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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, 172, 173, 174 }

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 66, 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, 100, 101, 102, 103, 108, 109, 110, 112, 113, 114, 115, 116, 117, 118, 122, 123, 124, 125, 126, 127, 128, 131, 132, 133, 134, 135, 136, 137, 138, 141, 142, 143, 144, 145, 146, 147, 148, 151, 152, 153, 154, 155, 156, 157, 158, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174 }

B grade: { 96, 97, 104 }

C grade: { 63, 64, 65, 67, 68, 98, 105, 106, 111, 119, 120, 121, 129, 130, 139, 140, 149, 150, 159, 160 }

F grade: { 99, 107, 161, 162, 163 }

2.1.3 Maple

A grade: { 1, 2, 3, 4, 6, 7, 8, 9, 11, 13, 14, 18, 19, 22, 26, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 58, 59, 60, 64, 65, 66, 69, 72, 73, 74, 75, 76, 77, 78, 79, 80, 83, 84, 85, 86, 87, 88, 89, 90, 114, 115, 116, 117, 118, 123, 124, 125, 126, 127, 128, 134, 135, 136, 137, 144, 145, 146, 147, 154, 155, 156, 157, 164, 165, 166, 167, 168, 169, 173, 174 }

B grade: { 5, 10, 12, 15, 16, 17, 20, 21, 23, 24, 25, 28, 29, 30, 31, 32, 56, 57, 61, 62, 63, 67, 68, 70, 71, 81, 82, 98, 105, 106 }

C grade: { 91, 92, 93, 94, 95, 96, 97, 99, 100, 101, 102, 103, 104, 107, 108, 109, 110 }

F grade: { 27, 53, 111, 112, 113, 119, 120, 121, 122, 129, 130, 131, 132, 133, 138, 139, 140, 141, 142, 143, 148, 149, 150, 151, 152, 153, 158, 159, 160, 161, 162, 163, 170, 171, 172 }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 20, 22, 29, 33, 34, 35, 39, 40, 41, 45, 46, 47, 51, 54, 55, 56, 57, 58, 59, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 81, 82, 83, 84, 85, 86, 87, 88, 114, 115, 116, 117, 118, 123, 124, 125, 126, 127, 128, 134, 135, 136, 137, 144, 145, 146, 147, 154, 155, 156, 157, 164, 165, 166, 167, 168, 169, 173, 174 }

B grade: { 31 }

C grade: { }

F grade: { 8, 16, 18, 19, 21, 23, 24, 25, 26, 27, 28, 30, 32, 36, 37, 38, 42, 43, 44, 48, 49, 50, 52, 53, 60, 61, 62, 63, 64, 65, 66, 67, 68, 79, 80, 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, 119, 120, 121, 122, 129, 130, 131, 132, 133, 138, 139, 140, 141, 142, 143, 148, 149, 150, 151, 152, 153, 158, 159, 160, 161, 162, 163, 170, 171, 172 }

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, 41, 45, 46, 47, 51, 52, 54, 55, 56, 57, 58, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 81, 82, 83, 84, 85, 86, 87, 88, 98, 111, 112, 113, 114, 115, 116, 117, 118, 121, 122, 123, 124, 125, 126, 127, 128, 131, 132, 133, 134, 135, 136, 137, 141, 142, 143, 144, 145, 146, 147, 154, 155, 156, 157, 164, 165, 166, 167, 168, 169, 173, 174 }

B grade: { 7, 17, 59, 61, 62, 105, 106, 151, 152, 153 }

C grade: { }

F grade: { 8, 16, 18, 19, 24, 25, 26, 27, 28, 36, 37, 38, 42, 43, 44, 48, 49, 50, 53, 60, 63, 64, 65, 66, 67, 68, 79, 80, 89, 90, 91, 92, 93, 94, 95, 96, 97, 99, 100, 101, 102, 103, 104, 107, 108, 109, 110, 119, 120, 129, 130, 138, 139, 140, 148, 149, 150, 158, 159, 160, 161, 162, 163, 170, 171, 172 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 33, 34, 35, 39, 40, 41, 45, 46, 47, 51, 52, 54, 55, 56, 57, 58, 59, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 81, 82, 83, 84, 85, 86, 87, 88, 114, 115, 116, 117, 118, 123, 124, 126, 127, 128, 134, 135, 136, 147, 164, 167, 168, 173, 174 }

B grade: { }

C grade: { }

F grade: { 8, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 36, 37, 38, 42, 43, 44, 48, 49, 50, 53, 60, 61, 62, 63, 64, 65, 66, 67, 68, 79, 80, 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, 119, 120, 121, 122, 125, 129, 130, 131, 132, 133, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 165, 166, 169, 170, 171, 172 }

2.1.7 Giac

A grade: { 9, 10, 11, 12, 13, 14, 21, 22, 23, 33, 34, 35, 36, 37, 38, 39, 40, 41, 46, 47, 51, 52, 54, 55, 73, 74, 75, 85, 86, 114, 115, 116, 117, 118, 123, 124, 125, 126, 127, 128, 134, 135, 136, 137, 144, 145, 146, 147, 154, 155, 156, 157, 164, 165, 166, 167, 168, 169, 173, 174 }

B grade: { 1, 2, 3, 4, 5, 6, 7, 15, 17, 20, 29, 30, 31, 32, 42, 43, 44, 48, 49, 50, 56, 57, 58, 59, 70, 71, 72, 77, 78, 83, 84, 88 }

C grade: { }

F grade: { 8, 16, 18, 19, 24, 25, 26, 27, 28, 45, 53, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 76, 79, 80, 81, 82, 87, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 119, 120, 121, 122, 129, 130, 131, 132, 133, 138, 139, 140, 141, 142, 143, 148, 149, 150, 151, 152, 153, 158, 159, 160, 161, 162, 163, 170, 171, 172 }

2.1.8 Mupad

A grade: { 33, 34, 35, 39, 40, 41, 45, 46, 47, 51, 52, 54, 55, 114, 115, 116, 117, 118, 123, 124, 125, 126, 127, 128, 134, 135, 136, 137, 144, 145, 146, 147, 154, 155, 156, 157, 164, 165, 166, 167, 168, 169, 173, 174 }

B grade: { 6, 7, 9, 10, 20, 29, 58, 59, 72 }

C grade: { }

F grade: { 1, 2, 3, 4, 5, 8, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 36, 37, 38, 42, 43, 44, 48, 49, 50, 53, 56, 57, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 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, 119, 120, 121, 122, 129, 130, 131, 132, 133, 138, 139, 140, 141, 142, 143, 148, 149, 150, 151, 152, 153, 158, 159, 160, 161, 162, 163, 170, 171, 172 }

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 F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 114 114 107 177 162 116 221 8644 -1
normalized size 1 1.00 0.94 1.55 1.42 1.02 1.94 75.82 -0.01
time (sec) N/A 0.061 0.143 0.075 0.418 0.943 8.461 1.754 0.000
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 89 89 72 83 81 63 153 3862 -1
normalized size 1 1.00 0.81 0.93 0.91 0.71 1.72 43.39 -0.01
time (sec) N/A 0.041 0.091 0.048 0.326 0.713 4.192 0.233 0.000
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 89 89 97 150 131 107 175 4828 -1
normalized size 1 1.00 1.09 1.69 1.47 1.20 1.97 54.25 -0.01
time (sec) N/A 0.046 0.076 0.049 0.309 0.686 5.401 1.316 0.000
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 64 64 62 74 60 53 107 1926 -1
normalized size 1 1.00 0.97 1.16 0.94 0.83 1.67 30.09 -0.02
time (sec) N/A 0.027 0.106 0.050 0.308 0.698 2.789 0.197 0.000
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 64 64 85 123 98 94 107 2101 -1
normalized size 1 1.00 1.33 1.92 1.53 1.47 1.67 32.83 -0.02
time (sec) N/A 0.035 0.054 0.048 0.314 0.760 3.286 0.824 0.000
Problem 6 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 39 39 50 65 37 40 58 634 40
normalized size 1 1.00 1.28 1.67 0.95 1.03 1.49 16.26 1.03
time (sec) N/A 0.012 0.023 0.046 0.314 0.545 1.992 0.177 0.672
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 32 32 59 38 53 63 32 63 34
normalized size 1 1.00 1.84 1.19 1.66 1.97 1.00 1.97 1.06
time (sec) N/A 0.020 0.068 0.043 0.314 0.990 2.326 0.136 0.842
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 64 64 59 86 0 0 0 0 -1
normalized size 1 1.00 0.92 1.34 0.00 0.00 0.00 0.00 -0.02
time (sec) N/A 0.084 0.017 0.186 0.000 0.576 0.000 0.000 0.000
Problem 9 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 31 31 40 62 33 27 36 43 36
normalized size 1 1.00 1.29 2.00 1.06 0.87 1.16 1.39 1.16
time (sec) N/A 0.020 0.031 0.047 0.313 1.226 1.773 0.147 0.636
Problem 10 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 51 51 66 118 83 39 119 58 50
normalized size 1 1.00 1.29 2.31 1.63 0.76 2.33 1.14 0.98
time (sec) N/A 0.033 0.035 0.049 0.412 0.581 3.139 0.137 0.729
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 59 75 58 40 110 65 -1
normalized size 1 1.00 0.98 1.25 0.97 0.67 1.83 1.08 -0.02
time (sec) N/A 0.039 0.048 0.048 0.318 0.680 2.930 0.148 0.000
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 76 76 78 147 125 52 192 83 -1
normalized size 1 1.00 1.03 1.93 1.64 0.68 2.53 1.09 -0.01
time (sec) N/A 0.045 0.062 0.048 0.422 0.709 5.235 0.151 0.000
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 69 83 76 51 156 87 -1
normalized size 1 1.00 0.84 1.01 0.93 0.62 1.90 1.06 -0.01
time (sec) N/A 0.049 0.072 0.049 0.335 0.796 6.985 0.133 0.000
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 101 101 88 174 165 62 241 104 -1
normalized size 1 1.00 0.87 1.72 1.63 0.61 2.39 1.03 -0.01
time (sec) N/A 0.059 0.079 0.051 0.426 0.763 8.433 0.138 0.000
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 107 107 124 208 163 146 0 6625 -1
normalized size 1 1.00 1.16 1.94 1.52 1.36 0.00 61.92 -0.01
time (sec) N/A 0.107 0.224 0.229 0.688 0.915 0.000 0.808 0.000
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 147 147 225 343 0 0 0 0 -1
normalized size 1 1.00 1.53 2.33 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.123 1.271 0.906 0.000 0.491 0.000 0.000 0.000
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A B F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 56 56 90 134 87 111 0 2181 -1
normalized size 1 1.00 1.61 2.39 1.55 1.98 0.00 38.95 -0.02
time (sec) N/A 0.068 0.151 0.257 0.328 0.764 0.000 0.481 0.000
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 92 92 163 212 0 0 0 0 -1
normalized size 1 1.00 1.77 2.30 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.072 0.182 0.255 0.000 1.022 0.000 0.000 0.000
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 93 93 129 215 0 0 0 0 -1
normalized size 1 1.00 1.39 2.31 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.119 0.130 0.215 0.000 0.413 0.000 0.000 0.000
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 50 50 75 117 78 57 0 105 89
normalized size 1 1.00 1.50 2.34 1.56 1.14 0.00 2.10 1.78
time (sec) N/A 0.059 0.130 0.143 0.328 0.481 0.000 0.168 0.818
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 94 94 102 199 0 82 0 147 -1
normalized size 1 1.00 1.09 2.12 0.00 0.87 0.00 1.56 -0.01
time (sec) N/A 0.079 0.121 0.149 0.000 0.589 0.000 0.164 0.000
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 102 102 108 154 164 93 0 168 -1
normalized size 1 1.00 1.06 1.51 1.61 0.91 0.00 1.65 -0.01
time (sec) N/A 0.094 0.197 0.485 0.704 0.618 0.000 0.156 0.000
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 134 134 148 265 0 120 0 215 -1
normalized size 1 1.00 1.10 1.98 0.00 0.90 0.00 1.60 -0.01
time (sec) N/A 0.111 0.180 0.430 0.000 0.708 0.000 0.149 0.000
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 207 207 288 447 0 0 0 0 -1
normalized size 1 1.00 1.39 2.16 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.211 0.827 1.019 0.000 0.662 0.000 0.000 0.000
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 236 236 403 687 0 0 0 0 -1
normalized size 1 1.00 1.71 2.91 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.192 1.444 1.047 0.000 0.682 0.000 0.000 0.000
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 126 126 184 285 0 0 0 0 -1
normalized size 1 1.00 1.46 2.26 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.142 0.495 0.796 0.000 0.658 0.000 0.000 0.000
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 158 158 289 0 0 0 0 0 -1
normalized size 1 1.00 1.83 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.118 0.246 0.622 0.000 0.631 0.000 0.000 0.000
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 128 128 204 390 0 0 0 0 -1
normalized size 1 1.00 1.59 3.05 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.141 0.194 0.263 0.000 0.473 0.000 0.000 0.000
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A F B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 80 80 141 198 146 98 0 196 156
normalized size 1 1.00 1.76 2.48 1.82 1.22 0.00 2.45 1.95
time (sec) N/A 0.083 0.174 0.181 0.335 0.688 0.000 0.185 0.801
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 137 137 185 324 0 150 0 278 -1
normalized size 1 1.00 1.35 2.36 0.00 1.09 0.00 2.03 -0.01
time (sec) N/A 0.105 0.219 0.374 0.000 0.674 0.000 0.177 0.000
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B B A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 170 170 204 299 575 172 0 336 -1
normalized size 1 1.00 1.20 1.76 3.38 1.01 0.00 1.98 -0.01
time (sec) N/A 0.147 0.305 0.594 0.981 0.706 0.000 0.190 0.000
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F A F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 208 208 283 472 0 225 0 427 -1
normalized size 1 1.00 1.36 2.27 0.00 1.08 0.00 2.05 -0.00
time (sec) N/A 0.173 0.366 0.641 0.000 0.725 0.000 0.192 0.000
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 15 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.07
time (sec) N/A 0.014 2.585 2.017 0.000 0.720 0.000 0.000 0.000
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 13 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.08
time (sec) N/A 0.006 2.314 0.611 0.000 0.600 0.000 0.000 0.000
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 17 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06
time (sec) N/A 0.025 0.291 0.924 0.000 0.516 0.000 0.000 0.000
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 46 46 43 47 0 0 0 55 -1
normalized size 1 1.00 0.93 1.02 0.00 0.00 0.00 1.20 -0.02
time (sec) N/A 0.105 0.080 0.140 0.000 0.674 0.000 0.149 0.000
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 63 63 56 58 0 0 0 95 -1
normalized size 1 1.00 0.89 0.92 0.00 0.00 0.00 1.51 -0.02
time (sec) N/A 0.136 0.077 0.103 0.000 0.535 0.000 0.130 0.000
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 117 117 91 102 0 0 0 199 -1
normalized size 1 1.00 0.78 0.87 0.00 0.00 0.00 1.70 -0.01
time (sec) N/A 0.225 0.179 0.106 0.000 0.426 0.000 0.141 0.000
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 15 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.07
time (sec) N/A 0.015 10.296 2.241 0.000 0.459 0.000 0.000 0.000
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 13 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.08
time (sec) N/A 0.006 22.775 0.593 0.000 0.592 0.000 0.000 0.000
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 17 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06
time (sec) N/A 0.024 3.467 1.003 0.000 0.981 0.000 0.000 0.000
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 75 75 69 78 0 0 0 226 -1
normalized size 1 1.00 0.92 1.04 0.00 0.00 0.00 3.01 -0.01
time (sec) N/A 0.129 0.280 0.150 0.000 1.433 0.000 0.129 0.000
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 84 84 80 77 0 0 0 357 -1
normalized size 1 1.00 0.95 0.92 0.00 0.00 0.00 4.25 -0.01
time (sec) N/A 0.149 0.368 0.105 0.000 0.674 0.000 0.155 0.000
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 178 178 223 153 0 0 0 694 -1
normalized size 1 1.00 1.25 0.86 0.00 0.00 0.00 3.90 -0.01
time (sec) N/A 0.267 0.476 0.114 0.000 0.705 0.000 0.219 0.000
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 15 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.07
time (sec) N/A 0.014 3.675 2.550 0.000 0.488 0.000 0.000 0.000
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 13 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.08
time (sec) N/A 0.006 12.210 0.689 0.000 0.546 0.000 0.000 0.000
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 17 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.06
time (sec) N/A 0.025 1.793 1.183 0.000 0.815 0.000 0.000 0.000
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 103 103 88 154 0 0 0 580 -1
normalized size 1 1.00 0.85 1.50 0.00 0.00 0.00 5.63 -0.01
time (sec) N/A 0.147 0.393 0.156 0.000 0.457 0.000 0.141 0.000
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 112 112 114 157 0 0 0 929 -1
normalized size 1 1.00 1.02 1.40 0.00 0.00 0.00 8.29 -0.01
time (sec) N/A 0.180 0.381 0.107 0.000 0.437 0.000 0.144 0.000
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 228 228 169 307 0 0 0 1640 -1
normalized size 1 1.00 0.74 1.35 0.00 0.00 0.00 7.19 -0.00
time (sec) N/A 0.313 0.465 0.121 0.000 0.435 0.000 0.160 0.000
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 19 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.022 6.791 3.314 0.000 0.467 0.000 0.000 0.000
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A F(-1) A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 19 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.022 4.514 3.118 0.000 0.473 0.000 0.000 0.000
Problem 53 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 67 67 82 0 0 0 0 0 -1
normalized size 1 1.00 1.22 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.043 0.257 4.371 0.000 0.429 0.000 0.000 0.000
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 19 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.026 0.832 3.829 0.000 0.401 0.000 0.000 0.000
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 19 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.05
time (sec) N/A 0.024 1.713 2.131 0.000 0.407 0.000 0.000 0.000
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 167 167 166 486 272 291 362 9404 -1
normalized size 1 1.00 0.99 2.91 1.63 1.74 2.17 56.31 -0.01
time (sec) N/A 0.401 0.300 0.056 0.329 0.656 7.876 2.941 0.000
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 124 124 124 362 200 209 228 6418 -1
normalized size 1 1.00 1.00 2.92 1.61 1.69 1.84 51.76 -0.01
time (sec) N/A 0.266 0.190 0.054 0.327 0.576 6.600 4.956 0.000
Problem 58 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 84 84 114 141 93 130 104 1555 77
normalized size 1 1.00 1.36 1.68 1.11 1.55 1.24 18.51 0.92
time (sec) N/A 0.167 0.223 0.051 0.322 0.449 4.423 0.677 0.899
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A B A B B
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 32 32 59 38 53 63 32 63 34
normalized size 1 1.00 1.84 1.19 1.66 1.97 1.00 1.97 1.06
time (sec) N/A 0.022 0.054 0.044 0.322 0.432 2.270 0.150 0.851
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 247 247 333 456 0 0 0 0 -1
normalized size 1 1.00 1.35 1.85 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.373 0.622 0.820 0.000 0.434 0.000 0.000 0.000
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 104 104 142 214 0 477 0 0 -1
normalized size 1 1.00 1.37 2.06 0.00 4.59 0.00 0.00 -0.01
time (sec) N/A 0.156 0.229 0.060 0.000 0.487 0.000 0.000 0.000
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B F B F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 172 172 247 1005 0 1117 0 0 -1
normalized size 1 1.00 1.44 5.84 0.00 6.49 0.00 0.00 -0.01
time (sec) N/A 0.292 0.495 0.067 0.000 0.994 0.000 0.000 0.000
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-2) F(-1) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 372 372 333 810 0 0 0 0 -1
normalized size 1 1.00 0.90 2.18 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.759 1.480 0.204 0.000 0.000 0.000 0.000 0.000
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 315 315 277 388 0 0 0 0 -1
normalized size 1 1.00 0.88 1.23 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.463 6.601 0.069 0.000 0.000 0.000 0.000 0.000
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C A F(-2) F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 212 212 212 254 0 0 0 0 -1
normalized size 1 1.00 1.00 1.20 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.304 2.815 0.066 0.000 1.849 0.000 0.000 0.000
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F(-2) F(-1) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 119 119 124 217 0 0 0 0 -1
normalized size 1 1.00 1.04 1.82 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.219 0.290 0.066 0.000 0.000 0.000 0.000 0.000
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-2) F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 298 298 326 886 0 0 0 0 -1
normalized size 1 1.00 1.09 2.97 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.406 6.636 0.082 0.000 1.407 0.000 0.000 0.000
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F(-2) F(-1) F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 540 637 407 1640 0 0 0 0 -1
normalized size 1 1.18 0.75 3.04 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.711 8.914 0.088 0.000 0.000 0.000 0.000 0.000
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 206 206 141 338 296 192 408 0 -1
normalized size 1 1.00 0.68 1.64 1.44 0.93 1.98 0.00 -0.00
time (sec) N/A 0.128 0.238 0.055 0.330 1.929 11.684 0.000 0.000
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 161 161 123 282 232 170 294 9820 -1
normalized size 1 1.00 0.76 1.75 1.44 1.06 1.83 60.99 -0.01
time (sec) N/A 0.103 0.173 0.053 0.326 2.032 7.296 3.035 0.000
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 109 109 150 195 154 141 153 4069 -1
normalized size 1 1.00 1.38 1.79 1.41 1.29 1.40 37.33 -0.01
time (sec) N/A 0.051 0.283 0.052 0.313 2.086 5.720 2.054 0.000
Problem 72 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 87 104 137 89 123 73 1098 72
normalized size 1 1.00 1.20 1.57 1.02 1.41 0.84 12.62 0.83
time (sec) N/A 0.063 0.121 0.058 0.319 0.454 5.110 0.619 0.788
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 105 105 69 121 94 67 150 116 -1
normalized size 1 1.00 0.66 1.15 0.90 0.64 1.43 1.10 -0.01
time (sec) N/A 0.075 0.081 0.059 0.320 2.058 4.541 0.163 0.000
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 152 152 94 140 137 89 279 162 -1
normalized size 1 1.00 0.62 0.92 0.90 0.59 1.84 1.07 -0.01
time (sec) N/A 0.094 0.130 0.059 0.323 1.066 9.293 0.161 0.000
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 197 197 110 158 172 110 371 207 -1
normalized size 1 1.00 0.56 0.80 0.87 0.56 1.88 1.05 -0.01
time (sec) N/A 0.117 0.151 0.062 0.319 1.486 55.096 0.160 0.000
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 196 196 118 152 185 128 364 0 -1
normalized size 1 1.00 0.60 0.78 0.94 0.65 1.86 0.00 -0.01
time (sec) N/A 0.147 0.237 0.054 0.333 1.977 7.924 0.000 0.000
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 153 153 98 134 144 107 272 7840 -1
normalized size 1 1.00 0.64 0.88 0.94 0.70 1.78 51.24 -0.01
time (sec) N/A 0.122 0.265 0.052 0.313 0.647 5.293 0.310 0.000
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 138 138 79 115 100 86 177 3360 -1
normalized size 1 1.00 0.57 0.83 0.72 0.62 1.28 24.35 -0.01
time (sec) N/A 0.093 0.108 0.052 0.317 0.670 3.658 0.228 0.000
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 124 124 115 142 0 0 0 0 -1
normalized size 1 1.00 0.93 1.15 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.284 0.090 2.625 0.000 1.981 0.000 0.000 0.000
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 137 137 132 145 0 0 0 0 -1
normalized size 1 1.00 0.96 1.06 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.291 0.097 0.851 0.000 0.579 0.000 0.000 0.000
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 252 252 186 494 405 273 542 0 -1
normalized size 1 1.00 0.74 1.96 1.61 1.08 2.15 0.00 -0.00
time (sec) N/A 0.236 0.374 0.054 0.344 4.040 13.680 0.000 0.000
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A B A A A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 191 191 153 372 296 237 355 0 -1
normalized size 1 1.00 0.80 1.95 1.55 1.24 1.86 0.00 -0.01
time (sec) N/A 0.115 0.241 0.053 0.344 2.285 9.792 0.000 0.000
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 162 162 136 286 198 230 207 6010 -1
normalized size 1 1.00 0.84 1.77 1.22 1.42 1.28 37.10 -0.01
time (sec) N/A 0.127 0.205 0.060 0.338 1.106 8.564 2.946 0.000
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 158 158 127 255 159 221 211 4960 -1
normalized size 1 1.00 0.80 1.61 1.01 1.40 1.34 31.39 -0.01
time (sec) N/A 0.131 0.228 0.063 0.319 3.064 7.988 14.579 0.000
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 183 183 127 191 181 127 333 223 -1
normalized size 1 1.00 0.69 1.04 0.99 0.69 1.82 1.22 -0.01
time (sec) N/A 0.157 0.227 0.063 0.332 1.322 10.529 0.154 0.000
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 241 241 153 223 241 159 508 294 -1
normalized size 1 1.00 0.63 0.93 1.00 0.66 2.11 1.22 -0.00
time (sec) N/A 0.193 0.239 0.065 0.330 1.548 57.340 0.158 0.000
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 242 242 162 214 256 187 493 0 -1
normalized size 1 1.00 0.67 0.88 1.06 0.77 2.04 0.00 -0.00
time (sec) N/A 0.224 0.292 0.054 0.336 0.983 9.006 0.000 0.000
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A A A A B F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 195 195 125 182 192 153 352 11858 -1
normalized size 1 1.00 0.64 0.93 0.98 0.78 1.81 60.81 -0.01
time (sec) N/A 0.148 0.308 0.052 0.333 1.438 6.163 0.406 0.000
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 186 186 160 242 0 0 0 0 -1
normalized size 1 1.00 0.86 1.30 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.412 0.388 3.521 0.000 0.446 0.000 0.000 0.000
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A A F F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 189 189 187 218 0 0 0 0 -1
normalized size 1 1.00 0.99 1.15 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.417 0.664 2.877 0.000 0.498 0.000 0.000 0.000
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 546 546 1023 374 0 0 0 0 -1
normalized size 1 1.00 1.87 0.68 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.294 1.469 3.800 0.000 0.522 0.000 0.000 0.000
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 487 487 891 453 0 0 0 0 -1
normalized size 1 1.00 1.83 0.93 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.152 0.458 1.041 0.000 0.605 0.000 0.000 0.000
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 509 509 871 272 0 0 0 0 -1
normalized size 1 1.00 1.71 0.53 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.869 0.401 1.893 0.000 0.600 0.000 0.000 0.000
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 459 459 402 2933 0 0 0 0 -1
normalized size 1 1.00 0.88 6.39 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.896 0.926 1.028 0.000 0.502 0.000 0.000 0.000
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 551 551 997 331 0 0 0 0 -1
normalized size 1 1.00 1.81 0.60 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.096 1.501 3.666 0.000 0.848 0.000 0.000 0.000
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B C F F F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 608 608 1255 783 0 0 0 0 -1
normalized size 1 1.00 2.06 1.29 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.306 4.251 1.668 0.000 0.594 0.000 0.000 0.000
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B C F F F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 570 570 1213 594 0 0 0 0 -1
normalized size 1 1.00 2.13 1.04 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.216 1.322 1.369 0.000 0.844 0.000 0.000 0.000
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F A F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 131 131 286 354 0 384 0 0 -1
normalized size 1 1.00 2.18 2.70 0.00 2.93 0.00 0.00 -0.01
time (sec) N/A 0.121 0.644 0.076 0.000 0.606 0.000 0.000 0.000
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F C F F F(-1) F(-2) F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 546 546 0 3095 0 0 0 0 -1
normalized size 1 1.00 0.00 5.67 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.140 37.048 2.679 0.000 0.528 0.000 0.000 0.000
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 784 784 1331 1887 0 0 0 0 -1
normalized size 1 1.00 1.70 2.41 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.354 2.537 16.500 0.000 0.646 0.000 0.000 0.000
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F(-1) F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 745 745 1245 1756 0 0 0 0 -1
normalized size 1 1.00 1.67 2.36 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.217 1.803 3.780 0.000 1.362 0.000 0.000 0.000
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F(-1) F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 739 739 1239 1748 0 0 0 0 -1
normalized size 1 1.00 1.68 2.37 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.211 2.283 4.343 0.000 0.623 0.000 0.000 0.000
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 785 785 1291 1817 0 0 0 0 -1
normalized size 1 1.00 1.64 2.31 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.307 2.247 15.836 0.000 0.771 0.000 0.000 0.000
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A B C F F F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 707 707 1805 1626 0 0 0 0 -1
normalized size 1 1.00 2.55 2.30 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.404 8.014 1.964 0.000 0.710 0.000 0.000 0.000
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F(-1) F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 157 157 389 1870 0 1015 0 0 -1
normalized size 1 1.00 2.48 11.91 0.00 6.46 0.00 0.00 -0.01
time (sec) N/A 0.175 1.420 0.082 0.000 1.797 0.000 0.000 0.000
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C B F B F(-1) F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 193 193 386 1840 0 888 0 0 -1
normalized size 1 1.00 2.00 9.53 0.00 4.60 0.00 0.00 -0.01
time (sec) N/A 0.190 0.977 0.074 0.000 1.888 0.000 0.000 0.000
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F C F F F(-1) F(-2) F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 685 685 0 5373 0 0 0 0 -1
normalized size 1 1.00 0.00 7.84 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.291 52.487 6.522 0.000 0.672 0.000 0.000 0.000
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F(-1) F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 1124 1124 1819 3223 0 0 0 0 -1
normalized size 1 1.00 1.62 2.87 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.583 6.201 4.414 0.000 0.657 0.000 0.000 0.000
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F(-1) F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 1124 1124 1827 2357 0 0 0 0 -1
normalized size 1 1.00 1.63 2.10 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 3.022 6.138 6.712 0.000 1.112 0.000 0.000 0.000
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A C F F F(-1) F(-2) F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 1114 1114 1812 3214 0 0 0 0 -1
normalized size 1 1.00 1.63 2.89 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 3.791 6.062 7.829 0.000 0.651 0.000 0.000 0.000
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F A F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 403 403 366 0 0 1701 0 0 -1
normalized size 1 1.00 0.91 0.00 0.00 4.22 0.00 0.00 -0.00
time (sec) N/A 1.275 0.671 4.859 0.000 7.031 0.000 0.000 0.000
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 294 294 327 0 0 1383 0 0 -1
normalized size 1 1.00 1.11 0.00 0.00 4.70 0.00 0.00 -0.00
time (sec) N/A 0.398 0.773 4.493 0.000 4.130 0.000 0.000 0.000
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 195 195 266 0 0 1100 0 0 -1
normalized size 1 1.00 1.36 0.00 0.00 5.64 0.00 0.00 -0.01
time (sec) N/A 0.190 0.486 3.336 0.000 2.293 0.000 0.000 0.000
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.098 4.472 2.209 0.000 0.956 0.000 0.000 0.000
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.101 4.673 0.947 0.000 0.743 0.000 0.000 0.000
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.094 9.232 3.904 0.000 1.002 0.000 0.000 0.000
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.034 4.372 2.306 0.000 0.624 0.000 0.000 0.000
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.086 1.503 1.748 0.000 0.531 0.000 0.000 0.000
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 328 328 247 0 0 0 0 0 -1
normalized size 1 1.00 0.75 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.424 0.651 3.297 0.000 1.427 0.000 0.000 0.000
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 453 453 325 0 0 0 0 0 -1
normalized size 1 1.00 0.72 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.601 0.739 4.681 0.000 0.673 0.000 0.000 0.000
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F A F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 374 374 339 0 0 1701 0 0 -1
normalized size 1 1.00 0.91 0.00 0.00 4.55 0.00 0.00 -0.00
time (sec) N/A 0.508 0.627 4.330 0.000 12.021 0.000 0.000 0.000
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 262 262 305 0 0 1377 0 0 -1
normalized size 1 1.00 1.16 0.00 0.00 5.26 0.00 0.00 -0.00
time (sec) N/A 0.270 0.768 3.270 0.000 3.166 0.000 0.000 0.000
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.115 4.969 2.196 0.000 0.593 0.000 0.000 0.000
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.119 5.541 0.834 0.000 0.693 0.000 0.000 0.000
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.112 9.593 3.938 0.000 0.813 0.000 0.000 0.000
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.042 5.534 2.263 0.000 0.775 0.000 0.000 0.000
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.103 8.888 1.678 0.000 1.039 0.000 0.000 0.000
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.104 11.479 3.175 0.000 0.644 0.000 0.000 0.000
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 416 416 303 0 0 0 0 0 -1
normalized size 1 1.00 0.73 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.539 0.678 4.555 0.000 1.221 0.000 0.000 0.000
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 554 554 383 0 0 0 0 0 -1
normalized size 1 1.00 0.69 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.778 0.856 5.489 0.000 1.149 0.000 0.000 0.000
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 321 321 328 0 0 1385 0 0 -1
normalized size 1 1.00 1.02 0.00 0.00 4.31 0.00 0.00 -0.00
time (sec) N/A 1.012 0.752 5.363 0.000 5.855 0.000 0.000 0.000
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 225 225 272 0 0 1111 0 0 -1
normalized size 1 1.00 1.21 0.00 0.00 4.94 0.00 0.00 -0.00
time (sec) N/A 0.308 0.520 4.820 0.000 1.401 0.000 0.000 0.000
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 132 132 211 0 0 869 0 0 -1
normalized size 1 1.00 1.60 0.00 0.00 6.58 0.00 0.00 -0.01
time (sec) N/A 0.146 0.238 3.495 0.000 0.880 0.000 0.000 0.000
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.097 1.490 2.375 0.000 1.366 0.000 0.000 0.000
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.108 11.128 1.442 0.000 1.015 0.000 0.000 0.000
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.091 9.689 3.167 0.000 0.550 0.000 0.000 0.000
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 23 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.030 0.849 2.528 0.000 1.979 0.000 0.000 0.000
Problem 138 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 246 246 143 0 0 0 0 0 -1
normalized size 1 1.00 0.58 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.255 0.206 2.226 0.000 0.846 0.000 0.000 0.000
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 362 362 249 0 0 0 0 0 -1
normalized size 1 1.00 0.69 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.447 0.665 4.688 0.000 1.380 0.000 0.000 0.000
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 1006 1006 329 0 0 0 0 0 -1
normalized size 1 1.00 0.33 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.780 0.740 6.309 0.000 0.808 0.000 0.000 0.000
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 252 252 303 0 0 1483 0 0 -1
normalized size 1 1.00 1.20 0.00 0.00 5.88 0.00 0.00 -0.00
time (sec) N/A 1.006 0.637 5.162 0.000 1.033 0.000 0.000 0.000
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 157 157 221 0 0 1070 0 0 -1
normalized size 1 1.00 1.41 0.00 0.00 6.82 0.00 0.00 -0.01
time (sec) N/A 0.259 0.363 4.655 0.000 1.003 0.000 0.000 0.000
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 80 80 95 0 0 283 0 0 -1
normalized size 1 1.00 1.19 0.00 0.00 3.54 0.00 0.00 -0.01
time (sec) N/A 0.102 0.152 3.364 0.000 0.641 0.000 0.000 0.000
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.110 15.675 2.135 0.000 0.609 0.000 0.000 0.000
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.123 22.172 1.276 0.000 0.887 0.000 0.000 0.000
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.106 8.194 3.350 0.000 0.582 0.000 0.000 0.000
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.099 3.870 3.146 0.000 1.299 0.000 0.000 0.000
Problem 148 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 109 109 113 0 0 0 0 0 -1
normalized size 1 1.00 1.04 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.088 0.199 2.310 0.000 0.685 0.000 0.000 0.000
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 274 274 212 0 0 0 0 0 -1
normalized size 1 1.00 0.77 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.310 0.485 2.118 0.000 0.782 0.000 0.000 0.000
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 701 701 292 0 0 0 0 0 -1
normalized size 1 1.00 0.42 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.392 0.739 4.457 0.000 1.107 0.000 0.000 0.000
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 244 244 312 0 0 2123 0 0 -1
normalized size 1 1.00 1.28 0.00 0.00 8.70 0.00 0.00 -0.00
time (sec) N/A 1.063 0.539 5.329 0.000 1.257 0.000 0.000 0.000
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 163 163 172 0 0 664 0 0 -1
normalized size 1 1.00 1.06 0.00 0.00 4.07 0.00 0.00 -0.01
time (sec) N/A 0.243 0.273 4.628 0.000 0.977 0.000 0.000 0.000
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F B F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 138 138 158 0 0 571 0 0 -1
normalized size 1 1.00 1.14 0.00 0.00 4.14 0.00 0.00 -0.01
time (sec) N/A 0.131 0.210 3.471 0.000 1.537 0.000 0.000 0.000
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.120 26.800 2.136 0.000 0.567 0.000 0.000 0.000
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.138 33.123 1.258 0.000 0.503 0.000 0.000 0.000
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.116 10.322 3.691 0.000 1.490 0.000 0.000 0.000
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.106 9.674 3.365 0.000 1.650 0.000 0.000 0.000
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 276 276 186 0 0 0 0 0 -1
normalized size 1 1.00 0.67 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.276 0.292 3.151 0.000 0.906 0.000 0.000 0.000
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 296 296 248 0 0 0 0 0 -1
normalized size 1 1.00 0.84 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.235 0.554 2.311 0.000 2.144 0.000 0.000 0.000
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A C F F F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 631 631 323 0 0 0 0 0 -1
normalized size 1 1.00 0.51 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 1.396 0.783 2.075 0.000 0.807 0.000 0.000 0.000
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F F(-1) F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 589 570 0 0 0 0 0 0 -1
normalized size 1 0.97 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.415 0.222 9.227 0.000 1.768 0.000 0.000 0.000
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F F F F F
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 374 355 0 0 0 0 0 0 -1
normalized size 1 0.95 0.00 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 0.432 0.146 7.521 0.000 0.865 0.000 0.000 0.000
Problem 163 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A F F F(-1) F F F F
verified N/A NO N/A TBD TBD TBD TBD TBD TBD
size 178 204 0 0 0 0 0 0 -1
normalized size 1 1.15 0.00 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.187 0.110 6.105 0.000 1.527 0.000 0.000 0.000
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.071 2.040 3.145 0.000 0.561 0.000 0.000 0.000
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 26 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.071 5.387 5.103 0.000 0.555 0.000 0.000 0.000
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 28 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.105 0.898 2.835 0.000 0.546 0.000 0.000 0.000
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 28 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.094 0.113 2.798 0.000 1.015 0.000 0.000 0.000
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 28 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.096 1.147 3.767 0.000 0.881 0.000 0.000 0.000
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A F(-1) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 28 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.04
time (sec) N/A 0.105 1.417 3.786 0.000 1.647 0.000 0.000 0.000
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-1) F(-2) F(-1) F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 401 401 194 0 0 0 0 0 -1
normalized size 1 1.00 0.48 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.484 0.251 10.870 0.000 0.000 0.000 0.000 0.000
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-1) F(-2) F(-1) F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 268 268 159 0 0 0 0 0 -1
normalized size 1 1.00 0.59 0.00 0.00 0.00 0.00 0.00 -0.00
time (sec) N/A 2.018 0.325 7.001 0.000 0.000 0.000 0.000 0.000
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade A A A F F(-1) F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 126 135 118 0 0 0 0 0 -1
normalized size 1 1.07 0.94 0.00 0.00 0.00 0.00 0.00 -0.01
time (sec) N/A 0.208 0.220 4.447 0.000 0.000 0.000 0.000 0.000
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 29 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.088 0.360 4.082 0.000 1.767 0.000 0.000 0.000
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Mupad
grade N/A A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD TBD
size 29 0 0 0 0 0 0 0 -1
normalized size 1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.03
time (sec) N/A 0.099 6.548 4.770 0.000 1.772 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 [160] had the largest ratio of [.7826]

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 7 5 1.00 12 0.417
2 A 4 3 1.00 12 0.250
3 A 6 5 1.00 12 0.417
4 A 3 3 1.00 12 0.250
5 A 5 5 1.00 12 0.417
6 A 2 2 1.00 10 0.200
7 A 5 4 1.00 8 0.500
8 A 6 6 1.00 12 0.500
9 A 2 2 1.00 12 0.167
10 A 4 4 1.00 12 0.333
11 A 4 3 1.00 12 0.250
12 A 5 4 1.00 12 0.333
13 A 4 3 1.00 12 0.250
14 A 6 4 1.00 12 0.333
15 A 5 5 1.00 14 0.357
16 A 8 6 1.00 14 0.429
17 A 4 4 1.00 12 0.333
18 A 7 5 1.00 10 0.500
19 A 6 6 1.00 14 0.429
20 A 4 3 1.00 14 0.214
21 A 4 3 1.00 14 0.214
22 A 5 5 1.00 14 0.357
23 A 5 3 1.00 14 0.214
24 A 10 10 1.00 14 0.714
25 A 11 8 1.00 14 0.571
26 A 7 7 1.00 12 0.583
27 A 9 6 1.00 10 0.600
28 A 7 7 1.00 14 0.500
29 A 5 3 1.00 14 0.214
30 A 6 6 1.00 14 0.429
31 A 8 6 1.00 14 0.429
32 A 10 6 1.00 14 0.429
33 A 0 0 0.00 0 0.000
34 A 0 0 0.00 0 0.000
35 A 0 0 0.00 0 0.000
36 A 4 4 1.00 14 0.286
37 A 6 6 1.00 14 0.429
38 A 9 5 1.00 14 0.357
39 A 0 0 0.00 0 0.000
40 A 0 0 0.00 0 0.000
41 A 0 0 0.00 0 0.000
42 A 5 5 1.00 14 0.357
43 A 7 7 1.00 14 0.500
44 A 11 6 1.00 14 0.429
45 A 0 0 0.00 0 0.000
46 A 0 0 0.00 0 0.000
47 A 0 0 0.00 0 0.000
48 A 6 5 1.00 14 0.357
49 A 8 7 1.00 14 0.500
50 A 13 6 1.00 14 0.429
51 A 0 0 0.00 0 0.000
52 A 0 0 0.00 0 0.000
53 A 3 3 1.00 14 0.214
54 A 0 0 0.00 0 0.000
55 A 0 0 0.00 0 0.000
56 A 11 9 1.00 16 0.562
57 A 10 9 1.00 16 0.562
58 A 9 9 1.00 14 0.643
59 A 5 4 1.00 8 0.500
60 A 4 2 1.00 16 0.125
61 A 7 7 1.00 16 0.438
62 A 8 8 1.00 16 0.500
63 A 22 13 1.00 18 0.722
64 A 15 11 1.00 18 0.611
65 A 9 9 1.00 18 0.500
66 A 6 6 1.00 18 0.333
67 A 12 11 1.00 18 0.611
68 A 19 14 1.18 18 0.778
69 A 7 7 1.00 19 0.368
70 A 6 7 1.00 19 0.368
71 A 5 5 1.00 16 0.312
72 A 4 5 1.00 19 0.263
73 A 4 5 1.00 19 0.263
74 A 5 6 1.00 19 0.316
75 A 6 6 1.00 19 0.316
76 A 5 5 1.00 19 0.263
77 A 5 5 1.00 19 0.263
78 A 6 5 1.00 17 0.294
79 A 11 11 1.00 19 0.579
80 A 13 13 1.00 19 0.684
81 A 7 8 1.00 21 0.381
82 A 6 7 1.00 18 0.389
83 A 6 7 1.00 21 0.333
84 A 6 7 1.00 21 0.333
85 A 5 6 1.00 21 0.286
86 A 6 7 1.00 21 0.333
87 A 5 6 1.00 21 0.286
88 A 6 5 1.00 19 0.263
89 A 12 13 1.00 21 0.619
90 A 14 15 1.00 21 0.714
91 A 25 12 1.00 21 0.571
92 A 26 9 1.00 19 0.474
93 A 19 7 1.00 18 0.389
94 A 19 7 1.00 21 0.333
95 A 24 10 1.00 21 0.476
96 A 31 14 1.00 21 0.667
97 A 29 12 1.00 21 0.571
98 A 7 5 1.00 19 0.263
99 A 24 10 1.00 21 0.476
100 A 51 15 1.00 21 0.714
101 A 27 10 1.00 21 0.476
102 A 47 11 1.00 18 0.611
103 A 50 13 1.00 21 0.619
104 A 33 13 1.00 21 0.619
105 A 6 7 1.00 21 0.333
106 A 8 6 1.00 19 0.316
107 A 28 11 1.00 21 0.524
108 A 35 11 1.00 21 0.524
109 A 63 12 1.00 21 0.571
110 A 81 12 1.00 18 0.667
111 A 12 12 1.00 23 0.522
112 A 11 12 1.00 23 0.522
113 A 9 9 1.00 21 0.429
114 A 0 0 0.00 0 0.000
115 A 0 0 0.00 0 0.000
116 A 0 0 0.00 0 0.000
117 A 0 0 0.00 0 0.000
118 A 0 0 0.00 0 0.000
119 A 11 11 1.00 23 0.478
120 A 12 12 1.00 23 0.522
121 A 12 12 1.00 23 0.522
122 A 10 10 1.00 21 0.476
123 A 0 0 0.00 0 0.000
124 A 0 0 0.00 0 0.000
125 A 0 0 0.00 0 0.000
126 A 0 0 0.00 0 0.000
127 A 0 0 0.00 0 0.000
128 A 0 0 0.00 0 0.000
129 A 12 12 1.00 23 0.522
130 A 13 12 1.00 23 0.522
131 A 11 12 1.00 23 0.522
132 A 10 12 1.00 23 0.522
133 A 8 8 1.00 21 0.381
134 A 0 0 0.00 0 0.000
135 A 0 0 0.00 0 0.000
136 A 0 0 0.00 0 0.000
137 A 0 0 0.00 0 0.000
138 A 11 11 1.00 23 0.478
139 A 11 12 1.00 23 0.522
140 A 32 15 1.00 23 0.652
141 A 10 11 1.00 23 0.478
142 A 9 11 1.00 23 0.478
143 A 4 4 1.00 21 0.190
144 A 0 0 0.00 0 0.000
145 A 0 0 0.00 0 0.000
146 A 0 0 0.00 0 0.000
147 A 0 0 0.00 0 0.000
148 A 5 5 1.00 20 0.250
149 A 10 11 1.00 23 0.478
150 A 25 14 1.00 23 0.609
151 A 10 11 1.00 23 0.478
152 A 7 8 1.00 23 0.348
153 A 5 5 1.00 21 0.238
154 A 0 0 0.00 0 0.000
155 A 0 0 0.00 0 0.000
156 A 0 0 0.00 0 0.000
157 A 0 0 0.00 0 0.000
158 A 10 10 1.00 23 0.435
159 A 10 11 1.00 20 0.550
160 A 26 18 1.00 23 0.783
161 A 6 7 0.97 23 0.304
162 A 6 7 0.95 23 0.304
163 A 5 6 1.15 21 0.286
164 A 0 0 0.00 0 0.000
165 A 0 0 0.00 0 0.000
166 A 0 0 0.00 0 0.000
167 A 0 0 0.00 0 0.000
168 A 0 0 0.00 0 0.000
169 A 0 0 0.00 0 0.000
170 A 16 11 1.00 26 0.423
171 A 13 11 1.00 26 0.423
172 A 8 9 1.07 26 0.346
173 A 0 0 0.00 0 0.000
174 A 0 0 0.00 0 0.000

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