[next] [prev] [prev-tail] [tail] [up]

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 74 74 74 61 81 1 68 86 68
normalized size 1 1. 1. 0.82 1.09 0.01 0.92 1.16 0.92
time (sec) N/A 0.155 0.034 0.002 0.698 0.228 0.103 0.281 23.235
Problem 2 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 74 74 74 61 81 1 68 86 0
normalized size 1 1. 1. 0.82 1.09 0.01 0.92 1.16 0.
time (sec) N/A 0.118 0.022 0.001 0.704 0.24 0.101 0.279 0.
Problem 3 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 69 69 69 58 77 1 65 82 0
normalized size 1 1. 1. 0.84 1.12 0.01 0.94 1.19 0.
time (sec) N/A 0.081 0.027 0.001 0.707 0.232 0.101 0.281 0.
Problem 4 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 65 65 65 60 74 74 63 81 0
normalized size 1 1. 1. 0.92 1.14 1.14 0.97 1.25 0.
time (sec) N/A 0.085 0.03 0.004 0.701 0.255 1.162 0.278 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 63 63 63 57 74 84 58 77 0
normalized size 1 1. 1. 0.9 1.17 1.33 0.92 1.22 0.
time (sec) N/A 0.106 0.041 0.008 0.7 0.249 1.226 0.281 0.
Problem 6 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 63 63 58 58 74 84 60 78 0
normalized size 1 1. 0.92 0.92 1.17 1.33 0.95 1.24 0.
time (sec) N/A 0.101 0.076 0.008 0.712 0.249 1.7 0.281 0.
Problem 7 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 63 63 60 57 76 84 61 76 0
normalized size 1 1. 0.95 0.9 1.21 1.33 0.97 1.21 0.
time (sec) N/A 0.106 0.088 0.009 0.704 0.246 2.534 0.28 0.
Problem 8 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 63 63 62 58 76 84 61 77 0
normalized size 1 1. 0.98 0.92 1.21 1.33 0.97 1.22 0.
time (sec) N/A 0.105 0.052 0.01 0.701 0.247 7.428 0.282 0.
Problem 9 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 63 63 63 60 76 84 63 77 0
normalized size 1 1. 1. 0.95 1.21 1.33 1. 1.22 0.
time (sec) N/A 0.102 0.136 0.009 0.699 0.251 21.738 0.282 0.
Problem 10 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 68 68 68 63 80 84 66 81 63
normalized size 1 1. 1. 0.93 1.18 1.24 0.97 1.19 0.93
time (sec) N/A 0.095 0.094 0.009 0.711 0.248 59.196 0.281 18.88
Problem 11 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 159 159 159 142 193 1 168 208 160
normalized size 1 1. 1. 0.89 1.21 0.01 1.06 1.31 1.01
time (sec) N/A 0.422 0.088 0.001 0.701 0.23 0.172 0.28 48.55
Problem 12 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 159 159 159 142 193 1 163 208 0
normalized size 1 1. 1. 0.89 1.21 0.01 1.03 1.31 0.
time (sec) N/A 0.358 0.086 0.001 0.698 0.242 0.17 0.282 0.
Problem 13 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 154 154 154 139 189 1 165 204 0
normalized size 1 1. 1. 0.9 1.23 0.01 1.07 1.32 0.
time (sec) N/A 0.283 0.057 0.001 0.698 0.231 0.168 0.278 0.
Problem 14 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 150 150 150 149 186 186 156 201 0
normalized size 1 1. 1. 0.99 1.24 1.24 1.04 1.34 0.
time (sec) N/A 0.225 0.076 0.004 0.702 0.257 1.713 0.281 0.
Problem 15 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 145 145 145 147 185 196 156 198 0
normalized size 1 1. 1. 1.01 1.28 1.35 1.08 1.37 0.
time (sec) N/A 0.289 0.31 0.01 0.702 0.246 1.847 0.286 0.
Problem 16 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 149 149 139 148 188 196 151 200 0
normalized size 1 1. 0.93 0.99 1.26 1.32 1.01 1.34 0.
time (sec) N/A 0.308 0.218 0.01 0.695 0.252 2.301 0.28 0.
Problem 17 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 149 149 151 146 189 196 158 197 0
normalized size 1 1. 1.01 0.98 1.27 1.32 1.06 1.32 0.
time (sec) N/A 0.305 0.174 0.01 0.69 0.248 3.336 0.286 0.
Problem 18 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 148 148 130 144 188 196 151 192 0
normalized size 1 1. 0.88 0.97 1.27 1.32 1.02 1.3 0.
time (sec) N/A 0.327 0.19 0.011 0.693 0.247 9.81 0.283 0.
Problem 19 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 143 143 142 144 186 196 151 189 0
normalized size 1 1. 0.99 1.01 1.3 1.37 1.06 1.32 0.
time (sec) N/A 0.34 0.172 0.012 0.694 0.25 31.229 0.28 0.
Problem 20 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 149 149 144 148 189 196 153 190 0
normalized size 1 1. 0.97 0.99 1.27 1.32 1.03 1.28 0.
time (sec) N/A 0.317 0.208 0.012 0.704 0.251 98.901 0.282 0.
Problem 21 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-2) F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 339 339 460 1622 0 0 0 1 347
normalized size 1 1. 1.36 4.78 0. 0. 0. 0. 1.02
time (sec) N/A 4.187 1.234 0.068 0. 0. 0. 1.585 163.925
Problem 22 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-2) F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 278 278 377 1171 0 0 0 1 0
normalized size 1 1. 1.36 4.21 0. 0. 0. 0. 0.
time (sec) N/A 1.092 0.843 0.048 0. 0. 0. 1.305 0.
Problem 23 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-2) F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 270 270 360 1327 0 0 0 1 274
normalized size 1 1. 1.33 4.91 0. 0. 0. 0. 1.01
time (sec) N/A 1.898 0.764 0.05 0. 0. 0. 1.439 104.165
Problem 24 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-2) F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 223 223 240 728 0 0 0 1 209
normalized size 1 1. 1.08 3.26 0. 0. 0. 0. 0.94
time (sec) N/A 0.521 0.79 0.035 0. 0. 0. 1.215 64.451
Problem 25 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-2) F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 211 211 234 616 0 0 0 1 221
normalized size 1 1. 1.11 2.92 0. 0. 0. 0. 1.05
time (sec) N/A 0.597 0.403 0.025 0. 0. 0. 1.069 53.705
Problem 26 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 229 229 285 488 0 0 0 1 216
normalized size 1 1. 1.24 2.13 0. 0. 0. 0. 0.94
time (sec) N/A 0.628 0.932 0.038 0. 0. 0. 0.867 76.694
Problem 27 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 260 260 315 811 0 0 0 1 264
normalized size 1 1. 1.21 3.12 0. 0. 0. 0. 1.02
time (sec) N/A 1.059 2.891 0.042 0. 0. 0. 1.095 100.472
Problem 28 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 288 288 377 1054 0 0 0 1 287
normalized size 1 1. 1.31 3.66 0. 0. 0. 0. 1.
time (sec) N/A 1.102 1.954 0.057 0. 0. 0. 1.293 117.703
Problem 29 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 412 412 444 5283 0 0 0 0 376
normalized size 1 1. 1.08 12.82 0. 0. 0. 0. 0.91
time (sec) N/A 2.982 2.805 0.13 0. 0. 0. 0. 179.049
Problem 30 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-2) F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 347 347 358 3041 0 0 0 0 289
normalized size 1 1. 1.03 8.76 0. 0. 0. 0. 0.83
time (sec) N/A 1.366 1.842 0.101 0. 0. 0. 0. 136.213
Problem 31 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-2) F(-1) F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 356 356 378 4063 0 0 0 0 0
normalized size 1 1. 1.06 11.41 0. 0. 0. 0. 0.
time (sec) N/A 1.985 2.056 0.088 0. 0. 0. 0. 0.
Problem 32 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-2) F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 317 317 335 1344 0 0 0 0 291
normalized size 1 1. 1.06 4.24 0. 0. 0. 0. 0.92
time (sec) N/A 0.992 3.315 0.162 0. 0. 0. 0. 98.381
Problem 33 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 368 368 393 2851 0 0 0 0 0
normalized size 1 1. 1.07 7.75 0. 0. 0. 0. 0.
time (sec) N/A 1.954 2.88 0.141 0. 0. 0. 0. 0.
Problem 34 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 403 403 458 4871 0 0 0 0 382
normalized size 1 1. 1.14 12.09 0. 0. 0. 0. 0.95
time (sec) N/A 2.008 3.003 0.097 0. 0. 0. 0. 167.269
Problem 35 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 514 514 559 6960 0 0 0 0 0
normalized size 1 1. 1.09 13.54 0. 0. 0. 0. 0.
time (sec) N/A 3.792 4.337 0.119 0. 0. 0. 0. 0.
Problem 36 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 534 534 655 6930 0 0 0 0 0
normalized size 1 1. 1.23 12.98 0. 0. 0. 0. 0.
time (sec) N/A 4.173 5.209 0.122 0. 0. 0. 0. 0.
Problem 37 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 399 399 296 5520 0 5262 0 1 396
normalized size 1 1. 0.74 13.83 0. 13.19 0. 0. 0.99
time (sec) N/A 0.945 4.458 0.017 0. 0.353 0. 0.347 120.922
Problem 38 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 260 260 187 2187 0 2164 0 1 248
normalized size 1 1. 0.72 8.41 0. 8.32 0. 0. 0.95
time (sec) N/A 0.488 1.565 0.013 0. 0.346 0. 0.302 75.846
Problem 39 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 137 137 92 585 0 599 3735 1 122
normalized size 1 1. 0.67 4.27 0. 4.37 27.26 0.01 0.89
time (sec) N/A 0.198 0.248 0.007 0. 0.312 7.635 0.297 39.764
Problem 40 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F F A
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 368 368 438 0 0 0 0 0 335
normalized size 1 1. 1.19 0. 0. 0. 0. 0. 0.91
time (sec) N/A 1.481 0.429 0.041 0. 0. 0. 0. 117.687
Problem 41 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C F F F F(-1) F(-2) F(-1)
verified N/A Yes NO TBD TBD TBD TBD TBD TBD
size 685 670 1136 0 0 0 0 0 0
normalized size 1 0.98 1.66 0. 0. 0. 0. 0. 0.
time (sec) N/A 5.212 9.019 0.041 0. 0. 0. 0. 0.
Problem 42 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 356 356 378 4063 0 0 0 0 0
normalized size 1 1. 1.06 11.41 0. 0. 0. 0. 0.
time (sec) N/A 2.024 2.101 0. 0. 0. 0. 0. 0.
Problem 43 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 356 356 378 4063 0 0 0 0 0
normalized size 1 1. 1.06 11.41 0. 0. 0. 0. 0.
time (sec) N/A 1.198 0.281 0.007 0. 0. 0. 0. 0.
Problem 44 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 356 356 378 4063 0 0 0 0 0
normalized size 1 1. 1.06 11.41 0. 0. 0. 0. 0.
time (sec) N/A 1.11 0.273 0.007 0. 0. 0. 0. 0.
Problem 45 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 356 356 378 4063 0 0 0 0 0
normalized size 1 1. 1.06 11.41 0. 0. 0. 0. 0.
time (sec) N/A 1.119 0.269 0.007 0. 0. 0. 0. 0.
Problem 46 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 356 356 378 4063 0 0 0 0 0
normalized size 1 1. 1.06 11.41 0. 0. 0. 0. 0.
time (sec) N/A 1.233 0.268 0.007 0. 0. 0. 0. 0.
Problem 47 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 273 273 260 622 0 1 1392 413 0
normalized size 1 1. 0.95 2.28 0. 0. 5.1 1.51 0.
time (sec) N/A 1.636 0.394 0.009 0. 0.612 149.096 0.318 0.
Problem 48 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A A A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 203 203 193 474 0 1 1044 289 0
normalized size 1 1. 0.95 2.33 0. 0. 5.14 1.42 0.
time (sec) N/A 0.85 0.262 0.008 0. 0.458 110.105 0.304 0.
Problem 49 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 144 144 136 321 0 1 721 190 0
normalized size 1 1. 0.94 2.23 0. 0.01 5.01 1.32 0.
time (sec) N/A 0.536 0.192 0.006 0. 0.324 63.468 0.295 0.
Problem 50 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 103 103 100 211 0 1 498 134 0
normalized size 1 1. 0.97 2.05 0. 0.01 4.83 1.3 0.
time (sec) N/A 0.347 0.119 0.005 0. 0.29 36.95 0.318 0.
Problem 51 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 97 97 178 165 0 1 0 131 90
normalized size 1 1. 1.84 1.7 0. 0.01 0. 1.35 0.93
time (sec) N/A 0.398 0.265 0.01 0. 0.447 0. 0.322 62.573
Problem 52 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 118 118 203 227 0 1 0 182 112
normalized size 1 1. 1.72 1.92 0. 0.01 0. 1.54 0.95
time (sec) N/A 0.556 0.274 0.013 0. 0.527 0. 0.323 85.631
Problem 53 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 174 174 314 356 0 1 0 286 167
normalized size 1 1. 1.8 2.05 0. 0.01 0. 1.64 0.96
time (sec) N/A 0.782 0.681 0.016 0. 0.927 0. 0.295 136.097
Problem 54 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 244 244 416 523 0 1 0 423 0
normalized size 1 1. 1.7 2.14 0. 0. 0. 1.73 0.
time (sec) N/A 1.177 0.789 0.019 0. 2.047 0. 0.295 0.
Problem 55 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 369 369 456 1450 0 20880 0 1 405
normalized size 1 1. 1.24 3.93 0. 56.59 0. 0. 1.1
time (sec) N/A 10.939 1.169 0.05 0. 14.722 0. 1.822 164.076
Problem 56 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 282 282 365 1035 0 12641 0 1 294
normalized size 1 1. 1.29 3.67 0. 44.83 0. 0. 1.04
time (sec) N/A 7.573 1.025 0.04 0. 3.656 0. 1.69 69.889
Problem 57 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 219 219 258 676 0 7814 0 1 221
normalized size 1 1. 1.18 3.09 0. 35.68 0. 0. 1.01
time (sec) N/A 1.34 0.658 0.031 0. 1.895 0. 1.257 51.899
Problem 58 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 213 213 253 563 0 8006 0 1 235
normalized size 1 1. 1.19 2.64 0. 37.59 0. 0. 1.1
time (sec) N/A 1.754 0.607 0.031 0. 0.931 0. 1.268 74.169
Problem 59 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 267 267 284 727 0 13298 0 1 258
normalized size 1 1. 1.06 2.72 0. 49.81 0. 0. 0.97
time (sec) N/A 2.248 0.688 0.036 0. 5.123 0. 1.309 72.48
Problem 60 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A F(-1) A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 329 329 394 1121 0 21371 0 1 0
normalized size 1 1. 1.2 3.41 0. 64.96 0. 0. 0.
time (sec) N/A 4.143 1.111 0.044 0. 18.487 0. 1.761 0.
Problem 61 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 320 320 309 1764 0 1 0 0 0
normalized size 1 1. 0.97 5.51 0. 0. 0. 0. 0.
time (sec) N/A 2.463 1.041 0.026 0. 0.658 0. 0. 0.
Problem 62 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) F(-2) F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 236 236 236 1266 0 1 0 0 0
normalized size 1 1. 1. 5.36 0. 0. 0. 0. 0.
time (sec) N/A 0.928 0.683 0.021 0. 0.429 0. 0. 0.
Problem 63 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 165 165 175 671 0 1 0 0 231
normalized size 1 1. 1.06 4.07 0. 0.01 0. 0. 1.4
time (sec) N/A 0.562 0.488 0.019 0. 0.329 0. 0. 59.545
Problem 64 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 123 123 130 205 0 1 474 0 114
normalized size 1 1. 1.06 1.67 0. 0.01 3.85 0. 0.93
time (sec) N/A 0.352 0.197 0.014 0. 0.295 131.162 0. 19.585
Problem 65 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 166 166 268 744 0 1 0 0 194
normalized size 1 1. 1.61 4.48 0. 0.01 0. 0. 1.17
time (sec) N/A 0.826 0.928 0.024 0. 1.349 0. 0. 37.104
Problem 66 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 234 234 403 1156 0 1 0 0 265
normalized size 1 1. 1.72 4.94 0. 0. 0. 0. 1.13
time (sec) N/A 1.444 1.432 0.03 0. 3.096 0. 0. 59.252
Problem 67 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F(-2) A F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 329 329 592 1675 0 1 0 0 384
normalized size 1 1. 1.8 5.09 0. 0. 0. 0. 1.17
time (sec) N/A 2.363 3.257 0.038 0. 6.938 0. 0. 119.625
Problem 68 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 550 550 648 6868 0 0 0 0 0
normalized size 1 1. 1.18 12.49 0. 0. 0. 0. 0.
time (sec) N/A 25.03 5.352 0.101 0. 0. 0. 0. 0.
Problem 69 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 436 436 511 5928 0 17006 0 0 478
normalized size 1 1. 1.17 13.6 0. 39. 0. 0. 1.1
time (sec) N/A 12.662 3.499 0.086 0. 9.911 0. 0. 127.085
Problem 70 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 362 362 414 5528 0 12084 0 0 374
normalized size 1 1. 1.14 15.27 0. 33.38 0. 0. 1.03
time (sec) N/A 5.507 2.363 0.079 0. 5.475 0. 0. 75.033
Problem 71 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 346 346 382 5350 0 12138 0 0 364
normalized size 1 1. 1.1 15.46 0. 35.08 0. 0. 1.05
time (sec) N/A 3.999 2.183 0.12 0. 5.474 0. 0. 72.8
Problem 72 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F A F(-1) F(-2) F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 399 399 444 5142 0 17700 0 0 0
normalized size 1 1. 1.11 12.89 0. 44.36 0. 0. 0.
time (sec) N/A 6.044 2.645 0.086 0. 11.933 0. 0. 0.
Problem 73 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 575 575 548 6122 0 0 0 0 216
normalized size 1 1. 0.95 10.65 0. 0. 0. 0. 0.38
time (sec) N/A 18.204 3.605 0.095 0. 0. 0. 0. 76.151
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 68 68 62 56 78 111 61 85 0
normalized size 1 1. 0.91 0.82 1.15 1.63 0.9 1.25 0.
time (sec) N/A 0.199 0.048 0.024 0.731 0.26 0.412 0.286 0.
Problem 75 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 61 61 61 51 72 104 54 78 0
normalized size 1 1. 1. 0.84 1.18 1.7 0.89 1.28 0.
time (sec) N/A 0.18 0.05 0.022 0.737 0.274 0.416 0.275 0.
Problem 76 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 54 54 54 46 65 97 48 72 0
normalized size 1 1. 1. 0.85 1.2 1.8 0.89 1.33 0.
time (sec) N/A 0.173 0.043 0.022 0.723 0.256 0.407 0.271 0.
Problem 77 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 49 41 58 90 42 61 48
normalized size 1 1. 1. 0.84 1.18 1.84 0.86 1.24 0.98
time (sec) N/A 0.144 0.04 0.025 0.739 0.283 0.413 0.274 22.557
Problem 78 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 42 42 42 36 51 77 36 54 48
normalized size 1 1. 1. 0.86 1.21 1.83 0.86 1.29 1.14
time (sec) N/A 0.084 0.031 0.022 0.725 0.252 0.395 0.274 17.386
Problem 79 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 44 44 44 38 59 96 39 63 56
normalized size 1 1. 1. 0.86 1.34 2.18 0.89 1.43 1.27
time (sec) N/A 0.141 0.035 0.027 0.722 0.26 0.453 0.272 22.162
Problem 80 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 55 55 50 45 72 124 51 72 61
normalized size 1 1. 0.91 0.82 1.31 2.25 0.93 1.31 1.11
time (sec) N/A 0.168 0.043 0.028 0.72 0.279 0.545 0.272 22.649
Problem 81 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 64 64 56 50 76 131 56 89 75
normalized size 1 1. 0.88 0.78 1.19 2.05 0.88 1.39 1.17
time (sec) N/A 0.172 0.051 0.029 0.739 0.265 0.614 0.277 22.832
Problem 82 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 70 70 71 56 78 107 66 78 66
normalized size 1 1. 1.01 0.8 1.11 1.53 0.94 1.11 0.94
time (sec) N/A 0.137 0.092 0.029 0.801 0.276 0.604 0.272 25.135
Problem 83 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A F(-1)
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 57 57 58 49 69 100 54 69 0
normalized size 1 1. 1.02 0.86 1.21 1.75 0.95 1.21 0.
time (sec) N/A 0.13 0.087 0.016 0.793 0.266 0.586 0.275 0.
Problem 84 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 56 56 57 46 65 93 53 65 53
normalized size 1 1. 1.02 0.82 1.16 1.66 0.95 1.16 0.95
time (sec) N/A 0.122 0.083 0.019 0.797 0.265 0.579 0.272 21.632
Problem 85 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 49 49 50 41 58 99 48 58 48
normalized size 1 1. 1.02 0.84 1.18 2.02 0.98 1.18 0.98
time (sec) N/A 0.114 0.07 0.016 0.793 0.271 0.581 0.276 19.503
Problem 86 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 48 48 46 38 54 92 44 54 44
normalized size 1 1. 0.96 0.79 1.12 1.92 0.92 1.12 0.92
time (sec) N/A 0.058 0.072 0.015 0.792 0.27 0.58 0.27 10.463
Problem 87 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 53 53 51 43 61 104 49 61 48
normalized size 1 1. 0.96 0.81 1.15 1.96 0.92 1.15 0.91
time (sec) N/A 0.119 0.098 0.018 0.792 0.277 0.656 0.27 19.025
Problem 88 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 62 62 56 48 70 117 56 70 32
normalized size 1 1. 0.9 0.77 1.13 1.89 0.9 1.13 0.52
time (sec) N/A 0.132 0.112 0.021 0.794 0.271 0.731 0.271 18.923
Problem 89 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 69 69 61 53 77 124 61 77 41
normalized size 1 1. 0.88 0.77 1.12 1.8 0.88 1.12 0.59
time (sec) N/A 0.144 0.112 0.023 0.797 0.282 0.806 0.27 22.456
Problem 90 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 76 76 77 58 84 131 66 84 48
normalized size 1 1. 1.01 0.76 1.11 1.72 0.87 1.11 0.63
time (sec) N/A 0.154 0.127 0.023 0.794 0.291 0.905 0.27 25.909
Problem 91 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 81 81 71 64 96 154 75 82 76
normalized size 1 1. 0.88 0.79 1.19 1.9 0.93 1.01 0.94
time (sec) N/A 0.177 0.12 0.018 0.796 0.265 0.8 0.272 37.397
Problem 92 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 80 80 66 62 92 159 75 78 76
normalized size 1 1. 0.82 0.78 1.15 1.99 0.94 0.98 0.95
time (sec) N/A 0.165 0.101 0.018 0.797 0.284 0.775 0.272 32.119
Problem 93 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 75 75 60 56 85 151 68 72 70
normalized size 1 1. 0.8 0.75 1.13 2.01 0.91 0.96 0.93
time (sec) N/A 0.156 0.112 0.018 0.786 0.269 0.791 0.27 27.439
Problem 94 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 55 54 81 146 65 68 66
normalized size 1 1. 0.76 0.75 1.12 2.03 0.9 0.94 0.92
time (sec) N/A 0.122 0.109 0.016 0.798 0.28 0.764 0.274 20.768
Problem 95 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 56 53 81 146 65 68 66
normalized size 1 1. 0.78 0.74 1.12 2.03 0.9 0.94 0.92
time (sec) N/A 0.119 0.105 0.017 0.791 0.272 0.796 0.271 19.413
Problem 96 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 72 72 56 53 81 146 65 68 66
normalized size 1 1. 0.78 0.74 1.12 2.03 0.9 0.94 0.92
time (sec) N/A 0.084 0.104 0.016 0.797 0.266 0.806 0.272 13.393
Problem 97 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 79 79 63 58 88 158 70 74 71
normalized size 1 1. 0.8 0.73 1.11 2. 0.89 0.94 0.9
time (sec) N/A 0.17 0.113 0.021 0.785 0.268 0.905 0.272 26.93
Problem 98 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 86 86 78 64 97 173 76 84 58
normalized size 1 1. 0.91 0.74 1.13 2.01 0.88 0.98 0.67
time (sec) N/A 0.191 0.116 0.024 0.789 0.273 0.952 0.271 22.941
Problem 99 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 93 93 73 68 104 180 82 90 65
normalized size 1 1. 0.78 0.73 1.12 1.94 0.88 0.97 0.7
time (sec) N/A 0.209 0.147 0.024 0.776 0.278 1.052 0.271 26.496
Problem 100 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 86 86 78 74 96 140 85 103 0
normalized size 1 1. 0.91 0.86 1.12 1.63 0.99 1.2 0.
time (sec) N/A 0.239 0.079 0.014 0.79 0.271 0.453 0.271 0.
Problem 101 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 81 81 73 69 89 132 80 96 0
normalized size 1 1. 0.9 0.85 1.1 1.63 0.99 1.19 0.
time (sec) N/A 0.219 0.054 0.013 0.792 0.276 0.455 0.27 0.
Problem 102 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 74 74 66 64 80 126 73 89 78
normalized size 1 1. 0.89 0.86 1.08 1.7 0.99 1.2 1.05
time (sec) N/A 0.215 0.051 0.013 0.798 0.262 0.449 0.271 29.305
Problem 103 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 65 65 61 59 73 120 66 73 73
normalized size 1 1. 0.94 0.91 1.12 1.85 1.02 1.12 1.12
time (sec) N/A 0.18 0.047 0.012 0.793 0.271 0.455 0.274 26.339
Problem 104 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 58 58 58 54 66 104 60 66 53
normalized size 1 1. 1. 0.93 1.14 1.79 1.03 1.14 0.91
time (sec) N/A 0.119 0.038 0.012 0.784 0.274 0.442 0.273 17.505
Problem 105 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 66 66 93 58 74 127 65 84 80
normalized size 1 1. 1.41 0.88 1.12 1.92 0.98 1.27 1.21
time (sec) N/A 0.199 0.103 0.016 0.784 0.268 0.487 0.272 25.851
Problem 106 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 71 71 97 63 89 158 75 89 85
normalized size 1 1. 1.37 0.89 1.25 2.23 1.06 1.25 1.2
time (sec) N/A 0.219 0.086 0.02 0.799 0.271 0.583 0.272 26.494
Problem 107 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 80 80 105 68 96 165 80 107 95
normalized size 1 1. 1.31 0.85 1.2 2.06 1. 1.34 1.19
time (sec) N/A 0.231 0.105 0.02 0.805 0.288 0.642 0.274 27.022
Problem 108 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C A A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 87 87 110 73 103 171 85 113 102
normalized size 1 1. 1.26 0.84 1.18 1.97 0.98 1.3 1.17
time (sec) N/A 0.244 0.112 0.02 0.79 0.258 0.725 0.27 27.674
Problem 109 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 248 248 145 427 0 1040 71 0 352
normalized size 1 1. 0.58 1.72 0. 4.19 0.29 0. 1.42
time (sec) N/A 0.731 0.337 0.106 0. 0.313 1.954 0. 62.769
Problem 110 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 237 237 132 419 0 1031 63 0 342
normalized size 1 1. 0.56 1.77 0. 4.35 0.27 0. 1.44
time (sec) N/A 0.725 0.299 0.043 0. 0.303 1.969 0. 50.098
Problem 111 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 232 232 129 416 0 1013 58 0 338
normalized size 1 1. 0.56 1.79 0. 4.37 0.25 0. 1.46
time (sec) N/A 0.701 0.319 0.037 0. 0.29 1.973 0. 44.317
Problem 112 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 225 225 121 412 0 1057 51 0 332
normalized size 1 1. 0.54 1.83 0. 4.7 0.23 0. 1.48
time (sec) N/A 0.741 0.315 0.038 0. 0.301 1.932 0. 36.78
Problem 113 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 224 224 115 408 0 1038 48 0 328
normalized size 1 1. 0.51 1.82 0. 4.63 0.21 0. 1.46
time (sec) N/A 0.618 0.525 0.036 0. 0.315 1.928 0. 27.55
Problem 114 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 229 229 126 414 0 1077 53 0 313
normalized size 1 1. 0.55 1.81 0. 4.7 0.23 0. 1.37
time (sec) N/A 0.728 0.35 0.035 0. 0.336 2.003 0. 33.395
Problem 115 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 238 238 131 419 0 1112 60 0 320
normalized size 1 1. 0.55 1.76 0. 4.67 0.25 0. 1.34
time (sec) N/A 0.745 0.555 0.038 0. 0.3 2.179 0. 37.298
Problem 116 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 245 245 140 424 0 1126 65 0 326
normalized size 1 1. 0.57 1.73 0. 4.6 0.27 0. 1.33
time (sec) N/A 0.734 0.609 0.037 0. 0.291 2.18 0. 41.361
Problem 117 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 243 243 156 429 0 1202 82 0 362
normalized size 1 1. 0.64 1.77 0. 4.95 0.34 0. 1.49
time (sec) N/A 0.854 0.423 0.033 0. 0.298 2.152 0. 65.015
Problem 118 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 242 242 155 426 0 1188 80 0 360
normalized size 1 1. 0.64 1.76 0. 4.91 0.33 0. 1.49
time (sec) N/A 0.757 0.392 0.033 0. 0.316 2.192 0. 53.118
Problem 119 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 235 235 138 422 0 1173 71 0 354
normalized size 1 1. 0.59 1.8 0. 4.99 0.3 0. 1.51
time (sec) N/A 0.758 0.699 0.033 0. 0.307 2.218 0. 43.103
Problem 120 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 238 238 129 418 0 1165 68 0 350
normalized size 1 1. 0.54 1.76 0. 4.89 0.29 0. 1.47
time (sec) N/A 0.725 0.665 0.039 0. 0.302 2.128 0. 38.595
Problem 121 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 246 246 133 418 0 1079 68 0 350
normalized size 1 1. 0.54 1.7 0. 4.39 0.28 0. 1.42
time (sec) N/A 0.763 0.607 0.038 0. 0.317 2.163 0. 37.209
Problem 122 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 248 248 129 418 0 1177 68 0 350
normalized size 1 1. 0.52 1.69 0. 4.75 0.27 0. 1.41
time (sec) N/A 0.705 0.616 0.037 0. 0.316 2.092 0. 31.126
Problem 123 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 253 253 140 424 0 1189 73 0 333
normalized size 1 1. 0.55 1.68 0. 4.7 0.29 0. 1.32
time (sec) N/A 0.833 0.785 0.037 0. 0.297 2.267 0. 38.16
Problem 124 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A C B F A A F A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 262 262 139 429 0 1241 80 0 342
normalized size 1 1. 0.53 1.64 0. 4.74 0.31 0. 1.31
time (sec) N/A 0.872 0.676 0.04 0. 0.292 2.338 0. 42.001
Problem 125 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 149 149 142 357 0 1 789 197 0
normalized size 1 1. 0.95 2.4 0. 0.01 5.3 1.32 0.
time (sec) N/A 0.594 0.231 0.006 0. 0.357 164.926 0.298 0.
Problem 126 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 594 594 721 8533 0 0 0 0 0
normalized size 1 1. 1.21 14.37 0. 0. 0. 0. 0.
time (sec) N/A 28.539 6.641 0.115 0. 0. 0. 0. 0.
Problem 127 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 471 471 575 7318 0 0 0 0 547
normalized size 1 1. 1.22 15.54 0. 0. 0. 0. 1.16
time (sec) N/A 15.823 4.393 0.093 0. 0. 0. 0. 168.249
Problem 128 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A B F F(-1) F(-1) F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 449 449 512 8358 0 0 0 0 508
normalized size 1 1. 1.14 18.61 0. 0. 0. 0. 1.13
time (sec) N/A 7.177 3.529 0.126 0. 0. 0. 0. 99.317
Problem 129 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 460 460 529 6807 0 0 0 0 0
normalized size 1 1. 1.15 14.8 0. 0. 0. 0. 0.
time (sec) N/A 8.157 5.957 0.092 0. 0. 0. 0. 0.
Problem 130 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 542 542 612 7512 0 0 0 0 0
normalized size 1 1. 1.13 13.86 0. 0. 0. 0. 0.
time (sec) N/A 19.333 4.885 0.095 0. 0. 0. 0. 0.
Problem 131 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 20 20 20 21 42 42 0 86 17
normalized size 1 1. 1. 1.05 2.1 2.1 0. 4.3 0.85
time (sec) N/A 0.021 0.053 0.011 0.806 0.28 0. 0.303 13.607
Problem 132 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A A A A F(-1) A F
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 210 278 149 145 398 554 0 328 0
normalized size 1 1.32 0.71 0.69 1.9 2.64 0. 1.56 0.
time (sec) N/A 0.818 0.164 0.011 0.789 0.284 0. 0.3 0.
Problem 133 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 159 213 116 109 293 435 0 239 177
normalized size 1 1.34 0.73 0.69 1.84 2.74 0. 1.5 1.11
time (sec) N/A 0.556 0.128 0.01 0.789 0.274 0. 0.295 29.005
Problem 134 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 109 149 80 73 188 313 0 153 117
normalized size 1 1.37 0.73 0.67 1.72 2.87 0. 1.4 1.07
time (sec) N/A 0.357 0.093 0.007 0.798 0.272 0. 0.286 19.777
Problem 135 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 93 151 84 143 0 270 304 4 114
normalized size 1 1.62 0.9 1.54 0. 2.9 3.27 0.04 1.23
time (sec) N/A 0.482 0.21 0.048 0. 0.279 101.102 0.67 33.853
Problem 136 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F(-2) A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 99 155 102 163 0 378 270 4 114
normalized size 1 1.57 1.03 1.65 0. 3.82 2.73 0.04 1.15
time (sec) N/A 0.555 0.272 0.032 0. 0.266 144.224 0.684 36.235
Problem 137 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 126 182 135 222 0 567 0 4 143
normalized size 1 1.44 1.07 1.76 0. 4.5 0. 0.03 1.13
time (sec) N/A 0.625 0.248 0.033 0. 0.304 0. 0.706 38.391
Problem 138 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F(-2) A F(-2) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 212 248 177 306 0 923 0 4 196
normalized size 1 1.17 0.83 1.44 0. 4.35 0. 0.02 0.92
time (sec) N/A 0.759 0.41 0.052 0. 0.484 0. 0.743 42.982
Problem 139 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A F(-1) A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 216 245 136 273 309 921 0 257 194
normalized size 1 1.13 0.63 1.26 1.43 4.26 0. 1.19 0.9
time (sec) N/A 0.601 0.229 0.046 0.787 0.387 0. 0.316 27.855
Problem 140 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C A A A A A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 128 179 99 191 201 571 325 170 141
normalized size 1 1.4 0.77 1.49 1.57 4.46 2.54 1.33 1.1
time (sec) N/A 0.26 0.149 0.029 0.796 0.283 104.666 0.309 19.001
Problem 141 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F(-2) A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 102 155 82 148 0 424 287 0 114
normalized size 1 1.52 0.8 1.45 0. 4.16 2.81 0. 1.12
time (sec) N/A 0.392 0.167 0.031 0. 0.277 118.302 0. 20.133
Problem 142 Optimal Rubi Mathematica Maple Maxima Fricas Sympy Giac Rubi in Sympy
grade A A A C F(-2) A A F(-2) A
verified N/A Yes Yes TBD TBD TBD TBD TBD TBD
size 157 157 84 146 0 396 257 0 133
normalized size 1 1. 0.54 0.93 0. 2.52 1.64 0. 0.85
time (sec) N/A 0.418 0.181 0.031 0. 0.289 167.912 0. 19.851
Problem 143 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 160 160 87 82 0 505 0 1 153
normalized size 1 1. 0.54 0.51 0. 3.16 0. 0.01 0.96
time (sec) N/A 0.445 0.119 0.009 0. 0.334 0. 0.536 21.905
Problem 144 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 226 226 122 118 0 713 0 1 207
normalized size 1 1. 0.54 0.52 0. 3.15 0. 0. 0.92
time (sec) N/A 0.545 0.15 0.009 0. 0.557 0. 0.864 26.383
Problem 145 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 292 292 157 154 0 922 0 1 262
normalized size 1 1. 0.54 0.53 0. 3.16 0. 0. 0.9
time (sec) N/A 0.684 0.187 0.014 0. 1.143 0. 1.167 31.379

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 [35] had the largest ratio of [ 0.4643 ]

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. 26 0.038
2 A 2 1 1. 24 0.042
3 A 2 1 1. 23 0.043
4 A 2 1 1. 26 0.038
5 A 2 1 1. 26 0.038
6 A 2 1 1. 26 0.038
7 A 2 1 1. 26 0.038
8 A 2 1 1. 26 0.038
9 A 2 1 1. 26 0.038
10 A 2 1 1. 26 0.038
11 A 2 1 1. 28 0.036
12 A 2 1 1. 26 0.038
13 A 2 1 1. 25 0.04
14 A 2 1 1. 28 0.036
15 A 2 1 1. 28 0.036
16 A 2 1 1. 28 0.036
17 A 2 1 1. 28 0.036
18 A 2 1 1. 28 0.036
19 A 2 1 1. 28 0.036
20 A 2 1 1. 28 0.036
21 A 13 11 1. 28 0.393
22 A 12 11 1. 28 0.393
23 A 11 10 1. 28 0.357
24 A 10 9 1. 26 0.346
25 A 8 7 1. 25 0.28
26 A 12 10 1. 28 0.357
27 A 13 12 1. 28 0.429
28 A 13 11 1. 28 0.393
29 A 11 10 1. 28 0.357
30 A 10 9 1. 28 0.321
31 A 10 9 1. 28 0.321
32 A 10 9 1. 26 0.346
33 A 10 9 1. 25 0.36
34 A 14 12 1. 28 0.429
35 A 15 13 1. 28 0.464
36 A 15 13 1. 28 0.464
37 A 2 1 1. 30 0.033
38 A 2 1 1. 30 0.033
39 A 2 1 1. 28 0.036
40 A 8 5 1. 30 0.167
41 A 10 6 0.98 30 0.2
42 A 10 9 1. 28 0.321
43 A 11 10 1. 30 0.333
44 A 11 10 1. 31 0.323
45 A 11 10 1. 34 0.294
46 A 11 10 1. 34 0.294
47 A 7 6 1. 30 0.2
48 A 7 6 1. 30 0.2
49 A 7 6 1. 30 0.2
50 A 7 6 1. 28 0.214
51 A 7 6 1. 30 0.2
52 A 7 6 1. 30 0.2
53 A 7 6 1. 30 0.2
54 A 7 6 1. 30 0.2
55 A 5 3 1. 30 0.1
56 A 5 3 1. 30 0.1
57 A 5 3 1. 27 0.111
58 A 5 3 1. 30 0.1
59 A 5 3 1. 30 0.1
60 A 5 3 1. 30 0.1
61 A 8 7 1. 30 0.233
62 A 7 7 1. 30 0.233
63 A 6 6 1. 30 0.2
64 A 5 5 1. 28 0.179
65 A 8 7 1. 30 0.233
66 A 8 7 1. 30 0.233
67 A 8 7 1. 30 0.233
68 A 6 4 1. 30 0.133
69 A 6 4 1. 30 0.133
70 A 4 3 1. 30 0.1
71 A 4 3 1. 27 0.111
72 A 6 4 1. 30 0.133
73 A 6 4 1. 30 0.133
74 A 7 5 1. 31 0.161
75 A 7 5 1. 31 0.161
76 A 7 5 1. 31 0.161
77 A 7 5 1. 31 0.161
78 A 5 4 1. 29 0.138
79 A 4 3 1. 31 0.097
80 A 4 3 1. 31 0.097
81 A 4 3 1. 31 0.097
82 A 6 4 1. 31 0.129
83 A 6 4 1. 31 0.129
84 A 6 4 1. 31 0.129
85 A 6 4 1. 31 0.129
86 A 4 3 1. 28 0.107
87 A 5 3 1. 31 0.097
88 A 5 3 1. 31 0.097
89 A 5 3 1. 31 0.097
90 A 5 3 1. 31 0.097
91 A 7 5 1. 31 0.161
92 A 7 5 1. 31 0.161
93 A 7 5 1. 31 0.161
94 A 5 4 1. 31 0.129
95 A 5 4 1. 31 0.129
96 A 5 4 1. 28 0.143
97 A 6 3 1. 31 0.097
98 A 6 3 1. 31 0.097
99 A 6 3 1. 31 0.097
100 A 8 7 1. 31 0.226
101 A 8 7 1. 31 0.226
102 A 8 7 1. 31 0.226
103 A 8 7 1. 31 0.226
104 A 6 6 1. 29 0.207
105 A 8 7 1. 31 0.226
106 A 8 7 1. 31 0.226
107 A 8 7 1. 31 0.226
108 A 8 7 1. 31 0.226
109 A 12 7 1. 31 0.226
110 A 12 7 1. 31 0.226
111 A 12 7 1. 31 0.226
112 A 12 7 1. 31 0.226
113 A 10 6 1. 28 0.214
114 A 12 7 1. 31 0.226
115 A 12 7 1. 31 0.226
116 A 12 7 1. 31 0.226
117 A 13 8 1. 31 0.258
118 A 13 8 1. 31 0.258
119 A 13 8 1. 31 0.258
120 A 11 7 1. 31 0.226
121 A 11 7 1. 31 0.226
122 A 11 7 1. 28 0.25
123 A 13 7 1. 31 0.226
124 A 13 7 1. 31 0.226
125 A 7 6 1. 33 0.182
126 A 6 4 1. 35 0.114
127 A 6 4 1. 35 0.114
128 A 4 3 1. 32 0.094
129 A 6 4 1. 35 0.114
130 A 6 4 1. 35 0.114
131 A 1 1 1. 42 0.024
132 A 5 4 1.32 35 0.114
133 A 4 3 1.34 35 0.086
134 A 4 3 1.37 33 0.091
135 A 6 5 1.62 35 0.143
136 A 6 6 1.57 35 0.171
137 A 6 6 1.44 35 0.171
138 A 7 7 1.17 35 0.2
139 A 6 6 1.13 35 0.171
140 A 5 5 1.4 32 0.156
141 A 6 6 1.52 35 0.171
142 A 6 6 1. 35 0.171
143 A 5 4 1. 35 0.114
144 A 6 5 1. 35 0.143
145 A 7 5 1. 35 0.143

[next] [prev] [prev-tail] [front] [up]