Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 197 | 223 | 200 | 611 | 0 | 1947 | 0 | 856 | 700 |
N.S. |
1 | 1.13 | 1.02 | 3.10 | 0.00 | 9.88 | 0.00 | 4.35 | 3.55 |
time (sec) |
N/A | 0.626 | 0.734 | 1.723 | 0.000 | 0.351 | 0.000 | 0.320 | 32.720 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | C | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 292 | 338 | 606 | 1655 | 0 | 4069 | 0 | 2558 | 1946 |
N.S. |
1 | 1.16 | 2.08 | 5.67 | 0.00 | 13.93 | 0.00 | 8.76 | 6.66 |
time (sec) |
N/A | 1.044 | 1.713 | 4.406 | 0.000 | 0.466 | 0.000 | 0.425 | 29.885 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 185 | 193 | 399 | 821 | 0 | 180 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 2.16 | 4.44 | 0.00 | 0.97 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.003 | 4.940 | 2.045 | 0.000 | 0.099 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 139 | 142 | 349 | 806 | 0 | 159 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 2.51 | 5.80 | 0.00 | 1.14 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.699 | 2.856 | 1.339 | 0.000 | 0.095 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 326 | 461 | 0 | 120 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 7.24 | 10.24 | 0.00 | 2.67 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.238 | 1.937 | 2.762 | 0.000 | 0.085 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 128 | 152 | 0 | 60 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.84 | 3.38 | 0.00 | 1.33 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.248 | 0.334 | 1.592 | 0.000 | 0.080 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 390 | 425 | 0 | 278 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 4.15 | 4.52 | 0.00 | 2.96 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.377 | 4.788 | 1.348 | 0.000 | 0.097 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 187 | 193 | 430 | 586 | 0 | 431 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 2.30 | 3.13 | 0.00 | 2.30 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.944 | 2.466 | 1.621 | 0.000 | 0.099 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 233 | 244 | 436 | 649 | 0 | 577 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 1.87 | 2.79 | 0.00 | 2.48 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.233 | 2.998 | 1.697 | 0.000 | 0.109 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 347 | 359 | 3767 | 2270 | 0 | 1595 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 10.86 | 6.54 | 0.00 | 4.60 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.624 | 6.765 | 3.022 | 0.000 | 0.152 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 283 | 284 | 2190 | 1494 | 0 | 1483 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 7.74 | 5.28 | 0.00 | 5.24 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.066 | 6.344 | 1.985 | 0.000 | 0.135 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 108 | 108 | 1408 | 691 | 0 | 1371 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 13.04 | 6.40 | 0.00 | 12.69 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.361 | 6.308 | 5.309 | 0.000 | 0.117 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 108 | 108 | 285 | 295 | 0 | 506 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.64 | 2.73 | 0.00 | 4.69 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.366 | 0.677 | 1.348 | 0.000 | 0.106 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 186 | 186 | 1540 | 2645 | 0 | 1737 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 8.28 | 14.22 | 0.00 | 9.34 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.547 | 6.436 | 2.437 | 0.000 | 0.147 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 382 | 397 | 2408 | 3642 | 0 | 2805 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 6.30 | 9.53 | 0.00 | 7.34 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.532 | 6.694 | 9.276 | 0.000 | 0.213 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 490 | 526 | 4116 | 5028 | 0 | 4955 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 8.40 | 10.26 | 0.00 | 10.11 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.255 | 6.565 | 30.194 | 0.000 | 0.513 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 139 | 142 | 130 | 74 | 0 | 101 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.94 | 0.53 | 0.00 | 0.73 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.407 | 6.248 | 1.062 | 0.000 | 0.236 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 104 | 60 | 0 | 81 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.12 | 0.65 | 0.00 | 0.87 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.292 | 1.850 | 0.668 | 0.000 | 0.237 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 75 | 50 | 0 | 61 | 0 | 0 | 39 |
N.S. |
1 | 1.00 | 1.70 | 1.14 | 0.00 | 1.39 | 0.00 | 0.00 | 0.89 |
time (sec) |
N/A | 0.188 | 0.037 | 0.764 | 0.000 | 0.239 | 0.000 | 0.000 | 0.416 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 101 | 77 | 0 | 147 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.10 | 1.60 | 0.00 | 3.06 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.260 | 0.204 | 2.901 | 0.000 | 0.251 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 96 | 96 | 154 | 117 | 0 | 268 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.60 | 1.22 | 0.00 | 2.79 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.364 | 0.312 | 0.769 | 0.000 | 0.262 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 142 | 147 | 180 | 190 | 0 | 341 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.27 | 1.34 | 0.00 | 2.40 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.502 | 0.413 | 0.907 | 0.000 | 0.259 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 185 | 193 | 151 | 86 | 0 | 121 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.82 | 0.46 | 0.00 | 0.65 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.547 | 7.295 | 1.194 | 0.000 | 0.245 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 139 | 142 | 127 | 74 | 0 | 101 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.91 | 0.53 | 0.00 | 0.73 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.407 | 5.842 | 0.840 | 0.000 | 0.254 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 103 | 60 | 0 | 80 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.11 | 0.65 | 0.00 | 0.86 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.294 | 4.045 | 0.684 | 0.000 | 0.238 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 75 | 50 | 0 | 59 | 0 | 0 | 39 |
N.S. |
1 | 1.00 | 1.70 | 1.14 | 0.00 | 1.34 | 0.00 | 0.00 | 0.89 |
time (sec) |
N/A | 0.190 | 0.032 | 0.648 | 0.000 | 0.240 | 0.000 | 0.000 | 0.551 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 99 | 77 | 0 | 88 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.02 | 1.57 | 0.00 | 1.80 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.256 | 0.163 | 2.324 | 0.000 | 0.248 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 96 | 96 | 152 | 118 | 0 | 210 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.58 | 1.23 | 0.00 | 2.19 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.364 | 0.310 | 0.773 | 0.000 | 0.257 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 142 | 147 | 178 | 190 | 0 | 280 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.25 | 1.34 | 0.00 | 1.97 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.499 | 0.441 | 0.881 | 0.000 | 0.251 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 258 | 272 | 5490 | 306 | 0 | 268 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 21.28 | 1.19 | 0.00 | 1.04 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.757 | 37.941 | 1.635 | 0.000 | 0.261 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 190 | 199 | 5377 | 200 | 0 | 189 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 28.30 | 1.05 | 0.00 | 0.99 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.535 | 18.056 | 1.350 | 0.000 | 0.256 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 126 | 126 | 5279 | 126 | 0 | 125 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 41.90 | 1.00 | 0.00 | 0.99 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.370 | 17.981 | 1.361 | 0.000 | 0.256 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 565 | 113 | 0 | 80 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 10.27 | 2.05 | 0.00 | 1.45 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.221 | 16.601 | 1.279 | 0.000 | 0.247 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-2) | B | F | F(-2) | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 63264 | 172 | 0 | 349 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 718.91 | 1.95 | 0.00 | 3.97 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.352 | 54.766 | 5.571 | 0.000 | 0.425 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F(-1) | B | F(-2) | B | F | F(-1) | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 160 | 160 | 0 | 350 | 0 | 646 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 2.19 | 0.00 | 4.04 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.516 | 0.000 | 1.540 | 0.000 | 0.509 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F(-1) | A | F(-2) | B | F | F(-1) | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 226 | 244 | 0 | 350 | 0 | 895 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 0.00 | 1.55 | 0.00 | 3.96 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.739 | 0.000 | 1.597 | 0.000 | 0.499 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 196 | 205 | 5238 | 204 | 0 | 192 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 26.72 | 1.04 | 0.00 | 0.98 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.560 | 39.428 | 1.451 | 0.000 | 0.261 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 130 | 130 | 5142 | 130 | 0 | 127 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 39.55 | 1.00 | 0.00 | 0.98 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.372 | 13.034 | 1.381 | 0.000 | 0.257 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 5053 | 117 | 0 | 80 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 88.65 | 2.05 | 0.00 | 1.40 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.226 | 18.300 | 1.338 | 0.000 | 0.252 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 61904 | 175 | 0 | 107 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 680.26 | 1.92 | 0.00 | 1.18 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.345 | 61.111 | 4.727 | 0.000 | 0.257 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F(-1) | B | F(-2) | B | F | F(-1) | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 164 | 164 | 0 | 364 | 0 | 442 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 2.22 | 0.00 | 2.70 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.528 | 0.000 | 1.582 | 0.000 | 0.305 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F(-1) | A | F(-2) | B | F | F(-1) | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 232 | 250 | 0 | 364 | 0 | 655 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 0.00 | 1.57 | 0.00 | 2.82 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.758 | 0.000 | 1.629 | 0.000 | 0.349 | 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) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 107 | 80 | 176 | 0 | 579 | 0 | 160 | 950 |
N.S. |
1 | 1.06 | 0.79 | 1.74 | 0.00 | 5.73 | 0.00 | 1.58 | 9.41 |
time (sec) |
N/A | 0.333 | 0.278 | 0.799 | 0.000 | 0.315 | 0.000 | 0.285 | 40.867 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 30 | 22 | 20 | 41 | 11 | 22 | 25 | 34 |
N.S. |
1 | 1.36 | 1.00 | 0.91 | 1.86 | 0.50 | 1.00 | 1.14 | 1.55 |
time (sec) |
N/A | 0.227 | 0.080 | 0.544 | 0.296 | 0.246 | 0.142 | 0.292 | 26.115 |
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 | 97 | 102 | 79 | 171 | 0 | 553 | 0 | 158 | 988 |
N.S. |
1 | 1.05 | 0.81 | 1.76 | 0.00 | 5.70 | 0.00 | 1.63 | 10.19 |
time (sec) |
N/A | 0.386 | 0.229 | 0.766 | 0.000 | 0.315 | 0.000 | 0.272 | 42.593 |
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 | 51 | 56 | 50 | 53 | 0 | 349 | 0 | 73 | 47 |
N.S. |
1 | 1.10 | 0.98 | 1.04 | 0.00 | 6.84 | 0.00 | 1.43 | 0.92 |
time (sec) |
N/A | 0.274 | 0.044 | 0.654 | 0.000 | 0.316 | 0.000 | 0.289 | 27.996 |
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 | 142 | 148 | 120 | 180 | 0 | 663 | 0 | 161 | 977 |
N.S. |
1 | 1.04 | 0.85 | 1.27 | 0.00 | 4.67 | 0.00 | 1.13 | 6.88 |
time (sec) |
N/A | 0.653 | 0.341 | 1.510 | 0.000 | 1.620 | 0.000 | 0.310 | 39.084 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 371 | 337 | 2490 | 64069 | 0 | 1504 | 0 | 0 | 0 |
N.S. |
1 | 0.91 | 6.71 | 172.69 | 0.00 | 4.05 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.448 | 6.819 | 29.328 | 0.000 | 0.159 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 1580 | 2660 | 0 | 1367 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 13.39 | 22.54 | 0.00 | 11.58 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.506 | 6.803 | 26.931 | 0.000 | 0.138 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 339 | 1018 | 0 | 504 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.87 | 8.63 | 0.00 | 4.27 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.498 | 1.262 | 25.329 | 0.000 | 0.101 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | F(-1) | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 240 | 237 | 1732 | 40064 | 0 | 1724 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 7.22 | 166.93 | 0.00 | 7.18 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.738 | 6.943 | 20.450 | 0.000 | 0.158 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 492 | 443 | 2708 | 155460 | 0 | 2769 | 0 | 0 | 0 |
N.S. |
1 | 0.90 | 5.50 | 315.98 | 0.00 | 5.63 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.849 | 7.014 | 25.615 | 0.000 | 0.295 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 371 | 337 | 81485 | 64099 | 0 | 1500 | 0 | 0 | 0 |
N.S. |
1 | 0.91 | 219.64 | 172.77 | 0.00 | 4.04 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.315 | 36.993 | 26.216 | 0.000 | 0.150 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 54676 | 2660 | 0 | 1371 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 463.36 | 22.54 | 0.00 | 11.62 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.513 | 32.799 | 24.267 | 0.000 | 0.136 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 506 | 1012 | 0 | 506 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 4.29 | 8.58 | 0.00 | 4.29 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.511 | 16.024 | 25.260 | 0.000 | 0.101 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 240 | 237 | 54829 | 40403 | 0 | 1752 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 228.45 | 168.35 | 0.00 | 7.30 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.739 | 32.543 | 21.589 | 0.000 | 0.154 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 492 | 443 | 81703 | 155452 | 0 | 2816 | 0 | 0 | 0 |
N.S. |
1 | 0.90 | 166.06 | 315.96 | 0.00 | 5.72 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.790 | 33.649 | 25.230 | 0.000 | 0.248 | 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 | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 103 | 80 | 176 | 0 | 555 | 0 | 158 | 965 |
N.S. |
1 | 1.05 | 0.82 | 1.80 | 0.00 | 5.66 | 0.00 | 1.61 | 9.85 |
time (sec) |
N/A | 0.377 | 0.332 | 0.758 | 0.000 | 0.305 | 0.000 | 0.283 | 41.768 |
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 | 51 | 56 | 50 | 53 | 0 | 349 | 0 | 73 | 47 |
N.S. |
1 | 1.10 | 0.98 | 1.04 | 0.00 | 6.84 | 0.00 | 1.43 | 0.92 |
time (sec) |
N/A | 0.270 | 0.054 | 0.682 | 0.000 | 0.305 | 0.000 | 0.276 | 27.288 |
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 | 120 | 120 | 104 | 123 | 0 | 669 | 0 | 142 | 531 |
N.S. |
1 | 1.00 | 0.87 | 1.02 | 0.00 | 5.58 | 0.00 | 1.18 | 4.42 |
time (sec) |
N/A | 0.599 | 0.982 | 1.052 | 0.000 | 1.667 | 0.000 | 0.286 | 35.161 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 17 | 51 | 10 | 14 | 24 | 0 | 22 | 9 |
N.S. |
1 | 0.81 | 2.43 | 0.48 | 0.67 | 1.14 | 0.00 | 1.05 | 0.43 |
time (sec) |
N/A | 0.240 | 0.037 | 0.437 | 0.317 | 0.248 | 0.000 | 0.271 | 27.333 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 371 | 337 | 2490 | 21493 | 0 | 1511 | 0 | 0 | 0 |
N.S. |
1 | 0.91 | 6.71 | 57.93 | 0.00 | 4.07 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.438 | 6.813 | 29.776 | 0.000 | 0.149 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 1580 | 1862 | 0 | 1361 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 13.39 | 15.78 | 0.00 | 11.53 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.521 | 6.678 | 28.197 | 0.000 | 0.142 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 339 | 644 | 0 | 508 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.87 | 5.46 | 0.00 | 4.31 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.508 | 1.082 | 31.073 | 0.000 | 0.102 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 240 | 237 | 1732 | 12702 | 0 | 1711 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 7.22 | 52.92 | 0.00 | 7.13 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.770 | 6.876 | 25.719 | 0.000 | 0.161 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 492 | 443 | 2708 | 59351 | 0 | 2777 | 0 | 0 | 0 |
N.S. |
1 | 0.90 | 5.50 | 120.63 | 0.00 | 5.64 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.827 | 7.193 | 29.434 | 0.000 | 0.296 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 371 | 337 | 5904 | 21719 | 0 | 1500 | 0 | 0 | 0 |
N.S. |
1 | 0.91 | 15.91 | 58.54 | 0.00 | 4.04 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.358 | 26.310 | 28.387 | 0.000 | 0.147 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 5835 | 1851 | 0 | 1371 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 49.45 | 15.69 | 0.00 | 11.62 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.517 | 16.941 | 23.301 | 0.000 | 0.136 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 519 | 716 | 0 | 506 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 4.40 | 6.07 | 0.00 | 4.29 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.541 | 18.765 | 28.566 | 0.000 | 0.098 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 240 | 237 | 5959 | 12838 | 0 | 1746 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 24.83 | 53.49 | 0.00 | 7.28 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.786 | 17.465 | 26.129 | 0.000 | 0.148 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 492 | 443 | 6066 | 60004 | 0 | 2798 | 0 | 0 | 0 |
N.S. |
1 | 0.90 | 12.33 | 121.96 | 0.00 | 5.69 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.829 | 18.635 | 28.204 | 0.000 | 0.253 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 1 | 1 | 1 | 2 | 1 | 1 | 10 | 1 | 1 |
N.S. |
1 | 1.00 | 1.00 | 2.00 | 1.00 | 1.00 | 10.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.150 | 0.019 | 0.300 | 0.305 | 0.221 | 0.195 | 0.285 | 28.216 |
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 | 1 | 1 | 1 | 2 | 1 | 1 | 22 | 1 | 1 |
N.S. |
1 | 1.00 | 1.00 | 2.00 | 1.00 | 1.00 | 22.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.153 | 0.004 | 0.241 | 0.288 | 0.225 | 0.326 | 0.281 | 27.814 |
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 | 1 | 1 | 1 | 2 | 1 | 1 | 34 | 1 | 1 |
N.S. |
1 | 1.00 | 1.00 | 2.00 | 1.00 | 1.00 | 34.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.156 | 0.001 | 0.230 | 0.304 | 0.217 | 0.604 | 0.281 | 27.169 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 11 | 3 | 9 | 4 | 15 | 23 | 36 | 33 | 3 |
N.S. |
1 | 0.27 | 0.82 | 0.36 | 1.36 | 2.09 | 3.27 | 3.00 | 0.27 |
time (sec) |
N/A | 0.168 | 0.049 | 0.595 | 0.205 | 0.243 | 0.174 | 0.284 | 27.891 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 8 | 13 | 12 | 15 | 48 | 6 | 6 |
N.S. |
1 | 1.00 | 0.62 | 1.00 | 0.92 | 1.15 | 3.69 | 0.46 | 0.46 |
time (sec) |
N/A | 0.177 | 0.027 | 0.524 | 0.205 | 0.229 | 0.634 | 0.279 | 27.177 |
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 | 32 | 30 | 22 | 48 | 38 | 74 | 765 | 37 | 32 |
N.S. |
1 | 0.94 | 0.69 | 1.50 | 1.19 | 2.31 | 23.91 | 1.16 | 1.00 |
time (sec) |
N/A | 0.193 | 0.034 | 0.766 | 0.225 | 0.246 | 1.614 | 0.276 | 27.572 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 10 | 9 | 35 | 12007 | 20 | 9 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 1.00 | 3.89 | 1334.11 | 2.22 | 1.00 |
time (sec) |
N/A | 0.181 | 0.124 | 1.798 | 0.284 | 0.253 | 8.295 | 0.278 | 29.704 |
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 | 11 | 11 | 11 | 12 | 11 | 31 | 30189 | 22 | 11 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 1.00 | 2.82 | 2744.45 | 2.00 | 1.00 |
time (sec) |
N/A | 0.183 | 0.085 | 3.571 | 0.300 | 0.254 | 10.340 | 0.270 | 27.904 |
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 | 15 | 15 | 15 | 16 | 15 | 43 | 71839 | 26 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.00 | 2.87 | 4789.27 | 1.73 | 1.00 |
time (sec) |
N/A | 0.193 | 0.074 | 3.513 | 0.315 | 0.255 | 15.531 | 0.286 | 28.071 |
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 | 53 | 25 | 25 | 18 | 17 | 43 | 87 | 61 | 36 |
N.S. |
1 | 0.47 | 0.47 | 0.34 | 0.32 | 0.81 | 1.64 | 1.15 | 0.68 |
time (sec) |
N/A | 0.187 | 0.156 | 0.677 | 0.315 | 0.245 | 0.321 | 0.294 | 28.914 |
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 | 45 | 36 | 38 | 35 | 182 | 216 | 48 | 51 |
N.S. |
1 | 1.05 | 0.84 | 0.88 | 0.81 | 4.23 | 5.02 | 1.12 | 1.19 |
time (sec) |
N/A | 0.291 | 0.305 | 0.530 | 0.302 | 0.276 | 0.583 | 0.280 | 27.917 |
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 | 45 | 36 | 38 | 35 | 181 | 211 | 48 | 48 |
N.S. |
1 | 1.05 | 0.84 | 0.88 | 0.81 | 4.21 | 4.91 | 1.12 | 1.12 |
time (sec) |
N/A | 0.266 | 0.089 | 0.516 | 0.323 | 0.260 | 0.594 | 0.272 | 27.645 |
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 | 36 | 21 | 19 | 18 | 15 | 35 | 0 | 15 | 15 |
N.S. |
1 | 0.58 | 0.53 | 0.50 | 0.42 | 0.97 | 0.00 | 0.42 | 0.42 |
time (sec) |
N/A | 0.191 | 0.141 | 3.813 | 0.282 | 0.254 | 0.000 | 0.264 | 27.151 |
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 | 49 | 33 | 42 | 27 | 27 | 68 | 0 | 27 | 27 |
N.S. |
1 | 0.67 | 0.86 | 0.55 | 0.55 | 1.39 | 0.00 | 0.55 | 0.55 |
time (sec) |
N/A | 0.210 | 0.255 | 0.280 | 0.297 | 0.252 | 0.000 | 0.268 | 27.224 |
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 | 74 | 64 | 79 | 2 | 45 | 100 | 0 | 39 | 40 |
N.S. |
1 | 0.86 | 1.07 | 0.03 | 0.61 | 1.35 | 0.00 | 0.53 | 0.54 |
time (sec) |
N/A | 0.222 | 0.254 | 14.445 | 0.291 | 0.259 | 0.000 | 0.271 | 28.557 |
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 | 1 | 1 | 1 | 2 | 1 | 1 | 0 | 1 | 1 |
N.S. |
1 | 1.00 | 1.00 | 2.00 | 1.00 | 1.00 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.157 | 0.001 | 0.518 | 0.297 | 0.229 | 0.000 | 0.263 | 27.835 |
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 | 1 | 1 | 1 | 2 | 1 | 1 | 0 | 1 | 1 |
N.S. |
1 | 1.00 | 1.00 | 2.00 | 1.00 | 1.00 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.160 | 0.003 | 5.348 | 0.296 | 0.224 | 0.000 | 0.257 | 27.109 |
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 | 1 | 1 | 1 | 2 | 1 | 1 | 0 | 1 | 1 |
N.S. |
1 | 1.00 | 1.00 | 2.00 | 1.00 | 1.00 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.159 | 0.001 | 59.677 | 0.289 | 0.220 | 0.000 | 0.266 | 28.384 |
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 | 37 | 21 | 19 | 19 | 16 | 35 | 0 | 49 | 16 |
N.S. |
1 | 0.57 | 0.51 | 0.51 | 0.43 | 0.95 | 0.00 | 1.32 | 0.43 |
time (sec) |
N/A | 0.187 | 0.123 | 3.243 | 0.288 | 0.247 | 0.000 | 0.278 | 27.624 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 32 | 64 | 28 | 27 | 66 | 0 | 60 | 27 |
N.S. |
1 | 0.68 | 1.36 | 0.60 | 0.57 | 1.40 | 0.00 | 1.28 | 0.57 |
time (sec) |
N/A | 0.200 | 0.174 | 0.320 | 0.311 | 0.267 | 0.000 | 0.263 | 27.913 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 62 | 66 | 2 | 42 | 98 | 0 | 69 | 43 |
N.S. |
1 | 0.86 | 0.92 | 0.03 | 0.58 | 1.36 | 0.00 | 0.96 | 0.60 |
time (sec) |
N/A | 0.238 | 0.237 | 11.542 | 0.312 | 0.244 | 0.000 | 0.269 | 29.586 |
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 | 3 | 3 | 3 | 4 | 3 | 3 | 0 | 3 | 3 |
N.S. |
1 | 1.00 | 1.00 | 1.33 | 1.00 | 1.00 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.163 | 0.001 | 0.463 | 0.306 | 0.230 | 0.000 | 0.273 | 26.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 1 | 1 | 1 | 2 | 1 | 1 | 0 | 1 | 1 |
N.S. |
1 | 1.00 | 1.00 | 2.00 | 1.00 | 1.00 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.162 | 0.001 | 3.673 | 0.310 | 0.233 | 0.000 | 0.279 | 27.007 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 3 | 3 | 3 | 4 | 3 | 3 | 0 | 3 | 3 |
N.S. |
1 | 1.00 | 1.00 | 1.33 | 1.00 | 1.00 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.168 | 0.001 | 37.707 | 0.292 | 0.226 | 0.000 | 0.267 | 26.513 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 27 | 26 | 259 | 0 | 61 | 43 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.79 | 7.85 | 0.00 | 1.85 | 1.30 |
time (sec) |
N/A | 0.209 | 0.116 | 0.598 | 0.290 | 0.282 | 0.000 | 0.264 | 27.186 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 239 | 261 | 1022 | 820 | 0 | 2869 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 4.28 | 3.43 | 0.00 | 12.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.880 | 1.229 | 0.909 | 0.000 | 4.762 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 365 | 369 | 279 | 1161 | 0 | 4289 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.76 | 3.18 | 0.00 | 11.75 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.292 | 5.661 | 0.914 | 0.000 | 3.362 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 195 | 234 | 149 | 172 | 246 | 150 | 566 | 158 | 456 |
N.S. |
1 | 1.20 | 0.76 | 0.88 | 1.26 | 0.77 | 2.90 | 0.81 | 2.34 |
time (sec) |
N/A | 0.882 | 2.400 | 2.348 | 0.218 | 0.258 | 0.326 | 0.310 | 29.601 |
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 | 109 | 113 | 77 | 90 | 112 | 76 | 204 | 79 | 88 |
N.S. |
1 | 1.04 | 0.71 | 0.83 | 1.03 | 0.70 | 1.87 | 0.72 | 0.81 |
time (sec) |
N/A | 0.360 | 1.125 | 1.093 | 0.223 | 0.258 | 0.138 | 0.269 | 27.241 |