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 | 54 | 54 | 37 | 37 | 74 | 74 | 80 | 36 | 77 |
N.S. |
1 | 1.00 | 0.69 | 0.69 | 1.37 | 1.37 | 1.48 | 0.67 | 1.43 |
time (sec) |
N/A | 0.215 | 0.013 | 2.448 | 0.182 | 0.279 | 0.240 | 0.275 | 9.851 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 19 | 52 | 52 | 58 | 18 | 54 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 2.60 | 2.60 | 2.90 | 0.90 | 2.70 |
time (sec) |
N/A | 0.161 | 0.002 | 2.499 | 0.184 | 0.250 | 0.173 | 0.279 | 9.877 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 139 | 139 | 117 | 135 | 412 | 484 | 668 | 273 | 372 |
N.S. |
1 | 1.00 | 0.84 | 0.97 | 2.96 | 3.48 | 4.81 | 1.96 | 2.68 |
time (sec) |
N/A | 0.316 | 0.061 | 3.071 | 0.196 | 0.275 | 1.122 | 0.278 | 10.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 173 | 173 | 157 | 173 | 656 | 837 | 1006 | 386 | 617 |
N.S. |
1 | 1.00 | 0.91 | 1.00 | 3.79 | 4.84 | 5.82 | 2.23 | 3.57 |
time (sec) |
N/A | 0.377 | 0.091 | 2.457 | 0.204 | 0.276 | 2.793 | 0.281 | 10.260 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 226 | 226 | 206 | 221 | 956 | 1242 | 1363 | 503 | 891 |
N.S. |
1 | 1.00 | 0.91 | 0.98 | 4.23 | 5.50 | 6.03 | 2.23 | 3.94 |
time (sec) |
N/A | 0.444 | 0.114 | 2.538 | 0.229 | 0.313 | 13.432 | 0.284 | 10.389 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 262 | 281 | 234 | 253 | 1278 | 1618 | 1748 | 635 | 0 |
N.S. |
1 | 1.07 | 0.89 | 0.97 | 4.88 | 6.18 | 6.67 | 2.42 | 0.00 |
time (sec) |
N/A | 0.596 | 0.153 | 2.688 | 0.218 | 0.308 | 28.798 | 0.278 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 388 | 418 | 344 | 2775 | 0 | 1040 | 2686 | 507 | 0 |
N.S. |
1 | 1.08 | 0.89 | 7.15 | 0.00 | 2.68 | 6.92 | 1.31 | 0.00 |
time (sec) |
N/A | 0.624 | 1.000 | 3.184 | 0.000 | 0.390 | 1.250 | 0.391 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 328 | 351 | 278 | 1543 | 0 | 844 | 1646 | 400 | 0 |
N.S. |
1 | 1.07 | 0.85 | 4.70 | 0.00 | 2.57 | 5.02 | 1.22 | 0.00 |
time (sec) |
N/A | 0.512 | 0.591 | 2.686 | 0.000 | 0.459 | 0.990 | 0.342 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 268 | 284 | 223 | 816 | 0 | 672 | 989 | 305 | 0 |
N.S. |
1 | 1.06 | 0.83 | 3.04 | 0.00 | 2.51 | 3.69 | 1.14 | 0.00 |
time (sec) |
N/A | 0.398 | 0.428 | 2.542 | 0.000 | 0.386 | 0.877 | 0.327 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 210 | 219 | 179 | 373 | 0 | 532 | 571 | 222 | 307 |
N.S. |
1 | 1.04 | 0.85 | 1.78 | 0.00 | 2.53 | 2.72 | 1.06 | 1.46 |
time (sec) |
N/A | 0.316 | 0.334 | 2.712 | 0.000 | 0.413 | 0.900 | 0.322 | 10.205 |
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 | 159 | 159 | 144 | 154 | 0 | 412 | 306 | 156 | 131 |
N.S. |
1 | 1.00 | 0.91 | 0.97 | 0.00 | 2.59 | 1.92 | 0.98 | 0.82 |
time (sec) |
N/A | 0.260 | 0.310 | 2.679 | 0.000 | 0.376 | 0.389 | 0.292 | 9.893 |
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 | 131 | 131 | 112 | 131 | 0 | 337 | 0 | 114 | 0 |
N.S. |
1 | 1.00 | 0.85 | 1.00 | 0.00 | 2.57 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.251 | 0.198 | 2.808 | 0.000 | 0.398 | 0.000 | 0.323 | 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 | 124 | 124 | 110 | 212 | 0 | 326 | 0 | 185 | 0 |
N.S. |
1 | 1.00 | 0.89 | 1.71 | 0.00 | 2.63 | 0.00 | 1.49 | 0.00 |
time (sec) |
N/A | 0.250 | 0.149 | 2.687 | 0.000 | 0.393 | 0.000 | 0.315 | 0.000 |
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 | 54 | 54 | 43 | 58 | 0 | 90 | 0 | 0 | 58 |
N.S. |
1 | 1.00 | 0.80 | 1.07 | 0.00 | 1.67 | 0.00 | 0.00 | 1.07 |
time (sec) |
N/A | 0.182 | 0.031 | 3.038 | 0.000 | 0.458 | 0.000 | 0.000 | 10.260 |
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 | 111 | 111 | 81 | 90 | 0 | 205 | 0 | 0 | 562 |
N.S. |
1 | 1.00 | 0.73 | 0.81 | 0.00 | 1.85 | 0.00 | 0.00 | 5.06 |
time (sec) |
N/A | 0.255 | 0.198 | 3.280 | 0.000 | 0.841 | 0.000 | 0.000 | 10.572 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 186 | 124 | 146 | 0 | 373 | 0 | 711 | 877 |
N.S. |
1 | 1.09 | 0.73 | 0.85 | 0.00 | 2.18 | 0.00 | 4.16 | 5.13 |
time (sec) |
N/A | 0.328 | 1.385 | 3.239 | 0.000 | 2.513 | 0.000 | 0.329 | 11.307 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 231 | 261 | 180 | 217 | 0 | 572 | 0 | 0 | 1192 |
N.S. |
1 | 1.13 | 0.78 | 0.94 | 0.00 | 2.48 | 0.00 | 0.00 | 5.16 |
time (sec) |
N/A | 0.401 | 10.049 | 4.065 | 0.000 | 5.644 | 0.000 | 0.000 | 11.891 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 461 | 505 | 525 | 3891 | 0 | 1520 | 8100 | 776 | 0 |
N.S. |
1 | 1.10 | 1.14 | 8.44 | 0.00 | 3.30 | 17.57 | 1.68 | 0.00 |
time (sec) |
N/A | 0.676 | 1.265 | 3.203 | 0.000 | 0.356 | 3.931 | 0.350 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 401 | 438 | 437 | 2194 | 0 | 1268 | 4896 | 641 | 0 |
N.S. |
1 | 1.09 | 1.09 | 5.47 | 0.00 | 3.16 | 12.21 | 1.60 | 0.00 |
time (sec) |
N/A | 0.618 | 1.117 | 2.770 | 0.000 | 0.338 | 2.270 | 0.344 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 341 | 371 | 361 | 1188 | 0 | 1042 | 2909 | 519 | 0 |
N.S. |
1 | 1.09 | 1.06 | 3.48 | 0.00 | 3.06 | 8.53 | 1.52 | 0.00 |
time (sec) |
N/A | 0.473 | 0.907 | 2.848 | 0.000 | 0.348 | 1.761 | 0.344 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 283 | 306 | 295 | 559 | 0 | 844 | 1681 | 411 | 646 |
N.S. |
1 | 1.08 | 1.04 | 1.98 | 0.00 | 2.98 | 5.94 | 1.45 | 2.28 |
time (sec) |
N/A | 0.394 | 0.763 | 2.921 | 0.000 | 0.336 | 1.296 | 0.345 | 11.029 |
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 | 232 | 246 | 239 | 247 | 0 | 666 | 1853 | 310 | 225 |
N.S. |
1 | 1.06 | 1.03 | 1.06 | 0.00 | 2.87 | 7.99 | 1.34 | 0.97 |
time (sec) |
N/A | 0.325 | 0.638 | 2.348 | 0.000 | 0.367 | 1.706 | 0.331 | 10.188 |
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 | 201 | 215 | 180 | 230 | 0 | 532 | 751 | 229 | 0 |
N.S. |
1 | 1.07 | 0.90 | 1.14 | 0.00 | 2.65 | 3.74 | 1.14 | 0.00 |
time (sec) |
N/A | 0.318 | 0.409 | 2.520 | 0.000 | 0.278 | 3.283 | 0.342 | 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 | 187 | 194 | 150 | 311 | 0 | 418 | 0 | 471 | 0 |
N.S. |
1 | 1.04 | 0.80 | 1.66 | 0.00 | 2.24 | 0.00 | 2.52 | 0.00 |
time (sec) |
N/A | 0.314 | 0.342 | 2.798 | 0.000 | 0.299 | 0.000 | 0.426 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 175 | 186 | 148 | 392 | 0 | 414 | 0 | 224 | 0 |
N.S. |
1 | 1.06 | 0.85 | 2.24 | 0.00 | 2.37 | 0.00 | 1.28 | 0.00 |
time (sec) |
N/A | 0.344 | 0.378 | 3.119 | 0.000 | 0.340 | 0.000 | 0.341 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 169 | 174 | 130 | 473 | 0 | 426 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.77 | 2.80 | 0.00 | 2.52 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.319 | 0.288 | 2.935 | 0.000 | 0.467 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 43 | 58 | 0 | 130 | 0 | 845 | 901 |
N.S. |
1 | 1.00 | 0.80 | 1.07 | 0.00 | 2.41 | 0.00 | 15.65 | 16.69 |
time (sec) |
N/A | 0.180 | 0.051 | 3.261 | 0.000 | 0.820 | 0.000 | 0.376 | 11.357 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 61 | 90 | 0 | 275 | 0 | 0 | 1477 |
N.S. |
1 | 1.00 | 0.55 | 0.81 | 0.00 | 2.48 | 0.00 | 0.00 | 13.31 |
time (sec) |
N/A | 0.239 | 0.223 | 4.734 | 0.000 | 1.972 | 0.000 | 0.000 | 12.441 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 186 | 94 | 146 | 0 | 472 | 0 | 0 | 2067 |
N.S. |
1 | 1.09 | 0.55 | 0.85 | 0.00 | 2.76 | 0.00 | 0.00 | 12.09 |
time (sec) |
N/A | 0.317 | 0.505 | 4.294 | 0.000 | 6.726 | 0.000 | 0.000 | 13.559 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 231 | 261 | 138 | 217 | 0 | 699 | 0 | 0 | 2657 |
N.S. |
1 | 1.13 | 0.60 | 0.94 | 0.00 | 3.03 | 0.00 | 0.00 | 11.50 |
time (sec) |
N/A | 0.408 | 1.280 | 4.927 | 0.000 | 16.976 | 0.000 | 0.000 | 14.888 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 534 | 592 | 735 | 5007 | 0 | 2114 | 24405 | 1099 | 0 |
N.S. |
1 | 1.11 | 1.38 | 9.38 | 0.00 | 3.96 | 45.70 | 2.06 | 0.00 |
time (sec) |
N/A | 0.767 | 2.252 | 3.127 | 0.000 | 0.696 | 34.885 | 0.407 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 474 | 525 | 625 | 2845 | 0 | 1806 | 14834 | 936 | 0 |
N.S. |
1 | 1.11 | 1.32 | 6.00 | 0.00 | 3.81 | 31.30 | 1.97 | 0.00 |
time (sec) |
N/A | 0.696 | 1.659 | 2.944 | 0.000 | 0.720 | 19.596 | 0.384 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 414 | 458 | 526 | 1560 | 0 | 1520 | 8918 | 786 | 0 |
N.S. |
1 | 1.11 | 1.27 | 3.77 | 0.00 | 3.67 | 21.54 | 1.90 | 0.00 |
time (sec) |
N/A | 0.567 | 1.295 | 2.575 | 0.000 | 0.504 | 8.453 | 0.372 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 356 | 393 | 437 | 745 | 0 | 1270 | 5268 | 650 | 0 |
N.S. |
1 | 1.10 | 1.23 | 2.09 | 0.00 | 3.57 | 14.80 | 1.83 | 0.00 |
time (sec) |
N/A | 0.477 | 1.018 | 2.439 | 0.000 | 0.376 | 6.150 | 0.342 | 0.000 |
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 | 305 | 333 | 361 | 340 | 0 | 1034 | 6698 | 524 | 319 |
N.S. |
1 | 1.09 | 1.18 | 1.11 | 0.00 | 3.39 | 21.96 | 1.72 | 1.05 |
time (sec) |
N/A | 0.413 | 0.858 | 2.592 | 0.000 | 0.343 | 7.956 | 0.355 | 9.949 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 274 | 302 | 295 | 327 | 0 | 844 | 0 | 415 | 0 |
N.S. |
1 | 1.10 | 1.08 | 1.19 | 0.00 | 3.08 | 0.00 | 1.51 | 0.00 |
time (sec) |
N/A | 0.397 | 0.673 | 2.844 | 0.000 | 0.334 | 0.000 | 0.390 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 261 | 279 | 222 | 408 | 0 | 672 | 0 | 1319 | 0 |
N.S. |
1 | 1.07 | 0.85 | 1.56 | 0.00 | 2.57 | 0.00 | 5.05 | 0.00 |
time (sec) |
N/A | 0.413 | 0.486 | 2.604 | 0.000 | 0.344 | 0.000 | 0.704 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 244 | 264 | 183 | 489 | 0 | 534 | 0 | 235 | 0 |
N.S. |
1 | 1.08 | 0.75 | 2.00 | 0.00 | 2.19 | 0.00 | 0.96 | 0.00 |
time (sec) |
N/A | 0.382 | 0.421 | 2.883 | 0.000 | 0.318 | 0.000 | 0.355 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 235 | 257 | 186 | 570 | 0 | 554 | 0 | 302 | 0 |
N.S. |
1 | 1.09 | 0.79 | 2.43 | 0.00 | 2.36 | 0.00 | 1.29 | 0.00 |
time (sec) |
N/A | 0.592 | 0.422 | 3.552 | 0.000 | 0.411 | 0.000 | 0.403 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 226 | 239 | 185 | 651 | 0 | 594 | 0 | 462 | 0 |
N.S. |
1 | 1.06 | 0.82 | 2.88 | 0.00 | 2.63 | 0.00 | 2.04 | 0.00 |
time (sec) |
N/A | 0.412 | 0.385 | 3.394 | 0.000 | 0.535 | 0.000 | 0.521 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 218 | 224 | 173 | 732 | 0 | 578 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.79 | 3.36 | 0.00 | 2.65 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.374 | 0.340 | 4.048 | 0.000 | 1.128 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 43 | 58 | 0 | 170 | 0 | 0 | 2156 |
N.S. |
1 | 1.00 | 0.80 | 1.07 | 0.00 | 3.15 | 0.00 | 0.00 | 39.93 |
time (sec) |
N/A | 0.176 | 0.043 | 5.555 | 0.000 | 2.411 | 0.000 | 0.000 | 13.140 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 61 | 90 | 0 | 344 | 0 | 0 | 3125 |
N.S. |
1 | 1.00 | 0.55 | 0.81 | 0.00 | 3.10 | 0.00 | 0.00 | 28.15 |
time (sec) |
N/A | 0.244 | 0.251 | 5.827 | 0.000 | 8.392 | 0.000 | 0.000 | 14.573 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 186 | 104 | 146 | 0 | 569 | 0 | 0 | 4096 |
N.S. |
1 | 1.09 | 0.61 | 0.85 | 0.00 | 3.33 | 0.00 | 0.00 | 23.95 |
time (sec) |
N/A | 0.324 | 0.646 | 8.393 | 0.000 | 22.486 | 0.000 | 0.000 | 16.924 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 231 | 261 | 148 | 217 | 0 | 823 | 0 | 0 | 5069 |
N.S. |
1 | 1.13 | 0.64 | 0.94 | 0.00 | 3.56 | 0.00 | 0.00 | 21.94 |
time (sec) |
N/A | 0.414 | 1.565 | 10.879 | 0.000 | 46.466 | 0.000 | 0.000 | 19.508 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 255 | 267 | 187 | 888 | 0 | 534 | 782 | 230 | 0 |
N.S. |
1 | 1.05 | 0.73 | 3.48 | 0.00 | 2.09 | 3.07 | 0.90 | 0.00 |
time (sec) |
N/A | 0.408 | 0.299 | 2.719 | 0.000 | 0.352 | 0.944 | 0.368 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 195 | 200 | 155 | 442 | 0 | 418 | 502 | 163 | 0 |
N.S. |
1 | 1.03 | 0.79 | 2.27 | 0.00 | 2.14 | 2.57 | 0.84 | 0.00 |
time (sec) |
N/A | 0.328 | 0.249 | 3.022 | 0.000 | 0.319 | 0.832 | 0.357 | 0.000 |
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 | 134 | 135 | 136 | 186 | 0 | 338 | 335 | 120 | 144 |
N.S. |
1 | 1.01 | 1.01 | 1.39 | 0.00 | 2.52 | 2.50 | 0.90 | 1.07 |
time (sec) |
N/A | 0.250 | 0.184 | 2.401 | 0.000 | 0.280 | 0.722 | 0.343 | 10.369 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 94 | 62 | 0 | 244 | 218 | 156 | 49 |
N.S. |
1 | 1.00 | 1.15 | 0.76 | 0.00 | 2.98 | 2.66 | 1.90 | 0.60 |
time (sec) |
N/A | 0.192 | 0.080 | 2.404 | 0.000 | 0.290 | 0.559 | 0.302 | 9.902 |
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 | 52 | 52 | 42 | 50 | 0 | 59 | 0 | 0 | 50 |
N.S. |
1 | 1.00 | 0.81 | 0.96 | 0.00 | 1.13 | 0.00 | 0.00 | 0.96 |
time (sec) |
N/A | 0.178 | 0.026 | 2.937 | 0.000 | 0.316 | 0.000 | 0.000 | 10.239 |
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 | 111 | 111 | 61 | 81 | 0 | 140 | 0 | 176 | 69 |
N.S. |
1 | 1.00 | 0.55 | 0.73 | 0.00 | 1.26 | 0.00 | 1.59 | 0.62 |
time (sec) |
N/A | 0.240 | 0.081 | 2.775 | 0.000 | 0.460 | 0.000 | 0.324 | 10.244 |
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 | 171 | 186 | 94 | 138 | 0 | 279 | 0 | 0 | 110 |
N.S. |
1 | 1.09 | 0.55 | 0.81 | 0.00 | 1.63 | 0.00 | 0.00 | 0.64 |
time (sec) |
N/A | 0.318 | 0.114 | 2.753 | 0.000 | 1.063 | 0.000 | 0.000 | 10.245 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 231 | 261 | 138 | 209 | 0 | 452 | 0 | 0 | 252 |
N.S. |
1 | 1.13 | 0.60 | 0.90 | 0.00 | 1.96 | 0.00 | 0.00 | 1.09 |
time (sec) |
N/A | 0.409 | 0.195 | 3.104 | 0.000 | 3.467 | 0.000 | 0.000 | 10.386 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 302 | 349 | 234 | 3117 | 0 | 759 | 0 | 0 | 0 |
N.S. |
1 | 1.16 | 0.77 | 10.32 | 0.00 | 2.51 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.929 | 0.493 | 3.652 | 0.000 | 1.309 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 241 | 257 | 180 | 1770 | 0 | 585 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.75 | 7.34 | 0.00 | 2.43 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.543 | 0.366 | 2.900 | 0.000 | 0.694 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 180 | 190 | 143 | 960 | 0 | 447 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.79 | 5.33 | 0.00 | 2.48 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.348 | 0.236 | 2.750 | 0.000 | 0.776 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 125 | 125 | 113 | 485 | 0 | 349 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.90 | 3.88 | 0.00 | 2.79 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.242 | 0.142 | 2.943 | 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 | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 39 | 53 | 0 | 65 | 0 | 0 | 53 |
N.S. |
1 | 1.00 | 0.78 | 1.06 | 0.00 | 1.30 | 0.00 | 0.00 | 1.06 |
time (sec) |
N/A | 0.171 | 0.034 | 2.414 | 0.000 | 0.349 | 0.000 | 0.000 | 10.116 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 49 | 60 | 0 | 153 | 0 | 101 | 75 |
N.S. |
1 | 1.00 | 0.79 | 0.97 | 0.00 | 2.47 | 0.00 | 1.63 | 1.21 |
time (sec) |
N/A | 0.172 | 0.077 | 2.356 | 0.000 | 0.637 | 0.000 | 0.351 | 9.777 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 95 | 138 | 0 | 306 | 0 | 0 | 120 |
N.S. |
1 | 1.00 | 0.79 | 1.14 | 0.00 | 2.53 | 0.00 | 0.00 | 0.99 |
time (sec) |
N/A | 0.230 | 0.126 | 2.866 | 0.000 | 1.337 | 0.000 | 0.000 | 10.003 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 181 | 196 | 136 | 216 | 0 | 494 | 0 | 3930 | 1005 |
N.S. |
1 | 1.08 | 0.75 | 1.19 | 0.00 | 2.73 | 0.00 | 21.71 | 5.55 |
time (sec) |
N/A | 0.310 | 0.151 | 2.835 | 0.000 | 3.696 | 0.000 | 0.447 | 10.824 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 241 | 271 | 193 | 307 | 0 | 733 | 0 | 0 | 2121 |
N.S. |
1 | 1.12 | 0.80 | 1.27 | 0.00 | 3.04 | 0.00 | 0.00 | 8.80 |
time (sec) |
N/A | 0.390 | 0.234 | 2.803 | 0.000 | 9.657 | 0.000 | 0.000 | 11.793 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 301 | 346 | 258 | 389 | 0 | 1004 | 0 | 0 | 3925 |
N.S. |
1 | 1.15 | 0.86 | 1.29 | 0.00 | 3.34 | 0.00 | 0.00 | 13.04 |
time (sec) |
N/A | 0.492 | 0.339 | 3.491 | 0.000 | 30.208 | 0.000 | 0.000 | 13.987 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 294 | 315 | 230 | 7420 | 0 | 833 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.78 | 25.24 | 0.00 | 2.83 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.587 | 0.457 | 3.832 | 0.000 | 1.797 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 231 | 248 | 189 | 4447 | 0 | 641 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.82 | 19.25 | 0.00 | 2.77 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.398 | 0.384 | 3.639 | 0.000 | 1.011 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 172 | 180 | 137 | 2599 | 0 | 469 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.80 | 15.11 | 0.00 | 2.73 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.312 | 0.233 | 3.371 | 0.000 | 0.958 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 46 | 58 | 0 | 103 | 0 | 0 | 58 |
N.S. |
1 | 1.00 | 0.85 | 1.07 | 0.00 | 1.91 | 0.00 | 0.00 | 1.07 |
time (sec) |
N/A | 0.177 | 0.034 | 3.511 | 0.000 | 0.796 | 0.000 | 0.000 | 10.814 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 116 | 116 | 59 | 85 | 0 | 156 | 0 | 0 | 72 |
N.S. |
1 | 1.00 | 0.51 | 0.73 | 0.00 | 1.34 | 0.00 | 0.00 | 0.62 |
time (sec) |
N/A | 0.224 | 0.080 | 2.872 | 0.000 | 1.114 | 0.000 | 0.000 | 10.171 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 90 | 146 | 0 | 316 | 0 | 0 | 120 |
N.S. |
1 | 1.00 | 0.76 | 1.24 | 0.00 | 2.68 | 0.00 | 0.00 | 1.02 |
time (sec) |
N/A | 0.233 | 0.119 | 2.741 | 0.000 | 2.033 | 0.000 | 0.000 | 10.386 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 132 | 132 | 132 | 153 | 0 | 491 | 0 | 366 | 131 |
N.S. |
1 | 1.00 | 1.00 | 1.16 | 0.00 | 3.72 | 0.00 | 2.77 | 0.99 |
time (sec) |
N/A | 0.230 | 0.157 | 2.868 | 0.000 | 5.769 | 0.000 | 0.341 | 9.803 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 192 | 207 | 193 | 242 | 0 | 769 | 0 | 0 | 253 |
N.S. |
1 | 1.08 | 1.01 | 1.26 | 0.00 | 4.01 | 0.00 | 0.00 | 1.32 |
time (sec) |
N/A | 0.305 | 0.225 | 3.111 | 0.000 | 19.207 | 0.000 | 0.000 | 10.953 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 252 | 282 | 259 | 323 | 0 | 1058 | 0 | 10592 | 3654 |
N.S. |
1 | 1.12 | 1.03 | 1.28 | 0.00 | 4.20 | 0.00 | 42.03 | 14.50 |
time (sec) |
N/A | 0.370 | 0.305 | 3.030 | 0.000 | 41.941 | 0.000 | 0.641 | 12.444 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 312 | 357 | 336 | 404 | 0 | 1392 | 0 | 0 | 10949 |
N.S. |
1 | 1.14 | 1.08 | 1.29 | 0.00 | 4.46 | 0.00 | 0.00 | 35.09 |
time (sec) |
N/A | 0.467 | 0.416 | 3.096 | 0.000 | 83.185 | 0.000 | 0.000 | 15.629 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1485 | 1719 | 88 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.16 | 0.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.279 | 0.048 | 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 | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1432 | 1661 | 95 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.16 | 0.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.011 | 0.030 | 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 | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 34 | 32 | 38 | 98 | 53 | 313 | 34 |
N.S. |
1 | 1.00 | 0.79 | 0.74 | 0.88 | 2.28 | 1.23 | 7.28 | 0.79 |
time (sec) |
N/A | 0.190 | 0.038 | 2.457 | 0.188 | 0.356 | 0.880 | 0.281 | 9.638 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 34 | 32 | 38 | 74 | 53 | 198 | 34 |
N.S. |
1 | 1.00 | 0.79 | 0.74 | 0.88 | 1.72 | 1.23 | 4.60 | 0.79 |
time (sec) |
N/A | 0.186 | 0.034 | 2.567 | 0.187 | 0.345 | 0.836 | 0.280 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 34 | 32 | 90 | 51 | 104 | 105 | 34 |
N.S. |
1 | 1.00 | 0.79 | 0.74 | 2.09 | 1.19 | 2.42 | 2.44 | 0.79 |
time (sec) |
N/A | 0.184 | 0.032 | 2.740 | 0.189 | 0.409 | 0.646 | 0.273 | 0.047 |
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 | 41 | 41 | 33 | 31 | 37 | 30 | 51 | 41 | 33 |
N.S. |
1 | 1.00 | 0.80 | 0.76 | 0.90 | 0.73 | 1.24 | 1.00 | 0.80 |
time (sec) |
N/A | 0.180 | 0.032 | 2.729 | 0.191 | 0.431 | 0.834 | 0.276 | 9.639 |
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 | 39 | 39 | 31 | 31 | 42 | 40 | 58 | 39 | 30 |
N.S. |
1 | 1.00 | 0.79 | 0.79 | 1.08 | 1.03 | 1.49 | 1.00 | 0.77 |
time (sec) |
N/A | 0.181 | 0.031 | 2.556 | 0.184 | 0.382 | 0.270 | 0.273 | 0.056 |
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 | 41 | 41 | 33 | 31 | 33 | 51 | 126 | 33 | 34 |
N.S. |
1 | 1.00 | 0.80 | 0.76 | 0.80 | 1.24 | 3.07 | 0.80 | 0.83 |
time (sec) |
N/A | 0.180 | 0.033 | 2.468 | 0.183 | 0.401 | 0.465 | 0.275 | 9.679 |
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 | 43 | 43 | 34 | 32 | 34 | 63 | 187 | 34 | 34 |
N.S. |
1 | 1.00 | 0.79 | 0.74 | 0.79 | 1.47 | 4.35 | 0.79 | 0.79 |
time (sec) |
N/A | 0.185 | 0.036 | 2.530 | 0.200 | 0.455 | 0.680 | 0.287 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 34 | 32 | 34 | 74 | 248 | 34 | 31 |
N.S. |
1 | 1.00 | 0.79 | 0.74 | 0.79 | 1.72 | 5.77 | 0.79 | 0.72 |
time (sec) |
N/A | 0.177 | 0.035 | 2.626 | 0.200 | 0.346 | 1.011 | 0.271 | 9.764 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 67 | 65 | 80 | 184 | 110 | 566 | 80 |
N.S. |
1 | 1.00 | 0.81 | 0.78 | 0.96 | 2.22 | 1.33 | 6.82 | 0.96 |
time (sec) |
N/A | 0.229 | 0.054 | 3.271 | 0.186 | 0.289 | 0.932 | 0.277 | 9.865 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 67 | 65 | 280 | 147 | 110 | 368 | 80 |
N.S. |
1 | 1.00 | 0.81 | 0.78 | 3.37 | 1.77 | 1.33 | 4.43 | 0.96 |
time (sec) |
N/A | 0.229 | 0.047 | 2.752 | 0.190 | 0.295 | 0.912 | 0.296 | 0.062 |
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 | 83 | 83 | 67 | 65 | 80 | 109 | 110 | 208 | 80 |
N.S. |
1 | 1.00 | 0.81 | 0.78 | 0.96 | 1.31 | 1.33 | 2.51 | 0.96 |
time (sec) |
N/A | 0.220 | 0.043 | 2.821 | 0.178 | 0.302 | 0.933 | 0.273 | 9.710 |
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 | 81 | 66 | 65 | 80 | 74 | 109 | 86 | 80 |
N.S. |
1 | 1.00 | 0.81 | 0.80 | 0.99 | 0.91 | 1.35 | 1.06 | 0.99 |
time (sec) |
N/A | 0.220 | 0.043 | 3.025 | 0.186 | 0.361 | 0.941 | 0.279 | 0.059 |
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 | 79 | 79 | 65 | 65 | 87 | 83 | 133 | 94 | 80 |
N.S. |
1 | 1.00 | 0.82 | 0.82 | 1.10 | 1.05 | 1.68 | 1.19 | 1.01 |
time (sec) |
N/A | 0.218 | 0.049 | 3.063 | 0.184 | 0.268 | 0.468 | 0.272 | 9.756 |
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 | 79 | 79 | 68 | 62 | 84 | 95 | 264 | 84 | 80 |
N.S. |
1 | 1.00 | 0.86 | 0.78 | 1.06 | 1.20 | 3.34 | 1.06 | 1.01 |
time (sec) |
N/A | 0.218 | 0.050 | 2.751 | 0.198 | 0.279 | 0.737 | 0.278 | 9.787 |
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 | 81 | 81 | 67 | 65 | 77 | 105 | 388 | 80 | 78 |
N.S. |
1 | 1.00 | 0.83 | 0.80 | 0.95 | 1.30 | 4.79 | 0.99 | 0.96 |
time (sec) |
N/A | 0.219 | 0.054 | 2.711 | 0.179 | 0.372 | 1.053 | 0.271 | 0.079 |
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 | 83 | 83 | 67 | 65 | 77 | 117 | 510 | 80 | 78 |
N.S. |
1 | 1.00 | 0.81 | 0.78 | 0.93 | 1.41 | 6.14 | 0.96 | 0.94 |
time (sec) |
N/A | 0.217 | 0.048 | 2.985 | 0.189 | 0.361 | 1.532 | 0.269 | 9.657 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 119 | 111 | 97 | 137 | 335 | 178 | 1214 | 106 |
N.S. |
1 | 1.00 | 0.93 | 0.82 | 1.15 | 2.82 | 1.50 | 10.20 | 0.89 |
time (sec) |
N/A | 0.280 | 0.088 | 3.209 | 0.183 | 0.367 | 1.076 | 0.291 | 0.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 119 | 111 | 97 | 611 | 283 | 178 | 874 | 106 |
N.S. |
1 | 1.00 | 0.93 | 0.82 | 5.13 | 2.38 | 1.50 | 7.34 | 0.89 |
time (sec) |
N/A | 0.249 | 0.084 | 2.716 | 0.206 | 0.419 | 1.064 | 0.306 | 0.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 119 | 111 | 97 | 137 | 231 | 178 | 582 | 106 |
N.S. |
1 | 1.00 | 0.93 | 0.82 | 1.15 | 1.94 | 1.50 | 4.89 | 0.89 |
time (sec) |
N/A | 0.256 | 0.073 | 2.726 | 0.187 | 0.404 | 1.082 | 0.273 | 0.068 |
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 | 119 | 119 | 111 | 97 | 137 | 179 | 178 | 337 | 106 |
N.S. |
1 | 1.00 | 0.93 | 0.82 | 1.15 | 1.50 | 1.50 | 2.83 | 0.89 |
time (sec) |
N/A | 0.250 | 0.071 | 2.857 | 0.195 | 0.350 | 1.103 | 0.277 | 0.068 |
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 | 115 | 115 | 110 | 95 | 137 | 130 | 177 | 145 | 106 |
N.S. |
1 | 1.00 | 0.96 | 0.83 | 1.19 | 1.13 | 1.54 | 1.26 | 0.92 |
time (sec) |
N/A | 0.248 | 0.076 | 3.058 | 0.192 | 0.292 | 1.146 | 0.278 | 0.067 |
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 | 113 | 113 | 109 | 105 | 144 | 139 | 230 | 167 | 133 |
N.S. |
1 | 1.00 | 0.96 | 0.93 | 1.27 | 1.23 | 2.04 | 1.48 | 1.18 |
time (sec) |
N/A | 0.249 | 0.073 | 3.077 | 0.198 | 0.273 | 0.816 | 0.293 | 0.074 |
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 | 115 | 115 | 110 | 83 | 141 | 151 | 450 | 158 | 147 |
N.S. |
1 | 1.00 | 0.96 | 0.72 | 1.23 | 1.31 | 3.91 | 1.37 | 1.28 |
time (sec) |
N/A | 0.244 | 0.088 | 2.499 | 0.193 | 0.290 | 1.196 | 0.276 | 10.011 |
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 | 113 | 113 | 109 | 106 | 140 | 163 | 654 | 150 | 129 |
N.S. |
1 | 1.00 | 0.96 | 0.94 | 1.24 | 1.44 | 5.79 | 1.33 | 1.14 |
time (sec) |
N/A | 0.245 | 0.090 | 2.698 | 0.196 | 0.292 | 1.599 | 0.289 | 10.132 |
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 | 180 | 207 | 179 | 185 | 0 | 510 | 0 | 298 | 207 |
N.S. |
1 | 1.15 | 0.99 | 1.03 | 0.00 | 2.83 | 0.00 | 1.66 | 1.15 |
time (sec) |
N/A | 0.306 | 0.190 | 3.966 | 0.000 | 0.310 | 0.000 | 0.286 | 0.070 |