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Chapter 2
detailed summary tables of results

 2.1 List of integrals sorted by grade for each CAS
  2.1.1 Rubi
  2.1.2 Mathematica
  2.1.3 Maple
  2.1.4 Maxima
  2.1.5 FriCAS
  2.1.6 Sympy
  2.1.7 Giac
 2.2 Detailed conclusion table per each integral for all CAS systems
 2.3 Detailed conclusion table specific for Rubi results

2.1 List of integrals sorted by grade for each CAS

2.1.1 Rubi

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 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, 54, 55, 60, 61, 62, 66, 67, 68, 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, 101, 108, 109, 110, 115, 116, 117, 119, 120, 121, 122, 123, 124, 125, 129, 130, 131, 132, 133, 134, 135, 138, 139, 140, 141, 142, 143, 144, 145, 147, 148, 149, 150, 151, 152, 153, 154, 156, 157, 158, 159, 160, 161, 162, 163, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178 }

B grade: { 25, 53, 72, 98, 99, 100, 102, 103, 104, 107, 111 }

C grade: { 51, 52, 56, 57, 58, 59, 63, 64, 65, 69, 70, 71, 105, 112, 113, 118, 126, 127, 128, 136, 137, 146, 155, 164 }

F grade: { 106, 114}

2.1.3 Maple

A grade: { 1, 2, 3, 4, 6, 7, 8, 9, 11, 13, 14, 18, 22, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 46, 47, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 73, 74, 76, 79, 80, 81, 82, 83, 84, 85, 86, 87, 90, 91, 92, 93, 94, 95, 96, 97, 121, 122, 123, 124, 125, 130, 131, 132, 133, 134, 135, 141, 142, 143, 144, 150, 151, 152, 153, 159, 160, 161, 162, 168, 169, 170, 171, 172, 173, 177, 178 }

B grade: { 5, 10, 12, 15, 16, 17, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 44, 45, 48, 49, 50, 51, 52, 56, 70, 71, 72, 75, 77, 78, 88, 89, 105, 112, 113 }

C grade: { 98, 99, 100, 101, 102, 103, 104, 106, 107, 108, 109, 110, 111, 114, 115, 116, 117 }

F grade: { 41, 118, 119, 120, 126, 127, 128, 129, 136, 137, 138, 139, 140, 145, 146, 147, 148, 149, 154, 155, 156, 157, 158, 163, 164, 165, 166, 167, 174, 175, 176 }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 20, 29, 33, 34, 35, 42, 43, 44, 45, 46, 47, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 88, 89, 90, 91, 92, 93, 94, 95, 168, 169, 170, 171, 172, 173, 177, 178

B grade: { 15, 22 }

C grade: { }

F grade: { 8, 16, 18, 19, 21, 23, 24, 25, 26, 27, 28, 30, 31, 32, 36, 37, 38, 39, 40, 41, 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, 86, 87, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 174, 175, 176 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 29, 30, 31, 32, 33, 34, 35, 39, 40, 42, 43, 44, 45, 46, 54, 55, 61, 62, 67, 68, 73, 74, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 88, 89, 90, 91, 92, 93, 94, 95, 105, 118, 119, 120, 121, 122, 123, 124, 125, 128, 129, 130, 131, 132, 133, 134, 135, 138, 139, 140, 141, 142, 143, 144, 147, 148, 149, 150, 151, 152, 153, 159, 160, 161, 162, 168, 169, 170, 171, 172, 173, 177, 178 }

B grade: { 7, 17, 47, 49, 50, 112, 113, 156, 157, 158 }

C grade: { }

F grade: { 8, 16, 18, 19, 24, 25, 26, 27, 28, 36, 37, 38, 41, 48, 51, 52, 53, 56, 57, 58, 59, 60, 63, 64, 65, 66, 69, 70, 71, 72, 75, 86, 87, 96, 97, 98, 99, 100, 101, 102, 103, 104, 106, 107, 108, 109, 110, 111, 114, 115, 116, 117, 126, 127, 136, 137, 145, 146, 154, 155, 163, 164, 165, 166, 167, 174, 175, 176 }

2.1.6 Sympy

A grade: { 9, 33, 34, 35, 40, 42, 43, 61, 121, 124, 125, 141, 144, 177 }

B grade: { }

C grade: { }

F grade: { 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 36, 37, 38, 39, 41, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 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, 122, 123, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 142, 143, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 178 }

2.1.7 Giac

A grade: { 7, 33, 34, 35, 39, 40, 42, 43, 47, 54, 55, 61, 62, 67, 68, 73, 74, 121, 122, 123, 124, 125, 130, 131, 132, 133, 134, 135, 141, 142, 143, 144, 150, 151, 152, 153, 159, 160, 161, 162, 168, 169, 170, 171, 172, 173, 177, 178 }

B grade: { }

C grade: { }

F grade: { 1, 2, 3, 4, 5, 6, 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, 36, 37, 38, 41, 44, 45, 46, 48, 49, 50, 51, 52, 53, 56, 57, 58, 59, 60, 63, 64, 65, 66, 69, 70, 71, 72, 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, 126, 127, 128, 129, 136, 137, 138, 139, 140, 145, 146, 147, 148, 149, 154, 155, 156, 157, 158, 163, 164, 165, 166, 167, 174, 175, 176 }

2.2 Detailed conclusion table per each integral for all CAS systems

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

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

Problem 1 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 114 114 107 177 217 275 0 0
normalized size 1 1. 0.94 1.55 1.9 2.41 0. 0.
time (sec) N/A 0.061 0.143 0.178 0.952 2.707 0. 0.
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 89 89 72 83 108 143 0 0
normalized size 1 1. 0.81 0.93 1.21 1.61 0. 0.
time (sec) N/A 0.042 0.132 0.174 0.957 2.464 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 89 89 97 150 178 248 0 0
normalized size 1 1. 1.09 1.69 2. 2.79 0. 0.
time (sec) N/A 0.048 0.075 0.177 0.975 2.567 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 64 64 62 74 80 119 0 0
normalized size 1 1. 0.97 1.16 1.25 1.86 0. 0.
time (sec) N/A 0.027 0.101 0.177 0.956 2.386 0. 0.
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 64 64 85 123 131 219 0 0
normalized size 1 1. 1.33 1.92 2.05 3.42 0. 0.
time (sec) N/A 0.036 0.054 0.178 0.971 2.475 0. 0.
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 39 39 50 65 49 90 0 0
normalized size 1 1. 1.28 1.67 1.26 2.31 0. 0.
time (sec) N/A 0.012 0.024 0.171 0.985 2.329 0. 0.
Problem 7 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 31 31 58 37 72 154 0 63
normalized size 1 1. 1.87 1.19 2.32 4.97 0. 2.03
time (sec) N/A 0.021 0.066 0.169 0.957 2.462 0. 1.095
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 64 64 53 140 0 0 0 0
normalized size 1 1. 0.83 2.19 0. 0. 0. 0.
time (sec) N/A 0.085 0.03 0.257 0. 0. 0. 0.
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 32 32 41 63 45 62 37 0
normalized size 1 1. 1.28 1.97 1.41 1.94 1.16 0.
time (sec) N/A 0.02 0.029 0.171 0.982 2.2 2.634 0.
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 51 51 66 118 112 93 0 0
normalized size 1 1. 1.29 2.31 2.2 1.82 0. 0.
time (sec) N/A 0.032 0.035 0.174 1.488 2.177 0. 0.
Problem 11 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 60 60 59 75 78 97 0 0
normalized size 1 1. 0.98 1.25 1.3 1.62 0. 0.
time (sec) N/A 0.038 0.065 0.176 0.977 2.238 0. 0.
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 76 76 78 147 169 122 0 0
normalized size 1 1. 1.03 1.93 2.22 1.61 0. 0.
time (sec) N/A 0.045 0.061 0.174 1.479 2.292 0. 0.
Problem 13 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 82 82 69 83 103 123 0 0
normalized size 1 1. 0.84 1.01 1.26 1.5 0. 0.
time (sec) N/A 0.049 0.085 0.173 0.978 2.269 0. 0.
Problem 14 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 101 101 88 174 223 150 0 0
normalized size 1 1. 0.87 1.72 2.21 1.49 0. 0.
time (sec) N/A 0.062 0.102 0.177 1.473 2.246 0. 0.
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B B A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 107 107 124 208 266 339 0 0
normalized size 1 1. 1.16 1.94 2.49 3.17 0. 0.
time (sec) N/A 0.106 0.223 0.225 2.107 2.966 0. 0.
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 139 139 210 327 0 0 0 0
normalized size 1 1. 1.51 2.35 0. 0. 0. 0.
time (sec) N/A 0.119 1.339 0.352 0. 0. 0. 0.
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 89 133 113 266 0 0
normalized size 1 1. 1.62 2.42 2.05 4.84 0. 0.
time (sec) N/A 0.07 0.146 0.222 1.002 2.219 0. 0.
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 84 84 147 196 0 0 0 0
normalized size 1 1. 1.75 2.33 0. 0. 0. 0.
time (sec) N/A 0.068 0.202 0.266 0. 0. 0. 0.
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 91 91 137 361 0 0 0 0
normalized size 1 1. 1.51 3.97 0. 0. 0. 0.
time (sec) N/A 0.123 0.142 0.295 0. 0. 0. 0.
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 50 50 71 118 107 140 0 0
normalized size 1 1. 1.42 2.36 2.14 2.8 0. 0.
time (sec) N/A 0.061 0.147 0.219 1.002 1.874 0. 0.
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 88 88 102 191 0 196 0 0
normalized size 1 1. 1.16 2.17 0. 2.23 0. 0.
time (sec) N/A 0.078 0.116 0.214 0. 2.031 0. 0.
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 102 102 108 154 266 224 0 0
normalized size 1 1. 1.06 1.51 2.61 2.2 0. 0.
time (sec) N/A 0.096 0.225 0.219 2.11 2.014 0. 0.
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 134 134 148 265 0 275 0 0
normalized size 1 1. 1.1 1.98 0. 2.05 0. 0.
time (sec) N/A 0.112 0.175 0.228 0. 1.883 0. 0.
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 207 207 285 510 0 0 0 0
normalized size 1 1. 1.38 2.46 0. 0. 0. 0.
time (sec) N/A 0.217 0.86 0.408 0. 0. 0. 0.
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 220 220 580 648 0 0 0 0
normalized size 1 1. 2.64 2.95 0. 0. 0. 0.
time (sec) N/A 0.188 7.751 0.446 0. 0. 0. 0.
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 126 126 182 349 0 0 0 0
normalized size 1 1. 1.44 2.77 0. 0. 0. 0.
time (sec) N/A 0.147 0.467 0.33 0. 0. 0. 0.
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 144 144 265 437 0 0 0 0
normalized size 1 1. 1.84 3.03 0. 0. 0. 0.
time (sec) N/A 0.112 0.294 0.319 0. 0. 0. 0.
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 124 124 242 666 0 0 0 0
normalized size 1 1. 1.95 5.37 0. 0. 0. 0.
time (sec) N/A 0.143 0.213 0.333 0. 0. 0. 0.
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 80 80 135 199 198 238 0 0
normalized size 1 1. 1.69 2.49 2.48 2.98 0. 0.
time (sec) N/A 0.086 0.201 0.25 1.027 2.378 0. 0.
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 125 125 186 315 0 342 0 0
normalized size 1 1. 1.49 2.52 0. 2.74 0. 0.
time (sec) N/A 0.105 0.211 0.26 0. 2.259 0. 0.
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 170 170 204 299 0 401 0 0
normalized size 1 1. 1.2 1.76 0. 2.36 0. 0.
time (sec) N/A 0.15 0.3 0.261 0. 2.352 0. 0.
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 208 208 283 472 0 512 0 0
normalized size 1 1. 1.36 2.27 0. 2.46 0. 0.
time (sec) N/A 0.176 0.34 0.268 0. 2.385 0. 0.
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.015 2.896 1.02 0. 0. 0. 0.
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.006 3.366 0.371 0. 0. 0. 0.
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 16 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.024 0.285 0.729 0. 0. 0. 0.
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 47 47 43 48 0 0 0 0
normalized size 1 1. 0.91 1.02 0. 0. 0. 0.
time (sec) N/A 0.106 0.081 0.214 0. 0. 0. 0.
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 63 63 56 58 0 0 0 0
normalized size 1 1. 0.89 0.92 0. 0. 0. 0.
time (sec) N/A 0.134 0.077 0.214 0. 0. 0. 0.
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 117 117 91 102 0 0 0 0
normalized size 1 1. 0.78 0.87 0. 0. 0. 0.
time (sec) N/A 0.229 0.172 0.218 0. 0. 0. 0.
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.024 5.503 2.495 0. 0. 0. 0.
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.024 3.582 2.259 0. 0. 0. 0.
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 66 66 83 0 0 0 0 0
normalized size 1 1. 1.26 0. 0. 0. 0. 0.
time (sec) N/A 0.043 0.173 2.089 0. 0. 0. 0.
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.026 0.391 1.878 0. 0. 0. 0.
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 18 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.026 0.778 1.842 0. 0. 0. 0.
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 167 167 165 485 363 633 0 0
normalized size 1 1. 0.99 2.9 2.17 3.79 0. 0.
time (sec) N/A 0.402 0.305 0.138 1.046 3.767 0. 0.
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 123 123 122 361 267 462 0 0
normalized size 1 1. 0.99 2.93 2.17 3.76 0. 0.
time (sec) N/A 0.277 0.185 0.141 1.003 2.872 0. 0.
Problem 46 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 83 83 113 140 124 302 0 0
normalized size 1 1. 1.36 1.69 1.49 3.64 0. 0.
time (sec) N/A 0.167 0.196 0.18 1.001 2.197 0. 0.
Problem 47 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 31 31 58 37 72 154 0 63
normalized size 1 1. 1.87 1.19 2.32 4.97 0. 2.03
time (sec) N/A 0.023 0.053 0.173 0.977 2.073 0. 1.13
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 257 257 411 881 0 0 0 0
normalized size 1 1. 1.6 3.43 0. 0. 0. 0.
time (sec) N/A 0.406 0.658 0.417 0. 0. 0. 0.
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-1) B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 102 102 141 214 0 960 0 0
normalized size 1 1. 1.38 2.1 0. 9.41 0. 0.
time (sec) N/A 0.155 0.221 0.263 0. 2.369 0. 0.
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 172 172 250 1007 0 2223 0 0
normalized size 1 1. 1.45 5.85 0. 12.92 0. 0.
time (sec) N/A 0.292 0.515 0.174 0. 6.219 0. 0.
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-2) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 496 693 870 1222 0 0 0 0
normalized size 1 1.4 1.75 2.46 0. 0. 0. 0.
time (sec) N/A 2.827 13.909 0.285 0. 0. 0. 0.
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-2) F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 404 502 368 836 0 0 0 0
normalized size 1 1.24 0.91 2.07 0. 0. 0. 0.
time (sec) N/A 2.195 1.614 0.281 0. 0. 0. 0.
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B A F(-2) F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 315 315 657 388 0 0 0 0
normalized size 1 1. 2.09 1.23 0. 0. 0. 0.
time (sec) N/A 0.485 13.262 0.273 0. 0. 0. 0.
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.071 17.512 5.796 0. 0. 0. 0.
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.076 7.997 4.339 0. 0. 0. 0.
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-2) F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 372 372 333 810 0 0 0 0
normalized size 1 1. 0.9 2.18 0. 0. 0. 0.
time (sec) N/A 0.755 1.423 0.278 0. 0. 0. 0.
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 714 714 873 1248 0 0 0 0
normalized size 1 1. 1.22 1.75 0. 0. 0. 0.
time (sec) N/A 2.589 13.747 0.286 0. 0. 0. 0.
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 530 530 784 862 0 0 0 0
normalized size 1 1. 1.48 1.63 0. 0. 0. 0.
time (sec) N/A 1.907 13.573 0.276 0. 0. 0. 0.
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 344 344 289 412 0 0 0 0
normalized size 1 1. 0.84 1.2 0. 0. 0. 0.
time (sec) N/A 1.6 1.429 0.278 0. 0. 0. 0.
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 212 212 243 254 0 0 0 0
normalized size 1 1. 1.15 1.2 0. 0. 0. 0.
time (sec) N/A 0.319 3.5 0.272 0. 0. 0. 0.
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.072 6.289 3.53 0. 0. 0. 0.
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.079 8.757 4.408 0. 0. 0. 0.
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 551 551 814 890 0 0 0 0
normalized size 1 1. 1.48 1.62 0. 0. 0. 0.
time (sec) N/A 2.474 13.83 0.281 0. 0. 0. 0.
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 369 369 750 441 0 0 0 0
normalized size 1 1. 2.03 1.2 0. 0. 0. 0.
time (sec) N/A 1.814 13.676 0.278 0. 0. 0. 0.
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 238 238 226 277 0 0 0 0
normalized size 1 1. 0.95 1.16 0. 0. 0. 0.
time (sec) N/A 1.575 1.74 0.276 0. 0. 0. 0.
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 119 119 124 217 0 0 0 0
normalized size 1 1. 1.04 1.82 0. 0. 0. 0.
time (sec) N/A 0.225 0.203 0.27 0. 0. 0. 0.
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.089 11.07 4.336 0. 0. 0. 0.
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.094 13.905 3.789 0. 0. 0. 0.
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 602 602 887 1077 0 0 0 0
normalized size 1 1. 1.47 1.79 0. 0. 0. 0.
time (sec) N/A 2.896 13.935 0.288 0. 0. 0. 0.
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 440 440 856 1038 0 0 0 0
normalized size 1 1. 1.95 2.36 0. 0. 0. 0.
time (sec) N/A 2.185 13.789 0.289 0. 0. 0. 0.
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 314 314 345 913 0 0 0 0
normalized size 1 1. 1.1 2.91 0. 0. 0. 0.
time (sec) N/A 2.001 1.649 0.286 0. 0. 0. 0.
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F(-2) F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 298 298 725 886 0 0 0 0
normalized size 1 1. 2.43 2.97 0. 0. 0. 0.
time (sec) N/A 0.409 13.513 0.279 0. 0. 0. 0.
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.088 25.151 3.867 0. 0. 0. 0.
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.101 25.371 4.704 0. 0. 0. 0.
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 540 637 1002 1640 0 0 0 0
normalized size 1 1.18 1.86 3.04 0. 0. 0. 0.
time (sec) N/A 0.752 14.053 0.296 0. 0. 0. 0.
Problem 76 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 206 206 140 338 400 459 0 0
normalized size 1 1. 0.68 1.64 1.94 2.23 0. 0.
time (sec) N/A 0.125 0.231 0.182 0.987 4.597 0. 0.
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 161 161 121 282 313 398 0 0
normalized size 1 1. 0.75 1.75 1.94 2.47 0. 0.
time (sec) N/A 0.108 0.166 0.184 0.987 3.564 0. 0.
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 109 109 149 194 207 327 0 0
normalized size 1 1. 1.37 1.78 1.9 3. 0. 0.
time (sec) N/A 0.051 0.261 0.184 1.017 3.453 0. 0.
Problem 79 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 87 87 104 136 120 288 0 0
normalized size 1 1. 1.2 1.56 1.38 3.31 0. 0.
time (sec) N/A 0.065 0.119 0.186 0.989 2.908 0. 0.
Problem 80 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 105 105 69 121 127 157 0 0
normalized size 1 1. 0.66 1.15 1.21 1.5 0. 0.
time (sec) N/A 0.078 0.104 0.187 0.983 2.603 0. 0.
Problem 81 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 152 152 94 140 185 217 0 0
normalized size 1 1. 0.62 0.92 1.22 1.43 0. 0.
time (sec) N/A 0.092 0.16 0.185 0.973 2.626 0. 0.
Problem 82 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 197 197 110 158 232 273 0 0
normalized size 1 1. 0.56 0.8 1.18 1.39 0. 0.
time (sec) N/A 0.118 0.165 0.19 0.979 2.523 0. 0.
Problem 83 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 196 196 115 152 247 304 0 0
normalized size 1 1. 0.59 0.78 1.26 1.55 0. 0.
time (sec) N/A 0.15 0.227 0.182 0.98 3.008 0. 0.
Problem 84 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 153 153 97 134 192 247 0 0
normalized size 1 1. 0.63 0.88 1.25 1.61 0. 0.
time (sec) N/A 0.122 0.206 0.183 0.992 2.916 0. 0.
Problem 85 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 138 138 78 115 132 192 0 0
normalized size 1 1. 0.57 0.83 0.96 1.39 0. 0.
time (sec) N/A 0.096 0.095 0.178 1.003 2.783 0. 0.
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 124 124 103 198 0 0 0 0
normalized size 1 1. 0.83 1.6 0. 0. 0. 0.
time (sec) N/A 0.286 0.128 0.554 0. 0. 0. 0.
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 137 137 137 201 0 0 0 0
normalized size 1 1. 1. 1.47 0. 0. 0. 0.
time (sec) N/A 0.302 0.414 0.384 0. 0. 0. 0.
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 252 252 184 494 545 641 0 0
normalized size 1 1. 0.73 1.96 2.16 2.54 0. 0.
time (sec) N/A 0.237 0.35 0.184 1.037 6.069 0. 0.
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 191 191 151 371 400 547 0 0
normalized size 1 1. 0.79 1.94 2.09 2.86 0. 0.
time (sec) N/A 0.114 0.236 0.183 0.969 4.948 0. 0.
Problem 90 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 163 163 134 286 266 502 0 0
normalized size 1 1. 0.82 1.75 1.63 3.08 0. 0.
time (sec) N/A 0.13 0.194 0.187 0.977 3.892 0. 0.
Problem 91 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 157 157 125 254 213 501 0 0
normalized size 1 1. 0.8 1.62 1.36 3.19 0. 0.
time (sec) N/A 0.132 0.268 0.189 0.995 3.296 0. 0.
Problem 92 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 183 183 127 191 244 302 0 0
normalized size 1 1. 0.69 1.04 1.33 1.65 0. 0.
time (sec) N/A 0.16 0.262 0.194 1.027 2.694 0. 0.
Problem 93 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 241 241 153 223 325 401 0 0
normalized size 1 1. 0.63 0.93 1.35 1.66 0. 0.
time (sec) N/A 0.197 0.261 0.191 1.017 2.569 0. 0.
Problem 94 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 242 242 159 214 342 431 0 0
normalized size 1 1. 0.66 0.88 1.41 1.78 0. 0.
time (sec) N/A 0.223 0.319 0.186 1.014 3.361 0. 0.
Problem 95 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 195 195 124 182 255 336 0 0
normalized size 1 1. 0.64 0.93 1.31 1.72 0. 0.
time (sec) N/A 0.144 0.281 0.188 1.002 3.043 0. 0.
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 186 186 157 301 0 0 0 0
normalized size 1 1. 0.84 1.62 0. 0. 0. 0.
time (sec) N/A 0.422 0.364 1.038 0. 0. 0. 0.
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 189 189 187 276 0 0 0 0
normalized size 1 1. 0.99 1.46 0. 0. 0. 0.
time (sec) N/A 0.43 0.64 0.7 0. 0. 0. 0.
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B C F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 565 565 1260 407 0 0 0 0
normalized size 1 1. 2.23 0.72 0. 0. 0. 0.
time (sec) N/A 1.257 1.696 1.534 0. 0. 0. 0.
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 507 507 1123 401 0 0 0 0
normalized size 1 1. 2.21 0.79 0. 0. 0. 0.
time (sec) N/A 1.139 0.367 0.422 0. 0. 0. 0.
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B C F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 529 529 1068 272 0 0 0 0
normalized size 1 1. 2.02 0.51 0. 0. 0. 0.
time (sec) N/A 0.87 0.381 0.94 0. 0. 0. 0.
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 479 479 407 2875 0 0 0 0
normalized size 1 1. 0.85 6. 0. 0. 0. 0.
time (sec) N/A 0.9 0.857 0.57 0. 0. 0. 0.
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B C F(-2) F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 572 572 1241 332 0 0 0 0
normalized size 1 1. 2.17 0.58 0. 0. 0. 0.
time (sec) N/A 1.1 1.62 1.537 0. 0. 0. 0.
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B C F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 628 628 1480 729 0 0 0 0
normalized size 1 1. 2.36 1.16 0. 0. 0. 0.
time (sec) N/A 1.321 5.614 0.734 0. 0. 0. 0.
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B C F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 590 590 1442 541 0 0 0 0
normalized size 1 1. 2.44 0.92 0. 0. 0. 0.
time (sec) N/A 1.238 2.045 0.536 0. 0. 0. 0.
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 131 131 286 354 0 833 0 0
normalized size 1 1. 2.18 2.7 0. 6.36 0. 0.
time (sec) N/A 0.121 0.726 0.276 0. 3.463 0. 0.
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F C F F F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 566 566 0 3036 0 0 0 0
normalized size 1 1. 0. 5.36 0. 0. 0. 0.
time (sec) N/A 1.161 41.937 0.839 0. 0. 0. 0.
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B C F(-2) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 803 803 1634 1888 0 0 0 0
normalized size 1 1. 2.03 2.35 0. 0. 0. 0.
time (sec) N/A 2.4 6.153 10.047 0. 0. 0. 0.
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 765 765 1482 1722 0 0 0 0
normalized size 1 1. 1.94 2.25 0. 0. 0. 0.
time (sec) N/A 1.255 2.338 1.572 0. 0. 0. 0.
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 759 759 1477 1716 0 0 0 0
normalized size 1 1. 1.95 2.26 0. 0. 0. 0.
time (sec) N/A 2.288 2.559 1.395 0. 0. 0. 0.
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 806 806 1525 1784 0 0 0 0
normalized size 1 1. 1.89 2.21 0. 0. 0. 0.
time (sec) N/A 2.364 2.468 10.007 0. 0. 0. 0.
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B C F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 727 727 2053 1498 0 0 0 0
normalized size 1 1. 2.82 2.06 0. 0. 0. 0.
time (sec) N/A 1.442 7.565 0.842 0. 0. 0. 0.
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 157 157 390 1870 0 2093 0 0
normalized size 1 1. 2.48 11.91 0. 13.33 0. 0.
time (sec) N/A 0.182 1.058 0.29 0. 6.485 0. 0.
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 193 193 385 1840 0 1839 0 0
normalized size 1 1. 1.99 9.53 0. 9.53 0. 0.
time (sec) N/A 0.191 0.878 0.283 0. 6.341 0. 0.
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F C F F F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 704 704 0 5294 0 0 0 0
normalized size 1 1. 0. 7.52 0. 0. 0. 0.
time (sec) N/A 1.318 60.225 1.979 0. 0. 0. 0.
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 1144 1144 2067 3175 0 0 0 0
normalized size 1 1. 1.81 2.78 0. 0. 0. 0.
time (sec) N/A 1.6 6.19 2.188 0. 0. 0. 0.
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 1144 1144 2075 2329 0 0 0 0
normalized size 1 1. 1.81 2.04 0. 0. 0. 0.
time (sec) N/A 3.069 6.128 2.568 0. 0. 0. 0.
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 1134 1134 2060 3166 0 0 0 0
normalized size 1 1. 1.82 2.79 0. 0. 0. 0.
time (sec) N/A 4.049 6.061 2.95 0. 0. 0. 0.
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-2) A F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 403 403 365 0 0 3779 0 0
normalized size 1 1. 0.91 0. 0. 9.38 0. 0.
time (sec) N/A 1.312 0.648 6.16 0. 41.437 0. 0.
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 294 294 326 0 0 3036 0 0
normalized size 1 1. 1.11 0. 0. 10.33 0. 0.
time (sec) N/A 0.409 0.721 5.756 0. 16.403 0. 0.
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 195 195 265 0 0 2427 0 0
normalized size 1 1. 1.36 0. 0. 12.45 0. 0.
time (sec) N/A 0.212 0.463 3.025 0. 6.778 0. 0.
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.102 5.346 6.236 0. 0. 0. 0.
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.107 5.688 1.717 0. 0. 0. 0.
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.096 9.034 5.807 0. 0. 0. 0.
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 22 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.034 6.109 5.31 0. 0. 0. 0.
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.087 1.682 4.628 0. 0. 0. 0.
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 328 328 247 0 0 0 0 0
normalized size 1 1. 0.75 0. 0. 0. 0. 0.
time (sec) N/A 0.432 0.627 9.214 0. 0. 0. 0.
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 453 453 325 0 0 0 0 0
normalized size 1 1. 0.72 0. 0. 0. 0. 0.
time (sec) N/A 0.62 0.698 7.089 0. 0. 0. 0.
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-2) A F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 374 374 339 0 0 3768 0 0
normalized size 1 1. 0.91 0. 0. 10.07 0. 0.
time (sec) N/A 0.538 0.601 3.198 0. 38.959 0. 0.
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 262 262 304 0 0 3006 0 0
normalized size 1 1. 1.16 0. 0. 11.47 0. 0.
time (sec) N/A 0.288 0.715 1.773 0. 16.302 0. 0.
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.116 5.962 1.941 0. 0. 0. 0.
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.122 4.794 1.263 0. 0. 0. 0.
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.124 9.565 3.258 0. 0. 0. 0.
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 22 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.045 6.676 2.795 0. 0. 0. 0.
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.106 12.612 3.097 0. 0. 0. 0.
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.107 6.427 6.571 0. 0. 0. 0.
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 416 416 303 0 0 0 0 0
normalized size 1 1. 0.73 0. 0. 0. 0. 0.
time (sec) N/A 0.573 0.658 5.984 0. 0. 0. 0.
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 554 554 383 0 0 0 0 0
normalized size 1 1. 0.69 0. 0. 0. 0. 0.
time (sec) N/A 0.891 0.852 5.132 0. 0. 0. 0.
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 321 321 328 0 0 3063 0 0
normalized size 1 1. 1.02 0. 0. 9.54 0. 0.
time (sec) N/A 1.048 0.745 6.129 0. 20.082 0. 0.
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 225 225 271 0 0 2449 0 0
normalized size 1 1. 1.2 0. 0. 10.88 0. 0.
time (sec) N/A 0.327 0.515 6.874 0. 8.089 0. 0.
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-1) A F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 132 132 210 0 0 1928 0 0
normalized size 1 1. 1.59 0. 0. 14.61 0. 0.
time (sec) N/A 0.151 0.223 4.49 0. 4.3 0. 0.
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.097 1.67 5.735 0. 0. 0. 0.
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.111 13.024 1.263 0. 0. 0. 0.
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.092 12.98 4.946 0. 0. 0. 0.
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 22 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.031 0.986 4.268 0. 0. 0. 0.
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 247 247 140 0 0 0 0 0
normalized size 1 1. 0.57 0. 0. 0. 0. 0.
time (sec) N/A 0.266 0.187 4.654 0. 0. 0. 0.
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 362 362 249 0 0 0 0 0
normalized size 1 1. 0.69 0. 0. 0. 0. 0.
time (sec) N/A 0.569 0.658 8.776 0. 0. 0. 0.
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 252 252 302 0 0 3167 0 0
normalized size 1 1. 1.2 0. 0. 12.57 0. 0.
time (sec) N/A 1.074 0.608 3.643 0. 7.196 0. 0.
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 156 156 220 0 0 2364 0 0
normalized size 1 1. 1.41 0. 0. 15.15 0. 0.
time (sec) N/A 0.321 0.349 3.068 0. 4.971 0. 0.
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-1) A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 79 79 96 0 0 625 0 0
normalized size 1 1. 1.22 0. 0. 7.91 0. 0.
time (sec) N/A 0.117 0.145 1.764 0. 3.675 0. 0.
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.125 18.216 3.144 0. 0. 0. 0.
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.136 23.796 1.072 0. 0. 0. 0.
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.113 9.31 2.306 0. 0. 0. 0.
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.102 4.774 2.06 0. 0. 0. 0.
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 108 108 112 0 0 0 0 0
normalized size 1 1. 1.04 0. 0. 0. 0. 0.
time (sec) N/A 0.091 0.192 1.883 0. 0. 0. 0.
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 275 275 213 0 0 0 0 0
normalized size 1 1. 0.77 0. 0. 0. 0. 0.
time (sec) N/A 0.318 0.477 3.06 0. 0. 0. 0.
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 243 243 311 0 0 4487 0 0
normalized size 1 1. 1.28 0. 0. 18.47 0. 0.
time (sec) N/A 1.057 0.552 3.697 0. 7.852 0. 0.
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 163 163 173 0 0 1378 0 0
normalized size 1 1. 1.06 0. 0. 8.45 0. 0.
time (sec) N/A 0.246 0.265 3.102 0. 5.39 0. 0.
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 138 138 157 0 0 1188 0 0
normalized size 1 1. 1.14 0. 0. 8.61 0. 0.
time (sec) N/A 0.135 0.206 1.777 0. 5.2 0. 0.
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.123 34.161 1.883 0. 0. 0. 0.
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.14 43.148 1.093 0. 0. 0. 0.
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.121 13.406 3.532 0. 0. 0. 0.
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.11 11.675 2.412 0. 0. 0. 0.
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 276 276 185 0 0 0 0 0
normalized size 1 1. 0.67 0. 0. 0. 0. 0.
time (sec) N/A 0.283 0.278 2.079 0. 0. 0. 0.
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 296 296 249 0 0 0 0 0
normalized size 1 1. 0.84 0. 0. 0. 0. 0.
time (sec) N/A 0.238 0.554 1.879 0. 0. 0. 0.
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 585 566 402 0 0 0 0 0
normalized size 1 0.97 0.69 0. 0. 0. 0. 0.
time (sec) N/A 2.405 1.672 8.362 0. 0. 0. 0.
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 371 352 293 0 0 0 0 0
normalized size 1 0.95 0.79 0. 0. 0. 0. 0.
time (sec) N/A 0.432 0.845 4.826 0. 0. 0. 0.
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 215 202 171 0 0 0 0 0
normalized size 1 0.94 0.8 0. 0. 0. 0. 0.
time (sec) N/A 0.194 0.511 3.074 0. 0. 0. 0.
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.075 1.923 2.106 0. 0. 0. 0.
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 25 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.074 2.643 2.455 0. 0. 0. 0.
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 27 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.115 1.084 3.12 0. 0. 0. 0.
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 27 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.097 0.108 5.697 0. 0. 0. 0.
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 27 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.1 1.407 7.631 0. 0. 0. 0.
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 27 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.117 1.637 4.121 0. 0. 0. 0.
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 401 401 194 0 0 0 0 0
normalized size 1 1. 0.48 0. 0. 0. 0. 0.
time (sec) N/A 2.527 0.291 22.796 0. 0. 0. 0.
Problem 175 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 268 268 159 0 0 0 0 0
normalized size 1 1. 0.59 0. 0. 0. 0. 0.
time (sec) N/A 2.027 0.401 7.663 0. 0. 0. 0.
Problem 176 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 126 135 138 0 0 0 0 0
normalized size 1 1.07 1.1 0. 0. 0. 0. 0.
time (sec) N/A 0.212 0.176 3.027 0. 0. 0. 0.
Problem 177 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 28 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.089 0.398 6.214 0. 0. 0. 0.
Problem 178 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 28 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.101 3.436 1.84 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 [69] had the largest ratio of [ 0.8571 ]

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 7 5 1. 12 0.417
2 A 4 3 1. 12 0.25
3 A 6 5 1. 12 0.417
4 A 3 3 1. 12 0.25
5 A 5 5 1. 12 0.417
6 A 2 2 1. 10 0.2
7 A 5 4 1. 8 0.5
8 A 6 6 1. 12 0.5
9 A 2 2 1. 12 0.167
10 A 4 4 1. 12 0.333
11 A 4 3 1. 12 0.25
12 A 5 4 1. 12 0.333
13 A 4 3 1. 12 0.25
14 A 6 4 1. 12 0.333
15 A 5 5 1. 14 0.357
16 A 8 6 1. 14 0.429
17 A 4 4 1. 12 0.333
18 A 7 5 1. 10 0.5
19 A 6 6 1. 14 0.429
20 A 4 3 1. 14 0.214
21 A 4 3 1. 14 0.214
22 A 5 5 1. 14 0.357
23 A 5 3 1. 14 0.214
24 A 10 10 1. 14 0.714
25 A 11 8 1. 14 0.571
26 A 7 7 1. 12 0.583
27 A 9 6 1. 10 0.6
28 A 7 7 1. 14 0.5
29 A 5 3 1. 14 0.214
30 A 6 6 1. 14 0.429
31 A 8 6 1. 14 0.429
32 A 10 6 1. 14 0.429
33 A 0 0 0. 0 0.
34 A 0 0 0. 0 0.
35 A 0 0 0. 0 0.
36 A 4 4 1. 14 0.286
37 A 6 6 1. 14 0.429
38 A 9 5 1. 14 0.357
39 A 0 0 0. 0 0.
40 A 0 0 0. 0 0.
41 A 3 3 1. 14 0.214
42 A 0 0 0. 0 0.
43 A 0 0 0. 0 0.
44 A 11 9 1. 16 0.562
45 A 10 9 1. 16 0.562
46 A 9 9 1. 14 0.643
47 A 5 4 1. 8 0.5
48 A 4 2 1. 16 0.125
49 A 7 7 1. 16 0.438
50 A 8 8 1. 16 0.5
51 A 31 16 1.4 21 0.762
52 A 24 15 1.24 19 0.79
53 A 15 11 1. 18 0.611
54 A 0 0 0. 0 0.
55 A 0 0 0. 0 0.
56 A 22 13 1. 18 0.722
57 A 27 17 1. 21 0.81
58 A 20 15 1. 21 0.714
59 A 14 13 1. 19 0.684
60 A 9 9 1. 18 0.5
61 A 0 0 0. 0 0.
62 A 0 0 0. 0 0.
63 A 23 15 1. 21 0.714
64 A 16 13 1. 21 0.619
65 A 11 11 1. 19 0.579
66 A 6 6 1. 18 0.333
67 A 0 0 0. 0 0.
68 A 0 0 0. 0 0.
69 A 31 18 1. 21 0.857
70 A 25 17 1. 21 0.81
71 A 19 14 1. 19 0.737
72 A 12 11 1. 18 0.611
73 A 0 0 0. 0 0.
74 A 0 0 0. 0 0.
75 A 19 14 1.18 18 0.778
76 A 7 7 1. 19 0.368
77 A 6 7 1. 19 0.368
78 A 5 5 1. 16 0.312
79 A 4 5 1. 19 0.263
80 A 4 5 1. 19 0.263
81 A 5 6 1. 19 0.316
82 A 6 6 1. 19 0.316
83 A 5 5 1. 19 0.263
84 A 5 5 1. 19 0.263
85 A 6 5 1. 17 0.294
86 A 11 11 1. 19 0.579
87 A 13 13 1. 19 0.684
88 A 7 8 1. 21 0.381
89 A 6 7 1. 18 0.389
90 A 6 7 1. 21 0.333
91 A 6 7 1. 21 0.333
92 A 5 6 1. 21 0.286
93 A 6 7 1. 21 0.333
94 A 5 6 1. 21 0.286
95 A 6 5 1. 19 0.263
96 A 12 13 1. 21 0.619
97 A 14 15 1. 21 0.714
98 A 25 12 1. 21 0.571
99 A 26 9 1. 19 0.474
100 A 19 7 1. 18 0.389
101 A 19 7 1. 21 0.333
102 A 24 10 1. 21 0.476
103 A 31 14 1. 21 0.667
104 A 29 12 1. 21 0.571
105 A 7 5 1. 19 0.263
106 A 24 10 1. 21 0.476
107 A 51 15 1. 21 0.714
108 A 27 10 1. 21 0.476
109 A 47 11 1. 18 0.611
110 A 50 13 1. 21 0.619
111 A 33 13 1. 21 0.619
112 A 6 7 1. 21 0.333
113 A 8 6 1. 19 0.316
114 A 28 11 1. 21 0.524
115 A 35 11 1. 21 0.524
116 A 63 12 1. 21 0.571
117 A 81 12 1. 18 0.667
118 A 12 12 1. 23 0.522
119 A 11 12 1. 23 0.522
120 A 9 9 1. 21 0.429
121 A 0 0 0. 0 0.
122 A 0 0 0. 0 0.
123 A 0 0 0. 0 0.
124 A 0 0 0. 0 0.
125 A 0 0 0. 0 0.
126 A 11 11 1. 23 0.478
127 A 12 12 1. 23 0.522
128 A 12 12 1. 23 0.522
129 A 10 10 1. 21 0.476
130 A 0 0 0. 0 0.
131 A 0 0 0. 0 0.
132 A 0 0 0. 0 0.
133 A 0 0 0. 0 0.
134 A 0 0 0. 0 0.
135 A 0 0 0. 0 0.
136 A 12 12 1. 23 0.522
137 A 13 12 1. 23 0.522
138 A 11 12 1. 23 0.522
139 A 10 12 1. 23 0.522
140 A 8 8 1. 21 0.381
141 A 0 0 0. 0 0.
142 A 0 0 0. 0 0.
143 A 0 0 0. 0 0.
144 A 0 0 0. 0 0.
145 A 11 11 1. 23 0.478
146 A 11 12 1. 23 0.522
147 A 10 11 1. 23 0.478
148 A 9 11 1. 23 0.478
149 A 4 4 1. 21 0.19
150 A 0 0 0. 0 0.
151 A 0 0 0. 0 0.
152 A 0 0 0. 0 0.
153 A 0 0 0. 0 0.
154 A 5 5 1. 20 0.25
155 A 10 11 1. 23 0.478
156 A 10 11 1. 23 0.478
157 A 7 8 1. 23 0.348
158 A 5 5 1. 21 0.238
159 A 0 0 0. 0 0.
160 A 0 0 0. 0 0.
161 A 0 0 0. 0 0.
162 A 0 0 0. 0 0.
163 A 10 10 1. 23 0.435
164 A 10 11 1. 20 0.55
165 A 6 7 0.97 23 0.304
166 A 6 7 0.95 23 0.304
167 A 5 6 0.94 21 0.286
168 A 0 0 0. 0 0.
169 A 0 0 0. 0 0.
170 A 0 0 0. 0 0.
171 A 0 0 0. 0 0.
172 A 0 0 0. 0 0.
173 A 0 0 0. 0 0.
174 A 16 11 1. 26 0.423
175 A 13 11 1. 26 0.423
176 A 8 9 1.07 26 0.346
177 A 0 0 0. 0 0.
178 A 0 0 0. 0 0.

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