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 | A | A | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 52 | 55 | 0 | 193 | 0 | 151 | 123 | 169 |
N.S. |
1 | 1.00 | 0.83 | 0.87 | 0.00 | 3.06 | 0.00 | 2.40 | 1.95 | 2.68 |
time (sec) |
N/A | 0.371 | 0.071 | 2.644 | 0.000 | 0.109 | 0.000 | 0.299 | 0.241 | 7.307 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 128 | 67 | 72 | 0 | 318 | 0 | 268 | 179 | 246 |
N.S. |
1 | 1.00 | 0.52 | 0.56 | 0.00 | 2.48 | 0.00 | 2.09 | 1.40 | 1.92 |
time (sec) |
N/A | 0.544 | 0.163 | 2.789 | 0.000 | 0.153 | 0.000 | 0.156 | 0.248 | 7.571 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 205 | 103 | 121 | 0 | 667 | 0 | 633 | 389 | 255 |
N.S. |
1 | 1.06 | 0.53 | 0.63 | 0.00 | 3.46 | 0.00 | 3.28 | 2.02 | 1.32 |
time (sec) |
N/A | 0.738 | 0.216 | 3.188 | 0.000 | 0.303 | 0.000 | 0.267 | 0.264 | 7.564 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 260 | 285 | 152 | 191 | 0 | 1065 | 0 | 1119 | 760 | 416 |
N.S. |
1 | 1.10 | 0.58 | 0.73 | 0.00 | 4.10 | 0.00 | 4.30 | 2.92 | 1.60 |
time (sec) |
N/A | 0.955 | 0.308 | 2.921 | 0.000 | 0.830 | 0.000 | 0.520 | 0.283 | 7.794 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 122 | 100 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.468 | 0.340 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.454 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 120 | 100 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.432 | 0.215 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.364 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 118 | 98 | 0 | 0 | 0 | 0 | 0 | 520 | 0 |
N.S. |
1 | 1.07 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 4.73 | 0.00 |
time (sec) |
N/A | 0.440 | 0.212 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.308 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 110 | 98 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.437 | 0.290 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.321 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 122 | 100 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.27 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.495 | 0.413 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.400 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 122 | 110 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.463 | 0.480 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.458 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 107 | 95 | 0 | 0 | 0 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.08 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.441 | 0.116 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 260 | 324 | 134 | 527 | 331 | 705 | 0 | 1926 | 180 | 615 |
N.S. |
1 | 1.25 | 0.52 | 2.03 | 1.27 | 2.71 | 0.00 | 7.41 | 0.69 | 2.37 |
time (sec) |
N/A | 0.997 | 0.437 | 10.310 | 0.083 | 0.106 | 0.000 | 0.211 | 0.268 | 6.360 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 237 | 131 | 235 | 193 | 350 | 0 | 929 | 131 | 327 |
N.S. |
1 | 1.25 | 0.69 | 1.24 | 1.02 | 1.84 | 0.00 | 4.89 | 0.69 | 1.72 |
time (sec) |
N/A | 0.711 | 0.327 | 5.908 | 0.092 | 0.098 | 0.000 | 0.184 | 0.250 | 6.401 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-2) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 150 | 67 | 89 | 94 | 145 | 0 | 347 | 82 | 139 |
N.S. |
1 | 1.25 | 0.56 | 0.74 | 0.78 | 1.21 | 0.00 | 2.89 | 0.68 | 1.16 |
time (sec) |
N/A | 0.479 | 0.181 | 3.747 | 0.054 | 0.111 | 0.000 | 0.222 | 0.267 | 6.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-2) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 42 | 57 | 33 | 57 | 0 | 81 | 38 | 57 |
N.S. |
1 | 1.00 | 0.78 | 1.06 | 0.61 | 1.06 | 0.00 | 1.50 | 0.70 | 1.06 |
time (sec) |
N/A | 0.303 | 0.015 | 2.940 | 0.068 | 0.083 | 0.000 | 0.176 | 0.270 | 6.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 99 | 82 | 0 | 0 | 0 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.04 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.415 | 0.111 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.276 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 101 | 84 | 0 | 0 | 0 | 0 | 0 | 107 | 0 |
N.S. |
1 | 1.04 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.10 | 0.00 |
time (sec) |
N/A | 0.409 | 0.110 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 105 | 88 | 0 | 0 | 0 | 0 | 0 | 144 | 0 |
N.S. |
1 | 1.04 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.43 | 0.00 |
time (sec) |
N/A | 0.421 | 0.122 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.268 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 93 | 0 | 0 | 0 | 0 | 0 | 94 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.433 | 0.292 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.364 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 93 | 0 | 0 | 0 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.416 | 0.197 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 91 | 0 | 0 | 0 | 0 | 0 | 76 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.416 | 0.221 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.296 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 91 | 0 | 0 | 0 | 0 | 0 | 113 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.10 | 0.00 |
time (sec) |
N/A | 0.410 | 0.290 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 93 | 0 | 0 | 0 | 0 | 0 | 150 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.43 | 0.00 |
time (sec) |
N/A | 0.425 | 0.362 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 65 | 52 | 64 | 49 | 66 | 0 | 106 | 48 | 63 |
N.S. |
1 | 1.03 | 0.83 | 1.02 | 0.78 | 1.05 | 0.00 | 1.68 | 0.76 | 1.00 |
time (sec) |
N/A | 0.352 | 0.022 | 9.397 | 0.045 | 0.090 | 0.000 | 0.130 | 0.248 | 6.243 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 81 | 64 | 0 | 32 | 35 | 0 | 0 | 99 | 0 |
N.S. |
1 | 1.04 | 0.82 | 0.00 | 0.41 | 0.45 | 0.00 | 0.00 | 1.27 | 0.00 |
time (sec) |
N/A | 0.510 | 0.042 | 0.000 | 0.049 | 0.083 | 0.000 | 0.000 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 222 | 145 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.735 | 0.393 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.521 | 0.000 |
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 | 438 | 438 | 380 | 623 | 693 | 597 | 0 | 1159 | 608 | 653 |
N.S. |
1 | 1.00 | 0.87 | 1.42 | 1.58 | 1.36 | 0.00 | 2.65 | 1.39 | 1.49 |
time (sec) |
N/A | 1.524 | 0.532 | 3.432 | 0.115 | 0.098 | 0.000 | 0.141 | 0.290 | 6.595 |
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 | 352 | 362 | 264 | 407 | 484 | 408 | 0 | 755 | 392 | 438 |
N.S. |
1 | 1.03 | 0.75 | 1.16 | 1.38 | 1.16 | 0.00 | 2.14 | 1.11 | 1.24 |
time (sec) |
N/A | 1.190 | 0.338 | 3.562 | 0.092 | 0.093 | 0.000 | 0.138 | 0.231 | 6.786 |
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 | 270 | 286 | 169 | 237 | 309 | 256 | 0 | 439 | 222 | 279 |
N.S. |
1 | 1.06 | 0.63 | 0.88 | 1.14 | 0.95 | 0.00 | 1.63 | 0.82 | 1.03 |
time (sec) |
N/A | 0.970 | 0.229 | 3.573 | 0.078 | 0.088 | 0.000 | 0.124 | 0.278 | 6.750 |
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 | 186 | 189 | 96 | 113 | 168 | 141 | 0 | 211 | 98 | 152 |
N.S. |
1 | 1.02 | 0.52 | 0.61 | 0.90 | 0.76 | 0.00 | 1.13 | 0.53 | 0.82 |
time (sec) |
N/A | 0.634 | 0.131 | 3.561 | 0.066 | 0.084 | 0.000 | 0.116 | 0.264 | 6.653 |
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 | 108 | 110 | 54 | 51 | 65 | 73 | 0 | 89 | 35 | 85 |
N.S. |
1 | 1.02 | 0.50 | 0.47 | 0.60 | 0.68 | 0.00 | 0.82 | 0.32 | 0.79 |
time (sec) |
N/A | 0.392 | 0.071 | 2.243 | 0.048 | 0.094 | 0.000 | 0.107 | 0.229 | 6.620 |
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 | 139 | 139 | 140 | 153 | 0 | 512 | 0 | 132 | 153 | 0 |
N.S. |
1 | 1.00 | 1.01 | 1.10 | 0.00 | 3.68 | 0.00 | 0.95 | 1.10 | 0.00 |
time (sec) |
N/A | 0.607 | 0.247 | 2.983 | 0.000 | 0.121 | 0.000 | 0.120 | 0.240 | 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 | 169 | 170 | 154 | 337 | 0 | 897 | 0 | 254 | 444 | 0 |
N.S. |
1 | 1.01 | 0.91 | 1.99 | 0.00 | 5.31 | 0.00 | 1.50 | 2.63 | 0.00 |
time (sec) |
N/A | 0.709 | 0.746 | 3.046 | 0.000 | 0.127 | 0.000 | 0.128 | 0.261 | 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 | 261 | 252 | 200 | 663 | 0 | 1705 | 0 | 533 | 927 | 0 |
N.S. |
1 | 0.97 | 0.77 | 2.54 | 0.00 | 6.53 | 0.00 | 2.04 | 3.55 | 0.00 |
time (sec) |
N/A | 0.922 | 1.460 | 2.971 | 0.000 | 0.164 | 0.000 | 0.140 | 0.270 | 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 | 351 | 332 | 279 | 1132 | 0 | 2737 | 0 | 875 | 1527 | 0 |
N.S. |
1 | 0.95 | 0.79 | 3.23 | 0.00 | 7.80 | 0.00 | 2.49 | 4.35 | 0.00 |
time (sec) |
N/A | 1.197 | 1.851 | 2.905 | 0.000 | 0.873 | 0.000 | 0.159 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 350 | 378 | 448 | 2477 | 0 | 1469 | 2919 | 755 | 2564 | 3311 |
N.S. |
1 | 1.08 | 1.28 | 7.08 | 0.00 | 4.20 | 8.34 | 2.16 | 7.33 | 9.46 |
time (sec) |
N/A | 1.191 | 1.612 | 3.415 | 0.000 | 0.771 | 1.608 | 0.156 | 2.053 | 9.641 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 277 | 313 | 349 | 1375 | 0 | 1117 | 1608 | 568 | 1875 | 1732 |
N.S. |
1 | 1.13 | 1.26 | 4.96 | 0.00 | 4.03 | 5.81 | 2.05 | 6.77 | 6.25 |
time (sec) |
N/A | 0.969 | 1.330 | 2.745 | 0.000 | 0.350 | 1.577 | 0.162 | 0.946 | 8.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 218 | 215 | 269 | 724 | 0 | 825 | 952 | 409 | 1300 | 801 |
N.S. |
1 | 0.99 | 1.23 | 3.32 | 0.00 | 3.78 | 4.37 | 1.88 | 5.96 | 3.67 |
time (sec) |
N/A | 0.688 | 0.893 | 2.250 | 0.000 | 0.195 | 2.364 | 0.155 | 0.490 | 7.272 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 148 | 181 | 293 | 0 | 395 | 0 | 178 | 490 | 0 |
N.S. |
1 | 1.03 | 1.27 | 2.05 | 0.00 | 2.76 | 0.00 | 1.24 | 3.43 | 0.00 |
time (sec) |
N/A | 0.673 | 0.895 | 2.447 | 0.000 | 0.111 | 0.000 | 0.142 | 0.265 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 176 | 129 | 372 | 0 | 399 | 0 | 294 | 692 | 0 |
N.S. |
1 | 1.12 | 0.82 | 2.37 | 0.00 | 2.54 | 0.00 | 1.87 | 4.41 | 0.00 |
time (sec) |
N/A | 0.715 | 0.482 | 2.941 | 0.000 | 0.399 | 0.000 | 0.212 | 0.269 | 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 | 163 | 186 | 160 | 299 | 0 | 579 | 0 | 517 | 1004 | 0 |
N.S. |
1 | 1.14 | 0.98 | 1.83 | 0.00 | 3.55 | 0.00 | 3.17 | 6.16 | 0.00 |
time (sec) |
N/A | 0.739 | 0.439 | 3.392 | 0.000 | 0.749 | 0.000 | 0.943 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 154 | 102 | 128 | 0 | 307 | 0 | 0 | 1197 | 1022 |
N.S. |
1 | 1.12 | 0.74 | 0.93 | 0.00 | 2.24 | 0.00 | 0.00 | 8.74 | 7.46 |
time (sec) |
N/A | 0.667 | 0.250 | 4.206 | 0.000 | 3.979 | 0.000 | 0.000 | 0.345 | 7.304 |
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 | 210 | 236 | 166 | 236 | 0 | 540 | 0 | 1619 | 1918 | 2325 |
N.S. |
1 | 1.12 | 0.79 | 1.12 | 0.00 | 2.57 | 0.00 | 7.71 | 9.13 | 11.07 |
time (sec) |
N/A | 0.836 | 0.296 | 5.193 | 0.000 | 26.503 | 0.000 | 0.167 | 0.663 | 8.894 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 285 | 317 | 244 | 382 | 0 | 817 | 0 | 0 | 2777 | 4962 |
N.S. |
1 | 1.11 | 0.86 | 1.34 | 0.00 | 2.87 | 0.00 | 0.00 | 9.74 | 17.41 |
time (sec) |
N/A | 1.016 | 0.392 | 6.715 | 0.000 | 107.640 | 0.000 | 0.000 | 1.511 | 13.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 360 | 394 | 347 | 564 | 0 | 0 | 0 | 0 | 3784 | 10084 |
N.S. |
1 | 1.09 | 0.96 | 1.57 | 0.00 | 0.00 | 0.00 | 0.00 | 10.51 | 28.01 |
time (sec) |
N/A | 1.194 | 0.516 | 8.764 | 0.000 | 0.000 | 0.000 | 0.000 | 3.704 | 21.584 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 439 | 476 | 466 | 782 | 0 | 0 | 0 | 0 | 4939 | 19572 |
N.S. |
1 | 1.08 | 1.06 | 1.78 | 0.00 | 0.00 | 0.00 | 0.00 | 11.25 | 44.58 |
time (sec) |
N/A | 1.421 | 0.676 | 11.363 | 0.000 | 0.000 | 0.000 | 0.000 | 8.320 | 37.472 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 424 | 441 | 733 | 3509 | 0 | 2337 | 9527 | 1229 | 4284 | 0 |
N.S. |
1 | 1.04 | 1.73 | 8.28 | 0.00 | 5.51 | 22.47 | 2.90 | 10.10 | 0.00 |
time (sec) |
N/A | 1.277 | 3.764 | 3.528 | 0.000 | 3.432 | 1.775 | 0.424 | 11.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 351 | 376 | 592 | 1977 | 0 | 1877 | 5834 | 983 | 3367 | 0 |
N.S. |
1 | 1.07 | 1.69 | 5.63 | 0.00 | 5.35 | 16.62 | 2.80 | 9.59 | 0.00 |
time (sec) |
N/A | 1.112 | 2.922 | 2.883 | 0.000 | 1.738 | 1.622 | 0.380 | 4.957 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 278 | 473 | 1068 | 0 | 1473 | 3228 | 765 | 2564 | 0 |
N.S. |
1 | 0.95 | 1.62 | 3.66 | 0.00 | 5.04 | 11.05 | 2.62 | 8.78 | 0.00 |
time (sec) |
N/A | 0.795 | 2.217 | 2.411 | 0.000 | 0.777 | 2.090 | 0.380 | 1.920 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 218 | 215 | 292 | 475 | 0 | 809 | 1958 | 408 | 1300 | 0 |
N.S. |
1 | 0.99 | 1.34 | 2.18 | 0.00 | 3.71 | 8.98 | 1.87 | 5.96 | 0.00 |
time (sec) |
N/A | 0.788 | 1.177 | 2.549 | 0.000 | 0.190 | 3.226 | 0.359 | 0.462 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 262 | 220 | 564 | 0 | 567 | 0 | 1297 | 839 | 0 |
N.S. |
1 | 1.24 | 1.04 | 2.67 | 0.00 | 2.69 | 0.00 | 6.15 | 3.98 | 0.00 |
time (sec) |
N/A | 0.818 | 0.830 | 2.864 | 0.000 | 0.216 | 0.000 | 0.663 | 0.332 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 220 | 258 | 217 | 732 | 0 | 635 | 0 | 405 | 1201 | 0 |
N.S. |
1 | 1.17 | 0.99 | 3.33 | 0.00 | 2.89 | 0.00 | 1.84 | 5.46 | 0.00 |
time (sec) |
N/A | 0.843 | 1.479 | 3.388 | 0.000 | 0.596 | 0.000 | 0.395 | 0.317 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 220 | 260 | 187 | 900 | 0 | 593 | 0 | 582 | 1184 | 0 |
N.S. |
1 | 1.18 | 0.85 | 4.09 | 0.00 | 2.70 | 0.00 | 2.65 | 5.38 | 0.00 |
time (sec) |
N/A | 0.925 | 0.620 | 4.451 | 0.000 | 1.093 | 0.000 | 1.605 | 0.355 | 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 | 210 | 221 | 237 | 563 | 0 | 879 | 0 | 1592 | 1667 | 0 |
N.S. |
1 | 1.05 | 1.13 | 2.68 | 0.00 | 4.19 | 0.00 | 7.58 | 7.94 | 0.00 |
time (sec) |
N/A | 0.816 | 0.733 | 5.424 | 0.000 | 5.385 | 0.000 | 0.436 | 0.451 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 137 | 104 | 128 | 0 | 464 | 0 | 0 | 1837 | 3763 |
N.S. |
1 | 0.99 | 0.75 | 0.93 | 0.00 | 3.36 | 0.00 | 0.00 | 13.31 | 27.27 |
time (sec) |
N/A | 0.603 | 0.304 | 6.592 | 0.000 | 25.682 | 0.000 | 0.000 | 0.747 | 11.117 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 213 | 168 | 236 | 0 | 739 | 0 | 0 | 2680 | 8039 |
N.S. |
1 | 1.01 | 0.80 | 1.12 | 0.00 | 3.52 | 0.00 | 0.00 | 12.76 | 38.28 |
time (sec) |
N/A | 0.752 | 0.372 | 8.709 | 0.000 | 102.834 | 0.000 | 0.000 | 1.699 | 17.587 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 285 | 286 | 249 | 382 | 0 | 0 | 0 | 0 | 3670 | 16485 |
N.S. |
1 | 1.00 | 0.87 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 | 12.88 | 57.84 |
time (sec) |
N/A | 0.868 | 0.503 | 11.036 | 0.000 | 0.000 | 0.000 | 0.000 | 4.036 | 30.258 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F(-1) | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 360 | 359 | 349 | 564 | 0 | 0 | 0 | 0 | 4808 | 33375 |
N.S. |
1 | 1.00 | 0.97 | 1.57 | 0.00 | 0.00 | 0.00 | 0.00 | 13.36 | 92.71 |
time (sec) |
N/A | 1.013 | 0.689 | 18.306 | 0.000 | 0.000 | 0.000 | 0.000 | 8.294 | 53.007 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 498 | 504 | 1013 | 4541 | 0 | 3437 | 29237 | 1818 | 6460 | 0 |
N.S. |
1 | 1.01 | 2.03 | 9.12 | 0.00 | 6.90 | 58.71 | 3.65 | 12.97 | 0.00 |
time (sec) |
N/A | 1.430 | 7.388 | 3.687 | 0.000 | 13.078 | 2.298 | 0.486 | 48.694 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 425 | 439 | 847 | 2579 | 0 | 2861 | 18144 | 1512 | 5315 | 0 |
N.S. |
1 | 1.03 | 1.99 | 6.07 | 0.00 | 6.73 | 42.69 | 3.56 | 12.51 | 0.00 |
time (sec) |
N/A | 1.285 | 7.179 | 2.856 | 0.000 | 6.430 | 1.837 | 0.409 | 20.642 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 366 | 341 | 733 | 1412 | 0 | 2345 | 11123 | 1234 | 4284 | 0 |
N.S. |
1 | 0.93 | 2.00 | 3.86 | 0.00 | 6.41 | 30.39 | 3.37 | 11.70 | 0.00 |
time (sec) |
N/A | 0.956 | 4.701 | 2.405 | 0.000 | 3.320 | 2.402 | 0.410 | 8.499 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 280 | 471 | 655 | 0 | 1457 | 7917 | 758 | 2564 | 0 |
N.S. |
1 | 0.96 | 1.61 | 2.24 | 0.00 | 4.99 | 27.11 | 2.60 | 8.78 | 0.00 |
time (sec) |
N/A | 0.957 | 2.571 | 2.501 | 0.000 | 0.725 | 8.626 | 0.398 | 1.734 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 285 | 330 | 376 | 752 | 1751 | 1097 | 4675 | 3630 | 1875 | 0 |
N.S. |
1 | 1.16 | 1.32 | 2.64 | 6.14 | 3.85 | 16.40 | 12.74 | 6.58 | 0.00 |
time (sec) |
N/A | 0.971 | 1.600 | 2.808 | 0.169 | 0.373 | 10.487 | 1.220 | 0.868 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 327 | 292 | 920 | 0 | 813 | 0 | 410 | 1300 | 0 |
N.S. |
1 | 1.12 | 1.00 | 3.15 | 0.00 | 2.78 | 0.00 | 1.40 | 4.45 | 0.00 |
time (sec) |
N/A | 1.029 | 1.457 | 3.257 | 0.000 | 0.377 | 0.000 | 0.400 | 0.442 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 290 | 309 | 258 | 1088 | 0 | 931 | 0 | 503 | 1826 | 0 |
N.S. |
1 | 1.07 | 0.89 | 3.75 | 0.00 | 3.21 | 0.00 | 1.73 | 6.30 | 0.00 |
time (sec) |
N/A | 1.008 | 1.520 | 4.227 | 0.000 | 1.037 | 0.000 | 0.432 | 0.414 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 297 | 326 | 267 | 1256 | 0 | 951 | 0 | 1076 | 2027 | 0 |
N.S. |
1 | 1.10 | 0.90 | 4.23 | 0.00 | 3.20 | 0.00 | 3.62 | 6.82 | 0.00 |
time (sec) |
N/A | 1.311 | 3.437 | 5.322 | 0.000 | 1.882 | 0.000 | 0.658 | 0.531 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 281 | 311 | 248 | 1424 | 0 | 917 | 0 | 818 | 2008 | 0 |
N.S. |
1 | 1.11 | 0.88 | 5.07 | 0.00 | 3.26 | 0.00 | 2.91 | 7.15 | 0.00 |
time (sec) |
N/A | 1.046 | 1.024 | 7.117 | 0.000 | 7.313 | 0.000 | 72.477 | 0.717 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 259 | 270 | 298 | 825 | 0 | 1239 | 0 | 0 | 2439 | 0 |
N.S. |
1 | 1.04 | 1.15 | 3.19 | 0.00 | 4.78 | 0.00 | 0.00 | 9.42 | 0.00 |
time (sec) |
N/A | 0.898 | 1.165 | 9.434 | 0.000 | 34.440 | 0.000 | 0.000 | 0.983 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 137 | 104 | 128 | 0 | 646 | 0 | 0 | 2583 | 12294 |
N.S. |
1 | 0.99 | 0.75 | 0.93 | 0.00 | 4.68 | 0.00 | 0.00 | 18.72 | 89.09 |
time (sec) |
N/A | 0.635 | 0.354 | 12.240 | 0.000 | 106.886 | 0.000 | 0.000 | 1.884 | 20.371 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 213 | 169 | 236 | 0 | 0 | 0 | 0 | 3556 | 25236 |
N.S. |
1 | 1.01 | 0.80 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 16.93 | 120.17 |
time (sec) |
N/A | 0.719 | 0.413 | 20.723 | 0.000 | 0.000 | 0.000 | 0.000 | 4.185 | 37.013 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F(-1) | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 285 | 286 | 250 | 382 | 0 | 0 | 0 | 0 | 4677 | 51074 |
N.S. |
1 | 1.00 | 0.88 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 | 16.41 | 179.21 |
time (sec) |
N/A | 0.864 | 0.589 | 26.774 | 0.000 | 0.000 | 0.000 | 0.000 | 9.057 | 67.586 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F(-1) | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 360 | 359 | 351 | 564 | 0 | 0 | 0 | 0 | 5946 | 38717 |
N.S. |
1 | 1.00 | 0.98 | 1.57 | 0.00 | 0.00 | 0.00 | 0.00 | 16.52 | 107.55 |
time (sec) |
N/A | 1.016 | 0.739 | 34.843 | 0.000 | 0.000 | 0.000 | 0.000 | 18.733 | 133.293 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 276 | 313 | 289 | 1445 | 0 | 825 | 1032 | 412 | 1300 | 0 |
N.S. |
1 | 1.13 | 1.05 | 5.24 | 0.00 | 2.99 | 3.74 | 1.49 | 4.71 | 0.00 |
time (sec) |
N/A | 0.967 | 0.952 | 3.892 | 0.000 | 0.331 | 1.470 | 0.402 | 0.430 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 248 | 223 | 773 | 0 | 585 | 660 | 282 | 839 | 0 |
N.S. |
1 | 1.22 | 1.10 | 3.81 | 0.00 | 2.88 | 3.25 | 1.39 | 4.13 | 0.00 |
time (sec) |
N/A | 0.814 | 0.723 | 3.136 | 0.000 | 0.174 | 1.437 | 0.400 | 0.314 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 149 | 181 | 380 | 0 | 403 | 416 | 190 | 492 | 0 |
N.S. |
1 | 1.03 | 1.26 | 2.64 | 0.00 | 2.80 | 2.89 | 1.32 | 3.42 | 0.00 |
time (sec) |
N/A | 0.538 | 0.891 | 2.485 | 0.000 | 0.115 | 2.070 | 0.374 | 0.222 | 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 | 117 | 121 | 141 | 134 | 0 | 405 | 0 | 288 | 486 | 0 |
N.S. |
1 | 1.03 | 1.21 | 1.15 | 0.00 | 3.46 | 0.00 | 2.46 | 4.15 | 0.00 |
time (sec) |
N/A | 0.513 | 0.323 | 2.599 | 0.000 | 0.344 | 0.000 | 0.394 | 0.248 | 0.000 |
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 | 137 | 137 | 89 | 115 | 0 | 182 | 0 | 302 | 627 | 101 |
N.S. |
1 | 1.00 | 0.65 | 0.84 | 0.00 | 1.33 | 0.00 | 2.20 | 4.58 | 0.74 |
time (sec) |
N/A | 0.572 | 0.245 | 2.997 | 0.000 | 0.916 | 0.000 | 0.435 | 0.240 | 6.391 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 213 | 166 | 224 | 0 | 368 | 0 | 0 | 1262 | 471 |
N.S. |
1 | 1.01 | 0.79 | 1.07 | 0.00 | 1.75 | 0.00 | 0.00 | 6.01 | 2.24 |
time (sec) |
N/A | 0.727 | 0.281 | 3.302 | 0.000 | 4.632 | 0.000 | 0.000 | 0.318 | 6.595 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 285 | 286 | 247 | 370 | 0 | 606 | 0 | 0 | 1998 | 624 |
N.S. |
1 | 1.00 | 0.87 | 1.30 | 0.00 | 2.13 | 0.00 | 0.00 | 7.01 | 2.19 |
time (sec) |
N/A | 0.859 | 0.391 | 4.161 | 0.000 | 31.989 | 0.000 | 0.000 | 0.506 | 7.689 |
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 | 360 | 359 | 348 | 552 | 0 | 906 | 0 | 900 | 2874 | 949 |
N.S. |
1 | 1.00 | 0.97 | 1.53 | 0.00 | 2.52 | 0.00 | 2.50 | 7.98 | 2.64 |
time (sec) |
N/A | 1.001 | 0.487 | 4.887 | 0.000 | 104.865 | 0.000 | 0.336 | 1.253 | 9.616 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 263 | 235 | 1535 | 0 | 745 | 0 | 495 | 918 | 0 |
N.S. |
1 | 1.06 | 0.95 | 6.19 | 0.00 | 3.00 | 0.00 | 2.00 | 3.70 | 0.00 |
time (sec) |
N/A | 1.072 | 2.040 | 3.665 | 0.000 | 0.635 | 0.000 | 0.407 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 182 | 142 | 836 | 0 | 503 | 0 | 439 | 551 | 0 |
N.S. |
1 | 1.08 | 0.85 | 4.98 | 0.00 | 2.99 | 0.00 | 2.61 | 3.28 | 0.00 |
time (sec) |
N/A | 0.655 | 0.391 | 3.007 | 0.000 | 0.410 | 0.000 | 0.358 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 129 | 139 | 421 | 0 | 483 | 0 | 374 | 424 | 344 |
N.S. |
1 | 1.04 | 1.12 | 3.40 | 0.00 | 3.90 | 0.00 | 3.02 | 3.42 | 2.77 |
time (sec) |
N/A | 0.471 | 0.311 | 2.332 | 0.000 | 0.345 | 0.000 | 0.322 | 0.261 | 12.877 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 136 | 149 | 228 | 0 | 407 | 0 | 0 | 1113 | 872 |
N.S. |
1 | 1.00 | 1.10 | 1.68 | 0.00 | 2.99 | 0.00 | 0.00 | 8.18 | 6.41 |
time (sec) |
N/A | 0.519 | 0.309 | 2.345 | 0.000 | 3.919 | 0.000 | 0.000 | 0.238 | 11.578 |
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 | 209 | 209 | 233 | 380 | 0 | 649 | 0 | 7557 | 1782 | 2126 |
N.S. |
1 | 1.00 | 1.11 | 1.82 | 0.00 | 3.11 | 0.00 | 36.16 | 8.53 | 10.17 |
time (sec) |
N/A | 0.647 | 0.392 | 2.569 | 0.000 | 15.754 | 0.000 | 0.508 | 0.347 | 13.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 284 | 282 | 331 | 562 | 0 | 974 | 0 | 0 | 2565 | 4339 |
N.S. |
1 | 0.99 | 1.17 | 1.98 | 0.00 | 3.43 | 0.00 | 0.00 | 9.03 | 15.28 |
time (sec) |
N/A | 0.790 | 0.497 | 2.881 | 0.000 | 74.106 | 0.000 | 0.000 | 0.677 | 16.416 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 311 | 340 | 139 | 6819 | 0 | 1233 | 0 | 1051 | 2003 | 0 |
N.S. |
1 | 1.09 | 0.45 | 21.93 | 0.00 | 3.96 | 0.00 | 3.38 | 6.44 | 0.00 |
time (sec) |
N/A | 1.293 | 10.354 | 5.935 | 0.000 | 3.209 | 0.000 | 2.931 | 0.471 | 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 | 230 | 276 | 204 | 4116 | 0 | 881 | 0 | 997 | 1231 | 0 |
N.S. |
1 | 1.20 | 0.89 | 17.90 | 0.00 | 3.83 | 0.00 | 4.33 | 5.35 | 0.00 |
time (sec) |
N/A | 0.878 | 0.780 | 4.579 | 0.000 | 1.946 | 0.000 | 2.019 | 0.296 | 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 | 173 | 186 | 187 | 2417 | 0 | 785 | 0 | 943 | 987 | 0 |
N.S. |
1 | 1.08 | 1.08 | 13.97 | 0.00 | 4.54 | 0.00 | 5.45 | 5.71 | 0.00 |
time (sec) |
N/A | 0.658 | 0.584 | 3.492 | 0.000 | 1.216 | 0.000 | 1.517 | 0.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 146 | 100 | 123 | 0 | 227 | 0 | 0 | 628 | 107 |
N.S. |
1 | 1.09 | 0.75 | 0.92 | 0.00 | 1.69 | 0.00 | 0.00 | 4.69 | 0.80 |
time (sec) |
N/A | 0.572 | 0.234 | 2.736 | 0.000 | 1.268 | 0.000 | 0.000 | 0.225 | 11.554 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 146 | 151 | 225 | 0 | 431 | 0 | 0 | 1117 | 795 |
N.S. |
1 | 1.00 | 1.03 | 1.54 | 0.00 | 2.95 | 0.00 | 0.00 | 7.65 | 5.45 |
time (sec) |
N/A | 0.513 | 0.306 | 2.369 | 0.000 | 5.191 | 0.000 | 0.000 | 0.251 | 11.878 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 205 | 345 | 418 | 0 | 1028 | 0 | 0 | 2763 | 3326 |
N.S. |
1 | 0.99 | 1.66 | 2.01 | 0.00 | 4.94 | 0.00 | 0.00 | 13.28 | 15.99 |
time (sec) |
N/A | 0.642 | 0.499 | 2.398 | 0.000 | 52.098 | 0.000 | 0.000 | 0.644 | 13.637 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 283 | 278 | 468 | 598 | 0 | 0 | 0 | 22347 | 3857 | 11539 |
N.S. |
1 | 0.98 | 1.65 | 2.11 | 0.00 | 0.00 | 0.00 | 78.96 | 13.63 | 40.77 |
time (sec) |
N/A | 0.766 | 0.645 | 2.505 | 0.000 | 0.000 | 0.000 | 0.786 | 1.572 | 18.942 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 358 | 351 | 505 | 766 | 0 | 0 | 0 | 0 | 4847 | 33819 |
N.S. |
1 | 0.98 | 1.41 | 2.14 | 0.00 | 0.00 | 0.00 | 0.00 | 13.54 | 94.47 |
time (sec) |
N/A | 0.904 | 1.245 | 2.856 | 0.000 | 0.000 | 0.000 | 0.000 | 3.722 | 32.173 |
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 | 343 | 322 | 262 | 359 | 501 | 499 | 0 | 3520 | 500 | 501 |
N.S. |
1 | 0.94 | 0.76 | 1.05 | 1.46 | 1.45 | 0.00 | 10.26 | 1.46 | 1.46 |
time (sec) |
N/A | 0.995 | 0.304 | 2.892 | 0.119 | 0.091 | 0.000 | 0.367 | 0.251 | 11.570 |
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 | 267 | 254 | 179 | 227 | 354 | 352 | 0 | 2139 | 332 | 337 |
N.S. |
1 | 0.95 | 0.67 | 0.85 | 1.33 | 1.32 | 0.00 | 8.01 | 1.24 | 1.26 |
time (sec) |
N/A | 0.822 | 0.221 | 2.911 | 0.091 | 0.093 | 0.000 | 0.304 | 0.225 | 11.205 |
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 | 190 | 187 | 119 | 131 | 236 | 233 | 0 | 804 | 200 | 219 |
N.S. |
1 | 0.98 | 0.63 | 0.69 | 1.24 | 1.23 | 0.00 | 4.23 | 1.05 | 1.15 |
time (sec) |
N/A | 0.668 | 0.134 | 2.477 | 0.089 | 0.099 | 0.000 | 0.334 | 0.206 | 11.040 |
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 | 116 | 118 | 76 | 71 | 112 | 140 | 0 | 379 | 103 | 100 |
N.S. |
1 | 1.02 | 0.66 | 0.61 | 0.97 | 1.21 | 0.00 | 3.27 | 0.89 | 0.86 |
time (sec) |
N/A | 0.546 | 0.095 | 2.802 | 0.064 | 0.083 | 0.000 | 0.327 | 0.232 | 10.953 |
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 | 186 | 183 | 152 | 322 | 0 | 421 | 0 | 157 | 166 | 0 |
N.S. |
1 | 0.98 | 0.82 | 1.73 | 0.00 | 2.26 | 0.00 | 0.84 | 0.89 | 0.00 |
time (sec) |
N/A | 0.720 | 0.362 | 2.100 | 0.000 | 0.099 | 0.000 | 0.359 | 0.242 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 217 | 136 | 351 | 0 | 661 | 0 | 158 | 413 | 0 |
N.S. |
1 | 1.16 | 0.73 | 1.88 | 0.00 | 3.53 | 0.00 | 0.84 | 2.21 | 0.00 |
time (sec) |
N/A | 0.783 | 0.402 | 2.134 | 0.000 | 0.100 | 0.000 | 0.291 | 0.215 | 0.000 |