO Yes TBD TBD TBD TBD TBD
size 90 612 85 113 170 200 0 135
normalized size 1 6.8 0.94 1.26 1.89 2.22 0. 1.5
time (sec) N/A 1.052 0.065 0.037 1.871 2.619 0. 1.158
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A A F F F F
verified N/A NO NO TBD TBD TBD TBD TBD
size 104 255 107 148 0 0 0 0
normalized size 1 2.45 1.03 1.42 0. 0. 0. 0.
time (sec) N/A 0.644 0.071 0.09 0. 0. 0. 0.
Problem 117 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 154 154 167 0 0 0 0 0
normalized size 1 1. 1.08 0. 0. 0. 0. 0.
time (sec) N/A 0.316 0.116 0.198 0. 0. 0. 0.
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A F F F F(-1) F
verified N/A NO NO TBD TBD TBD TBD TBD
size 100 290 125 0 0 0 0 0
normalized size 1 2.9 1.25 0. 0. 0. 0. 0.
time (sec) N/A 0.661 0.155 0.408 0. 0. 0. 0.
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A C A A A A F(-1) F
verified N/A NO Yes TBD TBD TBD TBD TBD
size 87 419 98 118 149 232 0 0
normalized size 1 4.82 1.13 1.36 1.71 2.67 0. 0.
time (sec) N/A 1.122 0.077 0.04 1.947 2.843 0. 0.
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A F F F F(-1) F
verified N/A NO NO TBD TBD TBD TBD TBD
size 154 536 167 0 0 0 0 0
normalized size 1 3.48 1.08 0. 0. 0. 0. 0.
time (sec) N/A 1.45 0.374 0.288 0. 0. 0. 0.
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A F F F F(-1) F
verified N/A NO NO TBD TBD TBD TBD TBD
size 240 1867 346 0 0 0 0 0
normalized size 1 7.78 1.44 0. 0. 0. 0. 0.
time (sec) N/A 7.034 0.505 0.279 0. 0. 0. 0.
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A C F F F(-1) F
verified N/A NO NO TBD TBD TBD TBD TBD
size 147 951 170 867 0 0 0 0
normalized size 1 6.47 1.16 5.9 0. 0. 0. 0.
time (sec) N/A 4.733 0.166 0.917 0. 0. 0. 0.
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A B F F F(-1) F
verified N/A NO NO TBD TBD TBD TBD TBD
size 139 545 224 303 0 0 0 0
normalized size 1 3.92 1.61 2.18 0. 0. 0. 0.
time (sec) N/A 2.702 0.1 0.129 0. 0. 0. 0.
Problem 124 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 232 232 248 0 0 0 0 0
normalized size 1 1. 1.07 0. 0. 0. 0. 0.
time (sec) N/A 0.523 0.195 0.194 0. 0. 0. 0.
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A F F F F(-1) F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 133 0 240 0 0 0 0 0
normalized size 1 0. 1.8 0. 0. 0. 0. 0.
time (sec) N/A 0.86 0.397 0.381 0. 0. 0. 0.
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A F F F F(-1) F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 146 0 196 0 0 0 0 0
normalized size 1 0. 1.34 0. 0. 0. 0. 0.
time (sec) N/A 1.67 0.329 0.557 0. 0. 0. 0.
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.024 1.798 0.261 0. 0. 0. 0.
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.024 1.192 0.23 0. 0. 0. 0.
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 75 75 65 0 0 0 0 0
normalized size 1 1. 0.87 0. 0. 0. 0. 0.
time (sec) N/A 0.042 0.061 0.239 0. 0. 0. 0.
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.027 0.314 0.158 0. 0. 0. 0.
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 20 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.026 0.331 0.205 0. 0. 0. 0.
Problem 132 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 50 50 55 46 61 101 46 81
normalized size 1 1. 1.1 0.92 1.22 2.02 0.92 1.62
time (sec) N/A 0.031 0.01 0.032 1.479 2.21 0.827 1.161
Problem 133 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 43 43 48 55 58 103 41 54
normalized size 1 1. 1.12 1.28 1.35 2.4 0.95 1.26
time (sec) N/A 0.03 0.007 0.033 0.989 2.182 0.545 1.125
Problem 134 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 39 39 44 37 49 77 36 69
normalized size 1 1. 1.13 0.95 1.26 1.97 0.92 1.77
time (sec) N/A 0.017 0.008 0.03 1.487 2.331 0.385 1.164
Problem 135 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 27 27 27 38 36 65 22 36
normalized size 1 1. 1. 1.41 1.33 2.41 0.81 1.33
time (sec) N/A 0.012 0.003 0.029 0.987 2.126 0.22 1.121
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 39 39 39 94 0 0 0 0
normalized size 1 1. 1. 2.41 0. 0. 0. 0.
time (sec) N/A 0.045 0.006 0.036 0. 0. 0. 0.
Problem 137 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 34 34 37 36 51 103 36 54
normalized size 1 1. 1.09 1.06 1.5 3.03 1.06 1.59
time (sec) N/A 0.019 0.008 0.021 1.026 2.227 0.977 1.116
Problem 138 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 43 43 48 41 57 84 44 84
normalized size 1 1. 1.12 0.95 1.33 1.95 1.02 1.95
time (sec) N/A 0.024 0.01 0.026 1.525 2.068 1.237 1.145
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 55 55 60 45 73 132 60 74
normalized size 1 1. 1.09 0.82 1.33 2.4 1.09 1.35
time (sec) N/A 0.036 0.01 0.026 1.026 2.232 1.637 1.135
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A C A A A A A A
verified N/A NO Yes TBD TBD TBD TBD TBD
size 122 862 111 157 177 290 144 228
normalized size 1 7.07 0.91 1.29 1.45 2.38 1.18 1.87
time (sec) N/A 1.791 0.09 0.043 1.604 2.19 1.148 1.176
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A B F F F F
verified N/A NO NO TBD TBD TBD TBD TBD
size 152 787 152 445 0 0 0 0
normalized size 1 5.18 1. 2.93 0. 0. 0. 0.
time (sec) N/A 1.49 0.328 0.104 0. 0. 0. 0.
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A C A A A A A A
verified N/A NO Yes TBD TBD TBD TBD TBD
size 82 663 73 116 136 201 97 173
normalized size 1 8.09 0.89 1.41 1.66 2.45 1.18 2.11
time (sec) N/A 1.126 0.054 0.04 1.54 2.282 0.587 1.175
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A B F F F F
verified N/A NO NO TBD TBD TBD TBD TBD
size 83 478 105 357 0 0 0 0
normalized size 1 5.76 1.27 4.3 0. 0. 0. 0.
time (sec) N/A 0.44 0.106 0.09 0. 0. 0. 0.
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 148 148 148 1249 0 0 0 0
normalized size 1 1. 1. 8.44 0. 0. 0. 0.
time (sec) N/A 0.294 0.085 0.394 0. 0. 0. 0.
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A A F(-1) F F F
verified N/A NO NO TBD TBD TBD TBD TBD
size 96 259 107 147 0 0 0 0
normalized size 1 2.7 1.11 1.53 0. 0. 0. 0.
time (sec) N/A 0.528 0.111 0.088 0. 0. 0. 0.
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A C A A A A A F
verified N/A NO Yes TBD TBD TBD TBD TBD
size 84 836 99 110 158 239 117 0
normalized size 1 9.95 1.18 1.31 1.88 2.85 1.39 0.
time (sec) N/A 1.294 0.074 0.034 1.62 2.312 1.438 0.
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A B F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 214 0 253 608 0 0 0 0
normalized size 1 0. 1.18 2.84 0. 0. 0. 0.
time (sec) N/A 4.629 0.591 0.108 0. 0. 0. 0.
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A C F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 229 0 330 6441 0 0 0 0
normalized size 1 0. 1.44 28.13 0. 0. 0. 0.
time (sec) N/A 3.52 0.678 1.027 0. 0. 0. 0.
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A B F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 145 0 174 507 0 0 0 0
normalized size 1 0. 1.2 3.5 0. 0. 0. 0.
time (sec) N/A 2.352 0.274 0.104 0. 0. 0. 0.
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A C F F F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 119 0 215 2363 0 0 0 0
normalized size 1 0. 1.81 19.86 0. 0. 0. 0.
time (sec) N/A 0.739 0.257 0.33 0. 0. 0. 0.
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 230 230 219 2542 0 0 0 0
normalized size 1 1. 0.95 11.05 0. 0. 0. 0.
time (sec) N/A 0.494 0.207 0.276 0. 0. 0. 0.
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A B F(-1) F F F
verified N/A NO NO TBD TBD TBD TBD TBD
size 136 551 222 306 0 0 0 0
normalized size 1 4.05 1.63 2.25 0. 0. 0. 0.
time (sec) N/A 2.359 0.119 0.125 0. 0. 0. 0.
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F A B F(-1) F F F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 147 0 178 396 0 0 0 0
normalized size 1 0. 1.21 2.69 0. 0. 0. 0.
time (sec) N/A 2.255 0.283 0.095 0. 0. 0. 0.
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 51 51 34 32 42 88 39 42
normalized size 1 1. 0.67 0.63 0.82 1.73 0.76 0.82
time (sec) N/A 0.015 0.013 0.023 1.506 2.213 4.159 1.138
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 42 42 28 27 35 72 32 35
normalized size 1 1. 0.67 0.64 0.83 1.71 0.76 0.83
time (sec) N/A 0.01 0.011 0.025 1.494 2.201 2.021 1.117
Problem 156 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 22 22 18 17 22 47 19 22
normalized size 1 1. 0.82 0.77 1. 2.14 0.86 1.
time (sec) N/A 0.006 0.006 0.02 1.468 2.209 1.358 1.105
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 31 61 47 0 0 0
normalized size 1 1. 1. 1.97 1.52 0. 0. 0.
time (sec) N/A 0.035 0.004 0.036 1.534 0. 0. 0.
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 30 22 28 54 94 28
normalized size 1 1. 1.11 0.81 1.04 2. 3.48 1.04
time (sec) N/A 0.012 0.01 0.026 1.466 2.132 3.14 1.345
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 42 42 34 27 35 80 160 35
normalized size 1 1. 0.81 0.64 0.83 1.9 3.81 0.83
time (sec) N/A 0.014 0.011 0.027 1.453 2.192 8.434 1.245
Problem 160 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 36 36 30 25 32 88 92 32
normalized size 1 1. 0.83 0.69 0.89 2.44 2.56 0.89
time (sec) N/A 0.015 0.015 0.023 0.977 2.225 7.674 1.109
Problem 161 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 29 29 25 20 26 73 24 26
normalized size 1 1. 0.86 0.69 0.9 2.52 0.83 0.9
time (sec) N/A 0.012 0.01 0.023 0.977 2.179 1.633 1.182
Problem 162 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 20 20 20 17 22 54 17 22
normalized size 1 1. 1. 0.85 1.1 2.7 0.85 1.1
time (sec) N/A 0.008 0.007 0.023 0.966 2.163 0.452 1.118
Problem 163 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 22 22 22 19 24 78 20 24
normalized size 1 1. 1. 0.86 1.09 3.55 0.91 1.09
time (sec) N/A 0.009 0.011 0.026 1.15 2.185 1.919 1.11
Problem 164 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 37 37 31 26 34 96 143 38
normalized size 1 1. 0.84 0.7 0.92 2.59 3.86 1.03
time (sec) N/A 0.014 0.018 0.029 0.996 2.192 8.499 1.158
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C B F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 33 33 33 57 84 0 0 0
normalized size 1 1. 1. 1.73 2.55 0. 0. 0.
time (sec) N/A 0.036 0.006 0.088 1.469 0. 0. 0.
Problem 166 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 39 39 32 94 0 181 0 0
normalized size 1 1. 0.82 2.41 0. 4.64 0. 0.
time (sec) N/A 0.036 0.013 0.033 0. 2.562 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 [142] had the largest ratio of [ 2.286 ]

Table 2.1Rubi specific breakdown of results for each integral
# grade
number of
steps
used
number of
unique
rules
normalized
antiderivative
leaf size
integrand
leaf size
\(\frac{\text{number of rules}}{\text{integrand leaf size}}\)
1 A 4 3 1. 12 0.25
2 A 4 3 1. 12 0.25
3 A 4 3 1. 12 0.25
4 A 4 3 1. 12 0.25
5 A 3 3 1. 10 0.3
6 A 3 2 1. 8 0.25
7 A 3 2 1. 12 0.167
8 A 5 5 1. 12 0.417
9 A 3 3 1. 12 0.25
10 A 4 3 1. 12 0.25
11 A 4 3 1. 12 0.25
12 A 4 3 1. 12 0.25
13 A 16 7 1. 14 0.5
14 A 14 9 1. 14 0.643
15 A 11 7 1. 14 0.5
16 A 9 8 1. 14 0.571
17 A 6 5 1. 12 0.417
18 A 5 5 1. 10 0.5
19 A 6 5 1. 14 0.357
20 A 4 4 1. 14 0.286
21 A 8 7 1. 14 0.5
22 A 8 7 1. 14 0.5
23 A 13 8 1. 14 0.571
24 A 33 11 1. 14 0.786
25 A 24 11 1. 14 0.786
26 A 18 10 1. 14 0.714
27 A 12 9 1. 14 0.643
28 A 8 8 1. 12 0.667
29 A 5 6 1. 10 0.6
30 A 8 6 1. 14 0.429
31 A 5 6 1. 14 0.429
32 A 7 6 1. 14 0.429
33 A 14 11 1. 14 0.786
34 A 16 8 1. 14 0.571
35 A 0 0 0. 0 0.
36 A 0 0 0. 0 0.
37 A 0 0 0. 0 0.
38 A 0 0 0. 0 0.
39 A 0 0 0. 0 0.
40 A 0 0 0. 0 0.
41 A 0 0 0. 0 0.
42 A 0 0 0. 0 0.
43 A 0 0 0. 0 0.
44 A 0 0 0. 0 0.
45 A 0 0 0. 0 0.
46 A 0 0 0. 0 0.
47 A 0 0 0. 0 0.
48 A 0 0 0. 0 0.
49 A 0 0 0. 0 0.
50 A 0 0 0. 0 0.
51 A 0 0 0. 0 0.
52 A 0 0 0. 0 0.
53 A 12 9 1. 8 1.125
54 A 0 0 0. 0 0.
55 A 0 0 0. 0 0.
56 A 2 2 1. 14 0.143
57 A 0 0 0. 0 0.
58 A 0 0 0. 0 0.
59 A 0 0 0. 0 0.
60 A 5 4 1. 14 0.286
61 A 4 3 1. 14 0.214
62 A 4 4 1. 14 0.286
63 A 2 2 1. 12 0.167
64 A 4 3 1. 14 0.214
65 A 5 5 1. 14 0.357
66 A 4 4 1. 14 0.286
67 A 4 3 1. 14 0.214
68 A 11 8 1. 14 0.571
69 A 11 8 1. 14 0.571
70 A 11 7 1. 10 0.7
71 A 10 7 1. 14 0.5
72 A 11 8 1. 14 0.571
73 A 11 8 1. 14 0.571
74 C 62 19 5.9 16 1.187
75 B 53 19 4.2 16 1.187
76 C 44 16 6.8 16 1.
77 B 28 12 2.52 14 0.857
78 A 7 6 1. 16 0.375
79 B 24 13 2.99 16 0.812
80 C 46 23 4.82 16 1.438
81 A 86 27 1. 16 1.687
82 A 69 23 1. 12 1.917
83 A 47 23 1. 16 1.438
84 A 64 25 1. 16 1.562
85 A 77 25 1. 16 1.562
86 B 155 30 6.38 16 1.875
87 B 82 23 3.78 14 1.643
88 A 9 7 1. 16 0.438
89 F 0 0 N/A 0 N/A
90 F 0 0 N/A 0 N/A
91 A 0 0 0. 0 0.
92 A 0 0 0. 0 0.
93 A 3 3 1. 16 0.188
94 A 0 0 0. 0 0.
95 A 0 0 0. 0 0.
96 A 5 4 1. 14 0.286
97 A 4 3 1. 14 0.214
98 A 4 4 1. 14 0.286
99 A 2 2 1. 14 0.143
100 A 4 3 1. 14 0.214
101 A 5 5 1. 14 0.357
102 A 4 4 1. 14 0.286
103 A 4 3 1. 14 0.214
104 A 12 8 1. 14 0.571
105 A 9 8 1. 10 0.8
106 A 11 7 1. 14 0.5
107 A 9 9 1. 14 0.643
108 A 12 8 1. 14 0.571
109 A 9 9 1. 14 0.643
110 A 11 7 1. 12 0.583
111 A 8 8 1. 14 0.571
112 A 12 8 1. 14 0.571
113 C 62 19 5.9 16 1.187
114 B 53 19 4.2 16 1.187
115 C 44 16 6.8 16 1.
116 B 28 12 2.45 16 0.75
117 A 7 6 1. 16 0.375
118 B 24 13 2.9 16 0.812
119 C 46 23 4.82 16 1.438
120 B 59 24 3.48 16 1.5
121 B 239 32 7.78 16 2.
122 B 155 30 6.47 16 1.875
123 B 82 23 3.92 16 1.438
124 A 9 7 1. 16 0.438
125 F 0 0 N/A 0 N/A
126 F 0 0 N/A 0 N/A
127 A 0 0 0. 0 0.
128 A 0 0 0. 0 0.
129 A 3 3 1. 16 0.188
130 A 0 0 0. 0 0.
131 A 0 0 0. 0 0.
132 A 5 4 1. 14 0.286
133 A 5 4 1. 14 0.286
134 A 4 4 1. 12 0.333
135 A 4 3 1. 10 0.3
136 A 4 3 1. 14 0.214
137 A 2 2 1. 14 0.143
138 A 4 4 1. 14 0.286
139 A 5 4 1. 14 0.286
140 C 88 34 7.07 16 2.125
141 B 73 34 5.18 16 2.125
142 C 58 32 8.09 14 2.286
143 B 31 14 5.76 12 1.167
144 A 7 6 1. 16 0.375
145 B 28 12 2.7 16 0.75
146 C 66 23 9.95 16 1.438
147 F 0 0 N/A 0 N/A
148 F 0 0 N/A 0 N/A
149 F 0 0 N/A 0 N/A
150 F 0 0 N/A 0 N/A
151 A 9 7 1. 16 0.438
152 B 82 23 4.05 16 1.438
153 F 0 0 N/A 0 N/A
154 A 6 4 1. 10 0.4
155 A 5 4 1. 8 0.5
156 A 4 4 1. 6 0.667
157 A 4 3 1. 10 0.3
158 A 4 4 1. 10 0.4
159 A 5 4 1. 10 0.4
160 A 3 2 1. 12 0.167
161 A 3 2 1. 12 0.167
162 A 2 2 1. 12 0.167
163 A 4 4 1. 12 0.333
164 A 3 2 1. 12 0.167
165 A 4 3 1. 10 0.3
166 A 4 3 1. 10 0.3

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