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Chapter 2
detailed summary tables of results

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

2.1 List of integrals sorted by grade for each CAS

2.1.1 Rubi

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

B grade: { }

C grade: { }

F grade: { }

2.1.2 Mathematica

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 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, 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 }

B grade: { }

C grade: { 11, 40 }

F grade: { }

2.1.3 Maple

A grade: { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 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, 77, 78, 79, 83, 84, 85, 89, 90, 91, 95, 96, 97, 98, 102, 103, 104, 108, 109, 110, 114, 115, 116, 117, 118, 121, 122, 123, 124, 125, 126, 127, 128, 134, 135 }

B grade: { }

C grade: { 132, 133 }

F grade: { 74, 75, 76, 80, 81, 82, 86, 87, 88, 92, 93, 94, 99, 100, 101, 105, 106, 107, 111, 112, 113, 119, 120, 129, 130, 131, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156 }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 16, 19, 21, 22, 24, 26, 33, 35, 37, 49, 50, 58, 59, 65, 66, 72, 73, 79, 85, 91, 97, 98, 104, 110, 116, 121, 122, 123, 124, 125, 126, 127, 128, 134, 135

B grade: { 15 }

C grade: { }

F grade: { 6, 17, 18, 20, 23, 25, 27, 28, 29, 30, 31, 32, 34, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 63, 64, 67, 68, 69, 70, 71, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 99, 100, 101, 102, 103, 105, 106, 107, 108, 109, 111, 112, 113, 114, 115, 117, 118, 119, 120, 129, 130, 131, 132, 133, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 4, 5, 8, 10, 12, 13, 14, 15, 16, 19, 21, 22, 23, 24, 25, 26, 32, 33, 34, 35, 36, 37, 49, 50, 58, 59, 65, 66, 72, 73, 117, 118, 121, 122, 128, 134, 135 }

B grade: { 7, 9, 11 }

C grade: { }

F grade: { 6, 17, 18, 20, 27, 28, 29, 30, 31, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 63, 64, 67, 68, 69, 70, 71, 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, 119, 120, 123, 124, 125, 126, 127, 129, 130, 131, 132, 133, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156 }

2.1.6 Sympy

A grade: { 1, 2, 3, 4, 5, 12, 13, 14, 15, 16, 22, 23, 24, 25, 26, 32, 33, 34, 35, 36, 37, 49, 50, 58, 59, 65, 66, 72, 73, 79, 85, 97, 98, 104, 110, 117, 118, 121, 122, 125, 126, 127, 128, 134, 135 }

B grade: { }

C grade: { }

F grade: { 6, 7, 8, 9, 10, 11, 17, 18, 19, 20, 21, 27, 28, 29, 30, 31, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 63, 64, 67, 68, 69, 70, 71, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 99, 100, 101, 102, 103, 105, 106, 107, 108, 109, 111, 112, 113, 114, 115, 116, 119, 120, 123, 124, 129, 130, 131, 132, 133, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156 }

2.1.7 Giac

A grade: { 1, 2, 3, 4, 5, 8, 9, 10, 11, 12, 14, 16, 22, 24, 26, 33, 35, 37, 49, 50, 58, 59, 65, 66, 72, 73, 79, 85, 91, 97, 98, 104, 110, 116, 117, 118, 121, 122, 126, 127, 134, 135 }

B grade: { 7, 19, 21 }

C grade: { }

F grade: { 6, 13, 15, 17, 18, 20, 23, 25, 27, 28, 29, 30, 31, 32, 34, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 60, 61, 62, 63, 64, 67, 68, 69, 70, 71, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 99, 100, 101, 102, 103, 105, 106, 107, 108, 109, 111, 112, 113, 114, 115, 119, 120, 123, 124, 125, 128, 129, 130, 131, 132, 133, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156 }

2.2 Detailed conclusion table per each integral for all CAS systems

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

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

Problem 1 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 72 72 50 69 92 135 70 90
normalized size 1 1. 0.69 0.96 1.28 1.88 0.97 1.25
time (sec) N/A 0.044 0.035 0.031 1.137 1.838 2.166 1.302
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 67 67 49 58 96 131 61 108
normalized size 1 1. 0.73 0.87 1.43 1.96 0.91 1.61
time (sec) N/A 0.026 0.017 0.005 1.179 1.863 1.16 1.377
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 52 52 41 50 65 113 48 70
normalized size 1 1. 0.79 0.96 1.25 2.17 0.92 1.35
time (sec) N/A 0.035 0.024 0.005 1.164 1.78 0.551 1.317
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 44 44 40 39 69 109 37 92
normalized size 1 1. 0.91 0.89 1.57 2.48 0.84 2.09
time (sec) N/A 0.016 0.01 0.003 1.193 1.768 0.237 1.287
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 25 25 25 26 34 78 20 47
normalized size 1 1. 1. 1.04 1.36 3.12 0.8 1.88
time (sec) N/A 0.008 0.007 0.002 1.108 1.753 0.153 1.352
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 43 43 43 94 0 0 0 0
normalized size 1 1. 1. 2.19 0. 0. 0. 0.
time (sec) N/A 0.06 0.003 0.148 0. 0. 0. 0.
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 27 30 32 212 0 76
normalized size 1 1. 1. 1.11 1.19 7.85 0. 2.81
time (sec) N/A 0.021 0.002 0.005 1.123 1.946 0. 1.39
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 33 33 28 37 36 88 0 68
normalized size 1 1. 0.85 1.12 1.09 2.67 0. 2.06
time (sec) N/A 0.014 0.006 0.004 1.184 1.948 0. 1.427
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 54 54 54 51 61 273 0 104
normalized size 1 1. 1. 0.94 1.13 5.06 0. 1.93
time (sec) N/A 0.032 0.01 0.006 1.119 2.03 0. 1.378
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 56 56 40 56 66 109 0 104
normalized size 1 1. 0.71 1. 1.18 1.95 0. 1.86
time (sec) N/A 0.02 0.012 0.003 1.175 1.83 0. 1.353
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A A B F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 77 77 49 70 88 302 0 128
normalized size 1 1. 0.64 0.91 1.14 3.92 0. 1.66
time (sec) N/A 0.045 0.011 0.006 1.164 1.958 0. 1.428
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 117 117 75 153 134 234 114 153
normalized size 1 1. 0.64 1.31 1.15 2. 0.97 1.31
time (sec) N/A 0.188 0.064 0.131 1.159 1.786 4.139 1.402
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 96 96 72 118 173 205 90 0
normalized size 1 1. 0.75 1.23 1.8 2.14 0.94 0.
time (sec) N/A 0.165 0.044 0.035 1.269 1.82 2.28 0.
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 80 80 59 92 95 188 76 120
normalized size 1 1. 0.74 1.15 1.19 2.35 0.95 1.5
time (sec) N/A 0.123 0.058 0.027 1.235 1.804 1.127 1.435
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A B A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 59 59 53 59 135 166 51 0
normalized size 1 1. 0.9 1. 2.29 2.81 0.86 0.
time (sec) N/A 0.092 0.028 0.026 1.127 2.006 0.541 0.
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 34 34 34 36 43 134 32 84
normalized size 1 1. 1. 1.06 1.26 3.94 0.94 2.47
time (sec) N/A 0.045 0.014 0.023 1.182 2.101 0.218 1.455
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 60 151 0 0 0 0
normalized size 1 1. 1. 2.52 0. 0. 0. 0.
time (sec) N/A 0.097 0.006 0.036 0. 0. 0. 0.
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 50 50 75 107 0 0 0 0
normalized size 1 1. 1.5 2.14 0. 0. 0. 0.
time (sec) N/A 0.1 0.192 0.049 0. 0. 0. 0.
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 43 43 43 67 53 157 0 149
normalized size 1 1. 1. 1.56 1.23 3.65 0. 3.47
time (sec) N/A 0.08 0.031 0.076 1.192 2.174 0. 1.482
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 99 99 125 144 0 0 0 0
normalized size 1 1. 1.26 1.45 0. 0. 0. 0.
time (sec) N/A 0.163 0.49 0.092 0. 0. 0. 0.
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 85 85 64 99 96 194 0 200
normalized size 1 1. 0.75 1.16 1.13 2.28 0. 2.35
time (sec) N/A 0.138 0.059 0.106 1.225 2.162 0. 1.594
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 195 195 120 222 223 359 196 243
normalized size 1 1. 0.62 1.14 1.14 1.84 1.01 1.25
time (sec) N/A 0.366 0.069 0.04 1.084 2.163 7.481 1.599
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 163 163 110 168 0 327 160 0
normalized size 1 1. 0.67 1.03 0. 2.01 0.98 0.
time (sec) N/A 0.298 0.069 0.034 0. 2.142 4.269 0.
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 132 132 93 136 157 281 128 190
normalized size 1 1. 0.7 1.03 1.19 2.13 0.97 1.44
time (sec) N/A 0.221 0.054 0.028 1.141 2.116 2.24 1.566
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 97 97 80 88 0 261 92 0
normalized size 1 1. 0.82 0.91 0. 2.69 0.95 0.
time (sec) N/A 0.153 0.044 0.025 0. 2.081 1.119 0.
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 58 58 58 55 77 205 54 132
normalized size 1 1. 1. 0.95 1.33 3.53 0.93 2.28
time (sec) N/A 0.081 0.016 0.027 1.308 2.02 0.518 1.43
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 83 83 83 204 0 0 0 0
normalized size 1 1. 1. 2.46 0. 0. 0. 0.
time (sec) N/A 0.112 0.007 0.036 0. 0. 0. 0.
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 84 84 117 162 0 0 0 0
normalized size 1 1. 1.39 1.93 0. 0. 0. 0.
time (sec) N/A 0.159 0.116 0.049 0. 0. 0. 0.
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 93 93 80 149 0 0 0 0
normalized size 1 1. 0.86 1.6 0. 0. 0. 0.
time (sec) N/A 0.168 0.317 0.068 0. 0. 0. 0.
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 151 151 268 228 0 0 0 0
normalized size 1 1. 1.77 1.51 0. 0. 0. 0.
time (sec) N/A 0.277 2.219 0.092 0. 0. 0. 0.
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 159 159 107 210 0 0 0 0
normalized size 1 1. 0.67 1.32 0. 0. 0. 0.
time (sec) N/A 0.286 0.607 0.106 0. 0. 0. 0.
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 276 276 165 319 0 497 269 0
normalized size 1 1. 0.6 1.16 0. 1.8 0.97 0.
time (sec) N/A 0.856 0.09 0.16 0. 2.14 21.536 0.
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 244 244 148 272 271 466 241 293
normalized size 1 1. 0.61 1.11 1.11 1.91 0.99 1.2
time (sec) N/A 0.657 0.081 0.04 1.236 2.144 12.465 1.817
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 194 194 133 208 0 402 190 0
normalized size 1 1. 0.69 1.07 0. 2.07 0.98 0.
time (sec) N/A 0.504 0.07 0.036 0. 2.108 7.516 0.
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 162 162 112 165 193 358 158 230
normalized size 1 1. 0.69 1.02 1.19 2.21 0.98 1.42
time (sec) N/A 0.363 0.07 0.03 1.235 2.143 4.244 1.809
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 110 110 94 105 0 316 104 0
normalized size 1 1. 0.85 0.95 0. 2.87 0.95 0.
time (sec) N/A 0.239 0.045 0.026 0. 2.051 2.141 0.
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 67 67 67 65 99 262 65 169
normalized size 1 1. 1. 0.97 1.48 3.91 0.97 2.52
time (sec) N/A 0.125 0.019 0.026 1.138 2.055 1.033 1.589
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 97 97 97 257 0 0 0 0
normalized size 1 1. 1. 2.65 0. 0. 0. 0.
time (sec) N/A 0.122 0.008 0.036 0. 0. 0. 0.
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 120 120 161 217 0 0 0 0
normalized size 1 1. 1.34 1.81 0. 0. 0. 0.
time (sec) N/A 0.188 0.226 0.05 0. 0. 0. 0.
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 108 108 113 208 0 0 0 0
normalized size 1 1. 1.05 1.93 0. 0. 0. 0.
time (sec) N/A 0.207 0.259 0.068 0. 0. 0. 0.
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 223 223 355 372 0 0 0 0
normalized size 1 1. 1.59 1.67 0. 0. 0. 0.
time (sec) N/A 0.393 2.538 0.091 0. 0. 0. 0.
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 55 55 40 40 0 0 0 0
normalized size 1 1. 0.73 0.73 0. 0. 0. 0.
time (sec) N/A 0.1 0.012 0.041 0. 0. 0. 0.
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 43 43 33 33 0 0 0 0
normalized size 1 1. 0.77 0.77 0. 0. 0. 0.
time (sec) N/A 0.083 0.11 0.033 0. 0. 0. 0.
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 41 41 31 31 0 0 0 0
normalized size 1 1. 0.76 0.76 0. 0. 0. 0.
time (sec) N/A 0.084 0.01 0.025 0. 0. 0. 0.
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 24 24 0 0 0 0
normalized size 1 1. 0.83 0.83 0. 0. 0. 0.
time (sec) N/A 0.068 0.072 0.024 0. 0. 0. 0.
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 27 27 22 22 0 0 0 0
normalized size 1 1. 0.81 0.81 0. 0. 0. 0.
time (sec) N/A 0.067 0.006 0.02 0. 0. 0. 0.
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 14 14 14 13 0 0 0 0
normalized size 1 1. 1. 0.93 0. 0. 0. 0.
time (sec) N/A 0.038 0.02 0.03 0. 0. 0. 0.
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 9 9 9 10 0 0 0 0
normalized size 1 1. 1. 1.11 0. 0. 0. 0.
time (sec) N/A 0.018 0.009 0.019 0. 0. 0. 0.
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.014 0.172 0.075 0. 0. 0. 0.
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.015 0.803 0.086 0. 0. 0. 0.
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 82 82 85 104 0 0 0 0
normalized size 1 1. 1.04 1.27 0. 0. 0. 0.
time (sec) N/A 0.081 0.28 0.043 0. 0. 0. 0.
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 70 70 78 78 0 0 0 0
normalized size 1 1. 1.11 1.11 0. 0. 0. 0.
time (sec) N/A 0.066 0.041 0.038 0. 0. 0. 0.
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 68 68 60 80 0 0 0 0
normalized size 1 1. 0.88 1.18 0. 0. 0. 0.
time (sec) N/A 0.066 0.202 0.028 0. 0. 0. 0.
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 56 56 56 54 0 0 0 0
normalized size 1 1. 1. 0.96 0. 0. 0. 0.
time (sec) N/A 0.049 0.026 0.025 0. 0. 0. 0.
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 54 54 49 56 0 0 0 0
normalized size 1 1. 0.91 1.04 0. 0. 0. 0.
time (sec) N/A 0.047 0.166 0.024 0. 0. 0. 0.
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 37 37 32 28 0 0 0 0
normalized size 1 1. 0.86 0.76 0. 0. 0. 0.
time (sec) N/A 0.025 0.003 0.026 0. 0. 0. 0.
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 34 34 31 30 0 0 0 0
normalized size 1 1. 0.91 0.88 0. 0. 0. 0.
time (sec) N/A 0.083 0.048 0.023 0. 0. 0. 0.
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 0.729 0.06 0. 0. 0. 0.
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.014 4.768 0.082 0. 0. 0. 0.
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 97 97 102 120 0 0 0 0
normalized size 1 1. 1.05 1.24 0. 0. 0. 0.
time (sec) N/A 0.354 0.14 0.039 0. 0. 0. 0.
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 82 82 69 82 0 0 0 0
normalized size 1 1. 0.84 1. 0. 0. 0. 0.
time (sec) N/A 0.304 0.203 0.03 0. 0. 0. 0.
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 81 81 64 81 0 0 0 0
normalized size 1 1. 0.79 1. 0. 0. 0. 0.
time (sec) N/A 0.253 0.137 0.029 0. 0. 0. 0.
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 63 63 62 43 0 0 0 0
normalized size 1 1. 0.98 0.68 0. 0. 0. 0.
time (sec) N/A 0.171 0.049 0.03 0. 0. 0. 0.
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 50 50 47 42 0 0 0 0
normalized size 1 1. 0.94 0.84 0. 0. 0. 0.
time (sec) N/A 0.083 0.018 0.022 0. 0. 0. 0.
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 0.54 0.06 0. 0. 0. 0.
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.014 4.992 0.084 0. 0. 0. 0.
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 155 155 156 169 0 0 0 0
normalized size 1 1. 1.01 1.09 0. 0. 0. 0.
time (sec) N/A 0.32 0.328 0.046 0. 0. 0. 0.
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 141 141 105 114 0 0 0 0
normalized size 1 1. 0.74 0.81 0. 0. 0. 0.
time (sec) N/A 0.283 0.373 0.031 0. 0. 0. 0.
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 138 138 99 115 0 0 0 0
normalized size 1 1. 0.72 0.83 0. 0. 0. 0.
time (sec) N/A 0.306 0.29 0.031 0. 0. 0. 0.
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 95 95 84 60 0 0 0 0
normalized size 1 1. 0.88 0.63 0. 0. 0. 0.
time (sec) N/A 0.163 0.116 0.025 0. 0. 0. 0.
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 76 76 69 61 0 0 0 0
normalized size 1 1. 0.91 0.8 0. 0. 0. 0.
time (sec) N/A 0.15 0.058 0.023 0. 0. 0. 0.
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 1.801 0.06 0. 0. 0. 0.
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.014 8.822 0.083 0. 0. 0. 0.
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 182 182 161 0 0 0 0 0
normalized size 1 1. 0.88 0. 0. 0. 0. 0.
time (sec) N/A 0.324 0.045 0.241 0. 0. 0. 0.
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 139 139 101 0 0 0 0 0
normalized size 1 1. 0.73 0. 0. 0. 0. 0.
time (sec) N/A 0.262 0.036 0.112 0. 0. 0. 0.
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 120 120 101 0 0 0 0 0
normalized size 1 1. 0.84 0. 0. 0. 0. 0.
time (sec) N/A 0.244 0.034 0.097 0. 0. 0. 0.
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 93 93 52 75 0 0 0 0
normalized size 1 1. 0.56 0.81 0. 0. 0. 0.
time (sec) N/A 0.191 0.033 0.105 0. 0. 0. 0.
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 53 53 45 42 0 0 0 0
normalized size 1 1. 0.85 0.79 0. 0. 0. 0.
time (sec) N/A 0.107 0.047 0.068 0. 0. 0. 0.
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.014 0.333 0.062 0. 0. 0. 0.
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 330 330 152 0 0 0 0 0
normalized size 1 1. 0.46 0. 0. 0. 0. 0.
time (sec) N/A 0.713 0.117 0.206 0. 0. 0. 0.
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 199 199 102 0 0 0 0 0
normalized size 1 1. 0.51 0. 0. 0. 0. 0.
time (sec) N/A 0.487 0.035 0.099 0. 0. 0. 0.
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 179 179 102 0 0 0 0 0
normalized size 1 1. 0.57 0. 0. 0. 0. 0.
time (sec) N/A 0.371 0.034 0.099 0. 0. 0. 0.
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 122 122 52 102 0 0 0 0
normalized size 1 1. 0.43 0.84 0. 0. 0. 0.
time (sec) N/A 0.219 0.021 0.091 0. 0. 0. 0.
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 81 81 47 65 0 0 0 0
normalized size 1 1. 0.58 0.8 0. 0. 0. 0.
time (sec) N/A 0.119 0.028 0.074 0. 0. 0. 0.
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.015 0.315 0.058 0. 0. 0. 0.
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 379 379 152 0 0 0 0 0
normalized size 1 1. 0.4 0. 0. 0. 0. 0.
time (sec) N/A 0.996 0.109 0.204 0. 0. 0. 0.
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 247 247 101 0 0 0 0 0
normalized size 1 1. 0.41 0. 0. 0. 0. 0.
time (sec) N/A 0.711 0.037 0.099 0. 0. 0. 0.
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 210 210 101 0 0 0 0 0
normalized size 1 1. 0.48 0. 0. 0. 0. 0.
time (sec) N/A 0.551 0.036 0.1 0. 0. 0. 0.
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 152 152 52 136 0 0 0 0
normalized size 1 1. 0.34 0.89 0. 0. 0. 0.
time (sec) N/A 0.337 0.032 0.095 0. 0. 0. 0.
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 94 94 45 78 0 0 0 0
normalized size 1 1. 0.48 0.83 0. 0. 0. 0.
time (sec) N/A 0.184 0.048 0.072 0. 0. 0. 0.
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 0.314 0.057 0. 0. 0. 0.
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 163 163 151 0 0 0 0 0
normalized size 1 1. 0.93 0. 0. 0. 0. 0.
time (sec) N/A 0.204 0.102 0.214 0. 0. 0. 0.
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 109 109 99 0 0 0 0 0
normalized size 1 1. 0.91 0. 0. 0. 0. 0.
time (sec) N/A 0.148 0.076 0.106 0. 0. 0. 0.
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 105 105 99 0 0 0 0 0
normalized size 1 1. 0.94 0. 0. 0. 0. 0.
time (sec) N/A 0.143 0.072 0.118 0. 0. 0. 0.
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 63 63 52 37 0 0 0 0
normalized size 1 1. 0.83 0.59 0. 0. 0. 0.
time (sec) N/A 0.077 0.026 0.051 0. 0. 0. 0.
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 43 43 47 24 0 0 0 0
normalized size 1 1. 1.09 0.56 0. 0. 0. 0.
time (sec) N/A 0.047 0.027 0.036 0. 0. 0. 0.
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 0.295 0.057 0. 0. 0. 0.
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.015 1.57 0.087 0. 0. 0. 0.
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 188 188 216 0 0 0 0 0
normalized size 1 1. 1.15 0. 0. 0. 0. 0.
time (sec) N/A 0.185 0.286 0.181 0. 0. 0. 0.
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 138 138 126 0 0 0 0 0
normalized size 1 1. 0.91 0. 0. 0. 0. 0.
time (sec) N/A 0.133 0.04 0.086 0. 0. 0. 0.
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 130 130 140 0 0 0 0 0
normalized size 1 1. 1.08 0. 0. 0. 0. 0.
time (sec) N/A 0.122 0.131 0.105 0. 0. 0. 0.
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 84 84 78 80 0 0 0 0
normalized size 1 1. 0.93 0.95 0. 0. 0. 0.
time (sec) N/A 0.066 0.026 0.086 0. 0. 0. 0.
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 64 64 69 65 0 0 0 0
normalized size 1 1. 1.08 1.02 0. 0. 0. 0.
time (sec) N/A 0.11 0.068 0.073 0. 0. 0. 0.
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 0.383 0.061 0. 0. 0. 0.
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 223 223 343 0 0 0 0 0
normalized size 1 1. 1.54 0. 0. 0. 0. 0.
time (sec) N/A 0.584 0.333 0.184 0. 0. 0. 0.
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 167 167 174 0 0 0 0 0
normalized size 1 1. 1.04 0. 0. 0. 0. 0.
time (sec) N/A 0.441 0.409 0.086 0. 0. 0. 0.
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 161 161 225 0 0 0 0 0
normalized size 1 1. 1.4 0. 0. 0. 0. 0.
time (sec) N/A 0.372 0.138 0.103 0. 0. 0. 0.
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 118 118 98 119 0 0 0 0
normalized size 1 1. 0.83 1.01 0. 0. 0. 0.
time (sec) N/A 0.223 0.164 0.086 0. 0. 0. 0.
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 84 84 105 81 0 0 0 0
normalized size 1 1. 1.25 0.96 0. 0. 0. 0.
time (sec) N/A 0.117 0.098 0.076 0. 0. 0. 0.
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.014 0.389 0.058 0. 0. 0. 0.
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 285 285 334 0 0 0 0 0
normalized size 1 1. 1.17 0. 0. 0. 0. 0.
time (sec) N/A 0.544 0.673 0.18 0. 0. 0. 0.
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 229 229 210 0 0 0 0 0
normalized size 1 1. 0.92 0. 0. 0. 0. 0.
time (sec) N/A 0.428 0.661 0.098 0. 0. 0. 0.
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 222 222 221 0 0 0 0 0
normalized size 1 1. 1. 0. 0. 0. 0. 0.
time (sec) N/A 0.434 0.353 0.098 0. 0. 0. 0.
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 147 147 118 147 0 0 0 0
normalized size 1 1. 0.8 1. 0. 0. 0. 0.
time (sec) N/A 0.212 0.295 0.092 0. 0. 0. 0.
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 112 112 111 105 0 0 0 0
normalized size 1 1. 0.99 0.94 0. 0. 0. 0.
time (sec) N/A 0.189 0.181 0.082 0. 0. 0. 0.
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.014 0.392 0.06 0. 0. 0. 0.
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 53 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.11 0.825 0.713 0. 0. 0. 0.
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A F(-2) A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 53 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.106 0.743 0.547 0. 0. 0. 0.
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 137 137 123 0 0 0 0 0
normalized size 1 1. 0.9 0. 0. 0. 0. 0.
time (sec) N/A 0.1 0.038 0.55 0. 0. 0. 0.
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F(-2) F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 60 55 0 0 0 0 0
normalized size 1 1. 0.92 0. 0. 0. 0. 0.
time (sec) N/A 0.02 0.022 0.546 0. 0. 0. 0.
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.015 0.397 0.429 0. 0. 0. 0.
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.014 0.411 0.435 0. 0. 0. 0.
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) F(-1) F(-1)
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.015 1.058 0.066 0. 0. 0. 0.
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) F(-1) F(-1)
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.014 1.06 0.058 0. 0. 0. 0.
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) A F(-1)
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.013 1.328 0.058 0. 0. 0. 0.
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.014 1.198 0.062 0. 0. 0. 0.
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A F(-2) A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.015 1.133 0.056 0. 0. 0. 0.
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A F(-1)
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 14 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.018 0.737 0.064 0. 0. 0. 0.
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 173 173 145 0 0 0 0 0
normalized size 1 1. 0.84 0. 0. 0. 0. 0.
time (sec) N/A 0.216 0.146 0.164 0. 0. 0. 0.
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 119 119 99 0 0 0 0 0
normalized size 1 1. 0.83 0. 0. 0. 0. 0.
time (sec) N/A 0.174 0.065 0.079 0. 0. 0. 0.
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 113 113 97 0 0 0 0 0
normalized size 1 1. 0.86 0. 0. 0. 0. 0.
time (sec) N/A 0.145 0.07 0.092 0. 0. 0. 0.
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 59 59 59 38 0 0 0 0
normalized size 1 1. 1. 0.64 0. 0. 0. 0.
time (sec) N/A 0.084 0.015 0.061 0. 0. 0. 0.
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 49 49 45 40 0 0 0 0
normalized size 1 1. 0.92 0.82 0. 0. 0. 0.
time (sec) N/A 0.047 0.025 0.053 0. 0. 0. 0.
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.015 0.276 0.046 0. 0. 0. 0.
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A A A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 12 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.016 0.895 0.053 0. 0. 0. 0.
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 213 213 215 0 0 0 0 0
normalized size 1 1. 1.01 0. 0. 0. 0. 0.
time (sec) N/A 0.605 0.402 0.134 0. 0. 0. 0.
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 145 145 127 0 0 0 0 0
normalized size 1 1. 0.88 0. 0. 0. 0. 0.
time (sec) N/A 0.432 0.095 0.059 0. 0. 0. 0.
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 102 102 101 0 0 0 0 0
normalized size 1 1. 0.99 0. 0. 0. 0. 0.
time (sec) N/A 0.25 0.225 0.039 0. 0. 0. 0.
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 282 282 215 0 0 0 0 0
normalized size 1 1. 0.76 0. 0. 0. 0. 0.
time (sec) N/A 0.862 0.287 0.113 0. 0. 0. 0.
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 179 179 129 0 0 0 0 0
normalized size 1 1. 0.72 0. 0. 0. 0. 0.
time (sec) N/A 0.478 0.1 0.052 0. 0. 0. 0.
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 135 135 251 0 0 0 0 0
normalized size 1 1. 1.86 0. 0. 0. 0. 0.
time (sec) N/A 0.255 1.034 0.037 0. 0. 0. 0.
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 327 327 215 0 0 0 0 0
normalized size 1 1. 0.66 0. 0. 0. 0. 0.
time (sec) N/A 1.25 0.432 180. 0. 0. 0. 0.
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 223 223 115 0 0 0 0 0
normalized size 1 1. 0.52 0. 0. 0. 0. 0.
time (sec) N/A 0.751 0.072 0.057 0. 0. 0. 0.
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 155 155 282 0 0 0 0 0
normalized size 1 1. 1.82 0. 0. 0. 0. 0.
time (sec) N/A 0.406 3.108 0.048 0. 0. 0. 0.
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 194 194 196 0 0 0 0 0
normalized size 1 1. 1.01 0. 0. 0. 0. 0.
time (sec) N/A 0.35 0.217 0.115 0. 0. 0. 0.
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 107 107 108 0 0 0 0 0
normalized size 1 1. 1.01 0. 0. 0. 0. 0.
time (sec) N/A 0.179 0.065 0.059 0. 0. 0. 0.
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 88 88 101 0 0 0 0 0
normalized size 1 1. 1.15 0. 0. 0. 0. 0.
time (sec) N/A 0.104 0.096 0.04 0. 0. 0. 0.
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 226 226 290 0 0 0 0 0
normalized size 1 1. 1.28 0. 0. 0. 0. 0.
time (sec) N/A 0.324 0.379 0.109 0. 0. 0. 0.
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 135 135 134 0 0 0 0 0
normalized size 1 1. 0.99 0. 0. 0. 0. 0.
time (sec) N/A 0.162 0.109 0.056 0. 0. 0. 0.
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 116 116 137 0 0 0 0 0
normalized size 1 1. 1.18 0. 0. 0. 0. 0.
time (sec) N/A 0.256 0.226 0.037 0. 0. 0. 0.
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 271 271 340 0 0 0 0 0
normalized size 1 1. 1.25 0. 0. 0. 0. 0.
time (sec) N/A 0.899 1.509 0.111 0. 0. 0. 0.
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 183 183 200 0 0 0 0 0
normalized size 1 1. 1.09 0. 0. 0. 0. 0.
time (sec) N/A 0.517 0.71 0.051 0. 0. 0. 0.
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 143 143 181 0 0 0 0 0
normalized size 1 1. 1.27 0. 0. 0. 0. 0.
time (sec) N/A 0.273 0.577 0.04 0. 0. 0. 0.
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 346 346 417 0 0 0 0 0
normalized size 1 1. 1.21 0. 0. 0. 0. 0.
time (sec) N/A 1.033 1.56 0.109 0. 0. 0. 0.
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 219 219 208 0 0 0 0 0
normalized size 1 1. 0.95 0. 0. 0. 0. 0.
time (sec) N/A 0.506 1.138 0.053 0. 0. 0. 0.
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F(-2) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 178 178 210 0 0 0 0 0
normalized size 1 1. 1.18 0. 0. 0. 0. 0.
time (sec) N/A 0.447 0.583 0.039 0. 0. 0. 0.

2.3 Detailed conclusion table specific for Rubi results

The following table is specific to Rubi. It gives additional statistics for each integral. the column steps is the number of steps used by Rubi to obtain the antiderivative. The rules column is the number of unique rules used. The integrand size column is the leaf size of the integrand. Finally the ratio \(\frac{\text{number of rules}}{\text{integrand size}}\) is given. The larger this ratio is, the harder the integral was to solve. In this test, problem number [30] had the largest ratio of [ 1. ]

Table 2.1Rubi specific breakdown of results for each integral
# grade
number of
steps
used
number of
unique
rules
normalized
antiderivative
leaf size
integrand
leaf size
\(\frac{\text{number of rules}}{\text{integrand leaf size}}\)
1 A 4 3 1. 8 0.375
2 A 4 3 1. 8 0.375
3 A 4 3 1. 8 0.375
4 A 3 3 1. 6 0.5
5 A 2 2 1. 4 0.5
6 A 5 5 1. 8 0.625
7 A 4 4 1. 8 0.5
8 A 2 2 1. 8 0.25
9 A 5 5 1. 8 0.625
10 A 3 3 1. 8 0.375
11 A 6 5 1. 8 0.625
12 A 7 5 1. 10 0.5
13 A 6 4 1. 10 0.4
14 A 5 5 1. 10 0.5
15 A 4 4 1. 8 0.5
16 A 3 3 1. 6 0.5
17 A 6 6 1. 10 0.6
18 A 7 5 1. 10 0.5
19 A 3 3 1. 10 0.3
20 A 9 7 1. 10 0.7
21 A 5 5 1. 10 0.5
22 A 14 7 1. 10 0.7
23 A 11 5 1. 10 0.5
24 A 9 7 1. 10 0.7
25 A 6 5 1. 8 0.625
26 A 4 3 1. 6 0.5
27 A 7 7 1. 10 0.7
28 A 9 6 1. 10 0.6
29 A 7 7 1. 10 0.7
30 A 14 10 1. 10 1.
31 A 10 9 1. 10 0.9
32 A 23 4 1. 10 0.4
33 A 19 6 1. 10 0.6
34 A 14 4 1. 10 0.4
35 A 11 6 1. 10 0.6
36 A 7 4 1. 8 0.5
37 A 5 3 1. 6 0.5
38 A 8 7 1. 10 0.7
39 A 11 7 1. 10 0.7
40 A 8 8 1. 10 0.8
41 A 19 10 1. 10 1.
42 A 7 3 1. 10 0.3
43 A 6 3 1. 10 0.3
44 A 6 3 1. 10 0.3
45 A 5 3 1. 10 0.3
46 A 5 3 1. 10 0.3
47 A 4 4 1. 8 0.5
48 A 2 2 1. 6 0.333
49 A 0 0 0. 0 0.
50 A 0 0 0. 0 0.
51 A 6 2 1. 10 0.2
52 A 5 2 1. 10 0.2
53 A 5 2 1. 10 0.2
54 A 4 2 1. 10 0.2
55 A 4 2 1. 10 0.2
56 A 2 2 1. 8 0.25
57 A 3 3 1. 6 0.5
58 A 0 0 0. 0 0.
59 A 0 0 0. 0 0.
60 A 14 5 1. 10 0.5
61 A 12 6 1. 10 0.6
62 A 10 6 1. 10 0.6
63 A 7 7 1. 8 0.875
64 A 4 4 1. 6 0.667
65 A 0 0 0. 0 0.
66 A 0 0 0. 0 0.
67 A 12 4 1. 10 0.4
68 A 9 4 1. 10 0.4
69 A 10 6 1. 10 0.6
70 A 5 5 1. 8 0.625
71 A 5 4 1. 6 0.667
72 A 0 0 0. 0 0.
73 A 0 0 0. 0 0.
74 A 19 7 1. 12 0.583
75 A 14 7 1. 12 0.583
76 A 14 7 1. 12 0.583
77 A 9 7 1. 10 0.7
78 A 7 6 1. 8 0.75
79 A 0 0 0. 0 0.
80 A 41 10 1. 12 0.833
81 A 25 10 1. 12 0.833
82 A 22 10 1. 12 0.833
83 A 11 10 1. 10 1.
84 A 8 7 1. 8 0.875
85 A 0 0 0. 0 0.
86 A 44 10 1. 12 0.833
87 A 27 9 1. 12 0.75
88 A 24 10 1. 12 0.833
89 A 12 9 1. 10 0.9
90 A 9 7 1. 8 0.875
91 A 0 0 0. 0 0.
92 A 18 6 1. 12 0.5
93 A 13 6 1. 12 0.5
94 A 13 6 1. 12 0.5
95 A 8 7 1. 10 0.7
96 A 6 5 1. 8 0.625
97 A 0 0 0. 0 0.
98 A 0 0 0. 0 0.
99 A 17 5 1. 12 0.417
100 A 12 5 1. 12 0.417
101 A 12 5 1. 12 0.417
102 A 6 5 1. 10 0.5
103 A 7 6 1. 8 0.75
104 A 0 0 0. 0 0.
105 A 34 8 1. 12 0.667
106 A 24 9 1. 12 0.75
107 A 22 9 1. 12 0.75
108 A 11 10 1. 10 1.
109 A 8 7 1. 8 0.875
110 A 0 0 0. 0 0.
111 A 32 7 1. 12 0.583
112 A 21 7 1. 12 0.583
113 A 22 9 1. 12 0.75
114 A 9 8 1. 10 0.8
115 A 9 7 1. 8 0.875
116 A 0 0 0. 0 0.
117 A 0 0 0. 0 0.
118 A 0 0 0. 0 0.
119 A 2 2 1. 10 0.2
120 A 2 2 1. 8 0.25
121 A 0 0 0. 0 0.
122 A 0 0 0. 0 0.
123 A 0 0 0. 0 0.
124 A 0 0 0. 0 0.
125 A 0 0 0. 0 0.
126 A 0 0 0. 0 0.
127 A 0 0 0. 0 0.
128 A 0 0 0. 0 0.
129 A 12 4 1. 10 0.4
130 A 9 4 1. 10 0.4
131 A 9 4 1. 10 0.4
132 A 6 5 1. 8 0.625
133 A 4 3 1. 6 0.5
134 A 0 0 0. 0 0.
135 A 0 0 0. 0 0.
136 A 14 7 1. 16 0.438
137 A 9 7 1. 14 0.5
138 A 7 6 1. 12 0.5
139 A 22 10 1. 16 0.625
140 A 11 10 1. 14 0.714
141 A 8 7 1. 12 0.583
142 A 24 10 1. 16 0.625
143 A 12 9 1. 14 0.643
144 A 9 7 1. 12 0.583
145 A 13 6 1. 16 0.375
146 A 8 7 1. 14 0.5
147 A 6 5 1. 12 0.417
148 A 12 5 1. 16 0.312
149 A 6 5 1. 14 0.357
150 A 7 6 1. 12 0.5
151 A 22 9 1. 16 0.562
152 A 11 10 1. 14 0.714
153 A 8 7 1. 12 0.583
154 A 22 9 1. 16 0.562
155 A 9 8 1. 14 0.571
156 A 9 7 1. 12 0.583

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