[next] [prev] [prev-tail] [tail] [up]

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, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175 }

B grade: { }

C grade: { 160 }

F grade: { }

2.1.2 Mathematica

A grade: { 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 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, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 71, 72, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 90, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 104, 105, 106, 107, 108, 109, 111, 114, 116, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 135, 137, 138, 139, 141, 143, 145, 147, 149, 152, 153, 156, 157, 158, 160, 163, 164, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175 }

B grade: { 1, 24, 55, 67, 68, 69, 70, 73, 89, 91, 103, 110, 112, 159, 161, 162, 165 }

C grade: { 113, 115, 117, 132, 134, 136, 140, 142, 144, 146, 148, 150, 151, 154, 155 }

F grade: { }

2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 42, 43, 44, 45, 49, 50, 66, 67, 68, 69, 70, 71, 72, 73, 74, 79, 80, 81, 82, 83, 85, 87, 96, 97, 98, 100, 102, 104, 106, 107, 109, 114, 116, 117, 118, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 138, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150, 151, 152, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175 }

B grade: { 17, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 46, 47, 48, 62, 63, 64, 65, 75, 76, 77, 78, 84, 86, 88, 89, 90, 91, 92, 93, 94, 95, 99, 101, 103, 105, 108, 110, 111, 112, 113, 115, 119, 120, 121, 122, 123, 124 }

C grade: { 160 }

F grade: { 13, 14, 15, 16, 18, 19, 20, 21, 36, 37, 38, 39, 40, 41, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 137, 139, 149, 153, 154, 155, 156, 157, 158, 159, 161, 162, 163, 164 }

2.1.4 Maxima

A grade: { 1, 2, 29, 30, 31, 32, 33, 34, 35, 45, 46, 47, 48, 49, 50, 62, 63, 64, 65, 66, 67, 71, 72, 73, 84, 87, 97, 105, 106, 107, 115, 117, 118, 126, 127, 128, 129, 130, 131, 133, 145, 162, 165, 166

B grade: { 3, 4, 5, 6, 42, 43, 44, 68, 69, 70, 85, 86, 88, 89, 90, 91, 92, 94, 96, 99, 101, 102, 103, 104, 108, 109, 110, 111, 112, 113, 120, 122, 124, 125, 141, 153, 160, 161, 167, 168, 169 }

C grade: { 22, 23, 24, 25, 26, 27, 28 }

F grade: { 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 36, 37, 38, 39, 40, 41, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 93, 95, 98, 100, 114, 116, 119, 121, 123, 132, 134, 135, 136, 137, 138, 139, 140, 142, 143, 144, 146, 147, 148, 149, 150, 151, 152, 154, 155, 156, 157, 158, 159, 163, 164, 170, 171, 172, 173, 174, 175 }

2.1.5 FriCAS

A grade: { 49, 50, 62, 63, 66, 84, 97, 107, 108, 117, 118, 128, 129, 130, 131, 133, 135, 137, 139, 141, 143, 147, 149, 151, 153, 155, 162 }

B grade: { 1, 2, 3, 4, 5, 6, 29, 30, 31, 32, 33, 34, 35, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 55, 56, 58, 59, 60, 61, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 101, 102, 103, 104, 105, 106, 109, 110, 111, 112, 113, 114, 115, 116, 119, 120, 121, 122, 123, 124, 125, 126, 127, 145, 160, 161, 163, 164, 165, 166, 167, 168, 169 }

C grade: { 22, 23, 24, 25, 26, 27, 28 }

F grade: { 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 36, 37, 38, 39, 40, 41, 54, 57, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 157, 158, 159, 170, 171, 172, 173, 174, 175 }

2.1.6 Sympy

A grade: { }

B grade: { }

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, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175 }

2.1.7 Giac

A grade: { 2, 4, 6, 29, 30, 31, 33, 34, 35, 42, 43, 44, 45, 46, 47, 48, 49, 50, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 89, 93, 94, 95, 96, 97, 98, 100, 102, 103, 105, 107, 108, 114, 116, 117, 118, 119, 123, 125, 126, 127, 128, 129, 130, 131, 161, 162, 166, 168 }

B grade: { 1, 3, 5, 32, 68, 73, 85, 86, 87, 88, 90, 91, 92, 99, 101, 104, 106, 109, 110, 111, 112, 113, 115, 120, 121, 122, 124, 165, 167, 169 }

C grade: { 22, 23, 24, 25, 26, 27, 28 }

F grade: { 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 36, 37, 38, 39, 40, 41, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 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, 170, 171, 172, 173, 174, 175 }

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 B A A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 12 12 38 15 19 116 0 39
normalized size 1 1. 3.17 1.25 1.58 9.67 0. 3.25
time (sec) N/A 0.006 0.018 0.003 1.005 1.553 0. 1.147
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 11 11 11 12 24 111 0 24
normalized size 1 1. 1. 1.09 2.18 10.09 0. 2.18
time (sec) N/A 0.01 0.01 0.005 0.99 1.514 0. 1.139
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 34 34 57 27 113 1088 0 122
normalized size 1 1. 1.68 0.79 3.32 32. 0. 3.59
time (sec) N/A 0.022 0.014 0.01 1.008 1.638 0. 1.147
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 26 26 35 23 122 448 0 42
normalized size 1 1. 1.35 0.88 4.69 17.23 0. 1.62
time (sec) N/A 0.012 0.013 0.01 1.025 1.574 0. 1.126
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 95 41 180 3087 0 154
normalized size 1 1. 1.73 0.75 3.27 56.13 0. 2.8
time (sec) N/A 0.043 0.016 0.011 1.03 1.722 0. 1.151
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 42 42 56 33 277 954 0 57
normalized size 1 1. 1.33 0.79 6.6 22.71 0. 1.36
time (sec) N/A 0.015 0.016 0.012 1.011 1.496 0. 1.171
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 80 80 61 101 0 0 0 0
normalized size 1 1. 0.76 1.26 0. 0. 0. 0.
time (sec) N/A 0.037 0.119 0.199 0. 0. 0. 0.
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 76 76 57 154 0 0 0 0
normalized size 1 1. 0.75 2.03 0. 0. 0. 0.
time (sec) N/A 0.03 0.205 0.151 0. 0. 0. 0.
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 54 54 48 87 0 0 0 0
normalized size 1 1. 0.89 1.61 0. 0. 0. 0.
time (sec) N/A 0.02 0.187 0.204 0. 0. 0. 0.
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 54 54 50 108 0 0 0 0
normalized size 1 1. 0.93 2. 0. 0. 0. 0.
time (sec) N/A 0.02 0.034 0.152 0. 0. 0. 0.
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 80 80 63 100 0 0 0 0
normalized size 1 1. 0.79 1.25 0. 0. 0. 0.
time (sec) N/A 0.032 0.065 0.174 0. 0. 0. 0.
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 80 80 67 164 0 0 0 0
normalized size 1 1. 0.84 2.05 0. 0. 0. 0.
time (sec) N/A 0.032 0.125 0.237 0. 0. 0. 0.
Problem 13 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 116 116 79 0 0 0 0 0
normalized size 1 1. 0.68 0. 0. 0. 0. 0.
time (sec) N/A 0.061 0.157 0.092 0. 0. 0. 0.
Problem 14 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 88 88 66 0 0 0 0 0
normalized size 1 1. 0.75 0. 0. 0. 0. 0.
time (sec) N/A 0.039 0.101 0.072 0. 0. 0. 0.
Problem 15 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 84 84 60 0 0 0 0 0
normalized size 1 1. 0.71 0. 0. 0. 0. 0.
time (sec) N/A 0.038 0.057 0.072 0. 0. 0. 0.
Problem 16 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 56 56 54 0 0 0 0 0
normalized size 1 1. 0.96 0. 0. 0. 0. 0.
time (sec) N/A 0.022 0.033 0.129 0. 0. 0. 0.
Problem 17 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 56 56 52 227 0 0 0 0
normalized size 1 1. 0.93 4.05 0. 0. 0. 0.
time (sec) N/A 0.023 0.045 0.138 0. 0. 0. 0.
Problem 18 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 90 90 73 0 0 0 0 0
normalized size 1 1. 0.81 0. 0. 0. 0. 0.
time (sec) N/A 0.039 0.088 0.071 0. 0. 0. 0.
Problem 19 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 90 90 68 0 0 0 0 0
normalized size 1 1. 0.76 0. 0. 0. 0. 0.
time (sec) N/A 0.038 0.13 0.069 0. 0. 0. 0.
Problem 20 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 118 118 80 0 0 0 0 0
normalized size 1 1. 0.68 0. 0. 0. 0. 0.
time (sec) N/A 0.056 0.157 0.073 0. 0. 0. 0.
Problem 21 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 74 74 67 0 0 0 0 0
normalized size 1 1. 0.91 0. 0. 0. 0. 0.
time (sec) N/A 0.035 0.097 0.214 0. 0. 0. 0.
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B C C F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 40 40 41 114 100 365 0 97
normalized size 1 1. 1.02 2.85 2.5 9.12 0. 2.42
time (sec) N/A 0.017 0.119 0.053 1.697 1.605 0. 1.187
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B C C F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 24 24 41 99 66 197 0 77
normalized size 1 1. 1.71 4.12 2.75 8.21 0. 3.21
time (sec) N/A 0.012 0.059 0.043 1.691 1.526 0. 1.138
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B C C F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 3 3 20 67 26 46 0 36
normalized size 1 1. 6.67 22.33 8.67 15.33 0. 12.
time (sec) N/A 0.008 0.005 0.052 1.747 1.508 0. 1.154
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B C C F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 13 13 13 58 15 39 0 34
normalized size 1 1. 1. 4.46 1.15 3. 0. 2.62
time (sec) N/A 0.01 0.005 0.049 1.613 1.502 0. 1.153
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B C C F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 33 33 27 118 31 80 0 68
normalized size 1 1. 0.82 3.58 0.94 2.42 0. 2.06
time (sec) N/A 0.015 0.014 0.039 1.641 1.557 0. 1.153
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B C C F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 33 178 47 135 0 86
normalized size 1 1. 0.67 3.63 0.96 2.76 0. 1.76
time (sec) N/A 0.02 0.025 0.04 1.579 1.405 0. 1.179
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B C C F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 65 65 39 238 63 184 0 103
normalized size 1 1. 0.6 3.66 0.97 2.83 0. 1.58
time (sec) N/A 0.024 0.034 0.044 1.7 1.706 0. 1.195
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 65 65 41 123 124 3120 0 101
normalized size 1 1. 0.63 1.89 1.91 48. 0. 1.55
time (sec) N/A 0.034 0.098 0.067 1.558 1.715 0. 1.14
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 30 103 81 1007 0 78
normalized size 1 1. 0.65 2.24 1.76 21.89 0. 1.7
time (sec) N/A 0.025 0.064 0.053 1.638 1.627 0. 1.135
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 26 26 20 67 32 296 0 39
normalized size 1 1. 0.77 2.58 1.23 11.38 0. 1.5
time (sec) N/A 0.018 0.005 0.072 1.582 1.901 0. 1.171
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 13 13 13 58 23 247 0 32
normalized size 1 1. 1. 4.46 1.77 19. 0. 2.46
time (sec) N/A 0.014 0.006 0.065 1.732 1.886 0. 1.145
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 36 36 27 130 47 856 0 73
normalized size 1 1. 0.75 3.61 1.31 23.78 0. 2.03
time (sec) N/A 0.022 0.023 0.049 1.7 1.842 0. 1.178
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 36 196 72 1885 0 90
normalized size 1 1. 0.65 3.56 1.31 34.27 0. 1.64
time (sec) N/A 0.03 0.027 0.05 1.652 1.91 0. 1.152
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 42 262 96 3340 0 108
normalized size 1 1. 0.57 3.54 1.3 45.14 0. 1.46
time (sec) N/A 0.04 0.052 0.052 1.715 2.003 0. 1.193
Problem 36 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 135 135 68 0 0 0 0 0
normalized size 1 1. 0.5 0. 0. 0. 0. 0.
time (sec) N/A 0.07 0.168 0.056 0. 0. 0. 0.
Problem 37 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 81 81 56 0 0 0 0 0
normalized size 1 1. 0.69 0. 0. 0. 0. 0.
time (sec) N/A 0.045 0.114 0.047 0. 0. 0. 0.
Problem 38 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 56 60 42 0 0 0 0 0
normalized size 1 1.07 0.75 0. 0. 0. 0. 0.
time (sec) N/A 0.034 0.028 0.066 0. 0. 0. 0.
Problem 39 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 62 62 43 0 0 0 0 0
normalized size 1 1. 0.69 0. 0. 0. 0. 0.
time (sec) N/A 0.034 0.073 0.066 0. 0. 0. 0.
Problem 40 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 89 89 57 0 0 0 0 0
normalized size 1 1. 0.64 0. 0. 0. 0. 0.
time (sec) N/A 0.048 0.075 0.048 0. 0. 0. 0.
Problem 41 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 135 135 71 0 0 0 0 0
normalized size 1 1. 0.53 0. 0. 0. 0. 0.
time (sec) N/A 0.071 0.12 0.048 0. 0. 0. 0.
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 164 164 59 72 837 9415 0 69
normalized size 1 1. 0.36 0.44 5.1 57.41 0. 0.42
time (sec) N/A 0.042 0.049 0.076 1.661 2.336 0. 1.153
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 118 118 47 60 435 4632 0 53
normalized size 1 1. 0.4 0.51 3.69 39.25 0. 0.45
time (sec) N/A 0.032 0.032 0.059 1.782 1.912 0. 1.168
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 62 62 33 46 162 1623 0 36
normalized size 1 1. 0.53 0.74 2.61 26.18 0. 0.58
time (sec) N/A 0.023 0.018 0.053 1.703 1.657 0. 1.163
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 16 29 18 230 0 18
normalized size 1 1. 1. 1.81 1.12 14.38 0. 1.12
time (sec) N/A 0.017 0.005 0.068 1.727 1.385 0. 1.167
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 36 36 24 89 30 771 0 35
normalized size 1 1. 0.67 2.47 0.83 21.42 0. 0.97
time (sec) N/A 0.016 0.024 0.069 1.582 1.64 0. 1.202
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 86 86 38 230 62 3687 0 68
normalized size 1 1. 0.44 2.67 0.72 42.87 0. 0.79
time (sec) N/A 0.033 0.038 0.053 1.579 1.779 0. 1.249
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 132 132 55 362 97 9443 0 103
normalized size 1 1. 0.42 2.74 0.73 71.54 0. 0.78
time (sec) N/A 0.051 0.111 0.056 1.679 1.954 0. 1.176
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 32 32 54 63 47 80 0 42
normalized size 1 1. 1.69 1.97 1.47 2.5 0. 1.31
time (sec) N/A 0.015 0.113 0.038 1.192 1.509 0. 1.152
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 32 32 54 63 47 80 0 42
normalized size 1 1. 1.69 1.97 1.47 2.5 0. 1.31
time (sec) N/A 0.015 0.103 0.043 1.139 1.595 0. 1.171
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 107 107 136 0 0 1403 0 0
normalized size 1 1. 1.27 0. 0. 13.11 0. 0.
time (sec) N/A 0.127 1.402 0.258 0. 2.419 0. 0.
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 72 72 100 0 0 1089 0 0
normalized size 1 1. 1.39 0. 0. 15.12 0. 0.
time (sec) N/A 0.042 1.172 0.206 0. 2.405 0. 0.
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 40 40 80 0 0 814 0 0
normalized size 1 1. 2. 0. 0. 20.35 0. 0.
time (sec) N/A 0.02 0.89 0.52 0. 2.396 0. 0.
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 91 91 118 0 0 0 0 0
normalized size 1 1. 1.3 0. 0. 0. 0. 0.
time (sec) N/A 0.087 1.081 0.324 0. 0. 0. 0.
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 123 123 327 0 0 2372 0 0
normalized size 1 1. 2.66 0. 0. 19.28 0. 0.
time (sec) N/A 0.146 2.367 0.176 0. 3.065 0. 0.
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 40 40 80 0 0 815 0 0
normalized size 1 1. 2. 0. 0. 20.38 0. 0.
time (sec) N/A 0.023 0.922 0.578 0. 2.39 0. 0.
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 91 91 117 0 0 0 0 0
normalized size 1 1. 1.29 0. 0. 0. 0. 0.
time (sec) N/A 0.084 1.071 0.446 0. 0. 0. 0.
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 46 0 0 581 0 0
normalized size 1 1. 2. 0. 0. 25.26 0. 0.
time (sec) N/A 0.017 0.686 0.261 0. 2.12 0. 0.
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 46 0 0 582 0 0
normalized size 1 1. 2. 0. 0. 25.3 0. 0.
time (sec) N/A 0.018 0.675 0.286 0. 2.112 0. 0.
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 46 0 0 590 0 0
normalized size 1 1. 2. 0. 0. 25.65 0. 0.
time (sec) N/A 0.016 0.657 0.188 0. 2.16 0. 0.
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 46 0 0 589 0 0
normalized size 1 1. 2. 0. 0. 25.61 0. 0.
time (sec) N/A 0.017 0.643 0.192 0. 2.157 0. 0.
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 58 58 63 182 96 244 0 89
normalized size 1 1. 1.09 3.14 1.66 4.21 0. 1.53
time (sec) N/A 0.071 0.14 0.048 1.145 1.658 0. 1.18
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 56 137 80 194 0 68
normalized size 1 1. 1.22 2.98 1.74 4.22 0. 1.48
time (sec) N/A 0.071 0.128 0.046 1.054 1.748 0. 1.196
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 36 36 46 96 63 151 0 54
normalized size 1 1. 1.28 2.67 1.75 4.19 0. 1.5
time (sec) N/A 0.06 0.124 0.042 1.003 1.592 0. 1.173
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 20 20 35 51 42 108 0 35
normalized size 1 1. 1.75 2.55 2.1 5.4 0. 1.75
time (sec) N/A 0.047 0.049 0.039 0.981 1.658 0. 1.216
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 14 14 27 12 16 20 0 11
normalized size 1 1. 1.93 0.86 1.14 1.43 0. 0.79
time (sec) N/A 0.021 0.019 0.02 1.029 1.357 0. 1.151
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 17 17 37 19 39 89 0 30
normalized size 1 1. 2.18 1.12 2.29 5.24 0. 1.76
time (sec) N/A 0.054 0.033 0.017 1.021 1.589 0. 1.18
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 26 26 70 35 74 216 0 62
normalized size 1 1. 2.69 1.35 2.85 8.31 0. 2.38
time (sec) N/A 0.084 0.109 0.018 1.025 1.64 0. 1.21
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 37 37 81 53 109 381 0 68
normalized size 1 1. 2.19 1.43 2.95 10.3 0. 1.84
time (sec) N/A 0.064 0.307 0.025 1.035 1.61 0. 1.164
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 109 109 508 92 316 3453 0 236
normalized size 1 1. 4.66 0.84 2.9 31.68 0. 2.17
time (sec) N/A 0.128 6.23 0.039 1.026 1.733 0. 1.136
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 75 75 118 66 184 1844 0 174
normalized size 1 1. 1.57 0.88 2.45 24.59 0. 2.32
time (sec) N/A 0.051 0.88 0.028 0.995 1.661 0. 1.185
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 34 34 61 37 59 603 0 90
normalized size 1 1. 1.79 1.09 1.74 17.74 0. 2.65
time (sec) N/A 0.031 0.219 0.009 1.042 1.657 0. 1.175
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 17 17 43 20 26 131 0 49
normalized size 1 1. 2.53 1.18 1.53 7.71 0. 2.88
time (sec) N/A 0.01 0.014 0.003 0.982 1.539 0. 1.16
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 54 54 64 87 0 473 0 115
normalized size 1 1. 1.19 1.61 0. 8.76 0. 2.13
time (sec) N/A 0.059 0.104 0.015 0. 1.607 0. 1.177
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 101 101 142 238 0 1503 0 223
normalized size 1 1. 1.41 2.36 0. 14.88 0. 2.21
time (sec) N/A 0.158 0.381 0.057 0. 1.929 0. 1.221
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 163 163 213 822 0 4658 0 402
normalized size 1 1. 1.31 5.04 0. 28.58 0. 2.47
time (sec) N/A 0.316 0.929 0.076 0. 2.217 0. 1.305
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 107 107 104 262 0 1947 0 209
normalized size 1 1. 0.97 2.45 0. 18.2 0. 1.95
time (sec) N/A 0.458 0.412 0.039 0. 2.056 0. 1.202
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 80 80 82 174 0 1142 0 155
normalized size 1 1. 1.02 2.17 0. 14.28 0. 1.94
time (sec) N/A 0.288 0.136 0.034 0. 1.966 0. 1.155
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 57 57 61 92 0 640 0 116
normalized size 1 1. 1.07 1.61 0. 11.23 0. 2.04
time (sec) N/A 0.107 0.105 0.033 0. 1.933 0. 1.177
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 37 37 45 35 0 321 0 76
normalized size 1 1. 1.22 0.95 0. 8.68 0. 2.05
time (sec) N/A 0.066 0.024 0.015 0. 1.798 0. 1.163
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 50 50 58 49 0 456 0 111
normalized size 1 1. 1.16 0.98 0. 9.12 0. 2.22
time (sec) N/A 0.115 0.049 0.014 0. 2.046 0. 1.184
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 59 59 71 73 0 926 0 132
normalized size 1 1. 1.2 1.24 0. 15.69 0. 2.24
time (sec) N/A 0.16 0.278 0.016 0. 2.2 0. 1.209
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 83 83 124 108 0 2288 0 190
normalized size 1 1. 1.49 1.3 0. 27.57 0. 2.29
time (sec) N/A 0.292 0.476 0.023 0. 2.81 0. 1.178
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 38 38 32 170 57 134 0 51
normalized size 1 1. 0.84 4.47 1.5 3.53 0. 1.34
time (sec) N/A 0.128 0.033 0.039 1.04 1.858 0. 1.181
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 19 19 19 15 53 108 0 47
normalized size 1 1. 1. 0.79 2.79 5.68 0. 2.47
time (sec) N/A 0.106 0.01 0.022 1.037 1.858 0. 1.141
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 20 20 20 84 41 89 0 35
normalized size 1 1. 1. 4.2 2.05 4.45 0. 1.75
time (sec) N/A 0.092 0.029 0.033 1.044 1.893 0. 1.241
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 16 20 28 81 0 34
normalized size 1 1. 1. 1.25 1.75 5.06 0. 2.12
time (sec) N/A 0.058 0.009 0.023 1.025 1.745 0. 1.131
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 28 28 20 43 55 155 0 72
normalized size 1 1. 0.71 1.54 1.96 5.54 0. 2.57
time (sec) N/A 0.08 0.03 0.033 1.044 1.634 0. 1.143
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 19 19 64 49 109 93 0 36
normalized size 1 1. 3.37 2.58 5.74 4.89 0. 1.89
time (sec) N/A 0.111 0.053 0.036 1.027 1.491 0. 1.2
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 40 40 32 89 124 431 0 127
normalized size 1 1. 0.8 2.22 3.1 10.78 0. 3.18
time (sec) N/A 0.13 0.059 0.043 1.055 1.696 0. 1.162
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 96 93 347 212 0 74
normalized size 1 1. 3.31 3.21 11.97 7.31 0. 2.55
time (sec) N/A 0.121 0.104 0.045 0.992 1.446 0. 1.166
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 102 102 97 600 327 3536 0 262
normalized size 1 1. 0.95 5.88 3.21 34.67 0. 2.57
time (sec) N/A 0.198 0.277 0.041 1.01 1.752 0. 1.159
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 125 125 180 486 0 2414 0 298
normalized size 1 1. 1.44 3.89 0. 19.31 0. 2.38
time (sec) N/A 0.378 1.146 0.04 0. 1.728 0. 1.173
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 57 57 56 274 171 1251 0 131
normalized size 1 1. 0.98 4.81 3. 21.95 0. 2.3
time (sec) N/A 0.16 0.108 0.035 1.007 1.614 0. 1.158
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 77 77 80 172 0 859 0 163
normalized size 1 1. 1.04 2.23 0. 11.16 0. 2.12
time (sec) N/A 0.206 0.228 0.03 0. 1.573 0. 1.168
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 20 20 19 31 65 246 0 53
normalized size 1 1. 0.95 1.55 3.25 12.3 0. 2.65
time (sec) N/A 0.08 0.012 0.022 1.016 1.582 0. 1.163
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 64 64 36 84 89 177 0 120
normalized size 1 1. 0.56 1.31 1.39 2.77 0. 1.88
time (sec) N/A 0.111 0.057 0.026 1.479 1.735 0. 1.149
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 67 81 0 693 0 115
normalized size 1 1. 1.12 1.35 0. 11.55 0. 1.92
time (sec) N/A 0.142 0.177 0.029 0. 1.628 0. 1.151
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 95 95 78 275 217 1748 0 294
normalized size 1 1. 0.82 2.89 2.28 18.4 0. 3.09
time (sec) N/A 0.22 0.149 0.036 1.512 1.739 0. 1.175
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 104 104 114 170 0 2822 0 235
normalized size 1 1. 1.1 1.63 0. 27.13 0. 2.26
time (sec) N/A 0.27 0.611 0.04 0. 1.809 0. 1.22
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 149 149 138 1168 470 6677 0 505
normalized size 1 1. 0.93 7.84 3.15 44.81 0. 3.39
time (sec) N/A 0.341 0.274 0.046 1.583 2.281 0. 1.178
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 109 109 75 155 194 991 0 162
normalized size 1 1. 0.69 1.42 1.78 9.09 0. 1.49
time (sec) N/A 0.086 0.187 0.062 1.022 1.737 0. 1.163
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 52 52 126 99 130 394 0 84
normalized size 1 1. 2.42 1.9 2.5 7.58 0. 1.62
time (sec) N/A 0.093 0.125 0.056 1.027 1.674 0. 1.212
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 77 77 61 109 130 568 0 132
normalized size 1 1. 0.79 1.42 1.69 7.38 0. 1.71
time (sec) N/A 0.067 0.115 0.055 1.048 1.582 0. 1.138
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 36 36 71 67 57 149 0 51
normalized size 1 1. 1.97 1.86 1.58 4.14 0. 1.42
time (sec) N/A 0.073 0.084 0.047 1.009 1.652 0. 1.175
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 39 65 61 207 0 74
normalized size 1 1. 0.87 1.44 1.36 4.6 0. 1.64
time (sec) N/A 0.048 0.037 0.045 1.038 1.631 0. 1.151
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 13 13 13 17 20 32 0 18
normalized size 1 1. 1. 1.31 1.54 2.46 0. 1.38
time (sec) N/A 0.023 0.007 0.023 1.01 1.683 0. 1.148
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 11 11 13 27 27 49 0 23
normalized size 1 1. 1.18 2.45 2.45 4.45 0. 2.09
time (sec) N/A 0.038 0.033 0.029 1.003 1.619 0. 1.191
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 12 12 12 12 49 107 0 51
normalized size 1 1. 1. 1. 4.08 8.92 0. 4.25
time (sec) N/A 0.039 0.01 0.017 1.035 1.779 0. 1.175
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 65 61 74 254 0 65
normalized size 1 1. 2.41 2.26 2.74 9.41 0. 2.41
time (sec) N/A 0.056 0.036 0.044 1.03 1.622 0. 1.165
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 30 30 30 78 101 292 0 92
normalized size 1 1. 1. 2.6 3.37 9.73 0. 3.07
time (sec) N/A 0.046 0.015 0.068 1.022 1.722 0. 1.155
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 43 43 129 95 130 478 0 104
normalized size 1 1. 3. 2.21 3.02 11.12 0. 2.42
time (sec) N/A 0.075 0.041 0.092 1.034 1.798 0. 1.156
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 194 194 253 1323 517 9482 0 583
normalized size 1 1. 1.3 6.82 2.66 48.88 0. 3.01
time (sec) N/A 0.255 0.493 0.063 1.608 2.645 0. 1.211
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 183 183 141 207 0 4128 0 290
normalized size 1 1. 0.77 1.13 0. 22.56 0. 1.58
time (sec) N/A 0.384 0.696 0.053 0. 1.855 0. 1.203
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 113 113 191 324 232 2379 0 316
normalized size 1 1. 1.69 2.87 2.05 21.05 0. 2.8
time (sec) N/A 0.163 0.19 0.049 1.587 1.96 0. 1.229
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 100 100 82 95 0 899 0 138
normalized size 1 1. 0.82 0.95 0. 8.99 0. 1.38
time (sec) N/A 0.221 0.318 0.04 0. 1.658 0. 1.216
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 61 61 63 108 100 211 0 120
normalized size 1 1. 1.03 1.77 1.64 3.46 0. 1.97
time (sec) N/A 0.099 0.059 0.036 1.519 1.55 0. 1.228
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 19 19 11 21 38 72 0 30
normalized size 1 1. 0.58 1.11 2. 3.79 0. 1.58
time (sec) N/A 0.032 0.008 0.021 1.011 1.549 0. 1.107
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 57 57 65 110 0 424 0 120
normalized size 1 1. 1.14 1.93 0. 7.44 0. 2.11
time (sec) N/A 0.178 0.081 0.027 0. 1.814 0. 1.162
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 32 32 37 106 111 543 0 108
normalized size 1 1. 1.16 3.31 3.47 16.97 0. 3.38
time (sec) N/A 0.072 0.05 0.03 1.007 1.665 0. 1.193
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 88 88 151 207 0 2174 0 217
normalized size 1 1. 1.72 2.35 0. 24.7 0. 2.47
time (sec) N/A 0.332 0.574 0.038 0. 2.26 0. 1.205
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 70 70 83 219 257 3216 0 230
normalized size 1 1. 1.19 3.13 3.67 45.94 0. 3.29
time (sec) N/A 0.094 0.124 0.04 1.049 1.833 0. 1.151
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 183 183 269 360 0 7830 0 412
normalized size 1 1. 1.47 1.97 0. 42.79 0. 2.25
time (sec) N/A 0.337 1.562 0.043 0. 3.258 0. 1.163
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 119 119 130 388 491 9682 0 398
normalized size 1 1. 1.09 3.26 4.13 81.36 0. 3.34
time (sec) N/A 0.141 0.253 0.046 1.083 2.273 0. 1.16
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 199 199 84 91 521 1512 0 122
normalized size 1 1. 0.42 0.46 2.62 7.6 0. 0.61
time (sec) N/A 0.303 0.077 0.203 1.564 1.615 0. 1.162
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 147 147 72 80 282 797 0 104
normalized size 1 1. 0.49 0.54 1.92 5.42 0. 0.71
time (sec) N/A 0.171 0.064 0.164 1.555 1.564 0. 1.154
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 58 58 56 69 113 300 0 86
normalized size 1 1. 0.97 1.19 1.95 5.17 0. 1.48
time (sec) N/A 0.118 0.043 0.16 1.571 1.58 0. 1.17
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 44 68 53 97 0 65
normalized size 1 1. 0.96 1.48 1.15 2.11 0. 1.41
time (sec) N/A 0.091 0.036 0.183 1.547 1.596 0. 1.154
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 48 106 49 165 0 96
normalized size 1 1. 0.65 1.43 0.66 2.23 0. 1.3
time (sec) N/A 0.115 0.05 0.175 1.613 1.493 0. 1.136
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 162 162 76 216 84 319 0 275
normalized size 1 1. 0.47 1.33 0.52 1.97 0. 1.7
time (sec) N/A 0.153 0.063 0.171 1.555 1.549 0. 1.193
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 250 250 106 326 122 559 0 375
normalized size 1 1. 0.42 1.3 0.49 2.24 0. 1.5
time (sec) N/A 0.2 0.103 0.174 1.569 1.585 0. 1.213
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 81 81 80 125 0 0 0 0
normalized size 1 1. 0.99 1.54 0. 0. 0. 0.
time (sec) N/A 0.068 0.169 0.058 0. 0. 0. 0.
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 30 30 44 39 62 103 0 0
normalized size 1 1. 1.47 1.3 2.07 3.43 0. 0.
time (sec) N/A 0.045 0.048 0.033 1.779 1.611 0. 0.
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 119 119 60 127 0 0 0 0
normalized size 1 1. 0.5 1.07 0. 0. 0. 0.
time (sec) N/A 0.086 0.111 0.039 0. 0. 0. 0.
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 69 69 74 97 0 193 0 0
normalized size 1 1. 1.07 1.41 0. 2.8 0. 0.
time (sec) N/A 0.058 0.136 0.05 0. 1.593 0. 0.
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 57 109 0 0 0 0
normalized size 1 1. 0.95 1.82 0. 0. 0. 0.
time (sec) N/A 0.041 0.103 0.033 0. 0. 0. 0.
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 77 0 0 184 0 0
normalized size 1 1. 1.28 0. 0. 3.07 0. 0.
time (sec) N/A 0.035 0.088 0.033 0. 1.535 0. 0.
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 43 90 0 0 0 0
normalized size 1 1. 0.93 1.96 0. 0. 0. 0.
time (sec) N/A 0.032 0.068 0.168 0. 0. 0. 0.
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 41 41 54 0 0 96 0 0
normalized size 1 1. 1.32 0. 0. 2.34 0. 0.
time (sec) N/A 0.046 0.111 0.033 0. 1.571 0. 0.
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 58 126 0 0 0 0
normalized size 1 1. 0.78 1.7 0. 0. 0. 0.
time (sec) N/A 0.066 0.094 0.036 0. 0. 0. 0.
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 25 25 33 38 120 80 0 0
normalized size 1 1. 1.32 1.52 4.8 3.2 0. 0.
time (sec) N/A 0.041 0.037 0.033 1.627 1.563 0. 0.
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 64 64 60 112 0 0 0 0
normalized size 1 1. 0.94 1.75 0. 0. 0. 0.
time (sec) N/A 0.055 0.094 0.036 0. 0. 0. 0.
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 128 128 95 121 0 240 0 0
normalized size 1 1. 0.74 0.95 0. 1.88 0. 0.
time (sec) N/A 0.08 0.199 0.038 0. 1.75 0. 0.
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 118 118 80 133 0 0 0 0
normalized size 1 1. 0.68 1.13 0. 0. 0. 0.
time (sec) N/A 0.078 0.166 0.033 0. 0. 0. 0.
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 30 30 44 47 62 122 0 0
normalized size 1 1. 1.47 1.57 2.07 4.07 0. 0.
time (sec) N/A 0.041 0.048 0.03 1.746 1.571 0. 0.
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 162 162 63 140 0 0 0 0
normalized size 1 1. 0.39 0.86 0. 0. 0. 0.
time (sec) N/A 0.1 0.121 0.035 0. 0. 0. 0.
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 96 96 87 113 0 219 0 0
normalized size 1 1. 0.91 1.18 0. 2.28 0. 0.
time (sec) N/A 0.067 0.175 0.035 0. 1.58 0. 0.
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 86 86 65 124 0 0 0 0
normalized size 1 1. 0.76 1.44 0. 0. 0. 0.
time (sec) N/A 0.063 0.121 0.032 0. 0. 0. 0.
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 91 91 88 0 0 203 0 0
normalized size 1 1. 0.97 0. 0. 2.23 0. 0.
time (sec) N/A 0.073 0.156 0.031 0. 1.55 0. 0.
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 130 130 60 152 0 0 0 0
normalized size 1 1. 0.46 1.17 0. 0. 0. 0.
time (sec) N/A 0.073 0.108 0.037 0. 0. 0. 0.
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F A F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 96 96 63 130 0 225 0 0
normalized size 1 1. 0.66 1.35 0. 2.34 0. 0.
time (sec) N/A 0.046 0.089 0.036 0. 1.703 0. 0.
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 67 67 54 163 0 0 0 0
normalized size 1 1. 0.81 2.43 0. 0. 0. 0.
time (sec) N/A 0.037 0.094 0.168 0. 0. 0. 0.
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F B A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 33 0 117 59 0 0
normalized size 1 1. 1.22 0. 4.33 2.19 0. 0.
time (sec) N/A 0.039 0.034 0.035 1.582 1.557 0. 0.
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 69 69 66 0 0 0 0 0
normalized size 1 1. 0.96 0. 0. 0. 0. 0.
time (sec) N/A 0.054 0.108 0.033 0. 0. 0. 0.
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F A F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 69 69 53 0 0 159 0 0
normalized size 1 1. 0.77 0. 0. 2.3 0. 0.
time (sec) N/A 0.061 0.104 0.035 0. 1.633 0. 0.
Problem 156 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 62 62 62 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.055 1.157 0.093 0. 0. 0. 0.
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 68 68 126 0 0 0 0 0
normalized size 1 1. 1.85 0. 0. 0. 0. 0.
time (sec) N/A 0.065 4.243 1.119 0. 0. 0. 0.
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 69 69 101 0 0 0 0 0
normalized size 1 1. 1.46 0. 0. 0. 0. 0.
time (sec) N/A 0.069 5.297 1.283 0. 0. 0. 0.
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 68 68 200 0 0 0 0 0
normalized size 1 1. 2.94 0. 0. 0. 0. 0.
time (sec) N/A 0.069 8.479 0.107 0. 0. 0. 0.
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A C A C B B F F
verified N/A NO Yes TBD TBD TBD TBD TBD
size 42 137 30 509 128 602 0 0
normalized size 1 3.26 0.71 12.12 3.05 14.33 0. 0.
time (sec) N/A 0.135 0.387 0.237 2.189 1.625 0. 0.
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 26 26 62 0 103 104 0 51
normalized size 1 1. 2.38 0. 3.96 4. 0. 1.96
time (sec) N/A 0.039 0.117 0.049 1.029 1.548 0. 1.186
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B F A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 26 26 65 0 66 107 0 53
normalized size 1 1. 2.5 0. 2.54 4.12 0. 2.04
time (sec) N/A 0.046 0.098 0.066 1.062 1.453 0. 1.172
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 90 90 115 0 0 1323 0 0
normalized size 1 1. 1.28 0. 0. 14.7 0. 0.
time (sec) N/A 0.087 5.955 0.105 0. 1.819 0. 0.
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 66 66 64 0 0 1347 0 0
normalized size 1 1. 0.97 0. 0. 20.41 0. 0.
time (sec) N/A 0.075 0.845 0.084 0. 1.702 0. 0.
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 20 20 54 23 30 219 0 190
normalized size 1 1. 2.7 1.15 1.5 10.95 0. 9.5
time (sec) N/A 0.018 0.064 0.008 1.097 1.842 0. 1.211
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 19 19 19 20 39 219 0 38
normalized size 1 1. 1. 1.05 2.05 11.53 0. 2.
time (sec) N/A 0.027 0.066 0.012 1.122 1.921 0. 1.145
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 81 51 203 2109 0 278
normalized size 1 1. 1.47 0.93 3.69 38.35 0. 5.05
time (sec) N/A 0.045 0.059 0.019 1.155 1.845 0. 1.209
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 42 42 56 36 124 869 0 63
normalized size 1 1. 1.33 0.86 2.95 20.69 0. 1.5
time (sec) N/A 0.033 0.065 0.01 1.132 1.936 0. 1.178
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 89 89 135 84 313 5852 0 329
normalized size 1 1. 1.52 0.94 3.52 65.75 0. 3.7
time (sec) N/A 0.07 0.058 0.015 1.268 2.23 0. 1.233
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 111 111 84 144 0 0 0 0
normalized size 1 1. 0.76 1.3 0. 0. 0. 0.
time (sec) N/A 0.068 0.207 0.036 0. 0. 0. 0.
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 107 107 80 212 0 0 0 0
normalized size 1 1. 0.75 1.98 0. 0. 0. 0.
time (sec) N/A 0.063 0.112 0.188 0. 0. 0. 0.
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 72 72 66 120 0 0 0 0
normalized size 1 1. 0.92 1.67 0. 0. 0. 0.
time (sec) N/A 0.043 0.092 0.118 0. 0. 0. 0.
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 72 72 68 146 0 0 0 0
normalized size 1 1. 0.94 2.03 0. 0. 0. 0.
time (sec) N/A 0.044 0.076 0.027 0. 0. 0. 0.
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 111 111 86 143 0 0 0 0
normalized size 1 1. 0.77 1.29 0. 0. 0. 0.
time (sec) N/A 0.06 0.128 0.027 0. 0. 0. 0.
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 111 111 95 227 0 0 0 0
normalized size 1 1. 0.86 2.05 0. 0. 0. 0.
time (sec) N/A 0.061 0.176 0.197 0. 0. 0. 0.

2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. It gives additional statistics for each integral. the column steps is the number of steps used by Rubi to obtain the antiderivative. The rules column is the number of unique rules used. The integrand size column is the leaf size of the integrand. Finally the ratio \(\frac{\text{number of rules}}{\text{integrand size}}\) is given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [114] had the largest ratio of [ 0.6923 ]

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 1 1 1. 6 0.167
2 A 2 2 1. 8 0.25
3 A 2 2 1. 8 0.25
4 A 2 1 1. 8 0.125
5 A 3 2 1. 8 0.25
6 A 2 1 1. 8 0.125
7 A 3 3 1. 10 0.3
8 A 3 3 1. 10 0.3
9 A 2 2 1. 10 0.2
10 A 2 2 1. 10 0.2
11 A 3 3 1. 10 0.3
12 A 3 3 1. 10 0.3
13 A 4 3 1. 12 0.25
14 A 3 3 1. 12 0.25
15 A 3 3 1. 12 0.25
16 A 2 2 1. 12 0.167
17 A 2 2 1. 12 0.167
18 A 3 3 1. 12 0.25
19 A 3 3 1. 12 0.25
20 A 4 3 1. 12 0.25
21 A 2 2 1. 10 0.2
22 A 4 3 1. 10 0.3
23 A 3 3 1. 10 0.3
24 A 2 2 1. 10 0.2
25 A 2 2 1. 10 0.2
26 A 3 3 1. 10 0.3
27 A 4 3 1. 10 0.3
28 A 5 3 1. 10 0.3
29 A 5 4 1. 10 0.4
30 A 4 4 1. 10 0.4
31 A 3 3 1. 10 0.3
32 A 2 2 1. 10 0.2
33 A 3 3 1. 10 0.3
34 A 4 3 1. 10 0.3
35 A 5 3 1. 10 0.3
36 A 7 4 1. 10 0.4
37 A 5 4 1. 10 0.4
38 A 4 4 1.07 10 0.4
39 A 4 4 1. 10 0.4
40 A 5 4 1. 10 0.4
41 A 7 4 1. 10 0.4
42 A 3 2 1. 10 0.2
43 A 3 2 1. 10 0.2
44 A 3 2 1. 10 0.2
45 A 3 3 1. 10 0.3
46 A 3 3 1. 10 0.3
47 A 5 3 1. 10 0.3
48 A 7 3 1. 10 0.3
49 A 2 2 1. 15 0.133
50 A 2 2 1. 15 0.133
51 A 5 5 1. 17 0.294
52 A 4 4 1. 17 0.235
53 A 2 2 1. 17 0.118
54 A 5 4 1. 17 0.235
55 A 6 5 1. 17 0.294
56 A 2 2 1. 17 0.118
57 A 5 4 1. 17 0.235
58 A 2 2 1. 12 0.167
59 A 2 2 1. 12 0.167
60 A 2 2 1. 12 0.167
61 A 2 2 1. 12 0.167
62 A 7 5 1. 13 0.385
63 A 6 5 1. 13 0.385
64 A 5 5 1. 13 0.385
65 A 4 4 1. 11 0.364
66 A 1 1 1. 11 0.091
67 A 3 3 1. 13 0.231
68 A 4 4 1. 13 0.308
69 A 6 6 1. 13 0.462
70 A 6 5 1. 12 0.417
71 A 5 4 1. 12 0.333
72 A 4 4 1. 12 0.333
73 A 2 1 1. 10 0.1
74 A 4 4 1. 12 0.333
75 A 6 6 1. 12 0.5
76 A 7 7 1. 12 0.583
77 A 8 7 1. 13 0.538
78 A 7 7 1. 13 0.538
79 A 6 6 1. 11 0.546
80 A 4 4 1. 11 0.364
81 A 6 6 1. 13 0.462
82 A 7 7 1. 13 0.538
83 A 8 8 1. 13 0.615
84 A 7 7 1. 13 0.538
85 A 6 4 1. 13 0.308
86 A 5 5 1. 13 0.385
87 A 4 3 1. 11 0.273
88 A 6 6 1. 11 0.546
89 A 6 5 1. 13 0.385
90 A 7 7 1. 13 0.538
91 A 7 6 1. 13 0.462
92 A 5 4 1. 13 0.308
93 A 7 6 1. 13 0.462
94 A 5 4 1. 13 0.308
95 A 6 6 1. 13 0.462
96 A 5 4 1. 11 0.364
97 A 4 3 1. 11 0.273
98 A 6 6 1. 13 0.462
99 A 6 5 1. 13 0.385
100 A 7 6 1. 13 0.462
101 A 7 5 1. 13 0.385
102 A 3 2 1. 13 0.154
103 A 5 3 1. 13 0.231
104 A 3 2 1. 13 0.154
105 A 4 3 1. 13 0.231
106 A 3 2 1. 11 0.182
107 A 2 2 1. 11 0.182
108 A 3 2 1. 13 0.154
109 A 3 2 1. 13 0.154
110 A 4 3 1. 13 0.231
111 A 3 2 1. 13 0.154
112 A 5 3 1. 13 0.231
113 A 11 7 1. 13 0.538
114 A 16 9 1. 13 0.692
115 A 8 6 1. 13 0.462
116 A 10 9 1. 13 0.692
117 A 6 5 1. 11 0.454
118 A 4 4 1. 11 0.364
119 A 8 8 1. 13 0.615
120 A 3 2 1. 13 0.154
121 A 7 7 1. 13 0.538
122 A 3 2 1. 13 0.154
123 A 16 9 1. 13 0.692
124 A 3 2 1. 13 0.154
125 A 6 5 1. 25 0.2
126 A 6 5 1. 25 0.2
127 A 4 4 1. 25 0.16
128 A 4 4 1. 25 0.16
129 A 5 4 1. 25 0.16
130 A 6 5 1. 25 0.2
131 A 6 5 1. 25 0.2
132 A 6 6 1. 15 0.4
133 A 3 3 1. 15 0.2
134 A 9 9 1. 15 0.6
135 A 6 6 1. 15 0.4
136 A 5 5 1. 13 0.385
137 A 6 6 1. 11 0.546
138 A 3 2 1. 15 0.133
139 A 5 5 1. 15 0.333
140 A 7 7 1. 15 0.467
141 A 3 3 1. 15 0.2
142 A 5 5 1. 15 0.333
143 A 8 7 1. 15 0.467
144 A 7 6 1. 15 0.4
145 A 3 3 1. 15 0.2
146 A 10 9 1. 15 0.6
147 A 7 6 1. 15 0.4
148 A 6 5 1. 15 0.333
149 A 7 6 1. 15 0.4
150 A 9 8 1. 13 0.615
151 A 7 7 1. 11 0.636
152 A 4 3 1. 15 0.2
153 A 3 3 1. 15 0.2
154 A 5 5 1. 15 0.333
155 A 6 6 1. 15 0.4
156 A 4 4 1. 11 0.364
157 A 4 4 1. 13 0.308
158 A 4 4 1. 13 0.308
159 A 4 4 1. 13 0.308
160 C 9 4 3.26 45 0.089
161 A 3 3 1. 15 0.2
162 A 4 4 1. 15 0.267
163 A 3 3 1. 20 0.15
164 A 3 3 1. 21 0.143
165 A 2 1 1. 15 0.067
166 A 3 2 1. 17 0.118
167 A 3 2 1. 17 0.118
168 A 3 1 1. 17 0.059
169 A 4 2 1. 17 0.118
170 A 4 3 1. 19 0.158
171 A 4 3 1. 19 0.158
172 A 3 2 1. 19 0.105
173 A 3 2 1. 19 0.105
174 A 4 3 1. 19 0.158
175 A 4 3 1. 19 0.158

[next] [prev] [prev-tail] [front] [up]