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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, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 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, 158, 159 }

B grade: { 97, 155, 156, 157 }

C grade: { }

F grade: { 111}

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, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 60, 61, 62, 63, 64, 65, 66, 67, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 98, 100, 101, 102, 103, 104, 105, 106, 109, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 134, 135, 136, 137, 138, 142, 143, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 157, 158, 159 }

B grade: { 54, 97, 99, 107, 108, 110, 111, 155, 156 }

C grade: { 33, 34, 43, 58, 59, 68, 69, 70, 71, 72, 73, 74, 75, 76, 132 }

F grade: { 139, 140, 141, 144}

2.1.3 Maple

A grade: { 1, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 16, 17, 18, 19, 20, 21, 27, 28, 29, 30, 31, 32, 35, 36, 37, 38, 39, 44, 45, 46, 47, 48, 51, 52, 53, 55, 58, 60, 61, 62, 63, 65, 70, 88, 95, 102, 104, 109, 143 }

B grade: { 2, 3, 12, 14, 33, 34, 40, 41, 42, 43, 49, 50, 56, 57, 59, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 94, 96, 97, 98, 99, 100, 101, 103, 105, 106, 107, 108, 110, 111, 119, 130, 131, 134, 135 }

C grade: { 22, 23, 24, 25, 26, 54, 64, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159 }

F grade: { 112, 113, 114, 115, 116, 117, 118, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 132, 133, 136, 137, 138, 139, 140, 141, 142, 144, 145, 146, 147, 148 }

2.1.4 Maxima

A grade: { 1, 2, 3, 4, 5, 6, 7, 31, 32, 143, 149, 150, 151, 152, 153, 154, 156, 157, 158, 159

B grade: { 155 }

C grade: { }

F grade: { 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 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, 144, 145, 146, 147, 148 }

2.1.5 FriCAS

A grade: { 1, 2, 3, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 18, 19, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 143, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159 }

B grade: { 13, 14, 20, 21, 26, 119, 130, 131, 134, 135 }

C grade: { }

F grade: { 4, 5, 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, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 132, 133, 136, 137, 138, 139, 140, 141, 142, 144, 145, 146, 147, 148 }

2.1.6 Sympy

A grade: { 1, 2, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 18, 19, 119 }

B grade: { 3, 13, 20 }

C grade: { 22, 23, 24, 25, 26, 27, 28, 29, 30, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159 }

F grade: { 4, 5, 14, 21, 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, 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 }

2.1.7 Giac

A grade: { 1, 2, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 31, 32, 143, 149, 150, 154, 155, 156, 157 }

B grade: { 27, 28, 29, 30, 119, 158, 159 }

C grade: { }

F grade: { 3, 4, 5, 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, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 144, 145, 146, 147, 148, 151, 152, 153 }

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 112 112 112 109 146 379 148 203
normalized size 1 1. 1. 0.97 1.3 3.38 1.32 1.81
time (sec) N/A 0.158 0.049 0.002 1.144 1.08 0.074 1.41
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 126 126 123 246 219 359 141 281
normalized size 1 1. 0.98 1.95 1.74 2.85 1.12 2.23
time (sec) N/A 0.211 0.089 0.004 1.15 1.212 0.972 1.304
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B A A B F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 84 84 85 196 140 242 507 0
normalized size 1 1. 1.01 2.33 1.67 2.88 6.04 0.
time (sec) N/A 0.086 0.071 0.008 1.375 1.484 10.499 0.
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A F(-1) F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 108 108 102 179 181 0 0 0
normalized size 1 1. 0.94 1.66 1.68 0. 0. 0.
time (sec) N/A 0.11 0.086 0.007 1.647 0. 0. 0.
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A F(-1) F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 163 163 164 164 419 0 0 0
normalized size 1 1. 1.01 1.01 2.57 0. 0. 0.
time (sec) N/A 0.212 0.247 0.007 1.282 0. 0. 0.
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 23 23 23 20 26 66 20 30
normalized size 1 1. 1. 0.87 1.13 2.87 0.87 1.3
time (sec) N/A 0.011 0.006 0.006 2.159 1.685 0.115 2.225
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 43 43 33 34 46 170 32 42
normalized size 1 1. 0.77 0.79 1.07 3.95 0.74 0.98
time (sec) N/A 0.037 0.02 0.007 1.232 1.675 0.142 2.168
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 227 227 205 301 0 1419 274 456
normalized size 1 1. 0.9 1.33 0. 6.25 1.21 2.01
time (sec) N/A 0.257 0.264 0.008 0. 1.83 26.773 2.38
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 146 146 145 176 0 914 167 271
normalized size 1 1. 0.99 1.21 0. 6.26 1.14 1.86
time (sec) N/A 0.098 0.176 0.008 0. 1.838 18.801 1.734
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 77 77 81 89 0 517 92 142
normalized size 1 1. 1.05 1.16 0. 6.71 1.19 1.84
time (sec) N/A 0.024 0.15 0.006 0. 1.349 18.418 1.477
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 54 54 55 46 0 279 54 77
normalized size 1 1. 1.02 0.85 0. 5.17 1. 1.43
time (sec) N/A 0.017 0.046 0.008 0. 1.324 3.872 1.531
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 101 101 101 196 0 1013 97 151
normalized size 1 1. 1. 1.94 0. 10.03 0.96 1.5
time (sec) N/A 0.114 0.115 0.011 0. 1.693 17.092 1.436
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 127 127 124 192 0 2114 1204 192
normalized size 1 1. 0.98 1.51 0. 16.65 9.48 1.51
time (sec) N/A 0.109 0.468 0.013 0. 1.91 52.541 1.673
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 208 208 260 424 0 4552 0 405
normalized size 1 1. 1.25 2.04 0. 21.88 0. 1.95
time (sec) N/A 0.274 0.636 0.016 0. 4.495 0. 1.745
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 226 226 204 301 0 1419 274 456
normalized size 1 1. 0.9 1.33 0. 6.28 1.21 2.02
time (sec) N/A 0.252 0.273 0.008 0. 1.427 26.157 2.56
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 145 145 146 176 0 914 167 271
normalized size 1 1. 1.01 1.21 0. 6.3 1.15 1.87
time (sec) N/A 0.094 0.163 0.007 0. 1.364 18.678 1.754
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 77 77 87 89 0 517 92 142
normalized size 1 1. 1.13 1.16 0. 6.71 1.19 1.84
time (sec) N/A 0.024 0.123 0.007 0. 1.226 18.186 2.756
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 54 54 55 46 0 279 54 77
normalized size 1 1. 1.02 0.85 0. 5.17 1. 1.43
time (sec) N/A 0.016 0.046 0.006 0. 1.293 3.901 2.643
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 101 101 100 103 0 1013 100 151
normalized size 1 1. 0.99 1.02 0. 10.03 0.99 1.5
time (sec) N/A 0.119 0.218 0.013 0. 1.647 15.252 2.624
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B B A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 128 128 122 137 0 2118 1149 192
normalized size 1 1. 0.95 1.07 0. 16.55 8.98 1.5
time (sec) N/A 0.116 0.191 0.016 0. 1.959 54.016 2.685
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) B F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 205 205 259 221 0 4551 0 406
normalized size 1 1. 1.26 1.08 0. 22.2 0. 1.98
time (sec) N/A 0.279 0.55 0.014 0. 4.975 0. 1.829
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) A C A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 111 111 89 132 0 165 484 85
normalized size 1 1. 0.8 1.19 0. 1.49 4.36 0.77
time (sec) N/A 0.045 0.085 0.03 0. 1.263 25.737 1.779
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) A C A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 87 87 81 111 0 146 393 72
normalized size 1 1. 0.93 1.28 0. 1.68 4.52 0.83
time (sec) N/A 0.034 0.031 0.013 0. 1.379 18.821 2.59
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) A C A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 63 63 73 90 0 124 269 54
normalized size 1 1. 1.16 1.43 0. 1.97 4.27 0.86
time (sec) N/A 0.023 0.027 0.011 0. 1.319 14.384 2.491
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) A C A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 37 37 61 70 0 100 133 38
normalized size 1 1. 1.65 1.89 0. 2.7 3.59 1.03
time (sec) N/A 0.013 0.024 0.015 0. 1.303 7.767 2.546
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C F(-2) B C A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 29 29 53 69 0 111 71 59
normalized size 1 1. 1.83 2.38 0. 3.83 2.45 2.03
time (sec) N/A 0.016 0.024 0.016 0. 1.314 10.317 2.979
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A C B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 45 45 29 25 0 69 107 119
normalized size 1 1. 0.64 0.56 0. 1.53 2.38 2.64
time (sec) N/A 0.01 0.012 0.003 0. 1.452 8.864 1.572
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A C B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 73 73 37 33 0 85 189 176
normalized size 1 1. 0.51 0.45 0. 1.16 2.59 2.41
time (sec) N/A 0.019 0.015 0.004 0. 1.499 12.744 1.869
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A C B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 97 97 45 41 0 111 274 236
normalized size 1 1. 0.46 0.42 0. 1.14 2.82 2.43
time (sec) N/A 0.027 0.017 0.003 0. 1.444 18.872 2.893
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F(-2) A C B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 121 121 53 49 0 131 359 293
normalized size 1 1. 0.44 0.4 0. 1.08 2.97 2.42
time (sec) N/A 0.038 0.019 0.005 0. 1.401 29.943 2.93
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 39 39 48 44 28 104 0 58
normalized size 1 1. 1.23 1.13 0.72 2.67 0. 1.49
time (sec) N/A 0.007 0.015 0.015 3.19 1.324 0. 1.865
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 39 39 48 44 28 104 0 58
normalized size 1 1. 1.23 1.13 0.72 2.67 0. 1.49
time (sec) N/A 0.011 0.006 0.004 1.766 1.328 0. 2.334
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 145 145 309 624 0 0 0 0
normalized size 1 1. 2.13 4.3 0. 0. 0. 0.
time (sec) N/A 0.108 1.447 0.047 0. 0. 0. 0.
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 221 221 312 940 0 0 0 0
normalized size 1 1. 1.41 4.25 0. 0. 0. 0.
time (sec) N/A 0.199 2.175 0.039 0. 0. 0. 0.
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 281 281 135 160 0 0 0 0
normalized size 1 1. 0.48 0.57 0. 0. 0. 0.
time (sec) N/A 0.389 0.416 0.047 0. 0. 0. 0.
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 243 243 130 155 0 0 0 0
normalized size 1 1. 0.53 0.64 0. 0. 0. 0.
time (sec) N/A 0.3 0.268 0.011 0. 0. 0. 0.
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 193 193 125 150 0 0 0 0
normalized size 1 1. 0.65 0.78 0. 0. 0. 0.
time (sec) N/A 0.077 0.232 0.012 0. 0. 0. 0.
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 162 162 120 145 0 0 0 0
normalized size 1 1. 0.74 0.9 0. 0. 0. 0.
time (sec) N/A 0.063 0.17 0.008 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 Yes TBD TBD TBD TBD TBD
size 182 182 141 183 0 0 0 0
normalized size 1 1. 0.77 1.01 0. 0. 0. 0.
time (sec) N/A 0.213 0.766 0.02 0. 0. 0. 0.
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 189 189 132 320 0 0 0 0
normalized size 1 1. 0.7 1.69 0. 0. 0. 0.
time (sec) N/A 0.211 0.752 0.025 0. 0. 0. 0.
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 227 227 136 461 0 0 0 0
normalized size 1 1. 0.6 2.03 0. 0. 0. 0.
time (sec) N/A 0.309 0.696 0.025 0. 0. 0. 0.
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 263 263 141 602 0 0 0 0
normalized size 1 1. 0.54 2.29 0. 0. 0. 0.
time (sec) N/A 0.397 0.754 0.026 0. 0. 0. 0.
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 570 570 1250 3678 0 0 0 0
normalized size 1 1. 2.19 6.45 0. 0. 0. 0.
time (sec) N/A 1.286 13.841 0.059 0. 0. 0. 0.
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 243 243 130 155 0 0 0 0
normalized size 1 1. 0.53 0.64 0. 0. 0. 0.
time (sec) N/A 0.297 0.368 0.02 0. 0. 0. 0.
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 205 205 125 150 0 0 0 0
normalized size 1 1. 0.61 0.73 0. 0. 0. 0.
time (sec) N/A 0.213 0.3 0.012 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 162 162 120 145 0 0 0 0
normalized size 1 1. 0.74 0.9 0. 0. 0. 0.
time (sec) N/A 0.062 0.193 0.01 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 131 131 115 140 0 0 0 0
normalized size 1 1. 0.88 1.07 0. 0. 0. 0.
time (sec) N/A 0.051 0.187 0.007 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 151 151 97 76 0 0 0 0
normalized size 1 1. 0.64 0.5 0. 0. 0. 0.
time (sec) N/A 0.121 0.404 0.013 0. 0. 0. 0.
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 189 189 132 320 0 0 0 0
normalized size 1 1. 0.7 1.69 0. 0. 0. 0.
time (sec) N/A 0.214 0.623 0.016 0. 0. 0. 0.
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 225 225 137 461 0 0 0 0
normalized size 1 1. 0.61 2.05 0. 0. 0. 0.
time (sec) N/A 0.301 0.562 0.016 0. 0. 0. 0.
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 205 205 125 150 0 0 0 0
normalized size 1 1. 0.61 0.73 0. 0. 0. 0.
time (sec) N/A 0.212 0.35 0.023 0. 0. 0. 0.
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 167 167 120 145 0 0 0 0
normalized size 1 1. 0.72 0.87 0. 0. 0. 0.
time (sec) N/A 0.145 0.281 0.014 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 131 131 115 140 0 0 0 0
normalized size 1 1. 0.88 1.07 0. 0. 0. 0.
time (sec) N/A 0.051 0.183 0.012 0. 0. 0. 0.
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B C F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 47 47 111 55 0 0 0 0
normalized size 1 1. 2.36 1.17 0. 0. 0. 0.
time (sec) N/A 0.015 0.34 0.011 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 103 103 70 56 0 0 0 0
normalized size 1 1. 0.68 0.54 0. 0. 0. 0.
time (sec) N/A 0.096 0.401 0.015 0. 0. 0. 0.
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 189 189 132 320 0 0 0 0
normalized size 1 1. 0.7 1.69 0. 0. 0. 0.
time (sec) N/A 0.21 0.653 0.016 0. 0. 0. 0.
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 225 225 144 461 0 0 0 0
normalized size 1 1. 0.64 2.05 0. 0. 0. 0.
time (sec) N/A 0.31 0.421 0.018 0. 0. 0. 0.
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 293 293 202 382 0 0 0 0
normalized size 1 1. 0.69 1.3 0. 0. 0. 0.
time (sec) N/A 0.504 1.713 0.043 0. 0. 0. 0.
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 449 449 1195 968 0 0 0 0
normalized size 1 1. 2.66 2.16 0. 0. 0. 0.
time (sec) N/A 0.672 8.35 0.024 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 203 203 125 150 0 0 0 0
normalized size 1 1. 0.62 0.74 0. 0. 0. 0.
time (sec) N/A 0.216 0.497 0.024 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 165 165 120 145 0 0 0 0
normalized size 1 1. 0.73 0.88 0. 0. 0. 0.
time (sec) N/A 0.153 0.347 0.017 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 129 129 115 140 0 0 0 0
normalized size 1 1. 0.89 1.09 0. 0. 0. 0.
time (sec) N/A 0.063 0.239 0.017 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 98 98 187 57 0 0 0 0
normalized size 1 1. 1.91 0.58 0. 0. 0. 0.
time (sec) N/A 0.037 0.452 0.015 0. 0. 0. 0.
Problem 64 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 48 48 79 36 0 0 0 0
normalized size 1 1. 1.65 0.75 0. 0. 0. 0.
time (sec) N/A 0.014 0.109 0.013 0. 0. 0. 0.
Problem 65 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 51 51 99 37 0 0 0 0
normalized size 1 1. 1.94 0.73 0. 0. 0. 0.
time (sec) N/A 0.07 0.468 0.016 0. 0. 0. 0.
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 189 189 132 320 0 0 0 0
normalized size 1 1. 0.7 1.69 0. 0. 0. 0.
time (sec) N/A 0.22 0.634 0.019 0. 0. 0. 0.
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 225 225 147 461 0 0 0 0
normalized size 1 1. 0.65 2.05 0. 0. 0. 0.
time (sec) N/A 0.31 0.439 0.02 0. 0. 0. 0.
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 137 137 180 552 0 0 0 0
normalized size 1 1. 1.31 4.03 0. 0. 0. 0.
time (sec) N/A 0.061 0.586 0.022 0. 0. 0. 0.
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 284 284 319 559 0 0 0 0
normalized size 1 1. 1.12 1.97 0. 0. 0. 0.
time (sec) N/A 0.169 1.911 0.033 0. 0. 0. 0.
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C A F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 165 165 225 223 0 0 0 0
normalized size 1 1. 1.36 1.35 0. 0. 0. 0.
time (sec) N/A 0.374 1.365 0.026 0. 0. 0. 0.
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 393 393 321 2842 0 0 0 0
normalized size 1 1. 0.82 7.23 0. 0. 0. 0.
time (sec) N/A 0.624 4.384 0.08 0. 0. 0. 0.
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 875 875 12191 17330 0 0 0 0
normalized size 1 1. 13.93 19.81 0. 0. 0. 0.
time (sec) N/A 1.339 17.494 0.257 0. 0. 0. 0.
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 203 184 0 0 0 0
normalized size 1 1. 2.74 2.49 0. 0. 0. 0.
time (sec) N/A 0.16 0.868 0.097 0. 0. 0. 0.
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 74 74 203 181 0 0 0 0
normalized size 1 1. 2.74 2.45 0. 0. 0. 0.
time (sec) N/A 0.176 0.103 0.025 0. 0. 0. 0.
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 86 86 218 212 0 0 0 0
normalized size 1 1. 2.53 2.47 0. 0. 0. 0.
time (sec) N/A 0.16 0.813 0.096 0. 0. 0. 0.
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C B F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 86 86 218 205 0 0 0 0
normalized size 1 1. 2.53 2.38 0. 0. 0. 0.
time (sec) N/A 0.175 0.107 0.024 0. 0. 0. 0.
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 471 471 350 895 0 0 0 0
normalized size 1 1. 0.74 1.9 0. 0. 0. 0.
time (sec) N/A 0.665 4.381 0.074 0. 0. 0. 0.
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 429 429 345 890 0 0 0 0
normalized size 1 1. 0.8 2.07 0. 0. 0. 0.
time (sec) N/A 0.542 4.156 0.018 0. 0. 0. 0.
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 391 391 340 885 0 0 0 0
normalized size 1 1. 0.87 2.26 0. 0. 0. 0.
time (sec) N/A 0.429 4.066 0.02 0. 0. 0. 0.
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 351 351 347 880 0 0 0 0
normalized size 1 1. 0.99 2.51 0. 0. 0. 0.
time (sec) N/A 0.324 2.933 0.03 0. 0. 0. 0.
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 349 349 330 875 0 0 0 0
normalized size 1 1. 0.95 2.51 0. 0. 0. 0.
time (sec) N/A 0.319 2.793 0.041 0. 0. 0. 0.
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 391 391 366 1149 0 0 0 0
normalized size 1 1. 0.94 2.94 0. 0. 0. 0.
time (sec) N/A 0.429 2.974 0.04 0. 0. 0. 0.
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 330 330 251 973 0 0 0 0
normalized size 1 1. 0.76 2.95 0. 0. 0. 0.
time (sec) N/A 0.395 2.258 0.042 0. 0. 0. 0.
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 370 370 259 1160 0 0 0 0
normalized size 1 1. 0.7 3.14 0. 0. 0. 0.
time (sec) N/A 0.515 2.595 0.044 0. 0. 0. 0.
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 429 429 345 890 0 0 0 0
normalized size 1 1. 0.8 2.07 0. 0. 0. 0.
time (sec) N/A 0.526 3.661 0.031 0. 0. 0. 0.
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 391 391 340 885 0 0 0 0
normalized size 1 1. 0.87 2.26 0. 0. 0. 0.
time (sec) N/A 0.412 3.596 0.02 0. 0. 0. 0.
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 351 351 347 880 0 0 0 0
normalized size 1 1. 0.99 2.51 0. 0. 0. 0.
time (sec) N/A 0.316 3.875 0.019 0. 0. 0. 0.
Problem 88 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 365 365 318 875 0 0 0 0
normalized size 1 1. 0.87 2.4 0. 0. 0. 0.
time (sec) N/A 0.216 1.23 0.021 0. 0. 0. 0.
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 279 279 326 870 0 0 0 0
normalized size 1 1. 1.17 3.12 0. 0. 0. 0.
time (sec) N/A 0.195 2.297 0.026 0. 0. 0. 0.
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 290 290 246 786 0 0 0 0
normalized size 1 1. 0.85 2.71 0. 0. 0. 0.
time (sec) N/A 0.32 1.819 0.028 0. 0. 0. 0.
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 330 330 251 973 0 0 0 0
normalized size 1 1. 0.76 2.95 0. 0. 0. 0.
time (sec) N/A 0.398 1.789 0.031 0. 0. 0. 0.
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 370 370 258 1160 0 0 0 0
normalized size 1 1. 0.7 3.14 0. 0. 0. 0.
time (sec) N/A 0.521 2.196 0.031 0. 0. 0. 0.
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 391 391 340 885 0 0 0 0
normalized size 1 1. 0.87 2.26 0. 0. 0. 0.
time (sec) N/A 0.421 2.445 0.036 0. 0. 0. 0.
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 351 351 349 880 0 0 0 0
normalized size 1 1. 0.99 2.51 0. 0. 0. 0.
time (sec) N/A 0.322 3.148 0.024 0. 0. 0. 0.
Problem 95 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 365 365 347 875 0 0 0 0
normalized size 1 1. 0.95 2.4 0. 0. 0. 0.
time (sec) N/A 0.202 1.369 0.023 0. 0. 0. 0.
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 101 101 170 172 0 0 0 0
normalized size 1 1. 1.68 1.7 0. 0. 0. 0.
time (sec) N/A 0.037 0.546 0.025 0. 0. 0. 0.
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B B B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 60 195 237 330 0 0 0 0
normalized size 1 3.25 3.95 5.5 0. 0. 0. 0.
time (sec) N/A 0.131 1.729 0.025 0. 0. 0. 0.
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 290 290 248 786 0 0 0 0
normalized size 1 1. 0.86 2.71 0. 0. 0. 0.
time (sec) N/A 0.296 1.805 0.029 0. 0. 0. 0.
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F F(-1) F F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 721 721 6667 18077 0 0 0 0
normalized size 1 1. 9.25 25.07 0. 0. 0. 0.
time (sec) N/A 0.675 15.126 0.151 0. 0. 0. 0.
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 161 208 206 4590 0 0 0 0
normalized size 1 1.29 1.28 28.51 0. 0. 0. 0.
time (sec) N/A 0.093 4.707 0.118 0. 0. 0. 0.
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 351 351 347 880 0 0 0 0
normalized size 1 1. 0.99 2.51 0. 0. 0. 0.
time (sec) N/A 0.319 2.431 0.037 0. 0. 0. 0.
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A A F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 469 469 347 875 0 0 0 0
normalized size 1 1. 0.74 1.87 0. 0. 0. 0.
time (sec) N/A 0.28 1.223 0.023 0. 0. 0. 0.
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 100 100 95 170 0 0 0 0
normalized size 1 1. 0.95 1.7 0. 0. 0. 0.
time (sec) N/A 0.038 0.158 0.021 0. 0. 0. 0.
Problem 104 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 71 71 90 134 0 0 0 0
normalized size 1 1. 1.27 1.89 0. 0. 0. 0.
time (sec) N/A 0.043 0.139 0.022 0. 0. 0. 0.
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 195 270 237 599 0 0 0 0
normalized size 1 1.38 1.22 3.07 0. 0. 0. 0.
time (sec) N/A 0.183 1.575 0.03 0. 0. 0. 0.
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 288 288 246 786 0 0 0 0
normalized size 1 1. 0.85 2.73 0. 0. 0. 0.
time (sec) N/A 0.303 1.719 0.031 0. 0. 0. 0.
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F F(-1) F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 968 968 6638 16526 0 0 0 0
normalized size 1 1. 6.86 17.07 0. 0. 0. 0.
time (sec) N/A 0.882 14.274 0.087 0. 0. 0. 0.
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F F(-1) F F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 228 228 584 2465 0 0 0 0
normalized size 1 1. 2.56 10.81 0. 0. 0. 0.
time (sec) N/A 0.15 5.571 0.053 0. 0. 0. 0.
Problem 109 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 161 198 227 270 0 0 0 0
normalized size 1 1.23 1.41 1.68 0. 0. 0. 0.
time (sec) N/A 0.082 1.289 0.059 0. 0. 0. 0.
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A B B F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 429 429 3247 4660 0 0 0 0
normalized size 1 1. 7.57 10.86 0. 0. 0. 0.
time (sec) N/A 0.256 14.337 0.095 0. 0. 0. 0.
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A F B B F F F(-1) F
verified N/A N/A NO TBD TBD TBD TBD TBD
size 786 0 7061 21094 0 0 0 0
normalized size 1 0. 8.98 26.84 0. 0. 0. 0.
time (sec) N/A 0.01 17.458 0.224 0. 0. 0. 0.
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 319 319 285 0 0 0 0 0
normalized size 1 1. 0.89 0. 0. 0. 0. 0.
time (sec) N/A 0.279 1.322 0.089 0. 0. 0. 0.
Problem 113 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 216 216 174 0 0 0 0 0
normalized size 1 1. 0.81 0. 0. 0. 0. 0.
time (sec) N/A 0.154 0.496 0.077 0. 0. 0. 0.
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 158 158 153 0 0 0 0 0
normalized size 1 1. 0.97 0. 0. 0. 0. 0.
time (sec) N/A 0.107 0.074 0.069 0. 0. 0. 0.
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 124 124 116 0 0 0 0 0
normalized size 1 1. 0.94 0. 0. 0. 0. 0.
time (sec) N/A 0.039 0.026 0.068 0. 0. 0. 0.
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 124 124 116 0 0 0 0 0
normalized size 1 1. 0.94 0. 0. 0. 0. 0.
time (sec) N/A 0.033 0.03 0.063 0. 0. 0. 0.
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 175 175 170 0 0 0 0 0
normalized size 1 1. 0.97 0. 0. 0. 0. 0.
time (sec) N/A 0.119 0.184 0.052 0. 0. 0. 0.
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 222 222 177 0 0 0 0 0
normalized size 1 1. 0.8 0. 0. 0. 0. 0.
time (sec) N/A 0.151 0.267 0.082 0. 0. 0. 0.
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F(-2) B A B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 167 167 149 726 0 1847 8218 2248
normalized size 1 1. 0.89 4.35 0. 11.06 49.21 13.46
time (sec) N/A 0.131 0.233 0.007 0. 1.607 7.096 2.658
Problem 120 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 134 134 120 0 0 0 0 0
normalized size 1 1. 0.9 0. 0. 0. 0. 0.
time (sec) N/A 0.086 0.19 0.053 0. 0. 0. 0.
Problem 121 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 140 140 115 0 0 0 0 0
normalized size 1 1. 0.82 0. 0. 0. 0. 0.
time (sec) N/A 0.059 0.094 0.066 0. 0. 0. 0.
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 224 224 193 0 0 0 0 0
normalized size 1 1. 0.86 0. 0. 0. 0. 0.
time (sec) N/A 0.195 0.395 0.101 0. 0. 0. 0.
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 140 140 104 0 0 0 0 0
normalized size 1 1. 0.74 0. 0. 0. 0. 0.
time (sec) N/A 0.123 0.217 0.066 0. 0. 0. 0.
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 266 266 195 0 0 0 0 0
normalized size 1 1. 0.73 0. 0. 0. 0. 0.
time (sec) N/A 0.165 0.236 0.065 0. 0. 0. 0.
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 245 245 195 0 0 0 0 0
normalized size 1 1. 0.8 0. 0. 0. 0. 0.
time (sec) N/A 0.155 0.261 0.061 0. 0. 0. 0.
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 235 235 189 0 0 0 0 0
normalized size 1 1. 0.8 0. 0. 0. 0. 0.
time (sec) N/A 0.138 0.206 0.061 0. 0. 0. 0.
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 261 261 221 0 0 0 0 0
normalized size 1 1. 0.85 0. 0. 0. 0. 0.
time (sec) N/A 0.186 0.186 0.056 0. 0. 0. 0.
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 203 205 198 0 0 0 0 0
normalized size 1 1.01 0.98 0. 0. 0. 0. 0.
time (sec) N/A 0.107 0.249 0.054 0. 0. 0. 0.
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 246 246 237 0 0 0 0 0
normalized size 1 1. 0.96 0. 0. 0. 0. 0.
time (sec) N/A 0.16 0.331 0.052 0. 0. 0. 0.
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 362 362 220 894 0 3309 0 0
normalized size 1 1. 0.61 2.47 0. 9.14 0. 0.
time (sec) N/A 0.362 0.55 0.008 0. 1.46 0. 0.
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 507 507 279 2343 0 6969 0 0
normalized size 1 1. 0.55 4.62 0. 13.75 0. 0.
time (sec) N/A 0.586 0.769 0.01 0. 1.971 0. 0.
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A C F F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 815 803 3579 0 0 0 0 0
normalized size 1 0.99 4.39 0. 0. 0. 0. 0.
time (sec) N/A 1.435 48.597 0.063 0. 0. 0. 0.
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 572 566 422 0 0 0 0 0
normalized size 1 0.99 0.74 0. 0. 0. 0. 0.
time (sec) N/A 0.662 1.816 0.059 0. 0. 0. 0.
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 363 360 227 906 0 3272 0 0
normalized size 1 0.99 0.63 2.5 0. 9.01 0. 0.
time (sec) N/A 0.397 0.573 0.008 0. 1.604 0. 0.
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A B F B F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 188 186 182 509 0 1805 0 0
normalized size 1 0.99 0.97 2.71 0. 9.6 0. 0.
time (sec) N/A 0.098 0.119 0.008 0. 1.505 0. 0.
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A NO NO TBD TBD TBD TBD TBD
size 177 190 199 0 0 0 0 0
normalized size 1 1.07 1.12 0. 0. 0. 0. 0.
time (sec) N/A 0.119 0.399 0.071 0. 0. 0. 0.
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 233 220 174 0 0 0 0 0
normalized size 1 0.94 0.75 0. 0. 0. 0. 0.
time (sec) N/A 0.127 0.137 0.068 0. 0. 0. 0.
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 250 250 184 0 0 0 0 0
normalized size 1 1. 0.74 0. 0. 0. 0. 0.
time (sec) N/A 0.217 0.208 0.059 0. 0. 0. 0.
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F(-1) F(-1)
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 530 530 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 1.179 4.524 0.25 0. 0. 0. 0.
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F(-1) F(-1)
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 393 393 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.493 1.486 0.173 0. 0. 0. 0.
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 256 256 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.21 0.905 0.148 0. 0. 0. 0.
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 123 123 121 0 0 0 0 0
normalized size 1 1. 0.98 0. 0. 0. 0. 0.
time (sec) N/A 0.083 0.134 0.002 0. 0. 0. 0.
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade N/A A A A A A F(-1) A
verified N/A N/A N/A TBD TBD TBD TBD TBD
size 31 0 0 0 0 0 0 0
normalized size 1 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.008 0.254 0.157 0. 0. 0. 0.
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A F F F F F(-1) F
verified N/A Yes N/A TBD TBD TBD TBD TBD
size 268 268 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0.
time (sec) N/A 0.212 0.637 0.151 0. 0. 0. 0.
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 283 283 208 0 0 0 0 0
normalized size 1 1. 0.73 0. 0. 0. 0. 0.
time (sec) N/A 0.208 0.32 0.145 0. 0. 0. 0.
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes NO TBD TBD TBD TBD TBD
size 277 277 215 0 0 0 0 0
normalized size 1 1. 0.78 0. 0. 0. 0. 0.
time (sec) N/A 0.147 0.443 0.143 0. 0. 0. 0.
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 263 261 223 0 0 0 0 0
normalized size 1 0.99 0.85 0. 0. 0. 0. 0.
time (sec) N/A 0.227 0.315 0.151 0. 0. 0. 0.
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A F F F F(-1) F
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 558 558 508 0 0 0 0 0
normalized size 1 1. 0.91 0. 0. 0. 0. 0.
time (sec) N/A 0.981 1.872 0.152 0. 0. 0. 0.
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A C A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 79 79 57 139 134 189 313 123
normalized size 1 1. 0.72 1.76 1.7 2.39 3.96 1.56
time (sec) N/A 0.142 0.062 0.038 3.068 1.047 46.125 2.052
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A C A
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 63 63 45 117 105 167 282 97
normalized size 1 1. 0.71 1.86 1.67 2.65 4.48 1.54
time (sec) N/A 0.061 0.031 0.015 4.261 1.043 21.009 2.571
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A C F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 48 48 48 96 89 196 245 0
normalized size 1 1. 1. 2. 1.85 4.08 5.1 0.
time (sec) N/A 0.184 0.05 0.024 3.423 1.142 27.867 0.
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A C F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 48 48 48 97 89 201 221 0
normalized size 1 1. 1. 2.02 1.85 4.19 4.6 0.
time (sec) N/A 0.183 0.055 0.02 3.045 1.149 27.566 0.
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A C F(-2)
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 71 71 56 108 132 154 218 0
normalized size 1 1. 0.79 1.52 1.86 2.17 3.07 0.
time (sec) N/A 0.188 0.047 0.019 2.734 1.049 34.59 0.
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A C A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 87 151 149 137 147 176 308 130
normalized size 1 1.74 1.71 1.57 1.69 2.02 3.54 1.49
time (sec) N/A 0.146 0.331 0.023 1.352 1.052 44.788 2.124
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B B C B A C A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 52 135 126 120 142 150 277 104
normalized size 1 2.6 2.42 2.31 2.73 2.88 5.33 2.
time (sec) N/A 0.071 0.21 0.016 1.36 1.102 20.739 2.571
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B B C A A C A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 55 135 128 95 86 184 240 96
normalized size 1 2.45 2.33 1.73 1.56 3.35 4.36 1.75
time (sec) N/A 0.184 0.399 0.019 3.912 1.086 26.248 1.986
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A B A C A A C A
verified N/A Yes NO TBD TBD TBD TBD TBD
size 55 135 89 96 86 203 216 112
normalized size 1 2.45 1.62 1.75 1.56 3.69 3.93 2.04
time (sec) N/A 0.182 0.167 0.017 2.016 1.143 27.925 2.665
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A C B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 83 129 82 103 88 173 212 196
normalized size 1 1.55 0.99 1.24 1.06 2.08 2.55 2.36
time (sec) N/A 0.189 0.121 0.018 2.21 1.057 34.178 1.469
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac
grade A A A C A A C B
verified N/A Yes Yes TBD TBD TBD TBD TBD
size 116 171 94 123 119 216 219 266
normalized size 1 1.47 0.81 1.06 1.03 1.86 1.89 2.29
time (sec) N/A 0.221 0.116 0.019 1.794 1.032 56.645 1.69

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 [72] had the largest ratio of [ 0.3429 ]

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 2 1 1. 21 0.048
2 A 2 1 1. 23 0.043
3 A 2 1 1. 25 0.04
4 A 2 1 1. 27 0.037
5 A 2 1 1. 29 0.034
6 A 2 1 1. 17 0.059
7 A 3 2 1. 22 0.091
8 A 6 5 1. 25 0.2
9 A 5 5 1. 25 0.2
10 A 4 4 1. 23 0.174
11 A 4 4 1. 18 0.222
12 A 6 4 1. 25 0.16
13 A 6 4 1. 25 0.16
14 A 7 5 1. 25 0.2
15 A 6 5 1. 25 0.2
16 A 5 5 1. 25 0.2
17 A 4 4 1. 23 0.174
18 A 4 4 1. 18 0.222
19 A 6 5 1. 25 0.2
20 A 6 5 1. 25 0.2
21 A 7 6 1. 25 0.24
22 A 8 6 1. 26 0.231
23 A 7 6 1. 26 0.231
24 A 6 6 1. 24 0.25
25 A 4 4 1. 23 0.174
26 A 5 5 1. 26 0.192
27 A 3 3 1. 26 0.115
28 A 4 4 1. 26 0.154
29 A 5 4 1. 26 0.154
30 A 6 4 1. 26 0.154
31 A 4 4 1. 24 0.167
32 A 5 5 1. 36 0.139
33 A 3 3 1. 45 0.067
34 A 5 5 1. 39 0.128
35 A 10 8 1. 35 0.229
36 A 9 8 1. 35 0.229
37 A 8 6 1. 33 0.182
38 A 7 7 1. 28 0.25
39 A 10 10 1. 35 0.286
40 A 10 10 1. 35 0.286
41 A 11 11 1. 35 0.314
42 A 12 11 1. 35 0.314
43 A 12 10 1. 35 0.286
44 A 9 8 1. 35 0.229
45 A 8 8 1. 35 0.229
46 A 7 6 1. 33 0.182
47 A 6 6 1. 28 0.214
48 A 9 9 1. 35 0.257
49 A 10 10 1. 35 0.286
50 A 11 11 1. 35 0.314
51 A 8 8 1. 35 0.229
52 A 7 7 1. 35 0.2
53 A 6 6 1. 33 0.182
54 A 2 2 1. 28 0.071
55 A 6 6 1. 35 0.171
56 A 10 10 1. 35 0.286
57 A 11 11 1. 35 0.314
58 A 8 6 1. 35 0.171
59 A 11 8 1. 35 0.229
60 A 8 8 1. 35 0.229
61 A 7 7 1. 35 0.2
62 A 7 7 1. 35 0.2
63 A 5 5 1. 33 0.152
64 A 2 2 1. 28 0.071
65 A 3 3 1. 35 0.086
66 A 10 10 1. 35 0.286
67 A 11 11 1. 35 0.314
68 A 3 3 1. 36 0.083
69 A 6 5 1. 33 0.152
70 A 4 3 1. 35 0.086
71 A 10 8 1. 35 0.229
72 A 18 12 1. 35 0.343
73 A 3 3 1. 36 0.083
74 A 4 4 1. 31 0.129
75 A 3 3 1. 40 0.075
76 A 4 4 1. 31 0.129
77 A 12 10 1. 37 0.27
78 A 11 10 1. 37 0.27
79 A 10 10 1. 37 0.27
80 A 9 9 1. 37 0.243
81 A 9 9 1. 37 0.243
82 A 10 10 1. 37 0.27
83 A 9 9 1. 37 0.243
84 A 10 9 1. 37 0.243
85 A 11 10 1. 37 0.27
86 A 10 10 1. 37 0.27
87 A 9 9 1. 37 0.243
88 A 9 8 1. 37 0.216
89 A 7 7 1. 37 0.189
90 A 8 8 1. 37 0.216
91 A 9 9 1. 37 0.243
92 A 10 9 1. 37 0.243
93 A 10 10 1. 37 0.27
94 A 9 9 1. 37 0.243
95 A 9 8 1. 37 0.216
96 A 2 2 1. 37 0.054
97 B 5 5 3.25 37 0.135
98 A 8 8 1. 37 0.216
99 A 7 7 1. 37 0.189
100 A 2 2 1.29 37 0.054
101 A 9 9 1. 37 0.243
102 A 12 10 1. 37 0.27
103 A 2 2 1. 37 0.054
104 A 2 2 1. 37 0.054
105 A 8 7 1.38 37 0.189
106 A 8 8 1. 37 0.216
107 A 10 8 1. 37 0.216
108 A 2 2 1. 37 0.054
109 A 2 2 1.23 37 0.054
110 A 5 5 1. 37 0.135
111 F 0 0 N/A 0 N/A
112 A 8 3 1. 25 0.12
113 A 6 3 1. 25 0.12
114 A 4 2 1. 25 0.08
115 A 3 2 1. 23 0.087
116 A 3 2 1. 22 0.091
117 A 5 3 1. 25 0.12
118 A 6 3 1. 25 0.12
119 A 2 1 1. 23 0.043
120 A 2 2 1. 25 0.08
121 A 3 2 1. 27 0.074
122 A 5 2 1. 29 0.069
123 A 6 3 1. 25 0.12
124 A 3 3 1. 25 0.12
125 A 3 3 1. 29 0.103
126 A 3 3 1. 27 0.111
127 A 3 3 1. 29 0.103
128 A 3 3 1.01 29 0.103
129 A 3 3 1. 29 0.103
130 A 3 3 1. 29 0.103
131 A 4 3 1. 29 0.103
132 A 10 9 0.99 31 0.29
133 A 9 8 0.99 31 0.258
134 A 3 3 0.99 29 0.103
135 A 3 3 0.99 24 0.125
136 A 5 5 1.07 27 0.185
137 A 7 5 0.94 29 0.172
138 A 7 4 1. 29 0.138
139 A 31 5 1. 29 0.172
140 A 15 5 1. 29 0.172
141 A 7 4 1. 27 0.148
142 A 3 3 1. 22 0.136
143 A 0 0 0. 0 0.
144 A 7 4 1. 33 0.121
145 A 7 4 1. 34 0.118
146 A 5 5 1. 34 0.147
147 A 3 3 0.99 34 0.088
148 A 4 3 1. 34 0.088
149 A 4 4 1. 31 0.129
150 A 4 4 1. 30 0.133
151 A 7 7 1. 33 0.212
152 A 7 7 1. 33 0.212
153 A 6 6 1. 33 0.182
154 A 5 5 1.74 30 0.167
155 B 5 5 2.6 29 0.172
156 B 8 8 2.45 32 0.25
157 B 8 8 2.45 32 0.25
158 A 6 6 1.55 32 0.188
159 A 7 7 1.47 32 0.219

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