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 | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 106 | 229 | 280 | 0 | 304 | 0 | 501 | 192 | 577 |
N.S. |
1 | 1.02 | 2.20 | 2.69 | 0.00 | 2.92 | 0.00 | 4.82 | 1.85 | 5.55 |
time (sec) |
N/A | 0.422 | 1.127 | 1.904 | 0.000 | 0.079 | 0.000 | 0.180 | 0.215 | 11.882 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 158 | 229 | 282 | 0 | 317 | 0 | 517 | 240 | 577 |
N.S. |
1 | 0.98 | 1.42 | 1.75 | 0.00 | 1.97 | 0.00 | 3.21 | 1.49 | 3.58 |
time (sec) |
N/A | 0.459 | 1.112 | 2.255 | 0.000 | 0.079 | 0.000 | 0.167 | 0.232 | 11.676 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 222 | 191 | 233 | 286 | 0 | 332 | 0 | 532 | 251 | 577 |
N.S. |
1 | 0.86 | 1.05 | 1.29 | 0.00 | 1.50 | 0.00 | 2.40 | 1.13 | 2.60 |
time (sec) |
N/A | 0.674 | 1.113 | 2.619 | 0.000 | 0.077 | 0.000 | 0.177 | 0.200 | 11.214 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 298 | 191 | 229 | 278 | 0 | 335 | 0 | 543 | 262 | 577 |
N.S. |
1 | 0.64 | 0.77 | 0.93 | 0.00 | 1.12 | 0.00 | 1.82 | 0.88 | 1.94 |
time (sec) |
N/A | 0.646 | 1.112 | 3.128 | 0.000 | 0.082 | 0.000 | 0.196 | 0.209 | 11.617 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 298 | 191 | 232 | 286 | 0 | 354 | 0 | 560 | 273 | 577 |
N.S. |
1 | 0.64 | 0.78 | 0.96 | 0.00 | 1.19 | 0.00 | 1.88 | 0.92 | 1.94 |
time (sec) |
N/A | 0.614 | 1.119 | 3.759 | 0.000 | 0.090 | 0.000 | 0.180 | 0.216 | 11.637 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 298 | 191 | 232 | 286 | 0 | 365 | 0 | 575 | 284 | 577 |
N.S. |
1 | 0.64 | 0.78 | 0.96 | 0.00 | 1.22 | 0.00 | 1.93 | 0.95 | 1.94 |
time (sec) |
N/A | 0.624 | 1.115 | 4.579 | 0.000 | 0.085 | 0.000 | 0.191 | 0.203 | 11.650 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-2) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 298 | 191 | 233 | 286 | 0 | 376 | 0 | 588 | 295 | 577 |
N.S. |
1 | 0.64 | 0.78 | 0.96 | 0.00 | 1.26 | 0.00 | 1.97 | 0.99 | 1.94 |
time (sec) |
N/A | 0.634 | 1.118 | 5.904 | 0.000 | 0.093 | 0.000 | 0.174 | 0.246 | 11.518 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 436 | 275 | 876 | 1198 | 1744 | 964 | 137712 | 1945 | 690 | 0 |
N.S. |
1 | 0.63 | 2.01 | 2.75 | 4.00 | 2.21 | 315.85 | 4.46 | 1.58 | 0.00 |
time (sec) |
N/A | 1.670 | 1.408 | 2.247 | 0.050 | 0.088 | 2.575 | 0.210 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 383 | 271 | 740 | 1033 | 1330 | 813 | 82268 | 1647 | 581 | 0 |
N.S. |
1 | 0.71 | 1.93 | 2.70 | 3.47 | 2.12 | 214.80 | 4.30 | 1.52 | 0.00 |
time (sec) |
N/A | 1.430 | 1.329 | 1.820 | 0.055 | 0.084 | 2.222 | 0.208 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 324 | 232 | 611 | 861 | 1004 | 677 | 48020 | 1351 | 472 | 0 |
N.S. |
1 | 0.72 | 1.89 | 2.66 | 3.10 | 2.09 | 148.21 | 4.17 | 1.46 | 0.00 |
time (sec) |
N/A | 1.210 | 1.268 | 1.625 | 0.049 | 0.079 | 2.352 | 0.177 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 259 | 187 | 478 | 676 | 698 | 532 | 26879 | 1051 | 363 | 0 |
N.S. |
1 | 0.72 | 1.85 | 2.61 | 2.69 | 2.05 | 103.78 | 4.06 | 1.40 | 0.00 |
time (sec) |
N/A | 0.981 | 1.234 | 1.453 | 0.054 | 0.079 | 1.759 | 0.204 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 146 | 347 | 480 | 456 | 384 | 13857 | 753 | 254 | 0 |
N.S. |
1 | 0.74 | 1.75 | 2.42 | 2.30 | 1.94 | 69.98 | 3.80 | 1.28 | 0.00 |
time (sec) |
N/A | 0.790 | 1.177 | 1.290 | 0.068 | 0.075 | 1.758 | 0.195 | 0.260 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 103 | 214 | 284 | 254 | 239 | 6004 | 458 | 145 | 0 |
N.S. |
1 | 0.76 | 1.59 | 2.10 | 1.88 | 1.77 | 44.47 | 3.39 | 1.07 | 0.00 |
time (sec) |
N/A | 0.585 | 1.114 | 1.216 | 0.038 | 0.070 | 1.732 | 0.189 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 121 | 138 | 125 | 115 | 2147 | 217 | 65 | 0 |
N.S. |
1 | 1.00 | 1.70 | 1.94 | 1.76 | 1.62 | 30.24 | 3.06 | 0.92 | 0.00 |
time (sec) |
N/A | 0.341 | 0.055 | 1.125 | 0.030 | 0.073 | 0.874 | 0.178 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 340 | 216 | 386 | 697 | 0 | 555 | 0 | 957 | 411 | 0 |
N.S. |
1 | 0.64 | 1.14 | 2.05 | 0.00 | 1.63 | 0.00 | 2.81 | 1.21 | 0.00 |
time (sec) |
N/A | 0.758 | 1.263 | 1.451 | 0.000 | 0.078 | 0.000 | 0.217 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 423 | 262 | 506 | 685 | 0 | 797 | 0 | 944 | 549 | 0 |
N.S. |
1 | 0.62 | 1.20 | 1.62 | 0.00 | 1.88 | 0.00 | 2.23 | 1.30 | 0.00 |
time (sec) |
N/A | 1.110 | 1.295 | 1.523 | 0.000 | 0.091 | 0.000 | 0.177 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 424 | 263 | 501 | 661 | 0 | 871 | 0 | 924 | 625 | 0 |
N.S. |
1 | 0.62 | 1.18 | 1.56 | 0.00 | 2.05 | 0.00 | 2.18 | 1.47 | 0.00 |
time (sec) |
N/A | 1.033 | 1.312 | 1.660 | 0.000 | 0.096 | 0.000 | 0.187 | 0.259 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 425 | 264 | 504 | 646 | 0 | 899 | 0 | 911 | 645 | 0 |
N.S. |
1 | 0.62 | 1.19 | 1.52 | 0.00 | 2.12 | 0.00 | 2.14 | 1.52 | 0.00 |
time (sec) |
N/A | 0.991 | 1.338 | 1.793 | 0.000 | 0.097 | 0.000 | 0.185 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 421 | 260 | 497 | 633 | 0 | 871 | 0 | 907 | 634 | 0 |
N.S. |
1 | 0.62 | 1.18 | 1.50 | 0.00 | 2.07 | 0.00 | 2.15 | 1.51 | 0.00 |
time (sec) |
N/A | 0.924 | 1.330 | 1.915 | 0.000 | 0.090 | 0.000 | 0.177 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 422 | 261 | 490 | 634 | 0 | 802 | 0 | 899 | 576 | 0 |
N.S. |
1 | 0.62 | 1.16 | 1.50 | 0.00 | 1.90 | 0.00 | 2.13 | 1.36 | 0.00 |
time (sec) |
N/A | 0.916 | 1.318 | 2.435 | 0.000 | 0.104 | 0.000 | 0.155 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-2) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 365 | 211 | 477 | 613 | 0 | 703 | 0 | 907 | 498 | 0 |
N.S. |
1 | 0.58 | 1.31 | 1.68 | 0.00 | 1.93 | 0.00 | 2.48 | 1.36 | 0.00 |
time (sec) |
N/A | 0.722 | 1.309 | 2.902 | 0.000 | 0.091 | 0.000 | 0.183 | 0.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 106 | 465 | 594 | 0 | 621 | 0 | 1017 | 383 | 1489 |
N.S. |
1 | 1.02 | 4.47 | 5.71 | 0.00 | 5.97 | 0.00 | 9.78 | 3.68 | 14.32 |
time (sec) |
N/A | 0.414 | 1.228 | 3.585 | 0.000 | 0.086 | 0.000 | 0.177 | 0.211 | 11.583 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 158 | 466 | 596 | 0 | 634 | 0 | 1033 | 453 | 1489 |
N.S. |
1 | 0.98 | 2.89 | 3.70 | 0.00 | 3.94 | 0.00 | 6.42 | 2.81 | 9.25 |
time (sec) |
N/A | 0.460 | 1.228 | 4.866 | 0.000 | 0.094 | 0.000 | 0.195 | 0.206 | 11.495 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 222 | 202 | 468 | 596 | 0 | 645 | 0 | 1046 | 464 | 1489 |
N.S. |
1 | 0.91 | 2.11 | 2.68 | 0.00 | 2.91 | 0.00 | 4.71 | 2.09 | 6.71 |
time (sec) |
N/A | 0.523 | 1.226 | 6.280 | 0.000 | 0.091 | 0.000 | 0.175 | 0.206 | 11.591 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 282 | 277 | 468 | 602 | 0 | 662 | 0 | 1063 | 475 | 1488 |
N.S. |
1 | 0.98 | 1.66 | 2.13 | 0.00 | 2.35 | 0.00 | 3.77 | 1.68 | 5.28 |
time (sec) |
N/A | 0.937 | 1.237 | 8.461 | 0.000 | 0.101 | 0.000 | 0.224 | 0.264 | 11.597 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-2) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 342 | 277 | 471 | 602 | 0 | 673 | 0 | 1076 | 486 | 1489 |
N.S. |
1 | 0.81 | 1.38 | 1.76 | 0.00 | 1.97 | 0.00 | 3.15 | 1.42 | 4.35 |
time (sec) |
N/A | 0.847 | 1.253 | 11.129 | 0.000 | 0.099 | 0.000 | 0.191 | 0.213 | 11.656 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-2) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 438 | 277 | 465 | 590 | 0 | 672 | 0 | 1087 | 497 | 1489 |
N.S. |
1 | 0.63 | 1.06 | 1.35 | 0.00 | 1.53 | 0.00 | 2.48 | 1.13 | 3.40 |
time (sec) |
N/A | 0.883 | 1.231 | 17.867 | 0.000 | 0.105 | 0.000 | 0.203 | 0.209 | 11.664 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-2) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 435 | 274 | 471 | 602 | 0 | 695 | 0 | 1104 | 508 | 1489 |
N.S. |
1 | 0.63 | 1.08 | 1.38 | 0.00 | 1.60 | 0.00 | 2.54 | 1.17 | 3.42 |
time (sec) |
N/A | 0.861 | 1.244 | 24.193 | 0.000 | 0.104 | 0.000 | 0.237 | 0.238 | 11.658 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 149 | 185 | 326 | 438 | 269 | 1110 | 442 | 32 | 0 |
N.S. |
1 | 0.60 | 0.75 | 1.31 | 1.77 | 1.08 | 4.48 | 1.78 | 0.13 | 0.00 |
time (sec) |
N/A | 0.554 | 1.148 | 1.290 | 0.048 | 0.075 | 2.748 | 0.174 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 117 | 118 | 193 | 244 | 158 | 638 | 256 | 21 | 0 |
N.S. |
1 | 0.61 | 0.62 | 1.01 | 1.28 | 0.83 | 3.34 | 1.34 | 0.11 | 0.00 |
time (sec) |
N/A | 0.486 | 1.094 | 1.038 | 0.037 | 0.073 | 2.114 | 0.180 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 85 | 72 | 99 | 101 | 75 | 316 | 117 | 10 | 0 |
N.S. |
1 | 0.63 | 0.54 | 0.74 | 0.75 | 0.56 | 2.36 | 0.87 | 0.07 | 0.00 |
time (sec) |
N/A | 0.428 | 1.055 | 0.802 | 0.034 | 0.082 | 1.536 | 0.175 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 177 | 43 | 52 | 25 | 134 | 45 | 1 | 79 |
N.S. |
1 | 1.00 | 2.57 | 0.62 | 0.75 | 0.36 | 1.94 | 0.65 | 0.01 | 1.14 |
time (sec) |
N/A | 0.336 | 0.183 | 0.865 | 0.031 | 0.079 | 0.843 | 0.122 | 0.228 | 11.459 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 83 | 255 | 76 | 0 | 53 | 0 | 84 | 10 | 0 |
N.S. |
1 | 0.78 | 2.38 | 0.71 | 0.00 | 0.50 | 0.00 | 0.79 | 0.09 | 0.00 |
time (sec) |
N/A | 0.424 | 0.968 | 1.074 | 0.000 | 0.080 | 0.000 | 0.156 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 127 | 97 | 160 | 0 | 148 | 0 | 186 | 12 | 0 |
N.S. |
1 | 1.20 | 0.92 | 1.51 | 0.00 | 1.40 | 0.00 | 1.75 | 0.11 | 0.00 |
time (sec) |
N/A | 0.454 | 1.134 | 1.158 | 0.000 | 0.083 | 0.000 | 0.110 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 212 | 138 | 131 | 257 | 0 | 343 | 0 | 311 | 23 | 0 |
N.S. |
1 | 0.65 | 0.62 | 1.21 | 0.00 | 1.62 | 0.00 | 1.47 | 0.11 | 0.00 |
time (sec) |
N/A | 0.567 | 1.159 | 1.246 | 0.000 | 0.086 | 0.000 | 0.155 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 271 | 172 | 168 | 413 | 0 | 608 | 0 | 508 | 34 | 0 |
N.S. |
1 | 0.63 | 0.62 | 1.52 | 0.00 | 2.24 | 0.00 | 1.87 | 0.13 | 0.00 |
time (sec) |
N/A | 0.633 | 1.165 | 1.488 | 0.000 | 0.096 | 0.000 | 0.155 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 329 | 217 | 373 | 466 | 761 | 668 | 0 | 466 | 297 | 0 |
N.S. |
1 | 0.66 | 1.13 | 1.42 | 2.31 | 2.03 | 0.00 | 1.42 | 0.90 | 0.00 |
time (sec) |
N/A | 0.841 | 1.269 | 2.094 | 0.050 | 0.089 | 0.000 | 0.147 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 249 | 167 | 256 | 305 | 487 | 442 | 0 | 323 | 197 | 0 |
N.S. |
1 | 0.67 | 1.03 | 1.22 | 1.96 | 1.78 | 0.00 | 1.30 | 0.79 | 0.00 |
time (sec) |
N/A | 0.685 | 1.186 | 1.697 | 0.041 | 0.083 | 0.000 | 0.155 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 129 | 151 | 196 | 277 | 258 | 0 | 181 | 112 | 0 |
N.S. |
1 | 0.69 | 0.81 | 1.05 | 1.49 | 1.39 | 0.00 | 0.97 | 0.60 | 0.00 |
time (sec) |
N/A | 0.586 | 1.114 | 1.599 | 0.046 | 0.084 | 0.000 | 0.161 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 95 | 86 | 97 | 120 | 110 | 0 | 88 | 49 | 0 |
N.S. |
1 | 0.75 | 0.68 | 0.76 | 0.94 | 0.87 | 0.00 | 0.69 | 0.39 | 0.00 |
time (sec) |
N/A | 0.457 | 1.057 | 1.303 | 0.036 | 0.078 | 0.000 | 0.196 | 0.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 176 | 32 | 56 | 38 | 0 | 32 | 12 | 42 |
N.S. |
1 | 1.00 | 2.55 | 0.46 | 0.81 | 0.55 | 0.00 | 0.46 | 0.17 | 0.61 |
time (sec) |
N/A | 0.328 | 0.157 | 1.219 | 0.033 | 0.072 | 0.000 | 0.120 | 0.209 | 11.160 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 139 | 132 | 253 | 0 | 361 | 0 | 288 | 115 | 0 |
N.S. |
1 | 0.71 | 0.67 | 1.29 | 0.00 | 1.84 | 0.00 | 1.47 | 0.59 | 0.00 |
time (sec) |
N/A | 0.568 | 1.121 | 1.713 | 0.000 | 0.086 | 0.000 | 0.170 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 266 | 184 | 174 | 421 | 0 | 803 | 0 | 468 | 459 | 0 |
N.S. |
1 | 0.69 | 0.65 | 1.58 | 0.00 | 3.02 | 0.00 | 1.76 | 1.73 | 0.00 |
time (sec) |
N/A | 0.691 | 1.167 | 1.728 | 0.000 | 0.102 | 0.000 | 0.166 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 332 | 225 | 220 | 651 | 0 | 1215 | 0 | 634 | 821 | 0 |
N.S. |
1 | 0.68 | 0.66 | 1.96 | 0.00 | 3.66 | 0.00 | 1.91 | 2.47 | 0.00 |
time (sec) |
N/A | 0.831 | 1.224 | 1.686 | 0.000 | 0.115 | 0.000 | 0.148 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 373 | 251 | 513 | 626 | 1010 | 914 | 0 | 653 | 469 | 0 |
N.S. |
1 | 0.67 | 1.38 | 1.68 | 2.71 | 2.45 | 0.00 | 1.75 | 1.26 | 0.00 |
time (sec) |
N/A | 0.970 | 1.368 | 2.057 | 0.143 | 0.102 | 0.000 | 0.194 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 310 | 213 | 331 | 456 | 755 | 619 | 0 | 454 | 309 | 0 |
N.S. |
1 | 0.69 | 1.07 | 1.47 | 2.44 | 2.00 | 0.00 | 1.46 | 1.00 | 0.00 |
time (sec) |
N/A | 0.805 | 1.246 | 1.828 | 0.106 | 0.089 | 0.000 | 0.169 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 157 | 239 | 292 | 533 | 359 | 0 | 297 | 180 | 0 |
N.S. |
1 | 0.69 | 1.05 | 1.29 | 2.35 | 1.58 | 0.00 | 1.31 | 0.79 | 0.00 |
time (sec) |
N/A | 0.584 | 1.171 | 1.550 | 0.063 | 0.090 | 0.000 | 0.147 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 106 | 142 | 161 | 279 | 189 | 0 | 174 | 69 | 302 |
N.S. |
1 | 1.02 | 1.37 | 1.55 | 2.68 | 1.82 | 0.00 | 1.67 | 0.66 | 2.90 |
time (sec) |
N/A | 0.419 | 1.095 | 1.378 | 0.042 | 0.077 | 0.000 | 0.161 | 0.265 | 11.618 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 101 | 75 | 77 | 121 | 106 | 0 | 77 | 48 | 87 |
N.S. |
1 | 0.75 | 0.56 | 0.57 | 0.90 | 0.79 | 0.00 | 0.57 | 0.36 | 0.64 |
time (sec) |
N/A | 0.454 | 1.052 | 1.225 | 0.029 | 0.079 | 0.000 | 0.174 | 0.232 | 11.490 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 39 | 33 | 56 | 61 | 0 | 33 | 34 | 43 |
N.S. |
1 | 1.00 | 0.55 | 0.46 | 0.79 | 0.86 | 0.00 | 0.46 | 0.48 | 0.61 |
time (sec) |
N/A | 0.327 | 0.026 | 1.194 | 0.035 | 0.074 | 0.000 | 0.178 | 0.222 | 11.260 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 302 | 205 | 182 | 624 | 0 | 969 | 0 | 624 | 499 | 0 |
N.S. |
1 | 0.68 | 0.60 | 2.07 | 0.00 | 3.21 | 0.00 | 2.07 | 1.65 | 0.00 |
time (sec) |
N/A | 0.725 | 1.159 | 1.523 | 0.000 | 0.107 | 0.000 | 0.241 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 388 | 266 | 250 | 953 | 0 | 1724 | 0 | 883 | 1236 | 0 |
N.S. |
1 | 0.69 | 0.64 | 2.46 | 0.00 | 4.44 | 0.00 | 2.28 | 3.19 | 0.00 |
time (sec) |
N/A | 0.978 | 1.256 | 1.708 | 0.000 | 0.167 | 0.000 | 0.173 | 0.283 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 460 | 313 | 302 | 1303 | 0 | 2466 | 0 | 1145 | 1840 | 0 |
N.S. |
1 | 0.68 | 0.66 | 2.83 | 0.00 | 5.36 | 0.00 | 2.49 | 4.00 | 0.00 |
time (sec) |
N/A | 1.157 | 1.355 | 1.623 | 0.000 | 0.300 | 0.000 | 0.168 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 111 | 88 | 79 | 263 | 230 | 0 | 1164 | 221 | 0 |
N.S. |
1 | 0.68 | 0.54 | 0.48 | 1.60 | 1.40 | 0.00 | 7.10 | 1.35 | 0.00 |
time (sec) |
N/A | 0.458 | 0.126 | 2.290 | 0.059 | 0.077 | 0.000 | 0.202 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 111 | 88 | 79 | 214 | 189 | 0 | 831 | 180 | 0 |
N.S. |
1 | 0.68 | 0.54 | 0.48 | 1.30 | 1.15 | 0.00 | 5.07 | 1.10 | 0.00 |
time (sec) |
N/A | 0.432 | 0.116 | 2.119 | 0.047 | 0.079 | 0.000 | 0.210 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 111 | 88 | 79 | 167 | 149 | 0 | 545 | 139 | 0 |
N.S. |
1 | 0.68 | 0.54 | 0.48 | 1.02 | 0.91 | 0.00 | 3.32 | 0.85 | 0.00 |
time (sec) |
N/A | 0.442 | 0.111 | 2.389 | 0.047 | 0.076 | 0.000 | 0.174 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 111 | 88 | 79 | 120 | 108 | 0 | 309 | 98 | 0 |
N.S. |
1 | 0.68 | 0.54 | 0.48 | 0.73 | 0.66 | 0.00 | 1.88 | 0.60 | 0.00 |
time (sec) |
N/A | 0.445 | 0.102 | 2.295 | 0.044 | 0.078 | 0.000 | 0.213 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 109 | 86 | 79 | 119 | 70 | 0 | 129 | 61 | 156 |
N.S. |
1 | 0.67 | 0.53 | 0.49 | 0.73 | 0.43 | 0.00 | 0.80 | 0.38 | 0.96 |
time (sec) |
N/A | 0.442 | 0.105 | 2.517 | 0.043 | 0.084 | 0.000 | 0.178 | 0.215 | 11.470 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 107 | 85 | 79 | 75 | 79 | 0 | 148 | 62 | 109 |
N.S. |
1 | 0.67 | 0.53 | 0.49 | 0.47 | 0.49 | 0.00 | 0.92 | 0.39 | 0.68 |
time (sec) |
N/A | 0.446 | 0.114 | 1.507 | 0.044 | 0.076 | 0.000 | 0.229 | 0.226 | 11.719 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 107 | 86 | 78 | 96 | 91 | 0 | 130 | 70 | 146 |
N.S. |
1 | 0.67 | 0.54 | 0.49 | 0.60 | 0.57 | 0.00 | 0.81 | 0.44 | 0.91 |
time (sec) |
N/A | 0.431 | 0.107 | 1.608 | 0.057 | 0.080 | 0.000 | 1.017 | 0.288 | 12.160 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 109 | 86 | 79 | 118 | 101 | 0 | 128 | 81 | 174 |
N.S. |
1 | 0.67 | 0.53 | 0.49 | 0.73 | 0.62 | 0.00 | 0.79 | 0.50 | 1.07 |
time (sec) |
N/A | 0.428 | 0.105 | 1.566 | 0.050 | 0.076 | 0.000 | 0.198 | 0.228 | 12.216 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 308 | 201 | 245 | 317 | 697 | 633 | 0 | 2924 | 480 | 0 |
N.S. |
1 | 0.65 | 0.80 | 1.03 | 2.26 | 2.06 | 0.00 | 9.49 | 1.56 | 0.00 |
time (sec) |
N/A | 0.660 | 0.329 | 1.961 | 0.061 | 0.089 | 0.000 | 1.001 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 308 | 201 | 246 | 317 | 592 | 539 | 0 | 2139 | 405 | 0 |
N.S. |
1 | 0.65 | 0.80 | 1.03 | 1.92 | 1.75 | 0.00 | 6.94 | 1.31 | 0.00 |
time (sec) |
N/A | 0.600 | 0.305 | 1.932 | 0.101 | 0.085 | 0.000 | 0.258 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 308 | 201 | 246 | 317 | 488 | 446 | 0 | 1450 | 330 | 0 |
N.S. |
1 | 0.65 | 0.80 | 1.03 | 1.58 | 1.45 | 0.00 | 4.71 | 1.07 | 0.00 |
time (sec) |
N/A | 0.603 | 0.288 | 1.845 | 0.088 | 0.080 | 0.000 | 0.310 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 308 | 201 | 245 | 317 | 384 | 353 | 0 | 857 | 255 | 0 |
N.S. |
1 | 0.65 | 0.80 | 1.03 | 1.25 | 1.15 | 0.00 | 2.78 | 0.83 | 0.00 |
time (sec) |
N/A | 0.572 | 0.271 | 1.853 | 0.063 | 0.087 | 0.000 | 0.255 | 0.268 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 306 | 199 | 244 | 317 | 382 | 263 | 0 | 377 | 184 | 434 |
N.S. |
1 | 0.65 | 0.80 | 1.04 | 1.25 | 0.86 | 0.00 | 1.23 | 0.60 | 1.42 |
time (sec) |
N/A | 0.582 | 0.263 | 1.852 | 0.066 | 0.080 | 0.000 | 0.170 | 0.231 | 12.531 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 302 | 195 | 240 | 317 | 282 | 272 | 0 | 529 | 186 | 327 |
N.S. |
1 | 0.65 | 0.79 | 1.05 | 0.93 | 0.90 | 0.00 | 1.75 | 0.62 | 1.08 |
time (sec) |
N/A | 0.609 | 0.275 | 1.380 | 0.060 | 0.090 | 0.000 | 0.226 | 0.230 | 12.644 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 304 | 197 | 243 | 211 | 304 | 284 | 0 | 508 | 193 | 362 |
N.S. |
1 | 0.65 | 0.80 | 0.69 | 1.00 | 0.93 | 0.00 | 1.67 | 0.63 | 1.19 |
time (sec) |
N/A | 0.586 | 0.325 | 1.439 | 0.072 | 0.086 | 0.000 | 0.251 | 0.212 | 12.904 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 304 | 197 | 244 | 252 | 326 | 294 | 0 | 502 | 204 | 377 |
N.S. |
1 | 0.65 | 0.80 | 0.83 | 1.07 | 0.97 | 0.00 | 1.65 | 0.67 | 1.24 |
time (sec) |
N/A | 0.585 | 0.347 | 1.389 | 0.077 | 0.083 | 0.000 | 0.236 | 0.226 | 12.632 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 452 | 291 | 490 | 689 | 1241 | 1137 | 0 | 5164 | 807 | 0 |
N.S. |
1 | 0.64 | 1.08 | 1.52 | 2.75 | 2.52 | 0.00 | 11.42 | 1.79 | 0.00 |
time (sec) |
N/A | 0.864 | 0.679 | 1.901 | 0.072 | 0.090 | 0.000 | 0.324 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 452 | 291 | 492 | 689 | 1080 | 993 | 0 | 3831 | 698 | 0 |
N.S. |
1 | 0.64 | 1.09 | 1.52 | 2.39 | 2.20 | 0.00 | 8.48 | 1.54 | 0.00 |
time (sec) |
N/A | 0.795 | 0.697 | 1.938 | 0.072 | 0.094 | 0.000 | 0.338 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 452 | 291 | 491 | 689 | 921 | 848 | 0 | 2642 | 589 | 0 |
N.S. |
1 | 0.64 | 1.09 | 1.52 | 2.04 | 1.88 | 0.00 | 5.85 | 1.30 | 0.00 |
time (sec) |
N/A | 0.763 | 0.646 | 1.918 | 0.062 | 0.082 | 0.000 | 0.243 | 0.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 452 | 291 | 490 | 689 | 760 | 702 | 0 | 1597 | 480 | 0 |
N.S. |
1 | 0.64 | 1.08 | 1.52 | 1.68 | 1.55 | 0.00 | 3.53 | 1.06 | 0.00 |
time (sec) |
N/A | 0.764 | 0.620 | 1.924 | 0.103 | 0.079 | 0.000 | 0.218 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 448 | 287 | 490 | 689 | 758 | 560 | 0 | 722 | 375 | 826 |
N.S. |
1 | 0.64 | 1.09 | 1.54 | 1.69 | 1.25 | 0.00 | 1.61 | 0.84 | 1.84 |
time (sec) |
N/A | 0.740 | 0.599 | 1.950 | 0.080 | 0.084 | 0.000 | 0.182 | 0.220 | 12.507 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 446 | 285 | 486 | 681 | 603 | 569 | 0 | 1133 | 377 | 659 |
N.S. |
1 | 0.64 | 1.09 | 1.53 | 1.35 | 1.28 | 0.00 | 2.54 | 0.85 | 1.48 |
time (sec) |
N/A | 0.710 | 0.670 | 1.290 | 0.064 | 0.082 | 0.000 | 0.228 | 0.256 | 13.130 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 446 | 285 | 487 | 467 | 625 | 581 | 0 | 1104 | 384 | 695 |
N.S. |
1 | 0.64 | 1.09 | 1.05 | 1.40 | 1.30 | 0.00 | 2.48 | 0.86 | 1.56 |
time (sec) |
N/A | 0.746 | 0.676 | 1.339 | 0.069 | 0.087 | 0.000 | 0.269 | 0.221 | 13.183 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 448 | 287 | 489 | 437 | 647 | 592 | 0 | 1099 | 395 | 718 |
N.S. |
1 | 0.64 | 1.09 | 0.98 | 1.44 | 1.32 | 0.00 | 2.45 | 0.88 | 1.60 |
time (sec) |
N/A | 0.742 | 0.643 | 1.486 | 0.079 | 0.090 | 0.000 | 0.230 | 0.277 | 13.154 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 289 | 179 | 204 | 351 | 0 | 591 | 0 | 497 | 38 | 0 |
N.S. |
1 | 0.62 | 0.71 | 1.21 | 0.00 | 2.04 | 0.00 | 1.72 | 0.13 | 0.00 |
time (sec) |
N/A | 0.537 | 0.486 | 1.264 | 0.000 | 0.090 | 0.000 | 0.226 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 230 | 150 | 148 | 225 | 0 | 373 | 0 | 304 | 27 | 0 |
N.S. |
1 | 0.65 | 0.64 | 0.98 | 0.00 | 1.62 | 0.00 | 1.32 | 0.12 | 0.00 |
time (sec) |
N/A | 0.485 | 0.376 | 1.095 | 0.000 | 0.089 | 0.000 | 0.230 | 0.248 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 121 | 114 | 133 | 0 | 211 | 0 | 164 | 16 | 0 |
N.S. |
1 | 0.70 | 0.66 | 0.77 | 0.00 | 1.22 | 0.00 | 0.95 | 0.09 | 0.00 |
time (sec) |
N/A | 0.462 | 0.306 | 1.162 | 0.000 | 0.082 | 0.000 | 0.178 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 100 | 105 | 97 | 0 | 209 | 0 | 84 | 11 | 0 |
N.S. |
1 | 0.81 | 0.85 | 0.78 | 0.00 | 1.69 | 0.00 | 0.68 | 0.09 | 0.00 |
time (sec) |
N/A | 0.399 | 0.196 | 1.198 | 0.000 | 0.086 | 0.000 | 0.202 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 114 | 121 | 148 | 0 | 363 | 0 | 111 | 13 | 0 |
N.S. |
1 | 0.83 | 0.88 | 1.07 | 0.00 | 2.63 | 0.00 | 0.80 | 0.09 | 0.00 |
time (sec) |
N/A | 0.434 | 0.338 | 1.155 | 0.000 | 0.097 | 0.000 | 0.225 | 0.262 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 149 | 136 | 233 | 0 | 486 | 0 | 201 | 20 | 0 |
N.S. |
1 | 0.77 | 0.70 | 1.20 | 0.00 | 2.51 | 0.00 | 1.04 | 0.10 | 0.00 |
time (sec) |
N/A | 0.492 | 0.485 | 1.223 | 0.000 | 0.105 | 0.000 | 0.195 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 185 | 193 | 386 | 0 | 882 | 0 | 360 | 31 | 0 |
N.S. |
1 | 0.74 | 0.77 | 1.54 | 0.00 | 3.51 | 0.00 | 1.43 | 0.12 | 0.00 |
time (sec) |
N/A | 0.522 | 0.623 | 1.115 | 0.000 | 0.122 | 0.000 | 0.204 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 362 | 251 | 331 | 308 | 0 | 1060 | 0 | 621 | 449 | 0 |
N.S. |
1 | 0.69 | 0.91 | 0.85 | 0.00 | 2.93 | 0.00 | 1.72 | 1.24 | 0.00 |
time (sec) |
N/A | 0.651 | 1.542 | 1.727 | 0.000 | 0.107 | 0.000 | 0.237 | 0.283 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 296 | 222 | 235 | 234 | 0 | 680 | 0 | 414 | 273 | 0 |
N.S. |
1 | 0.75 | 0.79 | 0.79 | 0.00 | 2.30 | 0.00 | 1.40 | 0.92 | 0.00 |
time (sec) |
N/A | 0.589 | 1.217 | 1.608 | 0.000 | 0.108 | 0.000 | 0.212 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 192 | 162 | 204 | 0 | 703 | 0 | 250 | 127 | 0 |
N.S. |
1 | 0.82 | 0.69 | 0.87 | 0.00 | 2.99 | 0.00 | 1.06 | 0.54 | 0.00 |
time (sec) |
N/A | 0.569 | 1.081 | 1.665 | 0.000 | 0.101 | 0.000 | 0.190 | 0.283 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 171 | 166 | 555 | 0 | 721 | 0 | 259 | 129 | 0 |
N.S. |
1 | 0.84 | 0.81 | 2.72 | 0.00 | 3.53 | 0.00 | 1.27 | 0.63 | 0.00 |
time (sec) |
N/A | 0.525 | 1.047 | 1.546 | 0.000 | 0.102 | 0.000 | 0.204 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 215 | 177 | 167 | 556 | 0 | 808 | 0 | 294 | 156 | 0 |
N.S. |
1 | 0.82 | 0.78 | 2.59 | 0.00 | 3.76 | 0.00 | 1.37 | 0.73 | 0.00 |
time (sec) |
N/A | 0.542 | 1.042 | 1.506 | 0.000 | 0.136 | 0.000 | 0.190 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 263 | 213 | 215 | 681 | 0 | 1410 | 0 | 412 | 220 | 0 |
N.S. |
1 | 0.81 | 0.82 | 2.59 | 0.00 | 5.36 | 0.00 | 1.57 | 0.84 | 0.00 |
time (sec) |
N/A | 0.597 | 1.486 | 1.702 | 0.000 | 0.130 | 0.000 | 0.197 | 0.273 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 330 | 250 | 311 | 928 | 0 | 1756 | 0 | 536 | 493 | 0 |
N.S. |
1 | 0.76 | 0.94 | 2.81 | 0.00 | 5.32 | 0.00 | 1.62 | 1.49 | 0.00 |
time (sec) |
N/A | 0.649 | 2.035 | 1.835 | 0.000 | 0.185 | 0.000 | 0.239 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 398 | 286 | 427 | 1230 | 0 | 2657 | 0 | 717 | 804 | 0 |
N.S. |
1 | 0.72 | 1.07 | 3.09 | 0.00 | 6.68 | 0.00 | 1.80 | 2.02 | 0.00 |
time (sec) |
N/A | 0.697 | 2.275 | 1.649 | 0.000 | 0.401 | 0.000 | 0.221 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 492 | 315 | 583 | 513 | 0 | 2006 | 0 | 1121 | 1000 | 0 |
N.S. |
1 | 0.64 | 1.18 | 1.04 | 0.00 | 4.08 | 0.00 | 2.28 | 2.03 | 0.00 |
time (sec) |
N/A | 0.723 | 3.412 | 2.173 | 0.000 | 0.186 | 0.000 | 0.236 | 0.271 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 424 | 286 | 444 | 439 | 0 | 1414 | 0 | 824 | 674 | 0 |
N.S. |
1 | 0.67 | 1.05 | 1.04 | 0.00 | 3.33 | 0.00 | 1.94 | 1.59 | 0.00 |
time (sec) |
N/A | 0.688 | 3.831 | 1.535 | 0.000 | 0.158 | 0.000 | 0.210 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 361 | 256 | 329 | 409 | 0 | 1485 | 0 | 570 | 383 | 0 |
N.S. |
1 | 0.71 | 0.91 | 1.13 | 0.00 | 4.11 | 0.00 | 1.58 | 1.06 | 0.00 |
time (sec) |
N/A | 0.642 | 3.417 | 1.602 | 0.000 | 0.135 | 0.000 | 0.185 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 329 | 235 | 328 | 1273 | 0 | 1547 | 0 | 579 | 410 | 0 |
N.S. |
1 | 0.71 | 1.00 | 3.87 | 0.00 | 4.70 | 0.00 | 1.76 | 1.25 | 0.00 |
time (sec) |
N/A | 0.594 | 3.376 | 1.520 | 0.000 | 0.145 | 0.000 | 0.158 | 0.299 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 339 | 241 | 328 | 1273 | 0 | 1706 | 0 | 617 | 470 | 0 |
N.S. |
1 | 0.71 | 0.97 | 3.76 | 0.00 | 5.03 | 0.00 | 1.82 | 1.39 | 0.00 |
time (sec) |
N/A | 0.605 | 3.145 | 1.511 | 0.000 | 0.172 | 0.000 | 0.179 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 348 | 255 | 326 | 1296 | 0 | 1841 | 0 | 659 | 536 | 0 |
N.S. |
1 | 0.73 | 0.94 | 3.72 | 0.00 | 5.29 | 0.00 | 1.89 | 1.54 | 0.00 |
time (sec) |
N/A | 0.608 | 2.367 | 1.526 | 0.000 | 0.156 | 0.000 | 0.183 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 359 | 269 | 325 | 1296 | 0 | 1980 | 0 | 693 | 597 | 0 |
N.S. |
1 | 0.75 | 0.91 | 3.61 | 0.00 | 5.52 | 0.00 | 1.93 | 1.66 | 0.00 |
time (sec) |
N/A | 0.649 | 2.009 | 1.536 | 0.000 | 0.154 | 0.000 | 0.180 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 403 | 305 | 425 | 1493 | 0 | 2968 | 0 | 852 | 702 | 0 |
N.S. |
1 | 0.76 | 1.05 | 3.70 | 0.00 | 7.36 | 0.00 | 2.11 | 1.74 | 0.00 |
time (sec) |
N/A | 0.671 | 4.010 | 1.555 | 0.000 | 0.360 | 0.000 | 0.218 | 0.245 | 0.000 |