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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, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

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, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193 }

B grade: { }

C grade: { }

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, 45, 46, 47, 53, 69, 77, 85, 92, 98, 118, 125, 132, 139, 146, 171, 179, 187 }

B grade: { 54, 61 }

C grade: { 43, 44, 48, 49, 50, 51, 52, 55, 56, 57, 58, 59, 60, 62, 63, 64, 68, 76, 84, 89, 90, 91, 93, 94, 95, 96, 97, 99, 100, 110, 149, 150, 151, 152, 156, 157, 158 }

F grade: { 65, 66, 67, 70, 71, 72, 73, 74, 75, 78, 79, 80, 81, 82, 83, 86, 87, 88, 101, 102, 103, 104, 105, 106, 107, 108, 109, 111, 112, 113, 114, 115, 116, 117, 119, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 133, 134, 135, 136, 137, 138, 140, 141, 142, 143, 144, 145, 147, 148, 153, 154, 155, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 172, 173, 174, 175, 176, 177, 178, 180, 181, 182, 183, 184, 185, 186, 188, 189, 190, 191, 192, 193 }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 69, 77, 85, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 118, 125, 132, 139, 146, 176, 177, 178, 180, 181, 182, 184, 185, 186, 188, 189, 190

B grade: { }

C grade: { }

F grade: { 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 83, 84, 86, 87, 88, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 119, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 133, 134, 135, 136, 137, 138, 140, 141, 142, 143, 144, 145, 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, 179, 183, 187, 191, 192, 193 }

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, 53, 55, 56, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 89, 90, 91, 92, 93, 94, 96, 97, 98, 99, 100, 118, 132, 139, 149, 152, 153, 154, 156, 157, 158, 159, 160, 161, 170, 171, 178, 179, 187 }

B grade: { 50, 51, 52, 54, 57, 58, 59, 60, 61, 62, 63, 64, 81, 82, 83, 84, 85, 86, 87, 88, 95, 125, 146, 150, 151, 155 }

C grade: { }

F grade: { 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 119, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 133, 134, 135, 136, 137, 138, 140, 141, 142, 143, 144, 145, 147, 148, 162, 163, 164, 165, 166, 167, 168, 169, 172, 173, 174, 175, 176, 177, 180, 181, 182, 183, 184, 185, 186, 188, 189, 190, 191, 192, 193 }

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, 25, 26, 32, 33, 39, 40, 43, 44, 45, 46, 47, 48, 49, 54, 69, 77, 90, 91, 92, 93, 94, 118, 125, 132, 139, 149, 157, 158, 171, 179, 187 }

B grade: { 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 96, 97, 98, 99, 100 }

C grade: { }

F grade: { 22, 23, 24, 27, 28, 29, 30, 31, 34, 35, 36, 37, 38, 41, 42, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 95, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 119, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 133, 134, 135, 136, 137, 138, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150, 151, 152, 153, 154, 155, 156, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 172, 173, 174, 175, 176, 177, 178, 180, 181, 182, 183, 184, 185, 186, 188, 189, 190, 191, 192, 193 }

2.1.7 Giac

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, 29, 30, 31, 32, 33, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 48, 49, 55, 56, 65, 66, 67, 68, 77, 85, 92, 93, 94, 98, 105, 118, 125, 132, 139, 146, 157, 158, 171, 179, 187 }

B grade: { 50, 51, 52, 53, 54, 57, 58, 59, 60, 61, 62, 63, 64, 69, 73, 74, 75, 76, 81, 82, 83, 84, 99, 100, 111, 149, 150, 151, 152, 156 }

C grade: { 89, 90, 91, 95, 96, 97 }

F grade: { 26, 27, 28, 34, 35, 41, 42, 70, 71, 72, 78, 79, 80, 86, 87, 88, 101, 102, 103, 104, 106, 107, 108, 109, 110, 112, 113, 114, 115, 116, 117, 119, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 133, 134, 135, 136, 137, 138, 140, 141, 142, 143, 144, 145, 147, 148, 153, 154, 155, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 172, 173, 174, 175, 176, 177, 178, 180, 181, 182, 183, 184, 185, 186, 188, 189, 190, 191, 192, 193 }

2.2 Detailed conclusion table per each integral for all CAS systems

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

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

Problem 1 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 19 19 19 16 20 39 14 20
normalized size 1 1. 1. 0.84 1.05 2.05 0.74 1.05
time (sec) N/A 0.008 0.001 0.037 0.955 0.788 0.092 1.073
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 19 19 19 16 20 38 14 20
normalized size 1 1. 1. 0.84 1.05 2. 0.74 1.05
time (sec) N/A 0.007 0.001 0.036 0.959 0.839 0.097 1.081
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 19 19 19 16 20 38 14 20
normalized size 1 1. 1. 0.84 1.05 2. 0.74 1.05
time (sec) N/A 0.004 0.001 0.037 0.96 0.815 0.087 1.105
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 10 10 10 11 22 22 7 22
normalized size 1 1. 1. 1.1 2.2 2.2 0.7 2.2
time (sec) N/A 0.001 0.001 0.036 0.99 0.845 0.089 1.07
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 10 10 10 9 11 22 7 11
normalized size 1 1. 1. 0.9 1.1 2.2 0.7 1.1
time (sec) N/A 0.006 0.001 0.035 0.969 0.8 0.085 1.233
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 15 15 15 16 20 26 10 20
normalized size 1 1. 1. 1.07 1.33 1.73 0.67 1.33
time (sec) N/A 0.007 0.001 0.034 0.99 0.86 0.098 1.617
Problem 7 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 19 19 19 16 20 36 17 20
normalized size 1 1. 1. 0.84 1.05 1.89 0.89 1.05
time (sec) N/A 0.007 0.001 0.035 0.972 0.826 0.132 1.098
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 32 32 32 27 28 68 26 35
normalized size 1 1. 1. 0.84 0.88 2.12 0.81 1.09
time (sec) N/A 0.02 0.001 0.036 0.975 0.829 0.11 1.119
Problem 9 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 32 32 32 27 28 68 29 35
normalized size 1 1. 1. 0.84 0.88 2.12 0.91 1.09
time (sec) N/A 0.02 0.001 0.036 0.992 0.756 0.109 1.199
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 32 32 32 27 28 66 26 35
normalized size 1 1. 1. 0.84 0.88 2.06 0.81 1.09
time (sec) N/A 0.011 0.001 0.036 0.978 0.745 0.113 1.109
Problem 11 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 19 19 19 20 22 47 19 26
normalized size 1 1. 1. 1.05 1.16 2.47 1. 1.37
time (sec) N/A 0.005 0.001 0.036 0.996 0.816 0.096 1.097
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 10 10 10 9 11 22 7 11
normalized size 1 1. 1. 0.9 1.1 2.2 0.7 1.1
time (sec) N/A 0.012 0.001 0.035 0.968 0.79 0.087 1.11
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 26 26 26 27 26 46 20 35
normalized size 1 1. 1. 1.04 1. 1.77 0.77 1.35
time (sec) N/A 0.02 0.001 0.036 0.967 0.795 0.111 1.12
Problem 14 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 32 32 32 27 28 57 29 35
normalized size 1 1. 1. 0.84 0.88 1.78 0.91 1.09
time (sec) N/A 0.019 0.001 0.037 0.985 0.805 0.129 1.103
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 45 38 39 100 42 50
normalized size 1 1. 1. 0.84 0.87 2.22 0.93 1.11
time (sec) N/A 0.036 0.001 0.036 0.991 0.767 0.123 1.107
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 45 38 39 96 41 50
normalized size 1 1. 1. 0.84 0.87 2.13 0.91 1.11
time (sec) N/A 0.031 0.001 0.036 1.074 0.781 0.122 1.102
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 45 38 39 95 42 50
normalized size 1 1. 1. 0.84 0.87 2.11 0.93 1.11
time (sec) N/A 0.018 0.001 0.033 1.005 0.823 0.122 1.099
Problem 18 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 28 29 32 70 29 38
normalized size 1 1. 1. 1.04 1.14 2.5 1.04 1.36
time (sec) N/A 0.008 0.001 0.035 1.022 0.748 0.11 1.13
Problem 19 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 10 10 10 9 11 22 7 11
normalized size 1 1. 1. 0.9 1.1 2.2 0.7 1.1
time (sec) N/A 0.011 0.001 0.033 1.06 0.873 0.091 1.079
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 37 37 37 38 36 66 31 50
normalized size 1 1. 1. 1.03 0.97 1.78 0.84 1.35
time (sec) N/A 0.034 0.001 0.036 1.076 0.836 0.139 1.471
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 45 38 39 77 44 50
normalized size 1 1. 1. 0.84 0.87 1.71 0.98 1.11
time (sec) N/A 0.033 0.001 0.035 1.064 0.885 0.15 1.135
Problem 22 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 11 11 11 14 15 36 0 15
normalized size 1 1. 1. 1.27 1.36 3.27 0. 1.36
time (sec) N/A 0.024 0.014 0.04 1.121 0.731 0. 1.132
Problem 23 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 11 11 11 14 15 36 0 15
normalized size 1 1. 1. 1.27 1.36 3.27 0. 1.36
time (sec) N/A 0.023 0.014 0.039 1.14 0.699 0. 1.12
Problem 24 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 11 11 11 14 15 36 0 15
normalized size 1 1. 1. 1.27 1.36 3.27 0. 1.36
time (sec) N/A 0.017 0.013 0.043 1.132 0.836 0. 1.108
Problem 25 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 8 8 8 14 12 28 5 12
normalized size 1 1. 1. 1.75 1.5 3.5 0.62 1.5
time (sec) N/A 0.003 0.005 0.037 1.182 0.844 0.51 1.105
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 5 5 5 6 7 20 5 0
normalized size 1 1. 1. 1.2 1.4 4. 1. 0.
time (sec) N/A 0.012 0.005 0.033 1.031 0.853 0.101 0.
Problem 27 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 9 9 9 10 12 34 0 0
normalized size 1 1. 1. 1.11 1.33 3.78 0. 0.
time (sec) N/A 0.024 0.014 0.038 1.219 0.841 0. 0.
Problem 28 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 11 11 11 14 15 42 0 0
normalized size 1 1. 1. 1.27 1.36 3.82 0. 0.
time (sec) N/A 0.024 0.014 0.038 1.169 0.724 0. 0.
Problem 29 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 24 24 24 26 18 84 0 32
normalized size 1 1. 1. 1.08 0.75 3.5 0. 1.33
time (sec) N/A 0.038 0.015 0.033 1.184 0.707 0. 1.122
Problem 30 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 24 24 24 26 18 84 0 32
normalized size 1 1. 1. 1.08 0.75 3.5 0. 1.33
time (sec) N/A 0.037 0.015 0.033 1.229 0.756 0. 1.104
Problem 31 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 24 24 24 26 18 84 0 32
normalized size 1 1. 1. 1.08 0.75 3.5 0. 1.33
time (sec) N/A 0.026 0.013 0.036 1.254 0.887 0. 1.141
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 18 18 18 24 16 68 12 26
normalized size 1 1. 1. 1.33 0.89 3.78 0.67 1.44
time (sec) N/A 0.005 0.004 0.036 1.235 0.792 0.488 1.12
Problem 33 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 8 8 8 9 11 18 7 11
normalized size 1 1. 1. 1.12 1.38 2.25 0.88 1.38
time (sec) N/A 0.012 0.001 0.033 1.094 0.768 0.083 1.105
Problem 34 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 22 22 22 21 12 76 0 0
normalized size 1 1. 1. 0.95 0.55 3.45 0. 0.
time (sec) N/A 0.035 0.015 0.036 1.247 0.578 0. 0.
Problem 35 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 24 24 24 26 18 92 0 0
normalized size 1 1. 1. 1.08 0.75 3.83 0. 0.
time (sec) N/A 0.037 0.015 0.035 1.261 0.687 0. 0.
Problem 36 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 37 37 37 37 18 124 0 47
normalized size 1 1. 1. 1. 0.49 3.35 0. 1.27
time (sec) N/A 0.052 0.016 0.046 1.255 0.857 0. 1.125
Problem 37 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 41 41 41 37 18 123 0 47
normalized size 1 1. 1. 0.9 0.44 3. 0. 1.15
time (sec) N/A 0.053 0.015 0.034 1.125 0.756 0. 1.121
Problem 38 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 37 37 37 37 18 123 0 47
normalized size 1 1. 1. 1. 0.49 3.32 0. 1.27
time (sec) N/A 0.031 0.005 0.045 1.153 0.853 0. 1.134
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 34 34 34 33 18 99 26 39
normalized size 1 1. 1. 0.97 0.53 2.91 0.76 1.15
time (sec) N/A 0.009 0.005 0.035 1.165 0.664 0.519 1.118
Problem 40 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 10 10 10 9 11 23 10 11
normalized size 1 1. 1. 0.9 1.1 2.3 1. 1.1
time (sec) N/A 0.012 0.001 0.033 1.109 0.861 0.09 1.11
Problem 41 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 39 39 39 33 12 100 0 0
normalized size 1 1. 1. 0.85 0.31 2.56 0. 0.
time (sec) N/A 0.05 0.015 0.034 1.166 0.846 0. 0.
Problem 42 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 36 36 36 36 18 119 0 0
normalized size 1 1. 1. 1. 0.5 3.31 0. 0.
time (sec) N/A 0.049 0.016 0.033 1.241 0.717 0. 0.
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 32 112 35 84 36 42
normalized size 1 1. 1.19 4.15 1.3 3.11 1.33 1.56
time (sec) N/A 0.013 0.002 0.21 1.109 0.787 1.397 1.112
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 32 112 35 82 36 42
normalized size 1 1. 1.19 4.15 1.3 3.04 1.33 1.56
time (sec) N/A 0.012 0.001 0.167 1.026 0.862 0.819 1.097
Problem 45 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 32 29 35 82 36 42
normalized size 1 1. 1.19 1.07 1.3 3.04 1.33 1.56
time (sec) N/A 0.007 0.001 0.052 1.169 0.803 0.46 1.175
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 18 18 18 19 24 55 19 27
normalized size 1 1. 1. 1.06 1.33 3.06 1.06 1.5
time (sec) N/A 0.006 0.001 0.038 1.103 0.794 0.239 1.178
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 22 22 21 27 27 57 36 26
normalized size 1 1. 0.95 1.23 1.23 2.59 1.64 1.18
time (sec) N/A 0.012 0.001 0.035 1.117 0.878 6.95 1.139
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 26 112 35 51 24 32
normalized size 1 1. 1.13 4.87 1.52 2.22 1.04 1.39
time (sec) N/A 0.013 0.001 0.082 1.189 0.961 0.474 1.175
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 32 111 35 68 37 36
normalized size 1 1. 1.19 4.11 1.3 2.52 1.37 1.33
time (sec) N/A 0.013 0.001 0.073 1.138 0.835 1.24 1.15
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 52 52 43 691 96 244 131 150
normalized size 1 1. 0.83 13.29 1.85 4.69 2.52 2.88
time (sec) N/A 0.036 0.016 0.191 1.128 0.891 2.911 1.157
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 52 52 46 692 96 247 143 150
normalized size 1 1. 0.88 13.31 1.85 4.75 2.75 2.88
time (sec) N/A 0.037 0.019 0.204 1.086 0.848 1.735 1.186
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 52 52 41 692 95 243 126 146
normalized size 1 1. 0.79 13.31 1.83 4.67 2.42 2.81
time (sec) N/A 0.023 0.013 0.213 1.119 0.879 1.02 1.15
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 43 43 33 63 77 197 109 119
normalized size 1 1. 0.77 1.47 1.79 4.58 2.53 2.77
time (sec) N/A 0.013 0.008 0.05 1.089 0.792 0.607 1.197
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 22 22 22 56 27 136 60 76
normalized size 1 1. 1. 2.55 1.23 6.18 2.73 3.45
time (sec) N/A 0.024 0.003 0.037 1.188 0.838 22.342 1.242
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 35 704 95 182 110 116
normalized size 1 1. 0.76 15.3 2.07 3.96 2.39 2.52
time (sec) N/A 0.035 0.011 0.122 1.118 0.86 1.075 1.156
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 52 52 41 703 96 204 128 122
normalized size 1 1. 0.79 13.52 1.85 3.92 2.46 2.35
time (sec) N/A 0.035 0.013 0.122 1.159 0.864 1.742 1.23
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 77 77 66 2649 182 517 338 354
normalized size 1 1. 0.86 34.4 2.36 6.71 4.39 4.6
time (sec) N/A 0.063 0.029 0.318 1.135 0.866 7.593 1.263
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 77 77 67 2650 181 512 311 346
normalized size 1 1. 0.87 34.42 2.35 6.65 4.04 4.49
time (sec) N/A 0.06 0.014 0.332 1.184 0.954 4.036 1.291
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 77 77 60 2650 182 505 337 354
normalized size 1 1. 0.78 34.42 2.36 6.56 4.38 4.6
time (sec) N/A 0.039 0.03 0.334 1.124 0.814 2.492 1.185
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 66 66 50 2641 153 435 270 296
normalized size 1 1. 0.76 40.02 2.32 6.59 4.09 4.48
time (sec) N/A 0.024 0.009 0.299 1.22 0.899 1.394 1.23
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 22 22 22 75 27 255 92 154
normalized size 1 1. 1. 3.41 1.23 11.59 4.18 7.
time (sec) N/A 0.022 0.003 0.036 1.102 0.81 37.442 1.224
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 69 69 52 2674 180 406 272 266
normalized size 1 1. 0.75 38.75 2.61 5.88 3.94 3.86
time (sec) N/A 0.06 0.018 0.24 1.159 0.882 1.601 1.219
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 77 77 60 2673 182 436 338 274
normalized size 1 1. 0.78 34.71 2.36 5.66 4.39 3.56
time (sec) N/A 0.059 0.021 0.237 1.176 0.938 1.69 1.222
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 77 77 60 2674 184 443 313 275
normalized size 1 1. 0.78 34.73 2.39 5.75 4.06 3.57
time (sec) N/A 0.061 0.024 0.249 1.1 0.788 3.781 1.172
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 51 51 51 0 0 108 0 65
normalized size 1 1. 1. 0. 0. 2.12 0. 1.27
time (sec) N/A 0.056 0.058 0.167 0. 0.904 0. 1.195
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 51 51 51 0 0 108 0 65
normalized size 1 1. 1. 0. 0. 2.12 0. 1.27
time (sec) N/A 0.055 0.055 0.168 0. 0.856 0. 1.183
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 51 51 51 0 0 108 0 65
normalized size 1 1. 1. 0. 0. 2.12 0. 1.27
time (sec) N/A 0.045 0.051 0.155 0. 0.819 0. 1.2
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 48 48 48 241 0 100 0 57
normalized size 1 1. 1. 5.02 0. 2.08 0. 1.19
time (sec) N/A 0.036 0.041 0.267 0. 0.837 0. 1.214
Problem 69 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 18 18 18 19 24 51 32 61
normalized size 1 1. 1. 1.06 1.33 2.83 1.78 3.39
time (sec) N/A 0.025 0.016 0.038 1.058 0.828 1.989 1.235
Problem 70 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 48 48 48 0 0 100 0 0
normalized size 1 1. 1. 0. 0. 2.08 0. 0.
time (sec) N/A 0.051 0.049 0.151 0. 0.737 0. 0.
Problem 71 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 51 51 51 0 0 108 0 0
normalized size 1 1. 1. 0. 0. 2.12 0. 0.
time (sec) N/A 0.051 0.05 0.165 0. 0.785 0. 0.
Problem 72 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 51 51 51 0 0 108 0 0
normalized size 1 1. 1. 0. 0. 2.12 0. 0.
time (sec) N/A 0.052 0.052 0.184 0. 0.8 0. 0.
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 76 76 70 0 0 257 0 352
normalized size 1 1. 0.92 0. 0. 3.38 0. 4.63
time (sec) N/A 0.079 0.118 0.747 0. 0.834 0. 1.282
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 76 76 70 0 0 257 0 352
normalized size 1 1. 0.92 0. 0. 3.38 0. 4.63
time (sec) N/A 0.079 0.121 0.691 0. 0.888 0. 1.339
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 76 76 70 0 0 257 0 352
normalized size 1 1. 0.92 0. 0. 3.38 0. 4.63
time (sec) N/A 0.059 0.118 0.65 0. 0.899 0. 1.326
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 70 70 66 351 0 240 0 321
normalized size 1 1. 0.94 5.01 0. 3.43 0. 4.59
time (sec) N/A 0.04 0.098 0.265 0. 0.952 0. 1.222
Problem 77 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 21 27 59 70 28
normalized size 1 1. 1. 1.05 1.35 2.95 3.5 1.4
time (sec) N/A 0.024 0.005 0.034 1.132 0.805 49.5 1.188
Problem 78 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 73 73 76 0 0 220 0 0
normalized size 1 1. 1.04 0. 0. 3.01 0. 0.
time (sec) N/A 0.075 0.089 0.659 0. 0.773 0. 0.
Problem 79 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 76 76 80 0 0 247 0 0
normalized size 1 1. 1.05 0. 0. 3.25 0. 0.
time (sec) N/A 0.078 0.091 0.725 0. 0.952 0. 0.
Problem 80 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 76 76 80 0 0 247 0 0
normalized size 1 1. 1.05 0. 0. 3.25 0. 0.
time (sec) N/A 0.075 0.094 0.756 0. 0.857 0. 0.
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 101 101 89 0 0 520 0 1389
normalized size 1 1. 0.88 0. 0. 5.15 0. 13.75
time (sec) N/A 0.108 0.135 0.705 0. 0.827 0. 1.441
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 105 105 89 0 0 518 0 1389
normalized size 1 1. 0.85 0. 0. 4.93 0. 13.23
time (sec) N/A 0.108 0.131 0.662 0. 0.95 0. 1.6
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 101 101 89 0 0 518 0 1389
normalized size 1 1. 0.88 0. 0. 5.13 0. 13.75
time (sec) N/A 0.08 0.13 0.652 0. 0.783 0. 1.804
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 98 98 82 460 0 489 0 1326
normalized size 1 1. 0.84 4.69 0. 4.99 0. 13.53
time (sec) N/A 0.052 0.114 0.268 0. 0.762 0. 1.329
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 22 22 22 21 27 150 0 28
normalized size 1 1. 1. 0.95 1.23 6.82 0. 1.27
time (sec) N/A 0.024 0.004 0.035 1.096 0.792 0. 1.288
Problem 86 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 102 102 94 0 0 473 0 0
normalized size 1 1. 0.92 0. 0. 4.64 0. 0.
time (sec) N/A 0.106 0.094 0.719 0. 0.904 0. 0.
Problem 87 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 100 100 89 0 0 524 0 0
normalized size 1 1. 0.89 0. 0. 5.24 0. 0.
time (sec) N/A 0.108 0.119 0.709 0. 0.739 0. 0.
Problem 88 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 105 105 89 0 0 524 0 0
normalized size 1 1. 0.85 0. 0. 4.99 0. 0.
time (sec) N/A 0.107 0.115 0.741 0. 0.739 0. 0.
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A F(-1) C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 41 41 29 128 55 119 0 158
normalized size 1 1. 0.71 3.12 1.34 2.9 0. 3.85
time (sec) N/A 0.016 0.014 0.108 1.193 0.913 0. 1.437
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A A C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 41 41 29 128 55 108 70 146
normalized size 1 1. 0.71 3.12 1.34 2.63 1.71 3.56
time (sec) N/A 0.016 0.01 0.082 1.011 0.934 46.05 1.525
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A A C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 41 41 29 124 55 88 70 142
normalized size 1 1. 0.71 3.02 1.34 2.15 1.71 3.46
time (sec) N/A 0.014 0.007 0.08 1.135 0.916 2.538 1.553
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 37 37 24 42 55 69 63 55
normalized size 1 1. 0.65 1.14 1.49 1.86 1.7 1.49
time (sec) N/A 0.015 0.006 0.043 1.172 0.87 1.68 1.374
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 37 37 24 122 55 78 65 58
normalized size 1 1. 0.65 3.3 1.49 2.11 1.76 1.57
time (sec) N/A 0.016 0.007 0.083 1.178 0.865 5.865 1.362
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 41 41 29 128 55 92 71 90
normalized size 1 1. 0.71 3.12 1.34 2.24 1.73 2.2
time (sec) N/A 0.015 0.009 0.088 1.05 0.867 39.234 1.408
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A B F(-1) C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 73 73 61 716 138 321 0 574
normalized size 1 1. 0.84 9.81 1.89 4.4 0. 7.86
time (sec) N/A 0.045 0.02 0.139 1.155 0.796 0. 1.998
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A B C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 73 73 61 716 138 294 216 521
normalized size 1 1. 0.84 9.81 1.89 4.03 2.96 7.14
time (sec) N/A 0.046 0.018 0.134 1.101 0.899 124.624 1.944
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A B C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 73 73 61 710 138 243 216 517
normalized size 1 1. 0.84 9.73 1.89 3.33 2.96 7.08
time (sec) N/A 0.041 0.016 0.126 1.102 0.896 7.888 1.971
Problem 98 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 67 67 54 107 138 203 199 159
normalized size 1 1. 0.81 1.6 2.06 3.03 2.97 2.37
time (sec) N/A 0.041 0.013 0.054 1.181 0.956 4.274 1.303
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 67 67 54 707 136 212 201 201
normalized size 1 1. 0.81 10.55 2.03 3.16 3. 3.
time (sec) N/A 0.047 0.013 0.131 1.084 0.939 5.55 1.27
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 73 73 61 716 138 236 218 288
normalized size 1 1. 0.84 9.81 1.89 3.23 2.99 3.95
time (sec) N/A 0.046 0.015 0.137 1.131 0.849 42.533 1.303
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 64 64 62 0 0 0 0 0
normalized size 1 1. 0.97 0. 0. 0. 0. 0.
time (sec) N/A 0.064 0.081 0.118 0. 0. 0. 0.
Problem 102 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 64 64 62 0 0 0 0 0
normalized size 1 1. 0.97 0. 0. 0. 0. 0.
time (sec) N/A 0.064 0.071 0.116 0. 0. 0. 0.
Problem 103 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 64 64 62 0 0 0 0 0
normalized size 1 1. 0.97 0. 0. 0. 0. 0.
time (sec) N/A 0.06 0.069 0.115 0. 0. 0. 0.
Problem 104 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 64 64 62 0 0 0 0 0
normalized size 1 1. 0.97 0. 0. 0. 0. 0.
time (sec) N/A 0.061 0.063 0.108 0. 0. 0. 0.
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 64 64 62 0 0 0 0 66
normalized size 1 1. 0.97 0. 0. 0. 0. 1.03
time (sec) N/A 0.061 0.071 0.109 0. 0. 0. 1.286
Problem 106 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 64 64 62 0 0 0 0 0
normalized size 1 1. 0.97 0. 0. 0. 0. 0.
time (sec) N/A 0.059 0.073 0.108 0. 0. 0. 0.
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 98 98 84 0 0 0 0 0
normalized size 1 1. 0.86 0. 0. 0. 0. 0.
time (sec) N/A 0.091 0.154 4.648 0. 0. 0. 0.
Problem 108 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 98 98 84 0 0 0 0 0
normalized size 1 1. 0.86 0. 0. 0. 0. 0.
time (sec) N/A 0.096 0.144 4.5 0. 0. 0. 0.
Problem 109 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 98 98 84 0 0 0 0 0
normalized size 1 1. 0.86 0. 0. 0. 0. 0.
time (sec) N/A 0.087 0.133 4.658 0. 0. 0. 0.
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 98 98 83 427 0 0 0 0
normalized size 1 1. 0.85 4.36 0. 0. 0. 0.
time (sec) N/A 0.088 0.115 1.596 0. 0. 0. 0.
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 98 98 93 0 0 0 0 379
normalized size 1 1. 0.95 0. 0. 0. 0. 3.87
time (sec) N/A 0.093 0.12 4.557 0. 0. 0. 1.313
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 98 98 94 0 0 0 0 0
normalized size 1 1. 0.96 0. 0. 0. 0. 0.
time (sec) N/A 0.092 0.123 4.664 0. 0. 0. 0.
Problem 113 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 85 85 85 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.072 0.038 0.485 0. 0. 0. 0.
Problem 114 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 64 64 61 0 0 0 0 0
normalized size 1 1. 0.95 0. 0. 0. 0. 0.
time (sec) N/A 0.054 0.022 0.293 0. 0. 0. 0.
Problem 115 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 72 72 67 0 0 0 0 0
normalized size 1 1. 0.93 0. 0. 0. 0. 0.
time (sec) N/A 0.065 0.033 0.174 0. 0. 0. 0.
Problem 116 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 72 72 67 0 0 0 0 0
normalized size 1 1. 0.93 0. 0. 0. 0. 0.
time (sec) N/A 0.054 0.032 0.177 0. 0. 0. 0.
Problem 117 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 56 56 56 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.028 0.016 0.181 0. 0. 0. 0.
Problem 118 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 17 17 17 14 18 45 29 19
normalized size 1 1. 1. 0.82 1.06 2.65 1.71 1.12
time (sec) N/A 0.014 0.002 0.038 1.019 1.029 1.924 1.232
Problem 119 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 59 59 65 0 0 0 0 0
normalized size 1 1. 1.1 0. 0. 0. 0. 0.
time (sec) N/A 0.05 0.047 0.178 0. 0. 0. 0.
Problem 120 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 72 72 73 0 0 0 0 0
normalized size 1 1. 1.01 0. 0. 0. 0. 0.
time (sec) N/A 0.056 0.048 0.184 0. 0. 0. 0.
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 82 82 73 0 0 0 0 0
normalized size 1 1. 0.89 0. 0. 0. 0. 0.
time (sec) N/A 0.068 0.043 0.166 0. 0. 0. 0.
Problem 122 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 90 90 76 0 0 0 0 0
normalized size 1 1. 0.84 0. 0. 0. 0. 0.
time (sec) N/A 0.074 0.051 0.171 0. 0. 0. 0.
Problem 123 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 90 90 79 0 0 0 0 0
normalized size 1 1. 0.88 0. 0. 0. 0. 0.
time (sec) N/A 0.057 0.057 0.173 0. 0. 0. 0.
Problem 124 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 72 72 72 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.035 0.038 0.17 0. 0. 0. 0.
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 17 17 17 14 18 104 75 19
normalized size 1 1. 1. 0.82 1.06 6.12 4.41 1.12
time (sec) N/A 0.014 0.002 0.039 1.098 0.994 37.164 1.334
Problem 126 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 77 77 79 0 0 0 0 0
normalized size 1 1. 1.03 0. 0. 0. 0. 0.
time (sec) N/A 0.067 0.056 0.169 0. 0. 0. 0.
Problem 127 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 90 90 88 0 0 0 0 0
normalized size 1 1. 0.98 0. 0. 0. 0. 0.
time (sec) N/A 0.073 0.064 0.174 0. 0. 0. 0.
Problem 128 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 46 46 46 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.035 0.005 0.178 0. 0. 0. 0.
Problem 129 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 51 51 51 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.036 0.009 0.169 0. 0. 0. 0.
Problem 130 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 51 51 51 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.033 0.009 0.181 0. 0. 0. 0.
Problem 131 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 40 40 40 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.022 0.004 0.178 0. 0. 0. 0.
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 15 15 15 14 18 39 24 19
normalized size 1 1. 1. 0.93 1.2 2.6 1.6 1.27
time (sec) N/A 0.013 0.001 0.039 1.101 0.943 3.27 1.284
Problem 133 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 40 40 52 0 0 0 0 0
normalized size 1 1. 1.3 0. 0. 0. 0. 0.
time (sec) N/A 0.033 0.034 0.171 0. 0. 0. 0.
Problem 134 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 51 51 60 0 0 0 0 0
normalized size 1 1. 1.18 0. 0. 0. 0. 0.
time (sec) N/A 0.039 0.035 0.174 0. 0. 0. 0.
Problem 135 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 63 63 73 0 0 0 0 0
normalized size 1 1. 1.16 0. 0. 0. 0. 0.
time (sec) N/A 0.053 0.045 0.189 0. 0. 0. 0.
Problem 136 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 69 69 78 0 0 0 0 0
normalized size 1 1. 1.13 0. 0. 0. 0. 0.
time (sec) N/A 0.058 0.049 0.175 0. 0. 0. 0.
Problem 137 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 69 69 78 0 0 0 0 0
normalized size 1 1. 1.13 0. 0. 0. 0. 0.
time (sec) N/A 0.049 0.046 0.171 0. 0. 0. 0.
Problem 138 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 58 58 69 0 0 0 0 0
normalized size 1 1. 1.19 0. 0. 0. 0. 0.
time (sec) N/A 0.029 0.034 0.175 0. 0. 0. 0.
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 15 15 15 14 18 70 48 19
normalized size 1 1. 1. 0.93 1.2 4.67 3.2 1.27
time (sec) N/A 0.014 0.002 0.039 1.139 0.944 165.01 1.198
Problem 140 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 60 60 58 0 0 0 0 0
normalized size 1 1. 0.97 0. 0. 0. 0. 0.
time (sec) N/A 0.05 0.049 0.173 0. 0. 0. 0.
Problem 141 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 69 69 66 0 0 0 0 0
normalized size 1 1. 0.96 0. 0. 0. 0. 0.
time (sec) N/A 0.057 0.047 0.168 0. 0. 0. 0.
Problem 142 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 87 87 87 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.073 0.059 0.17 0. 0. 0. 0.
Problem 143 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 89 89 92 0 0 0 0 0
normalized size 1 1. 1.03 0. 0. 0. 0. 0.
time (sec) N/A 0.073 0.064 0.168 0. 0. 0. 0.
Problem 144 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 93 93 92 0 0 0 0 0
normalized size 1 1. 0.99 0. 0. 0. 0. 0.
time (sec) N/A 0.058 0.064 0.168 0. 0. 0. 0.
Problem 145 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 80 80 83 0 0 0 0 0
normalized size 1 1. 1.04 0. 0. 0. 0. 0.
time (sec) N/A 0.037 0.048 0.174 0. 0. 0. 0.
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 17 17 17 14 18 108 0 19
normalized size 1 1. 1. 0.82 1.06 6.35 0. 1.12
time (sec) N/A 0.014 0.002 0.039 0.98 0.984 0. 1.27
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 84 84 70 0 0 0 0 0
normalized size 1 1. 0.83 0. 0. 0. 0. 0.
time (sec) N/A 0.069 0.054 0.182 0. 0. 0. 0.
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 93 93 78 0 0 0 0 0
normalized size 1 1. 0.84 0. 0. 0. 0. 0.
time (sec) N/A 0.076 0.053 0.178 0. 0. 0. 0.
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 21 21 17 260 0 74 27 289
normalized size 1 1. 0.81 12.38 0. 3.52 1.29 13.76
time (sec) N/A 0.02 0.011 0.117 0. 1.006 1.356 1.351
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) B F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 116 116 76 9684 0 1242 0 1530
normalized size 1 1. 0.66 83.48 0. 10.71 0. 13.19
time (sec) N/A 0.091 0.045 0.698 0. 1.058 0. 1.93
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) B F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 81 81 76 2126 0 478 0 543
normalized size 1 1. 0.94 26.25 0. 5.9 0. 6.7
time (sec) N/A 0.046 0.032 0.197 0. 1.046 0. 1.31
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) A F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 46 46 32 371 0 142 0 128
normalized size 1 1. 0.7 8.07 0. 3.09 0. 2.78
time (sec) N/A 0.015 0.012 0.103 0. 1.035 0. 1.285
Problem 153 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 66 66 67 0 0 163 0 0
normalized size 1 1. 1.02 0. 0. 2.47 0. 0.
time (sec) N/A 0.074 0.106 0.245 0. 0.989 0. 0.
Problem 154 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 100 100 89 0 0 332 0 0
normalized size 1 1. 0.89 0. 0. 3.32 0. 0.
time (sec) N/A 0.093 0.233 1.303 0. 1.003 0. 0.
Problem 155 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 142 142 113 0 0 765 0 0
normalized size 1 1. 0.8 0. 0. 5.39 0. 0.
time (sec) N/A 0.139 0.357 1.312 0. 1.033 0. 0.
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 40 2008 0 197 0 219
normalized size 1 1. 0.54 27.14 0. 2.66 0. 2.96
time (sec) N/A 0.053 0.008 0.257 0. 0.995 0. 1.268
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 53 53 30 750 0 113 163 123
normalized size 1 1. 0.57 14.15 0. 2.13 3.08 2.32
time (sec) N/A 0.032 0.006 0.121 0. 1.027 113.492 1.254
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 32 32 20 263 0 55 68 57
normalized size 1 1. 0.62 8.22 0. 1.72 2.12 1.78
time (sec) N/A 0.011 0.004 0.088 0. 0.993 39.605 1.386
Problem 159 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 27 27 27 0 0 53 0 0
normalized size 1 1. 1. 0. 0. 1.96 0. 0.
time (sec) N/A 0.037 0.008 0.254 0. 1.014 0. 0.
Problem 160 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 49 49 49 0 0 132 0 0
normalized size 1 1. 1. 0. 0. 2.69 0. 0.
time (sec) N/A 0.053 0.017 1.202 0. 1.006 0. 0.
Problem 161 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 77 77 61 0 0 240 0 0
normalized size 1 1. 0.79 0. 0. 3.12 0. 0.
time (sec) N/A 0.076 0.024 1.195 0. 1.01 0. 0.
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 111 111 101 0 0 0 0 0
normalized size 1 1. 0.91 0. 0. 0. 0. 0.
time (sec) N/A 0.126 0.194 0.206 0. 0. 0. 0.
Problem 163 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 86 86 86 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.067 0.051 0.178 0. 0. 0. 0.
Problem 164 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 61 61 61 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.047 0.011 0.201 0. 0. 0. 0.
Problem 165 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 83 83 86 0 0 0 0 0
normalized size 1 1. 1.04 0. 0. 0. 0. 0.
time (sec) N/A 0.068 0.194 0.185 0. 0. 0. 0.
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 112 112 103 0 0 0 0 0
normalized size 1 1. 0.92 0. 0. 0. 0. 0.
time (sec) N/A 0.092 0.413 0.188 0. 0. 0. 0.
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 106 106 107 0 0 0 0 0
normalized size 1 1. 1.01 0. 0. 0. 0. 0.
time (sec) N/A 0.069 0.135 1.076 0. 0. 0. 0.
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 89 89 89 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.064 0.087 0.479 0. 0. 0. 0.
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 89 89 89 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.052 0.081 0.411 0. 0. 0. 0.
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 80 80 80 0 0 132 0 0
normalized size 1 1. 1. 0. 0. 1.65 0. 0.
time (sec) N/A 0.038 0.068 0.344 0. 1.308 0. 0.
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 26 26 26 27 0 99 56 36
normalized size 1 1. 1. 1.04 0. 3.81 2.15 1.38
time (sec) N/A 0.032 0.008 0.04 0. 1.035 2.609 1.318
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 78 78 78 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.054 0.073 0.36 0. 0. 0. 0.
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 89 89 89 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.058 0.078 0.174 0. 0. 0. 0.
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 89 89 89 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.059 0.08 0.185 0. 0. 0. 0.
Problem 175 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 86 86 82 0 0 0 0 0
normalized size 1 1. 0.95 0. 0. 0. 0. 0.
time (sec) N/A 0.072 0.109 0.198 0. 0. 0. 0.
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 63 63 63 0 59 0 0 0
normalized size 1 1. 1. 0. 0.94 0. 0. 0.
time (sec) N/A 0.059 0.036 0.058 1.195 0. 0. 0.
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 63 63 63 0 59 0 0 0
normalized size 1 1. 1. 0. 0.94 0. 0. 0.
time (sec) N/A 0.047 0.031 0.051 1.261 0. 0. 0.
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 56 56 56 0 59 86 0 0
normalized size 1 1. 1. 0. 1.05 1.54 0. 0.
time (sec) N/A 0.033 0.026 0.048 1.248 1.053 0. 0.
Problem 179 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 21 21 21 22 0 63 39 28
normalized size 1 1. 1. 1.05 0. 3. 1.86 1.33
time (sec) N/A 0.028 0.006 0.037 0. 1.03 1.333 1.286
Problem 180 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 52 52 48 0 54 0 0 0
normalized size 1 1. 0.92 0. 1.04 0. 0. 0.
time (sec) N/A 0.049 0.033 0.054 1.259 0. 0. 0.
Problem 181 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 63 63 63 0 59 0 0 0
normalized size 1 1. 1. 0. 0.94 0. 0. 0.
time (sec) N/A 0.055 0.035 0.047 1.335 0. 0. 0.
Problem 182 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 63 63 63 0 59 0 0 0
normalized size 1 1. 1. 0. 0.94 0. 0. 0.
time (sec) N/A 0.054 0.035 0.048 1.262 0. 0. 0.
Problem 183 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 107 107 103 0 0 0 0 0
normalized size 1 1. 0.96 0. 0. 0. 0. 0.
time (sec) N/A 0.084 0.188 0.086 0. 0. 0. 0.
Problem 184 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 80 80 80 0 65 0 0 0
normalized size 1 1. 1. 0. 0.81 0. 0. 0.
time (sec) N/A 0.062 0.052 0.043 1.288 0. 0. 0.
Problem 185 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 75 75 75 0 65 0 0 0
normalized size 1 1. 1. 0. 0.87 0. 0. 0.
time (sec) N/A 0.055 0.045 0.043 1.335 0. 0. 0.
Problem 186 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 73 73 73 0 65 0 0 0
normalized size 1 1. 1. 0. 0.89 0. 0. 0.
time (sec) N/A 0.035 0.026 0.044 1.247 0. 0. 0.
Problem 187 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 26 26 26 25 0 82 48 34
normalized size 1 1. 1. 0.96 0. 3.15 1.85 1.31
time (sec) N/A 0.028 0.007 0.04 0. 1.043 16.297 1.263
Problem 188 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 73 73 73 0 65 0 0 0
normalized size 1 1. 1. 0. 0.89 0. 0. 0.
time (sec) N/A 0.052 0.048 0.046 1.351 0. 0. 0.
Problem 189 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 75 75 75 0 65 0 0 0
normalized size 1 1. 1. 0. 0.87 0. 0. 0.
time (sec) N/A 0.058 0.045 0.041 1.247 0. 0. 0.
Problem 190 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 80 80 80 0 65 0 0 0
normalized size 1 1. 1. 0. 0.81 0. 0. 0.
time (sec) N/A 0.058 0.046 0.04 1.341 0. 0. 0.
Problem 191 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 65 65 65 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.051 0.024 1.768 0. 0. 0. 0.
Problem 192 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 114 114 118 0 0 0 0 0
normalized size 1 1. 1.04 0. 0. 0. 0. 0.
time (sec) N/A 0.107 0.151 1.508 0. 0. 0. 0.
Problem 193 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 136 136 142 0 0 0 0 0
normalized size 1 1. 1.04 0. 0. 0. 0. 0.
time (sec) N/A 0.168 0.227 19.344 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 [117] 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 1 1 1. 8 0.125
2 A 1 1 1. 8 0.125
3 A 1 1 1. 6 0.167
4 A 1 1 1. 4 0.25
5 A 1 1 1. 8 0.125
6 A 1 1 1. 8 0.125
7 A 1 1 1. 8 0.125
8 A 2 2 1. 10 0.2
9 A 2 2 1. 10 0.2
10 A 2 2 1. 8 0.25
11 A 2 2 1. 6 0.333
12 A 2 2 1. 10 0.2
13 A 2 2 1. 10 0.2
14 A 2 2 1. 10 0.2
15 A 3 2 1. 10 0.2
16 A 3 2 1. 10 0.2
17 A 3 2 1. 8 0.25
18 A 3 2 1. 6 0.333
19 A 2 2 1. 10 0.2
20 A 3 2 1. 10 0.2
21 A 3 2 1. 10 0.2
22 A 2 2 1. 10 0.2
23 A 2 2 1. 10 0.2
24 A 2 2 1. 8 0.25
25 A 1 1 1. 6 0.167
26 A 2 2 1. 10 0.2
27 A 2 2 1. 10 0.2
28 A 2 2 1. 10 0.2
29 A 3 3 1. 10 0.3
30 A 3 3 1. 10 0.3
31 A 3 3 1. 8 0.375
32 A 2 2 1. 6 0.333
33 A 2 2 1. 10 0.2
34 A 3 3 1. 10 0.3
35 A 3 3 1. 10 0.3
36 A 4 3 1. 10 0.3
37 A 4 3 1. 10 0.3
38 A 4 3 1. 8 0.375
39 A 3 2 1. 6 0.333
40 A 2 2 1. 10 0.2
41 A 4 3 1. 10 0.3
42 A 4 3 1. 10 0.3
43 A 1 1 1. 14 0.071
44 A 1 1 1. 14 0.071
45 A 1 1 1. 12 0.083
46 A 2 1 1. 10 0.1
47 A 1 1 1. 14 0.071
48 A 1 1 1. 14 0.071
49 A 1 1 1. 14 0.071
50 A 2 2 1. 16 0.125
51 A 2 2 1. 16 0.125
52 A 2 2 1. 14 0.143
53 A 3 2 1. 12 0.167
54 A 2 2 1. 16 0.125
55 A 2 2 1. 16 0.125
56 A 2 2 1. 16 0.125
57 A 3 2 1. 16 0.125
58 A 3 2 1. 16 0.125
59 A 3 2 1. 14 0.143
60 A 4 2 1. 12 0.167
61 A 2 2 1. 16 0.125
62 A 3 2 1. 16 0.125
63 A 3 2 1. 16 0.125
64 A 3 2 1. 16 0.125
65 A 2 2 1. 16 0.125
66 A 2 2 1. 16 0.125
67 A 2 2 1. 14 0.143
68 A 2 2 1. 12 0.167
69 A 2 2 1. 16 0.125
70 A 2 2 1. 16 0.125
71 A 2 2 1. 16 0.125
72 A 2 2 1. 16 0.125
73 A 3 3 1. 16 0.188
74 A 3 3 1. 16 0.188
75 A 3 3 1. 14 0.214
76 A 3 3 1. 12 0.25
77 A 2 2 1. 16 0.125
78 A 3 3 1. 16 0.188
79 A 3 3 1. 16 0.188
80 A 3 3 1. 16 0.188
81 A 4 3 1. 16 0.188
82 A 4 3 1. 16 0.188
83 A 4 3 1. 14 0.214
84 A 4 3 1. 12 0.25
85 A 2 2 1. 16 0.125
86 A 4 3 1. 16 0.188
87 A 4 3 1. 16 0.188
88 A 4 3 1. 16 0.188
89 A 1 1 1. 18 0.056
90 A 1 1 1. 18 0.056
91 A 1 1 1. 18 0.056
92 A 1 1 1. 18 0.056
93 A 1 1 1. 18 0.056
94 A 1 1 1. 18 0.056
95 A 2 2 1. 20 0.1
96 A 2 2 1. 20 0.1
97 A 2 2 1. 20 0.1
98 A 2 2 1. 20 0.1
99 A 2 2 1. 20 0.1
100 A 2 2 1. 20 0.1
101 A 2 2 1. 20 0.1
102 A 2 2 1. 20 0.1
103 A 2 2 1. 20 0.1
104 A 2 2 1. 20 0.1
105 A 2 2 1. 20 0.1
106 A 2 2 1. 20 0.1
107 A 3 3 1. 20 0.15
108 A 3 3 1. 20 0.15
109 A 3 3 1. 20 0.15
110 A 3 3 1. 20 0.15
111 A 3 3 1. 20 0.15
112 A 3 3 1. 20 0.15
113 A 4 4 1. 14 0.286
114 A 4 4 1. 14 0.286
115 A 4 4 1. 14 0.286
116 A 4 4 1. 12 0.333
117 A 4 4 1. 10 0.4
118 A 2 2 1. 14 0.143
119 A 4 4 1. 14 0.286
120 A 4 4 1. 14 0.286
121 A 5 4 1. 14 0.286
122 A 5 4 1. 14 0.286
123 A 5 4 1. 12 0.333
124 A 5 4 1. 10 0.4
125 A 2 2 1. 14 0.143
126 A 5 4 1. 14 0.286
127 A 5 4 1. 14 0.286
128 A 3 3 1. 14 0.214
129 A 3 3 1. 14 0.214
130 A 3 3 1. 12 0.25
131 A 3 3 1. 10 0.3
132 A 2 2 1. 14 0.143
133 A 3 3 1. 14 0.214
134 A 3 3 1. 14 0.214
135 A 4 4 1. 14 0.286
136 A 4 4 1. 14 0.286
137 A 4 4 1. 12 0.333
138 A 4 4 1. 10 0.4
139 A 2 2 1. 14 0.143
140 A 4 4 1. 14 0.286
141 A 4 4 1. 14 0.286
142 A 5 4 1. 14 0.286
143 A 5 4 1. 14 0.286
144 A 5 4 1. 12 0.333
145 A 5 4 1. 10 0.4
146 A 2 2 1. 14 0.143
147 A 5 4 1. 14 0.286
148 A 5 4 1. 14 0.286
149 A 1 1 1. 22 0.045
150 A 3 2 1. 18 0.111
151 A 2 2 1. 18 0.111
152 A 1 1 1. 16 0.062
153 A 2 2 1. 18 0.111
154 A 3 3 1. 18 0.167
155 A 4 3 1. 18 0.167
156 A 3 2 1. 16 0.125
157 A 2 2 1. 16 0.125
158 A 1 1 1. 14 0.071
159 A 3 3 1. 16 0.188
160 A 4 4 1. 16 0.25
161 A 5 4 1. 16 0.25
162 A 5 4 1. 14 0.286
163 A 4 4 1. 14 0.286
164 A 3 3 1. 14 0.214
165 A 4 4 1. 14 0.286
166 A 5 4 1. 14 0.286
167 A 2 2 1. 18 0.111
168 A 2 2 1. 16 0.125
169 A 2 2 1. 14 0.143
170 A 2 2 1. 12 0.167
171 A 2 2 1. 16 0.125
172 A 2 2 1. 16 0.125
173 A 2 2 1. 16 0.125
174 A 2 2 1. 16 0.125
175 A 2 2 1. 16 0.125
176 A 2 2 1. 14 0.143
177 A 2 2 1. 12 0.167
178 A 2 2 1. 10 0.2
179 A 2 2 1. 14 0.143
180 A 2 2 1. 14 0.143
181 A 2 2 1. 14 0.143
182 A 2 2 1. 14 0.143
183 A 2 2 1. 20 0.1
184 A 2 2 1. 18 0.111
185 A 2 2 1. 16 0.125
186 A 2 2 1. 14 0.143
187 A 2 2 1. 18 0.111
188 A 2 2 1. 18 0.111
189 A 2 2 1. 18 0.111
190 A 2 2 1. 18 0.111
191 A 2 2 1. 18 0.111
192 A 3 3 1. 20 0.15
193 A 4 3 1. 27 0.111

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