Detailed conclusion table per each integral is given by the 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 as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 84 | 85 | 79 | 211 | 157 | 186 | 0 | 1270 | 0 |
N.S. |
1 | 1.01 | 0.94 | 2.51 | 1.87 | 2.21 | 0.00 | 15.12 | 0.00 |
time (sec) |
N/A | 0.254 | 0.165 | 1.273 | 0.315 | 0.489 | 0.000 | 0.707 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 78 | 79 | 69 | 86 | 61 | 175 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.88 | 1.10 | 0.78 | 2.24 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.265 | 0.116 | 0.934 | 0.200 | 0.721 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 140 | 123 | 90 | 165 | 148 | 282 | 0 | 0 | 0 |
N.S. |
1 | 0.88 | 0.64 | 1.18 | 1.06 | 2.01 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.303 | 0.474 | 1.145 | 0.216 | 0.970 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 208 | 177 | 123 | 257 | 272 | 442 | 0 | 0 | 0 |
N.S. |
1 | 0.85 | 0.59 | 1.24 | 1.31 | 2.12 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.340 | 0.842 | 1.280 | 0.204 | 1.355 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 275 | 283 | 211 | 419 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.77 | 1.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.545 | 3.337 | 4.976 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 222 | 223 | 174 | 389 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.78 | 1.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.423 | 3.168 | 5.137 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 154 | 155 | 156 | 266 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.01 | 1.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.838 | 0.756 | 2.523 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 223 | 224 | 173 | 204 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.78 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.445 | 2.616 | 4.186 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 276 | 282 | 218 | 419 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.79 | 1.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.538 | 5.360 | 3.812 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 134 | 149 | 108 | 644 | 248 | 328 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 0.81 | 4.81 | 1.85 | 2.45 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.334 | 0.497 | 1.582 | 0.296 | 0.394 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 81 | 83 | 77 | 353 | 124 | 220 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.95 | 4.36 | 1.53 | 2.72 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.273 | 0.229 | 1.309 | 0.292 | 0.364 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 38 | 103 | 106 | 112 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.06 | 2.86 | 2.94 | 3.11 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.231 | 0.038 | 1.373 | 0.319 | 0.332 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 42 | 25 | 100 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.27 | 0.76 | 3.03 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.238 | 0.036 | 0.791 | 0.209 | 0.336 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 71 | 71 | 109 | 77 | 220 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.95 | 1.45 | 1.03 | 2.93 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.269 | 0.165 | 0.946 | 0.229 | 0.366 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 126 | 127 | 101 | 205 | 158 | 388 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.80 | 1.63 | 1.25 | 3.08 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.313 | 0.382 | 1.117 | 0.215 | 0.394 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 246 | 249 | 188 | 377 | 0 | 845 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.76 | 1.53 | 0.00 | 3.43 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.455 | 2.563 | 3.796 | 0.000 | 0.172 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 109 | 123 | 100 | 222 | 0 | 730 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 0.92 | 2.04 | 0.00 | 6.70 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.305 | 0.681 | 2.827 | 0.000 | 0.153 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 60 | 52 | 0 | 305 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.18 | 1.02 | 0.00 | 5.98 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.276 | 0.054 | 0.546 | 0.000 | 0.116 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 106 | 120 | 101 | 120 | 0 | 723 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 0.95 | 1.13 | 0.00 | 6.82 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.308 | 0.718 | 2.043 | 0.000 | 0.142 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | C | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 240 | 243 | 186 | 351 | 0 | 1045 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.78 | 1.46 | 0.00 | 4.35 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.465 | 4.617 | 2.864 | 0.000 | 0.192 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | B | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 177 | 182 | 107 | 3767 | 334 | 593 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.60 | 21.28 | 1.89 | 3.35 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.354 | 0.508 | 6.502 | 0.326 | 0.507 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 75 | 2537 | 193 | 445 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.64 | 21.50 | 1.64 | 3.77 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.303 | 0.116 | 4.020 | 0.357 | 0.454 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 65 | 54 | 1317 | 143 | 281 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.86 | 20.90 | 2.27 | 4.46 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.249 | 0.073 | 3.615 | 0.343 | 0.350 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 59 | 46 | 62 | 46 | 225 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.81 | 1.09 | 0.81 | 3.95 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.255 | 0.055 | 0.882 | 0.251 | 0.380 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 103 | 70 | 148 | 117 | 406 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 0.64 | 1.35 | 1.06 | 3.69 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.292 | 0.108 | 1.146 | 0.232 | 0.379 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 167 | 158 | 94 | 265 | 219 | 652 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.56 | 1.59 | 1.31 | 3.90 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.331 | 0.332 | 1.296 | 0.269 | 0.414 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-1) | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 292 | 311 | 197 | 368 | 0 | 1228 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.67 | 1.26 | 0.00 | 4.21 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.506 | 2.783 | 4.669 | 0.000 | 0.211 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 224 | 233 | 145 | 278 | 0 | 1048 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.65 | 1.24 | 0.00 | 4.68 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.432 | 1.196 | 3.883 | 0.000 | 0.184 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 90 | 103 | 0 | 938 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.89 | 1.02 | 0.00 | 9.29 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.422 | 0.134 | 1.550 | 0.000 | 0.156 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 209 | 222 | 142 | 141 | 0 | 996 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.68 | 0.67 | 0.00 | 4.77 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.441 | 1.114 | 3.211 | 0.000 | 0.178 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-1) | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 297 | 312 | 199 | 353 | 0 | 1465 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.67 | 1.19 | 0.00 | 4.93 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.582 | 4.304 | 3.732 | 0.000 | 0.187 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 218 | 212 | 107 | 1909 | 424 | 995 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 0.49 | 8.76 | 1.94 | 4.56 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.384 | 0.504 | 4.226 | 0.384 | 0.580 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 153 | 150 | 76 | 834 | 262 | 769 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.50 | 5.45 | 1.71 | 5.03 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.318 | 0.119 | 3.283 | 0.342 | 0.438 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 97 | 56 | 963 | 203 | 521 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.62 | 10.58 | 2.23 | 5.73 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.267 | 0.085 | 2.342 | 0.476 | 0.373 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 83 | 87 | 49 | 260 | 66 | 382 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.59 | 3.13 | 0.80 | 4.60 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.273 | 0.054 | 1.642 | 0.273 | 0.353 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 143 | 131 | 69 | 1038 | 156 | 666 | 0 | 0 | 0 |
N.S. |
1 | 0.92 | 0.48 | 7.26 | 1.09 | 4.66 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.309 | 0.270 | 2.248 | 0.263 | 0.384 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | A | B | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 208 | 186 | 117 | 988 | 280 | 984 | 0 | 0 | 0 |
N.S. |
1 | 0.89 | 0.56 | 4.75 | 1.35 | 4.73 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.352 | 0.879 | 3.512 | 0.248 | 0.433 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-1) | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 348 | 380 | 235 | 667 | 0 | 1730 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 0.68 | 1.92 | 0.00 | 4.97 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.623 | 4.171 | 5.885 | 0.000 | 0.334 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 292 | 310 | 199 | 851 | 0 | 1632 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.68 | 2.91 | 0.00 | 5.59 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.524 | 3.221 | 5.924 | 0.000 | 0.257 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 223 | 228 | 172 | 547 | 0 | 1531 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.77 | 2.45 | 0.00 | 6.87 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.201 | 1.341 | 2.112 | 0.000 | 0.197 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 287 | 308 | 209 | 411 | 0 | 1595 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.73 | 1.43 | 0.00 | 5.56 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.560 | 3.241 | 5.289 | 0.000 | 0.221 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-1) | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 348 | 375 | 226 | 633 | 0 | 1971 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 0.65 | 1.82 | 0.00 | 5.66 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.678 | 3.708 | 4.472 | 0.000 | 0.285 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 120 | 147 | 121 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.22 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.384 | 1.142 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 102 | 104 | 83 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.277 | 0.249 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 61 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.228 | 0.067 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 54 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.232 | 0.063 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 95 | 91 | 73 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.262 | 0.539 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 102 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.295 | 4.617 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 102 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.280 | 0.641 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 98 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.282 | 0.555 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 102 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.287 | 3.310 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | C | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 153 | 153 | 143 | 110 | 152 | 874 | 0 | 144 | 2003 |
N.S. |
1 | 1.00 | 0.93 | 0.72 | 0.99 | 5.71 | 0.00 | 0.94 | 13.09 |
time (sec) |
N/A | 0.434 | 0.330 | 3.436 | 0.306 | 1.106 | 0.000 | 0.310 | 15.390 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | F(-1) | F | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 45 | 0 | 52 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 1.16 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.244 | 0.030 | 0.000 | 0.291 | 0.000 | 0.000 | 0.296 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | F(-2) | F | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 0 | 39 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 1.39 | 0.00 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.241 | 0.017 | 0.000 | 0.283 | 0.000 | 0.000 | 0.299 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 56 | 54 | 60 | 68 | 195 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.92 | 1.02 | 1.15 | 3.31 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.261 | 0.057 | 0.621 | 0.301 | 0.388 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 89 | 93 | 89 | 0 | 0 | 361 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.00 | 0.00 | 0.00 | 4.06 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.298 | 0.187 | 0.000 | 0.000 | 0.414 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 54 | 65 | 72 | 0 | 240 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 1.27 | 1.41 | 0.00 | 4.71 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.236 | 0.100 | 2.186 | 0.000 | 0.393 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 35 | 42 | 50 | 140 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.20 | 1.43 | 4.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.250 | 0.030 | 0.618 | 0.308 | 0.347 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 70 | 66 | 66 | 0 | 79 | 247 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 0.94 | 0.00 | 1.13 | 3.53 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.281 | 0.096 | 0.000 | 0.303 | 0.355 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 108 | 109 | 141 | 0 | 166 | 371 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.31 | 0.00 | 1.54 | 3.44 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.328 | 3.060 | 0.000 | 0.340 | 0.394 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 411 | 454 | 291 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.581 | 4.949 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 162 | 162 | 195 | 396 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.20 | 2.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.290 | 0.464 | 3.054 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 477 | 502 | 378 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.593 | 9.877 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 25 | 37 | 0 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.61 | 0.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.211 | 5.573 | 1.908 | 2.423 | 1.674 | 0.000 | 2.871 | 17.103 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 279 | 265 | 810 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 2.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.447 | 14.108 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 141 | 139 | 463 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 3.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.301 | 9.505 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 54 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.236 | 0.095 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 127 | 126 | 119 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.293 | 0.574 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 25 | 37 | 0 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.61 | 0.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.217 | 21.007 | 1.556 | 14.075 | 0.361 | 0.000 | 2.999 | 18.601 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 25 | 37 | 0 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.61 | 0.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.216 | 2.145 | 1.593 | 5.311 | 0.309 | 0.000 | 1.577 | 17.634 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 14 | 16 | 28 | 0 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 2.00 | 0.00 | 1.14 | 1.14 |
time (sec) |
N/A | 0.180 | 0.205 | 0.944 | 1.086 | 0.277 | 0.000 | 0.847 | 14.779 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 25 | 37 | 0 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.61 | 0.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.218 | 1.912 | 1.464 | 5.354 | 0.299 | 0.000 | 1.559 | 16.690 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 25 | 37 | 0 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.61 | 0.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.211 | 14.591 | 1.630 | 14.883 | 0.353 | 0.000 | 1.638 | 17.767 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 306 | 306 | 3544 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 11.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.681 | 20.717 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 215 | 215 | 2368 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 11.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.527 | 16.740 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 124 | 124 | 1395 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 11.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.365 | 14.193 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 25 | 25 | 20 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.87 | 1.09 | 1.09 |
time (sec) |
N/A | 0.225 | 5.255 | 1.089 | 1.489 | 0.283 | 5.172 | 1.376 | 13.931 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 25 | 43 | 22 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.87 | 0.96 | 1.09 | 1.09 |
time (sec) |
N/A | 0.225 | 47.942 | 1.204 | 3.247 | 0.289 | 107.532 | 1.804 | 15.282 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 45 | 45 | 38 | 57 | 97 | 0 | 46 | 0 |
N.S. |
1 | 0.96 | 0.96 | 0.81 | 1.21 | 2.06 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 0.255 | 0.033 | 2.559 | 0.315 | 0.293 | 0.000 | 0.362 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 24 | 41 | 74 | 0 | 27 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 1.41 | 2.55 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.256 | 0.018 | 0.747 | 0.312 | 0.318 | 0.000 | 0.369 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 25 | 25 | 0 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.221 | 5.774 | 1.214 | 4.441 | 0.289 | 0.000 | 6.229 | 15.319 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 25 | 25 | 0 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.221 | 25.095 | 0.911 | 5.112 | 0.263 | 0.000 | 8.010 | 15.446 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 23 | 21 | 23 | 23 | 20 | 23 | 23 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 0.95 | 1.10 | 1.10 |
time (sec) |
N/A | 0.204 | 1.508 | 0.823 | 3.130 | 0.268 | 109.766 | 6.171 | 14.697 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 55 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.251 | 0.061 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 136 | 134 | 129 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.397 | 1.171 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 25 | 25 | 0 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.222 | 25.689 | 0.903 | 6.046 | 0.261 | 0.000 | 8.382 | 15.010 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 25 | 25 | 0 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.225 | 3.453 | 0.866 | 4.415 | 0.267 | 0.000 | 6.726 | 14.401 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 14 | 16 | 16 | 14 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 1.14 | 1.00 | 1.14 | 1.14 |
time (sec) |
N/A | 0.185 | 0.692 | 0.391 | 2.442 | 0.251 | 4.079 | 2.994 | 14.974 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 25 | 25 | 22 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.96 | 1.09 | 1.09 |
time (sec) |
N/A | 0.226 | 2.671 | 0.755 | 4.446 | 0.267 | 113.302 | 3.389 | 14.568 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 25 | 25 | 0 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.226 | 32.475 | 0.856 | 6.239 | 0.262 | 0.000 | 4.024 | 14.870 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 107 | 148 | 102 | 387 | 0 | 125 | 0 | 0 | 0 |
N.S. |
1 | 1.38 | 0.95 | 3.62 | 0.00 | 1.17 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.420 | 0.201 | 7.072 | 0.000 | 0.103 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 137 | 137 | 135 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.403 | 2.523 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 325 | 315013 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 4.11 | 3987.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.441 | 2.144 | 7.423 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 529 | 2174 | 0 | 1623 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 6.70 | 27.52 | 0.00 | 20.54 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.456 | 1.861 | 6.638 | 0.000 | 0.140 | 0.000 | 0.000 | 0.000 |