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Chapter 2
detailed summary tables of results

 2.1 List of integrals sorted by grade for each CAS
  2.1.1 Rubi
  2.1.2 Mathematica
  2.1.3 Maple
  2.1.4 Maxima
  2.1.5 FriCAS
  2.1.6 Sympy
  2.1.7 Giac
 2.2 Detailed conclusion table per each integral for all CAS systems
 2.3 Detailed conclusion table specific for Rubi results

2.1 List of integrals sorted by grade for each CAS

2.1.1 Rubi

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 18, 19, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174 }

B grade: { }

C grade: { 13, 14, 20, 21, 148, 149, 150 }

F grade: { }

2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 163, 164, 165, 166, 167, 168, 169, 170, 171, 174 }

B grade: { 48, 161, 162, 172, 173 }

C grade: { }

F grade: { 58, 59, 60, 61 }

2.1.4 Maxima

A grade: { 32, 37, 38, 39, 43, 44, 45, 46, 50, 51, 52, 53, 54, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 110, 111, 112, 113

B grade: { 49, 163 }

C grade: { }

F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 40, 41, 42, 47, 48, 55, 56, 57, 58, 59, 60, 61, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 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, 62, 63, 64, 65, 70, 71, 72, 73, 78, 79, 80, 81, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 169, 170, 171 }

B grade: { }

C grade: { }

F grade: { 58, 59, 60, 61, 66, 67, 68, 69, 74, 75, 76, 77, 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, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 172, 173, 174 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 35, 36, 38, 43, 44, 45, 46, 51, 53, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 105, 106, 110, 111, 112, 113, 114, 115, 116, 117, 120, 123, 124, 125, 126, 127, 128, 129, 130, 132, 133, 134, 135, 136, 137, 138, 139, 140, 143, 144, 145, 146, 147, 148, 153, 154, 155, 156, 169, 170, 171 }

B grade: { 25, 33, 34, 37, 39, 40, 41, 42, 52, 54, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 107, 108, 109, 118, 119, 121, 122, 131, 149, 150, 151, 152, 157, 158 }

C grade: { 58, 59, 60, 61 }

F grade: { 47, 48, 49, 50, 55, 56, 57, 141, 142, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 172, 173, 174 }

2.1.7 Giac

A grade: { 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 151, 152, 153, 154, 155, 159, 160, 161, 162, 163, 164, 165, 169, 170, 171, 172, 173, 174 }

B grade: { 7, 14, 28, 35, 45, 150, 156, 157, 158, 166, 167, 168 }

C grade: { }

F grade: { 58, 59, 60, 61 }

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 A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 127 127 107 115 0 501 192 126
normalized size 1 1. 0.84 0.91 0. 3.94 1.51 0.99
time (sec) N/A 0.082 0.187 0.008 0. 1.578 6.529 1.19
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 104 104 93 94 0 435 165 109
normalized size 1 1. 0.89 0.9 0. 4.18 1.59 1.05
time (sec) N/A 0.049 0.174 0.006 0. 1.555 4.431 1.182
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 80 80 86 75 0 381 124 92
normalized size 1 1. 1.08 0.94 0. 4.76 1.55 1.15
time (sec) N/A 0.026 0.141 0.005 0. 1.586 4.38 1.171
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 67 67 67 53 0 316 70 74
normalized size 1 1. 1. 0.79 0. 4.72 1.04 1.1
time (sec) N/A 0.019 0.05 0.004 0. 1.546 2.726 1.179
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 79 79 100 78 0 859 107 105
normalized size 1 1. 1.27 0.99 0. 10.87 1.35 1.33
time (sec) N/A 0.061 0.208 0.004 0. 1.661 5.044 1.19
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 75 75 99 97 0 821 124 138
normalized size 1 1. 1.32 1.29 0. 10.95 1.65 1.84
time (sec) N/A 0.059 0.159 0.006 0. 1.621 3.552 1.194
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 80 80 108 121 0 934 107 220
normalized size 1 1. 1.35 1.51 0. 11.68 1.34 2.75
time (sec) N/A 0.06 0.091 0.008 0. 1.62 3.755 1.224
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 150 150 126 134 0 630 318 155
normalized size 1 1. 0.84 0.89 0. 4.2 2.12 1.03
time (sec) N/A 0.095 0.228 0.008 0. 1.603 15.786 1.221
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 127 127 113 113 0 559 287 139
normalized size 1 1. 0.89 0.89 0. 4.4 2.26 1.09
time (sec) N/A 0.062 0.215 0.007 0. 1.648 10.718 1.255
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 103 103 107 94 0 500 223 120
normalized size 1 1. 1.04 0.91 0. 4.85 2.17 1.17
time (sec) N/A 0.033 0.184 0.005 0. 1.613 10.032 1.171
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 87 87 88 69 0 425 219 103
normalized size 1 1. 1.01 0.79 0. 4.89 2.52 1.18
time (sec) N/A 0.026 0.07 0.004 0. 1.63 6.309 1.181
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 106 106 118 107 0 1094 218 135
normalized size 1 1. 1.11 1.01 0. 10.32 2.06 1.27
time (sec) N/A 0.094 0.247 0.006 0. 1.743 14.508 1.19
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 108 108 105 126 0 1033 184 167
normalized size 1 1. 0.97 1.17 0. 9.56 1.7 1.55
time (sec) N/A 0.089 0.167 0.007 0. 1.672 5.773 1.217
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 111 111 90 150 0 1048 182 258
normalized size 1 1. 0.81 1.35 0. 9.44 1.64 2.32
time (sec) N/A 0.085 0.036 0.007 0. 1.715 6.862 1.241
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 173 173 145 153 0 775 469 189
normalized size 1 1. 0.84 0.88 0. 4.48 2.71 1.09
time (sec) N/A 0.105 0.276 0.008 0. 1.7 30.433 1.237
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 150 150 131 132 0 687 442 173
normalized size 1 1. 0.87 0.88 0. 4.58 2.95 1.15
time (sec) N/A 0.069 0.259 0.006 0. 1.62 21.051 1.23
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 126 126 112 113 0 635 354 154
normalized size 1 1. 0.89 0.9 0. 5.04 2.81 1.22
time (sec) N/A 0.044 0.516 0.006 0. 1.66 19.883 1.228
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 107 107 108 85 0 549 348 136
normalized size 1 1. 1.01 0.79 0. 5.13 3.25 1.27
time (sec) N/A 0.037 0.081 0.005 0. 1.59 12.57 1.214
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 132 132 139 138 0 1353 323 169
normalized size 1 1. 1.05 1.05 0. 10.25 2.45 1.28
time (sec) N/A 0.159 0.329 0.005 0. 1.745 24.432 1.186
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 136 136 117 158 0 1319 318 203
normalized size 1 1. 0.86 1.16 0. 9.7 2.34 1.49
time (sec) N/A 0.132 0.222 0.009 0. 1.704 10.135 1.215
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 141 141 92 181 0 1316 279 296
normalized size 1 1. 0.65 1.28 0. 9.33 1.98 2.1
time (sec) N/A 0.117 0.026 0.007 0. 1.702 11.318 1.186
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 104 104 76 96 0 385 150 100
normalized size 1 1. 0.73 0.92 0. 3.7 1.44 0.96
time (sec) N/A 0.077 0.044 0.007 0. 1.588 5.284 1.231
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 81 81 64 75 0 320 94 82
normalized size 1 1. 0.79 0.93 0. 3.95 1.16 1.01
time (sec) N/A 0.042 0.036 0.005 0. 1.576 3.528 1.212
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 56 56 57 55 0 275 70 68
normalized size 1 1. 1.02 0.98 0. 4.91 1.25 1.21
time (sec) N/A 0.023 0.032 0.004 0. 1.793 3.293 1.183
Problem 25 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 43 43 46 37 0 223 102 53
normalized size 1 1. 1.07 0.86 0. 5.19 2.37 1.23
time (sec) N/A 0.015 0.029 0.004 0. 1.776 1.016 1.181
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 53 53 53 52 0 683 99 78
normalized size 1 1. 1. 0.98 0. 12.89 1.87 1.47
time (sec) N/A 0.04 0.014 0.006 0. 1.585 2.407 1.217
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 47 47 47 49 0 240 41 88
normalized size 1 1. 1. 1.04 0. 5.11 0.87 1.87
time (sec) N/A 0.033 0.015 0.007 0. 1.556 2.149 1.186
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 72 72 63 68 0 306 66 197
normalized size 1 1. 0.88 0.94 0. 4.25 0.92 2.74
time (sec) N/A 0.053 0.102 0.008 0. 1.564 3.156 1.263
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 81 81 72 93 0 448 117 95
normalized size 1 1. 0.89 1.15 0. 5.53 1.44 1.17
time (sec) N/A 0.043 0.052 0.008 0. 1.6 7.672 1.217
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 66 66 67 72 0 369 83 78
normalized size 1 1. 1.02 1.09 0. 5.59 1.26 1.18
time (sec) N/A 0.036 0.034 0.006 0. 1.595 5.857 1.229
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 48 48 64 54 0 336 66 65
normalized size 1 1. 1.33 1.12 0. 7. 1.38 1.35
time (sec) N/A 0.02 0.054 0.005 0. 1.581 4.694 1.196
Problem 32 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 28 28 27 26 42 69 46 31
normalized size 1 1. 0.96 0.93 1.5 2.46 1.64 1.11
time (sec) N/A 0.007 0.014 0.001 0.992 1.605 3.635 1.204
Problem 33 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 47 47 47 60 0 338 206 80
normalized size 1 1. 1. 1.28 0. 7.19 4.38 1.7
time (sec) N/A 0.038 0.027 0.007 0. 1.85 5.909 1.189
Problem 34 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 70 70 72 80 0 381 235 130
normalized size 1 1. 1.03 1.14 0. 5.44 3.36 1.86
time (sec) N/A 0.057 0.038 0.008 0. 1.885 8.088 1.223
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 95 95 75 101 0 474 124 231
normalized size 1 1. 0.79 1.06 0. 4.99 1.31 2.43
time (sec) N/A 0.078 0.16 0.008 0. 1.878 8.607 1.255
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 79 79 69 91 0 536 400 95
normalized size 1 1. 0.87 1.15 0. 6.78 5.06 1.2
time (sec) N/A 0.042 0.076 0.008 0. 1.74 12.579 1.416
Problem 37 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 53 53 44 41 95 128 141 49
normalized size 1 1. 0.83 0.77 1.79 2.42 2.66 0.92
time (sec) N/A 0.022 0.017 0.004 1.013 1.549 10.608 1.183
Problem 38 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 32 29 69 99 95 35
normalized size 1 1. 0.68 0.62 1.47 2.11 2.02 0.74
time (sec) N/A 0.014 0.017 0.004 0.992 1.548 9.037 1.168
Problem 39 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 51 51 43 40 65 126 146 50
normalized size 1 1. 0.84 0.78 1.27 2.47 2.86 0.98
time (sec) N/A 0.01 0.02 0.003 1.009 1.589 8.949 1.223
Problem 40 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 76 76 69 92 0 537 840 111
normalized size 1 1. 0.91 1.21 0. 7.07 11.05 1.46
time (sec) N/A 0.063 0.055 0.007 0. 1.692 22.992 1.196
Problem 41 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 104 104 95 112 0 589 910 161
normalized size 1 1. 0.91 1.08 0. 5.66 8.75 1.55
time (sec) N/A 0.088 0.055 0.008 0. 1.688 20.084 1.203
Problem 42 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 129 129 106 134 0 683 1034 266
normalized size 1 1. 0.82 1.04 0. 5.29 8.02 2.06
time (sec) N/A 0.119 0.149 0.008 0. 1.69 35.277 1.245
Problem 43 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 24 29 38 82 24 26
normalized size 1 1. 0.89 1.07 1.41 3.04 0.89 0.96
time (sec) N/A 0.008 0.015 0.007 1.851 1.448 0.206 1.181
Problem 44 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 24 29 38 82 24 26
normalized size 1 1. 0.89 1.07 1.41 3.04 0.89 0.96
time (sec) N/A 0.017 0.007 0.003 1.529 1.525 0.214 1.234
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 17 17 33 15 30 70 27 41
normalized size 1 1. 1.94 0.88 1.76 4.12 1.59 2.41
time (sec) N/A 0.006 0.007 0.002 1.45 1.418 0.082 1.13
Problem 46 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 6 6 6 7 8 23 5 8
normalized size 1 1. 1. 1.17 1.33 3.83 0.83 1.33
time (sec) N/A 0.003 0.004 0.001 1.603 1.447 0.08 1.153
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 213 213 165 265 0 1160 0 275
normalized size 1 1. 0.77 1.24 0. 5.45 0. 1.29
time (sec) N/A 0.324 0.433 0.043 0. 1.813 0. 1.217
Problem 48 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 150 150 147 277 0 1044 0 186
normalized size 1 1. 0.98 1.85 0. 6.96 0. 1.24
time (sec) N/A 0.165 0.268 0.012 0. 1.745 0. 1.225
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 132 132 89 95 324 290 0 151
normalized size 1 1. 0.67 0.72 2.45 2.2 0. 1.14
time (sec) N/A 0.166 0.079 0.005 1.081 1.604 0. 1.2
Problem 50 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 149 149 78 76 342 254 0 109
normalized size 1 1. 0.52 0.51 2.3 1.7 0. 0.73
time (sec) N/A 0.181 0.082 0.006 1.022 1.632 0. 1.19
Problem 51 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 139 139 84 85 242 271 660 128
normalized size 1 1. 0.6 0.61 1.74 1.95 4.75 0.92
time (sec) N/A 0.151 0.09 0.005 0.988 1.66 142.489 1.218
Problem 52 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 139 139 87 88 266 277 904 127
normalized size 1 1. 0.63 0.63 1.91 1.99 6.5 0.91
time (sec) N/A 0.131 0.095 0.006 1.034 1.672 110.567 1.185
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 119 119 75 73 166 250 796 111
normalized size 1 1. 0.63 0.61 1.39 2.1 6.69 0.93
time (sec) N/A 0.088 0.058 0.005 1.174 1.699 71.287 1.228
Problem 54 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 127 127 92 96 207 289 1880 151
normalized size 1 1. 0.72 0.76 1.63 2.28 14.8 1.19
time (sec) N/A 0.069 0.063 0.003 1.025 1.627 111.682 1.196
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 138 138 120 169 0 1040 0 205
normalized size 1 1. 0.87 1.22 0. 7.54 0. 1.49
time (sec) N/A 0.162 0.156 0.009 0. 1.856 0. 1.221
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 188 188 158 240 0 1172 0 323
normalized size 1 1. 0.84 1.28 0. 6.23 0. 1.72
time (sec) N/A 0.381 0.156 0.009 0. 1.883 0. 1.174
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 219 219 178 288 0 1527 0 439
normalized size 1 1. 0.81 1.32 0. 6.97 0. 2.
time (sec) N/A 0.48 0.377 0.011 0. 2.123 0. 1.209
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 43 0 0 0 97 0
normalized size 1 1. 0.96 0. 0. 0. 2.16 0.
time (sec) N/A 0.017 0.009 0.03 0. 0. 1.515 0.
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 91 91 82 0 0 0 192 0
normalized size 1 1. 0.9 0. 0. 0. 2.11 0.
time (sec) N/A 0.043 0.029 0.031 0. 0. 4.736 0.
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 76 76 56 0 0 0 204 0
normalized size 1 1. 0.74 0. 0. 0. 2.68 0.
time (sec) N/A 0.039 0.054 0.036 0. 0. 5.379 0.
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 121 121 99 0 0 0 298 0
normalized size 1 1. 0.82 0. 0. 0. 2.46 0.
time (sec) N/A 0.122 0.075 0.032 0. 0. 6.414 0.
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 65 65 65 54 72 150 60 77
normalized size 1 1. 1. 0.83 1.11 2.31 0.92 1.18
time (sec) N/A 0.074 0.015 0.002 1.063 1.235 0.065 1.561
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 65 65 65 54 72 150 60 77
normalized size 1 1. 1. 0.83 1.11 2.31 0.92 1.18
time (sec) N/A 0.076 0.016 0.002 1.053 1.23 0.065 1.53
Problem 64 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 65 65 65 54 72 150 60 77
normalized size 1 1. 1. 0.83 1.11 2.31 0.92 1.18
time (sec) N/A 0.061 0.009 0. 1.224 1.222 0.064 1.533
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 60 60 60 51 68 142 56 73
normalized size 1 1. 1. 0.85 1.13 2.37 0.93 1.22
time (sec) N/A 0.041 0.009 0.001 1.039 1.289 0.063 1.152
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 56 56 56 53 65 0 54 72
normalized size 1 1. 1. 0.95 1.16 0. 0.96 1.29
time (sec) N/A 0.04 0.015 0.004 1.03 0. 0.285 1.165
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 54 54 54 50 65 0 49 68
normalized size 1 1. 1. 0.93 1.2 0. 0.91 1.26
time (sec) N/A 0.048 0.033 0.007 1.218 0. 0.302 1.18
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 54 54 51 48 65 0 49 65
normalized size 1 1. 0.94 0.89 1.2 0. 0.91 1.2
time (sec) N/A 0.048 0.026 0.005 1.062 0. 0.416 1.152
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 54 54 55 51 66 0 53 68
normalized size 1 1. 1.02 0.94 1.22 0. 0.98 1.26
time (sec) N/A 0.049 0.017 0.005 1.007 0. 0.805 1.194
Problem 70 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 109 109 98 102 136 263 110 142
normalized size 1 1. 0.9 0.94 1.25 2.41 1.01 1.3
time (sec) N/A 0.124 0.037 0.001 1.129 1.227 0.077 1.125
Problem 71 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 109 109 92 102 136 261 110 142
normalized size 1 1. 0.84 0.94 1.25 2.39 1.01 1.3
time (sec) N/A 0.112 0.048 0.001 0.971 1.253 0.078 1.131
Problem 72 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 92 102 136 258 110 142
normalized size 1 1. 0.88 0.98 1.31 2.48 1.06 1.37
time (sec) N/A 0.074 0.038 0.001 0.99 1.29 0.079 1.165
Problem 73 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 99 99 88 99 132 250 107 138
normalized size 1 1. 0.89 1. 1.33 2.53 1.08 1.39
time (sec) N/A 0.072 0.036 0.002 1.058 1.267 0.075 1.157
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 92 92 88 100 130 0 104 135
normalized size 1 1. 0.96 1.09 1.41 0. 1.13 1.47
time (sec) N/A 0.069 0.043 0.003 0.971 0. 0.366 1.163
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 90 90 88 98 130 0 99 132
normalized size 1 1. 0.98 1.09 1.44 0. 1.1 1.47
time (sec) N/A 0.08 0.05 0.006 0.994 0. 0.379 1.224
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 98 98 87 97 130 0 99 131
normalized size 1 1. 0.89 0.99 1.33 0. 1.01 1.34
time (sec) N/A 0.086 0.038 0.006 0.988 0. 0.511 1.161
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 98 98 83 97 131 0 99 131
normalized size 1 1. 0.85 0.99 1.34 0. 1.01 1.34
time (sec) N/A 0.086 0.047 0.006 0.984 0. 0.975 1.165
Problem 78 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 149 149 149 150 196 382 163 207
normalized size 1 1. 1. 1.01 1.32 2.56 1.09 1.39
time (sec) N/A 0.186 0.027 0.003 1.011 1.371 0.091 1.155
Problem 79 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 149 149 125 150 196 377 165 207
normalized size 1 1. 0.84 1.01 1.32 2.53 1.11 1.39
time (sec) N/A 0.141 0.06 0.002 1.477 1.316 0.086 1.143
Problem 80 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 138 138 124 150 196 371 163 207
normalized size 1 1. 0.9 1.09 1.42 2.69 1.18 1.5
time (sec) N/A 0.095 0.05 0.001 1.001 1.28 0.085 1.229
Problem 81 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 133 133 121 147 192 355 158 201
normalized size 1 1. 0.91 1.11 1.44 2.67 1.19 1.51
time (sec) N/A 0.093 0.047 0.003 1.014 1.357 0.085 1.125
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 129 129 121 148 189 0 158 200
normalized size 1 1. 0.94 1.15 1.47 0. 1.22 1.55
time (sec) N/A 0.09 0.061 0.003 0.977 0. 0.444 1.171
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 124 124 123 145 188 0 150 196
normalized size 1 1. 0.99 1.17 1.52 0. 1.21 1.58
time (sec) N/A 0.109 0.08 0.006 1.007 0. 0.456 1.154
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 135 135 124 144 188 0 150 194
normalized size 1 1. 0.92 1.07 1.39 0. 1.11 1.44
time (sec) N/A 0.112 0.061 0.007 1.029 0. 0.593 1.149
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 139 139 124 146 192 0 153 197
normalized size 1 1. 0.89 1.05 1.38 0. 1.1 1.42
time (sec) N/A 0.114 0.048 0.008 1.001 0. 1.061 1.168
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 151 151 130 176 0 0 308 217
normalized size 1 1. 0.86 1.17 0. 0. 2.04 1.44
time (sec) N/A 0.145 0.073 0.005 0. 0. 1.115 1.199
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 130 130 114 152 0 0 269 185
normalized size 1 1. 0.88 1.17 0. 0. 2.07 1.42
time (sec) N/A 0.124 0.09 0.006 0. 0. 1.077 1.187
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 111 111 95 128 0 0 243 151
normalized size 1 1. 0.86 1.15 0. 0. 2.19 1.36
time (sec) N/A 0.113 0.053 0.004 0. 0. 1.033 1.183
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 92 92 81 106 0 0 211 119
normalized size 1 1. 0.88 1.15 0. 0. 2.29 1.29
time (sec) N/A 0.085 0.064 0.004 0. 0. 0.968 1.188
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 73 73 68 83 0 0 219 89
normalized size 1 1. 0.93 1.14 0. 0. 3. 1.22
time (sec) N/A 0.065 0.04 0.004 0. 0. 0.96 1.196
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 72 72 73 80 0 0 1268 89
normalized size 1 1. 1.01 1.11 0. 0. 17.61 1.24
time (sec) N/A 0.098 0.051 0.006 0. 0. 25.449 1.123
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 76 76 75 83 0 0 1258 92
normalized size 1 1. 0.99 1.09 0. 0. 16.55 1.21
time (sec) N/A 0.098 0.046 0.007 0. 0. 23.343 1.158
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 92 92 84 102 0 0 1686 108
normalized size 1 1. 0.91 1.11 0. 0. 18.33 1.17
time (sec) N/A 0.109 0.08 0.009 0. 0. 24.608 1.164
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 176 176 139 201 0 0 333 215
normalized size 1 1. 0.79 1.14 0. 0. 1.89 1.22
time (sec) N/A 0.268 0.126 0.01 0. 0. 3.681 1.18
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 154 154 128 177 0 0 287 177
normalized size 1 1. 0.83 1.15 0. 0. 1.86 1.15
time (sec) N/A 0.241 0.077 0.008 0. 0. 3.464 1.204
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 134 134 100 154 0 0 284 150
normalized size 1 1. 0.75 1.15 0. 0. 2.12 1.12
time (sec) N/A 0.226 0.075 0.008 0. 0. 3.332 1.194
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 101 101 92 127 0 0 212 109
normalized size 1 1. 0.91 1.26 0. 0. 2.1 1.08
time (sec) N/A 0.118 0.049 0.008 0. 0. 2.656 1.146
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 93 93 83 97 0 0 233 119
normalized size 1 1. 0.89 1.04 0. 0. 2.51 1.28
time (sec) N/A 0.065 0.081 0.006 0. 0. 2.154 1.174
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 95 95 85 125 0 0 797 126
normalized size 1 1. 0.89 1.32 0. 0. 8.39 1.33
time (sec) N/A 0.122 0.071 0.01 0. 0. 8.108 1.205
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 110 110 110 136 0 0 782 139
normalized size 1 1. 1. 1.24 0. 0. 7.11 1.26
time (sec) N/A 0.142 0.07 0.012 0. 0. 8.452 1.186
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 135 135 112 169 0 0 1807 170
normalized size 1 1. 0.83 1.25 0. 0. 13.39 1.26
time (sec) N/A 0.204 0.102 0.015 0. 0. 39.576 1.168
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 185 185 139 235 0 0 357 212
normalized size 1 1. 0.75 1.27 0. 0. 1.93 1.15
time (sec) N/A 0.338 0.116 0.01 0. 0. 23.307 1.197
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 155 155 126 206 0 0 282 165
normalized size 1 1. 0.81 1.33 0. 0. 1.82 1.06
time (sec) N/A 0.232 0.076 0.01 0. 0. 21.829 1.139
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 136 136 122 133 0 0 303 173
normalized size 1 1. 0.9 0.98 0. 0. 2.23 1.27
time (sec) N/A 0.158 0.093 0.009 0. 0. 18.111 1.191
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 119 119 99 110 0 0 177 131
normalized size 1 1. 0.83 0.92 0. 0. 1.49 1.1
time (sec) N/A 0.114 0.112 0.008 0. 0. 13.417 1.196
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 116 116 104 111 0 0 184 143
normalized size 1 1. 0.9 0.96 0. 0. 1.59 1.23
time (sec) N/A 0.068 0.099 0.007 0. 0. 7.954 1.218
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 130 130 117 184 0 0 872 173
normalized size 1 1. 0.9 1.42 0. 0. 6.71 1.33
time (sec) N/A 0.135 0.103 0.013 0. 0. 16.359 1.671
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 144 144 141 195 0 0 860 190
normalized size 1 1. 0.98 1.35 0. 0. 5.97 1.32
time (sec) N/A 0.228 0.096 0.013 0. 0. 20.804 1.703
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 174 174 147 250 0 0 1904 219
normalized size 1 1. 0.84 1.44 0. 0. 10.94 1.26
time (sec) N/A 0.311 0.15 0.017 0. 0. 60.189 1.199
Problem 110 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 19 24 63 15 34
normalized size 1 1. 1. 0.95 1.2 3.15 0.75 1.7
time (sec) N/A 0.023 0.007 0.007 0.987 1.395 0.093 1.152
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 23 23 18 15 30 39 22 23
normalized size 1 1. 0.78 0.65 1.3 1.7 0.96 1.
time (sec) N/A 0.021 0.008 0.005 0.97 1.428 0.343 1.144
Problem 112 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 25 25 25 21 27 61 20 27
normalized size 1 1. 1. 0.84 1.08 2.44 0.8 1.08
time (sec) N/A 0.024 0.01 0.003 1.529 1.41 0.088 1.18
Problem 113 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 30 30 30 25 32 73 22 32
normalized size 1 1. 1. 0.83 1.07 2.43 0.73 1.07
time (sec) N/A 0.025 0.005 0.002 1.522 1.452 0.09 1.136
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 210 210 210 278 0 953 366 338
normalized size 1 1. 1. 1.32 0. 4.54 1.74 1.61
time (sec) N/A 0.161 0.146 0.006 0. 1.519 0.9 1.2
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 172 172 162 230 0 770 325 270
normalized size 1 1. 0.94 1.34 0. 4.48 1.89 1.57
time (sec) N/A 0.123 0.114 0.004 0. 1.507 0.867 1.175
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 136 136 128 182 0 606 180 205
normalized size 1 1. 0.94 1.34 0. 4.46 1.32 1.51
time (sec) N/A 0.105 0.089 0.004 0. 1.562 0.813 1.169
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 100 100 98 135 0 505 158 143
normalized size 1 1. 0.98 1.35 0. 5.05 1.58 1.43
time (sec) N/A 0.062 0.08 0.002 0. 1.504 0.927 1.145
Problem 118 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 84 84 83 114 0 444 150 116
normalized size 1 1. 0.99 1.36 0. 5.29 1.79 1.38
time (sec) N/A 0.094 0.063 0.005 0. 1.507 1.304 1.19
Problem 119 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 82 82 83 115 0 455 151 109
normalized size 1 1. 1.01 1.4 0. 5.55 1.84 1.33
time (sec) N/A 0.087 0.08 0.007 0. 1.565 2.428 1.167
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 104 104 103 142 0 522 167 142
normalized size 1 1. 0.99 1.37 0. 5.02 1.61 1.37
time (sec) N/A 0.102 0.083 0.007 0. 1.501 5.304 1.151
Problem 121 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 137 137 139 190 0 624 301 204
normalized size 1 1. 1.01 1.39 0. 4.55 2.2 1.49
time (sec) N/A 0.13 0.115 0.009 0. 1.51 13.263 1.182
Problem 122 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 175 175 174 238 0 788 354 271
normalized size 1 1. 0.99 1.36 0. 4.5 2.02 1.55
time (sec) N/A 0.146 0.133 0.008 0. 1.504 27.46 1.184
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 211 211 211 286 0 976 398 336
normalized size 1 1. 1. 1.36 0. 4.63 1.89 1.59
time (sec) N/A 0.175 0.161 0.011 0. 1.54 51.001 1.175
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 240 240 227 309 0 1260 430 340
normalized size 1 1. 0.95 1.29 0. 5.25 1.79 1.42
time (sec) N/A 0.294 0.124 0.011 0. 1.587 2.449 1.155
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 202 202 187 258 0 1041 250 271
normalized size 1 1. 0.93 1.28 0. 5.15 1.24 1.34
time (sec) N/A 0.235 0.101 0.01 0. 1.492 2.522 1.153
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 163 163 148 212 0 902 216 205
normalized size 1 1. 0.91 1.3 0. 5.53 1.33 1.26
time (sec) N/A 0.229 0.082 0.009 0. 1.496 2.431 1.164
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 118 118 122 177 0 761 199 170
normalized size 1 1. 1.03 1.5 0. 6.45 1.69 1.44
time (sec) N/A 0.12 0.088 0.009 0. 1.701 1.943 1.164
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 112 112 115 165 0 714 197 165
normalized size 1 1. 1.03 1.47 0. 6.38 1.76 1.47
time (sec) N/A 0.132 0.062 0.013 0. 1.835 4.611 1.166
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 121 121 125 182 0 786 212 166
normalized size 1 1. 1.03 1.5 0. 6.5 1.75 1.37
time (sec) N/A 0.158 0.072 0.011 0. 1.465 12.21 1.254
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 152 152 151 219 0 926 226 204
normalized size 1 1. 0.99 1.44 0. 6.09 1.49 1.34
time (sec) N/A 0.213 0.082 0.014 0. 1.394 30.535 1.173
Problem 131 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 189 189 190 268 0 1057 394 271
normalized size 1 1. 1.01 1.42 0. 5.59 2.08 1.43
time (sec) N/A 0.293 0.102 0.016 0. 1.38 76.736 1.197
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 230 230 230 318 0 1284 449 340
normalized size 1 1. 1. 1.38 0. 5.58 1.95 1.48
time (sec) N/A 0.376 0.114 0.016 0. 1.303 144.033 1.243
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 287 287 272 394 0 1748 491 406
normalized size 1 1. 0.95 1.37 0. 6.09 1.71 1.41
time (sec) N/A 0.492 0.155 0.014 0. 1.253 16.19 1.18
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 247 247 232 343 0 1517 311 338
normalized size 1 1. 0.94 1.39 0. 6.14 1.26 1.37
time (sec) N/A 0.411 0.137 0.013 0. 1.306 16.214 1.214
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 207 207 176 294 0 1362 279 270
normalized size 1 1. 0.85 1.42 0. 6.58 1.35 1.3
time (sec) N/A 0.334 0.159 0.013 0. 1.315 15.871 1.205
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 167 167 156 259 0 1195 258 234
normalized size 1 1. 0.93 1.55 0. 7.16 1.54 1.4
time (sec) N/A 0.262 0.121 0.011 0. 1.5 12.917 1.228
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 147 147 141 234 0 1062 243 201
normalized size 1 1. 0.96 1.59 0. 7.22 1.65 1.37
time (sec) N/A 0.15 0.114 0.01 0. 1.508 8.284 1.167
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 153 153 155 237 0 1076 250 207
normalized size 1 1. 1.01 1.55 0. 7.03 1.63 1.35
time (sec) N/A 0.176 0.124 0.013 0. 1.527 22.808 1.171
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 168 168 169 264 0 1219 270 230
normalized size 1 1. 1.01 1.57 0. 7.26 1.61 1.37
time (sec) N/A 0.242 0.138 0.016 0. 1.514 58.453 1.17
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 196 196 196 300 0 1386 284 267
normalized size 1 1. 1. 1.53 0. 7.07 1.45 1.36
time (sec) N/A 0.35 0.111 0.016 0. 1.546 135.007 1.235
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 234 234 234 351 0 1539 0 338
normalized size 1 1. 1. 1.5 0. 6.58 0. 1.44
time (sec) N/A 0.486 0.136 0.016 0. 1.468 0. 1.213
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 277 277 276 401 0 1778 0 406
normalized size 1 1. 1. 1.45 0. 6.42 0. 1.47
time (sec) N/A 0.603 0.148 0.02 0. 1.317 0. 1.216
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 214 214 158 193 0 433 442 387
normalized size 1 1. 0.74 0.9 0. 2.02 2.07 1.81
time (sec) N/A 0.252 0.166 0.008 0. 1.313 4.459 1.215
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 167 167 122 145 0 316 340 296
normalized size 1 1. 0.73 0.87 0. 1.89 2.04 1.77
time (sec) N/A 0.194 0.121 0.007 0. 1.358 2.752 1.244
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 121 121 89 99 0 221 238 207
normalized size 1 1. 0.74 0.82 0. 1.83 1.97 1.71
time (sec) N/A 0.133 0.082 0.005 0. 1.372 1.63 1.171
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 103 103 86 134 0 483 102 171
normalized size 1 1. 0.83 1.3 0. 4.69 0.99 1.66
time (sec) N/A 0.14 0.124 0.008 0. 1.394 24.939 1.229
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 100 100 131 127 0 482 138 154
normalized size 1 1. 1.31 1.27 0. 4.82 1.38 1.54
time (sec) N/A 0.203 0.382 0.009 0. 1.46 40.125 1.23
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 114 114 141 162 0 501 194 190
normalized size 1 1. 1.24 1.42 0. 4.39 1.7 1.67
time (sec) N/A 0.233 0.345 0.01 0. 1.478 78.677 1.17
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 146 146 162 238 0 605 303 313
normalized size 1 1. 1.11 1.63 0. 4.14 2.08 2.14
time (sec) N/A 0.276 0.962 0.01 0. 1.628 110.921 1.213
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 195 195 140 320 0 803 444 487
normalized size 1 1. 0.72 1.64 0. 4.12 2.28 2.5
time (sec) N/A 0.35 0.328 0.014 0. 2.054 176.308 1.224
Problem 151 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 245 245 184 368 0 983 586 302
normalized size 1 1. 0.75 1.5 0. 4.01 2.39 1.23
time (sec) N/A 0.258 0.224 0.022 0. 2.07 33.212 1.187
Problem 152 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 194 194 149 284 0 779 444 236
normalized size 1 1. 0.77 1.46 0. 4.02 2.29 1.22
time (sec) N/A 0.208 0.158 0.008 0. 1.716 21.593 1.224
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 145 145 118 203 0 581 362 174
normalized size 1 1. 0.81 1.4 0. 4.01 2.5 1.2
time (sec) N/A 0.119 0.109 0.006 0. 1.523 12.11 1.191
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 117 117 103 140 0 489 250 163
normalized size 1 1. 0.88 1.2 0. 4.18 2.14 1.39
time (sec) N/A 0.136 0.11 0.007 0. 1.411 6.778 1.21
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 110 110 93 117 0 479 197 238
normalized size 1 1. 0.85 1.06 0. 4.35 1.79 2.16
time (sec) N/A 0.127 0.105 0.009 0. 1.47 3.979 1.204
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 118 118 95 136 0 509 456 437
normalized size 1 1. 0.81 1.15 0. 4.31 3.86 3.7
time (sec) N/A 0.133 0.107 0.007 0. 1.405 3.2 1.295
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 140 140 103 111 0 232 891 748
normalized size 1 1. 0.74 0.79 0. 1.66 6.36 5.34
time (sec) N/A 0.184 0.078 0.005 0. 1.664 4.744 1.23
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 189 189 134 157 0 327 1642 900
normalized size 1 1. 0.71 0.83 0. 1.73 8.69 4.76
time (sec) N/A 0.254 0.086 0.006 0. 2.269 6.782 1.243
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 381 381 273 517 0 0 0 462
normalized size 1 1. 0.72 1.36 0. 0. 0. 1.21
time (sec) N/A 0.662 0.534 0.301 0. 0. 0. 1.248
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 279 279 229 460 0 0 0 358
normalized size 1 1. 0.82 1.65 0. 0. 0. 1.28
time (sec) N/A 0.455 0.431 0.008 0. 0. 0. 1.204
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-2) F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 210 210 194 405 0 0 0 274
normalized size 1 1. 0.92 1.93 0. 0. 0. 1.3
time (sec) N/A 0.387 0.441 0.012 0. 0. 0. 1.203
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-2) F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 179 192 168 363 0 0 0 216
normalized size 1 1.07 0.94 2.03 0. 0. 0. 1.21
time (sec) N/A 0.314 0.41 0.008 0. 0. 0. 1.343
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B F(-2) F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 134 134 98 109 452 0 0 177
normalized size 1 1. 0.73 0.81 3.37 0. 0. 1.32
time (sec) N/A 0.21 0.101 0.005 1.058 0. 0. 1.202
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 185 179 133 157 0 0 0 285
normalized size 1 0.97 0.72 0.85 0. 0. 0. 1.54
time (sec) N/A 0.246 0.152 0.006 0. 0. 0. 1.216
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 242 242 165 205 0 0 0 471
normalized size 1 1. 0.68 0.85 0. 0. 0. 1.95
time (sec) N/A 0.322 0.129 0.007 0. 0. 0. 1.216
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 281 275 202 253 0 0 0 799
normalized size 1 0.98 0.72 0.9 0. 0. 0. 2.84
time (sec) N/A 0.429 0.146 0.007 0. 0. 0. 1.259
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 334 334 234 301 0 0 0 1266
normalized size 1 1. 0.7 0.9 0. 0. 0. 3.79
time (sec) N/A 0.48 0.146 0.008 0. 0. 0. 1.337
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 392 380 270 349 0 0 0 1569
normalized size 1 0.97 0.69 0.89 0. 0. 0. 4.
time (sec) N/A 0.546 0.163 0.008 0. 0. 0. 1.323
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 214 214 158 193 0 433 442 387
normalized size 1 1. 0.74 0.9 0. 2.02 2.07 1.81
time (sec) N/A 0.222 0.179 0.007 0. 1.423 4.555 1.228
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 167 167 122 145 0 316 340 296
normalized size 1 1. 0.73 0.87 0. 1.89 2.04 1.77
time (sec) N/A 0.175 0.126 0.006 0. 1.291 2.785 1.18
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 121 121 89 99 0 221 238 207
normalized size 1 1. 0.74 0.82 0. 1.83 1.97 1.71
time (sec) N/A 0.15 0.088 0.004 0. 1.366 1.611 1.162
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-2) F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 261 257 221 478 0 0 0 302
normalized size 1 0.98 0.85 1.83 0. 0. 0. 1.16
time (sec) N/A 0.716 0.505 0.01 0. 0. 0. 1.427
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-2) F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 214 250 197 427 0 0 0 275
normalized size 1 1.17 0.92 2. 0. 0. 0. 1.29
time (sec) N/A 0.41 0.446 0.008 0. 0. 0. 1.243
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-2) F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 193 193 138 166 0 0 0 297
normalized size 1 1. 0.72 0.86 0. 0. 0. 1.54
time (sec) N/A 0.341 0.165 0.006 0. 0. 0. 1.24

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 [13] had the largest ratio of [ 0.4 ]

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 6 5 1. 20 0.25
2 A 5 5 1. 20 0.25
3 A 4 4 1. 18 0.222
4 A 4 4 1. 17 0.235
5 A 7 7 1. 20 0.35
6 A 7 7 1. 20 0.35
7 A 7 7 1. 20 0.35
8 A 7 5 1. 20 0.25
9 A 6 5 1. 20 0.25
10 A 5 4 1. 18 0.222
11 A 5 4 1. 17 0.235
12 A 8 7 1. 20 0.35
13 A 8 8 1. 20 0.4
14 A 8 7 1. 20 0.35
15 A 8 5 1. 20 0.25
16 A 7 5 1. 20 0.25
17 A 6 4 1. 18 0.222
18 A 6 4 1. 17 0.235
19 A 9 7 1. 20 0.35
20 A 9 8 1. 20 0.4
21 A 9 8 1. 20 0.4
22 A 5 4 1. 20 0.2
23 A 4 4 1. 20 0.2
24 A 3 3 1. 18 0.167
25 A 3 3 1. 17 0.176
26 A 6 6 1. 20 0.3
27 A 4 4 1. 20 0.2
28 A 5 5 1. 20 0.25
29 A 4 4 1. 20 0.2
30 A 4 4 1. 20 0.2
31 A 3 3 1. 18 0.167
32 A 1 1 1. 17 0.059
33 A 5 5 1. 20 0.25
34 A 5 5 1. 20 0.25
35 A 6 6 1. 20 0.3
36 A 4 4 1. 20 0.2
37 A 2 2 1. 20 0.1
38 A 2 2 1. 18 0.111
39 A 2 2 1. 17 0.118
40 A 6 5 1. 20 0.25
41 A 6 5 1. 20 0.25
42 A 7 6 1. 20 0.3
43 A 2 2 1. 18 0.111
44 A 3 3 1. 19 0.158
45 A 2 2 1. 13 0.154
46 A 2 2 1. 13 0.154
47 A 7 5 1. 25 0.2
48 A 6 5 1. 25 0.2
49 A 5 4 1. 25 0.16
50 A 4 4 1. 25 0.16
51 A 4 4 1. 25 0.16
52 A 4 4 1. 25 0.16
53 A 4 4 1. 23 0.174
54 A 5 4 1. 22 0.182
55 A 8 6 1. 25 0.24
56 A 8 5 1. 25 0.2
57 A 9 6 1. 25 0.24
58 A 2 2 1. 16 0.125
59 A 3 2 1. 20 0.1
60 A 2 2 1. 22 0.091
61 A 5 3 1. 25 0.12
62 A 2 1 1. 26 0.038
63 A 2 1 1. 26 0.038
64 A 2 1 1. 24 0.042
65 A 2 1 1. 23 0.043
66 A 2 1 1. 26 0.038
67 A 2 1 1. 26 0.038
68 A 2 1 1. 26 0.038
69 A 2 1 1. 26 0.038
70 A 2 1 1. 28 0.036
71 A 2 1 1. 28 0.036
72 A 3 2 1. 26 0.077
73 A 3 2 1. 25 0.08
74 A 3 2 1. 28 0.071
75 A 3 2 1. 28 0.071
76 A 2 1 1. 28 0.036
77 A 2 1 1. 28 0.036
78 A 2 1 1. 28 0.036
79 A 2 1 1. 28 0.036
80 A 3 2 1. 26 0.077
81 A 3 2 1. 25 0.08
82 A 3 2 1. 28 0.071
83 A 3 2 1. 28 0.071
84 A 2 1 1. 28 0.036
85 A 2 1 1. 28 0.036
86 A 5 4 1. 28 0.143
87 A 5 4 1. 28 0.143
88 A 5 4 1. 28 0.143
89 A 5 4 1. 26 0.154
90 A 5 4 1. 25 0.16
91 A 5 4 1. 28 0.143
92 A 5 4 1. 28 0.143
93 A 5 4 1. 28 0.143
94 A 6 5 1. 28 0.179
95 A 6 5 1. 28 0.179
96 A 6 5 1. 28 0.179
97 A 6 5 1. 26 0.192
98 A 4 4 1. 25 0.16
99 A 6 5 1. 28 0.179
100 A 6 5 1. 28 0.179
101 A 6 5 1. 28 0.179
102 A 7 5 1. 28 0.179
103 A 6 5 1. 28 0.179
104 A 5 4 1. 28 0.143
105 A 4 4 1. 26 0.154
106 A 3 3 1. 25 0.12
107 A 7 6 1. 28 0.214
108 A 7 5 1. 28 0.179
109 A 7 5 1. 28 0.179
110 A 4 3 1. 17 0.176
111 A 4 3 1. 17 0.176
112 A 4 4 1. 21 0.19
113 A 6 5 1. 15 0.333
114 A 3 2 1. 30 0.067
115 A 3 2 1. 30 0.067
116 A 3 2 1. 30 0.067
117 A 3 2 1. 27 0.074
118 A 3 2 1. 30 0.067
119 A 3 2 1. 30 0.067
120 A 3 2 1. 30 0.067
121 A 3 2 1. 30 0.067
122 A 3 2 1. 30 0.067
123 A 3 2 1. 30 0.067
124 A 5 4 1. 30 0.133
125 A 5 4 1. 30 0.133
126 A 5 4 1. 30 0.133
127 A 4 3 1. 27 0.111
128 A 4 3 1. 30 0.1
129 A 4 3 1. 30 0.1
130 A 4 3 1. 30 0.1
131 A 4 3 1. 30 0.1
132 A 4 3 1. 30 0.1
133 A 6 5 1. 30 0.167
134 A 6 5 1. 30 0.167
135 A 6 5 1. 30 0.167
136 A 6 5 1. 30 0.167
137 A 4 4 1. 27 0.148
138 A 4 4 1. 30 0.133
139 A 5 4 1. 30 0.133
140 A 5 3 1. 30 0.1
141 A 5 3 1. 30 0.1
142 A 5 3 1. 30 0.1
143 A 3 2 1. 32 0.062
144 A 3 2 1. 32 0.062
145 A 3 2 1. 30 0.067
146 A 5 4 1. 32 0.125
147 A 6 5 1. 32 0.156
148 A 6 6 1. 32 0.188
149 A 6 6 1. 32 0.188
150 A 7 7 1. 32 0.219
151 A 7 6 1. 32 0.188
152 A 6 6 1. 32 0.188
153 A 5 5 1. 29 0.172
154 A 6 6 1. 32 0.188
155 A 6 6 1. 32 0.188
156 A 6 6 1. 32 0.188
157 A 5 3 1. 32 0.094
158 A 6 4 1. 32 0.125
159 A 11 9 1. 32 0.281
160 A 10 9 1. 32 0.281
161 A 9 9 1. 32 0.281
162 A 8 8 1.07 32 0.25
163 A 5 4 1. 29 0.138
164 A 6 5 0.97 32 0.156
165 A 7 5 1. 32 0.156
166 A 8 4 0.98 32 0.125
167 A 9 5 1. 32 0.156
168 A 10 5 0.97 32 0.156
169 A 4 3 1. 33 0.091
170 A 4 3 1. 33 0.091
171 A 4 3 1. 31 0.097
172 A 10 9 0.98 37 0.243
173 A 6 5 1.17 34 0.147
174 A 6 4 1. 37 0.108

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