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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 A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 50 50 50 41 54 1 46 58 0
normalized size 1 1. 1. 0.82 1.08 0.02 0.92 1.16 0.
time (sec) N/A 0.087 0.005 0.001 0.696 0.255 0.09 0.278 0.
Problem 2 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 69 69 69 58 77 1 65 86 0
normalized size 1 1. 1. 0.84 1.12 0.01 0.94 1.25 0.
time (sec) N/A 0.091 0.037 0.001 0.697 0.241 0.103 0.286 0.
Problem 3 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 88 88 88 75 100 1 83 115 0
normalized size 1 1. 1. 0.85 1.14 0.01 0.94 1.31 0.
time (sec) N/A 0.145 0.037 0.001 0.702 0.241 0.12 0.287 0.
Problem 4 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 105 105 105 90 120 1 102 143 0
normalized size 1 1. 1. 0.86 1.14 0.01 0.97 1.36 0.
time (sec) N/A 0.203 0.065 0.001 0.701 0.24 0.144 0.291 0.
Problem 5 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 122 122 122 105 140 1 121 171 0
normalized size 1 1. 1. 0.86 1.15 0.01 0.99 1.4 0.
time (sec) N/A 0.243 0.077 0.001 0.701 0.242 0.156 0.29 0.
Problem 6 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 112 112 97 95 127 1 116 143 0
normalized size 1 1. 0.87 0.85 1.13 0.01 1.04 1.28 0.
time (sec) N/A 0.262 0.089 0.001 0.701 0.236 0.154 0.295 0.
Problem 7 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 154 154 154 139 186 1 165 212 0
normalized size 1 1. 1. 0.9 1.21 0.01 1.07 1.38 0.
time (sec) N/A 0.275 0.097 0.001 0.702 0.239 0.174 0.294 0.
Problem 8 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 196 196 196 183 246 1 209 281 0
normalized size 1 1. 1. 0.93 1.26 0.01 1.07 1.43 0.
time (sec) N/A 0.388 0.118 0.001 0.699 0.24 0.206 0.286 0.
Problem 9 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 234 234 234 219 294 1 258 350 0
normalized size 1 1. 1. 0.94 1.26 0. 1.1 1.5 0.
time (sec) N/A 0.582 0.286 0.001 0.706 0.241 0.231 0.288 0.
Problem 10 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 45 45 50 58 58 58 515 69 34
normalized size 1 1. 1.11 1.29 1.29 1.29 11.44 1.53 0.76
time (sec) N/A 0.066 0.032 0.013 0.702 0.272 6.81 0.302 22.007
Problem 11 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 58 86 69 69 2195 80 42
normalized size 1 1. 1.14 1.69 1.35 1.35 43.04 1.57 0.82
time (sec) N/A 0.117 0.05 0.011 0.702 0.324 88.818 0.29 23.52
Problem 12 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 57 57 68 114 82 82 0 93 51
normalized size 1 1. 1.19 2. 1.44 1.44 0. 1.63 0.89
time (sec) N/A 0.175 0.059 0.013 0.706 0.484 0. 0.292 33.667
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 64 64 81 145 97 97 0 108 0
normalized size 1 1. 1.27 2.27 1.52 1.52 0. 1.69 0.
time (sec) N/A 0.315 0.088 0.014 0.705 1.518 0. 0.298 0.
Problem 14 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 76 76 98 179 119 119 0 130 0
normalized size 1 1. 1.29 2.36 1.57 1.57 0. 1.71 0.
time (sec) N/A 0.364 0.135 0.014 0.708 6.913 0. 0.302 0.
Problem 15 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 NO TBD TBD TBD TBD TBD TBD
size 92 92 98 92 88 93 923 90 95
normalized size 1 1. 1.07 1. 0.96 1.01 10.03 0.98 1.03
time (sec) N/A 0.159 0.325 0.008 0.783 0.267 6.457 0.281 21.704
Problem 16 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 NO TBD TBD TBD TBD TBD TBD
size 104 104 121 148 101 107 3589 104 105
normalized size 1 1. 1.16 1.42 0.97 1.03 34.51 1. 1.01
time (sec) N/A 0.189 0.271 0.007 0.79 0.29 81.866 0.274 33.262
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A A A F(-1) A A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 127 127 150 204 112 117 0 115 122
normalized size 1 1. 1.18 1.61 0.88 0.92 0. 0.91 0.96
time (sec) N/A 0.239 1.422 0.007 0.785 0.45 0. 0.275 43.082
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B A A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 136 136 165 241 124 135 0 127 133
normalized size 1 1. 1.21 1.77 0.91 0.99 0. 0.93 0.98
time (sec) N/A 0.303 1.193 0.006 0.779 1.397 0. 0.274 66.066
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B A A F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 151 151 187 303 143 157 0 146 0
normalized size 1 1. 1.24 2.01 0.95 1.04 0. 0.97 0.
time (sec) N/A 0.353 1.444 0.011 0.795 5.727 0. 0.274 0.
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F F(-2) F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 189 189 194 231 0 0 0 1 177
normalized size 1 1. 1.03 1.22 0. 0. 0. 0.01 0.94
time (sec) N/A 0.459 0.706 0.039 0. 0. 0. 0.648 42.969
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-2) F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 211 211 234 616 0 0 0 1 221
normalized size 1 1. 1.11 2.92 0. 0. 0. 0. 1.05
time (sec) N/A 0.551 0.433 0.03 0. 0. 0. 1.053 53.876
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-2) F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 245 245 280 866 0 0 0 1 250
normalized size 1 1. 1.14 3.53 0. 0. 0. 0. 1.02
time (sec) N/A 0.516 0.573 0.031 0. 0. 0. 1.288 69.66
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 290 290 383 1132 0 0 0 1 286
normalized size 1 1. 1.32 3.9 0. 0. 0. 0. 0.99
time (sec) N/A 1.519 1.078 0.039 0. 0. 0. 1.697 143.637
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 321 321 441 1435 0 0 0 1 0
normalized size 1 1. 1.37 4.47 0. 0. 0. 0. 0.
time (sec) N/A 1.341 1.566 0.041 0. 0. 0. 2.034 0.
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F(-1) F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 545 545 816 3835 0 0 0 0 0
normalized size 1 1. 1.5 7.04 0. 0. 0. 0. 0.
time (sec) N/A 10.772 3.525 0.067 0. 0. 0. 0. 0.
Problem 26 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 94 94 90 122 112 228 604 126 71
normalized size 1 1. 0.96 1.3 1.19 2.43 6.43 1.34 0.76
time (sec) N/A 0.121 0.121 0.026 0.705 0.325 8.946 0.29 31.853
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 115 115 112 182 143 293 2689 155 88
normalized size 1 1. 0.97 1.58 1.24 2.55 23.38 1.35 0.77
time (sec) N/A 0.286 0.219 0.026 0.705 0.33 109.052 0.273 40.634
Problem 28 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 138 138 134 242 171 354 0 184 105
normalized size 1 1. 0.97 1.75 1.24 2.57 0. 1.33 0.76
time (sec) N/A 0.352 0.101 0.027 0.704 0.561 0. 0.274 45.987
Problem 29 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 150 150 159 302 196 410 0 213 122
normalized size 1 1. 1.06 2.01 1.31 2.73 0. 1.42 0.81
time (sec) N/A 0.431 0.14 0.028 0.699 1.766 0. 0.278 58.549
Problem 30 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 162 162 185 362 220 467 0 242 139
normalized size 1 1. 1.14 2.23 1.36 2.88 0. 1.49 0.86
time (sec) N/A 0.47 0.188 0.028 0.71 8.518 0. 0.276 69.378
Problem 31 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 NO TBD TBD TBD TBD TBD TBD
size 140 140 146 146 130 219 952 135 126
normalized size 1 1. 1.04 1.04 0.93 1.56 6.8 0.96 0.9
time (sec) N/A 0.218 0.986 0.016 0.778 0.273 8.573 0.274 39.682
Problem 32 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 NO TBD TBD TBD TBD TBD TBD
size 165 165 186 214 162 297 4107 173 144
normalized size 1 1. 1.13 1.3 0.98 1.8 24.89 1.05 0.87
time (sec) N/A 0.297 0.828 0.016 0.781 0.312 91.825 0.281 52.599
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A A A F(-1) A A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 179 179 200 260 182 333 0 192 151
normalized size 1 1. 1.12 1.45 1.02 1.86 0. 1.07 0.84
time (sec) N/A 0.348 0.98 0.016 0.78 0.476 0. 0.275 59.469
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A A A F(-1) A A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 187 187 234 328 193 355 0 209 167
normalized size 1 1. 1.25 1.75 1.03 1.9 0. 1.12 0.89
time (sec) N/A 0.413 1.279 0.017 0.782 1.377 0. 0.275 71.168
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B A A F(-1) A A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 194 194 243 374 209 387 0 228 175
normalized size 1 1. 1.25 1.93 1.08 1.99 0. 1.18 0.9
time (sec) N/A 0.403 1.424 0.018 0.779 6.361 0. 0.276 82.39
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-2) F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 330 330 341 1241 0 0 0 0 296
normalized size 1 1. 1.03 3.76 0. 0. 0. 0. 0.9
time (sec) N/A 1.56 1.608 0.143 0. 0. 0. 0. 110.156
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-2) F(-1) F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 368 368 398 2851 0 0 0 0 0
normalized size 1 1. 1.08 7.75 0. 0. 0. 0. 0.
time (sec) N/A 1.925 2.533 0.163 0. 0. 0. 0. 0.
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F(-1) F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 386 386 421 3544 0 0 0 0 0
normalized size 1 1. 1.09 9.18 0. 0. 0. 0. 0.
time (sec) N/A 1.387 2.967 0.161 0. 0. 0. 0. 0.
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F(-1) F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 439 439 489 7598 0 0 0 0 0
normalized size 1 1. 1.11 17.31 0. 0. 0. 0. 0.
time (sec) N/A 4.413 4.529 0.153 0. 0. 0. 0. 0.
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F(-1) F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 468 468 524 8189 0 0 0 0 0
normalized size 1 1. 1.12 17.5 0. 0. 0. 0. 0.
time (sec) N/A 3.876 5.208 0.093 0. 0. 0. 0. 0.
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F(-1) F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 770 770 1109 16517 0 0 0 0 0
normalized size 1 1. 1.44 21.45 0. 0. 0. 0. 0.
time (sec) N/A 25.763 8.767 0.151 0. 0. 0. 0. 0.
Problem 42 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 143 143 128 186 163 414 668 166 110
normalized size 1 1. 0.9 1.3 1.14 2.9 4.67 1.16 0.77
time (sec) N/A 0.175 0.178 0.029 0.711 0.303 9.177 0.28 48.481
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 175 175 161 278 209 525 2822 212 134
normalized size 1 1. 0.92 1.59 1.19 3. 16.13 1.21 0.77
time (sec) N/A 0.452 0.265 0.029 0.705 0.349 118.807 0.272 62.935
Problem 44 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 204 204 193 370 254 635 0 257 158
normalized size 1 1. 0.95 1.81 1.25 3.11 0. 1.26 0.77
time (sec) N/A 0.514 0.165 0.031 0.71 0.628 0. 0.266 75.312
Problem 45 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 224 224 231 462 289 734 0 302 182
normalized size 1 1. 1.03 2.06 1.29 3.28 0. 1.35 0.81
time (sec) N/A 0.626 0.236 0.032 0.707 2.014 0. 0.267 88.878
Problem 46 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 239 239 261 554 321 832 0 347 196
normalized size 1 1. 1.09 2.32 1.34 3.48 0. 1.45 0.82
time (sec) N/A 0.661 0.305 0.034 0.71 8.885 0. 0.273 104.153
Problem 47 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 NO TBD TBD TBD TBD TBD TBD
size 185 185 186 180 185 387 1103 177 168
normalized size 1 1. 1.01 0.97 1. 2.09 5.96 0.96 0.91
time (sec) N/A 0.258 2.187 0.023 0.775 0.278 9.103 0.266 57.28
Problem 48 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 NO TBD TBD TBD TBD TBD TBD
size 223 223 235 264 234 531 4498 231 194
normalized size 1 1. 1.05 1.18 1.05 2.38 20.17 1.04 0.87
time (sec) N/A 0.468 1.147 0.022 0.784 0.317 106.84 0.266 75.624
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A A A F(-1) A A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 243 243 259 322 270 599 0 267 207
normalized size 1 1. 1.07 1.33 1.11 2.47 0. 1.1 0.85
time (sec) N/A 0.524 1.315 0.023 0.785 0.504 0. 0.273 83.973
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A A A F(-1) A A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 263 263 303 396 293 666 0 308 233
normalized size 1 1. 1.15 1.51 1.11 2.53 0. 1.17 0.89
time (sec) N/A 0.614 1.834 0.023 0.786 1.518 0. 0.268 102.35
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A A A F(-1) A A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 269 269 325 454 309 714 0 344 240
normalized size 1 1. 1.21 1.69 1.15 2.65 0. 1.28 0.89
time (sec) N/A 0.629 2.225 0.025 0.779 7.228 0. 0.268 115.85
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-2) F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 474 474 488 3733 0 0 0 1 0
normalized size 1 1. 1.03 7.88 0. 0. 0. 0. 0.
time (sec) N/A 4.503 4.371 0.326 0. 0. 0. 34.836 0.
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 621 621 683 10809 0 0 0 1 0
normalized size 1 1. 1.1 17.41 0. 0. 0. 0. 0.
time (sec) N/A 10.425 6.614 0.398 0. 0. 0. 50.972 0.
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F(-1) F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 646 646 733 13757 0 0 0 0 0
normalized size 1 1. 1.13 21.3 0. 0. 0. 0. 0.
time (sec) N/A 8.792 6.756 0.393 0. 0. 0. 0. 0.
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F(-1) F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 679 679 845 19742 0 0 0 0 0
normalized size 1 1. 1.24 29.08 0. 0. 0. 0. 0.
time (sec) N/A 10.095 7.075 0.314 0. 0. 0. 0. 0.
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 728 728 980 21161 0 0 0 1 0
normalized size 1 1. 1.35 29.07 0. 0. 0. 0. 0.
time (sec) N/A 8.19 7.398 0.143 0. 0. 0. 19.711 0.
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F(-1) F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 1150 1144 1590 36326 0 0 0 0 0
normalized size 1 0.99 1.38 31.59 0. 0. 0. 0. 0.
time (sec) N/A 24.669 9.317 0.344 0. 0. 0. 0. 0.
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F(-1) F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 645 645 908 14103 0 0 0 0 0
normalized size 1 1. 1.41 21.87 0. 0. 0. 0. 0.
time (sec) N/A 8.507 7.886 0.186 0. 0. 0. 0. 0.
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F(-1) F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 1177 1179 1649 35336 0 0 0 0 0
normalized size 1 1. 1.4 30.02 0. 0. 0. 0. 0.
time (sec) N/A 21.295 8.936 0.361 0. 0. 0. 0. 0.
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 416 416 416 829 564 1 503 645 0
normalized size 1 1. 1. 1.99 1.36 0. 1.21 1.55 0.
time (sec) N/A 1.221 0.208 0.002 0.71 0.248 0.36 0.304 0.
Problem 61 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 259 259 259 354 339 1 309 398 0
normalized size 1 1. 1. 1.37 1.31 0. 1.19 1.54 0.
time (sec) N/A 0.676 0.145 0.001 0.705 0.249 0.259 0.284 0.
Problem 62 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 154 154 154 161 186 1 165 212 0
normalized size 1 1. 1. 1.05 1.21 0.01 1.07 1.38 0.
time (sec) N/A 0.334 0.095 0.002 0.704 0.246 0.172 0.287 0.
Problem 63 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 20 20 20 17 22 22 15 23 0
normalized size 1 1. 1. 0.85 1.1 1.1 0.75 1.15 0.
time (sec) N/A 0.029 0.003 0.002 0.702 0.262 0.145 0.318 0.
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-2) F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 211 211 234 616 0 0 0 0 221
normalized size 1 1. 1.11 2.92 0. 0. 0. 0. 1.05
time (sec) N/A 0.652 0.466 0.004 0. 0. 0. 0. 72.682
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-2) F(-1) F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 368 368 398 2851 0 0 0 0 0
normalized size 1 1. 1.08 7.75 0. 0. 0. 0. 0.
time (sec) N/A 1.9 2.557 0.009 0. 0. 0. 0. 0.
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F(-1) F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 621 621 683 10809 0 0 0 0 0
normalized size 1 1. 1.1 17.41 0. 0. 0. 0. 0.
time (sec) N/A 10.327 6.606 0.015 0. 0. 0. 0. 0.
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 4 4 4 5 5 5 3 7 3
normalized size 1 1. 1. 1.25 1.25 1.25 0.75 1.75 0.75
time (sec) N/A 0.012 0.001 0.002 0.701 0.266 0.089 0.3 4.917
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 14 14 16 18 19 19 12 23 0
normalized size 1 1. 1.14 1.29 1.36 1.36 0.86 1.64 0.
time (sec) N/A 0.04 0.007 0.003 0.708 0.264 1.026 0.28 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 31 31 30 35 36 36 26 41 0
normalized size 1 1. 0.97 1.13 1.16 1.16 0.84 1.32 0.
time (sec) N/A 0.072 0.02 0.004 0.701 0.266 1.109 0.283 0.
Problem 70 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 51 51 45 58 58 58 41 66 0
normalized size 1 1. 0.88 1.14 1.14 1.14 0.8 1.29 0.
time (sec) N/A 0.128 0.043 0.004 0.693 0.268 1.216 0.289 0.
Problem 71 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 68 68 68 87 84 84 63 100 0
normalized size 1 1. 1. 1.28 1.24 1.24 0.93 1.47 0.
time (sec) N/A 0.2 0.041 0.005 0.7 0.247 1.322 0.282 0.
Problem 72 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 92 122 113 113 88 142 0
normalized size 1 1. 1. 1.33 1.23 1.23 0.96 1.54 0.
time (sec) N/A 0.268 0.064 0.004 0.703 0.282 1.463 0.285 0.
Problem 73 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 11 11 11 12 15 15 8 18 8
normalized size 1 1. 1. 1.09 1.36 1.36 0.73 1.64 0.73
time (sec) N/A 0.016 0.005 0.008 0.695 0.249 0.181 0.283 4.274
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 22 22 23 29 30 30 29 35 17
normalized size 1 1. 1.05 1.32 1.36 1.36 1.32 1.59 0.77
time (sec) N/A 0.05 0.013 0.008 0.703 0.257 0.726 0.283 8.674
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 29 29 30 45 39 39 44 45 0
normalized size 1 1. 1.03 1.55 1.34 1.34 1.52 1.55 0.
time (sec) N/A 0.082 0.023 0.009 0.703 0.254 2.243 0.283 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 47 47 44 69 61 61 66 66 0
normalized size 1 1. 0.94 1.47 1.3 1.3 1.4 1.4 0.
time (sec) N/A 0.122 0.041 0.009 0.704 0.256 3.353 0.286 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 66 66 67 98 84 84 94 93 0
normalized size 1 1. 1.02 1.48 1.27 1.27 1.42 1.41 0.
time (sec) N/A 0.173 0.055 0.01 0.705 0.259 5.442 0.285 0.
Problem 78 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 91 134 113 113 122 131 0
normalized size 1 1. 1.01 1.49 1.26 1.26 1.36 1.46 0.
time (sec) N/A 0.214 0.076 0.01 0.71 0.274 8.601 0.286 0.
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 29 29 29 20 26 26 19 30 22
normalized size 1 1. 1. 0.69 0.9 0.9 0.66 1.03 0.76
time (sec) N/A 0.039 0.01 0.01 0.7 0.262 0.277 0.288 26.83
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 42 42 39 44 43 43 304 51 36
normalized size 1 1. 0.93 1.05 1.02 1.02 7.24 1.21 0.86
time (sec) N/A 0.098 0.028 0.009 0.699 0.298 3.682 0.284 23.56
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 47 47 44 65 50 50 716 58 0
normalized size 1 1. 0.94 1.38 1.06 1.06 15.23 1.23 0.
time (sec) N/A 0.125 0.04 0.01 0.701 0.261 15.602 0.286 0.
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 57 57 55 89 63 63 1389 72 0
normalized size 1 1. 0.96 1.56 1.11 1.11 24.37 1.26 0.
time (sec) N/A 0.147 0.052 0.011 0.7 0.287 71.271 0.295 0.
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 71 120 84 84 0 92 0
normalized size 1 1. 0.96 1.62 1.14 1.14 0. 1.24 0.
time (sec) N/A 0.237 0.075 0.011 0.703 0.286 0. 0.283 0.
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 96 96 91 156 111 111 0 122 0
normalized size 1 1. 0.95 1.62 1.16 1.16 0. 1.27 0.
time (sec) N/A 0.275 0.104 0.011 0.704 0.33 0. 0.284 0.
Problem 85 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 46 46 42 33 43 61 34 49 34
normalized size 1 1. 0.91 0.72 0.93 1.33 0.74 1.07 0.74
time (sec) N/A 0.089 0.037 0.015 0.701 0.256 0.689 0.287 23.054
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 66 74 77 126 1188 89 0
normalized size 1 1. 0.93 1.04 1.08 1.77 16.73 1.25 0.
time (sec) N/A 0.329 0.071 0.016 0.702 0.271 16.666 0.284 0.
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 77 110 92 157 0 104 0
normalized size 1 1. 0.94 1.34 1.12 1.91 0. 1.27 0.
time (sec) N/A 0.363 0.102 0.017 0.701 0.357 0. 0.285 0.
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 95 95 90 146 109 190 0 122 0
normalized size 1 1. 0.95 1.54 1.15 2. 0. 1.28 0.
time (sec) N/A 0.42 0.09 0.016 0.702 0.875 0. 0.292 0.
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 106 106 102 182 124 221 0 136 0
normalized size 1 1. 0.96 1.72 1.17 2.08 0. 1.28 0.
time (sec) N/A 0.486 0.114 0.017 0.695 4.173 0. 0.284 0.
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 122 122 118 221 146 270 0 158 0
normalized size 1 1. 0.97 1.81 1.2 2.21 0. 1.3 0.
time (sec) N/A 0.603 0.139 0.018 0.716 25.419 0. 0.289 0.
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 56 56 48 40 57 97 44 62 44
normalized size 1 1. 0.86 0.71 1.02 1.73 0.79 1.11 0.79
time (sec) N/A 0.132 0.046 0.018 0.7 0.259 0.784 0.283 31.265
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 89 89 80 90 101 207 1255 115 78
normalized size 1 1. 0.9 1.01 1.13 2.33 14.1 1.29 0.88
time (sec) N/A 0.531 0.089 0.02 0.698 0.294 17.003 0.286 48.11
Problem 93 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 105 105 97 134 123 258 0 136 102
normalized size 1 1. 0.92 1.28 1.17 2.46 0. 1.3 0.97
time (sec) N/A 0.639 0.144 0.02 0.697 0.355 0. 0.286 63.156
Problem 94 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 117 117 114 178 144 309 0 158 122
normalized size 1 1. 0.97 1.52 1.23 2.64 0. 1.35 1.04
time (sec) N/A 0.486 0.114 0.021 0.706 0.899 0. 0.282 105.42
Problem 95 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 131 131 136 222 166 360 0 180 148
normalized size 1 1. 1.04 1.69 1.27 2.75 0. 1.37 1.13
time (sec) N/A 0.56 0.123 0.021 0.699 4.625 0. 0.284 137.068
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 147 147 153 266 188 412 0 201 0
normalized size 1 1. 1.04 1.81 1.28 2.8 0. 1.37 0.
time (sec) N/A 0.637 0.195 0.022 0.709 27.121 0. 0.287 0.
Problem 97 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 68 68 60 47 70 139 53 76 48
normalized size 1 1. 0.88 0.69 1.03 2.04 0.78 1.12 0.71
time (sec) N/A 0.109 0.055 0.021 0.707 0.255 0.846 0.288 21.859
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 105 105 97 106 119 285 1032 132 0
normalized size 1 1. 0.92 1.01 1.13 2.71 9.83 1.26 0.
time (sec) N/A 0.387 0.165 0.022 0.7 0.277 16.452 0.287 0.
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 122 122 121 158 146 360 0 159 0
normalized size 1 1. 0.99 1.3 1.2 2.95 0. 1.3 0.
time (sec) N/A 0.439 0.095 0.022 0.705 0.367 0. 0.286 0.
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 141 141 144 210 170 433 0 184 0
normalized size 1 1. 1.02 1.49 1.21 3.07 0. 1.3 0.
time (sec) N/A 0.508 0.15 0.024 0.715 0.913 0. 0.285 0.
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 158 158 169 262 196 508 0 209 0
normalized size 1 1. 1.07 1.66 1.24 3.22 0. 1.32 0.
time (sec) N/A 0.606 0.204 0.024 0.71 4.587 0. 0.287 0.
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 177 177 195 314 220 581 0 234 0
normalized size 1 1. 1.1 1.77 1.24 3.28 0. 1.32 0.
time (sec) N/A 0.725 0.226 0.025 0.707 26.779 0. 0.286 0.
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F F F A
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 717 717 2588 3038 0 0 0 0 709
normalized size 1 1. 3.61 4.24 0. 0. 0. 0. 0.99
time (sec) N/A 1.394 5.372 0.013 0. 0. 0. 0. 132.275
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F F F A
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 505 505 1534 1585 0 0 0 0 474
normalized size 1 1. 3.04 3.14 0. 0. 0. 0. 0.94
time (sec) N/A 0.772 6.341 0.01 0. 0. 0. 0. 85.169
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 359 359 526 453 0 0 0 0 325
normalized size 1 1. 1.47 1.26 0. 0. 0. 0. 0.91
time (sec) N/A 0.473 2.602 0.008 0. 0. 0. 0. 61.977
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 447 447 513 1005 0 0 0 0 435
normalized size 1 1. 1.15 2.25 0. 0. 0. 0. 0.97
time (sec) N/A 0.756 2.771 0.009 0. 0. 0. 0. 124.925
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F F(-1) F(-2) F(-1)
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 680 680 598 1395 0 0 0 0 0
normalized size 1 1. 0.88 2.05 0. 0. 0. 0. 0.
time (sec) N/A 1.235 4.795 0.082 0. 0. 0. 0. 0.
Problem 108 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 19 19 19 18 23 23 0 95 17
normalized size 1 1. 1. 0.95 1.21 1.21 0. 5. 0.89
time (sec) N/A 0.015 0.045 0.007 0.768 0.26 0. 0.329 13.007
Problem 109 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 57 57 51 52 69 111 0 228 48
normalized size 1 1. 0.89 0.91 1.21 1.95 0. 4. 0.84
time (sec) N/A 0.108 0.073 0.007 0.762 0.26 0. 0.316 17.885
Problem 110 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 57 57 48 53 66 108 0 221 46
normalized size 1 1. 0.84 0.93 1.16 1.89 0. 3.88 0.81
time (sec) N/A 0.132 0.075 0.008 0.771 0.282 0. 0.314 18.318
Problem 111 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 69 69 61 63 127 124 0 262 54
normalized size 1 1. 0.88 0.91 1.84 1.8 0. 3.8 0.78
time (sec) N/A 0.201 0.092 0.008 0.781 0.267 0. 0.314 22.647

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 [47] had the largest ratio of [ 0.6875 ]

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 2 1 1. 18 0.056
2 A 2 1 1. 23 0.043
3 A 2 1 1. 28 0.036
4 A 2 1 1. 33 0.03
5 A 2 1 1. 38 0.026
6 A 2 1 1. 20 0.05
7 A 2 1 1. 25 0.04
8 A 2 1 1. 30 0.033
9 A 2 1 1. 35 0.029
10 A 10 7 1. 18 0.389
11 A 9 7 1. 23 0.304
12 A 8 6 1. 28 0.214
13 A 10 7 1. 33 0.212
14 A 12 8 1. 38 0.21
15 A 15 8 1. 16 0.5
16 A 14 8 1. 21 0.381
17 A 15 7 1. 26 0.269
18 A 17 8 1. 31 0.258
19 A 19 9 1. 36 0.25
20 A 9 7 1. 20 0.35
21 A 8 7 1. 25 0.28
22 A 9 8 1. 30 0.267
23 A 11 9 1. 35 0.257
24 A 13 10 1. 40 0.25
25 A 13 10 1. 55 0.182
26 A 12 9 1. 18 0.5
27 A 11 9 1. 23 0.391
28 A 10 8 1. 28 0.286
29 A 10 8 1. 33 0.242
30 A 11 9 1. 38 0.237
31 A 17 10 1. 16 0.625
32 A 16 10 1. 21 0.476
33 A 15 9 1. 26 0.346
34 A 15 9 1. 31 0.29
35 A 16 10 1. 36 0.278
36 A 11 9 1. 20 0.45
37 A 10 9 1. 25 0.36
38 A 9 8 1. 30 0.267
39 A 9 8 1. 35 0.229
40 A 10 9 1. 40 0.225
41 A 13 11 1. 55 0.2
42 A 14 10 1. 18 0.556
43 A 13 9 1. 23 0.391
44 A 12 9 1. 28 0.321
45 A 12 10 1. 33 0.303
46 A 13 11 1. 38 0.29
47 A 19 11 1. 16 0.688
48 A 18 10 1. 21 0.476
49 A 17 10 1. 26 0.385
50 A 17 11 1. 31 0.355
51 A 18 12 1. 36 0.333
52 A 13 10 1. 20 0.5
53 A 12 9 1. 25 0.36
54 A 11 9 1. 30 0.3
55 A 11 10 1. 35 0.286
56 A 12 11 1. 40 0.275
57 A 11 9 0.99 55 0.164
58 A 11 10 1. 50 0.2
59 A 13 10 1. 50 0.2
60 A 2 1 1. 63 0.016
61 A 2 1 1. 63 0.016
62 A 2 1 1. 61 0.016
63 A 2 1 1. 63 0.016
64 A 9 8 1. 63 0.127
65 A 11 10 1. 63 0.159
66 A 13 10 1. 63 0.159
67 A 2 2 1. 26 0.077
68 A 3 2 1. 31 0.065
69 A 3 2 1. 36 0.056
70 A 3 2 1. 41 0.049
71 A 3 2 1. 46 0.043
72 A 3 2 1. 51 0.039
73 A 4 3 1. 21 0.143
74 A 4 3 1. 26 0.115
75 A 6 4 1. 31 0.129
76 A 6 4 1. 36 0.111
77 A 6 4 1. 41 0.098
78 A 6 4 1. 46 0.087
79 A 3 2 1. 16 0.125
80 A 3 2 1. 21 0.095
81 A 3 2 1. 26 0.077
82 A 3 2 1. 31 0.065
83 A 3 2 1. 36 0.056
84 A 3 2 1. 41 0.049
85 A 3 2 1. 26 0.077
86 A 3 2 1. 31 0.065
87 A 3 2 1. 36 0.056
88 A 3 2 1. 41 0.049
89 A 3 2 1. 46 0.043
90 A 3 2 1. 51 0.039
91 A 9 5 1. 21 0.238
92 A 9 5 1. 26 0.192
93 A 9 5 1. 31 0.161
94 A 3 2 1. 36 0.056
95 A 3 2 1. 41 0.049
96 A 3 2 1. 46 0.043
97 A 3 2 1. 16 0.125
98 A 3 2 1. 21 0.095
99 A 3 2 1. 26 0.077
100 A 3 2 1. 31 0.065
101 A 3 2 1. 36 0.056
102 A 3 2 1. 41 0.049
103 A 12 10 1. 32 0.312
104 A 10 10 1. 32 0.312
105 A 8 8 1. 32 0.25
106 A 7 7 1. 32 0.219
107 A 9 8 1. 32 0.25
108 A 1 1 1. 28 0.036
109 A 5 5 1. 31 0.161
110 A 5 5 1. 33 0.152
111 A 4 4 1. 36 0.111

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