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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, 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: { 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 27, 28, 29, 49, 50, 51, 52, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 72, 78, 79, 80, 81, 82, 84, 85, 86, 87, 91, 92, 93, 94, 102, 103, 104, 105, 106, 107, 108, 109, 110, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 123, 124, 128, 129, 130, 131

B grade: { 17, 74, 75, 76, 77, 83, 98, 99, 100, 101 }

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

F grade: { 1, 25, 26, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 53, 54, 55, 56, 57, 58, 59, 88, 89, 90, 95, 96, 97, 125, 126, 127, 132, 133, 134, 135, 136, 137, 138, 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, 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, 111, 122 }

F grade: { 2, 3, 4, 5, 17, 18, 19, 20, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 67, 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
grade A A A A F(-2) A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 147 147 142 173 0 626 0 178
normalized size 1 1. 0.97 1.18 0. 4.26 0. 1.21
time (sec) N/A 0.054 0.199 0.05 0. 2.288 0. 1.25
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 121 121 119 91 176 320 0 0
normalized size 1 1. 0.98 0.75 1.45 2.64 0. 0.
time (sec) N/A 0.031 0.089 0.104 1.897 2.283 0. 0.
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 95 95 88 71 139 246 0 0
normalized size 1 1. 0.93 0.75 1.46 2.59 0. 0.
time (sec) N/A 0.022 0.087 0.094 1.785 2.279 0. 0.
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 69 69 76 51 103 184 0 0
normalized size 1 1. 1.1 0.74 1.49 2.67 0. 0.
time (sec) N/A 0.015 0.07 0.095 1.711 2.29 0. 0.
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 43 43 64 31 66 131 0 0
normalized size 1 1. 1.49 0.72 1.53 3.05 0. 0.
time (sec) N/A 0.01 0.052 0.094 1.79 2.116 0. 0.
Problem 6 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 101 101 88 82 158 247 0 77
normalized size 1 1. 0.87 0.81 1.56 2.45 0. 0.76
time (sec) N/A 0.028 0.072 0.045 1.725 2.24 0. 1.301
Problem 7 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 79 79 78 64 122 189 0 63
normalized size 1 1. 0.99 0.81 1.54 2.39 0. 0.8
time (sec) N/A 0.019 0.053 0.044 1.714 2.074 0. 1.294
Problem 8 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 57 57 68 46 85 143 0 50
normalized size 1 1. 1.19 0.81 1.49 2.51 0. 0.88
time (sec) N/A 0.013 0.051 0.044 1.824 2.187 0. 1.355
Problem 9 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 35 35 58 28 49 101 0 36
normalized size 1 1. 1.66 0.8 1.4 2.89 0. 1.03
time (sec) N/A 0.009 0.035 0.045 1.758 2.181 0. 1.306
Problem 10 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 35 35 32 28 49 82 0 34
normalized size 1 1. 0.91 0.8 1.4 2.34 0. 0.97
time (sec) N/A 0.01 0.043 0.056 1.79 2.17 0. 1.289
Problem 11 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 35 35 58 28 49 105 0 36
normalized size 1 1. 1.66 0.8 1.4 3. 0. 1.03
time (sec) N/A 0.01 0.036 0.044 1.776 2.075 0. 1.228
Problem 12 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 51 51 44 42 74 111 0 47
normalized size 1 1. 0.86 0.82 1.45 2.18 0. 0.92
time (sec) N/A 0.01 0.067 0.052 2.576 2.095 0. 1.374
Problem 13 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 35 35 40 33 55 85 0 45
normalized size 1 1. 1.14 0.94 1.57 2.43 0. 1.29
time (sec) N/A 0.007 0.03 0.052 1.129 2.162 0. 1.257
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 37 37 48 33 58 85 0 45
normalized size 1 1. 1.3 0.89 1.57 2.3 0. 1.22
time (sec) N/A 0.007 0.038 0.051 2.326 2.351 0. 1.285
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 39 39 46 33 58 90 0 50
normalized size 1 1. 1.18 0.85 1.49 2.31 0. 1.28
time (sec) N/A 0.007 0.029 0.049 1.229 2.174 0. 1.327
Problem 16 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 83 83 70 75 150 223 0 100
normalized size 1 1. 0.84 0.9 1.81 2.69 0. 1.2
time (sec) N/A 0.018 0.025 0.051 1.3 2.226 0. 1.302
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A B B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 16 16 53 10 28 62 0 0
normalized size 1 1. 3.31 0.62 1.75 3.88 0. 0.
time (sec) N/A 0.006 0.017 0.105 1.796 2.476 0. 0.
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 26 26 24 21 38 100 0 0
normalized size 1 1. 0.92 0.81 1.46 3.85 0. 0.
time (sec) N/A 0.003 0.005 0.123 1.222 2.646 0. 0.
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 53 53 36 42 74 178 0 0
normalized size 1 1. 0.68 0.79 1.4 3.36 0. 0.
time (sec) N/A 0.007 0.011 0.098 1.208 2.512 0. 0.
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 79 79 48 62 111 288 0 0
normalized size 1 1. 0.61 0.78 1.41 3.65 0. 0.
time (sec) N/A 0.012 0.015 0.108 1.379 2.413 0. 0.
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 12 12 40 9 11 47 0 11
normalized size 1 1. 3.33 0.75 0.92 3.92 0. 0.92
time (sec) N/A 0.006 0.014 0.048 1.787 2.331 0. 1.221
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 22 22 21 25 38 66 0 39
normalized size 1 1. 0.95 1.14 1.73 3. 0. 1.77
time (sec) N/A 0.002 0.006 0.047 1.168 2.165 0. 1.322
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 31 35 74 119 0 53
normalized size 1 1. 0.69 0.78 1.64 2.64 0. 1.18
time (sec) N/A 0.006 0.01 0.048 1.236 2.197 0. 1.355
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 67 67 51 45 111 180 0 66
normalized size 1 1. 0.76 0.67 1.66 2.69 0. 0.99
time (sec) N/A 0.012 0.015 0.048 1.363 2.247 0. 1.627
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 12 12 47 35 0 55 0 20
normalized size 1 1. 3.92 2.92 0. 4.58 0. 1.67
time (sec) N/A 0.008 0.014 0.05 0. 2.232 0. 2.638
Problem 26 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 24 24 45 37 0 59 0 49
normalized size 1 1. 1.88 1.54 0. 2.46 0. 2.04
time (sec) N/A 0.008 0.02 0.057 0. 2.158 0. 1.806
Problem 27 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 7 11 42 0 8
normalized size 1 1. 1.4 0.7 1.1 4.2 0. 0.8
time (sec) N/A 0.006 0.01 0.065 3.884 2.276 0. 1.617
Problem 28 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 16 16 33 14 23 43 0 24
normalized size 1 1. 2.06 0.88 1.44 2.69 0. 1.5
time (sec) N/A 0.004 0.006 0.052 2.496 2.281 0. 1.854
Problem 29 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 16 16 33 14 23 43 0 24
normalized size 1 1. 2.06 0.88 1.44 2.69 0. 1.5
time (sec) N/A 0.004 0.013 0.052 1.191 2.478 0. 1.262
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 448 448 48 0 0 0 0 0
normalized size 1 1. 0.11 0. 0. 0. 0. 0.
time (sec) N/A 0.717 0.016 0.456 0. 0. 0. 0.
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 387 387 45 0 0 0 0 0
normalized size 1 1. 0.12 0. 0. 0. 0. 0.
time (sec) N/A 0.449 0.01 0.435 0. 0. 0. 0.
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 322 322 43 0 0 0 0 0
normalized size 1 1. 0.13 0. 0. 0. 0. 0.
time (sec) N/A 0.394 0.011 0.651 0. 0. 0. 0.
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 384 384 47 0 0 0 0 0
normalized size 1 1. 0.12 0. 0. 0. 0. 0.
time (sec) N/A 0.457 0.012 0.613 0. 0. 0. 0.
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 448 448 50 0 0 0 0 0
normalized size 1 1. 0.11 0. 0. 0. 0. 0.
time (sec) N/A 0.51 0.013 1.226 0. 0. 0. 0.
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 842 842 48 0 0 0 0 0
normalized size 1 1. 0.06 0. 0. 0. 0. 0.
time (sec) N/A 1.058 0.014 0.574 0. 0. 0. 0.
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 781 781 45 0 0 0 0 0
normalized size 1 1. 0.06 0. 0. 0. 0. 0.
time (sec) N/A 0.947 0.009 0.61 0. 0. 0. 0.
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 715 715 45 0 0 0 0 0
normalized size 1 1. 0.06 0. 0. 0. 0. 0.
time (sec) N/A 0.86 0.01 0.699 0. 0. 0. 0.
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 773 773 45 0 0 0 0 0
normalized size 1 1. 0.06 0. 0. 0. 0. 0.
time (sec) N/A 0.947 0.012 0.928 0. 0. 0. 0.
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 838 838 50 0 0 0 0 0
normalized size 1 1. 0.06 0. 0. 0. 0. 0.
time (sec) N/A 1.036 0.012 1.415 0. 0. 0. 0.
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 119 119 48 0 0 0 0 0
normalized size 1 1. 0.4 0. 0. 0. 0. 0.
time (sec) N/A 0.046 0.015 0.477 0. 0. 0. 0.
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 90 90 45 0 0 0 0 0
normalized size 1 1. 0.5 0. 0. 0. 0. 0.
time (sec) N/A 0.034 0.013 0.656 0. 0. 0. 0.
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 90 90 45 0 0 0 0 0
normalized size 1 1. 0.5 0. 0. 0. 0. 0.
time (sec) N/A 0.033 0.01 0.401 0. 0. 0. 0.
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 58 58 45 0 0 0 0 0
normalized size 1 1. 0.78 0. 0. 0. 0. 0.
time (sec) N/A 0.023 0.01 0.608 0. 0. 0. 0.
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 59 59 43 0 0 0 0 0
normalized size 1 1. 0.73 0. 0. 0. 0. 0.
time (sec) N/A 0.023 0.01 0.678 0. 0. 0. 0.
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 83 83 45 0 0 0 0 0
normalized size 1 1. 0.54 0. 0. 0. 0. 0.
time (sec) N/A 0.032 0.013 0.861 0. 0. 0. 0.
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 115 115 50 0 0 0 0 0
normalized size 1 1. 0.43 0. 0. 0. 0. 0.
time (sec) N/A 0.044 0.013 1.42 0. 0. 0. 0.
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 146 146 50 0 0 0 0 0
normalized size 1 1. 0.34 0. 0. 0. 0. 0.
time (sec) N/A 0.06 0.012 0.652 0. 0. 0. 0.
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 45 0 0 0 0 0
normalized size 1 1. 0.82 0. 0. 0. 0. 0.
time (sec) N/A 0.01 0.01 0.441 0. 0. 0. 0.
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 51 51 51 44 58 96 49 58
normalized size 1 1. 1. 0.86 1.14 1.88 0.96 1.14
time (sec) N/A 0.017 0.002 0.045 1.168 1.797 0.074 1.232
Problem 50 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 35 32 42 66 32 42
normalized size 1 1. 1. 0.91 1.2 1.89 0.91 1.2
time (sec) N/A 0.011 0.001 0.046 1.14 1.86 0.067 1.196
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 25 25 25 22 28 47 22 28
normalized size 1 1. 1. 0.88 1.12 1.88 0.88 1.12
time (sec) N/A 0.007 0.001 0.051 1.236 1.833 0.084 1.315
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 12 12 12 11 14 23 8 14
normalized size 1 1. 1. 0.92 1.17 1.92 0.67 1.17
time (sec) N/A 0.002 0. 0.046 1.154 1.813 0.071 1.227
Problem 53 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 0.005 0.005 0.047 0. 2.112 0.154 1.237
Problem 54 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 45 45 45 36 0 261 78 47
normalized size 1 1. 1. 0.8 0. 5.8 1.73 1.04
time (sec) N/A 0.01 0.027 0.054 0. 2.164 0.393 1.291
Problem 55 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 62 62 55 51 0 401 105 61
normalized size 1 1. 0.89 0.82 0. 6.47 1.69 0.98
time (sec) N/A 0.016 0.038 0.05 0. 2.076 0.503 1.196
Problem 56 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 84 84 76 66 0 347 97 85
normalized size 1 1. 0.9 0.79 0. 4.13 1.15 1.01
time (sec) N/A 0.022 0.111 0.047 0. 2.337 5.604 1.211
Problem 57 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 65 65 65 51 0 294 70 66
normalized size 1 1. 1. 0.78 0. 4.52 1.08 1.02
time (sec) N/A 0.014 0.089 0.051 0. 2.363 3.863 1.228
Problem 58 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 46 46 49 36 0 232 41 50
normalized size 1 1. 1.07 0.78 0. 5.04 0.89 1.09
time (sec) N/A 0.009 0.021 0.047 0. 2.389 2.716 1.245
Problem 59 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 25 25 25 21 0 153 17 31
normalized size 1 1. 1. 0.84 0. 6.12 0.68 1.24
time (sec) N/A 0.005 0.006 0.046 0. 2.138 1.592 1.343
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 16 16 16 15 19 47 17 19
normalized size 1 1. 1. 0.94 1.19 2.94 1.06 1.19
time (sec) N/A 0.002 0.004 0.047 1.059 2.133 0.849 1.234
Problem 61 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 39 39 29 26 42 99 95 36
normalized size 1 1. 0.74 0.67 1.08 2.54 2.44 0.92
time (sec) N/A 0.006 0.009 0.049 1.135 2.261 1.182 1.239
Problem 62 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 58 58 40 37 62 146 413 55
normalized size 1 1. 0.69 0.64 1.07 2.52 7.12 0.95
time (sec) N/A 0.01 0.011 0.048 1.068 2.259 2.289 1.241
Problem 63 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 77 77 51 48 82 192 1265 74
normalized size 1 1. 0.66 0.62 1.06 2.49 16.43 0.96
time (sec) N/A 0.016 0.014 0.05 1.137 2.306 4.732 1.197
Problem 64 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 23 23 20 35 41 46 0 69
normalized size 1 1. 0.87 1.52 1.78 2. 0. 3.
time (sec) N/A 0.003 0.009 0.071 1.701 2.087 0. 1.204
Problem 65 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 23 23 25 25 41 20 0 35
normalized size 1 1. 1.09 1.09 1.78 0.87 0. 1.52
time (sec) N/A 0.003 0.005 0.069 1.766 2.135 0. 1.244
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 26 23 8 24 0 34
normalized size 1 1. 0.9 0.79 0.28 0.83 0. 1.17
time (sec) N/A 0.005 0.006 0.126 1.67 2.185 0. 1.227
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 25 25 20 17 12 34 0 0
normalized size 1 1. 0.8 0.68 0.48 1.36 0. 0.
time (sec) N/A 0.003 0.006 0.076 1.699 2.056 0. 0.
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 23 23 25 25 41 20 8 35
normalized size 1 1. 1.09 1.09 1.78 0.87 0.35 1.52
time (sec) N/A 0.003 0.011 0.075 1.699 2.03 0.09 1.258
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 29 29 26 23 8 24 7 20
normalized size 1 1. 0.9 0.79 0.28 0.83 0.24 0.69
time (sec) N/A 0.005 0.011 0.125 1.673 2.066 0.095 1.625
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A C F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 27 27 41 26 0 35
normalized size 1 1. 1.17 1.17 1.78 1.13 0. 1.52
time (sec) N/A 0.003 0.008 0.066 1.696 2.046 0. 1.331
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C C F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 28 25 8 28 0 31
normalized size 1 1. 0.97 0.86 0.28 0.97 0. 1.07
time (sec) N/A 0.005 0.007 0.11 1.631 2.103 0. 1.201
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A C F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 27 27 41 26 0 35
normalized size 1 1. 1.17 1.17 1.78 1.13 0. 1.52
time (sec) N/A 0.003 0.006 0.069 1.736 2.039 0. 1.238
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C C F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 28 25 8 28 0 31
normalized size 1 1. 0.97 0.86 0.28 0.97 0. 1.07
time (sec) N/A 0.006 0.004 0.122 1.699 2.021 0. 1.358
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 109 109 207 636 316 585 253 451
normalized size 1 1. 1.9 5.83 2.9 5.37 2.32 4.14
time (sec) N/A 0.14 0.034 0.079 1.125 2.103 0.21 1.336
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 109 109 207 636 316 632 250 451
normalized size 1 1. 1.9 5.83 2.9 5.8 2.29 4.14
time (sec) N/A 0.137 0.045 0.073 1.077 2.138 0.267 1.287
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 109 109 199 636 316 618 253 451
normalized size 1 1. 1.83 5.83 2.9 5.67 2.32 4.14
time (sec) N/A 0.142 0.031 0.072 1.143 2.208 0.292 1.372
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 109 109 207 636 316 676 248 451
normalized size 1 1. 1.9 5.83 2.9 6.2 2.28 4.14
time (sec) N/A 0.14 0.044 0.069 1.153 2.105 0.271 1.259
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 18 18 18 17 22 58 22 22
normalized size 1 1. 1. 0.94 1.22 3.22 1.22 1.22
time (sec) N/A 0.011 0.005 0.044 1.781 2.135 0.104 1.24
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 12 12 12 9 11 28 7 11
normalized size 1 1. 1. 0.75 0.92 2.33 0.58 0.92
time (sec) N/A 0.009 0.014 0.052 1.701 2.276 0.248 1.306
Problem 80 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 19 19 34 17 36 109 39 42
normalized size 1 1. 1.79 0.89 1.89 5.74 2.05 2.21
time (sec) N/A 0.019 0.02 0.046 1.498 2.199 0.146 1.233
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 13 13 13 14 18 36 10 20
normalized size 1 1. 1. 1.08 1.38 2.77 0.77 1.54
time (sec) N/A 0.005 0.003 0.048 1.229 2.126 0.119 1.259
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 21 21 21 16 20 47 14 23
normalized size 1 1. 1. 0.76 0.95 2.24 0.67 1.1
time (sec) N/A 0.006 0.003 0.049 1.093 2.141 0.163 1.208
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B B B B B B B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 6 17 17 14 18 46 12 20
normalized size 1 2.83 2.83 2.33 3. 7.67 2. 3.33
time (sec) N/A 0.004 0.003 0.047 1.137 2.095 0.095 1.261
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 27 24 51 130 76 54
normalized size 1 1. 1. 0.89 1.89 4.81 2.81 2.
time (sec) N/A 0.019 0.009 0.045 1.122 2.275 0.193 1.226
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 29 26 53 131 76 61
normalized size 1 1. 1.07 0.96 1.96 4.85 2.81 2.26
time (sec) N/A 0.019 0.008 0.044 1.148 2.189 0.32 1.273
Problem 86 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 31 31 31 28 36 108 87 36
normalized size 1 1. 1. 0.9 1.16 3.48 2.81 1.16
time (sec) N/A 0.02 0.01 0.045 1.109 2.312 0.306 1.245
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 29 26 53 135 76 61
normalized size 1 1. 1.07 0.96 1.96 5. 2.81 2.26
time (sec) N/A 0.018 0.008 0.054 1.218 2.359 0.292 1.312
Problem 88 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 38 38 38 35 0 259 124 46
normalized size 1 1. 1. 0.92 0. 6.82 3.26 1.21
time (sec) N/A 0.034 0.011 0.223 0. 2.092 0.291 1.184
Problem 89 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 35 35 34 35 0 261 100 41
normalized size 1 1. 0.97 1. 0. 7.46 2.86 1.17
time (sec) N/A 0.027 0.009 0.142 0. 2.176 0.235 1.317
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 32 32 41 31 0 149 102 74
normalized size 1 1. 1.28 0.97 0. 4.66 3.19 2.31
time (sec) N/A 0.025 0.01 0.136 0. 2.099 0.323 1.379
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 43 43 43 37 49 126 39 49
normalized size 1 1. 1. 0.86 1.14 2.93 0.91 1.14
time (sec) N/A 0.015 0.023 0.048 1.71 2.042 0.195 1.279
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 43 43 62 37 63 181 58 69
normalized size 1 1. 1.44 0.86 1.47 4.21 1.35 1.6
time (sec) N/A 0.016 0.029 0.049 2.847 2.111 0.163 1.297
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 34 34 33 32 46 132 29 49
normalized size 1 1. 0.97 0.94 1.35 3.88 0.85 1.44
time (sec) N/A 0.008 0.011 0.056 1.906 2.152 0.267 1.273
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 42 42 42 32 46 142 32 49
normalized size 1 1. 1. 0.76 1.1 3.38 0.76 1.17
time (sec) N/A 0.009 0.013 0.056 1.186 2.052 0.192 1.232
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 71 71 70 68 0 724 265 90
normalized size 1 1. 0.99 0.96 0. 10.2 3.73 1.27
time (sec) N/A 0.04 0.065 0.191 0. 2.199 1.171 1.24
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 72 72 72 86 0 664 228 101
normalized size 1 1. 1. 1.19 0. 9.22 3.17 1.4
time (sec) N/A 0.036 0.043 0.152 0. 2.414 1.393 1.197
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 69 69 78 84 0 360 218 122
normalized size 1 1. 1.13 1.22 0. 5.22 3.16 1.77
time (sec) N/A 0.034 0.061 0.149 0. 2.504 1.036 1.216
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 62 62 65 111 215 161 212 135
normalized size 1 1. 1.05 1.79 3.47 2.6 3.42 2.18
time (sec) N/A 0.157 0.095 0.423 1.706 2.676 1.401 1.367
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 33 58 34 31 88 128 56 76
normalized size 1 1.76 1.03 0.94 2.67 3.88 1.7 2.3
time (sec) N/A 0.036 0.032 0.178 1.147 2.706 0.57 1.264
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 58 32 31 82 128 56 73
normalized size 1 1.87 1.03 1. 2.65 4.13 1.81 2.35
time (sec) N/A 0.029 0.031 0.147 1.223 2.359 0.451 1.214
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A C B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 17 17 19 33 36 57 165 36
normalized size 1 1. 1.12 1.94 2.12 3.35 9.71 2.12
time (sec) N/A 0.018 0.02 0.064 1.795 2.25 0.244 1.406
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B A A C A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 23 23 56 39 45 69 70 45
normalized size 1 1. 2.43 1.7 1.96 3. 3.04 1.96
time (sec) N/A 0.028 0.04 0.091 1.71 2.466 0.732 1.211
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 38 38 39 29 51 109 0 54
normalized size 1 1. 1.03 0.76 1.34 2.87 0. 1.42
time (sec) N/A 0.011 0.017 0.049 1.619 2.41 0. 1.209
Problem 104 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 30 30 30 25 51 134 0 32
normalized size 1 1. 1. 0.83 1.7 4.47 0. 1.07
time (sec) N/A 0.01 0.013 0.048 1.701 1.908 0. 1.261
Problem 105 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 49 49 49 50 70 109 0 55
normalized size 1 1. 1. 1.02 1.43 2.22 0. 1.12
time (sec) N/A 0.01 0.016 0.049 1.49 2.165 0. 1.215
Problem 106 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 45 45 46 35 62 158 0 72
normalized size 1 1. 1.02 0.78 1.38 3.51 0. 1.6
time (sec) N/A 0.015 0.017 0.044 1.708 1.964 0. 1.213
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 46 35 62 166 0 49
normalized size 1 1. 1.02 0.78 1.38 3.69 0. 1.09
time (sec) N/A 0.016 0.019 0.047 1.718 1.944 0. 1.266
Problem 108 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 62 62 55 50 78 167 0 73
normalized size 1 1. 0.89 0.81 1.26 2.69 0. 1.18
time (sec) N/A 0.015 0.028 0.045 1.74 1.975 0. 1.251
Problem 109 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 43 43 44 32 55 170 0 42
normalized size 1 1. 1.02 0.74 1.28 3.95 0. 0.98
time (sec) N/A 0.012 0.019 0.046 1.719 1.901 0. 1.298
Problem 110 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 59 59 53 50 78 158 0 73
normalized size 1 1. 0.9 0.85 1.32 2.68 0. 1.24
time (sec) N/A 0.013 0.02 0.052 1.69 1.856 0. 1.165
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C C F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 59 59 54 46 62 244 0 49
normalized size 1 1. 0.92 0.78 1.05 4.14 0. 0.83
time (sec) N/A 0.016 0.025 0.047 1.724 2.009 0. 1.201
Problem 112 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 62 62 55 50 78 167 0 73
normalized size 1 1. 0.89 0.81 1.26 2.69 0. 1.18
time (sec) N/A 0.013 0.027 0.043 1.668 2.046 0. 1.208
Problem 113 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 39 39 40 32 55 169 0 42
normalized size 1 1. 1.03 0.82 1.41 4.33 0. 1.08
time (sec) N/A 0.008 0.019 0.045 1.743 1.966 0. 1.223
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 14 14 14 9 11 59 0 27
normalized size 1 1. 1. 0.64 0.79 4.21 0. 1.93
time (sec) N/A 0.007 0.005 0.045 1.7 2.119 0. 1.27
Problem 115 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 7 11 88 0 8
normalized size 1 1. 1.4 0.7 1.1 8.8 0. 0.8
time (sec) N/A 0.007 0.006 0.046 1.697 1.822 0. 1.16
Problem 116 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 25 25 24 30 30 59 0 28
normalized size 1 1. 0.96 1.2 1.2 2.36 0. 1.12
time (sec) N/A 0.006 0.005 0.046 1.708 1.98 0. 1.196
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 18 18 18 15 22 105 0 45
normalized size 1 1. 1. 0.83 1.22 5.83 0. 2.5
time (sec) N/A 0.01 0.006 0.048 1.765 1.912 0. 1.3
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 19 19 19 15 22 115 0 22
normalized size 1 1. 1. 0.79 1.16 6.05 0. 1.16
time (sec) N/A 0.01 0.006 0.051 1.69 2.018 0. 1.267
Problem 119 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 35 35 28 30 38 111 0 46
normalized size 1 1. 0.8 0.86 1.09 3.17 0. 1.31
time (sec) N/A 0.008 0.006 0.047 1.575 2.073 0. 1.288
Problem 120 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 17 17 17 12 15 115 0 15
normalized size 1 1. 1. 0.71 0.88 6.76 0. 0.88
time (sec) N/A 0.007 0.006 0.049 1.705 1.946 0. 1.319
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 32 32 26 30 38 104 0 46
normalized size 1 1. 0.81 0.94 1.19 3.25 0. 1.44
time (sec) N/A 0.008 0.007 0.049 1.741 1.769 0. 1.262
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A C C F C
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 33 33 28 26 22 190 0 22
normalized size 1 1. 0.85 0.79 0.67 5.76 0. 0.67
time (sec) N/A 0.008 0.007 0.057 1.824 1.921 0. 1.242
Problem 123 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 35 35 28 30 38 109 0 46
normalized size 1 1. 0.8 0.86 1.09 3.11 0. 1.31
time (sec) N/A 0.008 0.006 0.051 1.841 1.989 0. 1.273
Problem 124 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 13 13 13 12 15 115 0 15
normalized size 1 1. 1. 0.92 1.15 8.85 0. 1.15
time (sec) N/A 0.004 0.006 0.057 1.769 1.952 0. 1.3
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 22 22 22 51 0 320 0 66
normalized size 1 1. 1. 2.32 0. 14.55 0. 3.
time (sec) N/A 0.013 0.027 0.264 0. 2.077 0. 1.438
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 23 44 0 323 0 72
normalized size 1 1. 1. 1.91 0. 14.04 0. 3.13
time (sec) N/A 0.013 0.027 0.247 0. 1.98 0. 1.434
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 20 20 20 44 0 317 0 72
normalized size 1 1. 1. 2.2 0. 15.85 0. 3.6
time (sec) N/A 0.011 0.026 0.242 0. 2.184 0. 1.278
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 19 19 19 24 35 95 0 23
normalized size 1 1. 1. 1.26 1.84 5. 0. 1.21
time (sec) N/A 0.002 0.006 0.049 1.173 1.874 0. 1.193
Problem 129 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 23 23 23 28 41 112 0 23
normalized size 1 1. 1. 1.22 1.78 4.87 0. 1.
time (sec) N/A 0.003 0.007 0.042 1.181 1.875 0. 1.281
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 23 26 41 70 0 39
normalized size 1 1. 1. 1.13 1.78 3.04 0. 1.7
time (sec) N/A 0.005 0.03 0.045 1.182 1.929 0. 1.33
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 43 43 31 36 80 123 0 49
normalized size 1 1. 0.72 0.84 1.86 2.86 0. 1.14
time (sec) N/A 0.007 0.009 0.046 1.142 2.062 0. 1.314
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 122 122 126 0 0 0 0 0
normalized size 1 1. 1.03 0. 0. 0. 0. 0.
time (sec) N/A 0.036 0.101 1.167 0. 0. 0. 0.
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 37 37 37 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.016 0.01 3.641 0. 0. 0. 0.
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 32 32 32 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.014 0.007 3.586 0. 0. 0. 0.
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 37 37 37 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.016 0.01 2.441 0. 0. 0. 0.
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 21 21 21 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.01 0.005 3.654 0. 0. 0. 0.
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 54 54 48 0 0 0 0 0
normalized size 1 1. 0.89 0. 0. 0. 0. 0.
time (sec) N/A 0.01 0.02 0.841 0. 0. 0. 0.
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 18 18 17 17 0 47 20 22
normalized size 1 1. 0.94 0.94 0. 2.61 1.11 1.22
time (sec) N/A 0.002 0.007 0.044 0. 1.956 0.063 1.286
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 26 0 0 0 0 0
normalized size 1 1. 0.84 0. 0. 0. 0. 0.
time (sec) N/A 0.012 0.007 0.927 0. 0. 0. 0.
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 31 31 26 0 0 0 0 0
normalized size 1 1. 0.84 0. 0. 0. 0. 0.
time (sec) N/A 0.011 0.007 0.933 0. 0. 0. 0.
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 38 38 37 0 0 0 0 0
normalized size 1 1. 0.97 0. 0. 0. 0. 0.
time (sec) N/A 0.013 0.009 0.906 0. 0. 0. 0.
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 35 35 35 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 0.008 0.919 0. 0. 0. 0.
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 38 38 37 0 0 0 0 0
normalized size 1 1. 0.97 0. 0. 0. 0. 0.
time (sec) N/A 0.013 0.01 0.925 0. 0. 0. 0.

2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. It gives additional statistics for each integral. the column steps is the number of steps used by Rubi to obtain the antiderivative. The rules column is the number of unique rules used. The integrand size column is the leaf size of the integrand. Finally the ratio \(\frac{\text{number of rules}}{\text{integrand size}}\) is given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [35] had the largest ratio of [ 0.5385 ]

Table 2.1Rubi specific breakdown of results for each integral
# grade
number of
steps
used
number of
unique
rules
normalized
antiderivative
leaf size
integrand
leaf size
\(\frac{\text{number of rules}}{\text{integrand leaf size}}\)
1 A 6 3 1. 13 0.231
2 A 6 3 1. 15 0.2
3 A 5 3 1. 15 0.2
4 A 4 3 1. 15 0.2
5 A 3 3 1. 15 0.2
6 A 6 3 1. 13 0.231
7 A 5 3 1. 13 0.231
8 A 4 3 1. 13 0.231
9 A 3 3 1. 13 0.231
10 A 3 3 1. 13 0.231
11 A 3 3 1. 13 0.231
12 A 4 3 1. 11 0.273
13 A 3 3 1. 11 0.273
14 A 3 3 1. 11 0.273
15 A 3 3 1. 11 0.273
16 A 3 2 1. 13 0.154
17 A 2 2 1. 15 0.133
18 A 1 1 1. 15 0.067
19 A 2 2 1. 15 0.133
20 A 3 2 1. 15 0.133
21 A 2 2 1. 13 0.154
22 A 1 1 1. 13 0.077
23 A 2 2 1. 13 0.154
24 A 3 2 1. 13 0.154
25 A 2 2 1. 16 0.125
26 A 2 2 1. 15 0.133
27 A 2 2 1. 13 0.154
28 A 2 2 1. 11 0.182
29 A 2 2 1. 11 0.182
30 A 6 5 1. 13 0.385
31 A 5 5 1. 13 0.385
32 A 4 4 1. 13 0.308
33 A 5 5 1. 13 0.385
34 A 6 5 1. 13 0.385
35 A 8 7 1. 13 0.538
36 A 7 7 1. 13 0.538
37 A 6 6 1. 13 0.462
38 A 7 7 1. 13 0.538
39 A 8 7 1. 13 0.538
40 A 5 4 1. 13 0.308
41 A 4 4 1. 13 0.308
42 A 4 4 1. 13 0.308
43 A 3 3 1. 13 0.231
44 A 3 3 1. 13 0.231
45 A 4 4 1. 13 0.308
46 A 5 4 1. 13 0.308
47 A 6 4 1. 13 0.308
48 A 1 1 1. 11 0.091
49 A 2 1 1. 9 0.111
50 A 2 1 1. 9 0.111
51 A 2 1 1. 9 0.111
52 A 1 0 1. 7 0.
53 A 1 1 1. 9 0.111
54 A 2 2 1. 9 0.222
55 A 3 2 1. 9 0.222
56 A 5 3 1. 11 0.273
57 A 4 3 1. 11 0.273
58 A 3 3 1. 11 0.273
59 A 2 2 1. 11 0.182
60 A 1 1 1. 11 0.091
61 A 2 2 1. 11 0.182
62 A 3 2 1. 11 0.182
63 A 4 2 1. 11 0.182
64 A 1 1 1. 14 0.071
65 A 1 1 1. 14 0.071
66 A 2 2 1. 14 0.143
67 A 1 1 1. 14 0.071
68 A 1 1 1. 14 0.071
69 A 2 2 1. 14 0.143
70 A 1 1 1. 14 0.071
71 A 2 2 1. 14 0.143
72 A 1 1 1. 14 0.071
73 A 2 2 1. 14 0.143
74 A 3 2 1. 23 0.087
75 A 3 2 1. 23 0.087
76 A 3 2 1. 23 0.087
77 A 3 2 1. 23 0.087
78 A 2 2 1. 12 0.167
79 A 2 2 1. 15 0.133
80 A 2 2 1. 12 0.167
81 A 3 2 1. 12 0.167
82 A 3 2 1. 12 0.167
83 B 3 2 2.83 10 0.2
84 A 2 2 1. 12 0.167
85 A 2 2 1. 12 0.167
86 A 2 2 1. 12 0.167
87 A 2 2 1. 12 0.167
88 A 2 2 1. 12 0.167
89 A 2 2 1. 13 0.154
90 A 2 2 1. 14 0.143
91 A 3 3 1. 12 0.25
92 A 3 3 1. 12 0.25
93 A 4 3 1. 12 0.25
94 A 4 3 1. 12 0.25
95 A 3 3 1. 12 0.25
96 A 3 3 1. 13 0.231
97 A 3 3 1. 14 0.214
98 A 2 2 1. 40 0.05
99 A 3 2 1.76 30 0.067
100 A 3 2 1.87 31 0.065
101 A 2 2 1. 14 0.143
102 A 2 2 1. 16 0.125
103 A 3 3 1. 14 0.214
104 A 3 3 1. 14 0.214
105 A 3 3 1. 14 0.214
106 A 3 3 1. 14 0.214
107 A 3 3 1. 14 0.214
108 A 3 3 1. 14 0.214
109 A 3 3 1. 14 0.214
110 A 3 3 1. 14 0.214
111 A 3 3 1. 14 0.214
112 A 3 3 1. 14 0.214
113 A 3 3 1. 14 0.214
114 A 2 2 1. 14 0.143
115 A 2 2 1. 14 0.143
116 A 2 2 1. 14 0.143
117 A 2 2 1. 14 0.143
118 A 2 2 1. 14 0.143
119 A 2 2 1. 14 0.143
120 A 2 2 1. 14 0.143
121 A 2 2 1. 14 0.143
122 A 2 2 1. 14 0.143
123 A 2 2 1. 14 0.143
124 A 2 2 1. 14 0.143
125 A 2 2 1. 27 0.074
126 A 2 2 1. 30 0.067
127 A 2 2 1. 28 0.071
128 A 1 1 1. 12 0.083
129 A 1 1 1. 14 0.071
130 A 1 1 1. 16 0.062
131 A 2 2 1. 14 0.143
132 A 1 1 1. 12 0.083
133 A 2 2 1. 12 0.167
134 A 2 2 1. 12 0.167
135 A 2 2 1. 12 0.167
136 A 2 2 1. 12 0.167
137 A 1 1 1. 10 0.1
138 A 1 1 1. 7 0.143
139 A 2 2 1. 12 0.167
140 A 2 2 1. 12 0.167
141 A 2 2 1. 12 0.167
142 A 2 2 1. 12 0.167
143 A 2 2 1. 12 0.167

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