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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
  2.1.8 Mupad
 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, 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 }

B grade: { 83 }

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, 18, 19, 20, 22, 23, 24, 26, 27, 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, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143 }

B grade: { 17, 21, 25, 28, 29, 83, 102 }

C grade: { 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47 }

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, 26, 27, 28, 29, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 78, 79, 80, 81, 82, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 128, 129, 130, 131, 138 }

B grade: { 25, 74, 75, 76, 77, 83, 101, 102, 125, 126, 127 }

C grade: { }

F grade: { 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 132, 133, 134, 135, 136, 137, 139, 140, 141, 142, 143 }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 72, 78, 79, 80, 81, 82, 84, 85, 86, 87, 90, 91, 92, 93, 94, 97, 99, 100, 102, 103, 104, 105, 106, 107, 108, 109, 110, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 138 }

B grade: { 17, 74, 75, 76, 77, 83, 101 }

C grade: { 71, 73, 111, 122 }

F grade: { 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 88, 89, 95, 96, 98, 132, 133, 134, 135, 136, 137, 139, 140, 141, 142, 143 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 19, 20, 22, 23, 24, 26, 28, 29, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 78, 79, 81, 82, 86, 88, 89, 91, 92, 93, 94, 98, 101, 102, 103, 105, 106, 107, 108, 109, 110, 112, 113, 116, 119, 121, 123, 130, 131, 138 }

B grade: { 17, 18, 21, 25, 27, 74, 75, 76, 77, 80, 83, 84, 85, 87, 90, 95, 96, 97, 99, 100, 104, 114, 115, 117, 118, 120, 124, 125, 126, 127, 128, 129 }

C grade: { 70, 71, 72, 73, 111, 122 }

F grade: { 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 132, 133, 134, 135, 136, 137, 139, 140, 141, 142, 143 }

2.1.6 Sympy

A grade: { 49, 50, 51, 52, 55, 56, 57, 58, 59, 60, 68, 69, 78, 79, 80, 81, 82, 91, 92, 93, 94, 138 }

B grade: { 53, 54, 61, 62, 63, 74, 75, 76, 77, 83, 84, 85, 87, 88, 89, 90, 95, 96, 97, 98, 99, 100 }

C grade: { 86, 101, 102 }

F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 64, 65, 66, 67, 70, 71, 72, 73, 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, 139, 140, 141, 142, 143 }

2.1.7 Giac

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 27, 28, 29, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 68, 69, 78, 79, 80, 81, 82, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 102, 103, 104, 105, 106, 107, 108, 109, 110, 112, 113, 115, 116, 118, 119, 120, 121, 123, 124, 128, 129, 130, 131, 138 }

B grade: { 64, 74, 75, 76, 77, 83, 101, 114, 117, 125, 126, 127 }

C grade: { 70, 71, 72, 73 }

F grade: { 17, 18, 19, 20, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 67, 111, 122, 132, 133, 134, 135, 136, 137, 139, 140, 141, 142, 143 }

2.1.8 Mupad

A grade: { }

B 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, 138 }

C grade: { }

F grade: { 132, 133, 134, 135, 136, 137, 139, 140, 141, 142, 143 }

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 Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 147 147 142 173 180 258 0 132 151
normalized size 1 1.00 0.97 1.18 1.22 1.76 0.00 0.90 1.03
time (sec) N/A 0.054 0.223 0.046 1.341 0.703 0.000 0.632 0.735
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 121 121 119 91 130 69 0 1 100
normalized size 1 1.00 0.98 0.75 1.07 0.57 0.00 0.01 0.83
time (sec) N/A 0.031 0.095 0.118 3.001 0.909 0.000 0.573 0.292
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 95 95 88 71 103 59 0 1 80
normalized size 1 1.00 0.93 0.75 1.08 0.62 0.00 0.01 0.84
time (sec) N/A 0.022 0.079 0.093 3.012 0.969 0.000 0.460 0.298
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 69 69 76 51 76 49 0 1 60
normalized size 1 1.00 1.10 0.74 1.10 0.71 0.00 0.01 0.87
time (sec) N/A 0.015 0.064 0.118 2.985 1.173 0.000 0.610 0.162
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 64 31 49 39 0 1 39
normalized size 1 1.00 1.49 0.72 1.14 0.91 0.00 0.02 0.91
time (sec) N/A 0.010 0.049 0.105 2.963 0.803 0.000 0.625 0.087
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 101 101 88 82 117 68 0 57 81
normalized size 1 1.00 0.87 0.81 1.16 0.67 0.00 0.56 0.80
time (sec) N/A 0.028 0.067 0.044 3.058 0.722 0.000 0.471 0.166
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 78 64 90 58 0 47 63
normalized size 1 1.00 0.99 0.81 1.14 0.73 0.00 0.59 0.80
time (sec) N/A 0.019 0.047 0.046 2.944 0.690 0.000 0.454 0.242
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 57 57 68 46 63 48 0 37 45
normalized size 1 1.00 1.19 0.81 1.11 0.84 0.00 0.65 0.79
time (sec) N/A 0.013 0.046 0.048 2.898 0.861 0.000 0.523 0.112
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 35 35 58 28 36 38 0 27 26
normalized size 1 1.00 1.66 0.80 1.03 1.09 0.00 0.77 0.74
time (sec) N/A 0.009 0.032 0.051 2.885 1.010 0.000 0.477 0.052
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 35 35 32 28 36 35 0 25 26
normalized size 1 1.00 0.91 0.80 1.03 1.00 0.00 0.71 0.74
time (sec) N/A 0.010 0.039 0.047 2.974 0.726 0.000 0.361 0.048
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 35 35 58 28 36 38 0 27 26
normalized size 1 1.00 1.66 0.80 1.03 1.09 0.00 0.77 0.74
time (sec) N/A 0.010 0.034 0.045 2.926 1.313 0.000 0.435 0.054
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 44 42 55 43 0 35 39
normalized size 1 1.00 0.86 0.82 1.08 0.84 0.00 0.69 0.76
time (sec) N/A 0.010 0.063 0.043 2.888 0.857 0.000 0.543 0.194
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 35 35 40 33 41 32 0 33 29
normalized size 1 1.00 1.14 0.94 1.17 0.91 0.00 0.94 0.83
time (sec) N/A 0.007 0.027 0.046 1.418 0.838 0.000 0.520 0.199
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 37 37 48 33 43 32 0 33 29
normalized size 1 1.00 1.30 0.89 1.16 0.86 0.00 0.89 0.78
time (sec) N/A 0.007 0.036 0.045 1.314 0.710 0.000 0.517 0.109
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 39 39 46 33 43 36 0 37 29
normalized size 1 1.00 1.18 0.85 1.10 0.92 0.00 0.95 0.74
time (sec) N/A 0.007 0.026 0.048 1.349 0.872 0.000 0.415 0.195
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 83 83 70 75 111 105 0 74 96
normalized size 1 1.00 0.84 0.90 1.34 1.27 0.00 0.89 1.16
time (sec) N/A 0.018 0.021 0.048 1.343 0.803 0.000 0.492 0.271
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A B B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 53 10 21 19 0 0 19
normalized size 1 1.00 3.31 0.62 1.31 1.19 0.00 0.00 1.19
time (sec) N/A 0.006 0.012 0.105 2.932 0.937 0.000 0.000 0.276
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 26 26 24 21 28 39 0 0 20
normalized size 1 1.00 0.92 0.81 1.08 1.50 0.00 0.00 0.77
time (sec) N/A 0.003 0.005 0.102 1.372 0.813 0.000 0.000 0.045
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 36 42 55 62 0 0 31
normalized size 1 1.00 0.68 0.79 1.04 1.17 0.00 0.00 0.58
time (sec) N/A 0.007 0.010 0.099 1.368 1.030 0.000 0.000 0.124
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F(-2) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 48 62 82 82 0 0 40
normalized size 1 1.00 0.61 0.78 1.04 1.04 0.00 0.00 0.51
time (sec) N/A 0.012 0.012 0.101 1.370 0.811 0.000 0.000 0.286
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 40 9 8 19 0 8 8
normalized size 1 1.00 3.33 0.75 0.67 1.58 0.00 0.67 0.67
time (sec) N/A 0.006 0.012 0.043 2.953 0.943 0.000 0.498 0.106
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 22 22 21 25 28 29 0 29 18
normalized size 1 1.00 0.95 1.14 1.27 1.32 0.00 1.32 0.82
time (sec) N/A 0.002 0.005 0.051 1.344 0.960 0.000 0.507 0.136
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 31 35 55 46 0 39 28
normalized size 1 1.00 0.69 0.78 1.22 1.02 0.00 0.87 0.62
time (sec) N/A 0.006 0.009 0.044 1.363 0.967 0.000 0.408 0.032
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 51 45 82 61 0 49 73
normalized size 1 1.00 0.76 0.67 1.22 0.91 0.00 0.73 1.09
time (sec) N/A 0.012 0.013 0.047 1.366 0.923 0.000 0.504 0.195
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 47 35 21 27 0 15 42
normalized size 1 1.00 3.92 2.92 1.75 2.25 0.00 1.25 3.50
time (sec) N/A 0.008 0.013 0.072 2.916 0.943 0.000 0.520 0.312
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 45 37 29 27 0 36 36
normalized size 1 1.00 1.88 1.54 1.21 1.12 0.00 1.50 1.50
time (sec) N/A 0.008 0.017 0.052 1.375 0.815 0.000 0.546 0.226
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 14 7 8 18 0 6 6
normalized size 1 1.00 1.40 0.70 0.80 1.80 0.00 0.60 0.60
time (sec) N/A 0.006 0.008 0.046 3.034 0.598 0.000 0.392 0.109
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 33 14 17 17 0 18 11
normalized size 1 1.00 2.06 0.88 1.06 1.06 0.00 1.12 0.69
time (sec) N/A 0.004 0.006 0.041 1.311 0.914 0.000 0.540 0.511
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 33 14 17 17 0 18 11
normalized size 1 1.00 2.06 0.88 1.06 1.06 0.00 1.12 0.69
time (sec) N/A 0.004 0.012 0.051 1.327 0.825 0.000 0.539 0.529
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 448 448 48 0 0 0 0 0 36
normalized size 1 1.00 0.11 0.00 0.00 0.00 0.00 0.00 0.08
time (sec) N/A 0.717 0.014 0.852 0.000 0.682 0.000 0.000 0.234
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 387 387 45 0 0 0 0 0 36
normalized size 1 1.00 0.12 0.00 0.00 0.00 0.00 0.00 0.09
time (sec) N/A 0.449 0.009 0.547 0.000 0.874 0.000 0.000 0.173
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 322 322 43 0 0 0 0 0 36
normalized size 1 1.00 0.13 0.00 0.00 0.00 0.00 0.00 0.11
time (sec) N/A 0.394 0.011 0.767 0.000 1.001 0.000 0.000 0.215
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 384 384 47 0 0 0 0 0 36
normalized size 1 1.00 0.12 0.00 0.00 0.00 0.00 0.00 0.09
time (sec) N/A 0.457 0.011 0.750 0.000 0.727 0.000 0.000 0.249
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 448 448 50 0 0 0 0 0 36
normalized size 1 1.00 0.11 0.00 0.00 0.00 0.00 0.00 0.08
time (sec) N/A 0.510 0.012 1.260 0.000 1.051 0.000 0.000 0.275
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 842 842 48 0 0 0 0 0 36
normalized size 1 1.00 0.06 0.00 0.00 0.00 0.00 0.00 0.04
time (sec) N/A 1.058 0.013 0.759 0.000 0.909 0.000 0.000 0.181
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 781 781 45 0 0 0 0 0 36
normalized size 1 1.00 0.06 0.00 0.00 0.00 0.00 0.00 0.05
time (sec) N/A 0.947 0.009 0.708 0.000 1.190 0.000 0.000 0.160
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 715 715 45 0 0 0 0 0 36
normalized size 1 1.00 0.06 0.00 0.00 0.00 0.00 0.00 0.05
time (sec) N/A 0.860 0.010 0.701 0.000 0.759 0.000 0.000 0.200
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 773 773 45 0 0 0 0 0 36
normalized size 1 1.00 0.06 0.00 0.00 0.00 0.00 0.00 0.05
time (sec) N/A 0.947 0.011 0.882 0.000 0.973 0.000 0.000 0.231
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 838 838 50 0 0 0 0 0 36
normalized size 1 1.00 0.06 0.00 0.00 0.00 0.00 0.00 0.04
time (sec) N/A 1.036 0.012 1.336 0.000 0.923 0.000 0.000 0.245
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 119 119 48 0 0 0 0 0 36
normalized size 1 1.00 0.40 0.00 0.00 0.00 0.00 0.00 0.30
time (sec) N/A 0.046 0.014 0.625 0.000 0.898 0.000 0.000 0.190
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 90 90 45 0 0 0 0 0 36
normalized size 1 1.00 0.50 0.00 0.00 0.00 0.00 0.00 0.40
time (sec) N/A 0.034 0.012 0.740 0.000 1.039 0.000 0.000 0.169
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 90 90 45 0 0 0 0 0 36
normalized size 1 1.00 0.50 0.00 0.00 0.00 0.00 0.00 0.40
time (sec) N/A 0.033 0.009 0.570 0.000 0.962 0.000 0.000 0.172
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 58 58 45 0 0 0 0 0 36
normalized size 1 1.00 0.78 0.00 0.00 0.00 0.00 0.00 0.62
time (sec) N/A 0.023 0.010 0.723 0.000 1.060 0.000 0.000 0.199
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 43 0 0 0 0 0 36
normalized size 1 1.00 0.73 0.00 0.00 0.00 0.00 0.00 0.61
time (sec) N/A 0.023 0.009 0.723 0.000 0.761 0.000 0.000 0.189
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 83 83 45 0 0 0 0 0 36
normalized size 1 1.00 0.54 0.00 0.00 0.00 0.00 0.00 0.43
time (sec) N/A 0.032 0.011 0.918 0.000 0.968 0.000 0.000 0.224
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 115 115 50 0 0 0 0 0 36
normalized size 1 1.00 0.43 0.00 0.00 0.00 0.00 0.00 0.31
time (sec) N/A 0.044 0.011 1.370 0.000 0.856 0.000 0.000 0.256
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 146 146 50 0 0 0 0 0 36
normalized size 1 1.00 0.34 0.00 0.00 0.00 0.00 0.00 0.25
time (sec) N/A 0.060 0.012 0.768 0.000 1.107 0.000 0.000 0.288
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 45 0 0 0 0 0 48
normalized size 1 1.00 0.82 0.00 0.00 0.00 0.00 0.00 0.87
time (sec) N/A 0.010 0.009 0.503 0.000 0.952 0.000 0.000 0.316
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 51 44 43 43 49 43 43
normalized size 1 1.00 1.00 0.86 0.84 0.84 0.96 0.84 0.84
time (sec) N/A 0.017 0.002 0.041 1.313 0.725 0.070 0.389 0.026
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 35 35 35 32 31 31 32 31 31
normalized size 1 1.00 1.00 0.91 0.89 0.89 0.91 0.89 0.89
time (sec) N/A 0.011 0.002 0.040 1.348 0.753 0.070 0.529 0.039
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 25 22 21 21 22 21 21
normalized size 1 1.00 1.00 0.88 0.84 0.84 0.88 0.84 0.84
time (sec) N/A 0.007 0.001 0.038 1.364 0.728 0.063 0.432 0.029
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 12 11 10 10 8 10 10
normalized size 1 1.00 1.00 0.92 0.83 0.83 0.67 0.83 0.83
time (sec) N/A 0.002 0.000 0.042 1.293 0.708 0.062 0.352 0.017
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 24 16 15 67 53 15 16
normalized size 1 1.00 1.00 0.67 0.62 2.79 2.21 0.62 0.67
time (sec) N/A 0.005 0.009 0.040 2.902 0.814 0.141 0.395 0.066
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 45 36 35 120 78 35 33
normalized size 1 1.00 1.00 0.80 0.78 2.67 1.73 0.78 0.73
time (sec) N/A 0.010 0.024 0.047 3.112 0.827 0.223 0.417 0.143
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 62 62 55 51 58 188 105 45 55
normalized size 1 1.00 0.89 0.82 0.94 3.03 1.69 0.73 0.89
time (sec) N/A 0.016 0.033 0.049 2.987 0.873 0.339 0.339 0.162
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 84 84 76 66 58 146 97 63 37
normalized size 1 1.00 0.90 0.79 0.69 1.74 1.15 0.75 0.44
time (sec) N/A 0.022 0.108 0.044 1.380 0.818 4.426 0.359 0.204
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 65 65 65 51 43 124 70 49 37
normalized size 1 1.00 1.00 0.78 0.66 1.91 1.08 0.75 0.57
time (sec) N/A 0.014 0.080 0.044 1.303 0.956 3.008 0.427 0.157
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 49 36 28 94 41 37 35
normalized size 1 1.00 1.07 0.78 0.61 2.04 0.89 0.80 0.76
time (sec) N/A 0.009 0.019 0.043 1.357 0.932 1.907 0.399 0.127
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 25 21 13 59 17 23 20
normalized size 1 1.00 1.00 0.84 0.52 2.36 0.68 0.92 0.80
time (sec) N/A 0.005 0.006 0.042 1.390 0.994 1.051 0.406 0.187
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 16 15 14 23 17 14 14
normalized size 1 1.00 1.00 0.94 0.88 1.44 1.06 0.88 0.88
time (sec) N/A 0.002 0.004 0.044 1.253 0.740 0.647 0.476 0.032
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 39 39 29 26 31 47 95 27 28
normalized size 1 1.00 0.74 0.67 0.79 1.21 2.44 0.69 0.72
time (sec) N/A 0.006 0.008 0.045 1.020 0.713 0.862 0.511 0.192
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 58 58 40 37 46 69 413 41 44
normalized size 1 1.00 0.69 0.64 0.79 1.19 7.12 0.71 0.76
time (sec) N/A 0.010 0.010 0.043 1.313 1.085 1.461 0.456 0.193
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 51 48 61 91 1265 55 61
normalized size 1 1.00 0.66 0.62 0.79 1.18 16.43 0.71 0.79
time (sec) N/A 0.016 0.013 0.046 1.350 0.698 2.203 0.410 0.205
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 20 35 30 19 0 45 19
normalized size 1 1.00 0.87 1.52 1.30 0.83 0.00 1.96 0.83
time (sec) N/A 0.003 0.037 0.046 2.957 1.038 0.000 0.393 0.049
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 25 25 30 9 0 26 19
normalized size 1 1.00 1.09 1.09 1.30 0.39 0.00 1.13 0.83
time (sec) N/A 0.003 0.005 0.044 2.858 0.987 0.000 0.377 0.046
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 26 23 6 8 0 25 14
normalized size 1 1.00 0.90 0.79 0.21 0.28 0.00 0.86 0.48
time (sec) N/A 0.005 0.005 0.048 2.830 0.791 0.000 0.286 0.283
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 20 17 9 14 0 0 21
normalized size 1 1.00 0.80 0.68 0.36 0.56 0.00 0.00 0.84
time (sec) N/A 0.003 0.005 0.046 2.892 0.957 0.000 0.000 0.170
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 25 25 30 9 8 26 13
normalized size 1 1.00 1.09 1.09 1.30 0.39 0.35 1.13 0.57
time (sec) N/A 0.003 0.009 0.045 3.010 0.960 0.075 0.346 0.113
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 26 23 6 8 7 15 14
normalized size 1 1.00 0.90 0.79 0.21 0.28 0.24 0.52 0.48
time (sec) N/A 0.005 0.008 0.050 2.969 0.868 0.078 0.456 0.353
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A C F C B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 27 27 30 9 0 26 18
normalized size 1 1.00 1.17 1.17 1.30 0.39 0.00 1.13 0.78
time (sec) N/A 0.003 0.007 0.047 3.015 0.723 0.000 0.375 0.327
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C C F C B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 28 25 6 6 0 23 15
normalized size 1 1.00 0.97 0.86 0.21 0.21 0.00 0.79 0.52
time (sec) N/A 0.005 0.006 0.049 2.898 1.108 0.000 0.447 0.245
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A C F C B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 27 27 30 9 0 26 18
normalized size 1 1.00 1.17 1.17 1.30 0.39 0.00 1.13 0.78
time (sec) N/A 0.003 0.006 0.045 2.962 0.855 0.000 0.407 0.067
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C C F C B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 28 25 6 6 0 23 15
normalized size 1 1.00 0.97 0.86 0.21 0.21 0.00 0.79 0.52
time (sec) N/A 0.006 0.004 0.049 2.777 0.857 0.000 0.345 0.295
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 109 109 207 636 234 233 253 334 184
normalized size 1 1.00 1.90 5.83 2.15 2.14 2.32 3.06 1.69
time (sec) N/A 0.140 0.030 0.039 1.413 0.790 0.194 0.429 0.314
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 109 109 207 636 234 235 250 334 184
normalized size 1 1.00 1.90 5.83 2.15 2.16 2.29 3.06 1.69
time (sec) N/A 0.137 0.041 0.045 1.521 0.919 0.199 0.412 0.331
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 109 109 199 636 234 227 253 334 176
normalized size 1 1.00 1.83 5.83 2.15 2.08 2.32 3.06 1.61
time (sec) N/A 0.142 0.028 0.039 1.409 0.962 0.202 0.450 0.337
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 109 109 207 636 234 235 248 334 184
normalized size 1 1.00 1.90 5.83 2.15 2.16 2.28 3.06 1.69
time (sec) N/A 0.140 0.042 0.040 1.400 0.950 0.196 0.526 0.316
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 18 18 18 17 16 16 22 16 16
normalized size 1 1.00 1.00 0.94 0.89 0.89 1.22 0.89 0.89
time (sec) N/A 0.011 0.009 0.042 2.955 1.055 0.114 0.369 0.139
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 12 12 12 9 8 8 7 8 8
normalized size 1 1.00 1.00 0.75 0.67 0.67 0.58 0.67 0.67
time (sec) N/A 0.009 0.013 0.099 2.975 0.900 0.164 0.410 0.272
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 34 17 27 39 39 31 15
normalized size 1 1.00 1.79 0.89 1.42 2.05 2.05 1.63 0.79
time (sec) N/A 0.019 0.019 0.043 2.953 0.885 0.119 0.458 0.209
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 14 13 13 10 15 8
normalized size 1 1.00 1.00 1.08 1.00 1.00 0.77 1.15 0.62
time (sec) N/A 0.005 0.003 0.049 1.327 1.037 0.103 0.507 0.082
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 21 21 21 16 15 15 14 17 8
normalized size 1 1.00 1.00 0.76 0.71 0.71 0.67 0.81 0.38
time (sec) N/A 0.006 0.003 0.050 1.314 1.051 0.113 0.464 0.091
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A B B B B B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 6 17 17 14 13 13 12 15 6
normalized size 1 2.83 2.83 2.33 2.17 2.17 2.00 2.50 1.00
time (sec) N/A 0.004 0.003 0.048 1.288 1.063 0.104 0.330 0.176
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 27 24 38 50 76 40 23
normalized size 1 1.00 1.00 0.89 1.41 1.85 2.81 1.48 0.85
time (sec) N/A 0.019 0.008 0.056 1.314 1.034 0.223 0.346 0.359
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 29 26 39 51 76 45 23
normalized size 1 1.00 1.07 0.96 1.44 1.89 2.81 1.67 0.85
time (sec) N/A 0.019 0.008 0.050 1.326 0.990 0.233 0.383 0.386
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A C A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 31 28 27 41 87 27 23
normalized size 1 1.00 1.00 0.90 0.87 1.32 2.81 0.87 0.74
time (sec) N/A 0.020 0.008 0.049 1.317 0.797 0.196 0.482 0.381
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 29 26 39 51 76 45 23
normalized size 1 1.00 1.07 0.96 1.44 1.89 2.81 1.67 0.85
time (sec) N/A 0.018 0.007 0.051 1.441 0.927 0.234 0.532 0.418
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 38 38 38 35 0 113 124 34 46
normalized size 1 1.00 1.00 0.92 0.00 2.97 3.26 0.89 1.21
time (sec) N/A 0.034 0.010 0.062 0.000 0.925 0.221 0.432 0.229
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 35 35 34 35 0 124 100 30 33
normalized size 1 1.00 0.97 1.00 0.00 3.54 2.86 0.86 0.94
time (sec) N/A 0.027 0.009 0.064 0.000 1.106 0.232 0.365 0.273
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 32 32 41 31 49 67 102 55 28
normalized size 1 1.00 1.28 0.97 1.53 2.09 3.19 1.72 0.88
time (sec) N/A 0.025 0.010 0.072 2.910 0.899 0.255 0.445 0.227
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 43 37 36 45 39 36 33
normalized size 1 1.00 1.00 0.86 0.84 1.05 0.91 0.84 0.77
time (sec) N/A 0.015 0.022 0.037 2.274 0.909 0.150 0.580 0.038
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 62 37 47 68 58 51 34
normalized size 1 1.00 1.44 0.86 1.09 1.58 1.35 1.19 0.79
time (sec) N/A 0.016 0.024 0.055 2.807 0.851 0.151 0.522 0.163
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 34 34 33 32 34 53 31 36 34
normalized size 1 1.00 0.97 0.94 1.00 1.56 0.91 1.06 1.00
time (sec) N/A 0.008 0.010 0.053 1.316 0.925 0.140 0.454 0.200
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 42 32 34 53 32 36 34
normalized size 1 1.00 1.00 0.76 0.81 1.26 0.76 0.86 0.81
time (sec) N/A 0.009 0.013 0.049 1.347 1.069 0.151 0.318 0.080
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 70 68 0 334 265 67 119
normalized size 1 1.00 0.99 0.96 0.00 4.70 3.73 0.94 1.68
time (sec) N/A 0.040 0.058 0.056 0.000 1.079 0.589 0.404 0.171
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 72 86 0 317 230 75 107
normalized size 1 1.00 1.00 1.19 0.00 4.40 3.19 1.04 1.49
time (sec) N/A 0.036 0.044 0.048 0.000 0.948 0.548 0.514 0.320
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 69 69 78 84 97 171 218 90 100
normalized size 1 1.00 1.13 1.22 1.41 2.48 3.16 1.30 1.45
time (sec) N/A 0.034 0.060 0.052 2.839 0.965 0.603 0.526 0.316
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) A B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 62 62 65 111 0 89 212 100 110
normalized size 1 1.00 1.05 1.79 0.00 1.44 3.42 1.61 1.77
time (sec) N/A 0.157 0.096 0.573 0.000 1.260 0.982 0.570 0.253
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 33 58 34 31 55 63 56 56 38
normalized size 1 1.76 1.03 0.94 1.67 1.91 1.70 1.70 1.15
time (sec) N/A 0.036 0.032 0.080 1.389 1.285 0.292 0.527 0.258
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 58 32 31 51 59 56 54 38
normalized size 1 1.87 1.03 1.00 1.65 1.90 1.81 1.74 1.23
time (sec) N/A 0.029 0.029 0.049 1.322 0.855 0.282 0.546 0.135
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A C B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 19 33 27 15 165 27 27
normalized size 1 1.00 1.12 1.94 1.59 0.88 9.71 1.59 1.59
time (sec) N/A 0.018 0.020 0.241 2.954 1.112 0.192 0.466 0.117
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B A A C A B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 23 23 56 39 33 21 70 33 42
normalized size 1 1.00 2.43 1.70 1.43 0.91 3.04 1.43 1.83
time (sec) N/A 0.028 0.039 0.196 3.018 0.867 0.588 0.466 0.303
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 38 38 39 29 38 40 0 40 39
normalized size 1 1.00 1.03 0.76 1.00 1.05 0.00 1.05 1.03
time (sec) N/A 0.011 0.016 0.055 3.042 0.905 0.000 0.468 0.080
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 30 25 38 53 0 24 23
normalized size 1 1.00 1.00 0.83 1.27 1.77 0.00 0.80 0.77
time (sec) N/A 0.010 0.013 0.045 2.998 0.782 0.000 1.604 0.052
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 49 50 52 40 0 41 39
normalized size 1 1.00 1.00 1.02 1.06 0.82 0.00 0.84 0.80
time (sec) N/A 0.010 0.015 0.053 2.869 0.900 0.000 0.429 0.210
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 46 35 46 58 0 53 48
normalized size 1 1.00 1.02 0.78 1.02 1.29 0.00 1.18 1.07
time (sec) N/A 0.015 0.017 0.049 3.004 0.913 0.000 0.456 0.191
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 46 35 46 60 0 36 35
normalized size 1 1.00 1.02 0.78 1.02 1.33 0.00 0.80 0.78
time (sec) N/A 0.016 0.017 0.046 2.972 0.756 0.000 0.470 0.052
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 62 62 55 50 58 58 0 54 48
normalized size 1 1.00 0.89 0.81 0.94 0.94 0.00 0.87 0.77
time (sec) N/A 0.015 0.026 0.047 2.975 0.955 0.000 0.442 0.195
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 44 32 41 60 0 31 30
normalized size 1 1.00 1.02 0.74 0.95 1.40 0.00 0.72 0.70
time (sec) N/A 0.012 0.019 0.045 3.083 0.877 0.000 0.401 0.150
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 53 50 58 58 0 54 48
normalized size 1 1.00 0.90 0.85 0.98 0.98 0.00 0.92 0.81
time (sec) N/A 0.013 0.019 0.047 2.980 0.972 0.000 0.489 0.193
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C C F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 59 59 54 46 46 84 0 0 36
normalized size 1 1.00 0.92 0.78 0.78 1.42 0.00 0.00 0.61
time (sec) N/A 0.016 0.025 0.050 2.894 0.853 0.000 0.000 0.054
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 62 62 55 50 58 58 0 54 48
normalized size 1 1.00 0.89 0.81 0.94 0.94 0.00 0.87 0.77
time (sec) N/A 0.013 0.025 0.046 3.003 0.967 0.000 0.445 0.221
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 39 39 40 32 41 60 0 31 30
normalized size 1 1.00 1.03 0.82 1.05 1.54 0.00 0.79 0.77
time (sec) N/A 0.008 0.018 0.043 3.078 0.923 0.000 0.526 0.052
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 14 14 14 9 8 20 0 20 20
normalized size 1 1.00 1.00 0.64 0.57 1.43 0.00 1.43 1.43
time (sec) N/A 0.007 0.005 0.044 2.948 0.899 0.000 0.631 0.199
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 10 10 14 7 8 33 0 6 6
normalized size 1 1.00 1.40 0.70 0.80 3.30 0.00 0.60 0.60
time (sec) N/A 0.007 0.006 0.046 3.011 1.050 0.000 0.518 0.132
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 24 30 22 20 0 21 20
normalized size 1 1.00 0.96 1.20 0.88 0.80 0.00 0.84 0.80
time (sec) N/A 0.006 0.005 0.045 2.991 0.936 0.000 0.575 0.218
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 18 18 18 15 16 38 0 33 26
normalized size 1 1.00 1.00 0.83 0.89 2.11 0.00 1.83 1.44
time (sec) N/A 0.010 0.006 0.049 2.877 0.964 0.000 0.616 0.225
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 19 15 16 40 0 16 16
normalized size 1 1.00 1.00 0.79 0.84 2.11 0.00 0.84 0.84
time (sec) N/A 0.010 0.006 0.046 2.927 0.955 0.000 0.818 0.137
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 35 35 28 30 28 38 0 34 26
normalized size 1 1.00 0.80 0.86 0.80 1.09 0.00 0.97 0.74
time (sec) N/A 0.008 0.005 0.041 3.010 0.900 0.000 0.802 0.236
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 17 12 11 40 0 11 11
normalized size 1 1.00 1.00 0.71 0.65 2.35 0.00 0.65 0.65
time (sec) N/A 0.007 0.006 0.046 2.997 0.847 0.000 0.658 0.170
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 32 32 26 30 28 37 0 34 26
normalized size 1 1.00 0.81 0.94 0.88 1.16 0.00 1.06 0.81
time (sec) N/A 0.008 0.006 0.043 2.987 0.867 0.000 0.562 0.228
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A C C F F B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 33 33 28 26 16 65 0 0 17
normalized size 1 1.00 0.85 0.79 0.48 1.97 0.00 0.00 0.52
time (sec) N/A 0.008 0.008 0.039 2.910 0.931 0.000 0.000 0.136
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 35 35 28 30 28 38 0 34 26
normalized size 1 1.00 0.80 0.86 0.80 1.09 0.00 0.97 0.74
time (sec) N/A 0.008 0.006 0.043 2.927 1.029 0.000 0.731 0.226
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 13 13 13 12 11 40 0 11 11
normalized size 1 1.00 1.00 0.92 0.85 3.08 0.00 0.85 0.85
time (sec) N/A 0.004 0.006 0.045 3.073 1.021 0.000 0.638 0.164
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 22 22 22 51 16 137 0 46 40
normalized size 1 1.00 1.00 2.32 0.73 6.23 0.00 2.09 1.82
time (sec) N/A 0.013 0.026 0.076 1.402 0.894 0.000 0.754 0.423
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 23 44 19 141 0 53 46
normalized size 1 1.00 1.00 1.91 0.83 6.13 0.00 2.30 2.00
time (sec) N/A 0.013 0.026 0.088 3.084 0.996 0.000 1.085 0.406
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 20 20 20 44 19 143 0 53 44
normalized size 1 1.00 1.00 2.20 0.95 7.15 0.00 2.65 2.20
time (sec) N/A 0.011 0.025 0.079 2.890 0.942 0.000 0.817 0.400
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 19 24 26 38 0 17 15
normalized size 1 1.00 1.00 1.26 1.37 2.00 0.00 0.89 0.79
time (sec) N/A 0.002 0.005 0.047 1.340 0.879 0.000 0.828 0.053
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 23 28 30 41 0 17 17
normalized size 1 1.00 1.00 1.22 1.30 1.78 0.00 0.74 0.74
time (sec) N/A 0.003 0.006 0.046 1.236 1.189 0.000 0.774 0.057
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 23 26 30 29 0 29 19
normalized size 1 1.00 1.00 1.13 1.30 1.26 0.00 1.26 0.83
time (sec) N/A 0.005 0.052 0.048 1.342 0.857 0.000 0.615 0.055
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 31 36 59 49 0 36 29
normalized size 1 1.00 0.72 0.84 1.37 1.14 0.00 0.84 0.67
time (sec) N/A 0.007 0.009 0.044 1.411 0.889 0.000 0.777 0.035
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 122 122 126 0 0 0 0 0 -1
normalized size 1 1.00 1.03 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.036 0.145 1.234 0.000 1.069 0.000 0.000 0.000
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 37 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.016 0.010 3.092 0.000 0.931 0.000 0.000 0.000
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 32 32 32 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.014 0.007 3.275 0.000 0.887 0.000 0.000 0.000
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 37 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.016 0.009 2.552 0.000 0.997 0.000 0.000 0.000
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 21 21 21 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.010 0.005 3.224 0.000 0.707 0.000 0.000 0.000
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 48 0 0 0 0 0 -1
normalized size 1 1.00 0.89 0.00 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.010 0.020 1.017 0.000 1.008 0.000 0.000 0.000
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 18 18 17 17 16 19 20 16 32
normalized size 1 1.00 0.94 0.94 0.89 1.06 1.11 0.89 1.78
time (sec) N/A 0.002 0.007 0.043 1.246 0.876 0.063 0.624 0.390
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 26 0 0 0 0 0 -1
normalized size 1 1.00 0.84 0.00 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.012 0.006 1.126 0.000 1.059 0.000 0.000 0.000
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 26 0 0 0 0 0 -1
normalized size 1 1.00 0.84 0.00 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.011 0.007 1.116 0.000 1.012 0.000 0.000 0.000
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 38 38 37 0 0 0 0 0 -1
normalized size 1 1.00 0.97 0.00 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.013 0.009 1.076 0.000 0.954 0.000 0.000 0.000
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 35 35 35 0 0 0 0 0 -1
normalized size 1 1.00 1.00 0.00 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.013 0.008 1.035 0.000 0.889 0.000 0.000 0.000
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 38 38 37 0 0 0 0 0 -1
normalized size 1 1.00 0.97 0.00 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.013 0.010 1.050 0.000 0.885 0.000 0.000 0.000

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 [35] had the largest ratio of [.5385]

Table 2.1:Rubi specific breakdown of results for each integral
# grade
number of
steps
used
number of
unique
rules
normalized
antiderivative
leaf size
integrand
leaf size
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\)
1 A 6 3 1.00 13 0.231
2 A 6 3 1.00 15 0.200
3 A 5 3 1.00 15 0.200
4 A 4 3 1.00 15 0.200
5 A 3 3 1.00 15 0.200
6 A 6 3 1.00 13 0.231
7 A 5 3 1.00 13 0.231
8 A 4 3 1.00 13 0.231
9 A 3 3 1.00 13 0.231
10 A 3 3 1.00 13 0.231
11 A 3 3 1.00 13 0.231
12 A 4 3 1.00 11 0.273
13 A 3 3 1.00 11 0.273
14 A 3 3 1.00 11 0.273
15 A 3 3 1.00 11 0.273
16 A 3 2 1.00 13 0.154
17 A 2 2 1.00 15 0.133
18 A 1 1 1.00 15 0.067
19 A 2 2 1.00 15 0.133
20 A 3 2 1.00 15 0.133
21 A 2 2 1.00 13 0.154
22 A 1 1 1.00 13 0.077
23 A 2 2 1.00 13 0.154
24 A 3 2 1.00 13 0.154
25 A 2 2 1.00 16 0.125
26 A 2 2 1.00 15 0.133
27 A 2 2 1.00 13 0.154
28 A 2 2 1.00 11 0.182
29 A 2 2 1.00 11 0.182
30 A 6 5 1.00 13 0.385
31 A 5 5 1.00 13 0.385
32 A 4 4 1.00 13 0.308
33 A 5 5 1.00 13 0.385
34 A 6 5 1.00 13 0.385
35 A 8 7 1.00 13 0.538
36 A 7 7 1.00 13 0.538
37 A 6 6 1.00 13 0.462
38 A 7 7 1.00 13 0.538
39 A 8 7 1.00 13 0.538
40 A 5 4 1.00 13 0.308
41 A 4 4 1.00 13 0.308
42 A 4 4 1.00 13 0.308
43 A 3 3 1.00 13 0.231
44 A 3 3 1.00 13 0.231
45 A 4 4 1.00 13 0.308
46 A 5 4 1.00 13 0.308
47 A 6 4 1.00 13 0.308
48 A 1 1 1.00 11 0.091
49 A 2 1 1.00 9 0.111
50 A 2 1 1.00 9 0.111
51 A 2 1 1.00 9 0.111
52 A 1 0 1.00 7 0.000
53 A 1 1 1.00 9 0.111
54 A 2 2 1.00 9 0.222
55 A 3 2 1.00 9 0.222
56 A 5 3 1.00 11 0.273
57 A 4 3 1.00 11 0.273
58 A 3 3 1.00 11 0.273
59 A 2 2 1.00 11 0.182
60 A 1 1 1.00 11 0.091
61 A 2 2 1.00 11 0.182
62 A 3 2 1.00 11 0.182
63 A 4 2 1.00 11 0.182
64 A 1 1 1.00 14 0.071
65 A 1 1 1.00 14 0.071
66 A 2 2 1.00 14 0.143
67 A 1 1 1.00 14 0.071
68 A 1 1 1.00 14 0.071
69 A 2 2 1.00 14 0.143
70 A 1 1 1.00 14 0.071
71 A 2 2 1.00 14 0.143
72 A 1 1 1.00 14 0.071
73 A 2 2 1.00 14 0.143
74 A 3 2 1.00 23 0.087
75 A 3 2 1.00 23 0.087
76 A 3 2 1.00 23 0.087
77 A 3 2 1.00 23 0.087
78 A 2 2 1.00 12 0.167
79 A 2 2 1.00 15 0.133
80 A 2 2 1.00 12 0.167
81 A 3 2 1.00 12 0.167
82 A 3 2 1.00 12 0.167
83 B 3 2 2.83 10 0.200
84 A 2 2 1.00 12 0.167
85 A 2 2 1.00 12 0.167
86 A 2 2 1.00 12 0.167
87 A 2 2 1.00 12 0.167
88 A 2 2 1.00 12 0.167
89 A 2 2 1.00 13 0.154
90 A 2 2 1.00 14 0.143
91 A 3 3 1.00 12 0.250
92 A 3 3 1.00 12 0.250
93 A 4 3 1.00 12 0.250
94 A 4 3 1.00 12 0.250
95 A 3 3 1.00 12 0.250
96 A 3 3 1.00 13 0.231
97 A 3 3 1.00 14 0.214
98 A 2 2 1.00 40 0.050
99 A 3 2 1.76 30 0.067
100 A 3 2 1.87 31 0.065
101 A 2 2 1.00 14 0.143
102 A 2 2 1.00 16 0.125
103 A 3 3 1.00 14 0.214
104 A 3 3 1.00 14 0.214
105 A 3 3 1.00 14 0.214
106 A 3 3 1.00 14 0.214
107 A 3 3 1.00 14 0.214
108 A 3 3 1.00 14 0.214
109 A 3 3 1.00 14 0.214
110 A 3 3 1.00 14 0.214
111 A 3 3 1.00 14 0.214
112 A 3 3 1.00 14 0.214
113 A 3 3 1.00 14 0.214
114 A 2 2 1.00 14 0.143
115 A 2 2 1.00 14 0.143
116 A 2 2 1.00 14 0.143
117 A 2 2 1.00 14 0.143
118 A 2 2 1.00 14 0.143
119 A 2 2 1.00 14 0.143
120 A 2 2 1.00 14 0.143
121 A 2 2 1.00 14 0.143
122 A 2 2 1.00 14 0.143
123 A 2 2 1.00 14 0.143
124 A 2 2 1.00 14 0.143
125 A 2 2 1.00 27 0.074
126 A 2 2 1.00 30 0.067
127 A 2 2 1.00 28 0.071
128 A 1 1 1.00 12 0.083
129 A 1 1 1.00 14 0.071
130 A 1 1 1.00 16 0.062
131 A 2 2 1.00 14 0.143
132 A 1 1 1.00 12 0.083
133 A 2 2 1.00 12 0.167
134 A 2 2 1.00 12 0.167
135 A 2 2 1.00 12 0.167
136 A 2 2 1.00 12 0.167
137 A 1 1 1.00 10 0.100
138 A 1 1 1.00 7 0.143
139 A 2 2 1.00 12 0.167
140 A 2 2 1.00 12 0.167
141 A 2 2 1.00 12 0.167
142 A 2 2 1.00 12 0.167
143 A 2 2 1.00 12 0.167

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