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 | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 162 | 164 | 162 | 169 | 167 | 170 | 197 | 212 | 166 |
N.S. |
1 | 1.01 | 1.00 | 1.04 | 1.03 | 1.05 | 1.22 | 1.31 | 1.02 |
time (sec) |
N/A | 0.345 | 0.054 | 0.049 | 0.185 | 0.276 | 0.196 | 0.296 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 133 | 132 | 126 | 136 | 0 | 421 | 0 | 126 | 1343 |
N.S. |
1 | 0.99 | 0.95 | 1.02 | 0.00 | 3.17 | 0.00 | 0.95 | 10.10 |
time (sec) |
N/A | 0.335 | 0.045 | 0.203 | 0.000 | 0.290 | 0.000 | 0.616 | 7.875 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 96 | 93 | 98 | 0 | 312 | 434 | 91 | 979 |
N.S. |
1 | 0.99 | 0.96 | 1.01 | 0.00 | 3.22 | 4.47 | 0.94 | 10.09 |
time (sec) |
N/A | 0.283 | 0.046 | 0.142 | 0.000 | 0.284 | 72.994 | 0.616 | 8.008 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 71 | 72 | 71 | 65 | 0 | 219 | 287 | 67 | 606 |
N.S. |
1 | 1.01 | 1.00 | 0.92 | 0.00 | 3.08 | 4.04 | 0.94 | 8.54 |
time (sec) |
N/A | 0.245 | 0.033 | 0.096 | 0.000 | 0.276 | 5.220 | 0.686 | 7.711 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 78 | 81 | 128 | 76 | 0 | 249 | 0 | 78 | 2424 |
N.S. |
1 | 1.04 | 1.64 | 0.97 | 0.00 | 3.19 | 0.00 | 1.00 | 31.08 |
time (sec) |
N/A | 0.279 | 0.074 | 0.067 | 0.000 | 0.279 | 0.000 | 0.726 | 10.104 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 114 | 186 | 126 | 0 | 385 | 0 | 124 | 3729 |
N.S. |
1 | 1.02 | 1.66 | 1.12 | 0.00 | 3.44 | 0.00 | 1.11 | 33.29 |
time (sec) |
N/A | 0.358 | 0.146 | 0.090 | 0.000 | 0.392 | 0.000 | 0.629 | 10.265 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 261 | 272 | 327 | 95 | 0 | 5140 | 0 | 4391 | 10177 |
N.S. |
1 | 1.04 | 1.25 | 0.36 | 0.00 | 19.69 | 0.00 | 16.82 | 38.99 |
time (sec) |
N/A | 0.563 | 0.255 | 0.101 | 0.000 | 2.570 | 0.000 | 1.073 | 8.400 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 208 | 212 | 251 | 65 | 0 | 2632 | 0 | 3179 | 6366 |
N.S. |
1 | 1.02 | 1.21 | 0.31 | 0.00 | 12.65 | 0.00 | 15.28 | 30.61 |
time (sec) |
N/A | 0.416 | 0.105 | 0.070 | 0.000 | 0.618 | 0.000 | 0.958 | 8.233 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 172 | 172 | 173 | 45 | 0 | 1569 | 0 | 1402 | 4109 |
N.S. |
1 | 1.00 | 1.01 | 0.26 | 0.00 | 9.12 | 0.00 | 8.15 | 23.89 |
time (sec) |
N/A | 0.305 | 0.062 | 0.059 | 0.000 | 0.438 | 0.000 | 0.783 | 8.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 189 | 187 | 206 | 173 | 0 | 2914 | 0 | 2805 | 6335 |
N.S. |
1 | 0.99 | 1.09 | 0.92 | 0.00 | 15.42 | 0.00 | 14.84 | 33.52 |
time (sec) |
N/A | 0.392 | 0.187 | 0.093 | 0.000 | 0.786 | 0.000 | 1.051 | 0.779 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | B | F(-1) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 271 | 0 | 267 | 232 | 0 | 5442 | 0 | 2870 | 10101 |
N.S. |
1 | 0.00 | 0.99 | 0.86 | 0.00 | 20.08 | 0.00 | 10.59 | 37.27 |
time (sec) |
N/A | 0.000 | 0.206 | 0.108 | 0.000 | 2.886 | 0.000 | 0.908 | 8.694 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 212 | 220 | 208 | 282 | 0 | 1323 | 0 | 239 | 2282 |
N.S. |
1 | 1.04 | 0.98 | 1.33 | 0.00 | 6.24 | 0.00 | 1.13 | 10.76 |
time (sec) |
N/A | 0.488 | 0.193 | 0.227 | 0.000 | 0.347 | 0.000 | 0.647 | 8.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 147 | 169 | 160 | 211 | 0 | 849 | 0 | 194 | 1527 |
N.S. |
1 | 1.15 | 1.09 | 1.44 | 0.00 | 5.78 | 0.00 | 1.32 | 10.39 |
time (sec) |
N/A | 0.362 | 0.122 | 0.175 | 0.000 | 0.296 | 0.000 | 0.614 | 8.163 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 107 | 109 | 111 | 126 | 0 | 538 | 394 | 120 | 283 |
N.S. |
1 | 1.02 | 1.04 | 1.18 | 0.00 | 5.03 | 3.68 | 1.12 | 2.64 |
time (sec) |
N/A | 0.268 | 0.057 | 0.118 | 0.000 | 0.258 | 4.227 | 0.586 | 7.612 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 94 | 96 | 101 | 95 | 0 | 474 | 374 | 102 | 264 |
N.S. |
1 | 1.02 | 1.07 | 1.01 | 0.00 | 5.04 | 3.98 | 1.09 | 2.81 |
time (sec) |
N/A | 0.241 | 0.056 | 0.102 | 0.000 | 0.258 | 2.279 | 0.560 | 7.675 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 150 | 180 | 243 | 212 | 0 | 1014 | 0 | 201 | 7119 |
N.S. |
1 | 1.20 | 1.62 | 1.41 | 0.00 | 6.76 | 0.00 | 1.34 | 47.46 |
time (sec) |
N/A | 0.444 | 0.226 | 0.118 | 0.000 | 0.596 | 0.000 | 0.613 | 12.299 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 223 | 0 | 379 | 300 | 0 | 1635 | 0 | 250 | 10034 |
N.S. |
1 | 0.00 | 1.70 | 1.35 | 0.00 | 7.33 | 0.00 | 1.12 | 45.00 |
time (sec) |
N/A | 0.000 | 0.340 | 0.155 | 0.000 | 1.149 | 0.000 | 0.562 | 13.332 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 425 | 400 | 455 | 217 | 0 | 7252 | 0 | 5675 | 16604 |
N.S. |
1 | 0.94 | 1.07 | 0.51 | 0.00 | 17.06 | 0.00 | 13.35 | 39.07 |
time (sec) |
N/A | 0.759 | 0.761 | 0.131 | 0.000 | 7.531 | 0.000 | 1.513 | 10.139 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 336 | 318 | 362 | 178 | 0 | 4658 | 0 | 4538 | 12396 |
N.S. |
1 | 0.95 | 1.08 | 0.53 | 0.00 | 13.86 | 0.00 | 13.51 | 36.89 |
time (sec) |
N/A | 0.585 | 0.586 | 0.130 | 0.000 | 2.308 | 0.000 | 1.397 | 10.982 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 276 | 265 | 298 | 152 | 0 | 3467 | 0 | 3776 | 9444 |
N.S. |
1 | 0.96 | 1.08 | 0.55 | 0.00 | 12.56 | 0.00 | 13.68 | 34.22 |
time (sec) |
N/A | 0.441 | 0.422 | 0.106 | 0.000 | 1.158 | 0.000 | 1.140 | 10.412 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 293 | 279 | 304 | 178 | 0 | 4885 | 0 | 4426 | 12349 |
N.S. |
1 | 0.95 | 1.04 | 0.61 | 0.00 | 16.67 | 0.00 | 15.11 | 42.15 |
time (sec) |
N/A | 0.544 | 0.510 | 0.179 | 0.000 | 3.281 | 0.000 | 1.378 | 10.668 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 389 | 379 | 382 | 379 | 0 | 7583 | 0 | 5408 | 17591 |
N.S. |
1 | 0.97 | 0.98 | 0.97 | 0.00 | 19.49 | 0.00 | 13.90 | 45.22 |
time (sec) |
N/A | 0.703 | 0.698 | 0.160 | 0.000 | 8.891 | 0.000 | 1.358 | 11.087 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 522 | 518 | 487 | 484 | 0 | 10190 | 0 | 6327 | 21554 |
N.S. |
1 | 0.99 | 0.93 | 0.93 | 0.00 | 19.52 | 0.00 | 12.12 | 41.29 |
time (sec) |
N/A | 0.916 | 0.795 | 0.187 | 0.000 | 21.405 | 0.000 | 1.489 | 11.357 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 365 | 391 | 435 | 624 | 0 | 3196 | 0 | 598 | 4501 |
N.S. |
1 | 1.07 | 1.19 | 1.71 | 0.00 | 8.76 | 0.00 | 1.64 | 12.33 |
time (sec) |
N/A | 1.087 | 0.428 | 0.311 | 0.000 | 0.535 | 0.000 | 1.418 | 10.379 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 254 | 297 | 354 | 495 | 0 | 2167 | 0 | 466 | 3062 |
N.S. |
1 | 1.17 | 1.39 | 1.95 | 0.00 | 8.53 | 0.00 | 1.83 | 12.06 |
time (sec) |
N/A | 0.574 | 0.301 | 0.228 | 0.000 | 0.395 | 0.000 | 1.525 | 10.737 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 146 | 154 | 261 | 343 | 0 | 1378 | 0 | 318 | 593 |
N.S. |
1 | 1.05 | 1.79 | 2.35 | 0.00 | 9.44 | 0.00 | 2.18 | 4.06 |
time (sec) |
N/A | 0.316 | 0.200 | 0.146 | 0.000 | 0.304 | 0.000 | 1.453 | 7.846 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 185 | 203 | 233 | 303 | 0 | 1369 | 0 | 268 | 625 |
N.S. |
1 | 1.10 | 1.26 | 1.64 | 0.00 | 7.40 | 0.00 | 1.45 | 3.38 |
time (sec) |
N/A | 0.408 | 0.165 | 0.150 | 0.000 | 0.334 | 0.000 | 1.416 | 7.852 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 170 | 172 | 172 | 273 | 0 | 1226 | 0 | 228 | 587 |
N.S. |
1 | 1.01 | 1.01 | 1.61 | 0.00 | 7.21 | 0.00 | 1.34 | 3.45 |
time (sec) |
N/A | 0.328 | 0.148 | 0.149 | 0.000 | 0.314 | 0.000 | 1.548 | 7.818 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 139 | 148 | 142 | 147 | 0 | 1109 | 661 | 208 | 517 |
N.S. |
1 | 1.06 | 1.02 | 1.06 | 0.00 | 7.98 | 4.76 | 1.50 | 3.72 |
time (sec) |
N/A | 0.294 | 0.089 | 0.138 | 0.000 | 0.296 | 165.164 | 1.445 | 7.741 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 252 | 306 | 396 | 442 | 0 | 2494 | 0 | 421 | 11674 |
N.S. |
1 | 1.21 | 1.57 | 1.75 | 0.00 | 9.90 | 0.00 | 1.67 | 46.33 |
time (sec) |
N/A | 0.635 | 0.417 | 0.187 | 0.000 | 1.950 | 0.000 | 1.510 | 14.337 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 363 | 405 | 642 | 616 | 0 | 3956 | 0 | 648 | 16265 |
N.S. |
1 | 1.12 | 1.77 | 1.70 | 0.00 | 10.90 | 0.00 | 1.79 | 44.81 |
time (sec) |
N/A | 0.837 | 0.903 | 0.282 | 0.000 | 3.981 | 0.000 | 1.427 | 18.347 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 554 | 544 | 644 | 445 | 0 | 9636 | 0 | 3987 | 22911 |
N.S. |
1 | 0.98 | 1.16 | 0.80 | 0.00 | 17.39 | 0.00 | 7.20 | 41.36 |
time (sec) |
N/A | 1.052 | 1.520 | 0.169 | 0.000 | 18.804 | 0.000 | 2.019 | 10.325 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 461 | 458 | 543 | 375 | 0 | 7060 | 0 | 7578 | 19041 |
N.S. |
1 | 0.99 | 1.18 | 0.81 | 0.00 | 15.31 | 0.00 | 16.44 | 41.30 |
time (sec) |
N/A | 0.817 | 1.269 | 0.155 | 0.000 | 6.011 | 0.000 | 2.353 | 9.742 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 380 | 386 | 447 | 328 | 0 | 5650 | 0 | 3164 | 16688 |
N.S. |
1 | 1.02 | 1.18 | 0.86 | 0.00 | 14.87 | 0.00 | 8.33 | 43.92 |
time (sec) |
N/A | 0.710 | 1.080 | 0.160 | 0.000 | 4.207 | 0.000 | 1.745 | 9.432 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 438 | 403 | 436 | 374 | 0 | 7270 | 0 | 7267 | 18992 |
N.S. |
1 | 0.92 | 1.00 | 0.85 | 0.00 | 16.60 | 0.00 | 16.59 | 43.36 |
time (sec) |
N/A | 0.809 | 1.013 | 0.147 | 0.000 | 8.330 | 0.000 | 2.183 | 9.694 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 460 | 464 | 516 | 447 | 0 | 9909 | 0 | 4605 | 22914 |
N.S. |
1 | 1.01 | 1.12 | 0.97 | 0.00 | 21.54 | 0.00 | 10.01 | 49.81 |
time (sec) |
N/A | 0.872 | 1.297 | 0.389 | 0.000 | 21.044 | 0.000 | 1.787 | 10.184 |
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 | 25 | 23 | 25 | 18 | 17 | 17 | 17 | 19 | 17 |
N.S. |
1 | 0.92 | 1.00 | 0.72 | 0.68 | 0.68 | 0.68 | 0.76 | 0.68 |
time (sec) |
N/A | 0.190 | 0.008 | 0.042 | 0.196 | 0.256 | 0.052 | 0.273 | 0.033 |
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 | 25 | 23 | 25 | 18 | 25 | 17 | 17 | 19 | 17 |
N.S. |
1 | 0.92 | 1.00 | 0.72 | 1.00 | 0.68 | 0.68 | 0.76 | 0.68 |
time (sec) |
N/A | 0.213 | 0.004 | 0.035 | 0.184 | 0.254 | 0.049 | 0.277 | 0.017 |
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 | 37 | 38 | 37 | 31 | 30 | 30 | 37 | 30 | 32 |
N.S. |
1 | 1.03 | 1.00 | 0.84 | 0.81 | 0.81 | 1.00 | 0.81 | 0.86 |
time (sec) |
N/A | 0.200 | 0.010 | 0.047 | 0.271 | 0.262 | 0.056 | 0.263 | 7.558 |
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 | 37 | 38 | 37 | 31 | 53 | 30 | 37 | 30 | 32 |
N.S. |
1 | 1.03 | 1.00 | 0.84 | 1.43 | 0.81 | 1.00 | 0.81 | 0.86 |
time (sec) |
N/A | 0.217 | 0.005 | 0.034 | 0.264 | 0.257 | 0.051 | 0.261 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 54 | 45 | 38 | 0 | 47 | 44 | 38 | 41 |
N.S. |
1 | 1.20 | 1.00 | 0.84 | 0.00 | 1.04 | 0.98 | 0.84 | 0.91 |
time (sec) |
N/A | 0.219 | 0.023 | 0.053 | 0.000 | 0.255 | 0.062 | 0.409 | 0.031 |
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 | 116 | 69 | 58 | 104 | 61 | 105 | 102 | 102 |
N.S. |
1 | 1.14 | 0.68 | 0.57 | 1.02 | 0.60 | 1.03 | 1.00 | 1.00 |
time (sec) |
N/A | 0.265 | 0.107 | 0.334 | 0.201 | 0.252 | 0.776 | 0.307 | 0.272 |
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 | 81 | 90 | 64 | 53 | 87 | 56 | 94 | 88 | 85 |
N.S. |
1 | 1.11 | 0.79 | 0.65 | 1.07 | 0.69 | 1.16 | 1.09 | 1.05 |
time (sec) |
N/A | 0.231 | 0.083 | 0.203 | 0.186 | 0.254 | 0.735 | 0.287 | 7.680 |
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 | 74 | 79 | 59 | 48 | 70 | 51 | 80 | 74 | 67 |
N.S. |
1 | 1.07 | 0.80 | 0.65 | 0.95 | 0.69 | 1.08 | 1.00 | 0.91 |
time (sec) |
N/A | 0.213 | 0.081 | 0.179 | 0.189 | 0.263 | 0.703 | 0.271 | 7.666 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 94 | 99 | 88 | 83 | 89 | 95 | 0 | 98 | 86 |
N.S. |
1 | 1.05 | 0.94 | 0.88 | 0.95 | 1.01 | 0.00 | 1.04 | 0.91 |
time (sec) |
N/A | 0.269 | 0.132 | 0.521 | 0.276 | 0.272 | 0.000 | 0.294 | 0.245 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 102 | 91 | 83 | 89 | 112 | 0 | 138 | 84 |
N.S. |
1 | 1.05 | 0.94 | 0.86 | 0.92 | 1.15 | 0.00 | 1.42 | 0.87 |
time (sec) |
N/A | 0.286 | 0.153 | 0.503 | 0.268 | 0.268 | 0.000 | 0.305 | 8.006 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 99 | 104 | 91 | 86 | 106 | 112 | 0 | 169 | 0 |
N.S. |
1 | 1.05 | 0.92 | 0.87 | 1.07 | 1.13 | 0.00 | 1.71 | 0.00 |
time (sec) |
N/A | 0.283 | 0.182 | 0.480 | 0.268 | 0.260 | 0.000 | 0.322 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 90 | 99 | 70 | 66 | 99 | 90 | 0 | 189 | 0 |
N.S. |
1 | 1.10 | 0.78 | 0.73 | 1.10 | 1.00 | 0.00 | 2.10 | 0.00 |
time (sec) |
N/A | 0.242 | 0.219 | 0.409 | 0.273 | 0.249 | 0.000 | 0.309 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 111 | 125 | 80 | 71 | 116 | 95 | 0 | 233 | 0 |
N.S. |
1 | 1.13 | 0.72 | 0.64 | 1.05 | 0.86 | 0.00 | 2.10 | 0.00 |
time (sec) |
N/A | 0.275 | 0.245 | 0.398 | 0.276 | 0.266 | 0.000 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 132 | 151 | 80 | 76 | 133 | 100 | 0 | 255 | 0 |
N.S. |
1 | 1.14 | 0.61 | 0.58 | 1.01 | 0.76 | 0.00 | 1.93 | 0.00 |
time (sec) |
N/A | 0.305 | 0.307 | 0.435 | 0.283 | 0.260 | 0.000 | 0.314 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 322 | 344 | 237 | 226 | 0 | 139 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.74 | 0.70 | 0.00 | 0.43 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.494 | 6.063 | 5.582 | 0.000 | 0.085 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 305 | 316 | 234 | 221 | 0 | 134 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.77 | 0.72 | 0.00 | 0.44 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.398 | 5.090 | 1.998 | 0.000 | 0.097 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 279 | 292 | 229 | 216 | 0 | 129 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.82 | 0.77 | 0.00 | 0.46 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.347 | 5.058 | 1.745 | 0.000 | 0.093 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 284 | 287 | 231 | 225 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.81 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.349 | 4.815 | 1.407 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 305 | 320 | 237 | 228 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.78 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.406 | 9.679 | 2.151 | 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 | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 146 | 79 | 68 | 135 | 71 | 218 | 207 | 0 |
N.S. |
1 | 1.15 | 0.62 | 0.54 | 1.06 | 0.56 | 1.72 | 1.63 | 0.00 |
time (sec) |
N/A | 0.289 | 0.184 | 0.237 | 0.194 | 0.267 | 1.206 | 0.298 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 106 | 120 | 74 | 63 | 118 | 66 | 190 | 179 | 0 |
N.S. |
1 | 1.13 | 0.70 | 0.59 | 1.11 | 0.62 | 1.79 | 1.69 | 0.00 |
time (sec) |
N/A | 0.268 | 0.143 | 0.214 | 0.191 | 0.267 | 1.160 | 0.324 | 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 | 99 | 113 | 69 | 58 | 101 | 61 | 165 | 151 | 127 |
N.S. |
1 | 1.14 | 0.70 | 0.59 | 1.02 | 0.62 | 1.67 | 1.53 | 1.28 |
time (sec) |
N/A | 0.247 | 0.132 | 0.192 | 0.182 | 0.275 | 1.100 | 0.293 | 7.785 |
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 | 119 | 131 | 99 | 87 | 120 | 106 | 0 | 113 | 0 |
N.S. |
1 | 1.10 | 0.83 | 0.73 | 1.01 | 0.89 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 0.321 | 0.201 | 0.475 | 0.276 | 0.270 | 0.000 | 0.303 | 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 | 122 | 132 | 102 | 96 | 120 | 122 | 0 | 153 | 0 |
N.S. |
1 | 1.08 | 0.84 | 0.79 | 0.98 | 1.00 | 0.00 | 1.25 | 0.00 |
time (sec) |
N/A | 0.322 | 0.227 | 0.527 | 0.264 | 0.292 | 0.000 | 0.313 | 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 | 127 | 135 | 101 | 96 | 137 | 122 | 0 | 190 | 0 |
N.S. |
1 | 1.06 | 0.80 | 0.76 | 1.08 | 0.96 | 0.00 | 1.50 | 0.00 |
time (sec) |
N/A | 0.324 | 0.255 | 0.532 | 0.286 | 0.280 | 0.000 | 0.309 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 135 | 101 | 96 | 154 | 122 | 0 | 227 | 0 |
N.S. |
1 | 1.06 | 0.80 | 0.76 | 1.21 | 0.96 | 0.00 | 1.79 | 0.00 |
time (sec) |
N/A | 0.321 | 0.344 | 0.548 | 0.275 | 0.268 | 0.000 | 0.319 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 356 | 375 | 249 | 236 | 0 | 149 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.70 | 0.66 | 0.00 | 0.42 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.513 | 9.168 | 4.206 | 0.000 | 0.083 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 331 | 351 | 244 | 231 | 0 | 144 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.74 | 0.70 | 0.00 | 0.44 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.454 | 7.622 | 2.783 | 0.000 | 0.085 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 308 | 314 | 239 | 226 | 0 | 139 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.78 | 0.73 | 0.00 | 0.45 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.395 | 6.662 | 1.405 | 0.000 | 0.104 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 312 | 325 | 235 | 233 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.75 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.410 | 6.508 | 1.456 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 314 | 325 | 247 | 238 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.79 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.407 | 10.248 | 2.127 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 331 | 353 | 244 | 238 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.74 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.462 | 10.270 | 4.088 | 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(-2) | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 153 | 165 | 135 | 125 | 0 | 315 | 325 | 136 | 0 |
N.S. |
1 | 1.08 | 0.88 | 0.82 | 0.00 | 2.06 | 2.12 | 0.89 | 0.00 |
time (sec) |
N/A | 0.350 | 0.524 | 0.186 | 0.000 | 0.273 | 1.052 | 0.334 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 104 | 104 | 88 | 0 | 233 | 233 | 96 | 0 |
N.S. |
1 | 1.04 | 1.04 | 0.88 | 0.00 | 2.33 | 2.33 | 0.96 | 0.00 |
time (sec) |
N/A | 0.247 | 0.329 | 0.121 | 0.000 | 0.274 | 0.920 | 0.309 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 76 | 77 | 77 | 65 | 0 | 178 | 165 | 67 | 92 |
N.S. |
1 | 1.01 | 1.01 | 0.86 | 0.00 | 2.34 | 2.17 | 0.88 | 1.21 |
time (sec) |
N/A | 0.215 | 0.290 | 0.087 | 0.000 | 0.264 | 0.834 | 0.294 | 8.168 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 90 | 89 | 85 | 76 | 0 | 517 | 0 | 0 | 81 |
N.S. |
1 | 0.99 | 0.94 | 0.84 | 0.00 | 5.74 | 0.00 | 0.00 | 0.90 |
time (sec) |
N/A | 0.265 | 0.245 | 0.097 | 0.000 | 0.319 | 0.000 | 0.000 | 8.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 82 | 81 | 71 | 0 | 197 | 0 | 124 | 103 |
N.S. |
1 | 1.02 | 1.01 | 0.89 | 0.00 | 2.46 | 0.00 | 1.55 | 1.29 |
time (sec) |
N/A | 0.234 | 0.334 | 0.123 | 0.000 | 0.305 | 0.000 | 0.300 | 8.149 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 134 | 145 | 98 | 0 | 255 | 0 | 339 | 0 |
N.S. |
1 | 1.08 | 1.17 | 0.79 | 0.00 | 2.06 | 0.00 | 2.73 | 0.00 |
time (sec) |
N/A | 0.311 | 0.572 | 0.135 | 0.000 | 0.348 | 0.000 | 0.306 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 177 | 195 | 186 | 138 | 0 | 339 | 0 | 571 | 0 |
N.S. |
1 | 1.10 | 1.05 | 0.78 | 0.00 | 1.92 | 0.00 | 3.23 | 0.00 |
time (sec) |
N/A | 0.416 | 0.808 | 0.163 | 0.000 | 0.407 | 0.000 | 0.310 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 403 | 400 | 532 | 448 | 0 | 431 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 1.32 | 1.11 | 0.00 | 1.07 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.562 | 11.508 | 5.782 | 0.000 | 0.094 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 336 | 333 | 479 | 395 | 0 | 346 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 1.43 | 1.18 | 0.00 | 1.03 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.411 | 11.006 | 2.403 | 0.000 | 0.097 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 283 | 285 | 302 | 362 | 0 | 300 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.07 | 1.28 | 0.00 | 1.06 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.332 | 10.184 | 0.987 | 0.000 | 0.097 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 312 | 316 | 448 | 385 | 0 | 294 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.44 | 1.23 | 0.00 | 0.94 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.396 | 10.707 | 1.938 | 0.000 | 0.086 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 376 | 374 | 373 | 418 | 0 | 347 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.99 | 1.11 | 0.00 | 0.92 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.511 | 10.467 | 3.381 | 0.000 | 0.094 | 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 | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 112 | 64 | 53 | 90 | 56 | 65 | 60 | 0 |
N.S. |
1 | 1.14 | 0.65 | 0.54 | 0.92 | 0.57 | 0.66 | 0.61 | 0.00 |
time (sec) |
N/A | 0.271 | 0.115 | 0.206 | 0.184 | 0.248 | 0.912 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 83 | 59 | 48 | 73 | 51 | 54 | 53 | 0 |
N.S. |
1 | 1.08 | 0.77 | 0.62 | 0.95 | 0.66 | 0.70 | 0.69 | 0.00 |
time (sec) |
N/A | 0.234 | 0.102 | 0.195 | 0.239 | 0.241 | 0.871 | 0.270 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 60 | 54 | 43 | 56 | 46 | 51 | 46 | 0 |
N.S. |
1 | 1.07 | 0.96 | 0.77 | 1.00 | 0.82 | 0.91 | 0.82 | 0.00 |
time (sec) |
N/A | 0.200 | 0.097 | 0.181 | 0.193 | 0.240 | 0.816 | 0.273 | 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 | 49 | 51 | 47 | 36 | 39 | 39 | 42 | 39 | 35 |
N.S. |
1 | 1.04 | 0.96 | 0.73 | 0.80 | 0.80 | 0.86 | 0.80 | 0.71 |
time (sec) |
N/A | 0.192 | 0.091 | 0.165 | 0.192 | 0.252 | 0.796 | 0.275 | 8.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 69 | 71 | 63 | 52 | 58 | 75 | 0 | 78 | 56 |
N.S. |
1 | 1.03 | 0.91 | 0.75 | 0.84 | 1.09 | 0.00 | 1.13 | 0.81 |
time (sec) |
N/A | 0.235 | 0.121 | 0.448 | 0.270 | 0.264 | 0.000 | 0.283 | 8.203 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 62 | 66 | 58 | 49 | 51 | 78 | 0 | 101 | 83 |
N.S. |
1 | 1.06 | 0.94 | 0.79 | 0.82 | 1.26 | 0.00 | 1.63 | 1.34 |
time (sec) |
N/A | 0.206 | 0.141 | 0.332 | 0.273 | 0.257 | 0.000 | 0.292 | 0.277 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 83 | 90 | 63 | 64 | 68 | 83 | 0 | 145 | 0 |
N.S. |
1 | 1.08 | 0.76 | 0.77 | 0.82 | 1.00 | 0.00 | 1.75 | 0.00 |
time (sec) |
N/A | 0.242 | 0.177 | 0.355 | 0.273 | 0.269 | 0.000 | 0.294 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 116 | 75 | 66 | 85 | 90 | 0 | 167 | 0 |
N.S. |
1 | 1.12 | 0.72 | 0.63 | 0.82 | 0.87 | 0.00 | 1.61 | 0.00 |
time (sec) |
N/A | 0.274 | 0.240 | 0.375 | 0.283 | 0.264 | 0.000 | 0.301 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 298 | 309 | 229 | 216 | 0 | 129 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.77 | 0.72 | 0.00 | 0.43 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.390 | 10.226 | 3.891 | 0.000 | 0.099 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 270 | 277 | 222 | 208 | 0 | 122 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.82 | 0.77 | 0.00 | 0.45 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.341 | 10.228 | 2.597 | 0.000 | 0.093 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 257 | 260 | 159 | 194 | 0 | 117 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.62 | 0.75 | 0.00 | 0.46 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.306 | 10.125 | 0.840 | 0.000 | 0.086 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 278 | 287 | 224 | 211 | 0 | 124 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.81 | 0.76 | 0.00 | 0.45 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.356 | 10.233 | 1.400 | 0.000 | 0.082 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 302 | 311 | 237 | 228 | 0 | 140 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.78 | 0.75 | 0.00 | 0.46 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.397 | 10.241 | 2.114 | 0.000 | 0.081 | 0.000 | 0.000 | 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 | 77 | 84 | 59 | 48 | 73 | 86 | 0 | 52 | 0 |
N.S. |
1 | 1.09 | 0.77 | 0.62 | 0.95 | 1.12 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.232 | 0.179 | 0.216 | 0.196 | 0.246 | 0.000 | 0.273 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 58 | 54 | 43 | 56 | 81 | 0 | 46 | 52 |
N.S. |
1 | 1.04 | 0.96 | 0.77 | 1.00 | 1.45 | 0.00 | 0.82 | 0.93 |
time (sec) |
N/A | 0.206 | 0.144 | 0.199 | 0.197 | 0.259 | 0.000 | 0.292 | 7.849 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 22 | 32 | 46 | 0 | 21 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 1.28 | 1.84 | 0.00 | 0.84 | 0.84 |
time (sec) |
N/A | 0.166 | 0.144 | 0.065 | 0.185 | 0.260 | 0.000 | 0.292 | 7.578 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 66 | 70 | 62 | 53 | 65 | 107 | 0 | 78 | 0 |
N.S. |
1 | 1.06 | 0.94 | 0.80 | 0.98 | 1.62 | 0.00 | 1.18 | 0.00 |
time (sec) |
N/A | 0.212 | 0.206 | 0.339 | 0.277 | 0.266 | 0.000 | 0.295 | 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 | 90 | 97 | 70 | 61 | 82 | 124 | 0 | 122 | 0 |
N.S. |
1 | 1.08 | 0.78 | 0.68 | 0.91 | 1.38 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 0.252 | 0.229 | 0.370 | 0.286 | 0.247 | 0.000 | 0.311 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 307 | 318 | 219 | 216 | 0 | 184 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.71 | 0.70 | 0.00 | 0.60 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.404 | 10.230 | 4.031 | 0.000 | 0.082 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 286 | 292 | 219 | 216 | 0 | 179 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.77 | 0.76 | 0.00 | 0.63 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.374 | 10.251 | 2.625 | 0.000 | 0.080 | 0.000 | 0.000 | 0.000 |