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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 A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 127 127 100 115 0 1 192 126 114
normalized size 1 1. 0.79 0.91 0. 0.01 1.51 0.99 0.9
time (sec) N/A 0.312 0.119 0.011 0. 0.266 10.285 0.215 27.581
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 104 104 88 94 0 1 165 109 94
normalized size 1 1. 0.85 0.9 0. 0.01 1.59 1.05 0.9
time (sec) N/A 0.192 0.092 0.009 0. 0.268 6.905 0.218 15.769
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 80 80 79 75 0 1 124 92 70
normalized size 1 1. 0.99 0.94 0. 0.01 1.55 1.15 0.88
time (sec) N/A 0.094 0.07 0.007 0. 0.259 6.511 0.223 8.708
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 67 67 67 53 0 1 70 74 58
normalized size 1 1. 1. 0.79 0. 0.01 1.04 1.1 0.87
time (sec) N/A 0.064 0.058 0.007 0. 0.263 3.742 0.231 7.015
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 91 78 0 1 107 105 70
normalized size 1 1. 1.15 0.99 0. 0.01 1.35 1.33 0.89
time (sec) N/A 0.213 0.099 0.008 0. 0.285 5.413 0.23 20.151
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 75 75 87 97 0 1 124 138 65
normalized size 1 1. 1.16 1.29 0. 0.01 1.65 1.84 0.87
time (sec) N/A 0.205 0.084 0.011 0. 0.273 4.835 0.233 18.678
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 80 80 96 121 0 1 107 220 73
normalized size 1 1. 1.2 1.51 0. 0.01 1.34 2.75 0.91
time (sec) N/A 0.21 0.17 0.013 0. 0.275 5.66 0.231 21.717
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 150 150 119 134 0 1 318 155 139
normalized size 1 1. 0.79 0.89 0. 0.01 2.12 1.03 0.93
time (sec) N/A 0.327 0.143 0.012 0. 0.28 24.549 0.229 30.291
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 127 127 108 113 0 1 287 139 114
normalized size 1 1. 0.85 0.89 0. 0.01 2.26 1.09 0.9
time (sec) N/A 0.209 0.129 0.01 0. 0.261 16.405 0.222 17.954
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 103 103 100 94 0 1 223 120 90
normalized size 1 1. 0.97 0.91 0. 0.01 2.17 1.17 0.87
time (sec) N/A 0.113 0.114 0.007 0. 0.277 15.408 0.224 10.622
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 87 87 88 69 0 1 219 103 80
normalized size 1 1. 1.01 0.79 0. 0.01 2.52 1.18 0.92
time (sec) N/A 0.076 0.082 0.006 0. 0.264 9.32 0.223 8.661
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 106 106 112 107 0 1 218 135 97
normalized size 1 1. 1.06 1.01 0. 0.01 2.06 1.27 0.92
time (sec) N/A 0.311 0.166 0.008 0. 0.275 11.205 0.225 35.657
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 108 108 113 126 0 1 184 167 97
normalized size 1 1. 1.05 1.17 0. 0.01 1.7 1.55 0.9
time (sec) N/A 0.306 0.155 0.011 0. 0.283 7.99 0.229 30.454
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 111 111 113 150 0 1 182 258 109
normalized size 1 1. 1.02 1.35 0. 0.01 1.64 2.32 0.98
time (sec) N/A 0.292 0.181 0.01 0. 0.274 10.089 0.23 28.355
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 173 173 138 153 0 1 469 189 162
normalized size 1 1. 0.8 0.88 0. 0.01 2.71 1.09 0.94
time (sec) N/A 0.356 0.176 0.012 0. 0.282 46.672 0.229 34.775
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 150 150 126 132 0 1 442 173 139
normalized size 1 1. 0.84 0.88 0. 0.01 2.95 1.15 0.93
time (sec) N/A 0.23 0.154 0.008 0. 0.271 32.261 0.225 20.682
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 126 126 119 113 0 1 354 154 116
normalized size 1 1. 0.94 0.9 0. 0.01 2.81 1.22 0.92
time (sec) N/A 0.132 0.146 0.007 0. 0.268 30.001 0.231 13.41
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 107 107 108 85 0 1 348 136 100
normalized size 1 1. 1.01 0.79 0. 0.01 3.25 1.27 0.93
time (sec) N/A 0.098 0.137 0.006 0. 0.266 18.919 0.217 10.549
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 132 132 132 138 0 1 323 169 121
normalized size 1 1. 1. 1.05 0. 0.01 2.45 1.28 0.92
time (sec) N/A 0.414 0.251 0.009 0. 0.283 21.391 0.22 50.353
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 136 136 135 158 0 1 318 203 124
normalized size 1 1. 0.99 1.16 0. 0.01 2.34 1.49 0.91
time (sec) N/A 0.405 0.224 0.013 0. 0.286 15.052 0.225 45.502
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 141 141 135 181 0 1 279 296 136
normalized size 1 1. 0.96 1.28 0. 0.01 1.98 2.1 0.96
time (sec) N/A 0.398 0.25 0.013 0. 0.275 16.783 0.236 42.957
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 104 104 79 96 0 1 150 100 94
normalized size 1 1. 0.76 0.92 0. 0.01 1.44 0.96 0.9
time (sec) N/A 0.278 0.104 0.011 0. 0.261 8.067 0.227 24.688
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 81 81 67 75 0 1 94 82 73
normalized size 1 1. 0.83 0.93 0. 0.01 1.16 1.01 0.9
time (sec) N/A 0.17 0.068 0.009 0. 0.267 4.991 0.227 14.725
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 56 56 61 55 0 1 70 68 48
normalized size 1 1. 1.09 0.98 0. 0.02 1.25 1.21 0.86
time (sec) N/A 0.08 0.054 0.006 0. 0.262 4.575 0.219 7.393
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 43 43 46 37 0 1 102 53 37
normalized size 1 1. 1.07 0.86 0. 0.02 2.37 1.23 0.86
time (sec) N/A 0.048 0.032 0.007 0. 0.269 1.351 0.228 6.197
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 67 52 0 1 99 78 48
normalized size 1 1. 1.26 0.98 0. 0.02 1.87 1.47 0.91
time (sec) N/A 0.133 0.057 0.01 0. 0.294 2.548 0.223 11.299
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 47 47 58 49 0 1 41 88 39
normalized size 1 1. 1.23 1.04 0. 0.02 0.87 1.87 0.83
time (sec) N/A 0.122 0.068 0.01 0. 0.255 3.017 0.218 9.292
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 72 68 0 1 66 197 60
normalized size 1 1. 1. 0.94 0. 0.01 0.92 2.74 0.83
time (sec) N/A 0.193 0.08 0.012 0. 0.273 5.068 0.225 15.156
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 81 81 75 93 0 1 117 95 78
normalized size 1 1. 0.93 1.15 0. 0.01 1.44 1.17 0.96
time (sec) N/A 0.175 0.139 0.01 0. 0.272 9.077 0.222 16.402
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 66 66 60 72 0 1 83 78 65
normalized size 1 1. 0.91 1.09 0. 0.02 1.26 1.18 0.98
time (sec) N/A 0.137 0.105 0.009 0. 0.261 6.064 0.22 14.708
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 48 48 53 54 0 1 66 65 41
normalized size 1 1. 1.1 1.12 0. 0.02 1.38 1.35 0.85
time (sec) N/A 0.074 0.06 0.006 0. 0.26 5.964 0.219 7.
Problem 32 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 27 26 42 47 46 31 22
normalized size 1 1. 0.96 0.93 1.5 1.68 1.64 1.11 0.79
time (sec) N/A 0.033 0.028 0.005 1.343 0.265 4.233 0.215 4.261
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 47 47 58 60 0 1 206 80 39
normalized size 1 1. 1.23 1.28 0. 0.02 4.38 1.7 0.83
time (sec) N/A 0.135 0.102 0.01 0. 0.26 6.89 0.217 13.437
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 70 70 73 80 0 1 235 130 60
normalized size 1 1. 1.04 1.14 0. 0.01 3.36 1.86 0.86
time (sec) N/A 0.213 0.161 0.013 0. 0.264 9.374 0.223 20.015
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 95 95 83 101 0 1 124 231 88
normalized size 1 1. 0.87 1.06 0. 0.01 1.31 2.43 0.93
time (sec) N/A 0.304 0.266 0.011 0. 0.269 13.087 0.22 31.506
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 73 91 0 1 400 95 73
normalized size 1 1. 0.92 1.15 0. 0.01 5.06 1.2 0.92
time (sec) N/A 0.163 0.153 0.012 0. 0.27 22.728 0.229 16.12
Problem 37 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 44 41 95 85 141 49 46
normalized size 1 1. 0.83 0.77 1.79 1.6 2.66 0.92 0.87
time (sec) N/A 0.095 0.052 0.009 1.359 0.256 19.12 0.219 6.834
Problem 38 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 47 47 32 29 69 66 95 35 36
normalized size 1 1. 0.68 0.62 1.47 1.4 2.02 0.74 0.77
time (sec) N/A 0.072 0.04 0.004 1.331 0.266 18.796 0.217 5.806
Problem 39 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 51 51 43 40 65 84 146 50 42
normalized size 1 1. 0.84 0.78 1.27 1.65 2.86 0.98 0.82
time (sec) N/A 0.043 0.039 0.004 1.334 0.248 18.697 0.216 5.173
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 76 76 79 92 0 1 840 111 65
normalized size 1 1. 1.04 1.21 0. 0.01 11.05 1.46 0.86
time (sec) N/A 0.219 0.296 0.008 0. 0.257 29.072 0.221 26.638
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 104 104 95 112 0 1 910 161 88
normalized size 1 1. 0.91 1.08 0. 0.01 8.75 1.55 0.85
time (sec) N/A 0.304 0.219 0.014 0. 0.281 41.41 0.219 35.014
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 129 129 103 134 0 1 1034 266 119
normalized size 1 1. 0.8 1.04 0. 0.01 8.02 2.06 0.92
time (sec) N/A 0.405 0.355 0.012 0. 0.267 55.756 0.222 48.73
Problem 43 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 27 27 24 29 38 123 24 26 29
normalized size 1 1. 0.89 1.07 1.41 4.56 0.89 0.96 1.07
time (sec) N/A 0.046 0.034 0.01 1.504 0.252 0.274 0.213 5.943
Problem 44 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 27 27 24 29 38 123 24 26 29
normalized size 1 1. 0.89 1.07 1.41 4.56 0.89 0.96 1.07
time (sec) N/A 0.05 0.013 0.007 1.494 0.231 0.268 0.219 7.12
Problem 45 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 33 15 30 35 27 41 17
normalized size 1 1. 1.94 0.88 1.76 2.06 1.59 2.41 1.
time (sec) N/A 0.022 0.017 0.003 1.483 0.227 0.077 0.213 4.406
Problem 46 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 6 6 6 7 8 8 5 8 5
normalized size 1 1. 1. 1.17 1.33 1.33 0.83 1.33 0.83
time (sec) N/A 0.015 0.007 0.003 1.502 0.229 0.073 0.209 4.391
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 213 213 157 265 0 1 0 275 192
normalized size 1 1. 0.74 1.24 0. 0. 0. 1.29 0.9
time (sec) N/A 0.818 0.299 0.049 0. 0.293 0. 0.228 59.165
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 150 150 127 277 0 1 0 186 133
normalized size 1 1. 0.85 1.85 0. 0.01 0. 1.24 0.89
time (sec) N/A 0.431 0.311 0.018 0. 0.283 0. 0.222 42.434
Problem 49 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 132 132 89 95 324 185 0 151 117
normalized size 1 1. 0.67 0.72 2.45 1.4 0. 1.14 0.89
time (sec) N/A 0.383 0.13 0.009 1.361 0.263 0. 0.231 27.021
Problem 50 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 149 149 78 76 342 165 0 109 128
normalized size 1 1. 0.52 0.51 2.3 1.11 0. 0.73 0.86
time (sec) N/A 0.446 0.121 0.009 1.372 0.278 0. 0.217 31.039
Problem 51 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 139 139 84 85 242 177 0 128 124
normalized size 1 1. 0.6 0.61 1.74 1.27 0. 0.92 0.89
time (sec) N/A 0.359 0.096 0.011 1.385 0.286 0. 0.223 29.082
Problem 52 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 139 139 87 88 266 181 0 127 126
normalized size 1 1. 0.63 0.63 1.91 1.3 0. 0.91 0.91
time (sec) N/A 0.297 0.108 0.009 1.362 0.312 0. 0.219 23.569
Problem 53 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 119 119 75 73 166 161 0 111 107
normalized size 1 1. 0.63 0.61 1.39 1.35 0. 0.93 0.9
time (sec) N/A 0.182 0.078 0.008 1.35 0.361 0. 0.22 21.33
Problem 54 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 127 127 92 96 207 185 0 151 110
normalized size 1 1. 0.72 0.76 1.63 1.46 0. 1.19 0.87
time (sec) N/A 0.153 0.092 0.007 1.484 0.343 0. 0.221 13.633
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 138 138 131 169 0 1 0 205 121
normalized size 1 1. 0.95 1.22 0. 0.01 0. 1.49 0.88
time (sec) N/A 0.418 0.791 0.011 0. 0.328 0. 0.224 61.402
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 188 188 158 240 0 1 0 323 163
normalized size 1 1. 0.84 1.28 0. 0.01 0. 1.72 0.87
time (sec) N/A 0.698 0.348 0.014 0. 0.334 0. 0.224 72.815
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 219 219 183 288 0 1 0 439 207
normalized size 1 1. 0.84 1.32 0. 0. 0. 2. 0.95
time (sec) N/A 0.867 0.492 0.016 0. 0.379 0. 0.231 85.828
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 43 0 0 0 97 0 34
normalized size 1 1. 0.96 0. 0. 0. 2.16 0. 0.76
time (sec) N/A 0.055 0.026 0.039 0. 0. 2.261 0. 7.129
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 91 91 82 0 0 0 192 0 68
normalized size 1 1. 0.9 0. 0. 0. 2.11 0. 0.75
time (sec) N/A 0.136 0.082 0.045 0. 0. 6.034 0. 15.158
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 76 76 58 0 0 0 204 0 56
normalized size 1 1. 0.76 0. 0. 0. 2.68 0. 0.74
time (sec) N/A 0.124 0.068 0.047 0. 0. 7.888 0. 14.362
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 121 121 100 0 0 0 298 0 90
normalized size 1 1. 0.83 0. 0. 0. 2.46 0. 0.74
time (sec) N/A 0.279 0.104 0.047 0. 0. 9.679 0. 39.393
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 65 65 65 54 72 1 60 77 60
normalized size 1 1. 1. 0.83 1.11 0.02 0.92 1.18 0.92
time (sec) N/A 0.147 0.029 0.004 1.353 0.251 0.053 0.211 22.387
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 65 65 65 54 72 1 60 77 60
normalized size 1 1. 1. 0.83 1.11 0.02 0.92 1.18 0.92
time (sec) N/A 0.148 0.03 0.002 1.347 0.258 0.053 0.213 25.708
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 65 65 65 54 72 1 60 77 0
normalized size 1 1. 1. 0.83 1.11 0.02 0.92 1.18 0.
time (sec) N/A 0.123 0.019 0.002 1.351 0.228 0.052 0.212 0.
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 60 60 60 51 68 1 56 73 0
normalized size 1 1. 1. 0.85 1.13 0.02 0.93 1.22 0.
time (sec) N/A 0.091 0.017 0.003 1.345 0.228 0.05 0.218 0.
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 56 56 56 53 65 65 54 72 0
normalized size 1 1. 1. 0.95 1.16 1.16 0.96 1.29 0.
time (sec) N/A 0.081 0.03 0.006 1.345 0.247 0.597 0.226 0.
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 54 50 65 74 49 68 0
normalized size 1 1. 1. 0.93 1.2 1.37 0.91 1.26 0.
time (sec) N/A 0.099 0.059 0.01 1.347 0.257 0.623 0.215 0.
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 51 48 65 74 49 65 0
normalized size 1 1. 0.94 0.89 1.2 1.37 0.91 1.2 0.
time (sec) N/A 0.099 0.052 0.009 1.346 0.264 0.851 0.215 0.
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 55 51 66 74 53 68 0
normalized size 1 1. 1.02 0.94 1.22 1.37 0.98 1.26 0.
time (sec) N/A 0.1 0.033 0.01 1.348 0.223 1.687 0.212 0.
Problem 70 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 109 109 98 102 136 1 110 142 100
normalized size 1 1. 0.9 0.94 1.25 0.01 1.01 1.3 0.92
time (sec) N/A 0.259 0.085 0.003 1.347 0.206 0.074 0.208 35.627
Problem 71 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 109 109 92 102 136 1 110 142 100
normalized size 1 1. 0.84 0.94 1.25 0.01 1.01 1.3 0.92
time (sec) N/A 0.258 0.097 0.002 1.334 0.203 0.074 0.239 39.589
Problem 72 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 104 104 92 102 136 1 110 142 94
normalized size 1 1. 0.88 0.98 1.31 0.01 1.06 1.37 0.9
time (sec) N/A 0.317 0.096 0.003 1.346 0.205 0.073 0.221 40.116
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 99 99 88 99 132 1 107 138 0
normalized size 1 1. 0.89 1. 1.33 0.01 1.08 1.39 0.
time (sec) N/A 0.183 0.084 0.001 1.336 0.2 0.071 0.222 0.
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 92 92 88 100 130 130 104 135 0
normalized size 1 1. 0.96 1.09 1.41 1.41 1.13 1.47 0.
time (sec) N/A 0.152 0.096 0.005 1.349 0.221 0.722 0.23 0.
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 90 90 88 98 130 139 99 132 0
normalized size 1 1. 0.98 1.09 1.44 1.54 1.1 1.47 0.
time (sec) N/A 0.198 0.139 0.01 1.356 0.223 0.758 0.224 0.
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 98 98 87 97 130 139 99 131 0
normalized size 1 1. 0.89 0.99 1.33 1.42 1.01 1.34 0.
time (sec) N/A 0.186 0.085 0.01 1.351 0.219 1.029 0.223 0.
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 98 98 83 97 131 139 99 131 0
normalized size 1 1. 0.85 0.99 1.34 1.42 1.01 1.34 0.
time (sec) N/A 0.188 0.103 0.011 1.355 0.234 1.986 0.226 0.
Problem 78 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 149 149 149 150 196 1 163 207 139
normalized size 1 1. 1. 1.01 1.32 0.01 1.09 1.39 0.93
time (sec) N/A 0.373 0.058 0.002 1.347 0.202 0.086 0.222 46.281
Problem 79 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 149 149 125 150 196 1 165 207 141
normalized size 1 1. 0.84 1.01 1.32 0.01 1.11 1.39 0.95
time (sec) N/A 0.368 0.155 0.002 1.353 0.208 0.087 0.223 50.038
Problem 80 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 138 138 124 150 196 1 163 207 129
normalized size 1 1. 0.9 1.09 1.42 0.01 1.18 1.5 0.93
time (sec) N/A 0.405 0.146 0.003 1.386 0.199 0.086 0.239 46.683
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 133 133 121 147 192 1 158 201 0
normalized size 1 1. 0.91 1.11 1.44 0.01 1.19 1.51 0.
time (sec) N/A 0.25 0.138 0.003 1.427 0.197 0.085 0.222 0.
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 129 129 121 148 189 189 158 200 0
normalized size 1 1. 0.94 1.15 1.47 1.47 1.22 1.55 0.
time (sec) N/A 0.198 0.205 0.006 1.332 0.229 0.872 0.221 0.
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 124 124 123 145 188 198 150 196 0
normalized size 1 1. 0.99 1.17 1.52 1.6 1.21 1.58 0.
time (sec) N/A 0.266 0.272 0.01 1.34 0.227 0.903 0.222 0.
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 135 135 124 144 188 198 150 194 0
normalized size 1 1. 0.92 1.07 1.39 1.47 1.11 1.44 0.
time (sec) N/A 0.284 0.143 0.011 1.345 0.224 1.199 0.221 0.
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 139 139 124 146 192 198 153 197 0
normalized size 1 1. 0.89 1.05 1.38 1.42 1.1 1.42 0.
time (sec) N/A 0.284 0.138 0.011 1.363 0.229 2.157 0.223 0.
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 151 151 130 176 0 1 308 217 0
normalized size 1 1. 0.86 1.17 0. 0.01 2.04 1.44 0.
time (sec) N/A 0.325 0.156 0.008 0. 0.263 2.079 0.222 0.
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 130 130 114 152 0 1 269 185 0
normalized size 1 1. 0.88 1.17 0. 0.01 2.07 1.42 0.
time (sec) N/A 0.278 0.21 0.008 0. 0.258 2.047 0.223 0.
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 111 111 95 128 0 1 243 151 0
normalized size 1 1. 0.86 1.15 0. 0.01 2.19 1.36 0.
time (sec) N/A 0.249 0.102 0.007 0. 0.272 1.907 0.22 0.
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 92 92 81 106 0 1 211 119 0
normalized size 1 1. 0.88 1.15 0. 0.01 2.29 1.29 0.
time (sec) N/A 0.21 0.124 0.006 0. 0.239 1.803 0.238 0.
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 73 73 68 83 0 1 219 89 0
normalized size 1 1. 0.93 1.14 0. 0.01 3. 1.22 0.
time (sec) N/A 0.161 0.075 0.005 0. 0.233 1.791 0.237 0.
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 73 80 0 1 1268 89 0
normalized size 1 1. 1.01 1.11 0. 0.01 17.61 1.24 0.
time (sec) N/A 0.21 0.099 0.009 0. 0.271 39.118 0.225 0.
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 76 76 75 83 0 1 1258 92 61
normalized size 1 1. 0.99 1.09 0. 0.01 16.55 1.21 0.8
time (sec) N/A 0.206 0.096 0.012 0. 0.265 36.148 0.242 36.99
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 92 92 84 102 0 1 1686 108 76
normalized size 1 1. 0.91 1.11 0. 0.01 18.33 1.17 0.83
time (sec) N/A 0.238 0.145 0.011 0. 0.282 39.141 0.227 43.292
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 176 176 139 201 0 1 333 215 0
normalized size 1 1. 0.79 1.14 0. 0.01 1.89 1.22 0.
time (sec) N/A 0.553 0.24 0.013 0. 0.234 7.293 0.225 0.
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 154 154 128 177 0 1 287 177 0
normalized size 1 1. 0.83 1.15 0. 0.01 1.86 1.15 0.
time (sec) N/A 0.501 0.144 0.013 0. 0.239 6.904 0.223 0.
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 134 134 100 154 0 1 284 150 0
normalized size 1 1. 0.75 1.15 0. 0.01 2.12 1.12 0.
time (sec) N/A 0.478 0.148 0.013 0. 0.24 6.562 0.224 0.
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 101 101 92 127 0 1 212 109 83
normalized size 1 1. 0.91 1.26 0. 0.01 2.1 1.08 0.82
time (sec) N/A 0.255 0.1 0.013 0. 0.241 5.397 0.221 32.492
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 93 93 83 100 0 1 233 119 75
normalized size 1 1. 0.89 1.08 0. 0.01 2.51 1.28 0.81
time (sec) N/A 0.146 0.165 0.017 0. 0.235 4.377 0.24 32.482
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 95 95 85 127 0 1 797 126 85
normalized size 1 1. 0.89 1.34 0. 0.01 8.39 1.33 0.89
time (sec) N/A 0.269 0.144 0.019 0. 0.263 14.503 0.236 43.913
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 110 110 110 136 0 1 782 139 92
normalized size 1 1. 1. 1.24 0. 0.01 7.11 1.26 0.84
time (sec) N/A 0.283 0.134 0.018 0. 0.265 15.886 0.241 44.248
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 135 135 112 169 0 1 1807 170 105
normalized size 1 1. 0.83 1.25 0. 0.01 13.39 1.26 0.78
time (sec) N/A 0.413 0.216 0.02 0. 0.287 60.91 0.227 51.695
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 185 185 139 235 0 1 357 212 0
normalized size 1 1. 0.75 1.27 0. 0.01 1.93 1.15 0.
time (sec) N/A 0.713 0.235 0.017 0. 0.236 41.516 0.247 0.
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 155 155 126 206 0 1 282 165 131
normalized size 1 1. 0.81 1.33 0. 0.01 1.82 1.06 0.85
time (sec) N/A 0.494 0.151 0.015 0. 0.242 38.268 0.228 133.624
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 136 136 122 138 0 1 303 173 114
normalized size 1 1. 0.9 1.01 0. 0.01 2.23 1.27 0.84
time (sec) N/A 0.357 0.205 0.019 0. 0.238 33.89 0.227 100.162
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 119 119 99 110 0 1 177 131 88
normalized size 1 1. 0.83 0.92 0. 0.01 1.49 1.1 0.74
time (sec) N/A 0.25 0.204 0.013 0. 0.239 25.825 0.223 31.224
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 116 116 104 111 0 1 184 143 100
normalized size 1 1. 0.9 0.96 0. 0.01 1.59 1.23 0.86
time (sec) N/A 0.173 0.2 0.012 0. 0.238 16.448 0.22 34.503
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 130 130 117 186 0 1 872 173 121
normalized size 1 1. 0.9 1.43 0. 0.01 6.71 1.33 0.93
time (sec) N/A 0.341 0.212 0.019 0. 0.267 30.494 0.228 63.886
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 144 144 141 195 0 1 860 190 124
normalized size 1 1. 0.98 1.35 0. 0.01 5.97 1.32 0.86
time (sec) N/A 0.446 0.183 0.023 0. 0.251 37.928 0.226 71.766
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 174 174 147 250 0 1 1904 219 136
normalized size 1 1. 0.84 1.44 0. 0.01 10.94 1.26 0.78
time (sec) N/A 0.628 0.322 0.024 0. 0.3 96.732 0.225 74.116
Problem 110 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 20 19 24 32 15 34 15
normalized size 1 1. 1. 0.95 1.2 1.6 0.75 1.7 0.75
time (sec) N/A 0.05 0.013 0.014 1.347 0.223 0.097 0.22 9.174
Problem 111 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 23 23 18 15 30 93 22 23 17
normalized size 1 1. 0.78 0.65 1.3 4.04 0.96 1. 0.74
time (sec) N/A 0.053 0.012 0.008 1.329 0.237 0.48 0.215 7.203
Problem 112 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 25 25 25 21 27 34 20 27 20
normalized size 1 1. 1. 0.84 1.08 1.36 0.8 1.08 0.8
time (sec) N/A 0.059 0.019 0.005 1.504 0.22 0.086 0.221 11.698
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 30 30 30 25 32 32 22 32 0
normalized size 1 1. 1. 0.83 1.07 1.07 0.73 1.07 0.
time (sec) N/A 0.06 0.009 0.004 1.496 0.225 0.091 0.222 0.
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 210 210 210 278 0 1 366 338 0
normalized size 1 1. 1. 1.32 0. 0. 1.74 1.61 0.
time (sec) N/A 0.347 0.292 0.006 0. 0.231 1.776 0.224 0.
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 172 172 162 230 0 1 325 270 0
normalized size 1 1. 0.94 1.34 0. 0.01 1.89 1.57 0.
time (sec) N/A 0.262 0.258 0.004 0. 0.238 2.254 0.222 0.
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 136 136 128 182 0 1 180 205 0
normalized size 1 1. 0.94 1.34 0. 0.01 1.32 1.51 0.
time (sec) N/A 0.216 0.192 0.004 0. 0.231 1.575 0.22 0.
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 100 100 98 135 0 1 158 143 0
normalized size 1 1. 0.98 1.35 0. 0.01 1.58 1.43 0.
time (sec) N/A 0.14 0.161 0.005 0. 0.233 1.608 0.218 0.
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 84 84 83 114 0 1 150 116 0
normalized size 1 1. 0.99 1.36 0. 0.01 1.79 1.38 0.
time (sec) N/A 0.187 0.129 0.008 0. 0.233 2.311 0.217 0.
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 83 115 0 1 151 109 0
normalized size 1 1. 1.01 1.4 0. 0.01 1.84 1.33 0.
time (sec) N/A 0.175 0.177 0.01 0. 0.234 4.407 0.216 0.
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 104 104 103 142 0 1 167 142 90
normalized size 1 1. 0.99 1.37 0. 0.01 1.61 1.37 0.87
time (sec) N/A 0.208 0.182 0.01 0. 0.234 10.545 0.219 41.92
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 137 137 139 190 0 1 301 204 124
normalized size 1 1. 1.01 1.39 0. 0.01 2.2 1.49 0.91
time (sec) N/A 0.277 0.235 0.012 0. 0.24 25.544 0.223 51.974
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 175 175 174 238 0 1 354 271 156
normalized size 1 1. 0.99 1.36 0. 0.01 2.02 1.55 0.89
time (sec) N/A 0.33 0.348 0.014 0. 0.236 52.536 0.22 60.851
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 211 211 211 286 0 1 398 336 192
normalized size 1 1. 1. 1.36 0. 0. 1.89 1.59 0.91
time (sec) N/A 0.391 0.363 0.013 0. 0.238 90.198 0.217 71.655
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 240 240 227 309 0 1 430 340 0
normalized size 1 1. 0.95 1.29 0. 0. 1.79 1.42 0.
time (sec) N/A 0.649 0.238 0.017 0. 0.237 4.617 0.216 0.
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 202 202 187 258 0 1 250 271 0
normalized size 1 1. 0.93 1.28 0. 0. 1.24 1.34 0.
time (sec) N/A 0.545 0.187 0.017 0. 0.234 4.441 0.216 0.
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 163 163 148 212 0 1 216 205 141
normalized size 1 1. 0.91 1.3 0. 0.01 1.33 1.26 0.87
time (sec) N/A 0.51 0.15 0.018 0. 0.238 4.233 0.216 138.425
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 118 118 122 177 0 1 199 170 114
normalized size 1 1. 1.03 1.5 0. 0.01 1.69 1.44 0.97
time (sec) N/A 0.277 0.166 0.014 0. 0.24 3.69 0.216 81.022
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 112 112 115 165 0 1 197 165 122
normalized size 1 1. 1.03 1.47 0. 0.01 1.76 1.47 1.09
time (sec) N/A 0.322 0.115 0.017 0. 0.235 9.256 0.216 140.885
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 121 121 125 182 0 1 212 166 146
normalized size 1 1. 1.03 1.5 0. 0.01 1.75 1.37 1.21
time (sec) N/A 0.365 0.137 0.019 0. 0.241 23.851 0.216 143.952
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 152 152 151 219 0 1 226 204 175
normalized size 1 1. 0.99 1.44 0. 0.01 1.49 1.34 1.15
time (sec) N/A 0.417 0.169 0.021 0. 0.248 56.109 0.217 149.568
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 189 189 190 268 0 1 394 271 202
normalized size 1 1. 1.01 1.42 0. 0.01 2.08 1.43 1.07
time (sec) N/A 0.577 0.194 0.023 0. 0.239 127.943 0.217 160.894
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 230 230 230 318 0 1 0 340 231
normalized size 1 1. 1. 1.38 0. 0. 0. 1.48 1.
time (sec) N/A 0.739 0.221 0.024 0. 0.241 0. 0.214 168.751
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 311 311 272 394 0 1 491 406 0
normalized size 1 1. 0.87 1.27 0. 0. 1.58 1.31 0.
time (sec) N/A 1.082 0.312 0.02 0. 0.242 25.673 0.22 0.
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 273 273 232 343 0 1 311 338 0
normalized size 1 1. 0.85 1.26 0. 0. 1.14 1.24 0.
time (sec) N/A 0.967 0.292 0.019 0. 0.235 25.271 0.219 0.
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 235 235 176 294 0 1 279 270 0
normalized size 1 1. 0.75 1.25 0. 0. 1.19 1.15 0.
time (sec) N/A 0.868 0.307 0.018 0. 0.241 24.52 0.216 0.
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 193 193 156 259 0 1 258 234 0
normalized size 1 1. 0.81 1.34 0. 0.01 1.34 1.21 0.
time (sec) N/A 0.74 0.255 0.016 0. 0.236 21.23 0.217 0.
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 147 147 141 234 0 1 243 201 146
normalized size 1 1. 0.96 1.59 0. 0.01 1.65 1.37 0.99
time (sec) N/A 0.355 0.224 0.018 0. 0.24 15.37 0.219 84.462
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 150 150 155 237 0 1 250 207 160
normalized size 1 1. 1.03 1.58 0. 0.01 1.67 1.38 1.07
time (sec) N/A 0.464 0.237 0.02 0. 0.239 40.362 0.218 151.552
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 168 168 169 264 0 1 270 230 0
normalized size 1 1. 1.01 1.57 0. 0.01 1.61 1.37 0.
time (sec) N/A 0.557 0.294 0.022 0. 0.241 99.166 0.221 0.
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 196 196 196 300 0 1 0 267 0
normalized size 1 1. 1. 1.53 0. 0.01 0. 1.36 0.
time (sec) N/A 0.667 0.229 0.024 0. 0.237 0. 0.217 0.
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 234 234 234 351 0 1 0 338 0
normalized size 1 1. 1. 1.5 0. 0. 0. 1.44 0.
time (sec) N/A 0.912 0.253 0.026 0. 0.247 0. 0.219 0.
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 277 277 276 401 0 1 0 406 0
normalized size 1 1. 1. 1.45 0. 0. 0. 1.47 0.
time (sec) N/A 1.161 0.284 0.028 0. 0.236 0. 0.216 0.
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 214 214 158 193 0 239 442 387 206
normalized size 1 1. 0.74 0.9 0. 1.12 2.07 1.81 0.96
time (sec) N/A 0.465 0.22 0.01 0. 0.257 6.805 0.22 85.851
Problem 144 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 167 167 122 145 0 181 340 296 156
normalized size 1 1. 0.73 0.87 0. 1.08 2.04 1.77 0.93
time (sec) N/A 0.355 0.152 0.01 0. 0.249 4.047 0.224 62.436
Problem 145 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 121 121 89 99 0 127 238 207 110
normalized size 1 1. 0.74 0.82 0. 1.05 1.97 1.71 0.91
time (sec) N/A 0.271 0.121 0.007 0. 0.239 2.549 0.219 45.798
Problem 146 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 103 103 97 134 0 1 192 171 92
normalized size 1 1. 0.94 1.3 0. 0.01 1.86 1.66 0.89
time (sec) N/A 0.263 0.259 0.013 0. 0.249 23.53 0.221 49.328
Problem 147 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 100 100 101 127 0 1 138 154 87
normalized size 1 1. 1.01 1.27 0. 0.01 1.38 1.54 0.87
time (sec) N/A 0.408 0.303 0.013 0. 0.26 37.233 0.221 156.743
Problem 148 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 114 114 125 162 0 1 194 190 104
normalized size 1 1. 1.1 1.42 0. 0.01 1.7 1.67 0.91
time (sec) N/A 0.534 0.328 0.015 0. 0.275 62.403 0.224 147.611
Problem 149 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 146 146 166 238 0 1 303 313 141
normalized size 1 1. 1.14 1.63 0. 0.01 2.08 2.14 0.97
time (sec) N/A 0.6 0.273 0.016 0. 0.315 86.713 0.229 152.04
Problem 150 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 195 195 199 320 0 1 444 487 190
normalized size 1 1. 1.02 1.64 0. 0.01 2.28 2.5 0.97
time (sec) N/A 0.818 0.376 0.021 0. 0.527 145.495 0.229 162.471
Problem 151 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 245 245 188 368 0 1 586 302 238
normalized size 1 1. 0.77 1.5 0. 0. 2.39 1.23 0.97
time (sec) N/A 0.65 0.243 0.032 0. 0.557 52.53 0.228 70.83
Problem 152 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 194 194 152 284 0 1 444 236 187
normalized size 1 1. 0.78 1.46 0. 0.01 2.29 1.22 0.96
time (sec) N/A 0.532 0.22 0.014 0. 0.374 34.252 0.226 70.05
Problem 153 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 145 145 121 203 0 1 362 174 138
normalized size 1 1. 0.83 1.4 0. 0.01 2.5 1.2 0.95
time (sec) N/A 0.271 0.148 0.01 0. 0.281 19.264 0.221 47.392
Problem 154 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 117 117 100 140 0 1 250 163 104
normalized size 1 1. 0.85 1.2 0. 0.01 2.14 1.39 0.89
time (sec) N/A 0.29 0.238 0.014 0. 0.261 10.799 0.227 52.785
Problem 155 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 110 110 93 117 0 1 197 238 95
normalized size 1 1. 0.85 1.06 0. 0.01 1.79 2.16 0.86
time (sec) N/A 0.325 0.184 0.015 0. 0.268 6.069 0.231 82.593
Problem 156 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 118 118 98 136 0 1 456 437 117
normalized size 1 1. 0.83 1.15 0. 0.01 3.86 3.7 0.99
time (sec) N/A 0.36 0.215 0.015 0. 0.278 4.536 0.229 79.01
Problem 157 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 140 140 103 111 0 135 891 748 163
normalized size 1 1. 0.74 0.79 0. 0.96 6.36 5.34 1.16
time (sec) N/A 0.335 0.14 0.009 0. 0.416 7.218 0.23 94.433
Problem 158 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 189 189 134 157 0 190 1642 900 216
normalized size 1 1. 0.71 0.83 0. 1.01 8.69 4.76 1.14
time (sec) N/A 0.495 0.151 0.01 0. 0.717 11.069 0.229 101.347
Problem 159 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 381 381 252 517 0 1 0 462 0
normalized size 1 1. 0.66 1.36 0. 0. 0. 1.21 0.
time (sec) N/A 1.62 0.525 0.402 0. 1.113 0. 0.231 0.
Problem 160 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 279 279 208 460 0 1 0 358 0
normalized size 1 1. 0.75 1.65 0. 0. 0. 1.28 0.
time (sec) N/A 0.989 0.384 0.016 0. 0.722 0. 0.229 0.
Problem 161 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 210 210 174 405 0 1 0 274 0
normalized size 1 1. 0.83 1.93 0. 0. 0. 1.3 0.
time (sec) N/A 0.98 0.367 0.02 0. 0.518 0. 0.23 0.
Problem 162 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 179 192 147 363 0 1 0 216 0
normalized size 1 1.07 0.82 2.03 0. 0.01 0. 1.21 0.
time (sec) N/A 0.761 0.383 0.016 0. 0.462 0. 0.229 0.
Problem 163 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 134 134 98 109 452 190 0 177 206
normalized size 1 1. 0.73 0.81 3.37 1.42 0. 1.32 1.54
time (sec) N/A 0.404 0.133 0.008 1.37 0.359 0. 0.224 82.863
Problem 164 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 185 179 133 157 0 246 0 285 230
normalized size 1 0.97 0.72 0.85 0. 1.33 0. 1.54 1.24
time (sec) N/A 0.499 0.181 0.01 0. 0.418 0. 0.225 155.612
Problem 165 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 242 242 165 205 0 304 0 471 270
normalized size 1 1. 0.68 0.85 0. 1.26 0. 1.95 1.12
time (sec) N/A 0.67 0.212 0.012 0. 0.68 0. 0.227 163.22
Problem 166 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 281 275 202 253 0 365 0 799 309
normalized size 1 0.98 0.72 0.9 0. 1.3 0. 2.84 1.1
time (sec) N/A 0.843 0.294 0.012 0. 1.125 0. 0.233 171.121
Problem 167 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 334 334 234 301 0 420 0 1 354
normalized size 1 1. 0.7 0.9 0. 1.26 0. 0. 1.06
time (sec) N/A 0.993 0.428 0.012 0. 1.97 0. 0.255 179.705
Problem 168 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 392 380 270 349 0 478 0 1 0
normalized size 1 0.97 0.69 0.89 0. 1.22 0. 0. 0.
time (sec) N/A 1.135 0.475 0.013 0. 3.116 0. 0.259 0.
Problem 169 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 214 214 158 193 0 239 442 387 206
normalized size 1 1. 0.74 0.9 0. 1.12 2.07 1.81 0.96
time (sec) N/A 0.463 0.222 0.01 0. 0.263 6.768 0.231 86.485
Problem 170 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 167 167 122 145 0 181 340 296 156
normalized size 1 1. 0.73 0.87 0. 1.08 2.04 1.77 0.93
time (sec) N/A 0.366 0.154 0.008 0. 0.263 4.011 0.224 73.834
Problem 171 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 121 121 89 99 0 127 238 207 110
normalized size 1 1. 0.74 0.82 0. 1.05 1.97 1.71 0.91
time (sec) N/A 0.285 0.122 0.006 0. 0.275 2.493 0.22 58.647
Problem 172 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 261 257 201 478 0 1 0 302 0
normalized size 1 0.98 0.77 1.83 0. 0. 0. 1.16 0.
time (sec) N/A 1.543 0.438 0.016 0. 0.604 0. 0.229 0.
Problem 173 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 214 252 176 427 0 1 0 275 0
normalized size 1 1.18 0.82 2. 0. 0. 0. 1.29 0.
time (sec) N/A 0.947 0.424 0.01 0. 0.605 0. 0.228 0.
Problem 174 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 193 193 138 166 0 252 0 297 0
normalized size 1 1. 0.72 0.86 0. 1.31 0. 1.54 0.
time (sec) N/A 0.656 0.227 0.011 0. 0.513 0. 0.229 0.

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 [13] had the largest ratio of [ 0.4 ]

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 6 5 1. 20 0.25
2 A 5 5 1. 20 0.25
3 A 4 4 1. 18 0.222
4 A 4 4 1. 17 0.235
5 A 7 7 1. 20 0.35
6 A 7 7 1. 20 0.35
7 A 7 7 1. 20 0.35
8 A 7 5 1. 20 0.25
9 A 6 5 1. 20 0.25
10 A 5 4 1. 18 0.222
11 A 5 4 1. 17 0.235
12 A 8 7 1. 20 0.35
13 A 8 8 1. 20 0.4
14 A 8 7 1. 20 0.35
15 A 8 5 1. 20 0.25
16 A 7 5 1. 20 0.25
17 A 6 4 1. 18 0.222
18 A 6 4 1. 17 0.235
19 A 9 7 1. 20 0.35
20 A 9 8 1. 20 0.4
21 A 9 8 1. 20 0.4
22 A 5 4 1. 20 0.2
23 A 4 4 1. 20 0.2
24 A 3 3 1. 18 0.167
25 A 3 3 1. 17 0.176
26 A 6 6 1. 20 0.3
27 A 4 4 1. 20 0.2
28 A 5 5 1. 20 0.25
29 A 4 4 1. 20 0.2
30 A 4 4 1. 20 0.2
31 A 3 3 1. 18 0.167
32 A 1 1 1. 17 0.059
33 A 5 5 1. 20 0.25
34 A 5 5 1. 20 0.25
35 A 6 6 1. 20 0.3
36 A 4 4 1. 20 0.2
37 A 2 2 1. 20 0.1
38 A 2 2 1. 18 0.111
39 A 2 2 1. 17 0.118
40 A 6 5 1. 20 0.25
41 A 6 5 1. 20 0.25
42 A 7 6 1. 20 0.3
43 A 2 2 1. 18 0.111
44 A 3 3 1. 19 0.158
45 A 2 2 1. 13 0.154
46 A 2 2 1. 13 0.154
47 A 7 5 1. 25 0.2
48 A 6 5 1. 25 0.2
49 A 5 4 1. 25 0.16
50 A 4 4 1. 25 0.16
51 A 4 4 1. 25 0.16
52 A 4 4 1. 25 0.16
53 A 4 4 1. 23 0.174
54 A 5 4 1. 22 0.182
55 A 8 6 1. 25 0.24
56 A 8 5 1. 25 0.2
57 A 9 6 1. 25 0.24
58 A 2 2 1. 16 0.125
59 A 3 2 1. 20 0.1
60 A 2 2 1. 22 0.091
61 A 5 3 1. 25 0.12
62 A 2 1 1. 26 0.038
63 A 2 1 1. 26 0.038
64 A 2 1 1. 24 0.042
65 A 2 1 1. 23 0.043
66 A 2 1 1. 26 0.038
67 A 2 1 1. 26 0.038
68 A 2 1 1. 26 0.038
69 A 2 1 1. 26 0.038
70 A 2 1 1. 28 0.036
71 A 2 1 1. 28 0.036
72 A 4 3 1. 26 0.115
73 A 3 2 1. 25 0.08
74 A 3 2 1. 28 0.071
75 A 3 2 1. 28 0.071
76 A 2 1 1. 28 0.036
77 A 2 1 1. 28 0.036
78 A 2 1 1. 28 0.036
79 A 2 1 1. 28 0.036
80 A 4 3 1. 26 0.115
81 A 3 2 1. 25 0.08
82 A 3 2 1. 28 0.071
83 A 3 2 1. 28 0.071
84 A 2 1 1. 28 0.036
85 A 2 1 1. 28 0.036
86 A 5 4 1. 28 0.143
87 A 5 4 1. 28 0.143
88 A 5 4 1. 28 0.143
89 A 5 4 1. 26 0.154
90 A 5 4 1. 25 0.16
91 A 5 4 1. 28 0.143
92 A 5 4 1. 28 0.143
93 A 5 4 1. 28 0.143
94 A 6 5 1. 28 0.179
95 A 6 5 1. 28 0.179
96 A 6 5 1. 28 0.179
97 A 6 5 1. 26 0.192
98 A 4 4 1. 25 0.16
99 A 6 5 1. 28 0.179
100 A 6 5 1. 28 0.179
101 A 6 5 1. 28 0.179
102 A 7 5 1. 28 0.179
103 A 6 5 1. 28 0.179
104 A 5 4 1. 28 0.143
105 A 4 4 1. 26 0.154
106 A 3 3 1. 25 0.12
107 A 7 6 1. 28 0.214
108 A 7 5 1. 28 0.179
109 A 7 5 1. 28 0.179
110 A 4 3 1. 17 0.176
111 A 4 3 1. 17 0.176
112 A 4 4 1. 21 0.19
113 A 6 5 1. 15 0.333
114 A 3 2 1. 30 0.067
115 A 3 2 1. 30 0.067
116 A 3 2 1. 30 0.067
117 A 3 2 1. 27 0.074
118 A 3 2 1. 30 0.067
119 A 3 2 1. 30 0.067
120 A 3 2 1. 30 0.067
121 A 3 2 1. 30 0.067
122 A 3 2 1. 30 0.067
123 A 3 2 1. 30 0.067
124 A 5 4 1. 30 0.133
125 A 5 4 1. 30 0.133
126 A 5 4 1. 30 0.133
127 A 4 3 1. 27 0.111
128 A 4 3 1. 30 0.1
129 A 4 3 1. 30 0.1
130 A 4 3 1. 30 0.1
131 A 4 3 1. 30 0.1
132 A 4 3 1. 30 0.1
133 A 8 6 1. 30 0.2
134 A 8 6 1. 30 0.2
135 A 8 6 1. 30 0.2
136 A 7 6 1. 30 0.2
137 A 4 3 1. 27 0.111
138 A 4 3 1. 30 0.1
139 A 5 3 1. 30 0.1
140 A 5 3 1. 30 0.1
141 A 5 3 1. 30 0.1
142 A 5 3 1. 30 0.1
143 A 3 2 1. 32 0.062
144 A 3 2 1. 32 0.062
145 A 3 2 1. 30 0.067
146 A 5 4 1. 32 0.125
147 A 6 5 1. 32 0.156
148 A 6 6 1. 32 0.188
149 A 6 6 1. 32 0.188
150 A 7 7 1. 32 0.219
151 A 7 5 1. 32 0.156
152 A 6 5 1. 32 0.156
153 A 5 4 1. 29 0.138
154 A 6 6 1. 32 0.188
155 A 7 6 1. 32 0.188
156 A 7 6 1. 32 0.188
157 A 5 3 1. 32 0.094
158 A 6 4 1. 32 0.125
159 A 11 8 1. 32 0.25
160 A 10 8 1. 32 0.25
161 A 9 8 1. 32 0.25
162 A 8 7 1.07 32 0.219
163 A 5 4 1. 29 0.138
164 A 6 5 0.97 32 0.156
165 A 7 5 1. 32 0.156
166 A 8 4 0.98 32 0.125
167 A 9 5 1. 32 0.156
168 A 10 5 0.97 32 0.156
169 A 4 3 1. 33 0.091
170 A 4 3 1. 33 0.091
171 A 4 3 1. 31 0.097
172 A 10 8 0.98 37 0.216
173 A 6 4 1.18 34 0.118
174 A 6 4 1. 37 0.108

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