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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 A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 25 20 26 1 19 26 19
normalized size 1 1. 1. 0.8 1.04 0.04 0.76 1.04 0.76
time (sec) N/A 0.02 0.004 0.001 0.744 0.238 0.066 0.261 6.172
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 25 20 26 1 19 26 19
normalized size 1 1. 1. 0.8 1.04 0.04 0.76 1.04 0.76
time (sec) N/A 0.017 0.002 0.001 0.748 0.257 0.068 0.261 6.014
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 25 25 25 20 26 1 19 26 19
normalized size 1 1. 1. 0.8 1.04 0.04 0.76 1.04 0.76
time (sec) N/A 0.011 0. 0.001 0.754 0.24 0.062 0.261 1.906
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 25 25 25 20 26 26 19 26 0
normalized size 1 1. 1. 0.8 1.04 1.04 0.76 1.04 0.
time (sec) N/A 0.015 0.002 0.001 0.743 0.26 0.07 0.262 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 20 20 20 17 22 22 15 22 0
normalized size 1 1. 1. 0.85 1.1 1.1 0.75 1.1 0.
time (sec) N/A 0.015 0.002 0.001 0.75 0.255 0.068 0.264 0.
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 54 45 59 1 48 62 48
normalized size 1 1. 1. 0.83 1.09 0.02 0.89 1.15 0.89
time (sec) N/A 0.102 0.011 0.001 0.759 0.231 0.113 0.262 13.014
Problem 7 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 54 54 54 45 59 1 49 62 49
normalized size 1 1. 1. 0.83 1.09 0.02 0.91 1.15 0.91
time (sec) N/A 0.068 0.011 0.002 0.757 0.243 0.107 0.26 12.839
Problem 8 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 54 54 54 45 65 1 48 62 48
normalized size 1 1. 1. 0.83 1.2 0.02 0.89 1.15 0.89
time (sec) N/A 0.057 0.009 0.001 0.748 0.233 0.103 0.262 21.895
Problem 9 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 54 54 54 45 59 59 49 62 49
normalized size 1 1. 1. 0.83 1.09 1.09 0.91 1.15 0.91
time (sec) N/A 0.061 0.009 0.002 0.748 0.265 0.11 0.262 12.991
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 54 54 54 45 59 59 48 62 48
normalized size 1 1. 1. 0.83 1.09 1.09 0.89 1.15 0.89
time (sec) N/A 0.061 0.01 0.001 0.752 0.268 0.108 0.26 13.187
Problem 11 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 89 89 84 132 0 1 381 116 0
normalized size 1 1. 0.94 1.48 0. 0.01 4.28 1.3 0.
time (sec) N/A 0.175 0.197 0.005 0. 0.303 2.846 0.265 0.
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 70 70 73 101 0 1 306 90 65
normalized size 1 1. 1.04 1.44 0. 0.01 4.37 1.29 0.93
time (sec) N/A 0.105 0.106 0.004 0. 0.278 2.33 0.264 23.442
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 56 56 57 56 0 1 216 74 49
normalized size 1 1. 1.02 1. 0. 0.02 3.86 1.32 0.88
time (sec) N/A 0.07 0.057 0.003 0. 0.287 0.894 0.264 13.425
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 34 34 38 35 0 1 124 46 34
normalized size 1 1. 1.12 1.03 0. 0.03 3.65 1.35 1.
time (sec) N/A 0.04 0.011 0.002 0. 0.278 0.532 0.264 6.866
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 62 62 61 62 0 1 564 84 54
normalized size 1 1. 0.98 1. 0. 0.02 9.1 1.35 0.87
time (sec) N/A 0.091 0.112 0.006 0. 0.305 6.554 0.265 20.946
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 81 81 77 112 0 1 862 107 75
normalized size 1 1. 0.95 1.38 0. 0.01 10.64 1.32 0.93
time (sec) N/A 0.204 0.142 0.006 0. 0.291 12.141 0.264 45.617
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 104 104 102 150 0 1 1525 142 97
normalized size 1 1. 0.98 1.44 0. 0.01 14.66 1.37 0.93
time (sec) N/A 0.309 0.255 0.007 0. 0.32 17.267 0.264 44.282
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 137 137 131 214 0 1 2105 184 129
normalized size 1 1. 0.96 1.56 0. 0.01 15.36 1.34 0.94
time (sec) N/A 0.391 0.173 0.008 0. 0.367 28.052 0.264 57.4
Problem 19 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 150 150 132 569 0 1 842 217 0
normalized size 1 1. 0.88 3.79 0. 0.01 5.61 1.45 0.
time (sec) N/A 0.331 0.311 0.015 0. 0.306 5.991 0.269 0.
Problem 20 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 114 114 109 330 0 1 729 169 0
normalized size 1 1. 0.96 2.89 0. 0.01 6.39 1.48 0.
time (sec) N/A 0.209 0.232 0.013 0. 0.322 4.44 0.27 0.
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 67 67 81 97 0 1 280 119 61
normalized size 1 1. 1.21 1.45 0. 0.01 4.18 1.78 0.91
time (sec) N/A 0.074 0.152 0.009 0. 0.292 2.752 0.266 13.888
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 66 66 69 70 0 1 252 103 60
normalized size 1 1. 1.05 1.06 0. 0.02 3.82 1.56 0.91
time (sec) N/A 0.065 0.106 0.004 0. 0.289 2.625 0.268 11.811
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 66 66 70 68 0 1 265 103 60
normalized size 1 1. 1.06 1.03 0. 0.02 4.02 1.56 0.91
time (sec) N/A 0.06 0.123 0.003 0. 0.282 2.611 0.267 9.858
Problem 24 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 108 108 107 389 0 1 2236 170 102
normalized size 1 1. 0.99 3.6 0. 0.01 20.7 1.57 0.94
time (sec) N/A 0.311 0.319 0.011 0. 0.346 25.111 0.27 43.784
Problem 25 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 148 148 131 545 0 1 2672 231 143
normalized size 1 1. 0.89 3.68 0. 0.01 18.05 1.56 0.97
time (sec) N/A 0.395 0.467 0.013 0. 0.436 38.041 0.271 73.096
Problem 26 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 202 202 175 646 0 1 4083 309 192
normalized size 1 1. 0.87 3.2 0. 0. 20.21 1.53 0.95
time (sec) N/A 0.511 0.778 0.021 0. 0.546 58.744 0.274 82.886
Problem 27 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 252 252 218 808 0 1 4774 381 245
normalized size 1 1. 0.87 3.21 0. 0. 18.94 1.51 0.97
time (sec) N/A 0.647 0.516 0.024 0. 0.751 90.578 0.271 124.5
Problem 28 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 318 318 272 923 0 1 6181 468 308
normalized size 1 1. 0.86 2.9 0. 0. 19.44 1.47 0.97
time (sec) N/A 0.804 0.643 0.027 0. 1.041 137.52 0.275 127.985
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 257 257 180 310 0 1 0 382 241
normalized size 1 1. 0.7 1.21 0. 0. 0. 1.49 0.94
time (sec) N/A 0.945 0.438 0.013 0. 0.298 0. 0.302 91.259
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 205 205 150 265 0 1 0 311 190
normalized size 1 1. 0.73 1.29 0. 0. 0. 1.52 0.93
time (sec) N/A 0.59 0.333 0.011 0. 0.292 0. 0.304 59.514
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 163 163 117 167 0 1 0 224 146
normalized size 1 1. 0.72 1.02 0. 0.01 0. 1.37 0.9
time (sec) N/A 0.125 0.333 0.008 0. 0.28 0. 0.3 24.555
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 119 119 100 146 0 1 0 169 107
normalized size 1 1. 0.84 1.23 0. 0.01 0. 1.42 0.9
time (sec) N/A 0.132 0.236 0.007 0. 0.286 0. 0.294 19.825
Problem 33 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 173 173 144 126 0 1 0 0 158
normalized size 1 1. 0.83 0.73 0. 0.01 0. 0. 0.91
time (sec) N/A 0.261 0.165 0.007 0. 0.312 0. 0. 37.026
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 173 173 133 173 0 1 0 0 160
normalized size 1 1. 0.77 1. 0. 0.01 0. 0. 0.92
time (sec) N/A 0.261 0.223 0.009 0. 0.332 0. 0. 36.796
Problem 35 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 114 114 125 206 0 1 0 0 128
normalized size 1 1. 1.1 1.81 0. 0.01 0. 0. 1.12
time (sec) N/A 0.238 0.172 0.009 0. 0.293 0. 0. 41.954
Problem 36 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 155 155 145 234 0 1 0 0 167
normalized size 1 1. 0.94 1.51 0. 0.01 0. 0. 1.08
time (sec) N/A 0.413 0.39 0.009 0. 0.293 0. 0. 64.522
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 205 205 186 387 0 1 0 0 214
normalized size 1 1. 0.91 1.89 0. 0. 0. 0. 1.04
time (sec) N/A 0.619 0.392 0.011 0. 0.308 0. 0. 84.796
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 422 422 304 649 0 1 0 703 0
normalized size 1 1. 0.72 1.54 0. 0. 0. 1.67 0.
time (sec) N/A 1.871 0.647 0.014 0. 0.374 0. 0.34 0.
Problem 39 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 364 364 239 479 0 1 0 579 348
normalized size 1 1. 0.66 1.32 0. 0. 0. 1.59 0.96
time (sec) N/A 1.598 0.489 0.012 0. 0.338 0. 0.323 171.091
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 288 288 211 431 0 1 0 493 274
normalized size 1 1. 0.73 1.5 0. 0. 0. 1.71 0.95
time (sec) N/A 0.829 0.387 0.012 0. 0.311 0. 0.319 107.947
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 198 198 161 289 0 1 0 383 187
normalized size 1 1. 0.81 1.46 0. 0.01 0. 1.93 0.94
time (sec) N/A 0.297 0.286 0.008 0. 0.338 0. 0.315 40.016
Problem 42 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 165 165 130 265 0 1 0 313 155
normalized size 1 1. 0.79 1.61 0. 0.01 0. 1.9 0.94
time (sec) N/A 0.2 0.211 0.007 0. 0.298 0. 0.319 30.543
Problem 43 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 227 227 248 222 0 1 0 0 209
normalized size 1 1. 1.09 0.98 0. 0. 0. 0. 0.92
time (sec) N/A 0.467 0.326 0.009 0. 0.409 0. 0. 59.549
Problem 44 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 219 219 229 254 0 1 0 0 206
normalized size 1 1. 1.05 1.16 0. 0. 0. 0. 0.94
time (sec) N/A 0.46 0.258 0.009 0. 0.359 0. 0. 57.1
Problem 45 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 219 219 173 338 0 1 0 0 207
normalized size 1 1. 0.79 1.54 0. 0. 0. 0. 0.95
time (sec) N/A 0.453 0.356 0.01 0. 0.345 0. 0. 60.809
Problem 46 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 257 257 187 435 0 1 0 0 238
normalized size 1 1. 0.73 1.69 0. 0. 0. 0. 0.93
time (sec) N/A 0.644 0.752 0.013 0. 0.368 0. 0. 79.319
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 197 197 156 501 0 1 0 0 207
normalized size 1 1. 0.79 2.54 0. 0.01 0. 0. 1.05
time (sec) N/A 0.591 0.316 0.012 0. 0.328 0. 0. 83.266
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F F(-1) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 249 249 193 534 0 1 0 0 262
normalized size 1 1. 0.78 2.14 0. 0. 0. 0. 1.05
time (sec) N/A 0.808 0.409 0.014 0. 0.316 0. 0. 118.298
Problem 49 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 143 143 103 144 0 1 0 0 129
normalized size 1 1. 0.72 1.01 0. 0.01 0. 0. 0.9
time (sec) N/A 0.292 0.17 0.011 0. 0.299 0. 0. 31.519
Problem 50 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 103 103 87 88 0 1 0 146 92
normalized size 1 1. 0.84 0.85 0. 0.01 0. 1.42 0.89
time (sec) N/A 0.129 0.092 0.008 0. 0.294 0. 0.282 17.932
Problem 51 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 66 65 0 1 0 50 66
normalized size 1 1. 0.93 0.92 0. 0.01 0. 0.7 0.93
time (sec) N/A 0.063 0.04 0.007 0. 0.286 0. 0.281 10.336
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 70 66 0 1 0 80 68
normalized size 1 1. 1.56 1.47 0. 0.02 0. 1.78 1.51
time (sec) N/A 0.033 0.07 0.008 0. 0.278 0. 0.276 19.153
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 77 77 106 88 0 1 0 0 94
normalized size 1 1. 1.38 1.14 0. 0.01 0. 0. 1.22
time (sec) N/A 0.094 0.13 0.009 0. 0.297 0. 0. 28.709
Problem 54 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 119 119 138 152 0 1 0 0 134
normalized size 1 1. 1.16 1.28 0. 0.01 0. 0. 1.13
time (sec) N/A 0.25 0.231 0.01 0. 0.29 0. 0. 42.759
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 262 262 181 283 0 1 0 0 241
normalized size 1 1. 0.69 1.08 0. 0. 0. 0. 0.92
time (sec) N/A 0.785 0.327 0.012 0. 0.348 0. 0. 78.86
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 201 201 139 199 0 1 0 263 187
normalized size 1 1. 0.69 0.99 0. 0. 0. 1.31 0.93
time (sec) N/A 0.482 0.201 0.01 0. 0.329 0. 0.288 53.769
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 153 153 110 166 0 1 0 149 139
normalized size 1 1. 0.72 1.08 0. 0.01 0. 0.97 0.91
time (sec) N/A 0.274 0.18 0.011 0. 0.324 0. 0.293 33.372
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 37 53 0 99 0 61 36
normalized size 1 1. 0.92 1.32 0. 2.48 0. 1.52 0.9
time (sec) N/A 0.139 0.041 0.005 0. 0.291 0. 0.286 9.375
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 39 39 36 52 0 97 0 61 37
normalized size 1 1. 0.92 1.33 0. 2.49 0. 1.56 0.95
time (sec) N/A 0.056 0.03 0.005 0. 0.285 0. 0.285 9.387
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 94 94 132 166 0 1 0 0 112
normalized size 1 1. 1.4 1.77 0. 0.01 0. 0. 1.19
time (sec) N/A 0.11 0.261 0.009 0. 0.299 0. 0. 29.448
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F A F F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 144 144 163 201 0 1 0 0 162
normalized size 1 1. 1.13 1.4 0. 0.01 0. 0. 1.12
time (sec) N/A 0.268 0.28 0.01 0. 0.309 0. 0. 57.449
Problem 62 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 209 209 220 292 0 1 0 4 221
normalized size 1 1. 1.05 1.4 0. 0. 0. 0.02 1.06
time (sec) N/A 0.485 0.57 0.013 0. 0.353 0. 0.614 79.898
Problem 63 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 271 271 265 340 0 1 0 0 282
normalized size 1 1. 0.98 1.25 0. 0. 0. 0. 1.04
time (sec) N/A 0.74 0.582 0.015 0. 0.377 0. 0. 119.222
Problem 64 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 343 343 322 446 0 1 0 0 352
normalized size 1 1. 0.94 1.3 0. 0. 0. 0. 1.03
time (sec) N/A 0.975 0.926 0.017 0. 0.451 0. 0. 145.7
Problem 65 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 37 37 35 77 0 96 280 169 0
normalized size 1 1. 0.95 2.08 0. 2.59 7.57 4.57 0.
time (sec) N/A 0.03 0.037 0.004 0. 0.293 3.36 0.269 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 25 25 25 20 26 1 19 26 0
normalized size 1 1. 1. 0.8 1.04 0.04 0.76 1.04 0.
time (sec) N/A 0.018 0.003 0.001 0.777 0.238 0.069 0.249 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 25 25 25 20 26 1 19 26 19
normalized size 1 1. 1. 0.8 1.04 0.04 0.76 1.04 0.76
time (sec) N/A 0.016 0.003 0.001 0.771 0.235 0.067 0.25 6.748
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 25 25 25 20 26 1 19 26 0
normalized size 1 1. 1. 0.8 1.04 0.04 0.76 1.04 0.
time (sec) N/A 0.012 0. 0.001 0.762 0.235 0.07 0.253 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 20 20 20 17 22 22 15 22 0
normalized size 1 1. 1. 0.85 1.1 1.1 0.75 1.1 0.
time (sec) N/A 0.014 0.001 0.001 0.767 0.251 0.067 0.251 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 21 21 21 18 23 23 17 27 0
normalized size 1 1. 1. 0.86 1.1 1.1 0.81 1.29 0.
time (sec) N/A 0.016 0.003 0.003 0.766 0.255 0.169 0.279 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 18 18 18 17 22 27 12 22 0
normalized size 1 1. 1. 0.94 1.22 1.5 0.67 1.22 0.
time (sec) N/A 0.015 0.003 0.005 0.772 0.25 0.982 0.253 0.
Problem 72 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 76 76 70 300 0 325 1377 620 66
normalized size 1 1. 0.92 3.95 0. 4.28 18.12 8.16 0.87
time (sec) N/A 0.09 0.069 0.01 0. 0.28 12.458 0.286 26.186
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 54 54 54 45 59 1 51 62 51
normalized size 1 1. 1. 0.83 1.09 0.02 0.94 1.15 0.94
time (sec) N/A 0.076 0.012 0.001 0.772 0.247 0.112 0.248 14.021
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 54 54 48 45 59 1 46 62 0
normalized size 1 1. 0.89 0.83 1.09 0.02 0.85 1.15 0.
time (sec) N/A 0.13 0.013 0.001 0.773 0.248 0.112 0.249 0.
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 54 45 65 1 51 62 51
normalized size 1 1. 1. 0.83 1.2 0.02 0.94 1.15 0.94
time (sec) N/A 0.062 0.01 0.002 0.769 0.248 0.103 0.277 13.772
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 54 54 48 45 59 59 46 62 0
normalized size 1 1. 0.89 0.83 1.09 1.09 0.85 1.15 0.
time (sec) N/A 0.081 0.012 0.001 0.77 0.254 0.108 0.261 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 49 49 49 42 55 55 48 58 0
normalized size 1 1. 1. 0.86 1.12 1.12 0.98 1.18 0.
time (sec) N/A 0.048 0.008 0.002 0.78 0.272 0.112 0.248 0.
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 100 100 93 142 0 1 391 124 0
normalized size 1 1. 0.93 1.42 0. 0.01 3.91 1.24 0.
time (sec) N/A 0.241 0.171 0.005 0. 0.29 6.992 0.254 0.
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 203 203 250 467 0 2111 194 1 212
normalized size 1 1. 1.23 2.3 0. 10.4 0.96 0. 1.04
time (sec) N/A 1.137 0.284 0.03 0. 0.291 8.063 0.803 77.583
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 81 81 78 111 0 1 316 101 73
normalized size 1 1. 0.96 1.37 0. 0.01 3.9 1.25 0.9
time (sec) N/A 0.167 0.075 0.004 0. 0.268 5.63 0.258 32.595
Problem 81 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 179 179 202 343 0 1430 129 1 189
normalized size 1 1. 1.13 1.92 0. 7.99 0.72 0.01 1.06
time (sec) N/A 0.528 0.189 0.004 0. 0.277 5.896 0.775 55.566
Problem 82 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 63 63 62 60 0 1 223 80 54
normalized size 1 1. 0.98 0.95 0. 0.02 3.54 1.27 0.86
time (sec) N/A 0.123 0.038 0.003 0. 0.279 2.708 0.258 21.638
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 150 150 165 208 0 755 75 1 141
normalized size 1 1. 1.1 1.39 0. 5.03 0.5 0.01 0.94
time (sec) N/A 0.215 0.165 0.021 0. 0.27 2.563 0.691 27.373
Problem 84 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 36 36 39 36 0 1 131 47 34
normalized size 1 1. 1.08 1. 0. 0.03 3.64 1.31 0.94
time (sec) N/A 0.072 0.016 0.001 0. 0.263 1.41 0.25 12.48
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 150 150 129 116 0 828 87 1 138
normalized size 1 1. 0.86 0.77 0. 5.52 0.58 0.01 0.92
time (sec) N/A 0.183 0.134 0.018 0. 0.284 3.04 0.352 19.837
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 69 69 113 66 0 1 253 92 63
normalized size 1 1. 1.64 0.96 0. 0.01 3.67 1.33 0.91
time (sec) N/A 0.142 0.118 0.006 0. 0.279 9.405 0.251 28.98
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 174 174 191 232 0 1507 148 1 177
normalized size 1 1. 1.1 1.33 0. 8.66 0.85 0.01 1.02
time (sec) N/A 0.427 0.736 0.023 0. 0.307 6.541 0.777 46.816
Problem 88 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 89 89 135 119 0 1 345 127 87
normalized size 1 1. 1.52 1.34 0. 0.01 3.88 1.43 0.98
time (sec) N/A 0.263 0.235 0.01 0. 0.302 22.522 0.256 45.227
Problem 89 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 166 166 151 600 0 1 877 0 0
normalized size 1 1. 0.91 3.61 0. 0.01 5.28 0. 0.
time (sec) N/A 0.423 0.306 0.018 0. 0.299 17.107 0. 0.
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A A F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 331 331 327 2280 0 3856 450 0 0
normalized size 1 1. 0.99 6.89 0. 11.65 1.36 0. 0.
time (sec) N/A 1.42 1.109 0.069 0. 0.395 22.633 0. 0.
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A A F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 132 132 121 342 0 1 745 0 0
normalized size 1 1. 0.92 2.59 0. 0.01 5.64 0. 0.
time (sec) N/A 0.297 0.309 0.011 0. 0.304 12.883 0. 0.
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 271 271 282 2158 0 3047 379 0 267
normalized size 1 1. 1.04 7.96 0. 11.24 1.4 0. 0.99
time (sec) N/A 1.122 0.929 0.069 0. 0.325 16.15 0. 100.33
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 78 78 93 104 0 1 282 0 70
normalized size 1 1. 1.19 1.33 0. 0.01 3.62 0. 0.9
time (sec) N/A 0.129 0.15 0.005 0. 0.322 6.47 0. 20.403
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 237 237 235 1641 0 2252 294 0 218
normalized size 1 1. 0.99 6.92 0. 9.5 1.24 0. 0.92
time (sec) N/A 0.773 0.722 0.052 0. 0.303 11.96 0. 59.369
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 75 75 79 77 0 1 267 0 65
normalized size 1 1. 1.05 1.03 0. 0.01 3.56 0. 0.87
time (sec) N/A 0.12 0.122 0.005 0. 0.307 5.894 0. 18.357
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 221 221 222 342 0 2268 298 0 201
normalized size 1 1. 1. 1.55 0. 10.26 1.35 0. 0.91
time (sec) N/A 0.521 0.803 0.084 0. 0.323 12.467 0. 47.879
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 79 75 0 1 267 0 66
normalized size 1 1. 1.07 1.01 0. 0.01 3.61 0. 0.89
time (sec) N/A 0.119 0.144 0.005 0. 0.284 5.744 0. 14.874
Problem 98 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 252 252 243 733 0 3117 394 0 230
normalized size 1 1. 0.96 2.91 0. 12.37 1.56 0. 0.91
time (sec) N/A 0.925 0.753 0.073 0. 0.34 15.714 0. 67.413
Problem 99 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 122 122 207 405 0 1 772 0 116
normalized size 1 1. 1.7 3.32 0. 0.01 6.33 0. 0.95
time (sec) N/A 0.371 0.685 0.012 0. 0.361 111.429 0. 52.529
Problem 100 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 308 308 302 2012 0 3931 481 0 282
normalized size 1 1. 0.98 6.53 0. 12.76 1.56 0. 0.92
time (sec) N/A 2.588 1.09 0.059 0. 0.418 24.558 0. 140.539
Problem 101 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 162 162 248 569 0 1 0 0 153
normalized size 1 1. 1.53 3.51 0. 0.01 0. 0. 0.94
time (sec) N/A 0.493 0.466 0.015 0. 0.426 0. 0. 83.363
Problem 102 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A A F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 361 361 344 2349 0 4637 566 0 0
normalized size 1 1. 0.95 6.51 0. 12.84 1.57 0. 0.
time (sec) N/A 5.664 1.235 0.07 0. 0.574 43.168 0. 0.
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 219 219 328 671 0 1 0 0 209
normalized size 1 1. 1.5 3.06 0. 0. 0. 0. 0.95
time (sec) N/A 0.627 0.626 0.027 0. 0.528 0. 0. 96.251
Problem 104 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B F F F F F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 142 142 383 0 0 0 0 0 138
normalized size 1 1. 2.7 0. 0. 0. 0. 0. 0.97
time (sec) N/A 0.479 0.31 0.027 0. 0. 0. 0. 42.429
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 380 380 486 1042 0 0 0 0 350
normalized size 1 1. 1.28 2.74 0. 0. 0. 0. 0.92
time (sec) N/A 0.528 2.619 0.048 0. 0. 0. 0. 71.591
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 129 129 122 157 0 1 0 171 117
normalized size 1 1. 0.95 1.22 0. 0.01 0. 1.33 0.91
time (sec) N/A 0.167 0.135 0.014 0. 0.289 0. 0.301 22.449
Problem 107 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 347 347 452 508 0 0 0 0 314
normalized size 1 1. 1.3 1.46 0. 0. 0. 0. 0.9
time (sec) N/A 0.433 1.871 0.025 0. 0. 0. 0. 63.434
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 194 194 165 136 0 1 0 0 177
normalized size 1 1. 0.85 0.7 0. 0.01 0. 0. 0.91
time (sec) N/A 0.445 0.325 0.015 0. 0.324 0. 0. 46.393
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 244 244 181 369 0 1 0 0 230
normalized size 1 1. 0.74 1.51 0. 0. 0. 0. 0.94
time (sec) N/A 0.584 0.246 0.019 0. 0.307 0. 0. 63.789
Problem 110 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 487 487 609 1880 0 0 0 0 454
normalized size 1 1. 1.25 3.86 0. 0. 0. 0. 0.93
time (sec) N/A 0.847 3.989 0.033 0. 0. 0. 0. 103.107
Problem 111 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 177 177 150 295 0 1 0 624 167
normalized size 1 1. 0.85 1.67 0. 0.01 0. 3.53 0.94
time (sec) N/A 0.246 0.198 0.015 0. 0.323 0. 0.412 32.15
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F F F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 425 425 540 1394 0 0 0 0 394
normalized size 1 1. 1.27 3.28 0. 0. 0. 0. 0.93
time (sec) N/A 0.796 3.099 0.029 0. 0. 0. 0. 96.39
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 82 82 80 72 0 1 0 54 75
normalized size 1 1. 0.98 0.88 0. 0.01 0. 0.66 0.91
time (sec) N/A 0.11 0.058 0.013 0. 0.297 0. 0.337 14.876
Problem 114 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 121 121 193 177 0 0 0 0 109
normalized size 1 1. 1.6 1.46 0. 0. 0. 0. 0.9
time (sec) N/A 0.098 0.236 0.024 0. 0. 0. 0. 17.618
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 89 72 0 1 0 0 76
normalized size 1 1. 1.75 1.41 0. 0.02 0. 0. 1.49
time (sec) N/A 0.052 0.152 0.016 0. 0.288 0. 0. 20.18
Problem 116 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 330 330 303 508 0 0 0 0 296
normalized size 1 1. 0.92 1.54 0. 0. 0. 0. 0.9
time (sec) N/A 0.38 0.953 0.028 0. 0. 0. 0. 63.671
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A F F F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 391 391 463 533 0 0 0 0 362
normalized size 1 1. 1.18 1.36 0. 0. 0. 0. 0.93
time (sec) N/A 0.513 1.854 0.028 0. 0. 0. 0. 75.427
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 103 103 154 179 0 1 0 0 122
normalized size 1 1. 1.5 1.74 0. 0.01 0. 0. 1.18
time (sec) N/A 0.128 0.369 0.018 0. 0.31 0. 0. 28.549
Problem 119 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 468 468 519 1136 0 0 0 0 434
normalized size 1 1. 1.11 2.43 0. 0. 0. 0. 0.93
time (sec) N/A 0.789 2.407 0.032 0. 0. 0. 0. 108.185
Problem 120 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 154 154 192 220 0 1 0 0 172
normalized size 1 1. 1.25 1.43 0. 0.01 0. 0. 1.12
time (sec) N/A 0.295 0.393 0.019 0. 0.323 0. 0. 54.254
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 46 0 0 112 0 0 48
normalized size 1 1. 0.9 0. 0. 2.2 0. 0. 0.94
time (sec) N/A 0.071 0.128 0.112 0. 0.354 0. 0. 8.144
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A B F F F F F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 287 287 639 0 0 0 0 0 280
normalized size 1 1. 2.23 0. 0. 0. 0. 0. 0.98
time (sec) N/A 1.087 0.755 0.032 0. 0. 0. 0. 91.436
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 78 58 27 124 0 0 68
normalized size 1 1. 1.73 1.29 0.6 2.76 0. 0. 1.51
time (sec) N/A 0.021 0.074 0.017 0.879 0.288 0. 0. 17.946
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 78 58 27 124 0 0 68
normalized size 1 1. 1.73 1.29 0.6 2.76 0. 0. 1.51
time (sec) N/A 0.026 0.03 0.011 0.866 0.3 0. 0. 18.191
Problem 125 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 78 58 27 124 0 0 68
normalized size 1 1. 1.73 1.29 0.6 2.76 0. 0. 1.51
time (sec) N/A 0.027 0.03 0.007 0.862 0.295 0. 0. 18.371
Problem 126 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 86 86 70 81 63 95 0 93 85
normalized size 1 1. 0.81 0.94 0.73 1.1 0. 1.08 0.99
time (sec) N/A 0.079 0.055 0.013 0.881 0.286 0. 0.265 14.934
Problem 127 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 86 86 70 81 63 95 0 93 85
normalized size 1 1. 0.81 0.94 0.73 1.1 0. 1.08 0.99
time (sec) N/A 0.081 0.009 0.006 0.891 0.287 0. 0.266 15.17
Problem 128 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 86 86 70 81 63 95 0 93 85
normalized size 1 1. 0.81 0.94 0.73 1.1 0. 1.08 0.99
time (sec) N/A 0.08 0.009 0.006 0.866 0.276 0. 0.264 15.361
Problem 129 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 38 38 39 35 0 1 0 47 34
normalized size 1 1. 1.03 0.92 0. 0.03 0. 1.24 0.89
time (sec) N/A 0.043 0.056 0.005 0. 0.29 0. 0.271 6.565
Problem 130 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 45 45 70 64 0 1 0 80 68
normalized size 1 1. 1.56 1.42 0. 0.02 0. 1.78 1.51
time (sec) N/A 0.043 0.056 0.012 0. 0.284 0. 0.274 19.497
Problem 131 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 47 47 72 64 0 1 0 47 70
normalized size 1 1. 1.53 1.36 0. 0.02 0. 1. 1.49
time (sec) N/A 0.118 0.068 0.016 0. 0.348 0. 0.278 19.188
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 49 49 74 66 0 1 0 47 71
normalized size 1 1. 1.51 1.35 0. 0.02 0. 0.96 1.45
time (sec) N/A 0.147 0.061 0.012 0. 0.332 0. 0.284 17.595
Problem 133 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 44 44 50 39 0 1 0 0 39
normalized size 1 1. 1.14 0.89 0. 0.02 0. 0. 0.89
time (sec) N/A 0.087 0.082 0.006 0. 0.309 0. 0. 12.532
Problem 134 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 87 72 0 1 0 0 75
normalized size 1 1. 1.78 1.47 0. 0.02 0. 0. 1.53
time (sec) N/A 0.032 0.08 0.011 0. 0.3 0. 0. 26.121
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 51 51 89 72 0 1 0 0 76
normalized size 1 1. 1.75 1.41 0. 0.02 0. 0. 1.49
time (sec) N/A 0.106 0.086 0.015 0. 0.296 0. 0. 22.739
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A F(-2) A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 91 74 0 1 0 0 78
normalized size 1 1. 1.72 1.4 0. 0.02 0. 0. 1.47
time (sec) N/A 0.12 0.085 0.012 0. 0.282 0. 0. 22.717
Problem 137 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 40 40 45 31 27 111 0 0 36
normalized size 1 1. 1.12 0.78 0.68 2.78 0. 0. 0.9
time (sec) N/A 0.058 0.051 0.005 0.852 0.288 0. 0. 8.575
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-1) F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 45 45 78 58 27 124 0 0 68
normalized size 1 1. 1.73 1.29 0.6 2.76 0. 0. 1.51
time (sec) N/A 0.025 0.042 0. 0.873 0.29 0. 0. 18.018
Problem 139 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 43 43 67 50 34 69 0 69 65
normalized size 1 1. 1.56 1.16 0.79 1.6 0. 1.6 1.51
time (sec) N/A 0.073 0.034 0.017 0.901 0.305 0. 0.294 14.181
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A F F F(-2) F(-1) F A
verified N/A Yes N/A TBD TBD TBD TBD TBD TBD
size 70 70 0 0 0 0 0 0 99
normalized size 1 1. 0. 0. 0. 0. 0. 0. 1.41
time (sec) N/A 0.104 0.347 0.2 0. 0. 0. 0. 24.481

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 [86] had the largest ratio of [ 0.5 ]

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. 20 0.05
2 A 2 1 1. 18 0.056
3 A 1 0 1. 16 0.
4 A 2 1 1. 20 0.05
5 A 2 1 1. 20 0.05
6 A 3 2 1. 22 0.091
7 A 3 2 1. 20 0.1
8 A 3 2 1. 18 0.111
9 A 3 2 1. 22 0.091
10 A 3 2 1. 22 0.091
11 A 7 6 1. 22 0.273
12 A 6 6 1. 22 0.273
13 A 5 5 1. 22 0.227
14 A 3 3 1. 22 0.136
15 A 7 7 1. 20 0.35
16 A 8 7 1. 18 0.389
17 A 8 7 1. 22 0.318
18 A 8 7 1. 22 0.318
19 A 8 7 1. 22 0.318
20 A 7 7 1. 22 0.318
21 A 4 4 1. 22 0.182
22 A 4 4 1. 22 0.182
23 A 4 4 1. 22 0.182
24 A 8 7 1. 22 0.318
25 A 8 7 1. 22 0.318
26 A 8 7 1. 20 0.35
27 A 8 7 1. 18 0.389
28 A 8 7 1. 22 0.318
29 A 8 6 1. 24 0.25
30 A 7 6 1. 22 0.273
31 A 5 5 1. 20 0.25
32 A 4 4 1. 24 0.167
33 A 7 6 1. 24 0.25
34 A 7 6 1. 24 0.25
35 A 5 5 1. 24 0.208
36 A 6 5 1. 24 0.208
37 A 7 5 1. 24 0.208
38 A 10 7 1. 22 0.318
39 A 10 7 1. 20 0.35
40 A 8 7 1. 24 0.292
41 A 6 5 1. 24 0.208
42 A 5 4 1. 24 0.167
43 A 8 7 1. 24 0.292
44 A 8 7 1. 24 0.292
45 A 8 7 1. 24 0.292
46 A 9 8 1. 24 0.333
47 A 7 6 1. 24 0.25
48 A 8 6 1. 24 0.25
49 A 6 6 1. 24 0.25
50 A 4 4 1. 24 0.167
51 A 3 3 1. 22 0.136
52 A 2 2 1. 20 0.1
53 A 3 3 1. 24 0.125
54 A 5 5 1. 24 0.208
55 A 8 6 1. 24 0.25
56 A 7 6 1. 24 0.25
57 A 6 6 1. 24 0.25
58 A 1 1 1. 24 0.042
59 A 1 1 1. 24 0.042
60 A 3 3 1. 24 0.125
61 A 5 5 1. 22 0.227
62 A 6 5 1. 20 0.25
63 A 7 5 1. 24 0.208
64 A 8 5 1. 24 0.208
65 A 2 1 1. 18 0.056
66 A 2 1 1. 18 0.056
67 A 2 1 1. 16 0.062
68 A 1 0 1. 14 0.
69 A 2 1 1. 18 0.056
70 A 2 1 1. 18 0.056
71 A 2 1 1. 18 0.056
72 A 3 2 1. 20 0.1
73 A 3 2 1. 20 0.1
74 A 4 3 1. 18 0.167
75 A 3 2 1. 16 0.125
76 A 4 3 1. 20 0.15
77 A 3 2 1. 20 0.1
78 A 8 7 1. 20 0.35
79 A 6 5 1. 20 0.25
80 A 7 7 1. 20 0.35
81 A 5 4 1. 20 0.2
82 A 6 6 1. 20 0.3
83 A 4 3 1. 20 0.15
84 A 4 4 1. 20 0.2
85 A 4 3 1. 18 0.167
86 A 8 8 1. 16 0.5
87 A 5 4 1. 20 0.2
88 A 9 8 1. 20 0.4
89 A 9 8 1. 20 0.4
90 A 7 5 1. 20 0.25
91 A 8 8 1. 20 0.4
92 A 6 5 1. 20 0.25
93 A 5 5 1. 20 0.25
94 A 5 4 1. 20 0.2
95 A 5 5 1. 20 0.25
96 A 5 4 1. 20 0.2
97 A 5 5 1. 20 0.25
98 A 5 4 1. 20 0.2
99 A 9 8 1. 18 0.444
100 A 6 5 1. 16 0.312
101 A 9 8 1. 20 0.4
102 A 7 5 1. 20 0.25
103 A 9 8 1. 20 0.4
104 A 3 3 1. 20 0.15
105 A 5 5 1. 24 0.208
106 A 5 5 1. 24 0.208
107 A 5 5 1. 24 0.208
108 A 8 7 1. 24 0.292
109 A 8 8 1. 24 0.333
110 A 6 6 1. 24 0.25
111 A 6 5 1. 24 0.208
112 A 6 6 1. 24 0.25
113 A 4 4 1. 24 0.167
114 A 2 2 1. 24 0.083
115 A 2 2 1. 24 0.083
116 A 6 6 1. 24 0.25
117 A 5 5 1. 24 0.208
118 A 3 3 1. 24 0.125
119 A 6 6 1. 24 0.25
120 A 5 5 1. 24 0.208
121 A 1 1 1. 34 0.029
122 A 7 4 1. 27 0.148
123 A 2 2 1. 18 0.111
124 A 3 3 1. 18 0.167
125 A 3 3 1. 17 0.176
126 A 5 5 1. 18 0.278
127 A 6 6 1. 18 0.333
128 A 6 6 1. 17 0.353
129 A 2 2 1. 18 0.111
130 A 3 3 1. 18 0.167
131 A 3 3 1. 22 0.136
132 A 3 3 1. 24 0.125
133 A 3 3 1. 20 0.15
134 A 3 3 1. 20 0.15
135 A 3 3 1. 24 0.125
136 A 3 3 1. 26 0.115
137 A 3 3 1. 18 0.167
138 A 3 3 1. 18 0.167
139 A 3 3 1. 20 0.15
140 A 2 2 1. 36 0.056

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