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2 detailed summary tables of results

 2.1 Detailed conclusion table per each integral for all CAS systems
 2.2 Detailed conclusion table specific for Rubi results

2.1 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 Rubi in Sympy
grade A A A B A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 52 93 78 73 102 367 44
normalized size 1 1. 1.02 1.82 1.53 1.43 2. 7.2 0.86
time (sec) N/A 0.062 0.036 0.067 1.593 0.285 5.23 0.239 5.092
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 17 16 20 20 12 20 12
normalized size 1 1. 1. 0.94 1.18 1.18 0.71 1.18 0.71
time (sec) N/A 0.048 0.015 0.069 1.602 0.236 0.226 0.207 4.37
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A F B B F(-2) A F F(-2) F(-1)
verified N/A N/A Yes TBD TBD TBD TBD TBD TBD
size 69 0 205 251 0 66 0 0 0
normalized size 1 0. 2.97 3.64 0. 0.96 0. 0. 0.
time (sec) N/A 0.255 0.829 0.601 0. 43.609 0. 0. 0.
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A B A B F A F(-1) A F
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 97 332 184 426 0 481 0 317 0
normalized size 1 3.42 1.9 4.39 0. 4.96 0. 3.27 0.
time (sec) N/A 1.359 0.459 0.118 0. 0.262 0. 0.291 0.
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A C C C A A F(-1) F F(-1)
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 45 304 159 312 47 45 0 0 0
normalized size 1 6.76 3.53 6.93 1.04 1. 0. 0. 0.
time (sec) N/A 0.752 3.876 0.585 65.134 0.282 0. 0. 0.
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F(-2) A F A A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 56 56 7083 64 0 119 0 107 51
normalized size 1 1. 126.48 1.14 0. 2.12 0. 1.91 0.91
time (sec) N/A 0.154 28.644 0.053 0. 0.295 0. 0.207 8.514
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A A A F A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 296 12 36 41 0 38 0
normalized size 1 1. 19.73 0.8 2.4 2.73 0. 2.53 0.
time (sec) N/A 0.053 11.627 0.062 1.485 0.288 0. 0.22 0.
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F(-2) A F F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 137 137 7376 1604 0 1589 0 0 178
normalized size 1 1. 53.84 11.71 0. 11.6 0. 0. 1.3
time (sec) N/A 0.393 31.764 0.25 0. 0.565 0. 0. 157.999
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A A A F F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 41 41 285 42 81 43 0 0 42
normalized size 1 1. 6.95 1.02 1.98 1.05 0. 0. 1.02
time (sec) N/A 0.048 6.385 0.041 1.642 0.243 0. 0. 4.747
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 44 62 38 0 0 38 56 62 56
normalized size 1 1.41 0.86 0. 0. 0.86 1.27 1.41 1.27
time (sec) N/A 1.132 0.195 0.055 0. 0.249 3.261 0.215 14.986
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 68 68 64 0 0 58 0 0 65
normalized size 1 1. 0.94 0. 0. 0.85 0. 0. 0.96
time (sec) N/A 0.231 0.06 0.026 0. 0.229 0. 0. 24.177
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A C C C F A F(-1) A F(-1)
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 141 269 1822 439 0 240 0 491 0
normalized size 1 1.91 12.92 3.11 0. 1.7 0. 3.48 0.
time (sec) N/A 1.479 8.105 0.086 0. 0.256 0. 0.214 0.
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A C C F F A F(-1) A F
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 152 286 2408 0 0 252 0 504 0
normalized size 1 1.88 15.84 0. 0. 1.66 0. 3.32 0.
time (sec) N/A 0.952 6.576 0.082 0. 0.266 0. 0.25 0.
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 51 44 0 0 85 0 77 0
normalized size 1 1.13 0.98 0. 0. 1.89 0. 1.71 0.
time (sec) N/A 0.205 0.04 0.129 0. 0.254 0. 0.22 0.
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 34 34 64 0 0 84 0 49 27
normalized size 1 1. 1.88 0. 0. 2.47 0. 1.44 0.79
time (sec) N/A 0.068 0.134 0.029 0. 0.23 0. 0.213 5.872
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 22 22 22 0 24 68 78 24 19
normalized size 1 1. 1. 0. 1.09 3.09 3.55 1.09 0.86
time (sec) N/A 0.038 0.044 0.141 1.632 0.265 21.003 0.21 4.529
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B F F A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 32 32 89 0 0 78 0 49 27
normalized size 1 1. 2.78 0. 0. 2.44 0. 1.53 0.84
time (sec) N/A 0.085 0.118 0.016 0. 0.231 0. 0.208 4.871
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 43 89 55 89 37 84 34
normalized size 1 1. 1. 2.07 1.28 2.07 0.86 1.95 0.79
time (sec) N/A 0.08 0.02 0.109 1.592 0.228 150.189 0.203 5.195
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 28 21 46 46 48 47 24
normalized size 1 1. 1. 0.75 1.64 1.64 1.71 1.68 0.86
time (sec) N/A 0.029 0.016 0.024 1.434 0.213 1.818 0.197 1.918
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 26 26 26 0 30 30 20 30 20
normalized size 1 1. 1. 0. 1.15 1.15 0.77 1.15 0.77
time (sec) N/A 0.059 0.018 0.036 1.581 0.547 58.641 0.2 4.035
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B F A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 38 38 85 0 38 186 0 51 29
normalized size 1 1. 2.24 0. 1. 4.89 0. 1.34 0.76
time (sec) N/A 0.088 0.119 0.266 1.639 0.23 0. 0.213 5.18
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F A A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 70 94 88 0 38 149 0 70 68
normalized size 1 1.34 1.26 0. 0.54 2.13 0. 1. 0.97
time (sec) N/A 0.333 0.188 0.667 1.688 0.241 0. 0.216 10.835
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F A A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 58 58 58 0 84 65 0 0 58
normalized size 1 1. 1. 0. 1.45 1.12 0. 0. 1.
time (sec) N/A 0.226 0.044 0.106 1.813 0.242 0. 0. 9.599
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 41 37 49 47 31 49 39
normalized size 1 1. 0.75 0.67 0.89 0.85 0.56 0.89 0.71
time (sec) N/A 0.087 0.016 0.009 1.425 0.213 12.946 0.195 7.692
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 26 26 26 0 30 30 20 30 20
normalized size 1 1. 1. 0. 1.15 1.15 0.77 1.15 0.77
time (sec) N/A 0.053 0.018 0.022 1.648 0.221 59.308 0.202 4.151
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F A F A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 78 78 119 0 0 320 0 165 0
normalized size 1 1. 1.53 0. 0. 4.1 0. 2.12 0.
time (sec) N/A 0.522 0.086 0.036 0. 0.226 0. 0.233 0.
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 39 39 25 35 47 105 0 99 27
normalized size 1 1. 0.64 0.9 1.21 2.69 0. 2.54 0.69
time (sec) N/A 0.088 0.034 0.063 1.653 0.234 0. 0.209 5.541
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 17 54 20 31 29 31 14
normalized size 1 1. 1. 3.18 1.18 1.82 1.71 1.82 0.82
time (sec) N/A 0.046 0.016 0.129 1.62 0.235 4.254 0.2 3.032
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 57 57 77 0 0 109 0 140 44
normalized size 1 1. 1.35 0. 0. 1.91 0. 2.46 0.77
time (sec) N/A 0.179 0.098 0.38 0. 0.255 0. 0.211 11.107
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 45 0 0 78 0 146 36
normalized size 1 1. 1. 0. 0. 1.73 0. 3.24 0.8
time (sec) N/A 0.087 0.047 0.191 0. 0.253 0. 0.209 8.016
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 33 56 30 63 19 73 24
normalized size 1 1. 1.14 1.93 1.03 2.17 0.66 2.52 0.83
time (sec) N/A 0.082 0.029 0.129 1.646 0.247 50.908 0.203 5.639
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 21 21 21 20 26 30 0 54 15
normalized size 1 1. 1. 0.95 1.24 1.43 0. 2.57 0.71
time (sec) N/A 0.073 0.02 0.057 1.586 0.247 0. 0.21 4.413
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 34 34 27 119 36 93 29 38 29
normalized size 1 1. 0.79 3.5 1.06 2.74 0.85 1.12 0.85
time (sec) N/A 0.065 0.022 0.072 1.646 0.251 3.931 0.202 5.376
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 33 33 21 29 39 90 26 78 26
normalized size 1 1. 0.64 0.88 1.18 2.73 0.79 2.36 0.79
time (sec) N/A 0.074 0.028 0.05 1.633 0.253 11.566 0.204 6.089
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 35 97 20 20 0 30 22
normalized size 1 1. 1.4 3.88 0.8 0.8 0. 1.2 0.88
time (sec) N/A 0.046 0.058 0.465 1.471 0.246 0. 0.213 4.325
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 34 34 40 39 34 128 41 59 29
normalized size 1 1. 1.18 1.15 1. 3.76 1.21 1.74 0.85
time (sec) N/A 0.067 0.021 0.038 1.603 0.242 6.76 0.201 6.47
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 46 14 35 46 46 36 19
normalized size 1 1. 2.88 0.88 2.19 2.88 2.88 2.25 1.19
time (sec) N/A 0.033 0.058 0.016 1.631 0.239 52.23 0.202 3.373
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 36 112 0 57 0 0 22
normalized size 1 1. 1.57 4.87 0. 2.48 0. 0. 0.96
time (sec) N/A 0.058 0.072 0.135 0. 0.253 0. 0. 7.093
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C C F A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 23 23 40 112 0 24 0 0 22
normalized size 1 1. 1.74 4.87 0. 1.04 0. 0. 0.96
time (sec) N/A 0.056 0.065 0.023 0. 0.241 0. 0. 7.685
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 22 22 39 54 111 126 97 49 20
normalized size 1 1. 1.77 2.45 5.05 5.73 4.41 2.23 0.91
time (sec) N/A 0.109 0.047 0.135 1.623 0.225 2.961 0.237 3.216
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B F F(-1) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 87 0 0 142 0 1 46
normalized size 1 1. 2.07 0. 0. 3.38 0. 0.02 1.1
time (sec) N/A 0.238 0.106 0.207 0. 0.24 0. 0.432 10.849
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A B A B F A F F F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 59 43 91 0 73 0 0 0
normalized size 1 2.11 1.54 3.25 0. 2.61 0. 0. 0.
time (sec) N/A 0.297 0.107 0.161 0. 0.251 0. 0. 0.
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 34 34 55 37 19 255 0 68 32
normalized size 1 1. 1.62 1.09 0.56 7.5 0. 2. 0.94
time (sec) N/A 0.104 0.108 0.036 1.983 0.232 0. 0.208 5.999
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B A A F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 39 50 5825 67 28 86 0 0 82
normalized size 1 1.28 149.36 1.72 0.72 2.21 0. 0. 2.1
time (sec) N/A 0.073 28.074 0.369 1.734 0.279 0. 0. 9.941
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A F A F F A F F(-1) F(-1)
verified N/A N/A NO TBD TBD TBD TBD TBD TBD
size 337 0 552 0 0 1690 0 0 0
normalized size 1 0. 1.64 0. 0. 5.01 0. 0. 0.
time (sec) N/A 1.376 2.876 0.194 0. 5.377 0. 0. 0.
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 58 3138 90 70 87 0 87
normalized size 1 1. 0.75 40.75 1.17 0.91 1.13 0. 1.13
time (sec) N/A 0.323 0.023 1.375 1.687 0.216 4.581 0. 170.557
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 120 120 116 510 0 505 0 0 104
normalized size 1 1. 0.97 4.25 0. 4.21 0. 0. 0.87
time (sec) N/A 0.497 0.25 0.068 0. 0.242 0. 0. 43.819
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-2) A F(-1)
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 31 37 39 28 35 30 0 36 0
normalized size 1 1.19 1.26 0.9 1.13 0.97 0. 1.16 0.
time (sec) N/A 0.021 0.058 0.023 1.742 0.236 0. 0.213 0.
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 29 29 31 138 97 70 0 46 24
normalized size 1 1. 1.07 4.76 3.34 2.41 0. 1.59 0.83
time (sec) N/A 0.067 0.027 0.1 1.663 0.243 0. 0.226 6.423
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 106 106 102 198 0 208 0 150 94
normalized size 1 1. 0.96 1.87 0. 1.96 0. 1.42 0.89
time (sec) N/A 0.535 0.142 0.079 0. 0.24 0. 0.257 59.944

2.2 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 [1] had the largest ratio of [ 1.4 ]

Table 1: Rubi specific breakdown of results for each integral
# grade
number of
steps
used
number of
unique
rules
normalized
antiderivative
leaf size
integrand
leaf size
\(\frac{\text{number of rules}}{\text{integrand leaf size}}\)
1 A 8 7 1. 5 1.4
2 A 2 2 1. 15 0.133
3 F 0 0 N/A 0 N/A
4 B 32 13 3.42 14 0.929
5 C 4 3 6.76 19 0.158
6 A 7 7 1. 13 0.538
7 A 4 4 1. 13 0.308
8 A 9 7 1. 14 0.5
9 A 7 7 1. 12 0.583
10 A 5 5 1.41 19 0.263
11 A 7 8 1. 29 0.276
12 C 40 15 1.91 14 1.071
13 C 32 16 1.88 27 0.593
14 A 9 11 1.13 18 0.611
15 A 3 4 1. 24 0.167
16 A 3 4 1. 12 0.333
17 A 3 4 1. 22 0.182
18 A 4 4 1. 15 0.267
19 A 4 4 1. 13 0.308
20 A 2 3 1. 23 0.13
21 A 5 6 1. 17 0.353
22 A 7 8 1.34 15 0.533
23 A 4 9 1. 25 0.36
24 A 5 5 1. 27 0.185
25 A 2 3 1. 23 0.13
26 A 18 11 1. 27 0.407
27 A 3 3 1. 17 0.176
28 A 2 2 1. 13 0.154
29 A 7 6 1. 17 0.353
30 A 5 5 1. 15 0.333
31 A 4 4 1. 15 0.267
32 A 2 2 1. 17 0.118
33 A 5 5 1. 13 0.385
34 A 3 3 1. 15 0.2
35 A 2 2 1. 13 0.154
36 A 5 5 1. 13 0.385
37 A 2 2 1. 11 0.182
38 A 2 2 1. 24 0.083
39 A 2 2 1. 24 0.083
40 A 4 5 1. 10 0.5
41 A 6 7 1. 12 0.583
42 B 5 5 2.11 13 0.385
43 A 4 4 1. 13 0.308
44 A 4 4 1.28 15 0.267
45 F 0 0 N/A 0 N/A
46 A 13 10 1. 12 0.833
47 A 12 8 1. 12 0.667
48 A 6 6 1.19 18 0.333
49 A 4 4 1. 14 0.286
50 A 6 6 1. 14 0.429

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