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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 F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 94 94 86 133 0 1 332 117 0
normalized size 1 1. 0.91 1.41 0. 0.01 3.53 1.24 0.
time (sec) N/A 0.233 0.143 0.01 0. 0.271 3.848 0.264 0.
Problem 2 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 228 228 204 373 0 1 928 355 0
normalized size 1 1. 0.89 1.64 0. 0. 4.07 1.56 0.
time (sec) N/A 0.739 0.536 0.009 0. 0.278 12.608 0.265 0.
Problem 3 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 441 441 422 822 0 1 1940 841 0
normalized size 1 1. 0.96 1.86 0. 0. 4.4 1.91 0.
time (sec) N/A 1.581 1.816 0.012 0. 0.282 30.066 0.267 0.
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 274 274 212 745 0 0 0 359 0
normalized size 1 1. 0.77 2.72 0. 0. 0. 1.31 0.
time (sec) N/A 0.651 0.765 0.012 0. 0. 0. 0.267 0.
Problem 5 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 596 596 523 10537 0 0 0 1 0
normalized size 1 1. 0.88 17.68 0. 0. 0. 0. 0.
time (sec) N/A 3.941 4.053 0.04 0. 0. 0. 0.272 0.
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 331 331 450 3358 0 0 0 0 0
normalized size 1 1. 1.36 10.15 0. 0. 0. 0. 0.
time (sec) N/A 1.322 3. 0.075 0. 0. 0. 0. 0.
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 249 249 370 714 0 8253 0 0 238
normalized size 1 1. 1.49 2.87 0. 33.14 0. 0. 0.96
time (sec) N/A 0.492 2.255 0.029 0. 53.151 0. 0. 64.376
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 381 380 517 2758 0 0 0 0 439
normalized size 1 1. 1.36 7.24 0. 0. 0. 0. 1.15
time (sec) N/A 1.922 2.781 0.034 0. 0. 0. 0. 167.217
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F(-2) F(-1) F(-1) F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 797 796 1847 6422 0 0 0 0 0
normalized size 1 1. 2.32 8.06 0. 0. 0. 0. 0.
time (sec) N/A 4.318 7.371 0.04 0. 0. 0. 0. 0.
Problem 10 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 47 47 55 46 88 62 0 65 44
normalized size 1 1. 1.17 0.98 1.87 1.32 0. 1.38 0.94
time (sec) N/A 0.093 0.026 0.015 0.756 0.286 0. 0.27 15.265
Problem 11 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 117 117 394 637 0 1227 0 0 138
normalized size 1 1. 3.37 5.44 0. 10.49 0. 0. 1.18
time (sec) N/A 0.38 0.646 0.171 0. 0.304 0. 0. 29.971
Problem 12 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A F F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 484 484 182 6871419 0 16226 0 0 0
normalized size 1 1. 0.38 14197.2 0. 33.52 0. 0. 0.
time (sec) N/A 25.519 0.505 0.623 0. 0.649 0. 0. 0.
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 184 182 175 510 0 1 1260 258 0
normalized size 1 0.99 0.95 2.77 0. 0.01 6.85 1.4 0.
time (sec) N/A 0.7 0.363 0.01 0. 0.296 29.302 0.268 0.
Problem 14 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 542 542 535 1672 0 1 0 996 0
normalized size 1 1. 0.99 3.08 0. 0. 0. 1.84 0.
time (sec) N/A 2.961 1.853 0.013 0. 0.426 0. 0.278 0.
Problem 15 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F(-1) F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 406 398 267 1698 0 0 0 0 0
normalized size 1 0.98 0.66 4.18 0. 0. 0. 0. 0.
time (sec) N/A 1.127 1.062 0.014 0. 0. 0. 0. 0.
Problem 16 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 1075 1067 1376 54204 0 0 0 1 0
normalized size 1 0.99 1.28 50.42 0. 0. 0. 0. 0.
time (sec) N/A 11.087 8.889 0.054 0. 0. 0. 0.388 0.
Problem 17 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 140 140 131 340 0 1 709 296 131
normalized size 1 1. 0.94 2.43 0. 0.01 5.06 2.11 0.94
time (sec) N/A 0.308 0.263 0.007 0. 0.306 4.818 0.277 49.73
Problem 18 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 140 140 131 340 0 1 680 279 126
normalized size 1 1. 0.94 2.43 0. 0.01 4.86 1.99 0.9
time (sec) N/A 0.241 0.049 0.006 0. 0.302 4.752 0.276 50.043
Problem 19 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F(-2) F(-1) F F(-2) F(-1)
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 617 615 1629 16209 0 0 0 0 0
normalized size 1 1. 2.64 26.27 0. 0. 0. 0. 0.
time (sec) N/A 18.536 6.249 0.026 0. 0. 0. 0. 0.
Problem 20 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F(-2) F(-1) F(-1) F(-2) F(-1)
verified N/A NO NO TBD TBD TBD TBD TBD TBD
size 1092 1092 3733 59465 0 0 0 0 0
normalized size 1 1. 3.42 54.46 0. 0. 0. 0. 0.
time (sec) N/A 32.056 6.52 0.04 0. 0. 0. 0. 0.
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F F(-2) A
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 416 416 696 2269 0 0 0 0 394
normalized size 1 1. 1.67 5.45 0. 0. 0. 0. 0.95
time (sec) N/A 6.323 1.727 0.079 0. 0. 0. 0. 141.626
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F(-2) A F F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 780 780 411 784 0 9262 0 0 0
normalized size 1 1. 0.53 1.01 0. 11.87 0. 0. 0.
time (sec) N/A 10.709 2.732 0.065 0. 45.857 0. 0. 0.
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 302 302 512 1771 0 12119 0 0 308
normalized size 1 1. 1.7 5.86 0. 40.13 0. 0. 1.02
time (sec) N/A 2.143 1.207 0.067 0. 56.029 0. 0. 64.421
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 101 101 282 608 0 2045 0 1 155
normalized size 1 1. 2.79 6.02 0. 20.25 0. 0.01 1.53
time (sec) N/A 0.318 0.774 0.044 0. 0.4 0. 1.286 28.905
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A F F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 139 139 161 324 487 466 0 0 144
normalized size 1 1. 1.16 2.33 3.5 3.35 0. 0. 1.04
time (sec) N/A 0.485 0.675 0.079 0.8 0.301 0. 0. 39.843
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A F(-1) F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 166 166 263 760 915 586 0 0 168
normalized size 1 1. 1.58 4.58 5.51 3.53 0. 0. 1.01
time (sec) N/A 0.581 1.521 0.033 0.807 0.294 0. 0. 50.533
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B A A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 193 193 304 1560 1723 872 0 0 189
normalized size 1 1. 1.58 8.08 8.93 4.52 0. 0. 0.98
time (sec) N/A 0.709 0.936 0.027 0.853 0.299 0. 0. 84.182
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 151 151 220 186 490 431 0 0 150
normalized size 1 1. 1.46 1.23 3.25 2.85 0. 0. 0.99
time (sec) N/A 0.601 1.253 0.06 0.8 0.285 0. 0. 40.304
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 174 174 252 466 902 763 0 0 170
normalized size 1 1. 1.45 2.68 5.18 4.39 0. 0. 0.98
time (sec) N/A 0.725 1.792 0.026 0.805 0.288 0. 0. 53.005
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B A A F(-1) F(-2) A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 197 197 283 878 1723 1088 0 0 194
normalized size 1 1. 1.44 4.46 8.75 5.52 0. 0. 0.98
time (sec) N/A 0.816 3.365 0.023 0.837 0.29 0. 0. 79.285
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B A F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 41 14 0 66 36 78 14
normalized size 1 1. 2.73 0.93 0. 4.4 2.4 5.2 0.93
time (sec) N/A 0.052 0.018 0.011 0. 0.273 2.397 0.277 13.311
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B A F A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 44 44 109 40 0 134 0 146 42
normalized size 1 1. 2.48 0.91 0. 3.05 0. 3.32 0.95
time (sec) N/A 0.145 0.153 0.013 0. 0.276 0. 0.277 54.53
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 24 24 24 20 0 180 68 0 24
normalized size 1 1. 1. 0.83 0. 7.5 2.83 0. 1.
time (sec) N/A 0.057 0.019 0.018 0. 0.272 2.308 0. 14.814
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B A F A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 56 56 126 45 0 433 0 0 56
normalized size 1 1. 2.25 0.8 0. 7.73 0. 0. 1.
time (sec) N/A 0.136 0.212 0.014 0. 0.293 0. 0. 34.288
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F F(-1) F(-1) F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 249 249 767 3606 0 0 0 0 0
normalized size 1 1. 3.08 14.48 0. 0. 0. 0. 0.
time (sec) N/A 1.944 1.85 0.028 0. 0. 0. 0. 0.
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 48 48 46 48 0 115 0 109 46
normalized size 1 1. 0.96 1. 0. 2.4 0. 2.27 0.96
time (sec) N/A 0.148 0.068 0.007 0. 0.456 0. 0.275 33.254
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 17 17 1057 94 0 76 0 132 15
normalized size 1 1. 62.18 5.53 0. 4.47 0. 7.76 0.88
time (sec) N/A 0.067 6.283 0.015 0. 0.288 0. 0.274 18.129
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 86 86 1079 123 0 167 0 220 83
normalized size 1 1. 12.55 1.43 0. 1.94 0. 2.56 0.97
time (sec) N/A 0.438 6.27 0.011 0. 0.293 0. 0.273 61.225
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) F(-1) F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 136 136 108 121 0 0 0 0 129
normalized size 1 1. 0.79 0.89 0. 0. 0. 0. 0.95
time (sec) N/A 0.299 0.182 0.025 0. 0. 0. 0. 42.465
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 212 212 108 105 0 1 0 158 196
normalized size 1 1. 0.51 0.5 0. 0. 0. 0.75 0.92
time (sec) N/A 0.393 0.129 0.043 0. 0.324 0. 0.27 40.439
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 161 161 96 84 0 1 0 132 146
normalized size 1 1. 0.6 0.52 0. 0.01 0. 0.82 0.91
time (sec) N/A 0.226 0.095 0.013 0. 0.325 0. 0.272 28.43
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 148 148 85 65 0 1 0 107 136
normalized size 1 1. 0.57 0.44 0. 0.01 0. 0.72 0.92
time (sec) N/A 0.149 0.075 0.013 0. 0.34 0. 0.272 26.19
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 160 160 139 94 0 1 0 138 150
normalized size 1 1. 0.87 0.59 0. 0.01 0. 0.86 0.94
time (sec) N/A 0.377 0.106 0.014 0. 0.342 0. 0.275 42.121
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 156 156 120 108 0 1 0 170 146
normalized size 1 1. 0.77 0.69 0. 0.01 0. 1.09 0.94
time (sec) N/A 0.371 0.079 0.017 0. 0.336 0. 0.277 38.292
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 161 161 125 141 0 1 0 269 151
normalized size 1 1. 0.78 0.88 0. 0.01 0. 1.67 0.94
time (sec) N/A 0.38 0.179 0.018 0. 0.335 0. 0.282 41.578
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 317 317 236 532 0 1 0 497 313
normalized size 1 1. 0.74 1.68 0. 0. 0. 1.57 0.99
time (sec) N/A 0.833 0.431 0.022 0. 0.354 0. 0.289 71.228
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 227 227 176 383 0 1 0 362 221
normalized size 1 1. 0.78 1.69 0. 0. 0. 1.59 0.97
time (sec) N/A 0.376 0.36 0.016 0. 0.336 0. 0.288 47.435
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 198 198 132 259 0 1 0 250 180
normalized size 1 1. 0.67 1.31 0. 0.01 0. 1.26 0.91
time (sec) N/A 0.258 0.247 0.014 0. 0.329 0. 0.282 44.775
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F(-2) A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 211 211 246 214 0 1 0 0 197
normalized size 1 1. 1.17 1.01 0. 0. 0. 0. 0.93
time (sec) N/A 0.537 0.274 0.015 0. 0.995 0. 0. 68.453
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F(-2) A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 202 202 168 259 0 1 0 0 189
normalized size 1 1. 0.83 1.28 0. 0. 0. 0. 0.94
time (sec) N/A 0.501 0.39 0.018 0. 0.461 0. 0. 63.063
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F(-2) A F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 215 215 177 345 0 1 0 0 201
normalized size 1 1. 0.82 1.6 0. 0. 0. 0. 0.93
time (sec) N/A 0.537 0.447 0.019 0. 0.6 0. 0. 66.684
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 452 452 882 7739 0 0 0 1 0
normalized size 1 1. 1.95 17.12 0. 0. 0. 0. 0.
time (sec) N/A 4.096 3.326 0.077 0. 0. 0. 0.667 0.
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F F F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 395 395 785 5581 0 0 0 0 0
normalized size 1 1. 1.99 14.13 0. 0. 0. 0. 0.
time (sec) N/A 3.701 1.684 0.02 0. 0. 0. 0. 0.
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 298 298 472 3249 0 0 0 0 296
normalized size 1 1. 1.58 10.9 0. 0. 0. 0. 0.99
time (sec) N/A 0.894 2.38 0.019 0. 0. 0. 0. 77.585
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 358 358 667 3544 0 1 0 0 0
normalized size 1 1. 1.86 9.9 0. 0. 0. 0. 0.
time (sec) N/A 2.709 1.207 0.022 0. 39.914 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 F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 382 382 600 3703 0 0 0 0 0
normalized size 1 1. 1.57 9.69 0. 0. 0. 0. 0.
time (sec) N/A 3.126 1.159 0.051 0. 0. 0. 0. 0.
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 507 507 767 3993 0 0 0 1 0
normalized size 1 1. 1.51 7.88 0. 0. 0. 0. 0.
time (sec) N/A 4.11 2.691 0.026 0. 0. 0. 1.345 0.
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 795 795 1565 19148 0 0 0 1 0
normalized size 1 1. 1.97 24.09 0. 0. 0. 0. 0.
time (sec) N/A 9.888 6.225 0.043 0. 0. 0. 0.918 0.
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 591 591 1176 14709 0 0 0 1 0
normalized size 1 1. 1.99 24.89 0. 0. 0. 0. 0.
time (sec) N/A 7.026 4.085 0.024 0. 0. 0. 0.826 0.
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 484 482 932 8954 0 0 0 0 0
normalized size 1 1. 1.93 18.5 0. 0. 0. 0. 0.
time (sec) N/A 8.827 2.716 0.022 0. 0. 0. 0. 0.
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 496 496 956 9728 0 0 0 1 0
normalized size 1 1. 1.93 19.61 0. 0. 0. 0. 0.
time (sec) N/A 5.342 2.071 0.027 0. 0. 0. 1.315 0.
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 604 604 880 9912 0 0 0 1 0
normalized size 1 1. 1.46 16.41 0. 0. 0. 0. 0.
time (sec) N/A 5.933 1.498 0.029 0. 0. 0. 0.664 0.
Problem 63 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 668 668 949 10298 0 0 0 1 0
normalized size 1 1. 1.42 15.42 0. 0. 0. 0. 0.
time (sec) N/A 6.973 4.534 0.03 0. 0. 0. 1.619 0.
Problem 64 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 380 380 696 2397 0 0 0 0 371
normalized size 1 1. 1.83 6.31 0. 0. 0. 0. 0.98
time (sec) N/A 2.429 1.235 0.037 0. 0. 0. 0. 145.077
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 344 344 602 1796 0 0 0 0 337
normalized size 1 1. 1.75 5.22 0. 0. 0. 0. 0.98
time (sec) N/A 1.311 0.842 0.022 0. 0. 0. 0. 96.086
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 294 294 484 1172 0 6865 0 0 294
normalized size 1 1. 1.65 3.99 0. 23.35 0. 0. 1.
time (sec) N/A 0.682 4.295 0.018 0. 0.875 0. 0. 53.238
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 266 266 425 589 0 6849 0 0 267
normalized size 1 1. 1.6 2.21 0. 25.75 0. 0. 1.
time (sec) N/A 0.453 2.574 0.017 0. 0.865 0. 0. 45.554
Problem 68 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 330 330 513 681 0 0 0 0 325
normalized size 1 1. 1.55 2.06 0. 0. 0. 0. 0.98
time (sec) N/A 1.856 3.422 0.021 0. 0. 0. 0. 131.601
Problem 69 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 367 367 567 736 0 0 0 0 0
normalized size 1 1. 1.54 2.01 0. 0. 0. 0. 0.
time (sec) N/A 2.678 1.141 0.023 0. 0. 0. 0. 0.
Problem 70 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 457 457 678 911 0 0 0 0 439
normalized size 1 1. 1.48 1.99 0. 0. 0. 0. 0.96
time (sec) N/A 4.068 1.895 0.025 0. 0. 0. 0. 177.497
Problem 71 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 499 499 727 6124 0 0 0 0 0
normalized size 1 1. 1.46 12.27 0. 0. 0. 0. 0.
time (sec) N/A 4.639 1.826 0.039 0. 0. 0. 0. 0.
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 410 410 596 4752 0 0 0 0 398
normalized size 1 1. 1.45 11.59 0. 0. 0. 0. 0.97
time (sec) N/A 1.707 1.427 0.023 0. 0. 0. 0. 154.803
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 411 411 617 3000 0 0 0 0 400
normalized size 1 1. 1.5 7.3 0. 0. 0. 0. 0.97
time (sec) N/A 1.96 1.752 0.02 0. 0. 0. 0. 158.234
Problem 74 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 416 416 598 1713 0 0 0 0 0
normalized size 1 1. 1.44 4.12 0. 0. 0. 0. 0.
time (sec) N/A 1.512 1.403 0.02 0. 0. 0. 0. 0.
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 526 526 889 1945 0 0 0 0 0
normalized size 1 1. 1.69 3.7 0. 0. 0. 0. 0.
time (sec) N/A 4.828 2.179 0.023 0. 0. 0. 0. 0.
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 618 618 996 2046 0 0 0 0 0
normalized size 1 1. 1.61 3.31 0. 0. 0. 0. 0.
time (sec) N/A 5.442 3.16 0.025 0. 0. 0. 0. 0.
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 392 392 419 1817 0 0 0 0 0
normalized size 1 1. 1.07 4.64 0. 0. 0. 0. 0.
time (sec) N/A 1.875 2.742 0.025 0. 0. 0. 0. 0.
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 316 316 397 1810 0 0 0 0 0
normalized size 1 1. 1.26 5.73 0. 0. 0. 0. 0.
time (sec) N/A 1.106 2.395 0.021 0. 0. 0. 0. 0.
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 282 282 448 1667 0 0 0 0 257
normalized size 1 1. 1.59 5.91 0. 0. 0. 0. 0.91
time (sec) N/A 0.735 2.172 0.019 0. 0. 0. 0. 138.653
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 266 266 343 1669 0 1 0 0 240
normalized size 1 1. 1.29 6.27 0. 0. 0. 0. 0.9
time (sec) N/A 0.532 0.717 0.019 0. 100.791 0. 0. 89.738
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A F A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 267 267 473 1764 0 1 0 1 0
normalized size 1 1. 1.77 6.61 0. 0. 0. 0. 0.
time (sec) N/A 1.693 0.525 0.023 0. 17.468 0. 0.293 0.
Problem 82 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 286 286 379 1819 0 1 0 0 257
normalized size 1 1. 1.33 6.36 0. 0. 0. 0. 0.9
time (sec) N/A 1.545 1.395 0.032 0. 25.181 0. 0. 176.368
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A F F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 353 353 505 1953 0 1 0 0 0
normalized size 1 1. 1.43 5.53 0. 0. 0. 0. 0.
time (sec) N/A 1.939 0.79 0.026 0. 136.041 0. 0. 0.
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F(-1) F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 501 501 536 4884 0 0 0 0 0
normalized size 1 1. 1.07 9.75 0. 0. 0. 0. 0.
time (sec) N/A 2.857 1.575 0.04 0. 0. 0. 0. 0.
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 417 417 482 4900 0 0 0 0 0
normalized size 1 1. 1.16 11.75 0. 0. 0. 0. 0.
time (sec) N/A 2.215 1.263 0.025 0. 0. 0. 0. 0.
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 349 349 416 4567 0 0 0 0 0
normalized size 1 1. 1.19 13.09 0. 0. 0. 0. 0.
time (sec) N/A 1.345 0.97 0.022 0. 0. 0. 0. 0.
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 315 315 396 4574 0 0 0 0 0
normalized size 1 1. 1.26 14.52 0. 0. 0. 0. 0.
time (sec) N/A 1.156 1.107 0.022 0. 0. 0. 0. 0.
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F F(-1) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 469 469 443 4765 0 0 0 0 0
normalized size 1 1. 0.94 10.16 0. 0. 0. 0. 0.
time (sec) N/A 2.778 0.866 0.026 0. 0. 0. 0. 0.
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 463 463 433 4799 0 0 0 0 0
normalized size 1 1. 0.94 10.37 0. 0. 0. 0. 0.
time (sec) N/A 2.6 0.78 0.027 0. 0. 0. 0. 0.
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 614 614 429 5056 0 0 0 0 0
normalized size 1 1. 0.7 8.23 0. 0. 0. 0. 0.
time (sec) N/A 3.195 0.974 0.029 0. 0. 0. 0. 0.
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 189 189 207 1346 0 1 0 0 170
normalized size 1 1. 1.1 7.12 0. 0.01 0. 0. 0.9
time (sec) N/A 0.67 0.694 0.027 0. 166.762 0. 0. 98.292
Problem 92 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 75 75 79 102 112 95 0 99 56
normalized size 1 1. 1.05 1.36 1.49 1.27 0. 1.32 0.75
time (sec) N/A 0.143 0.021 0.02 0.795 0.299 0. 0.275 37.494
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 130 130 124 789 0 1806 0 0 141
normalized size 1 1. 0.95 6.07 0. 13.89 0. 0. 1.08
time (sec) N/A 0.382 0.2 0.08 0. 0.336 0. 0. 39.476
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) F(-1) F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 369 369 399 516 0 0 0 0 338
normalized size 1 1. 1.08 1.4 0. 0. 0. 0. 0.92
time (sec) N/A 1.576 4.762 0.025 0. 0. 0. 0. 144.552
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) F(-1) F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 287 287 404 410 0 0 0 0 260
normalized size 1 1. 1.41 1.43 0. 0. 0. 0. 0.91
time (sec) N/A 1.271 2.784 0.021 0. 0. 0. 0. 124.668
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) F(-1) F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 266 266 353 399 0 0 0 0 241
normalized size 1 1. 1.33 1.5 0. 0. 0. 0. 0.91
time (sec) N/A 0.533 0.788 0.02 0. 0. 0. 0. 78.789
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 220 220 289 354 0 3717 0 0 202
normalized size 1 1. 1.31 1.61 0. 16.9 0. 0. 0.92
time (sec) N/A 0.341 0.486 0.019 0. 0.641 0. 0. 57.718
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 220 220 301 358 0 3565 0 0 202
normalized size 1 1. 1.37 1.63 0. 16.2 0. 0. 0.92
time (sec) N/A 0.334 0.455 0.02 0. 0.702 0. 0. 55.761
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 267 267 351 391 0 1 0 1 241
normalized size 1 1. 1.31 1.46 0. 0. 0. 0. 0.9
time (sec) N/A 1.319 1.031 0.022 0. 71.979 0. 0.281 124.81
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F F(-1) F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 291 291 432 427 0 0 0 4 262
normalized size 1 1. 1.48 1.47 0. 0. 0. 0.01 0.9
time (sec) N/A 1.364 2.273 0.024 0. 0. 0. 0.658 131.872
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F F(-1) F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 376 376 418 519 0 0 0 4 342
normalized size 1 1. 1.11 1.38 0. 0. 0. 0.01 0.91
time (sec) N/A 1.593 2.714 0.026 0. 0. 0. 0.677 159.291
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F(-1) F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 466 466 480 1648 0 0 0 0 0
normalized size 1 1. 1.03 3.54 0. 0. 0. 0. 0.
time (sec) N/A 2.904 5.486 0.025 0. 0. 0. 0. 0.
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F(-1) F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 341 341 414 1480 0 0 0 0 0
normalized size 1 1. 1.21 4.34 0. 0. 0. 0. 0.
time (sec) N/A 2.181 3.658 0.023 0. 0. 0. 0. 0.
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 297 297 583 1427 0 0 0 0 338
normalized size 1 1. 1.96 4.8 0. 0. 0. 0. 1.14
time (sec) N/A 0.935 1.373 0.023 0. 0. 0. 0. 167.761
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 299 299 407 1360 0 0 0 0 342
normalized size 1 1. 1.36 4.55 0. 0. 0. 0. 1.14
time (sec) N/A 0.862 2.447 0.021 0. 0. 0. 0. 156.897
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 310 310 584 1376 0 0 0 0 352
normalized size 1 1. 1.88 4.44 0. 0. 0. 0. 1.14
time (sec) N/A 0.927 1.403 0.02 0. 0. 0. 0. 151.232
Problem 107 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 394 394 742 1518 0 0 0 1 0
normalized size 1 1. 1.88 3.85 0. 0. 0. 0. 0.
time (sec) N/A 2.334 6.481 0.024 0. 0. 0. 0.295 0.
Problem 108 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 454 454 537 1656 0 0 0 0 0
normalized size 1 1. 1.18 3.65 0. 0. 0. 0. 0.
time (sec) N/A 2.75 3.392 0.025 0. 0. 0. 0. 0.
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F(-2) F(-1) F F(-2) F(-1)
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 761 761 1546 14815 0 0 0 0 0
normalized size 1 1. 2.03 19.47 0. 0. 0. 0. 0.
time (sec) N/A 8.377 6.305 0.028 0. 0. 0. 0. 0.
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F(-2) F(-1) F F(-2) F(-1)
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 549 549 1112 10138 0 0 0 0 0
normalized size 1 1. 2.03 18.47 0. 0. 0. 0. 0.
time (sec) N/A 14.046 2.863 0.022 0. 0. 0. 0. 0.
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 431 431 699 6019 0 0 0 0 420
normalized size 1 1. 1.62 13.97 0. 0. 0. 0. 0.97
time (sec) N/A 1.636 4.703 0. 0. 0. 0. 0. 157.719
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F F(-2) F(-1)
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 523 521 903 6460 0 0 0 0 0
normalized size 1 1. 1.73 12.35 0. 0. 0. 0. 0.
time (sec) N/A 7.14 1.868 0.025 0. 0. 0. 0. 0.
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F F(-2) F(-1)
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 736 736 972 6765 0 0 0 0 0
normalized size 1 1. 1.32 9.19 0. 0. 0. 0. 0.
time (sec) N/A 8.042 3.755 0.028 0. 0. 0. 0. 0.
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F F(-2) F(-1)
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 545 545 918 3131 0 0 0 0 0
normalized size 1 1. 1.68 5.74 0. 0. 0. 0. 0.
time (sec) N/A 7.745 2.058 0.026 0. 0. 0. 0. 0.
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F F(-2) F(-1)
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 463 463 815 2321 0 0 0 0 0
normalized size 1 1. 1.76 5.01 0. 0. 0. 0. 0.
time (sec) N/A 7.394 1.39 0.023 0. 0. 0. 0. 0.
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F(-2) A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 402 402 874 1516 0 15270 0 0 384
normalized size 1 1. 2.17 3.77 0. 37.99 0. 0. 0.96
time (sec) N/A 2.555 6.179 0.02 0. 5.157 0. 0. 127.151
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 374 374 633 761 0 15237 0 0 357
normalized size 1 1. 1.69 2.03 0. 40.74 0. 0. 0.95
time (sec) N/A 0.791 4.572 0. 0. 6.795 0. 0. 107.217
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B B F F(-1) F F(-2) F(-1)
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 451 451 994 859 0 0 0 0 0
normalized size 1 1. 2.2 1.9 0. 0. 0. 0. 0.
time (sec) N/A 5.868 6.246 0.022 0. 0. 0. 0. 0.
Problem 119 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 NO Yes TBD TBD TBD TBD TBD TBD
size 543 543 866 983 0 0 0 0 0
normalized size 1 1. 1.59 1.81 0. 0. 0. 0. 0.
time (sec) N/A 10.059 1.872 0.026 0. 0. 0. 0. 0.
Problem 120 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 NO Yes TBD TBD TBD TBD TBD TBD
size 679 679 1008 1296 0 0 0 0 0
normalized size 1 1. 1.48 1.91 0. 0. 0. 0. 0.
time (sec) N/A 17.187 3.369 0.029 0. 0. 0. 0. 0.
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F(-1) F(-2) F(-1)
verified N/A NO Yes TBD TBD TBD TBD TBD TBD
size 779 779 1066 13951 0 0 0 0 0
normalized size 1 1. 1.37 17.91 0. 0. 0. 0. 0.
time (sec) N/A 24.266 5.97 0.034 0. 0. 0. 0. 0.
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F(-1) F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 609 609 897 10781 0 0 0 0 0
normalized size 1 1. 1.47 17.7 0. 0. 0. 0. 0.
time (sec) N/A 13.191 4.724 0.028 0. 0. 0. 0. 0.
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F(-1) F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 609 609 868 6813 0 0 0 0 0
normalized size 1 1. 1.43 11.19 0. 0. 0. 0. 0.
time (sec) N/A 12.776 3.99 0.024 0. 0. 0. 0. 0.
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) F(-1) F(-1) F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 666 666 906 3889 0 0 0 0 0
normalized size 1 1. 1.36 5.84 0. 0. 0. 0. 0.
time (sec) N/A 4.165 4.528 0. 0. 0. 0. 0. 0.
Problem 125 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 NO NO TBD TBD TBD TBD TBD TBD
size 816 814 1331 4384 0 0 0 0 0
normalized size 1 1. 1.63 5.37 0. 0. 0. 0. 0.
time (sec) N/A 24.85 5.879 0.026 0. 0. 0. 0. 0.
Problem 126 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 140 140 1101 159 0 242 0 254 153
normalized size 1 1. 7.86 1.14 0. 1.73 0. 1.81 1.09
time (sec) N/A 1.034 6.294 0.024 0. 0.308 0. 0.29 121.949
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 115 115 1093 144 0 236 0 250 129
normalized size 1 1. 9.5 1.25 0. 2.05 0. 2.17 1.12
time (sec) N/A 0.887 6.284 0.019 0. 0.3 0. 0.275 115.126
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 98 98 1087 130 0 213 0 231 116
normalized size 1 1. 11.09 1.33 0. 2.17 0. 2.36 1.18
time (sec) N/A 0.484 6.269 0.009 0. 0.305 0. 0.275 83.245
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 68 69 891 92 0 54 0 92 71
normalized size 1 1.01 13.1 1.35 0. 0.79 0. 1.35 1.04
time (sec) N/A 0.151 6.362 0.011 0. 0.292 0. 0.271 25.026
Problem 130 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F A F A A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 95 95 800 121 0 167 0 223 88
normalized size 1 1. 8.42 1.27 0. 1.76 0. 2.35 0.93
time (sec) N/A 0.26 4.356 0.009 0. 0.294 0. 0.272 52.695
Problem 131 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 130 130 1068 152 0 221 0 269 129
normalized size 1 1. 8.22 1.17 0. 1.7 0. 2.07 0.99
time (sec) N/A 0.865 6.25 0.023 0. 0.3 0. 0.272 124.364
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 151 151 1135 169 0 258 0 363 150
normalized size 1 1. 7.52 1.12 0. 1.71 0. 2.4 0.99
time (sec) N/A 1.001 6.298 0.023 0. 0.306 0. 0.274 118.371
Problem 133 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 149 149 111 147 209 128 0 115 138
normalized size 1 1. 0.74 0.99 1.4 0.86 0. 0.77 0.93
time (sec) N/A 0.232 0.157 0.022 0.789 0.287 0. 0.271 28.563
Problem 134 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 103 103 70 96 140 108 0 95 94
normalized size 1 1. 0.68 0.93 1.36 1.05 0. 0.92 0.91
time (sec) N/A 0.113 0.084 0.009 0.78 0.283 0. 0.268 17.707
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 28 28 37 163 0 72 0 85 26
normalized size 1 1. 1.32 5.82 0. 2.57 0. 3.04 0.93
time (sec) N/A 0.118 0.027 0.021 0. 0.295 0. 0.281 23.149
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 84 84 93 245 0 170 0 215 71
normalized size 1 1. 1.11 2.92 0. 2.02 0. 2.56 0.85
time (sec) N/A 0.209 0.24 0.027 0. 0.29 0. 0.29 32.086
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 139 139 129 306 0 251 0 313 126
normalized size 1 1. 0.93 2.2 0. 1.81 0. 2.25 0.91
time (sec) N/A 0.357 0.187 0.032 0. 0.295 0. 0.289 47.051
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 13 16 15 15 31 15 12
normalized size 1 1. 0.87 1.07 1. 1. 2.07 1. 0.8
time (sec) N/A 0.008 0.017 0.005 0.715 0.276 0.407 0.271 2.594
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 16 16 13 14 12 15 10 15 10
normalized size 1 1. 0.81 0.88 0.75 0.94 0.62 0.94 0.62
time (sec) N/A 0.008 0.009 0.004 0.702 0.274 15.185 0.271 1.904
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 13 20 0 15 0 0 12
normalized size 1 1. 0.87 1.33 0. 1. 0. 0. 0.8
time (sec) N/A 0.045 0.014 0.005 0. 0.27 0. 0. 9.685
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 15 15 13 18 0 15 0 0 12
normalized size 1 1. 0.87 1.2 0. 1. 0. 0. 0.8
time (sec) N/A 0.093 0.01 0.005 0. 0.279 0. 0. 11.966
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F(-1) F F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 242 242 331 0 0 0 0 0 224
normalized size 1 1. 1.37 0. 0. 0. 0. 0. 0.93
time (sec) N/A 0.344 1.038 0.314 0. 0. 0. 0. 29.789
Problem 143 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F(-1) F(-1) F F(-1)
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 488 488 0 0 0 0 0 0 0
normalized size 1 1. 0. 0. 0. 0. 0. 0. 0.
time (sec) N/A 1.378 0.93 0.668 0. 0. 0. 0. 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 [63] had the largest ratio of [ 0.5556 ]

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 5 4 1. 25 0.16
2 A 5 4 1. 27 0.148
3 A 5 4 1. 27 0.148
4 A 8 7 1. 27 0.259
5 A 9 8 1. 27 0.296
6 A 9 6 1. 30 0.2
7 A 5 3 1. 30 0.1
8 A 6 4 1. 30 0.133
9 A 7 5 1. 30 0.167
10 A 5 4 1. 23 0.174
11 A 5 4 1. 23 0.174
12 A 5 4 1. 30 0.133
13 A 6 5 0.99 28 0.179
14 A 6 5 1. 30 0.167
15 A 9 5 0.98 30 0.167
16 A 10 6 0.99 30 0.2
17 A 5 5 1. 34 0.147
18 A 5 5 1. 34 0.147
19 A 9 6 1. 32 0.188
20 A 10 7 1. 32 0.219
21 A 5 3 1. 32 0.094
22 A 5 3 1. 29 0.103
23 A 5 3 1. 29 0.103
24 A 6 6 1. 26 0.231
25 A 5 4 1. 30 0.133
26 A 7 6 1. 30 0.2
27 A 7 6 1. 30 0.2
28 A 5 3 1. 30 0.1
29 A 6 4 1. 30 0.133
30 A 7 5 1. 30 0.167
31 A 2 2 1. 26 0.077
32 A 5 5 1. 26 0.192
33 A 2 2 1. 24 0.083
34 A 5 5 1. 20 0.25
35 A 6 5 1. 36 0.139
36 A 2 2 1. 36 0.056
37 A 2 2 1. 32 0.062
38 A 13 9 1. 32 0.281
39 A 5 5 1. 38 0.132
40 A 6 6 1. 35 0.171
41 A 5 5 1. 33 0.152
42 A 5 5 1. 32 0.156
43 A 8 8 1. 35 0.229
44 A 8 8 1. 35 0.229
45 A 8 8 1. 35 0.229
46 A 6 6 1. 38 0.158
47 A 5 5 1. 36 0.139
48 A 5 5 1. 35 0.143
49 A 7 6 1. 38 0.158
50 A 7 6 1. 38 0.158
51 A 7 6 1. 38 0.158
52 A 9 6 1. 27 0.222
53 A 11 7 1. 25 0.28
54 A 8 5 1. 24 0.208
55 A 12 9 1. 27 0.333
56 A 18 12 1. 27 0.444
57 A 22 13 1. 27 0.482
58 A 10 7 1. 27 0.259
59 A 16 9 1. 25 0.36
60 A 9 6 1. 24 0.25
61 A 17 11 1. 27 0.407
62 A 21 14 1. 27 0.518
63 A 26 15 1. 27 0.556
64 A 10 6 1. 27 0.222
65 A 8 5 1. 27 0.185
66 A 5 3 1. 25 0.12
67 A 5 3 1. 24 0.125
68 A 10 7 1. 27 0.259
69 A 11 8 1. 27 0.296
70 A 15 9 1. 27 0.333
71 A 10 7 1. 27 0.259
72 A 6 4 1. 27 0.148
73 A 6 4 1. 25 0.16
74 A 6 4 1. 24 0.167
75 A 12 9 1. 27 0.333
76 A 14 11 1. 27 0.407
77 A 15 9 1. 28 0.321
78 A 9 6 1. 28 0.214
79 A 9 6 1. 26 0.231
80 A 8 5 1. 25 0.2
81 A 17 9 1. 28 0.321
82 A 16 8 1. 28 0.286
83 A 20 10 1. 28 0.357
84 A 17 10 1. 28 0.357
85 A 10 7 1. 28 0.25
86 A 10 7 1. 26 0.269
87 A 9 6 1. 25 0.24
88 A 19 11 1. 28 0.393
89 A 18 10 1. 28 0.357
90 A 26 13 1. 28 0.464
91 A 9 6 1. 24 0.25
92 A 8 6 1. 22 0.273
93 A 10 9 1. 17 0.529
94 A 13 7 1. 28 0.25
95 A 10 6 1. 28 0.214
96 A 8 5 1. 28 0.179
97 A 5 3 1. 26 0.115
98 A 5 3 1. 25 0.12
99 A 9 4 1. 28 0.143
100 A 10 5 1. 28 0.179
101 A 13 6 1. 28 0.214
102 A 13 9 1. 28 0.321
103 A 9 6 1. 28 0.214
104 A 6 4 1. 28 0.143
105 A 6 4 1. 26 0.154
106 A 6 4 1. 25 0.16
107 A 12 7 1. 28 0.25
108 A 12 7 1. 28 0.25
109 A 9 6 1. 30 0.2
110 A 9 6 1. 28 0.214
111 A 8 5 1. 27 0.185
112 A 17 9 1. 30 0.3
113 A 23 10 1. 30 0.333
114 A 12 6 1. 30 0.2
115 A 8 5 1. 30 0.167
116 A 5 3 1. 28 0.107
117 A 5 3 1. 27 0.111
118 A 9 4 1. 30 0.133
119 A 12 5 1. 30 0.167
120 A 16 7 1. 30 0.233
121 A 10 7 1. 30 0.233
122 A 6 4 1. 30 0.133
123 A 6 4 1. 28 0.143
124 A 6 4 1. 27 0.148
125 A 12 7 1. 30 0.233
126 A 24 14 1. 30 0.467
127 A 20 13 1. 30 0.433
128 A 16 12 1. 30 0.4
129 A 6 4 1.01 28 0.143
130 A 10 8 1. 27 0.296
131 A 17 11 1. 30 0.367
132 A 20 12 1. 30 0.4
133 A 8 6 1. 34 0.176
134 A 6 5 1. 30 0.167
135 A 3 3 1. 34 0.088
136 A 5 5 1. 34 0.147
137 A 7 7 1. 34 0.206
138 A 1 1 1. 17 0.059
139 A 1 1 1. 15 0.067
140 A 2 2 1. 23 0.087
141 A 3 3 1. 21 0.143
142 A 2 2 1. 40 0.05
143 A 2 2 1. 104 0.019

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