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Chapter 2
detailed summary tables of results

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

2.1 List of integrals sorted by grade for each CAS

2.1.1 Rubi

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 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 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 28, 45, 46, 47, 48, 53, 69, 74, 75, 76, 82, 84, 88, 91, 92, 93, 94, 98, 99, 100, 101, 104, 105, 106, 107, 111, 112, 113, 114, 115, 120, 128, 129, 130, 131, 133, 134, 135, 136, 137, 141, 142, 147, 148, 149, 150, 151, 152, 156, 157, 158, 161, 162, 163, 166, 167, 168, 169, 170 }

B grade: { 81, 83, 89, 90, 95, 96, 97, 102, 103, 108, 109, 110, 121, 126, 127, 140, 165, 171 }

C grade: { 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 77, 78, 79, 80, 85, 86, 87, 116, 117, 118, 119, 122, 123, 124, 125, 132, 138, 139, 143, 144, 145, 146, 153, 154, 155, 159, 160 }

F grade: { 49, 164 }

2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 31, 32, 33, 38, 53 }

B grade: { 28, 29, 30, 34, 35, 36, 37, 39, 40, 41, 42, 43, 44, 50, 51, 52, 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 }

C grade: { }

F grade: { 45, 46, 47, 48, 49, 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 }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 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, 77, 78, 79, 80, 81, 84, 85, 86, 87 }

B grade: { 76, 82, 83, 88, 89 }

C grade: { }

F grade: { 45, 46, 47, 48, 49, 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 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 34, 35, 50, 51, 52, 53, 54, 57, 58, 59, 60, 61, 64, 65, 66, 67, 70, 71, 72, 73, 74, 79, 80 }

B grade: { 32, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 55, 56, 62, 63, 68, 69, 75, 76, 77, 78, 81, 82, 83, 84, 85, 86, 87, 88, 89 }

C grade: { }

F grade: { 45, 46, 47, 48, 49, 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 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 64, 65, 66, 67, 70, 71, 72, 73, 79, 80 }

B grade: { }

C grade: { }

F grade: { 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 56, 62, 63, 68, 69, 74, 75, 76, 77, 78, 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 }

2.1.7 Giac

A grade: { 3, 4, 11, 12, 13, 18, 19, 20, 21, 25, 26, 27, 28, 29, 30, 31, 32, 33, 37, 38, 39, 44, 54, 61, 67, 70, 71, 72, 73, 74, 79 }

B grade: { 1, 2, 5, 6, 7, 8, 9, 10, 14, 15, 16, 17, 22, 23, 24, 34, 35, 36, 40, 41, 42, 43, 51, 52, 53, 55, 56, 59, 60, 62, 63, 66, 68, 69, 75, 76, 77, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89 }

C grade: { }

F grade: { 45, 46, 47, 48, 49, 50, 57, 58, 64, 65, 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 }

2.1.8 Mupad

A grade: { }

B grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 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, 92, 93, 94, 95, 100, 101, 106, 110, 111, 112, 113, 114, 115, 117, 118, 119, 123, 124, 125 }

C grade: { }

F grade: { 45, 46, 47, 48, 49, 90, 91, 96, 97, 98, 99, 102, 103, 104, 105, 107, 108, 109, 116, 120, 121, 122, 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 }

2.2 Detailed conclusion table per each integral for all CAS systems

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

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

Problem 1 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 87 87 86 135 86 85 139 1017 84
normalized size 1 1.00 0.99 1.55 0.99 0.98 1.60 11.69 0.97
time (sec) N/A 0.134 0.598 0.030 0.536 0.598 0.374 3.958 8.825
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 66 66 67 105 66 66 105 616 63
normalized size 1 1.00 1.02 1.59 1.00 1.00 1.59 9.33 0.95
time (sec) N/A 0.046 0.320 0.024 0.655 0.609 0.244 2.922 8.838
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 59 66 50 50 82 50 58
normalized size 1 1.00 1.40 1.57 1.19 1.19 1.95 1.19 1.38
time (sec) N/A 0.060 0.056 0.386 0.598 1.060 0.647 2.267 8.791
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 37 37 44 51 52 59 85 53 69
normalized size 1 1.00 1.19 1.38 1.41 1.59 2.30 1.43 1.86
time (sec) N/A 0.110 0.072 0.569 0.594 0.461 0.979 3.668 8.956
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 78 65 68 73 116 119 87
normalized size 1 1.00 1.81 1.51 1.58 1.70 2.70 2.77 2.02
time (sec) N/A 0.124 0.159 0.436 0.462 1.550 1.664 4.314 8.875
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 66 66 77 96 86 95 150 179 108
normalized size 1 1.00 1.17 1.45 1.30 1.44 2.27 2.71 1.64
time (sec) N/A 0.159 0.469 0.523 0.663 0.547 2.335 5.637 8.944
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 87 87 101 124 104 121 180 237 127
normalized size 1 1.00 1.16 1.43 1.20 1.39 2.07 2.72 1.46
time (sec) N/A 0.193 1.029 0.513 0.765 0.540 4.429 7.625 8.888
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 108 108 100 150 122 138 211 299 145
normalized size 1 1.00 0.93 1.39 1.13 1.28 1.95 2.77 1.34
time (sec) N/A 0.226 1.147 0.532 0.926 0.694 5.868 9.317 8.821
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 148 148 221 249 147 146 250 2228 151
normalized size 1 1.00 1.49 1.68 0.99 0.99 1.69 15.05 1.02
time (sec) N/A 0.302 6.253 0.025 0.626 0.598 0.600 14.820 8.844
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 112 112 172 199 120 119 194 1509 121
normalized size 1 1.00 1.54 1.78 1.07 1.06 1.73 13.47 1.08
time (sec) N/A 0.112 1.847 0.028 0.797 0.666 0.435 5.941 8.795
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 87 87 96 140 91 91 151 95 91
normalized size 1 1.00 1.10 1.61 1.05 1.05 1.74 1.09 1.05
time (sec) N/A 0.135 0.470 0.496 0.801 1.515 1.086 4.426 8.848
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 70 70 91 109 85 92 136 86 90
normalized size 1 1.00 1.30 1.56 1.21 1.31 1.94 1.23 1.29
time (sec) N/A 0.185 0.284 0.481 0.984 0.766 1.612 7.505 8.853
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 100 110 93 112 158 118 100
normalized size 1 1.00 1.39 1.53 1.29 1.56 2.19 1.64 1.39
time (sec) N/A 0.207 0.252 0.515 0.736 0.775 2.298 6.394 8.999
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 88 88 123 141 120 122 212 237 127
normalized size 1 1.00 1.40 1.60 1.36 1.39 2.41 2.69 1.44
time (sec) N/A 0.263 0.353 0.624 0.703 1.546 4.312 8.117 8.979
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 118 118 152 188 149 157 258 334 156
normalized size 1 1.00 1.29 1.59 1.26 1.33 2.19 2.83 1.32
time (sec) N/A 0.311 1.175 0.460 0.748 0.620 5.679 11.085 9.078
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 151 151 180 238 175 191 311 435 182
normalized size 1 1.00 1.19 1.58 1.16 1.26 2.06 2.88 1.21
time (sec) N/A 0.369 2.931 0.562 0.864 1.239 8.801 21.201 8.860
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 165 165 209 314 179 178 313 2870 181
normalized size 1 1.00 1.27 1.90 1.08 1.08 1.90 17.39 1.10
time (sec) N/A 0.177 1.629 0.030 0.520 0.592 0.667 12.648 8.835
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 140 140 130 234 143 142 248 158 142
normalized size 1 1.00 0.93 1.67 1.02 1.01 1.77 1.13 1.01
time (sec) N/A 0.208 1.070 0.473 1.019 0.683 1.817 5.958 8.963
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 117 117 113 183 124 133 211 129 118
normalized size 1 1.00 0.97 1.56 1.06 1.14 1.80 1.10 1.01
time (sec) N/A 0.336 0.471 0.566 0.600 0.647 2.322 8.844 8.963
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 119 119 113 168 125 145 214 152 114
normalized size 1 1.00 0.95 1.41 1.05 1.22 1.80 1.28 0.96
time (sec) N/A 0.331 0.493 0.452 0.784 0.649 4.424 12.044 8.860
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 127 127 126 186 142 162 260 193 135
normalized size 1 1.00 0.99 1.46 1.12 1.28 2.05 1.52 1.06
time (sec) N/A 0.355 0.462 0.570 0.603 0.918 5.602 22.948 8.967
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 154 154 164 233 180 181 330 390 169
normalized size 1 1.00 1.06 1.51 1.17 1.18 2.14 2.53 1.10
time (sec) N/A 0.427 1.275 0.521 0.574 0.625 8.559 27.330 8.999
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 191 191 199 302 215 225 398 528 204
normalized size 1 1.00 1.04 1.58 1.13 1.18 2.08 2.76 1.07
time (sec) N/A 0.514 0.790 0.551 0.738 0.744 11.005 90.465 8.941
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 233 233 237 376 250 266 469 670 238
normalized size 1 1.00 1.02 1.61 1.07 1.14 2.01 2.88 1.02
time (sec) N/A 0.558 1.210 0.536 0.764 1.406 27.646 61.538 9.120
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 127 127 138 211 130 190 1309 135 144
normalized size 1 1.00 1.09 1.66 1.02 1.50 10.31 1.06 1.13
time (sec) N/A 0.468 1.450 0.255 0.715 0.874 2.030 2.111 9.071
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 101 101 118 179 109 149 1020 110 117
normalized size 1 1.00 1.17 1.77 1.08 1.48 10.10 1.09 1.16
time (sec) N/A 0.243 0.700 0.255 0.549 0.667 1.454 1.809 8.768
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 85 85 98 159 94 110 724 95 100
normalized size 1 1.00 1.15 1.87 1.11 1.29 8.52 1.12 1.18
time (sec) N/A 0.163 0.198 0.276 0.774 2.313 1.122 1.523 9.065
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 58 58 67 153 88 76 541 94 93
normalized size 1 1.00 1.16 2.64 1.52 1.31 9.33 1.62 1.60
time (sec) N/A 0.144 0.126 0.732 0.635 0.751 2.954 2.153 9.125
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 80 80 113 174 107 118 966 113 115
normalized size 1 1.00 1.41 2.18 1.34 1.48 12.08 1.41 1.44
time (sec) N/A 0.201 0.366 0.936 0.465 0.667 5.746 4.111 9.457
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 103 103 138 214 131 177 2064 157 140
normalized size 1 1.00 1.34 2.08 1.27 1.72 20.04 1.52 1.36
time (sec) N/A 0.342 0.888 0.756 0.967 0.769 12.101 4.810 10.339
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 137 137 163 266 158 234 2621 214 175
normalized size 1 1.00 1.19 1.94 1.15 1.71 19.13 1.56 1.28
time (sec) N/A 0.682 1.422 0.981 0.617 0.634 33.891 5.475 10.929
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 208 208 444 364 220 434 4602 290 210
normalized size 1 1.00 2.13 1.75 1.06 2.09 22.12 1.39 1.01
time (sec) N/A 0.532 4.265 0.252 0.573 0.805 2.978 2.936 9.648
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 157 157 324 313 197 311 3497 244 165
normalized size 1 1.00 2.06 1.99 1.25 1.98 22.27 1.55 1.05
time (sec) N/A 0.311 2.178 0.316 0.613 0.823 2.289 2.015 9.107
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 115 115 140 305 185 221 2995 241 163
normalized size 1 1.00 1.22 2.65 1.61 1.92 26.04 2.10 1.42
time (sec) N/A 0.147 2.190 0.307 0.636 0.594 1.839 1.985 9.011
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 111 111 190 301 177 222 2895 234 153
normalized size 1 1.00 1.71 2.71 1.59 2.00 26.08 2.11 1.38
time (sec) N/A 0.208 2.224 0.765 0.573 0.804 4.995 2.613 9.094
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 137 137 159 325 208 323 4461 279 180
normalized size 1 1.00 1.16 2.37 1.52 2.36 32.56 2.04 1.31
time (sec) N/A 0.403 2.411 0.837 1.329 0.920 9.510 5.292 10.693
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A B A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 192 192 193 399 262 465 8097 362 230
normalized size 1 1.00 1.01 2.08 1.36 2.42 42.17 1.89 1.20
time (sec) N/A 0.608 3.567 0.856 0.823 0.910 15.712 6.712 12.148
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A A B F(-2) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 331 331 1146 619 389 890 0 505 335
normalized size 1 1.00 3.46 1.87 1.18 2.69 0.00 1.53 1.01
time (sec) N/A 0.861 6.856 0.283 1.040 0.927 0.000 4.343 10.428
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A B F(-2) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 250 250 462 566 366 666 0 458 307
normalized size 1 1.00 1.85 2.26 1.46 2.66 0.00 1.83 1.23
time (sec) N/A 0.581 4.918 0.283 0.649 1.460 0.000 3.009 9.316
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A B F(-2) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 189 189 288 495 333 478 0 410 280
normalized size 1 1.00 1.52 2.62 1.76 2.53 0.00 2.17 1.48
time (sec) N/A 0.427 5.453 0.342 0.871 0.592 0.000 2.269 9.181
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A B F(-2) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 179 179 188 488 330 488 0 410 282
normalized size 1 1.00 1.05 2.73 1.84 2.73 0.00 2.29 1.58
time (sec) N/A 0.255 4.066 0.287 0.638 0.897 0.000 2.647 9.280
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A B F(-2) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 175 175 243 483 321 482 0 409 279
normalized size 1 1.00 1.39 2.76 1.83 2.75 0.00 2.34 1.59
time (sec) N/A 0.316 4.771 0.740 0.476 0.785 0.000 4.717 8.941
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A B F(-2) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 215 215 223 540 372 683 0 479 315
normalized size 1 1.00 1.04 2.51 1.73 3.18 0.00 2.23 1.47
time (sec) N/A 0.680 3.151 1.059 0.935 0.726 0.000 8.669 10.976
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A B F(-2) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 287 287 288 651 454 917 0 560 380
normalized size 1 1.00 1.00 2.27 1.58 3.20 0.00 1.95 1.32
time (sec) N/A 0.941 6.425 0.930 0.722 0.890 0.000 9.825 13.986
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 132 132 110 0 0 0 0 0 -1
normalized size 1 1.00 0.83 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.155 0.408 1.112 0.000 1.122 0.000 0.000 0.000
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 154 154 115 0 0 0 0 0 -1
normalized size 1 1.00 0.75 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.138 0.393 180.000 0.000 0.760 0.000 0.000 0.000
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-1) F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 170 170 133 0 0 0 0 0 -1
normalized size 1 1.00 0.78 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.144 0.533 1.706 0.000 0.552 0.000 0.000 0.000
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-1) F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 170 170 133 0 0 0 0 0 -1
normalized size 1 1.00 0.78 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.137 0.537 1.761 0.000 0.664 0.000 0.000 0.000
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F F F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 328 328 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.561 28.559 2.042 0.000 0.819 0.000 0.000 0.000
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 353 353 300 994 416 415 1001 0 477
normalized size 1 1.00 0.85 2.82 1.18 1.18 2.84 0.00 1.35
time (sec) N/A 0.785 6.382 0.032 0.544 1.038 1.648 0.000 8.997
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 248 248 243 631 274 273 617 6502 300
normalized size 1 1.00 0.98 2.54 1.10 1.10 2.49 26.22 1.21
time (sec) N/A 0.451 3.434 0.028 0.566 0.572 0.981 23.118 8.982
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 161 161 161 334 151 150 326 2918 153
normalized size 1 1.00 1.00 2.07 0.94 0.93 2.02 18.12 0.95
time (sec) N/A 0.241 1.617 0.025 0.445 0.588 0.500 7.336 8.842
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 76 136 74 74 131 918 75
normalized size 1 1.00 1.04 1.86 1.01 1.01 1.79 12.58 1.03
time (sec) N/A 0.061 0.470 0.025 0.508 1.329 0.278 2.929 8.679
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 156 155 148 506 183 226 2429 186 186
normalized size 1 0.99 0.95 3.24 1.17 1.45 15.57 1.19 1.19
time (sec) N/A 0.349 1.193 0.244 0.440 1.441 2.370 1.793 10.127
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 265 265 589 948 338 556 9721 531 1875
normalized size 1 1.00 2.22 3.58 1.28 2.10 36.68 2.00 7.08
time (sec) N/A 0.474 6.864 0.296 0.460 1.342 3.952 2.355 21.136
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A B F(-2) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 320 320 379 1513 574 987 0 1037 502
normalized size 1 1.00 1.18 4.73 1.79 3.08 0.00 3.24 1.57
time (sec) N/A 0.703 6.382 0.332 0.643 2.056 0.000 3.169 15.885
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 661 661 573 1807 691 690 1819 0 891
normalized size 1 1.00 0.87 2.73 1.05 1.04 2.75 0.00 1.35
time (sec) N/A 2.384 6.646 0.034 0.632 1.236 3.184 0.000 9.287
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 443 443 383 1165 463 462 1134 0 561
normalized size 1 1.00 0.86 2.63 1.05 1.04 2.56 0.00 1.27
time (sec) N/A 1.278 6.498 0.031 0.460 1.155 1.913 0.000 9.119
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 266 264 241 631 260 259 617 6502 300
normalized size 1 0.99 0.91 2.37 0.98 0.97 2.32 24.44 1.13
time (sec) N/A 0.472 2.887 0.030 0.554 0.599 0.975 33.119 9.006
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 131 131 176 262 135 134 241 2128 141
normalized size 1 1.00 1.34 2.00 1.03 1.02 1.84 16.24 1.08
time (sec) N/A 0.155 1.183 0.026 0.501 0.557 0.467 5.570 8.808
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 254 252 190 861 290 397 4517 338 325
normalized size 1 0.99 0.75 3.39 1.14 1.56 17.78 1.33 1.28
time (sec) N/A 0.827 3.030 0.239 0.536 1.650 8.060 3.657 11.275
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 415 415 2640 1554 496 964 0 912 3958
normalized size 1 1.00 6.36 3.74 1.20 2.32 0.00 2.20 9.54
time (sec) N/A 1.053 8.020 0.292 0.489 3.000 0.000 3.065 34.031
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A B F(-2) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 597 597 2499 2465 839 1699 0 1714 807
normalized size 1 1.00 4.19 4.13 1.41 2.85 0.00 2.87 1.35
time (sec) N/A 1.290 8.161 0.334 0.566 2.651 0.000 2.698 29.277
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 603 603 419 1807 680 679 1819 0 891
normalized size 1 1.00 0.69 3.00 1.13 1.13 3.02 0.00 1.48
time (sec) N/A 1.533 6.574 0.033 0.480 0.643 3.221 0.000 9.310
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A A A F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 389 387 297 994 387 386 1001 0 478
normalized size 1 0.99 0.76 2.56 0.99 0.99 2.57 0.00 1.23
time (sec) N/A 0.705 6.332 0.036 0.449 1.481 1.654 0.000 9.038
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 191 191 212 420 202 201 410 4300 221
normalized size 1 1.00 1.11 2.20 1.06 1.05 2.15 22.51 1.16
time (sec) N/A 0.244 2.436 0.031 0.580 1.574 0.762 24.807 8.789
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 363 363 255 1304 436 623 7205 573 508
normalized size 1 1.00 0.70 3.59 1.20 1.72 19.85 1.58 1.40
time (sec) N/A 1.512 4.830 0.253 0.541 3.139 113.330 3.407 13.004
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 574 574 2467 2250 685 1512 0 1357 701
normalized size 1 1.00 4.30 3.92 1.19 2.63 0.00 2.36 1.22
time (sec) N/A 2.321 8.577 0.296 0.588 3.086 0.000 7.279 15.699
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F(-2) B B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 798 798 1451 3522 1119 2549 0 2505 1172
normalized size 1 1.00 1.82 4.41 1.40 3.19 0.00 3.14 1.47
time (sec) N/A 2.839 15.892 0.316 0.550 4.314 0.000 7.349 19.238
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 337 337 258 1304 445 627 7205 573 508
normalized size 1 1.00 0.77 3.87 1.32 1.86 21.38 1.70 1.51
time (sec) N/A 1.588 4.515 0.266 0.585 2.732 115.152 5.522 13.392
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 236 236 190 861 294 390 4517 338 325
normalized size 1 1.00 0.81 3.65 1.25 1.65 19.14 1.43 1.38
time (sec) N/A 0.804 2.990 0.291 0.550 1.174 8.128 3.056 11.200
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 156 156 148 506 178 212 2429 186 186
normalized size 1 1.00 0.95 3.24 1.14 1.36 15.57 1.19 1.19
time (sec) N/A 0.342 1.086 0.252 1.490 0.846 2.412 1.929 10.246
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 99 99 117 234 106 118 984 109 109
normalized size 1 1.00 1.18 2.36 1.07 1.19 9.94 1.10 1.10
time (sec) N/A 0.098 0.197 0.255 0.555 1.177 1.305 2.057 9.898
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F(-1) A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 165 164 313 647 243 301 0 272 196
normalized size 1 0.99 1.90 3.92 1.47 1.82 0.00 1.65 1.19
time (sec) N/A 0.256 1.505 0.517 0.467 0.922 0.000 2.334 21.398
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F(-2) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 281 281 543 1262 520 1345 0 846 393
normalized size 1 1.00 1.93 4.49 1.85 4.79 0.00 3.01 1.40
time (sec) N/A 0.795 6.957 0.548 0.510 2.537 0.000 6.617 63.656
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F(-2) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 477 477 898 2298 1096 3643 0 2127 65819
normalized size 1 1.00 1.88 4.82 2.30 7.64 0.00 4.46 137.99
time (sec) N/A 1.786 9.028 0.523 0.677 7.175 0.000 26.162 24.034
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 579 579 2463 2250 684 1477 0 1355 701
normalized size 1 1.00 4.25 3.89 1.18 2.55 0.00 2.34 1.21
time (sec) N/A 2.134 8.548 0.286 0.731 2.368 0.000 3.653 16.677
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A B F(-1) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 417 417 2636 1554 493 939 0 912 3958
normalized size 1 1.00 6.32 3.73 1.18 2.25 0.00 2.19 9.49
time (sec) N/A 1.113 7.943 0.267 0.538 1.278 0.000 3.090 35.258
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A A A A B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 292 288 606 948 319 505 9721 528 1875
normalized size 1 0.99 2.08 3.25 1.09 1.73 33.29 1.81 6.42
time (sec) N/A 0.554 6.783 0.270 0.496 0.647 4.099 6.681 22.014
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A A A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 140 140 207 438 205 256 4396 299 184
normalized size 1 1.00 1.48 3.13 1.46 1.83 31.40 2.14 1.31
time (sec) N/A 0.209 2.550 0.296 0.666 0.575 2.132 3.991 11.345
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B A B F(-2) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 293 293 592 1263 513 1275 0 846 430
normalized size 1 1.00 2.02 4.31 1.75 4.35 0.00 2.89 1.47
time (sec) N/A 0.812 7.504 0.547 0.505 2.708 0.000 5.673 85.865
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F(-2) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 509 508 984 2012 1185 4174 0 2893 73684
normalized size 1 1.00 1.93 3.95 2.33 8.20 0.00 5.68 144.76
time (sec) N/A 2.151 8.908 0.481 0.761 6.551 0.000 4.534 31.511
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F(-2) B B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 841 841 1758 3364 2519 9594 0 3176 128667
normalized size 1 1.00 2.09 4.00 3.00 11.41 0.00 3.78 152.99
time (sec) N/A 4.076 8.622 0.623 0.704 17.356 0.000 25.978 58.468
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F(-2) B B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 804 804 1445 3522 1110 2490 0 2505 1172
normalized size 1 1.00 1.80 4.38 1.38 3.10 0.00 3.12 1.46
time (sec) N/A 2.747 15.598 0.294 0.602 2.647 0.000 5.088 20.600
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A B F(-2) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 597 597 2499 2465 827 1618 0 1709 807
normalized size 1 1.00 4.19 4.13 1.39 2.71 0.00 2.86 1.35
time (sec) N/A 1.385 8.127 0.320 0.582 1.231 0.000 4.651 30.686
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A B F(-2) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 352 349 378 1513 543 897 0 1037 502
normalized size 1 0.99 1.07 4.30 1.54 2.55 0.00 2.95 1.43
time (sec) N/A 0.711 6.344 0.333 0.604 0.537 0.000 2.699 16.535
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B A B F(-2) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 209 209 261 713 367 566 0 548 327
normalized size 1 1.00 1.25 3.41 1.76 2.71 0.00 2.62 1.56
time (sec) N/A 0.376 5.279 0.292 0.644 0.717 0.000 1.386 11.877
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B B F(-2) B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 487 487 912 2298 1078 3496 0 2125 65817
normalized size 1 1.00 1.87 4.72 2.21 7.18 0.00 4.36 135.15
time (sec) N/A 1.830 9.244 0.528 0.560 6.767 0.000 17.821 24.606
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B B B F(-2) B B
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 861 860 1732 3364 2537 9567 0 3176 128666
normalized size 1 1.00 2.01 3.91 2.95 11.11 0.00 3.69 149.44
time (sec) N/A 4.276 8.740 0.620 0.787 20.867 0.000 90.117 47.926
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F(-1) F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 464 464 1232 6661 0 0 0 0 -1
normalized size 1 1.00 2.66 14.36 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.089 6.392 0.618 0.000 0.000 0.000 0.000 0.000
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-1) F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 325 325 314 4775 0 0 0 0 -1
normalized size 1 1.00 0.97 14.69 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.306 4.818 0.455 0.000 0.000 0.000 0.000 0.000
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F(-1) F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 224 224 220 3028 0 0 0 0 22955
normalized size 1 1.00 0.98 13.52 0.00 0.00 0.00 0.00 102.48
time (sec) N/A 0.628 1.991 0.500 0.000 0.000 0.000 0.000 60.113
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F(-1) F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 155 155 150 1472 0 0 0 0 1199
normalized size 1 1.00 0.97 9.50 0.00 0.00 0.00 0.00 7.74
time (sec) N/A 0.306 0.558 0.436 0.000 0.000 0.000 0.000 17.403
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) F(-1) F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 234 234 233 3576 0 0 0 0 62245
normalized size 1 1.00 1.00 15.28 0.00 0.00 0.00 0.00 266.00
time (sec) N/A 1.087 0.689 0.749 0.000 0.000 0.000 0.000 36.224
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F(-2) F(-1) F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 317 317 764 5778 0 0 0 0 138318
normalized size 1 1.00 2.41 18.23 0.00 0.00 0.00 0.00 436.33
time (sec) N/A 1.439 6.386 0.873 0.000 0.000 0.000 0.000 45.420
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F(-2) F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 543 543 2819 9797 0 0 0 0 -1
normalized size 1 1.00 5.19 18.04 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 4.037 6.382 0.881 0.000 0.000 0.000 0.000 0.000
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F(-1) F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 550 550 1290 11056 0 0 0 0 -1
normalized size 1 1.00 2.35 20.10 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.734 6.414 0.640 0.000 0.000 0.000 0.000 0.000
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-1) F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 396 396 350 8031 0 0 0 0 -1
normalized size 1 1.00 0.88 20.28 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.727 6.198 0.603 0.000 0.000 0.000 0.000 0.000
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-1) F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 273 273 260 5149 0 0 0 0 -1
normalized size 1 1.00 0.95 18.86 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.879 4.441 0.546 0.000 0.000 0.000 0.000 0.000
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F(-1) F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 187 187 202 2517 0 0 0 0 4260
normalized size 1 1.00 1.08 13.46 0.00 0.00 0.00 0.00 22.78
time (sec) N/A 0.460 1.235 0.407 0.000 0.000 0.000 0.000 44.865
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) F(-1) F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 271 271 266 6055 0 0 0 0 106783
normalized size 1 1.00 0.98 22.34 0.00 0.00 0.00 0.00 394.03
time (sec) N/A 1.814 2.552 0.830 0.000 0.000 0.000 0.000 58.881
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F(-2) F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 372 372 1732 9865 0 0 0 0 -1
normalized size 1 1.00 4.66 26.52 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.547 6.313 0.831 0.000 0.000 0.000 0.000 0.000
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F(-2) F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 532 532 7678 14441 0 0 0 0 -1
normalized size 1 1.00 14.43 27.14 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 4.087 6.564 0.829 0.000 0.000 0.000 0.000 0.000
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-1) F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 503 503 564 11478 0 0 0 0 -1
normalized size 1 1.00 1.12 22.82 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.312 6.450 0.595 0.000 0.000 0.000 0.000 0.000
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-1) F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 353 351 324 7402 0 0 0 0 -1
normalized size 1 0.99 0.92 20.97 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.212 5.359 0.519 0.000 0.000 0.000 0.000 0.000
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-1) F(-1) F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 229 229 262 3614 0 0 0 0 5863
normalized size 1 1.00 1.14 15.78 0.00 0.00 0.00 0.00 25.60
time (sec) N/A 0.629 2.066 0.408 0.000 0.000 0.000 0.000 117.306
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) F(-1) F(-1) F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 336 336 322 8698 0 0 0 0 -1
normalized size 1 1.00 0.96 25.89 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.812 5.306 0.842 0.000 0.000 0.000 0.000 0.000
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F(-2) F(-1) F(-1) F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 473 473 6112 14119 0 0 0 0 -1
normalized size 1 1.00 12.92 29.85 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 3.896 6.532 0.874 0.000 0.000 0.000 0.000 0.000
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F(-2) F(-1) F(-1) F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 643 643 18214 20663 0 0 0 0 -1
normalized size 1 1.00 28.33 32.14 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 6.065 6.891 0.839 0.000 0.000 0.000 0.000 0.000
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F(-1) F(-1) F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 407 407 1200 25426 0 0 0 0 28858
normalized size 1 1.00 2.95 62.47 0.00 0.00 0.00 0.00 70.90
time (sec) N/A 1.699 6.432 0.465 0.000 0.000 0.000 0.000 122.079
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-1) F(-1) F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 287 287 275 18289 0 0 0 0 21254
normalized size 1 1.00 0.96 63.72 0.00 0.00 0.00 0.00 74.06
time (sec) N/A 1.001 6.032 0.412 0.000 0.000 0.000 0.000 47.981
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-1) F(-1) F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 194 194 192 4138 0 0 0 0 16400
normalized size 1 1.00 0.99 21.33 0.00 0.00 0.00 0.00 84.54
time (sec) N/A 0.498 1.457 0.396 0.000 0.000 0.000 0.000 23.482
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F(-1) F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 133 133 129 5570 0 0 0 0 4326
normalized size 1 1.00 0.97 41.88 0.00 0.00 0.00 0.00 32.53
time (sec) N/A 0.216 0.216 0.372 0.000 0.000 0.000 0.000 14.206
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) F(-1) F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 210 210 194 13474 0 0 0 0 25341
normalized size 1 1.00 0.92 64.16 0.00 0.00 0.00 0.00 120.67
time (sec) N/A 0.615 0.418 0.522 0.000 0.000 0.000 0.000 69.145
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) F(-1) F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 327 327 521 20870 0 0 0 0 225004
normalized size 1 1.00 1.59 63.82 0.00 0.00 0.00 0.00 688.09
time (sec) N/A 1.379 6.217 0.643 0.000 0.000 0.000 0.000 57.653
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-1) F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 511 511 920 49725 0 0 0 0 -1
normalized size 1 1.00 1.80 97.31 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.465 6.787 0.578 0.000 0.000 0.000 0.000 0.000
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-1) F(-1) F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 343 343 476 36710 0 0 0 0 54886
normalized size 1 1.00 1.39 107.03 0.00 0.00 0.00 0.00 160.02
time (sec) N/A 1.354 6.510 0.464 0.000 0.000 0.000 0.000 66.251
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-1) F(-1) F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 201 201 290 23472 0 0 0 0 40542
normalized size 1 1.00 1.44 116.78 0.00 0.00 0.00 0.00 201.70
time (sec) N/A 0.554 2.591 0.436 0.000 0.000 0.000 0.000 41.071
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-1) F(-1) F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 157 157 218 11427 0 0 0 0 8588
normalized size 1 1.00 1.39 72.78 0.00 0.00 0.00 0.00 54.70
time (sec) N/A 0.294 1.011 0.360 0.000 0.000 0.000 0.000 19.614
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F(-2) F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 262 262 296 26343 0 0 0 0 -1
normalized size 1 1.00 1.13 100.55 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.277 4.950 0.625 0.000 0.000 0.000 0.000 0.000
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F(-2) F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 447 446 2078 40619 0 0 0 0 -1
normalized size 1 1.00 4.65 90.87 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.881 6.286 0.719 0.000 0.000 0.000 0.000 0.000
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-1) F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 585 585 670 85156 0 0 0 0 -1
normalized size 1 1.00 1.15 145.57 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.968 6.906 0.615 0.000 0.000 0.000 0.000 0.000
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-1) F(-1) F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 358 358 502 61833 0 0 0 0 88684
normalized size 1 1.00 1.40 172.72 0.00 0.00 0.00 0.00 247.72
time (sec) N/A 1.551 6.562 0.519 0.000 0.000 0.000 0.000 116.899
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-1) F(-1) F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 273 271 300 40201 0 0 0 0 64641
normalized size 1 0.99 1.10 147.26 0.00 0.00 0.00 0.00 236.78
time (sec) N/A 0.798 3.020 0.611 0.000 0.000 0.000 0.000 88.469
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-1) F(-1) F F(-1) B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 209 209 223 20647 0 0 0 0 14163
normalized size 1 1.00 1.07 98.79 0.00 0.00 0.00 0.00 67.77
time (sec) N/A 0.486 0.938 0.395 0.000 0.000 0.000 0.000 37.590
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F(-2) F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 365 365 1948 45119 0 0 0 0 -1
normalized size 1 1.00 5.34 123.61 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.466 6.276 0.674 0.000 0.000 0.000 0.000 0.000
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B B F(-2) F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 679 678 6052 67570 0 0 0 0 -1
normalized size 1 1.00 8.91 99.51 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 5.062 6.427 0.850 0.000 0.000 0.000 0.000 0.000
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F(-1) F(-1) F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 679 679 1202 0 0 0 0 0 -1
normalized size 1 1.00 1.77 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 9.926 9.951 180.000 0.000 0.000 0.000 0.000 0.000
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F F(-1) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 505 505 835 0 0 0 0 0 -1
normalized size 1 1.00 1.65 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 7.338 8.876 180.000 0.000 0.000 0.000 0.000 0.000
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 381 383 619 0 0 0 0 0 -1
normalized size 1 1.01 1.62 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 4.973 7.787 180.000 0.000 0.000 0.000 0.000 0.000
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 287 287 441 0 0 0 0 0 -1
normalized size 1 1.00 1.54 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.633 4.244 180.000 0.000 0.000 0.000 0.000 0.000
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F(-1) F(-1) F(-1) F F(-1) F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 300 300 621058 0 0 0 0 0 -1
normalized size 1 1.00 2070.19 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 3.796 35.731 180.000 0.000 0.000 0.000 0.000 0.000
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F(-2) F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 370 370 600 0 0 0 0 0 -1
normalized size 1 1.00 1.62 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.052 7.014 180.000 0.000 0.000 0.000 0.000 0.000
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F(-1) F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 597 597 1109 0 0 0 0 0 -1
normalized size 1 1.00 1.86 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 3.589 7.348 180.000 0.000 0.000 0.000 0.000 0.000
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F F(-1) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 682 682 1304 0 0 0 0 0 -1
normalized size 1 1.00 1.91 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 11.896 9.140 180.000 0.000 0.000 0.000 0.000 0.000
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F F(-1) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 508 508 867 0 0 0 0 0 -1
normalized size 1 1.00 1.71 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 7.488 9.002 180.000 0.000 0.000 0.000 0.000 0.000
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 384 384 613 0 0 0 0 0 -1
normalized size 1 1.00 1.60 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 4.311 7.691 180.000 0.000 0.000 0.000 0.000 0.000
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F(-1) F(-1) F(-1) F F(-1) F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 382 382 1073629 0 0 0 0 0 -1
normalized size 1 1.00 2810.55 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 5.739 39.709 180.000 0.000 0.000 0.000 0.000 0.000
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F(-1) F(-1) F(-1) F F(-1) F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 402 402 1347065 0 0 0 0 0 -1
normalized size 1 1.00 3350.91 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 7.127 41.050 180.000 0.000 0.000 0.000 0.000 0.000
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F(-1) F(-2) F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 586 586 3134 0 0 0 0 0 -1
normalized size 1 1.00 5.35 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 3.668 9.062 180.000 0.000 0.000 0.000 0.000 0.000
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F(-1) F(-1) F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 697 697 1261 0 0 0 0 0 -1
normalized size 1 1.00 1.81 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 10.416 9.731 180.000 0.000 0.000 0.000 0.000 0.000
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F(-1) F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 505 505 780 0 0 0 0 0 -1
normalized size 1 1.00 1.54 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 6.230 8.968 180.000 0.000 0.000 0.000 0.000 0.000
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F(-1) F(-1) F(-1) F F(-1) F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 535 535 1654245 0 0 0 0 0 -1
normalized size 1 1.00 3092.05 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 8.314 44.384 180.000 0.000 0.000 0.000 0.000 0.000
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F(-1) F(-1) F(-1) F F(-1) F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 545 545 2018669 0 0 0 0 0 -1
normalized size 1 1.00 3703.98 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 11.066 47.102 180.000 0.000 0.000 0.000 0.000 0.000
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F(-1) F(-1) F(-1) F(-1) F(-1) F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 590 590 2345519 0 0 0 0 0 -1
normalized size 1 1.00 3975.46 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 14.020 49.131 180.000 0.000 0.000 0.000 0.000 0.000
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F(-1) F(-2) F(-1) F(-1) F(-1) F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 946 946 2719441 0 0 0 0 0 -1
normalized size 1 1.00 2874.67 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 6.464 53.638 180.000 0.000 0.000 0.000 0.000 0.000
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F(-1) F(-1) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 505 505 785 0 0 0 0 0 -1
normalized size 1 1.00 1.55 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 5.953 8.498 180.000 0.000 0.000 0.000 0.000 0.000
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F F(-1) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 383 383 582 0 0 0 0 0 -1
normalized size 1 1.00 1.52 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 4.077 7.077 180.000 0.000 0.000 0.000 0.000 0.000
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 290 290 450 0 0 0 0 0 -1
normalized size 1 1.00 1.55 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.555 6.631 180.000 0.000 0.000 0.000 0.000 0.000
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F(-1) F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 239 239 362 0 0 0 0 0 -1
normalized size 1 1.00 1.51 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.457 2.301 180.000 0.000 0.000 0.000 0.000 0.000
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 251 251 264 0 0 0 0 0 -1
normalized size 1 1.00 1.05 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.969 2.582 180.000 0.000 0.000 0.000 0.000 0.000
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F(-1) F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 375 375 388 0 0 0 0 0 -1
normalized size 1 1.00 1.03 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.765 6.279 180.000 0.000 0.000 0.000 0.000 0.000
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F(-1) F(-1) F(-1) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 528 528 1653959 0 0 0 0 0 -1
normalized size 1 1.00 3132.50 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 8.188 44.531 180.000 0.000 0.000 0.000 0.000 0.000
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F(-1) F(-1) F(-1) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 380 380 1073499 0 0 0 0 0 -1
normalized size 1 1.00 2825.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 5.627 39.856 180.000 0.000 0.000 0.000 0.000 0.000
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F(-1) F(-1) F(-1) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 299 299 621084 0 0 0 0 0 -1
normalized size 1 1.00 2077.20 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 3.333 35.587 180.000 0.000 0.000 0.000 0.000 0.000
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 251 251 275 0 0 0 0 0 -1
normalized size 1 1.00 1.10 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.001 3.209 180.000 0.000 0.000 0.000 0.000 0.000
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F(-1) F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 383 382 484 0 0 0 0 0 -1
normalized size 1 1.00 1.26 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.878 6.720 180.000 0.000 0.000 0.000 0.000 0.000
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F(-1) F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 598 598 902 0 0 0 0 0 -1
normalized size 1 1.00 1.51 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 3.435 6.904 180.000 0.000 0.000 0.000 0.000 0.000
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F(-1) F(-1) F(-1) F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 549 549 2018643 0 0 0 0 0 -1
normalized size 1 1.00 3676.95 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 10.500 47.170 180.000 0.000 0.000 0.000 0.000 0.000
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F(-1) F(-1) F(-1) F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 407 407 1347117 0 0 0 0 0 -1
normalized size 1 1.00 3309.87 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 7.163 41.121 180.000 0.000 0.000 0.000 0.000 0.000
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F(-2) F(-1) F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 373 373 609 0 0 0 0 0 -1
normalized size 1 1.00 1.63 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.922 7.017 180.000 0.000 0.000 0.000 0.000 0.000
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F(-1) F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 379 379 403 0 0 0 0 0 -1
normalized size 1 1.00 1.06 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.814 5.591 180.000 0.000 0.000 0.000 0.000 0.000
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F(-1) F(-1) F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 651 650 903 0 0 0 0 0 -1
normalized size 1 1.00 1.39 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 3.431 6.994 180.000 0.000 0.000 0.000 0.000 0.000
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F F(-2) F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 376 376 0 0 0 0 0 0 -1
normalized size 1 1.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.900 25.497 4.344 0.000 1.700 0.000 0.000 0.000
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F(-1) F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 560 551 1390 0 0 0 0 0 -1
normalized size 1 0.98 2.48 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.377 6.408 2.622 0.000 0.913 0.000 0.000 0.000
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-1) F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 363 360 505 0 0 0 0 0 -1
normalized size 1 0.99 1.39 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.152 6.349 2.191 0.000 0.646 0.000 0.000 0.000
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 247 247 202 0 0 0 0 0 -1
normalized size 1 1.00 0.82 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.528 2.998 1.735 0.000 1.013 0.000 0.000 0.000
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 178 178 135 0 0 0 0 0 -1
normalized size 1 1.00 0.76 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.184 0.250 1.366 0.000 1.148 0.000 0.000 0.000
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 258 258 204 0 0 0 0 0 -1
normalized size 1 1.00 0.79 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.482 1.118 4.918 0.000 0.743 0.000 0.000 0.000
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-2) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 403 402 563 0 0 0 0 0 -1
normalized size 1 1.00 1.40 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.215 6.196 4.555 0.000 1.553 0.000 0.000 0.000
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B F F(-1) F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 702 702 2238 0 0 0 0 0 -1
normalized size 1 1.00 3.19 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.938 6.244 5.038 0.000 1.735 0.000 0.000 0.000

2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. It gives additional statistics for each integral. the column steps is the number of steps used by Rubi to obtain the antiderivative. The rules column is the number of unique rules used. The integrand size column is the leaf size of the integrand. Finally the ratio \(\frac {\text {number of rules}}{\text {integrand size}}\) is given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [38] had the largest ratio of [.2000]

Table 2.1:Rubi specific breakdown of results for each integral
# grade
number of
steps
used
number of
unique
rules
normalized
antiderivative
leaf size
integrand
leaf size
\(\frac {\text {number of rules}}{\text {integrand leaf size}}\)
1 A 5 5 1.00 36 0.139
2 A 3 3 1.00 30 0.100
3 A 3 3 1.00 36 0.083
4 A 5 4 1.00 38 0.105
5 A 4 4 1.00 38 0.105
6 A 5 5 1.00 38 0.132
7 A 6 5 1.00 38 0.132
8 A 7 5 1.00 38 0.132
9 A 6 6 1.00 38 0.158
10 A 4 4 1.00 32 0.125
11 A 4 4 1.00 38 0.105
12 A 5 4 1.00 40 0.100
13 A 5 4 1.00 40 0.100
14 A 5 5 1.00 40 0.125
15 A 6 6 1.00 40 0.150
16 A 7 6 1.00 40 0.150
17 A 5 4 1.00 32 0.125
18 A 5 4 1.00 38 0.105
19 A 6 5 1.00 40 0.125
20 A 6 5 1.00 40 0.125
21 A 6 5 1.00 40 0.125
22 A 6 6 1.00 40 0.150
23 A 7 7 1.00 40 0.175
24 A 8 7 1.00 40 0.175
25 A 7 7 1.00 40 0.175
26 A 6 6 1.00 38 0.158
27 A 6 4 1.00 32 0.125
28 A 3 3 1.00 38 0.079
29 A 4 4 1.00 40 0.100
30 A 5 5 1.00 40 0.125
31 A 6 6 1.00 40 0.150
32 A 7 7 1.00 40 0.175
33 A 6 6 1.00 38 0.158
34 A 3 3 1.00 32 0.094
35 A 4 4 1.00 38 0.105
36 A 5 5 1.00 40 0.125
37 A 6 6 1.00 40 0.150
38 A 8 8 1.00 40 0.200
39 A 7 7 1.00 40 0.175
40 A 5 5 1.00 38 0.132
41 A 4 4 1.00 32 0.125
42 A 5 4 1.00 38 0.105
43 A 6 6 1.00 40 0.150
44 A 7 6 1.00 40 0.150
45 A 7 5 1.00 39 0.128
46 A 7 5 1.00 39 0.128
47 A 7 5 1.00 41 0.122
48 A 7 5 1.00 41 0.122
49 A 13 7 1.00 43 0.163
50 A 6 5 1.00 43 0.116
51 A 5 5 1.00 43 0.116
52 A 4 4 1.00 41 0.098
53 A 3 3 1.00 31 0.097
54 A 5 5 0.99 43 0.116
55 A 5 5 1.00 43 0.116
56 A 4 4 1.00 43 0.093
57 A 7 6 1.00 45 0.133
58 A 6 6 1.00 45 0.133
59 A 5 5 0.99 43 0.116
60 A 4 4 1.00 33 0.121
61 A 6 6 0.99 45 0.133
62 A 6 6 1.00 45 0.133
63 A 6 6 1.00 45 0.133
64 A 7 6 1.00 45 0.133
65 A 6 5 0.99 43 0.116
66 A 5 4 1.00 33 0.121
67 A 7 6 1.00 45 0.133
68 A 7 7 1.00 45 0.156
69 A 7 6 1.00 45 0.133
70 A 7 6 1.00 45 0.133
71 A 6 6 1.00 45 0.133
72 A 5 5 1.00 43 0.116
73 A 4 4 1.00 33 0.121
74 A 3 2 0.99 45 0.044
75 A 4 3 1.00 45 0.067
76 A 5 3 1.00 45 0.067
77 A 7 7 1.00 45 0.156
78 A 6 6 1.00 45 0.133
79 A 5 5 0.99 43 0.116
80 A 3 3 1.00 33 0.091
81 A 4 3 1.00 45 0.067
82 A 5 3 1.00 45 0.067
83 A 6 3 1.00 45 0.067
84 A 7 6 1.00 45 0.133
85 A 6 6 1.00 45 0.133
86 A 4 4 0.99 43 0.093
87 A 4 4 1.00 33 0.121
88 A 5 3 1.00 45 0.067
89 A 6 3 1.00 45 0.067
90 A 12 8 1.00 47 0.170
91 A 11 8 1.00 47 0.170
92 A 10 7 1.00 45 0.156
93 A 9 6 1.00 35 0.171
94 A 12 7 1.00 47 0.149
95 A 12 7 1.00 47 0.149
96 A 13 8 1.00 47 0.170
97 A 13 8 1.00 47 0.170
98 A 12 8 1.00 47 0.170
99 A 11 7 1.00 45 0.156
100 A 10 6 1.00 35 0.171
101 A 13 7 1.00 47 0.149
102 A 13 8 1.00 47 0.170
103 A 13 7 1.00 47 0.149
104 A 13 8 1.00 47 0.170
105 A 12 7 0.99 45 0.156
106 A 11 6 1.00 35 0.171
107 A 14 7 1.00 47 0.149
108 A 14 8 1.00 47 0.170
109 A 14 8 1.00 47 0.170
110 A 11 7 1.00 47 0.149
111 A 10 7 1.00 47 0.149
112 A 9 6 1.00 45 0.133
113 A 8 5 1.00 35 0.143
114 A 11 6 1.00 47 0.128
115 A 12 7 1.00 47 0.149
116 A 11 8 1.00 47 0.170
117 A 10 7 1.00 47 0.149
118 A 9 6 1.00 45 0.133
119 A 8 5 1.00 35 0.143
120 A 12 7 1.00 47 0.149
121 A 13 7 1.00 47 0.149
122 A 11 7 1.00 47 0.149
123 A 10 7 1.00 47 0.149
124 A 9 6 0.99 45 0.133
125 A 9 6 1.00 35 0.171
126 A 13 7 1.00 47 0.149
127 A 14 7 1.00 47 0.149
128 A 16 8 1.00 49 0.163
129 A 15 8 1.00 49 0.163
130 A 14 8 1.01 49 0.163
131 A 13 8 1.00 49 0.163
132 A 13 8 1.00 49 0.163
133 A 9 6 1.00 49 0.122
134 A 10 6 1.00 49 0.122
135 A 16 8 1.00 49 0.163
136 A 15 8 1.00 49 0.163
137 A 14 8 1.00 49 0.163
138 A 14 9 1.00 49 0.184
139 A 14 8 1.00 49 0.163
140 A 10 6 1.00 49 0.122
141 A 16 8 1.00 49 0.163
142 A 15 8 1.00 49 0.163
143 A 15 9 1.00 49 0.184
144 A 15 9 1.00 49 0.184
145 A 15 8 1.00 49 0.163
146 A 11 6 1.00 49 0.122
147 A 15 8 1.00 49 0.163
148 A 14 8 1.00 49 0.163
149 A 13 8 1.00 49 0.163
150 A 12 7 1.00 49 0.143
151 A 8 5 1.00 49 0.102
152 A 9 5 1.00 49 0.102
153 A 15 9 1.00 49 0.184
154 A 14 9 1.00 49 0.184
155 A 13 8 1.00 49 0.163
156 A 8 5 1.00 49 0.102
157 A 9 5 1.00 49 0.102
158 A 10 5 1.00 49 0.102
159 A 15 9 1.00 49 0.184
160 A 14 8 1.00 49 0.163
161 A 9 6 1.00 49 0.122
162 A 9 5 1.00 49 0.102
163 A 10 5 1.00 49 0.102
164 A 9 6 1.00 45 0.133
165 A 9 6 0.98 45 0.133
166 A 8 6 0.99 45 0.133
167 A 7 5 1.00 43 0.116
168 A 6 4 1.00 33 0.121
169 A 8 5 1.00 45 0.111
170 A 9 6 1.00 45 0.133
171 A 10 6 1.00 45 0.133

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