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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 F F A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 66 0 0 88 0 0 60
normalized size 1 1. 0.99 0. 0. 1.31 0. 0. 0.9
time (sec) N/A 0.075 0.42 0.23 0. 0.257 0. 0. 6.511
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 141 141 100 260 417 306 350 1 139
normalized size 1 1. 0.71 1.84 2.96 2.17 2.48 0.01 0.99
time (sec) N/A 0.203 0.074 0.017 0.716 0.257 0.605 0.355 39.746
Problem 3 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 110 110 78 165 278 198 231 1 107
normalized size 1 1. 0.71 1.5 2.53 1.8 2.1 0.01 0.97
time (sec) N/A 0.134 0.061 0.012 0.703 0.237 0.494 0.325 27.086
Problem 4 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 79 79 56 91 166 113 133 1 75
normalized size 1 1. 0.71 1.15 2.1 1.43 1.68 0.01 0.95
time (sec) N/A 0.083 0.048 0.013 0.697 0.261 0.4 0.301 15.498
Problem 5 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 48 48 34 38 81 51 60 1 41
normalized size 1 1. 0.71 0.79 1.69 1.06 1.25 0.02 0.85
time (sec) N/A 0.037 0.026 0.004 0.692 0.234 0.294 0.261 6.634
Problem 6 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 20 20 21 21 27 28 20 27 14
normalized size 1 1. 1.05 1.05 1.35 1.4 1. 1.35 0.7
time (sec) N/A 0.011 0.002 0.003 0.681 0.23 0.166 0.241 2.002
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 31 31 31 56 50 53 0 0 27
normalized size 1 1. 1. 1.81 1.61 1.71 0. 0. 0.87
time (sec) N/A 0.04 0.016 0.034 0.753 0.247 0. 0. 5.153
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 57 57 55 97 59 104 0 0 51
normalized size 1 1. 0.96 1.7 1.04 1.82 0. 0. 0.89
time (sec) N/A 0.078 0.118 0.034 0.787 0.245 0. 0. 9.92
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 95 95 88 151 59 181 0 0 87
normalized size 1 1. 0.93 1.59 0.62 1.91 0. 0. 0.92
time (sec) N/A 0.126 0.112 0.043 0.789 0.239 0. 0. 17.269
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 128 128 99 193 59 282 0 0 119
normalized size 1 1. 0.77 1.51 0.46 2.2 0. 0. 0.93
time (sec) N/A 0.176 0.133 0.052 0.806 0.239 0. 0. 26.501
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 161 161 121 235 59 405 0 0 151
normalized size 1 1. 0.75 1.46 0.37 2.52 0. 0. 0.94
time (sec) N/A 0.234 0.147 0.066 0.789 0.248 0. 0. 37.737
Problem 12 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 141 141 100 260 417 306 350 1 139
normalized size 1 1. 0.71 1.84 2.96 2.17 2.48 0.01 0.99
time (sec) N/A 0.218 0.033 0.019 0.746 0.235 0.612 0.345 57.049
Problem 13 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 110 110 78 165 278 198 231 1 107
normalized size 1 1. 0.71 1.5 2.53 1.8 2.1 0.01 0.97
time (sec) N/A 0.154 0.017 0.011 0.734 0.231 0.494 0.309 36.464
Problem 14 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 79 79 56 91 166 113 133 1 75
normalized size 1 1. 0.71 1.15 2.1 1.43 1.68 0.01 0.95
time (sec) N/A 0.083 0.015 0.012 0.734 0.229 0.395 0.273 35.713
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 57 57 55 97 59 104 0 0 51
normalized size 1 1. 0.96 1.7 1.04 1.82 0. 0. 0.89
time (sec) N/A 0.075 0.02 0.052 0.783 0.241 0. 0. 25.081
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 95 95 88 151 59 181 0 0 87
normalized size 1 1. 0.93 1.59 0.62 1.91 0. 0. 0.92
time (sec) N/A 0.16 0.024 0.068 0.812 0.243 0. 0. 34.87
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 128 128 99 193 59 282 0 0 119
normalized size 1 1. 0.77 1.51 0.46 2.2 0. 0. 0.93
time (sec) N/A 0.227 0.027 0.094 0.844 0.24 0. 0. 54.404
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 161 161 121 235 59 405 0 0 151
normalized size 1 1. 0.75 1.46 0.37 2.52 0. 0. 0.94
time (sec) N/A 0.304 0.029 0.124 0.915 0.239 0. 0. 84.485
Problem 19 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 72 72 74 0 0 92 0 0 65
normalized size 1 1. 1.03 0. 0. 1.28 0. 0. 0.9
time (sec) N/A 0.095 0.048 0.072 0. 0.254 0. 0. 11.985
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 73 0 0 0 0 0 65
normalized size 1 1. 1.03 0. 0. 0. 0. 0. 0.92
time (sec) N/A 0.118 0.098 0.26 0. 0. 0. 0. 36.493
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 73 0 0 0 0 0 65
normalized size 1 1. 1.03 0. 0. 0. 0. 0. 0.92
time (sec) N/A 0.104 0.049 0.086 0. 0. 0. 0. 25.867
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 73 0 0 0 0 0 65
normalized size 1 1. 1.03 0. 0. 0. 0. 0. 0.92
time (sec) N/A 0.098 0.047 0.138 0. 0. 0. 0. 18.494
Problem 23 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 67 67 66 0 0 88 0 0 60
normalized size 1 1. 0.99 0. 0. 1.31 0. 0. 0.9
time (sec) N/A 0.046 0.018 0. 0. 0.269 0. 0. 6.744
Problem 24 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 69 69 68 0 0 90 0 0 60
normalized size 1 1. 0.99 0. 0. 1.3 0. 0. 0.87
time (sec) N/A 0.048 0.049 0.065 0. 0.263 0. 0. 6.738
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 75 0 0 0 0 0 65
normalized size 1 1. 1.03 0. 0. 0. 0. 0. 0.89
time (sec) N/A 0.098 0.046 0.119 0. 0. 0. 0. 18.702
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 75 0 0 0 0 0 65
normalized size 1 1. 1.03 0. 0. 0. 0. 0. 0.89
time (sec) N/A 0.104 0.047 0.082 0. 0. 0. 0. 26.248
Problem 27 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 15 15 15 14 18 18 15 18 10
normalized size 1 1. 1. 0.93 1.2 1.2 1. 1.2 0.67
time (sec) N/A 0.007 0.002 0.007 0.79 0.28 0.152 0.249 1.225
Problem 28 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 15 15 15 16 20 20 15 20 10
normalized size 1 1. 1. 1.07 1.33 1.33 1. 1.33 0.67
time (sec) N/A 0.008 0.002 0.006 0.784 0.27 0.156 0.252 1.535
Problem 29 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 19 19 19 14 18 18 10 18 10
normalized size 1 1. 1. 0.74 0.95 0.95 0.53 0.95 0.53
time (sec) N/A 0.011 0.004 0.033 0.788 0.275 0.152 0.259 1.049
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 131 131 99 99 120 119 0 130 129
normalized size 1 1. 0.76 0.76 0.92 0.91 0. 0.99 0.98
time (sec) N/A 0.243 0.097 0.158 0.82 0.275 0. 0.257 26.922
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 108 108 87 87 104 103 0 113 105
normalized size 1 1. 0.81 0.81 0.96 0.95 0. 1.05 0.97
time (sec) N/A 0.147 0.053 0.017 0.84 0.276 0. 0.261 19.77
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 85 85 75 75 88 86 0 97 82
normalized size 1 1. 0.88 0.88 1.04 1.01 0. 1.14 0.96
time (sec) N/A 0.11 0.042 0.016 0.847 0.28 0. 0.254 13.634
Problem 33 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 62 62 62 66 73 74 0 81 56
normalized size 1 1. 1. 1.06 1.18 1.19 0. 1.31 0.9
time (sec) N/A 0.075 0.032 0.014 0.822 0.276 0. 0.267 8.725
Problem 34 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 38 38 38 27 35 35 0 41 37
normalized size 1 1. 1. 0.71 0.92 0.92 0. 1.08 0.97
time (sec) N/A 0.044 0.007 0.019 0.796 0.269 0. 0.257 5.112
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 54 64 32 73 0 0 53
normalized size 1 1. 1. 1.19 0.59 1.35 0. 0. 0.98
time (sec) N/A 0.077 0.032 0.017 0.851 0.268 0. 0. 8.214
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 64 72 32 90 0 0 76
normalized size 1 1. 0.83 0.94 0.42 1.17 0. 0. 0.99
time (sec) N/A 0.106 0.065 0.019 0.836 0.277 0. 0. 11.79
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 100 100 76 84 32 107 0 0 100
normalized size 1 1. 0.76 0.84 0.32 1.07 0. 0. 1.
time (sec) N/A 0.139 0.08 0.02 0.836 0.27 0. 0. 15.763
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 123 123 92 96 32 123 0 0 124
normalized size 1 1. 0.75 0.78 0.26 1. 0. 0. 1.01
time (sec) N/A 0.175 0.053 0.02 0.838 0.269 0. 0. 20.711
Problem 39 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 208 208 239 0 240 306 0 1 202
normalized size 1 1. 1.15 0. 1.15 1.47 0. 0. 0.97
time (sec) N/A 0.445 0.779 0.026 0.821 0.31 0. 0.296 61.814
Problem 40 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 173 173 204 0 211 221 0 779 167
normalized size 1 1. 1.18 0. 1.22 1.28 0. 4.5 0.97
time (sec) N/A 0.262 0.439 0.027 0.835 0.269 0. 0.264 45.037
Problem 41 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 138 138 169 0 181 157 0 408 131
normalized size 1 1. 1.22 0. 1.31 1.14 0. 2.96 0.95
time (sec) N/A 0.198 0.333 0.026 0.816 0.27 0. 0.259 31.816
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 105 105 108 0 153 131 0 170 95
normalized size 1 1. 1.03 0. 1.46 1.25 0. 1.62 0.9
time (sec) N/A 0.137 0.187 0.024 0.851 0.258 0. 0.251 20.582
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 70 0 70 76 0 78 70
normalized size 1 1. 0.97 0. 0.97 1.06 0. 1.08 0.97
time (sec) N/A 0.084 0.076 0.029 0.862 0.259 0. 0.257 11.968
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F A A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 97 97 110 0 81 136 0 0 92
normalized size 1 1. 1.13 0. 0.84 1.4 0. 0. 0.95
time (sec) N/A 0.146 0.15 0.026 0.887 0.259 0. 0. 19.558
Problem 45 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 130 130 140 0 81 203 0 0 126
normalized size 1 1. 1.08 0. 0.62 1.56 0. 0. 0.97
time (sec) N/A 0.202 0.428 0.026 0.883 0.254 0. 0. 28.426
Problem 46 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 165 165 148 0 81 305 0 0 162
normalized size 1 1. 0.9 0. 0.49 1.85 0. 0. 0.98
time (sec) N/A 0.266 0.403 0.026 0.859 0.282 0. 0. 39.261
Problem 47 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 200 200 153 0 81 428 0 0 197
normalized size 1 1. 0.76 0. 0.4 2.14 0. 0. 0.98
time (sec) N/A 0.337 0.616 0.025 0.929 0.279 0. 0. 52.311
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 151 151 91 145 107 105 0 108 138
normalized size 1 1. 0.6 0.96 0.71 0.7 0. 0.72 0.91
time (sec) N/A 0.241 0.066 0.011 0.803 0.26 0. 0.253 30.593
Problem 49 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 71 71 63 0 81 151 0 0 71
normalized size 1 1. 0.89 0. 1.14 2.13 0. 0. 1.
time (sec) N/A 0.057 0.203 0.026 0.904 0.284 0. 0. 6.848
Problem 50 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 98 98 78 0 0 167 0 0 102
normalized size 1 1. 0.8 0. 0. 1.7 0. 0. 1.04
time (sec) N/A 0.17 0.302 0.093 0. 0.271 0. 0. 14.81
Problem 51 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 48 48 34 38 81 51 60 1 41
normalized size 1 1. 0.71 0.79 1.69 1.06 1.25 0.02 0.85
time (sec) N/A 0.038 0.023 0. 0.828 0.291 0.297 0.263 6.742
Problem 52 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 135 135 56 80 158 100 116 1 126
normalized size 1 1. 0.41 0.59 1.17 0.74 0.86 0.01 0.93
time (sec) N/A 0.193 0.049 0.004 0.858 0.307 0.384 0.253 23.661
Problem 53 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 229 229 84 138 262 165 190 1 223
normalized size 1 1. 0.37 0.6 1.14 0.72 0.83 0. 0.97
time (sec) N/A 0.35 0.078 0.006 0.822 0.268 0.487 0.289 38.517
Problem 54 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 348 348 117 212 393 246 284 1 347
normalized size 1 1. 0.34 0.61 1.13 0.71 0.82 0. 1.
time (sec) N/A 0.57 0.097 0.009 0.835 0.272 0.606 0.329 57.089
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 116 116 61 334 166 170 0 0 94
normalized size 1 1. 0.53 2.88 1.43 1.47 0. 0. 0.81
time (sec) N/A 0.29 0.1 0.13 1.181 0.271 0. 0. 25.023
Problem 56 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 397 397 121 182 265 163 236 273 371
normalized size 1 1. 0.3 0.46 0.67 0.41 0.59 0.69 0.93
time (sec) N/A 0.841 0.08 0.007 0.818 0.257 0.521 0.258 56.65
Problem 57 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 318 318 130 143 221 138 196 220 294
normalized size 1 1. 0.41 0.45 0.69 0.43 0.62 0.69 0.92
time (sec) N/A 0.656 0.037 0.009 0.796 0.263 0.464 0.275 47.551
Problem 58 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 184 184 96 102 178 105 148 166 168
normalized size 1 1. 0.52 0.55 0.97 0.57 0.8 0.9 0.91
time (sec) N/A 0.397 0.031 0.007 0.8 0.248 0.398 0.241 31.567
Problem 59 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 80 80 41 68 139 77 104 117 65
normalized size 1 1. 0.51 0.85 1.74 0.96 1.3 1.46 0.81
time (sec) N/A 0.111 0.016 0.006 0.837 0.242 0.355 0.25 11.973
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 102 102 52 113 93 68 0 128 92
normalized size 1 1. 0.51 1.11 0.91 0.67 0. 1.25 0.9
time (sec) N/A 0.274 0.026 0.01 0.847 0.261 0. 0.235 23.897
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 94 94 54 92 82 76 0 124 82
normalized size 1 1. 0.57 0.98 0.87 0.81 0. 1.32 0.87
time (sec) N/A 0.253 0.036 0.013 0.88 0.272 0. 0.263 21.576
Problem 62 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 130 130 68 112 86 95 133 169 116
normalized size 1 1. 0.52 0.86 0.66 0.73 1.02 1.3 0.89
time (sec) N/A 0.33 0.047 0.013 0.875 0.244 22.611 0.266 23.954
Problem 63 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 198 198 81 167 85 112 194 247 180
normalized size 1 1. 0.41 0.84 0.43 0.57 0.98 1.25 0.91
time (sec) N/A 0.46 0.08 0.012 0.855 0.253 28.621 0.265 30.665
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 139 139 86 433 166 217 0 0 148
normalized size 1 1. 0.62 3.12 1.19 1.56 0. 0. 1.06
time (sec) N/A 0.489 0.142 0.13 1.042 0.29 0. 0. 29.486
Problem 65 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 414 414 159 250 443 308 323 1 449
normalized size 1 1. 0.38 0.6 1.07 0.74 0.78 0. 1.08
time (sec) N/A 1.109 0.097 0.014 0.791 0.261 0.602 0.37 87.805
Problem 66 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 328 328 121 197 354 240 260 1 352
normalized size 1 1. 0.37 0.6 1.08 0.73 0.79 0. 1.07
time (sec) N/A 0.864 0.089 0.014 0.822 0.263 0.546 0.341 68.991
Problem 67 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 242 242 91 144 265 178 199 1 253
normalized size 1 1. 0.38 0.6 1.1 0.74 0.82 0. 1.05
time (sec) N/A 0.584 0.078 0.012 0.828 0.273 0.47 0.346 47.535
Problem 68 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 85 85 58 93 181 115 134 1 85
normalized size 1 1. 0.68 1.09 2.13 1.35 1.58 0.01 1.
time (sec) N/A 0.192 0.057 0.01 0.783 0.254 0.408 0.292 18.363
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 96 96 54 119 117 101 0 0 94
normalized size 1 1. 0.56 1.24 1.22 1.05 0. 0. 0.98
time (sec) N/A 0.407 0.098 0.033 0.81 0.264 0. 0. 24.085
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 85 85 58 129 92 112 0 0 87
normalized size 1 1. 0.68 1.52 1.08 1.32 0. 0. 1.02
time (sec) N/A 0.43 0.109 0.047 0.824 0.271 0. 0. 20.379
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 136 136 76 195 100 120 0 0 146
normalized size 1 1. 0.56 1.43 0.74 0.88 0. 0. 1.07
time (sec) N/A 0.562 0.076 0.055 0.852 0.284 0. 0. 25.395
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 217 217 116 275 115 185 0 0 230
normalized size 1 1. 0.53 1.27 0.53 0.85 0. 0. 1.06
time (sec) N/A 0.721 0.134 0.061 0.889 0.258 0. 0. 36.972
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 321 321 156 361 126 251 0 0 337
normalized size 1 1. 0.49 1.12 0.39 0.78 0. 0. 1.05
time (sec) N/A 0.908 0.199 0.069 0.84 0.263 0. 0. 50.17
Problem 74 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 754 754 458 1062 1207 734 1445 1 694
normalized size 1 1. 0.61 1.41 1.6 0.97 1.92 0. 0.92
time (sec) N/A 1.522 0.265 0.014 0.901 0.271 1.792 0.257 126.016
Problem 75 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 495 495 320 640 809 478 899 910 454
normalized size 1 1. 0.65 1.29 1.63 0.97 1.82 1.84 0.92
time (sec) N/A 1.047 0.172 0.008 0.793 0.251 1.215 0.255 83.493
Problem 76 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 271 271 191 297 464 266 447 447 246
normalized size 1 1. 0.7 1.1 1.71 0.98 1.65 1.65 0.91
time (sec) N/A 0.559 0.088 0.009 0.895 0.249 0.746 0.26 46.035
Problem 77 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 102 102 50 108 201 112 158 178 83
normalized size 1 1. 0.49 1.06 1.97 1.1 1.55 1.75 0.81
time (sec) N/A 0.154 0.024 0.007 0.855 0.237 0.429 0.259 16.162
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 277 277 175 489 0 317 0 240 238
normalized size 1 1. 0.63 1.77 0. 1.14 0. 0.87 0.86
time (sec) N/A 0.561 0.179 0.019 0. 0.25 0. 0.258 49.252
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 258 258 163 406 0 477 0 0 230
normalized size 1 1. 0.63 1.57 0. 1.85 0. 0. 0.89
time (sec) N/A 0.622 0.321 0.02 0. 0.267 0. 0. 63.1
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 294 294 267 418 0 743 0 1 258
normalized size 1 1. 0.91 1.42 0. 2.53 0. 0. 0.88
time (sec) N/A 0.683 0.72 0.02 0. 0.245 0. 0.245 69.932
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 396 396 389 511 0 1071 0 1 347
normalized size 1 1. 0.98 1.29 0. 2.7 0. 0. 0.88
time (sec) N/A 0.859 0.872 0.019 0. 0.272 0. 0.255 87.598
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 557 557 669 596 0 1463 0 0 493
normalized size 1 1. 1.2 1.07 0. 2.63 0. 0. 0.89
time (sec) N/A 1.152 0.707 0.019 0. 0.269 0. 0. 112.574
Problem 83 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 24 24 24 0 57 43 0 0 22
normalized size 1 1. 1. 0. 2.38 1.79 0. 0. 0.92
time (sec) N/A 0.221 0.117 0.098 0.966 0.26 0. 0. 11.118
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A F(-2) F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 22 22 23 198 57 0 0 0 20
normalized size 1 1. 1.05 9. 2.59 0. 0. 0. 0.91
time (sec) N/A 0.193 0.05 0.158 0.933 0. 0. 0. 11.126
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A F(-2) F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 22 22 23 198 57 0 0 0 20
normalized size 1 1. 1.05 9. 2.59 0. 0. 0. 0.91
time (sec) N/A 0.132 0.046 0.116 0.957 0. 0. 0. 8.157
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A F(-2) F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 20 20 21 186 51 0 0 0 19
normalized size 1 1. 1.05 9.3 2.55 0. 0. 0. 0.95
time (sec) N/A 0.07 0.043 0.139 0.95 0. 0. 0. 7.743
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A F(-2) F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 19 19 20 180 49 0 0 0 17
normalized size 1 1. 1.05 9.47 2.58 0. 0. 0. 0.89
time (sec) N/A 0.19 0.039 0.105 0.965 0. 0. 0. 15.164
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A F(-2) F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 22 22 23 136 53 0 0 0 19
normalized size 1 1. 1.05 6.18 2.41 0. 0. 0. 0.86
time (sec) N/A 0.198 0.064 0.128 0.968 0. 0. 0. 11.161
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A F(-2) F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 22 22 23 136 53 0 0 0 20
normalized size 1 1. 1.05 6.18 2.41 0. 0. 0. 0.91
time (sec) N/A 0.196 0.063 0.128 0.971 0. 0. 0. 11.181
Problem 90 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 91 91 45 43 81 58 51 58 85
normalized size 1 1. 0.49 0.47 0.89 0.64 0.56 0.64 0.93
time (sec) N/A 0.213 0.014 0.006 0.751 0.247 0.23 0.236 12.855
Problem 91 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 72 72 37 35 65 47 42 47 66
normalized size 1 1. 0.51 0.49 0.9 0.65 0.58 0.65 0.92
time (sec) N/A 0.152 0.011 0.006 0.835 0.26 0.218 0.25 9.152
Problem 92 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 53 53 29 27 49 36 34 36 48
normalized size 1 1. 0.55 0.51 0.92 0.68 0.64 0.68 0.91
time (sec) N/A 0.097 0.009 0.006 0.778 0.249 0.2 0.239 5.879
Problem 93 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 21 19 32 26 26 26 29
normalized size 1 1. 0.62 0.56 0.94 0.76 0.76 0.76 0.85
time (sec) N/A 0.043 0.006 0.003 0.772 0.245 0.176 0.252 3.054
Problem 94 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 16 16 16 14 19 19 14 19 12
normalized size 1 1. 1. 0.88 1.19 1.19 0.88 1.19 0.75
time (sec) N/A 0.013 0.003 0.003 0.787 0.248 0.137 0.238 1.193
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 27 27 27 57 14 14 0 14 32
normalized size 1 1. 1. 2.11 0.52 0.52 0. 0.52 1.19
time (sec) N/A 0.088 0.007 0.088 0.848 0.262 0. 0.231 5.481
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 48 48 47 116 18 39 0 39 48
normalized size 1 1. 0.98 2.42 0.38 0.81 0. 0.81 1.
time (sec) N/A 0.134 0.019 0.033 0.848 0.25 0. 0.243 7.81
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 56 155 20 51 0 62 68
normalized size 1 1. 0.79 2.18 0.28 0.72 0. 0.87 0.96
time (sec) N/A 0.18 0.031 0.043 0.832 0.244 0. 0.238 10.422
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 92 92 64 189 20 62 0 85 87
normalized size 1 1. 0.7 2.05 0.22 0.67 0. 0.92 0.95
time (sec) N/A 0.234 0.039 0.046 0.831 0.235 0. 0.264 13.476

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 [48] had the largest ratio of [ 0.25 ]

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 1 1 1. 17 0.059
2 A 5 2 1. 17 0.118
3 A 4 2 1. 17 0.118
4 A 3 2 1. 17 0.118
5 A 2 2 1. 15 0.133
6 A 1 1 1. 9 0.111
7 A 1 1 1. 17 0.059
8 A 2 2 1. 17 0.118
9 A 3 2 1. 17 0.118
10 A 4 2 1. 17 0.118
11 A 5 2 1. 17 0.118
12 A 6 3 1. 48 0.062
13 A 5 3 1. 37 0.081
14 A 4 3 1. 26 0.115
15 A 3 3 1. 28 0.107
16 A 4 3 1. 39 0.077
17 A 5 3 1. 50 0.06
18 A 6 3 1. 61 0.049
19 A 2 2 1. 19 0.105
20 A 2 2 1. 50 0.04
21 A 2 2 1. 39 0.051
22 A 2 2 1. 28 0.071
23 A 1 1 1. 17 0.059
24 A 1 1 1. 19 0.053
25 A 2 2 1. 30 0.067
26 A 2 2 1. 41 0.049
27 A 1 1 1. 7 0.143
28 A 1 1 1. 7 0.143
29 A 1 1 1. 7 0.143
30 A 6 3 1. 13 0.231
31 A 5 3 1. 13 0.231
32 A 4 3 1. 13 0.231
33 A 3 3 1. 13 0.231
34 A 2 2 1. 13 0.154
35 A 3 3 1. 13 0.231
36 A 4 3 1. 13 0.231
37 A 5 3 1. 13 0.231
38 A 6 3 1. 13 0.231
39 A 6 3 1. 19 0.158
40 A 5 3 1. 19 0.158
41 A 4 3 1. 19 0.158
42 A 3 3 1. 19 0.158
43 A 2 2 1. 19 0.105
44 A 3 3 1. 19 0.158
45 A 4 3 1. 19 0.158
46 A 5 3 1. 19 0.158
47 A 6 3 1. 19 0.158
48 A 9 3 1. 12 0.25
49 A 1 1 1. 19 0.053
50 A 2 2 1. 21 0.095
51 A 2 2 1. 15 0.133
52 A 8 3 1. 20 0.15
53 A 12 3 1. 25 0.12
54 A 17 3 1. 30 0.1
55 A 6 2 1. 21 0.095
56 A 24 3 1. 21 0.143
57 A 20 3 1. 21 0.143
58 A 11 3 1. 19 0.158
59 A 4 2 1. 18 0.111
60 A 9 4 1. 21 0.19
61 A 8 5 1. 21 0.238
62 A 9 4 1. 21 0.19
63 A 12 3 1. 21 0.143
64 A 5 2 1. 22 0.091
65 A 17 3 1. 22 0.136
66 A 14 3 1. 22 0.136
67 A 11 3 1. 20 0.15
68 A 4 3 1. 19 0.158
69 A 6 4 1. 22 0.182
70 A 6 4 1. 22 0.182
71 A 8 3 1. 22 0.136
72 A 11 3 1. 22 0.136
73 A 14 3 1. 22 0.136
74 A 28 3 1. 25 0.12
75 A 20 3 1. 25 0.12
76 A 13 3 1. 23 0.13
77 A 5 2 1. 18 0.111
78 A 13 4 1. 25 0.16
79 A 11 5 1. 25 0.2
80 A 11 5 1. 25 0.2
81 A 13 4 1. 25 0.16
82 A 17 3 1. 25 0.12
83 A 1 1 1. 39 0.026
84 A 1 1 1. 38 0.026
85 A 1 1 1. 36 0.028
86 A 1 1 1. 35 0.029
87 A 1 1 1. 35 0.029
88 A 1 1 1. 38 0.026
89 A 1 1 1. 38 0.026
90 A 5 2 1. 15 0.133
91 A 4 2 1. 15 0.133
92 A 3 2 1. 15 0.133
93 A 2 2 1. 13 0.154
94 A 1 1 1. 11 0.091
95 A 2 2 1. 15 0.133
96 A 3 3 1. 15 0.2
97 A 4 3 1. 15 0.2
98 A 5 3 1. 15 0.2

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