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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 }

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, 42, 43, 44, 45, 46, 47, 48, 49, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 99, 100, 101, 102, 103, 104, 106, 107, 108, 109, 110, 111, 112, 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, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174 }

B grade: { 50, 51, 83, 84, 105, 154 }

C grade: { 41, 98, 113, 175 }

F grade: { }

2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 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, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 171, 173, 174, 175 }

B grade: { 14, 17, 48, 50, 51, 114, 139, 158, 169, 170 }

C grade: { }

F grade: { 19, 172 }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 96, 97, 100, 101, 102, 103, 106, 107, 108, 109, 110, 111, 112, 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, 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, 170, 171, 172, 173

B grade: { 51, 83, 84, 113, 169 }

C grade: { }

F grade: { 19, 41, 62, 90, 98, 99, 104, 105, 141, 174, 175 }

2.1.5 FriCAS

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

B grade: { 16, 44, 45, 48, 50, 51, 61, 84, 88, 113, 114, 124, 131, 145, 146 }

C grade: { }

F grade: { 41, 156, 175 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 49, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 85, 86, 87, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 102, 106, 107, 108, 109, 110, 111, 112, 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, 145, 146, 147, 148, 149, 150, 152, 157, 158, 159, 160, 161, 166, 167, 168, 169, 170, 171, 172, 175 }

B grade: { 9, 17, 42, 47, 48, 50, 51, 90, 101, 114, 144 }

C grade: { 89, 156 }

F grade: { 19, 62, 83, 84, 88, 103, 104, 105, 113, 151, 153, 154, 155, 162, 163, 164, 165, 173, 174 }

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, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 46, 47, 48, 49, 50, 52, 53, 54, 56, 57, 58, 59, 60, 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, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 157, 158, 159, 160, 162, 163, 165, 166, 167, 168, 169, 170, 171, 173, 174 }

B grade: { 44, 45, 51, 55, 61, 113, 136, 155 }

C grade: { }

F grade: { 21, 41, 62, 98, 99, 156, 161, 164, 172, 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 A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 13 13 13 10 12 28 8 12
normalized size 1 1. 1. 0.77 0.92 2.15 0.62 0.92
time (sec) N/A 0.001 0.037 0.011 0.945 0.417 0.051 1.063
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 27 27 18 15 26 54 39 26
normalized size 1 1. 0.67 0.56 0.96 2. 1.44 0.96
time (sec) N/A 0.004 0.006 0.002 0.95 0.412 0.855 1.099
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 34 34 21 18 30 62 48 30
normalized size 1 1. 0.62 0.53 0.88 1.82 1.41 0.88
time (sec) N/A 0.005 0.006 0.003 0.938 0.418 1.197 1.066
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 27 27 18 15 26 43 61 26
normalized size 1 1. 0.67 0.56 0.96 1.59 2.26 0.96
time (sec) N/A 0.005 0.005 0.004 0.948 0.417 0.82 1.064
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 14 14 14 13 16 51 22 16
normalized size 1 1. 1. 0.93 1.14 3.64 1.57 1.14
time (sec) N/A 0.003 0.004 0.007 0.983 0.404 0.106 1.055
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 13 13 15 11 15 31 8 15
normalized size 1 1. 1.15 0.85 1.15 2.38 0.62 1.15
time (sec) N/A 0.006 0.004 0.062 0.98 0.455 0.058 1.104
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 23 23 16 13 20 49 92 20
normalized size 1 1. 0.7 0.57 0.87 2.13 4. 0.87
time (sec) N/A 0.004 0.005 0.002 0.932 0.415 0.855 1.141
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 8 8 8 7 8 27 8 14
normalized size 1 1. 1. 0.88 1. 3.38 1. 1.75
time (sec) N/A 0.013 0.005 0.007 0.942 0.435 0.06 1.081
Problem 9 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 16 16 16 13 16 54 29 16
normalized size 1 1. 1. 0.81 1. 3.38 1.81 1.
time (sec) N/A 0.023 0.012 0.013 0.947 0.46 0.296 1.085
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 6 6 6 7 8 22 5 8
normalized size 1 1. 1. 1.17 1.33 3.67 0.83 1.33
time (sec) N/A 0.018 0.013 0.027 0.946 0.433 0.414 1.076
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 12 12 12 11 14 36 12 8
normalized size 1 1. 1. 0.92 1.17 3. 1. 0.67
time (sec) N/A 0.028 0.013 0.046 0.931 0.457 0.616 1.094
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 28 10 11
normalized size 1 1. 1. 0.9 1.1 2.8 1. 1.1
time (sec) N/A 0.016 0.018 0.007 0.997 0.454 0.318 1.083
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 9 9 9 10 12 18 7 12
normalized size 1 1. 1. 1.11 1.33 2. 0.78 1.33
time (sec) N/A 0.011 0.014 0.005 0.946 0.465 17.818 1.07
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 15 15 15 32 15 28 10 15
normalized size 1 1. 1. 2.13 1. 1.87 0.67 1.
time (sec) N/A 0.003 0.003 0.006 0.96 0.419 0.249 1.072
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 23 23 16 13 20 49 34 20
normalized size 1 1. 0.7 0.57 0.87 2.13 1.48 0.87
time (sec) N/A 0.004 0.004 0.001 0.955 0.419 0.883 1.065
Problem 16 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 11 11 11 10 12 53 8 12
normalized size 1 1. 1. 0.91 1.09 4.82 0.73 1.09
time (sec) N/A 0.001 0.002 0.003 0.948 0.421 0.694 1.073
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 15 15 15 27 15 34 27 15
normalized size 1 1. 1. 1.8 1. 2.27 1.8 1.
time (sec) N/A 0.003 0.003 0.005 0.95 0.424 0.349 1.094
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 15 15 15 12 15 41 12 15
normalized size 1 1. 1. 0.8 1. 2.73 0.8 1.
time (sec) N/A 0.026 0.049 0.012 0.973 0.465 0.344 1.099
Problem 19 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 32 32 37 0 0 66 0 20
normalized size 1 1. 1.16 0. 0. 2.06 0. 0.62
time (sec) N/A 0.101 0.048 0.056 0. 0.556 0. 1.113
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 17 17 17 14 18 36 14 18
normalized size 1 1. 1. 0.82 1.06 2.12 0.82 1.06
time (sec) N/A 0.111 0.013 0.007 0.94 0.48 0.347 1.069
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 13 13 9 38 15 0
normalized size 1 1. 0.81 0.81 0.56 2.38 0.94 0.
time (sec) N/A 0.008 0.006 0.003 0.967 0.418 1.219 0.
Problem 22 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 27 7 11
normalized size 1 1. 1. 1.12 1.38 3.38 0.88 1.38
time (sec) N/A 0.009 0.002 0.005 0.972 0.451 0.194 1.071
Problem 23 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 15 18 20 43 17 20
normalized size 1 1. 0.88 1.06 1.18 2.53 1. 1.18
time (sec) N/A 0.021 0.013 0.005 0.958 0.452 0.321 1.068
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 19 24 27 55 26 27
normalized size 1 1. 0.83 1.04 1.17 2.39 1.13 1.17
time (sec) N/A 0.036 0.013 0.006 0.952 0.451 0.554 1.063
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 24 24 20 25 28 57 26 28
normalized size 1 1. 0.83 1.04 1.17 2.38 1.08 1.17
time (sec) N/A 0.036 0.012 0.004 0.96 0.452 0.57 1.07
Problem 26 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 7 8 20 5 8
normalized size 1 1. 1. 0.88 1. 2.5 0.62 1.
time (sec) N/A 0.007 0.001 0.001 0.952 0.451 0.055 1.095
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 18 18 19 61 24 19
normalized size 1 1. 0.78 0.78 0.83 2.65 1.04 0.83
time (sec) N/A 0.013 0.003 0.003 0.944 0.446 0.322 1.143
Problem 28 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 14 14 14 11 14 38 10 14
normalized size 1 1. 1. 0.79 1. 2.71 0.71 1.
time (sec) N/A 0.005 0.002 0.005 0.942 0.456 0.058 1.079
Problem 29 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 13 13 15 11 15 31 8 15
normalized size 1 1. 1.15 0.85 1.15 2.38 0.62 1.15
time (sec) N/A 0.006 0.001 0. 0.951 0.46 0.059 1.064
Problem 30 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 24 24 22 18 22 59 24 22
normalized size 1 1. 0.92 0.75 0.92 2.46 1. 0.92
time (sec) N/A 0.009 0.002 0.117 0.936 0.475 0.057 1.08
Problem 31 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 21 21 23 17 23 53 17 23
normalized size 1 1. 1.1 0.81 1.1 2.52 0.81 1.1
time (sec) N/A 0.007 0.002 0.03 0.956 0.481 0.06 1.071
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 34 34 30 24 32 84 36 30
normalized size 1 1. 0.88 0.71 0.94 2.47 1.06 0.88
time (sec) N/A 0.016 0.002 0.033 0.937 0.467 0.059 1.09
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 25 25 25 25 26 63 36 26
normalized size 1 1. 1. 1. 1.04 2.52 1.44 1.04
time (sec) N/A 0.014 0.011 0.005 0.952 0.455 0.325 1.102
Problem 34 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 33 33 31 23 31 74 39 31
normalized size 1 1. 0.94 0.7 0.94 2.24 1.18 0.94
time (sec) N/A 0.022 0.007 0.03 0.964 0.453 0.565 1.121
Problem 35 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 41 41 29 37 35 89 56 35
normalized size 1 1. 0.71 0.9 0.85 2.17 1.37 0.85
time (sec) N/A 0.031 0.032 0.02 0.966 0.456 0.665 1.078
Problem 36 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 14 14 14 11 14 36 10 14
normalized size 1 1. 1. 0.79 1. 2.57 0.71 1.
time (sec) N/A 0.006 0.002 0.005 0.931 0.454 0.057 1.097
Problem 37 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 11 11 15 11 12 36 8 12
normalized size 1 1. 1.36 1. 1.09 3.27 0.73 1.09
time (sec) N/A 0.006 0.001 0.026 0.95 0.454 0.058 1.125
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 24 24 22 18 22 59 24 22
normalized size 1 1. 0.92 0.75 0.92 2.46 1. 0.92
time (sec) N/A 0.011 0.002 0.03 0.963 0.46 0.056 1.081
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 84 84 62 69 84 132 182 68
normalized size 1 1. 0.74 0.82 1. 1.57 2.17 0.81
time (sec) N/A 0.015 0.067 0.006 1.437 0.441 3.843 1.106
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 38 38 25 22 46 58 39 38
normalized size 1 1. 0.66 0.58 1.21 1.53 1.03 1.
time (sec) N/A 0.013 0.006 0.003 1.431 0.425 1.241 1.084
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 172 172 34 168 0 0 31 0
normalized size 1 1. 0.2 0.98 0. 0. 0.18 0.
time (sec) N/A 0.029 0.005 0.098 0. 0. 0.61 0.
Problem 42 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 6 6 6 7 8 18 7 8
normalized size 1 1. 1. 1.17 1.33 3. 1.17 1.33
time (sec) N/A 0.004 0.005 0.004 1.442 0.446 0.058 1.077
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 14 14 18 13 16 36 19 16
normalized size 1 1. 1.29 0.93 1.14 2.57 1.36 1.14
time (sec) N/A 0.009 0.003 0.003 1.445 0.452 0.067 1.097
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 8 8 8 12 14 53 8 24
normalized size 1 1. 1. 1.5 1.75 6.62 1. 3.
time (sec) N/A 0.005 0.005 0.001 1.446 0.45 0.063 1.105
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 12 12 18 14 22 126 19 46
normalized size 1 1. 1.5 1.17 1.83 10.5 1.58 3.83
time (sec) N/A 0.01 0.003 0.003 1.419 0.451 0.067 1.129
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 22 22 26 21 27 55 26 24
normalized size 1 1. 1.18 0.95 1.23 2.5 1.18 1.09
time (sec) N/A 0.011 0.011 0.006 0.947 0.448 0.172 1.086
Problem 47 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 13 13 13 10 12 28 22 12
normalized size 1 1. 1. 0.77 0.92 2.15 1.69 0.92
time (sec) N/A 0.002 0.002 0.002 0.946 0.423 0.174 1.09
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 13 13 11 52 12 142 58 12
normalized size 1 1. 0.85 4. 0.92 10.92 4.46 0.92
time (sec) N/A 0.001 0.001 0.001 0.956 0.358 0.056 1.13
Problem 49 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 16 20 26 50 15 19
normalized size 1 1. 0.89 1.11 1.44 2.78 0.83 1.06
time (sec) N/A 0.002 0.003 0.004 0.959 0.408 0.096 1.072
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B A B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 11 11 43 32 12 88 31 12
normalized size 1 1. 3.91 2.91 1.09 8. 2.82 1.09
time (sec) N/A 0.002 0.001 0.001 0.949 0.357 0.051 1.093
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 56 56 140 107 143 373 131 143
normalized size 1 1. 2.5 1.91 2.55 6.66 2.34 2.55
time (sec) N/A 0.025 0.002 0.002 0.938 0.352 0.072 1.098
Problem 52 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 4 4 4 5 5 14 3 5
normalized size 1 1. 1. 1.25 1.25 3.5 0.75 1.25
time (sec) N/A 0.008 0.008 0.003 0.98 0.447 0.655 1.083
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 62 62 46 49 50 134 60 50
normalized size 1 1. 0.74 0.79 0.81 2.16 0.97 0.81
time (sec) N/A 0.043 0.029 0.005 0.969 0.512 2.368 1.109
Problem 54 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 7 11
normalized size 1 1. 1. 0.9 1.1 2.3 0.7 1.1
time (sec) N/A 0.007 0.002 0.003 0.96 0.517 0.301 1.109
Problem 55 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 16 16 16 13 16 39 15 248
normalized size 1 1. 1. 0.81 1. 2.44 0.94 15.5
time (sec) N/A 0.031 0.011 0.018 0.95 0.52 2.322 1.116
Problem 56 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 24 7 12
normalized size 1 1. 1. 0.9 1.1 2.4 0.7 1.2
time (sec) N/A 0.001 0.001 0.002 0.978 0.464 0.052 1.079
Problem 57 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 16 42 15 20
normalized size 1 1. 1. 1.07 1.07 2.8 1. 1.33
time (sec) N/A 0.004 0.001 0.003 0.952 0.508 0.089 1.068
Problem 58 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 35 12 18
normalized size 1 1. 1. 0.82 1.06 2.06 0.71 1.06
time (sec) N/A 0.003 0.001 0.002 0.953 0.511 0.085 1.087
Problem 59 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 23 23 61 22 30
normalized size 1 1. 1. 0.82 0.82 2.18 0.79 1.07
time (sec) N/A 0.009 0.001 0. 0.961 0.538 0.095 1.09
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 4 4 4 5 5 16 3 7
normalized size 1 1. 1. 1.25 1.25 4. 0.75 1.75
time (sec) N/A 0. 0.001 0. 0.947 0.48 0.055 1.102
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 3 3 3 4 4 41 3 15
normalized size 1 1. 1. 1.33 1.33 13.67 1. 5.
time (sec) N/A 0.003 0.002 0.001 0.952 0.502 0.06 1.09
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 28 28 21 36 0 85 0 0
normalized size 1 1. 0.75 1.29 0. 3.04 0. 0.
time (sec) N/A 0.01 0.005 0.013 0. 0.519 0. 0.
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 28 28 28 23 23 62 26 30
normalized size 1 1. 1. 0.82 0.82 2.21 0.93 1.07
time (sec) N/A 0.017 0.001 0.002 0.947 0.534 0.097 1.087
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 3 3 3 4 4 18 3 5
normalized size 1 1. 1. 1.33 1.33 6. 1. 1.67
time (sec) N/A 0.012 0.004 0. 1.014 0.494 0.087 1.104
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 12 12 12 11 14 27 8 14
normalized size 1 1. 1. 0.92 1.17 2.25 0.67 1.17
time (sec) N/A 0.015 0.002 0.002 0.962 0.516 0.084 1.063
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 16 18 23 47 20 23
normalized size 1 1. 0.7 0.78 1. 2.04 0.87 1.
time (sec) N/A 0.038 0.015 0.005 0.94 0.479 3.886 1.107
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 39 39 39 32 31 92 37 42
normalized size 1 1. 1. 0.82 0.79 2.36 0.95 1.08
time (sec) N/A 0.03 0.001 0.002 0.926 0.501 0.126 1.102
Problem 68 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 9 9 9 7 8 18 5 8
normalized size 1 1. 1. 0.78 0.89 2. 0.56 0.89
time (sec) N/A 0.012 0.001 0.002 0.952 0.49 0.082 1.102
Problem 69 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 14 14 14 12 16 27 10 15
normalized size 1 1. 1. 0.86 1.14 1.93 0.71 1.07
time (sec) N/A 0.009 0.003 0.003 0.929 0.512 0.142 1.075
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 10 10 10 8 9 24 7 9
normalized size 1 1. 1. 0.8 0.9 2.4 0.7 0.9
time (sec) N/A 0.009 0.007 0.005 0.936 0.51 0.293 1.069
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 19 19 14 14 15 46 15 15
normalized size 1 1. 0.74 0.74 0.79 2.42 0.79 0.79
time (sec) N/A 0.007 0.012 0.003 0.954 0.567 0.301 1.106
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 19 19 12 14 12 45 15 12
normalized size 1 1. 0.63 0.74 0.63 2.37 0.79 0.63
time (sec) N/A 0.007 0.008 0.005 1.047 0.497 0.286 1.099
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 10 10 10 12 12 24 7 12
normalized size 1 1. 1. 1.2 1.2 2.4 0.7 1.2
time (sec) N/A 0.006 0.003 0.006 0.961 0.478 0.071 1.08
Problem 74 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 11 11 7 7 8 18 5 8
normalized size 1 1. 0.64 0.64 0.73 1.64 0.45 0.73
time (sec) N/A 0.005 0.001 0. 0.967 0.525 0.074 1.097
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 11 10 12 23 7 12
normalized size 1 1. 0.69 0.62 0.75 1.44 0.44 0.75
time (sec) N/A 0.007 0.004 0.001 0.952 0.516 0.081 1.089
Problem 76 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 12 12 15 28 10 15
normalized size 1 1. 0.63 0.63 0.79 1.47 0.53 0.79
time (sec) N/A 0.015 0.004 0.002 0.957 0.513 0.075 1.083
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 32 32 19 19 22 45 17 22
normalized size 1 1. 0.59 0.59 0.69 1.41 0.53 0.69
time (sec) N/A 0.018 0.006 0.002 0.962 0.487 0.081 1.081
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 24 24 16 17 15 36 20 15
normalized size 1 1. 0.67 0.71 0.62 1.5 0.83 0.62
time (sec) N/A 0.008 0.005 0.003 0.95 0.493 0.174 1.08
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 26 26 16 14 18 34 12 18
normalized size 1 1. 0.62 0.54 0.69 1.31 0.46 0.69
time (sec) N/A 0.02 0.002 0.002 0.943 0.506 0.083 1.09
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 41 41 28 40 36 74 139 49
normalized size 1 1. 0.68 0.98 0.88 1.8 3.39 1.2
time (sec) N/A 0.011 0.025 0.01 0.967 0.559 1.323 1.089
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 42 42 29 41 39 76 136 51
normalized size 1 1. 0.69 0.98 0.93 1.81 3.24 1.21
time (sec) N/A 0.011 0.024 0.003 0.936 0.507 1.365 1.065
Problem 82 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 43 12 20
normalized size 1 1. 1. 0.93 1.2 2.87 0.8 1.33
time (sec) N/A 0.003 0.001 0. 0.931 0.514 0.186 1.082
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 19 19 64 22 47 103 0 34
normalized size 1 1. 3.37 1.16 2.47 5.42 0. 1.79
time (sec) N/A 0.009 0.064 0.002 0.929 0.626 0. 1.105
Problem 84 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 17 17 64 20 47 103 0 35
normalized size 1 1. 3.76 1.18 2.76 6.06 0. 2.06
time (sec) N/A 0.009 0.039 0.002 0.928 0.554 0. 1.099
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 25 25 25 24 31 68 22 31
normalized size 1 1. 1. 0.96 1.24 2.72 0.88 1.24
time (sec) N/A 0.034 0.007 0.037 1.424 0.504 0.184 1.112
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 22 22 22 21 45 105 22 51
normalized size 1 1. 1. 0.95 2.05 4.77 1. 2.32
time (sec) N/A 0.016 0.002 0.003 1.458 0.631 1.784 1.123
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 16 15 11 50 20 12
normalized size 1 1. 1. 0.94 0.69 3.12 1.25 0.75
time (sec) N/A 0.002 0.002 0.003 1.426 0.509 1.01 1.119
Problem 88 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 10 10 14 10 15 55 0 12
normalized size 1 1. 1.4 1. 1.5 5.5 0. 1.2
time (sec) N/A 0.009 0.005 0.003 1.432 0.51 0. 1.091
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A C A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 10 10 10 11 14 20 20 14
normalized size 1 1. 1. 1.1 1.4 2. 2. 1.4
time (sec) N/A 0.002 0.002 0.002 1.444 0.495 0.106 1.075
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 24 24 24 16 0 151 53 20
normalized size 1 1. 1. 0.67 0. 6.29 2.21 0.83
time (sec) N/A 0.004 0.005 0.002 0. 0.5 0.125 1.109
Problem 91 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 17 22 58 26 22
normalized size 1 1. 1. 0.89 1.16 3.05 1.37 1.16
time (sec) N/A 0.009 0.005 0.001 1.439 0.479 0.121 1.083
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 21 21 21 16 20 45 15 20
normalized size 1 1. 1. 0.76 0.95 2.14 0.71 0.95
time (sec) N/A 0.008 0.002 0.003 1.458 0.516 0.257 1.123
Problem 93 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 40 40 30 34 45 68 32 45
normalized size 1 1. 0.75 0.85 1.12 1.7 0.8 1.12
time (sec) N/A 0.022 0.01 0.003 1.453 0.548 0.331 1.093
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 35 35 26 30 46 81 29 39
normalized size 1 1. 0.74 0.86 1.31 2.31 0.83 1.11
time (sec) N/A 0.056 0.007 0.009 1.468 0.523 0.352 1.079
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 22 22 18 17 22 47 19 22
normalized size 1 1. 0.82 0.77 1. 2.14 0.86 1.
time (sec) N/A 0.005 0.005 0.003 1.443 0.544 1.354 1.105
Problem 96 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 7 8 26 7 8
normalized size 1 1. 1. 0.88 1. 3.25 0.88 1.
time (sec) N/A 0.03 0.006 0.004 0.937 0.52 2.047 1.075
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 20 18 23 74 15 23
normalized size 1 1. 0.87 0.78 1. 3.22 0.65 1.
time (sec) N/A 0.003 0.005 0.003 1.454 0.514 0.193 1.147
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F A A F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 22 22 37 16 0 53 31 0
normalized size 1 1. 1.68 0.73 0. 2.41 1.41 0.
time (sec) N/A 0.041 0.01 0.003 0. 0.664 119.363 0.
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 20 20 20 16 0 53 31 0
normalized size 1 1. 1. 0.8 0. 2.65 1.55 0.
time (sec) N/A 0.023 0.005 0.003 0. 0.93 117.73 0.
Problem 100 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 55 12 20
normalized size 1 1. 1. 0.84 1.05 2.89 0.63 1.05
time (sec) N/A 0.004 0.004 0.007 1.443 0.632 0.094 1.123
Problem 101 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 4 4 4 4 4 18 15 4
normalized size 1 1. 1. 1. 1. 4.5 3.75 1.
time (sec) N/A 0.016 0.003 0.003 1.434 0.746 0.107 1.07
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 27 25 26 84 19 28
normalized size 1 1. 1. 0.93 0.96 3.11 0.7 1.04
time (sec) N/A 0.018 0.016 0.005 0.967 0.853 12.155 1.083
Problem 103 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 42 42 78 64 66 90 0 49
normalized size 1 1. 1.86 1.52 1.57 2.14 0. 1.17
time (sec) N/A 0.013 0.037 0.013 1.411 0.832 0. 1.111
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 71 71 106 122 0 209 0 82
normalized size 1 1. 1.49 1.72 0. 2.94 0. 1.15
time (sec) N/A 0.022 0.146 0.011 0. 0.887 0. 1.09
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A F(-2) A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 32 32 72 28 0 111 0 30
normalized size 1 1. 2.25 0.88 0. 3.47 0. 0.94
time (sec) N/A 0.012 0.025 0.003 0. 0.746 0. 1.126
Problem 106 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 12 20
normalized size 1 1. 1. 0.93 1.2 2.6 0.8 1.33
time (sec) N/A 0.004 0.003 0.005 0.929 0.673 0.093 1.074
Problem 107 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 14 18 45 14 20
normalized size 1 1. 1. 0.74 0.95 2.37 0.74 1.05
time (sec) N/A 0.004 0.003 0.004 0.931 0.636 0.096 1.067
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 23 20 26 58 19 28
normalized size 1 1. 1. 0.87 1.13 2.52 0.83 1.22
time (sec) N/A 0.027 0.004 0.004 0.944 0.727 0.103 1.073
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 23 18 23 61 17 27
normalized size 1 1. 1. 0.78 1. 2.65 0.74 1.17
time (sec) N/A 0.033 0.005 0.007 0.929 0.655 0.127 1.097
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 24 24 22 19 24 84 19 32
normalized size 1 1. 0.92 0.79 1. 3.5 0.79 1.33
time (sec) N/A 0.014 0.008 0.007 0.948 0.666 0.105 1.09
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 28 28 28 29 38 101 3 39
normalized size 1 1. 1. 1.04 1.36 3.61 0.11 1.39
time (sec) N/A 0.028 0.01 0.005 1.443 0.789 0.116 1.093
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 61 37 49 154 14 50
normalized size 1 1. 1.24 0.76 1. 3.14 0.29 1.02
time (sec) N/A 0.067 0.027 0.009 1.481 0.759 0.156 1.079
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A B B F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 21 21 24 19 53 126 0 50
normalized size 1 1. 1.14 0.9 2.52 6. 0. 2.38
time (sec) N/A 0.009 0.018 0.022 1.448 0.72 0. 1.149
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 16 266 19 144 44 19
normalized size 1 1. 1. 16.62 1.19 9. 2.75 1.19
time (sec) N/A 0.045 0.027 0.043 1.015 0.824 2.642 1.109
Problem 115 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 11 11 9 9 12 28 8 15
normalized size 1 1. 0.82 0.82 1.09 2.55 0.73 1.36
time (sec) N/A 0.004 0.003 0.001 0.99 0.798 0.081 1.067
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 23 20 26 66 20 30
normalized size 1 1. 1. 0.87 1.13 2.87 0.87 1.3
time (sec) N/A 0.008 0.005 0.006 0.969 0.877 0.115 1.077
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 30 30 28 21 27 86 22 30
normalized size 1 1. 0.93 0.7 0.9 2.87 0.73 1.
time (sec) N/A 0.017 0.008 0.007 0.967 0.78 0.098 1.065
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 27 27 27 24 31 68 20 35
normalized size 1 1. 1. 0.89 1.15 2.52 0.74 1.3
time (sec) N/A 0.031 0.005 0.006 0.944 0.66 0.114 1.092
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 24 24 27 76 17 22
normalized size 1 1. 1.04 1.04 1.17 3.3 0.74 0.96
time (sec) N/A 0.026 0.009 0.007 0.939 0.745 0.104 1.156
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 16 15 19 45 14 20
normalized size 1 1. 1. 0.94 1.19 2.81 0.88 1.25
time (sec) N/A 0.017 0.004 0.003 1.406 0.748 0.085 1.089
Problem 121 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 13 16 53 14 16
normalized size 1 1. 1. 0.72 0.89 2.94 0.78 0.89
time (sec) N/A 0.012 0.006 0.007 1.422 0.709 0.133 1.077
Problem 122 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 11 11 11 12 15 32 8 18
normalized size 1 1. 1. 1.09 1.36 2.91 0.73 1.64
time (sec) N/A 0.005 0.002 0.005 0.933 0.717 0.087 1.097
Problem 123 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 24 24 24 21 32 89 19 39
normalized size 1 1. 1. 0.88 1.33 3.71 0.79 1.62
time (sec) N/A 0.01 0.007 0.009 0.972 0.756 0.095 1.096
Problem 124 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 46 46 44 39 62 239 46 70
normalized size 1 1. 0.96 0.85 1.35 5.2 1. 1.52
time (sec) N/A 0.013 0.014 0.01 0.937 0.79 0.18 1.122
Problem 125 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 14 46 8 15
normalized size 1 1. 1. 1.1 1.4 4.6 0.8 1.5
time (sec) N/A 0.004 0.002 0.005 0.927 0.665 0.076 1.118
Problem 126 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 18 23 36 10 22
normalized size 1 1. 1. 1.06 1.35 2.12 0.59 1.29
time (sec) N/A 0.007 0.002 0.006 0.929 0.877 0.083 1.078
Problem 127 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 15 19 50 17 22
normalized size 1 1. 1. 0.75 0.95 2.5 0.85 1.1
time (sec) N/A 0.008 0.003 0.005 0.933 0.963 0.096 1.111
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 12 13 16 46 8 18
normalized size 1 1. 0.75 0.81 1. 2.88 0.5 1.12
time (sec) N/A 0.005 0.003 0.003 0.962 1.147 0.075 1.077
Problem 129 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 14 14 14 15 19 51 10 19
normalized size 1 1. 1. 1.07 1.36 3.64 0.71 1.36
time (sec) N/A 0.01 0.007 0.005 1.427 1.061 0.125 1.097
Problem 130 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 21 21 21 18 23 61 20 27
normalized size 1 1. 1. 0.86 1.1 2.9 0.95 1.29
time (sec) N/A 0.018 0.004 0.005 0.957 1.156 0.123 1.106
Problem 131 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 21 21 27 28 31 90 20 34
normalized size 1 1. 1.29 1.33 1.48 4.29 0.95 1.62
time (sec) N/A 0.003 0.006 0.007 0.969 1.248 0.097 1.094
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 22 22 22 17 22 54 17 23
normalized size 1 1. 1. 0.77 1. 2.45 0.77 1.05
time (sec) N/A 0.011 0.003 0.004 1.43 0.974 0.086 1.116
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 10 10 10 11 19 46 8 19
normalized size 1 1. 1. 1.1 1.9 4.6 0.8 1.9
time (sec) N/A 0.015 0.004 0.006 0.935 1.125 0.095 1.098
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 31 22 26 66 19 28
normalized size 1 1. 1. 0.71 0.84 2.13 0.61 0.9
time (sec) N/A 0.009 0.002 0.006 0.937 1.13 0.101 1.068
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 18 18 18 17 22 59 15 23
normalized size 1 1. 1. 0.94 1.22 3.28 0.83 1.28
time (sec) N/A 0.025 0.005 0.006 1.422 1.057 0.11 1.114
Problem 136 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 13 13 25 10 23 68 17 26
normalized size 1 1. 1.92 0.77 1.77 5.23 1.31 2.
time (sec) N/A 0.003 0.003 0.001 1.437 0.99 0.118 1.114
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 85 85 64 58 97 302 73 97
normalized size 1 1. 0.75 0.68 1.14 3.55 0.86 1.14
time (sec) N/A 0.039 0.017 0.003 1.422 1.207 0.137 1.085
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 15 16 20 72 14 20
normalized size 1 1. 0.65 0.7 0.87 3.13 0.61 0.87
time (sec) N/A 0.007 0.007 0.005 1.412 1.011 0.104 1.086
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 11 11 11 41 15 24 8 15
normalized size 1 1. 1. 3.73 1.36 2.18 0.73 1.36
time (sec) N/A 0.006 0.006 0.008 0.933 1.015 0.12 1.124
Problem 140 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 23 20 31 126 39 63
normalized size 1 1. 0.51 0.44 0.69 2.8 0.87 1.4
time (sec) N/A 0.024 0.024 0.035 1.417 1.106 0.495 1.092
Problem 141 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 37 37 31 30 0 306 110 72
normalized size 1 1. 0.84 0.81 0. 8.27 2.97 1.95
time (sec) N/A 0.018 0.023 0.012 0. 1.168 5.919 1.093
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 56 56 20 16 50 155 36 47
normalized size 1 1. 0.36 0.29 0.89 2.77 0.64 0.84
time (sec) N/A 0.015 0.012 0.007 1.415 1.037 0.353 1.164
Problem 143 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 31 31 20 16 26 84 32 54
normalized size 1 1. 0.65 0.52 0.84 2.71 1.03 1.74
time (sec) N/A 0.011 0.01 0.013 1.417 1.181 0.281 1.081
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 36 36 18 15 19 105 581 65
normalized size 1 1. 0.5 0.42 0.53 2.92 16.14 1.81
time (sec) N/A 0.038 0.029 0.019 1.45 1.211 64.55 1.091
Problem 145 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 15 15 15 16 20 99 2866 35
normalized size 1 1. 1. 1.07 1.33 6.6 191.07 2.33
time (sec) N/A 0.023 0.039 0.04 1.427 1.163 40.991 1.189
Problem 146 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 19 95 228 18
normalized size 1 1. 1. 0.82 1.12 5.59 13.41 1.06
time (sec) N/A 0.012 0.028 0.077 0.952 1.004 123.877 1.105
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 30 30 22 25 55 39 22 34
normalized size 1 1. 0.73 0.83 1.83 1.3 0.73 1.13
time (sec) N/A 0.029 0.034 0.048 1.418 1.028 0.297 1.104
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 29 23 30 72 24 30
normalized size 1 1. 1. 0.79 1.03 2.48 0.83 1.03
time (sec) N/A 0.004 0.007 0.003 1.426 0.995 0.193 1.137
Problem 149 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 13 13 13 12 15 23 8 15
normalized size 1 1. 1. 0.92 1.15 1.77 0.62 1.15
time (sec) N/A 0.002 0.001 0.002 0.928 1.062 0.143 1.097
Problem 150 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 33 30 55 104 88 63
normalized size 1 1. 0.89 0.81 1.49 2.81 2.38 1.7
time (sec) N/A 0.02 0.007 0.004 1.424 1.129 1.379 1.091
Problem 151 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 22 22 31 22 34 72 0 35
normalized size 1 1. 1.41 1. 1.55 3.27 0. 1.59
time (sec) N/A 0.007 0.014 0.004 0.947 1.079 0. 1.106
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 27 21 27 69 24 34
normalized size 1 1. 1. 0.78 1. 2.56 0.89 1.26
time (sec) N/A 0.003 0.006 0.003 1.415 1.059 0.19 1.092
Problem 153 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 27 27 27 21 30 82 0 36
normalized size 1 1. 1. 0.78 1.11 3.04 0. 1.33
time (sec) N/A 0.011 0.004 0.004 1.395 1.009 0. 1.089
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 14 14 29 12 20 46 0 24
normalized size 1 1. 2.07 0.86 1.43 3.29 0. 1.71
time (sec) N/A 0.003 0.005 0.003 0.942 1.238 0. 1.114
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 68 68 68 88 80 232 0 227
normalized size 1 1. 1. 1.29 1.18 3.41 0. 3.34
time (sec) N/A 0.037 0.027 0.005 1.452 1.127 0. 1.134
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A F C F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 13 13 13 13 16 0 58 0
normalized size 1 1. 1. 1. 1.23 0. 4.46 0.
time (sec) N/A 0.015 0.002 0.002 0.943 0. 2.348 0.
Problem 157 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 15 3 11 2 3
normalized size 1 1. 1. 1. 0.2 0.73 0.13 0.2
time (sec) N/A 0.01 0.009 0.012 0.928 1.074 0.183 1.121
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 2 2 2 8 3 9 2 3
normalized size 1 1. 1. 4. 1.5 4.5 1. 1.5
time (sec) N/A 0.01 0.005 0.002 1.03 1.093 0.732 1.101
Problem 159 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 4 4 4 9 5 12 3 5
normalized size 1 1. 1. 2.25 1.25 3. 0.75 1.25
time (sec) N/A 0.012 0.006 0.003 1.03 0.998 0.781 1.077
Problem 160 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 11 11 11 16 7 26 7 18
normalized size 1 1. 1. 1.45 0.64 2.36 0.64 1.64
time (sec) N/A 0.02 0.007 0.002 1.022 1.043 0.965 1.102
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 14 14 14 15 12 28 10 0
normalized size 1 1. 1. 1.07 0.86 2. 0.71 0.
time (sec) N/A 0.012 0.002 0.002 1.022 0.999 1.065 0.
Problem 162 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 15 15 15 17 22 35 0 19
normalized size 1 1. 1. 1.13 1.47 2.33 0. 1.27
time (sec) N/A 0.015 0.012 0.006 1.039 1.148 0. 1.083
Problem 163 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 14 18 32 0 14
normalized size 1 1. 1. 1.08 1.38 2.46 0. 1.08
time (sec) N/A 0.065 0.018 0.006 1.035 1.122 0. 1.128
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 19 19 19 22 22 65 0 0
normalized size 1 1. 1. 1.16 1.16 3.42 0. 0.
time (sec) N/A 0.023 0.019 0.003 1.032 1.1 0. 0.
Problem 165 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 18 18 18 19 24 58 0 22
normalized size 1 1. 1. 1.06 1.33 3.22 0. 1.22
time (sec) N/A 0.02 0.008 0.02 1.04 1.169 0. 1.134
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 11 10 12 23 7 12
normalized size 1 1. 0.69 0.62 0.75 1.44 0.44 0.75
time (sec) N/A 0.009 0.004 0.002 0.942 1.155 0.074 1.094
Problem 167 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 16 15 19 34 12 19
normalized size 1 1. 0.62 0.58 0.73 1.31 0.46 0.73
time (sec) N/A 0.021 0.005 0.002 0.946 1.075 0.079 1.096
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 36 36 21 20 26 45 17 26
normalized size 1 1. 0.58 0.56 0.72 1.25 0.47 0.72
time (sec) N/A 0.034 0.006 0.001 0.94 1.191 0.081 1.088
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 48 48 39 111 244 144 360 104
normalized size 1 1. 0.81 2.31 5.08 3. 7.5 2.17
time (sec) N/A 0.034 0.095 0.079 1.442 1.284 2.493 1.118
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 2 2 2 9 4 23 2 4
normalized size 1 1. 1. 4.5 2. 11.5 1. 2.
time (sec) N/A 0.002 0.017 0.003 1.031 1.037 0.461 1.082
Problem 171 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 17 8 50 7 15
normalized size 1 1. 1. 1.7 0.8 5. 0.7 1.5
time (sec) N/A 0.004 0.001 0.002 1.023 1.324 0.472 1.086
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 22 22 22 0 30 47 24 0
normalized size 1 1. 1. 0. 1.36 2.14 1.09 0.
time (sec) N/A 0.017 0.011 0.02 1.038 1.156 4.908 0.
Problem 173 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 12 12 10 12 15 23 0 12
normalized size 1 1. 0.83 1. 1.25 1.92 0. 1.
time (sec) N/A 0.015 0.013 0.003 1.036 1.127 0. 1.086
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 22 22 22 23 0 47 0 27
normalized size 1 1. 1. 1.05 0. 2.14 0. 1.23
time (sec) N/A 0.056 0.033 0.006 0. 1.134 0. 1.095
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 103 103 17 116 0 0 27 0
normalized size 1 1. 0.17 1.13 0. 0. 0.26 0.
time (sec) N/A 0.008 0.002 0.039 0. 0. 0.531 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 [83] had the largest ratio of [ 2. ]

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. 9 0.111
2 A 2 1 1. 11 0.091
3 A 2 1 1. 11 0.091
4 A 2 1 1. 11 0.091
5 A 1 1 1. 14 0.071
6 A 2 1 1. 4 0.25
7 A 2 1 1. 9 0.111
8 A 2 2 1. 7 0.286
9 A 2 2 1. 17 0.118
10 A 2 2 1. 9 0.222
11 A 3 3 1. 11 0.273
12 A 3 3 1. 16 0.188
13 A 2 2 1. 10 0.2
14 A 1 1 1. 15 0.067
15 A 2 1 1. 9 0.111
16 A 1 1 1. 9 0.111
17 A 1 1 1. 15 0.067
18 A 1 1 1. 17 0.059
19 A 3 2 1. 20 0.1
20 A 1 1 1. 26 0.038
21 A 2 2 1. 20 0.1
22 A 2 2 1. 4 0.5
23 A 3 2 1. 6 0.333
24 A 4 2 1. 6 0.333
25 A 4 2 1. 6 0.333
26 A 2 2 1. 5 0.4
27 A 3 3 1. 6 0.5
28 A 2 2 1. 4 0.5
29 A 2 1 1. 4 0.25
30 A 3 2 1. 4 0.5
31 A 2 1 1. 4 0.25
32 A 4 2 1. 4 0.5
33 A 2 2 1. 6 0.333
34 A 3 3 1. 6 0.5
35 A 4 4 1. 8 0.5
36 A 2 2 1. 4 0.5
37 A 2 1 1. 4 0.25
38 A 3 2 1. 4 0.5
39 A 5 3 1. 13 0.231
40 A 3 2 1. 13 0.154
41 A 2 2 1. 13 0.154
42 A 2 2 1. 4 0.5
43 A 3 2 1. 4 0.5
44 A 2 2 1. 4 0.5
45 A 3 2 1. 4 0.5
46 A 2 2 1. 10 0.2
47 A 1 1 1. 11 0.091
48 A 1 1 1. 9 0.111
49 A 1 1 1. 13 0.077
50 A 1 1 1. 11 0.091
51 A 2 1 1. 11 0.091
52 A 2 2 1. 8 0.25
53 A 5 3 1. 8 0.375
54 A 1 1 1. 10 0.1
55 A 3 2 1. 17 0.118
56 A 1 1 1. 7 0.143
57 A 2 2 1. 4 0.5
58 A 1 1 1. 4 0.25
59 A 2 2 1. 6 0.333
60 A 1 1 1. 5 0.2
61 A 1 1 1. 2 0.5
62 A 1 1 1. 8 0.125
63 A 2 2 1. 8 0.25
64 A 2 2 1. 8 0.25
65 A 2 2 1. 14 0.143
66 A 3 2 1. 14 0.143
67 A 3 2 1. 8 0.25
68 A 1 1 1. 9 0.111
69 A 1 1 1. 13 0.077
70 A 2 2 1. 9 0.222
71 A 1 1 1. 6 0.167
72 A 1 1 1. 6 0.167
73 A 4 4 1. 7 0.571
74 A 2 2 1. 5 0.4
75 A 2 2 1. 7 0.286
76 A 3 2 1. 7 0.286
77 A 3 2 1. 9 0.222
78 A 3 3 1. 7 0.429
79 A 2 2 1. 11 0.182
80 A 1 1 1. 10 0.1
81 A 1 1 1. 10 0.1
82 A 2 2 1. 2 1.
83 A 4 4 1. 2 2.
84 A 4 4 1. 2 2.
85 A 3 3 1. 4 0.75
86 A 4 4 1. 6 0.667
87 A 2 2 1. 13 0.154
88 A 2 2 1. 14 0.143
89 A 1 1 1. 9 0.111
90 A 1 1 1. 9 0.111
91 A 2 2 1. 10 0.2
92 A 3 3 1. 4 0.75
93 A 4 3 1. 6 0.5
94 A 5 5 1. 6 0.833
95 A 4 4 1. 6 0.667
96 A 1 3 1. 17 0.176
97 A 2 2 1. 11 0.182
98 A 1 1 1. 15 0.067
99 A 1 1 1. 14 0.071
100 A 2 2 1. 11 0.182
101 A 2 2 1. 13 0.154
102 A 5 6 1. 10 0.6
103 A 3 3 1. 15 0.2
104 A 4 4 1. 15 0.267
105 A 3 3 1. 15 0.2
106 A 3 2 1. 16 0.125
107 A 3 2 1. 16 0.125
108 A 6 4 1. 18 0.222
109 A 3 2 1. 23 0.087
110 A 2 1 1. 19 0.053
111 A 5 5 1. 18 0.278
112 A 6 5 1. 31 0.161
113 A 2 2 1. 7 0.286
114 A 3 2 1. 22 0.091
115 A 2 1 1. 16 0.062
116 A 2 1 1. 17 0.059
117 A 2 1 1. 12 0.083
118 A 3 2 1. 21 0.095
119 A 2 1 1. 20 0.05
120 A 3 3 1. 16 0.188
121 A 4 3 1. 16 0.188
122 A 2 1 1. 11 0.091
123 A 3 2 1. 11 0.182
124 A 2 1 1. 16 0.062
125 A 2 1 1. 7 0.143
126 A 5 5 1. 9 0.556
127 A 4 3 1. 12 0.25
128 A 3 2 1. 14 0.143
129 A 4 4 1. 21 0.19
130 A 3 2 1. 18 0.111
131 A 2 2 1. 7 0.286
132 A 3 3 1. 11 0.273
133 A 3 2 1. 16 0.125
134 A 3 2 1. 11 0.182
135 A 5 4 1. 18 0.222
136 A 3 3 1. 7 0.429
137 A 9 6 1. 7 0.857
138 A 3 3 1. 14 0.214
139 A 1 1 1. 16 0.062
140 A 3 3 1. 12 0.25
141 A 2 2 1. 8 0.25
142 A 2 2 1. 8 0.25
143 A 1 1 1. 10 0.1
144 A 3 3 1. 13 0.231
145 A 2 1 1. 19 0.053
146 A 1 1 1. 11 0.091
147 A 3 3 1. 11 0.273
148 A 2 2 1. 11 0.182
149 A 1 1 1. 13 0.077
150 A 4 4 1. 15 0.267
151 A 3 3 1. 13 0.231
152 A 2 2 1. 9 0.222
153 A 3 3 1. 12 0.25
154 A 2 2 1. 9 0.222
155 A 6 6 1. 18 0.333
156 A 2 2 1. 8 0.25
157 A 3 3 1. 5 0.6
158 A 1 1 1. 7 0.143
159 A 1 1 1. 9 0.111
160 A 2 2 1. 7 0.286
161 A 2 2 1. 5 0.4
162 A 1 1 1. 14 0.071
163 A 2 2 1. 14 0.143
164 A 2 2 1. 9 0.222
165 A 2 3 1. 8 0.375
166 A 2 2 1. 7 0.286
167 A 3 2 1. 9 0.222
168 A 4 2 1. 9 0.222
169 A 1 1 1. 21 0.048
170 A 1 1 1. 4 0.25
171 A 2 2 1. 4 0.5
172 A 2 2 1. 8 0.25
173 A 1 1 1. 11 0.091
174 A 4 2 1. 16 0.125
175 A 1 1 1. 9 0.111

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