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 | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 66 | 64 | 62 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.334 | 0.105 | 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 | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 97 | 43 | 54 | 99 | 46 | 56 | 90 | 63 |
N.S. |
1 | 1.05 | 0.47 | 0.59 | 1.08 | 0.50 | 0.61 | 0.98 | 0.68 |
time (sec) |
N/A | 0.289 | 0.070 | 0.577 | 0.204 | 0.288 | 0.135 | 0.324 | 1.583 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 108 | 58 | 70 | 159 | 61 | 75 | 113 | 92 |
N.S. |
1 | 1.06 | 0.57 | 0.69 | 1.56 | 0.60 | 0.74 | 1.11 | 0.90 |
time (sec) |
N/A | 0.302 | 0.089 | 0.569 | 0.202 | 0.295 | 0.156 | 0.325 | 1.586 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 160 | 143 | 132 | 642 | 559 | 1409 | 609 | 1697 | 380 |
N.S. |
1 | 0.89 | 0.82 | 4.01 | 3.49 | 8.81 | 3.81 | 10.61 | 2.38 |
time (sec) |
N/A | 0.495 | 0.051 | 5.581 | 0.227 | 0.324 | 2.560 | 0.346 | 1.838 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 110 | 100 | 386 | 317 | 639 | 360 | 772 | 242 |
N.S. |
1 | 0.91 | 0.83 | 3.19 | 2.62 | 5.28 | 2.98 | 6.38 | 2.00 |
time (sec) |
N/A | 0.415 | 0.011 | 1.512 | 0.242 | 0.323 | 1.138 | 0.321 | 1.513 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 78 | 77 | 69 | 165 | 148 | 231 | 178 | 283 | 111 |
N.S. |
1 | 0.99 | 0.88 | 2.12 | 1.90 | 2.96 | 2.28 | 3.63 | 1.42 |
time (sec) |
N/A | 0.335 | 0.009 | 0.417 | 0.211 | 0.331 | 0.516 | 0.333 | 1.361 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 34 | 42 | 45 | 50 | 53 | 59 | 41 |
N.S. |
1 | 1.00 | 1.00 | 1.24 | 1.32 | 1.47 | 1.56 | 1.74 | 1.21 |
time (sec) |
N/A | 0.184 | 0.007 | 0.083 | 0.195 | 0.304 | 0.219 | 0.337 | 1.320 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | A | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 83 | 85 | 83 | 0 | 0 | 65 | 0 | 78 | 0 |
N.S. |
1 | 1.02 | 1.00 | 0.00 | 0.00 | 0.78 | 0.00 | 0.94 | 0.00 |
time (sec) |
N/A | 0.407 | 0.094 | 0.000 | 0.000 | 0.311 | 0.000 | 0.335 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | B | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 123 | 124 | 163 | 0 | 0 | 171 | 0 | 582 | 0 |
N.S. |
1 | 1.01 | 1.33 | 0.00 | 0.00 | 1.39 | 0.00 | 4.73 | 0.00 |
time (sec) |
N/A | 0.500 | 0.076 | 0.000 | 0.000 | 0.299 | 0.000 | 0.336 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | B | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 169 | 177 | 189 | 0 | 0 | 444 | 0 | 3401 | 0 |
N.S. |
1 | 1.05 | 1.12 | 0.00 | 0.00 | 2.63 | 0.00 | 20.12 | 0.00 |
time (sec) |
N/A | 0.606 | 0.120 | 0.000 | 0.000 | 0.313 | 0.000 | 0.381 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 219 | 214 | 190 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.824 | 0.221 | 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(-2) | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 176 | 177 | 160 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.698 | 0.054 | 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(-2) | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 139 | 140 | 134 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.595 | 0.044 | 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(-2) | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 104 | 106 | 104 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.516 | 0.017 | 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(-2) | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 147 | 148 | 181 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.646 | 0.171 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 194 | 203 | 211 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.787 | 0.200 | 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(-2) | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 237 | 258 | 272 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.907 | 0.279 | 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(-2) | A | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 131 | 135 | 131 | 0 | 0 | 80 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 1.00 | 0.00 | 0.00 | 0.61 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.449 | 0.143 | 0.000 | 0.000 | 0.094 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 109 | 106 | 109 | 0 | 70 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 1.00 | 0.00 | 0.64 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.418 | 0.147 | 0.000 | 0.061 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 158 | 141 | 232 | 466 | 304 | 405 | 457 | 987 | 370 |
N.S. |
1 | 0.89 | 1.47 | 2.95 | 1.92 | 2.56 | 2.89 | 6.25 | 2.34 |
time (sec) |
N/A | 0.414 | 0.210 | 5.982 | 0.201 | 0.364 | 2.503 | 0.340 | 1.541 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 128 | 117 | 156 | 290 | 202 | 268 | 286 | 544 | 225 |
N.S. |
1 | 0.91 | 1.22 | 2.27 | 1.58 | 2.09 | 2.23 | 4.25 | 1.76 |
time (sec) |
N/A | 0.371 | 0.127 | 1.970 | 0.191 | 0.305 | 1.229 | 0.362 | 1.592 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 93 | 113 | 173 | 112 | 148 | 156 | 236 | 113 |
N.S. |
1 | 0.95 | 1.15 | 1.77 | 1.14 | 1.51 | 1.59 | 2.41 | 1.15 |
time (sec) |
N/A | 0.317 | 0.038 | 0.438 | 0.200 | 0.324 | 0.587 | 0.323 | 1.444 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 34 | 42 | 45 | 50 | 53 | 59 | 41 |
N.S. |
1 | 1.00 | 1.00 | 1.24 | 1.32 | 1.47 | 1.56 | 1.74 | 1.21 |
time (sec) |
N/A | 0.183 | 0.007 | 0.102 | 0.183 | 0.305 | 0.208 | 0.322 | 1.347 |
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 | 68 | 68 | 67 | 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 | 0.404 | 0.012 | 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 | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 75 | 69 | 139 | 90 | 113 | 357 | 96 | 89 |
N.S. |
1 | 0.94 | 0.86 | 1.74 | 1.12 | 1.41 | 4.46 | 1.20 | 1.11 |
time (sec) |
N/A | 0.290 | 0.075 | 1.336 | 0.194 | 0.279 | 3.558 | 0.321 | 3.316 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 100 | 88 | 305 | 172 | 310 | 1984 | 221 | 180 |
N.S. |
1 | 0.84 | 0.74 | 2.56 | 1.45 | 2.61 | 16.67 | 1.86 | 1.51 |
time (sec) |
N/A | 0.369 | 0.094 | 3.759 | 0.197 | 0.307 | 15.248 | 0.402 | 3.492 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 149 | 126 | 115 | 487 | 306 | 563 | 5673 | 443 | 293 |
N.S. |
1 | 0.85 | 0.77 | 3.27 | 2.05 | 3.78 | 38.07 | 2.97 | 1.97 |
time (sec) |
N/A | 0.414 | 0.123 | 11.925 | 0.208 | 0.319 | 63.372 | 0.373 | 3.742 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 409 | 343 | 400 | 1537 | 895 | 1742 | 1421 | 3738 | 1154 |
N.S. |
1 | 0.84 | 0.98 | 3.76 | 2.19 | 4.26 | 3.47 | 9.14 | 2.82 |
time (sec) |
N/A | 1.143 | 0.196 | 16.244 | 0.228 | 0.354 | 5.391 | 0.387 | 1.964 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 323 | 278 | 277 | 939 | 605 | 1137 | 894 | 2106 | 652 |
N.S. |
1 | 0.86 | 0.86 | 2.91 | 1.87 | 3.52 | 2.77 | 6.52 | 2.02 |
time (sec) |
N/A | 1.002 | 0.110 | 5.678 | 0.218 | 0.340 | 2.594 | 0.338 | 1.741 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 211 | 211 | 164 | 540 | 348 | 622 | 466 | 939 | 302 |
N.S. |
1 | 1.00 | 0.78 | 2.56 | 1.65 | 2.95 | 2.21 | 4.45 | 1.43 |
time (sec) |
N/A | 0.642 | 0.059 | 1.533 | 0.214 | 0.328 | 1.244 | 0.324 | 1.497 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 78 | 77 | 69 | 165 | 148 | 231 | 178 | 283 | 111 |
N.S. |
1 | 0.99 | 0.88 | 2.12 | 1.90 | 2.96 | 2.28 | 3.63 | 1.42 |
time (sec) |
N/A | 0.326 | 0.013 | 0.423 | 0.202 | 0.287 | 0.470 | 0.315 | 1.309 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 123 | 117 | 324 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 2.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.684 | 0.141 | 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 | 144 | 128 | 200 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.89 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.589 | 0.181 | 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 | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 222 | 247 | 316 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 1.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.184 | 0.314 | 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 | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 492 | 492 | 378 | 2034 | 1245 | 3121 | 1846 | 5146 | 1400 |
N.S. |
1 | 1.00 | 0.77 | 4.13 | 2.53 | 6.34 | 3.75 | 10.46 | 2.85 |
time (sec) |
N/A | 1.258 | 0.193 | 16.190 | 0.247 | 0.381 | 5.381 | 0.420 | 2.342 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 306 | 306 | 231 | 1084 | 732 | 1692 | 991 | 2532 | 651 |
N.S. |
1 | 1.00 | 0.75 | 3.54 | 2.39 | 5.53 | 3.24 | 8.27 | 2.13 |
time (sec) |
N/A | 0.824 | 0.093 | 5.224 | 0.232 | 0.385 | 2.585 | 0.379 | 1.911 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 110 | 100 | 386 | 317 | 639 | 360 | 772 | 242 |
N.S. |
1 | 0.91 | 0.83 | 3.19 | 2.62 | 5.28 | 2.98 | 6.38 | 2.00 |
time (sec) |
N/A | 0.402 | 0.018 | 1.511 | 0.201 | 0.299 | 1.020 | 0.324 | 1.428 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 177 | 166 | 646 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 3.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.903 | 0.228 | 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 | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 209 | 177 | 444 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.85 | 2.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.889 | 0.343 | 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 | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 376 | 354 | 660 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 1.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.204 | 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 | B | B | B | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 160 | 143 | 132 | 642 | 559 | 1409 | 609 | 1697 | 380 |
N.S. |
1 | 0.89 | 0.82 | 4.01 | 3.49 | 8.81 | 3.81 | 10.61 | 2.38 |
time (sec) |
N/A | 0.498 | 0.034 | 5.170 | 0.225 | 0.309 | 2.070 | 0.358 | 1.600 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 231 | 214 | 1095 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 4.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.110 | 0.335 | 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 | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 274 | 226 | 1301 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.82 | 4.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.132 | 0.380 | 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 | A | A | A | A | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 35 | 29 | 41 | 40 | 42 | 48 | 53 | 36 |
N.S. |
1 | 1.21 | 1.00 | 1.41 | 1.38 | 1.45 | 1.66 | 1.83 | 1.24 |
time (sec) |
N/A | 0.243 | 0.006 | 0.086 | 0.194 | 0.312 | 0.207 | 0.328 | 0.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 279 | 279 | 252 | 0 | 0 | 243 | 0 | 517 | 0 |
N.S. |
1 | 1.00 | 0.90 | 0.00 | 0.00 | 0.87 | 0.00 | 1.85 | 0.00 |
time (sec) |
N/A | 1.104 | 0.550 | 0.000 | 0.000 | 0.303 | 0.000 | 0.365 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 179 | 179 | 164 | 0 | 0 | 140 | 0 | 248 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.78 | 0.00 | 1.39 | 0.00 |
time (sec) |
N/A | 0.725 | 0.117 | 0.000 | 0.000 | 0.311 | 0.000 | 0.348 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | A | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 83 | 85 | 83 | 0 | 0 | 65 | 0 | 78 | 0 |
N.S. |
1 | 1.02 | 1.00 | 0.00 | 0.00 | 0.78 | 0.00 | 0.94 | 0.00 |
time (sec) |
N/A | 0.396 | 0.036 | 0.000 | 0.000 | 0.294 | 0.000 | 0.333 | 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 | 28 | 28 | 30 | 28 | 30 | 35 | 24 | 30 | 30 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.07 | 1.25 | 0.86 | 1.07 | 1.07 |
time (sec) |
N/A | 0.228 | 0.207 | 0.157 | 0.856 | 0.294 | 1.503 | 0.348 | 1.282 |
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 | 28 | 28 | 30 | 28 | 30 | 59 | 26 | 30 | 30 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.07 | 2.11 | 0.93 | 1.07 | 1.07 |
time (sec) |
N/A | 0.225 | 0.478 | 0.188 | 0.858 | 0.303 | 3.772 | 0.347 | 1.244 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 326 | 538 | 1310 | 0 | 0 | 573 | 0 | 3975 | 0 |
N.S. |
1 | 1.65 | 4.02 | 0.00 | 0.00 | 1.76 | 0.00 | 12.19 | 0.00 |
time (sec) |
N/A | 1.763 | 0.413 | 0.000 | 0.000 | 0.323 | 0.000 | 0.463 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | B | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 224 | 329 | 269 | 0 | 0 | 328 | 0 | 1930 | 0 |
N.S. |
1 | 1.47 | 1.20 | 0.00 | 0.00 | 1.46 | 0.00 | 8.62 | 0.00 |
time (sec) |
N/A | 1.267 | 0.221 | 0.000 | 0.000 | 0.302 | 0.000 | 0.392 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | B | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 123 | 124 | 163 | 0 | 0 | 171 | 0 | 582 | 0 |
N.S. |
1 | 1.01 | 1.33 | 0.00 | 0.00 | 1.39 | 0.00 | 4.73 | 0.00 |
time (sec) |
N/A | 0.495 | 0.074 | 0.000 | 0.000 | 0.308 | 0.000 | 0.342 | 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 | 28 | 28 | 30 | 28 | 267 | 71 | 26 | 30 | 30 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 9.54 | 2.54 | 0.93 | 1.07 | 1.07 |
time (sec) |
N/A | 0.214 | 0.667 | 0.181 | 1.153 | 0.333 | 5.011 | 0.323 | 1.244 |
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 | 28 | 28 | 30 | 28 | 406 | 112 | 27 | 30 | 30 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 14.50 | 4.00 | 0.96 | 1.07 | 1.07 |
time (sec) |
N/A | 0.217 | 8.431 | 0.177 | 1.136 | 0.318 | 31.297 | 0.359 | 1.270 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | F | F | B | F | B | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 432 | 951 | 438 | 0 | 0 | 1682 | 0 | 5889 | 0 |
N.S. |
1 | 2.20 | 1.01 | 0.00 | 0.00 | 3.89 | 0.00 | 13.63 | 0.00 |
time (sec) |
N/A | 3.246 | 1.281 | 0.000 | 0.000 | 0.365 | 0.000 | 0.543 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | B | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 322 | 530 | 322 | 0 | 0 | 931 | 0 | 11278 | 0 |
N.S. |
1 | 1.65 | 1.00 | 0.00 | 0.00 | 2.89 | 0.00 | 35.02 | 0.00 |
time (sec) |
N/A | 2.034 | 0.378 | 0.000 | 0.000 | 0.389 | 0.000 | 0.553 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | B | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 169 | 177 | 189 | 0 | 0 | 444 | 0 | 3401 | 0 |
N.S. |
1 | 1.05 | 1.12 | 0.00 | 0.00 | 2.63 | 0.00 | 20.12 | 0.00 |
time (sec) |
N/A | 0.616 | 0.117 | 0.000 | 0.000 | 0.319 | 0.000 | 0.399 | 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 | 28 | 28 | 30 | 28 | 1116 | 107 | 26 | 30 | 30 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 39.86 | 3.82 | 0.93 | 1.07 | 1.07 |
time (sec) |
N/A | 0.219 | 0.553 | 0.173 | 1.570 | 0.319 | 17.311 | 0.348 | 1.298 |
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 | 28 | 28 | 30 | 28 | 1486 | 165 | 27 | 30 | 30 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 53.07 | 5.89 | 0.96 | 1.07 | 1.07 |
time (sec) |
N/A | 0.218 | 23.057 | 0.177 | 1.579 | 0.314 | 135.869 | 0.398 | 1.336 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 488 | 488 | 458 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.032 | 0.487 | 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(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 311 | 311 | 298 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.254 | 0.264 | 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(-2) | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 139 | 140 | 134 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.581 | 0.047 | 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 | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 32 | 28 | 30 | 0 | 26 | 30 | 30 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 0.00 | 0.87 | 1.00 | 1.00 |
time (sec) |
N/A | 0.249 | 4.541 | 0.161 | 11.956 | 0.000 | 0.608 | 0.429 | 1.360 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 32 | 28 | 30 | 0 | 27 | 30 | 30 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 0.00 | 0.90 | 1.00 | 1.00 |
time (sec) |
N/A | 0.304 | 0.257 | 0.164 | 10.690 | 0.000 | 2.502 | 0.402 | 1.416 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 625 | 625 | 545 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.474 | 0.936 | 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(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 396 | 396 | 348 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.498 | 0.386 | 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(-2) | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 176 | 177 | 160 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.675 | 0.134 | 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 | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 32 | 28 | 30 | 0 | 26 | 30 | 30 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 0.00 | 0.87 | 1.00 | 1.00 |
time (sec) |
N/A | 0.260 | 2.657 | 0.163 | 10.799 | 0.000 | 52.802 | 0.538 | 1.449 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 32 | 28 | 30 | 0 | 0 | 30 | 30 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 0.00 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.303 | 1.276 | 0.181 | 10.701 | 0.000 | 0.000 | 0.520 | 1.387 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 355 | 355 | 315 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.660 | 0.257 | 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(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 229 | 229 | 208 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.060 | 0.146 | 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(-2) | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 104 | 106 | 104 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.505 | 0.021 | 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 | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 32 | 28 | 30 | 0 | 27 | 30 | 30 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 0.00 | 0.90 | 1.00 | 1.00 |
time (sec) |
N/A | 0.258 | 0.079 | 0.191 | 10.492 | 0.000 | 1.499 | 0.490 | 1.351 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 404 | 666 | 1040 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.65 | 2.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.805 | 1.522 | 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(-2) | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 275 | 402 | 435 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.46 | 1.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.817 | 0.727 | 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(-2) | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 147 | 148 | 181 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.646 | 0.106 | 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 | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 32 | 28 | 30 | 0 | 27 | 30 | 30 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 0.00 | 0.90 | 1.00 | 1.00 |
time (sec) |
N/A | 0.281 | 0.323 | 0.191 | 10.750 | 0.000 | 24.357 | 0.511 | 1.565 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 514 | 1154 | 652 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 2.25 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 5.179 | 3.733 | 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(-2) | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 380 | 632 | 491 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.66 | 1.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.145 | 1.274 | 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(-2) | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 194 | 203 | 211 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.776 | 0.224 | 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 | F(-2) | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 32 | 28 | 30 | 0 | 0 | 30 | 30 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 0.00 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.275 | 0.568 | 0.185 | 12.525 | 0.000 | 0.000 | 0.835 | 1.702 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 171 | 166 | 153 | 0 | 0 | 624 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 0.89 | 0.00 | 0.00 | 3.65 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.491 | 0.247 | 0.000 | 0.000 | 0.341 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 139 | 137 | 124 | 0 | 0 | 353 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.89 | 0.00 | 0.00 | 2.54 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.404 | 0.127 | 0.000 | 0.000 | 0.344 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 103 | 104 | 89 | 118 | 0 | 201 | 0 | 124 | 0 |
N.S. |
1 | 1.01 | 0.86 | 1.15 | 0.00 | 1.95 | 0.00 | 1.20 | 0.00 |
time (sec) |
N/A | 0.362 | 0.182 | 0.652 | 0.000 | 0.298 | 0.000 | 0.289 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 84 | 0 | 0 | 240 | 0 | 110 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 2.79 | 0.00 | 1.28 | 0.00 |
time (sec) |
N/A | 0.335 | 0.113 | 0.000 | 0.000 | 0.336 | 0.000 | 0.310 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 120 | 115 | 91 | 0 | 0 | 467 | 0 | 184 | 0 |
N.S. |
1 | 0.96 | 0.76 | 0.00 | 0.00 | 3.89 | 0.00 | 1.53 | 0.00 |
time (sec) |
N/A | 0.402 | 0.118 | 0.000 | 0.000 | 0.349 | 0.000 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 152 | 151 | 91 | 0 | 0 | 863 | 0 | 324 | 0 |
N.S. |
1 | 0.99 | 0.60 | 0.00 | 0.00 | 5.68 | 0.00 | 2.13 | 0.00 |
time (sec) |
N/A | 0.437 | 0.063 | 0.000 | 0.000 | 0.368 | 0.000 | 0.344 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 184 | 187 | 91 | 0 | 0 | 1362 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.49 | 0.00 | 0.00 | 7.40 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.499 | 0.070 | 0.000 | 0.000 | 0.410 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 635 | 1036 | 4354 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.63 | 6.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 6.413 | 18.558 | 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(-2) | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 547 | 786 | 1323 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.44 | 2.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 4.854 | 11.765 | 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(-2) | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 447 | 570 | 1407 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.28 | 3.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.464 | 12.625 | 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(-2) | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 330 | 400 | 785 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.21 | 2.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.421 | 2.540 | 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(-2) | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 449 | 546 | 1289 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.22 | 2.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.522 | 12.812 | 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(-2) | F | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 537 | 732 | 1349 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.36 | 2.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 4.756 | 9.704 | 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(-2) | F | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 625 | 969 | 1457 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.55 | 2.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 6.398 | 11.041 | 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 | 30 | 30 | 32 | 28 | 30 | 30 | 26 | 30 | 30 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.00 | 0.87 | 1.00 | 1.00 |
time (sec) |
N/A | 0.240 | 0.524 | 0.191 | 0.935 | 0.302 | 33.766 | 0.399 | 1.242 |
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 | 30 | 30 | 32 | 28 | 30 | 30 | 26 | 30 | 30 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.00 | 0.87 | 1.00 | 1.00 |
time (sec) |
N/A | 0.227 | 0.161 | 0.158 | 0.938 | 0.291 | 0.933 | 0.376 | 1.221 |
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 | 30 | 30 | 32 | 28 | 30 | 43 | 27 | 30 | 30 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.43 | 0.90 | 1.00 | 1.00 |
time (sec) |
N/A | 0.233 | 0.519 | 0.179 | 0.940 | 0.312 | 2.781 | 0.360 | 1.308 |
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 | 30 | 30 | 32 | 28 | 30 | 67 | 27 | 30 | 30 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 2.23 | 0.90 | 1.00 | 1.00 |
time (sec) |
N/A | 0.240 | 0.799 | 0.187 | 0.930 | 0.313 | 15.332 | 0.488 | 1.222 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 34 | 28 | 30 | 0 | 29 | 30 | 30 |
N.S. |
1 | 1.00 | 1.06 | 0.88 | 0.94 | 0.00 | 0.91 | 0.94 | 0.94 |
time (sec) |
N/A | 0.447 | 1.135 | 0.180 | 11.059 | 0.000 | 3.559 | 1.014 | 1.335 |