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 | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 99 | 82 | 81 | 80 | 416 | 932 | 80 | 184 | 518 |
N.S. |
1 | 1.08 | 0.89 | 0.88 | 0.87 | 4.52 | 10.13 | 0.87 | 2.00 | 5.63 |
time (sec) |
N/A | 0.415 | 0.104 | 0.158 | 0.106 | 0.303 | 21.416 | 0.131 | 0.250 | 4.414 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 78 | 66 | 60 | 59 | 325 | 0 | 59 | 153 | 379 |
N.S. |
1 | 0.99 | 0.84 | 0.76 | 0.75 | 4.11 | 0.00 | 0.75 | 1.94 | 4.80 |
time (sec) |
N/A | 0.346 | 0.028 | 0.147 | 0.106 | 0.142 | 0.000 | 0.120 | 0.254 | 4.507 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 78 | 66 | 60 | 59 | 309 | 0 | 59 | 153 | 399 |
N.S. |
1 | 0.99 | 0.84 | 0.76 | 0.75 | 3.91 | 0.00 | 0.75 | 1.94 | 5.05 |
time (sec) |
N/A | 0.324 | 0.035 | 0.140 | 0.114 | 0.156 | 0.000 | 0.133 | 0.218 | 4.340 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 100 | 169 | 81 | 80 | 416 | 1103 | 80 | 193 | 354 |
N.S. |
1 | 1.09 | 1.84 | 0.88 | 0.87 | 4.52 | 11.99 | 0.87 | 2.10 | 3.85 |
time (sec) |
N/A | 0.413 | 0.151 | 0.158 | 0.109 | 0.372 | 72.161 | 0.125 | 0.245 | 4.733 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 133 | 193 | 101 | 101 | 576 | 0 | 103 | 231 | 535 |
N.S. |
1 | 1.19 | 1.72 | 0.90 | 0.90 | 5.14 | 0.00 | 0.92 | 2.06 | 4.78 |
time (sec) |
N/A | 0.553 | 0.247 | 0.186 | 0.107 | 1.816 | 0.000 | 0.130 | 0.277 | 4.970 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 335 | 449 | 377 | 234 | 375 | 1196 | 0 | 469 | 327 | 6361 |
N.S. |
1 | 1.34 | 1.13 | 0.70 | 1.12 | 3.57 | 0.00 | 1.40 | 0.98 | 18.99 |
time (sec) |
N/A | 1.227 | 0.253 | 0.132 | 0.112 | 0.227 | 0.000 | 0.133 | 0.251 | 4.773 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 327 | 426 | 340 | 226 | 363 | 1427 | 0 | 453 | 281 | 2553 |
N.S. |
1 | 1.30 | 1.04 | 0.69 | 1.11 | 4.36 | 0.00 | 1.39 | 0.86 | 7.81 |
time (sec) |
N/A | 1.083 | 0.123 | 0.124 | 0.111 | 0.145 | 0.000 | 0.138 | 0.250 | 4.560 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 327 | 426 | 340 | 218 | 361 | 1067 | 0 | 437 | 281 | 5889 |
N.S. |
1 | 1.30 | 1.04 | 0.67 | 1.10 | 3.26 | 0.00 | 1.34 | 0.86 | 18.01 |
time (sec) |
N/A | 1.065 | 0.076 | 0.119 | 0.116 | 0.108 | 0.000 | 0.125 | 0.267 | 4.773 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 327 | 426 | 340 | 218 | 363 | 1331 | 0 | 477 | 281 | 6633 |
N.S. |
1 | 1.30 | 1.04 | 0.67 | 1.11 | 4.07 | 0.00 | 1.46 | 0.86 | 20.28 |
time (sec) |
N/A | 1.070 | 0.081 | 0.115 | 0.111 | 0.139 | 0.000 | 0.136 | 0.244 | 4.473 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 327 | 426 | 340 | 226 | 365 | 1171 | 0 | 437 | 281 | 6153 |
N.S. |
1 | 1.30 | 1.04 | 0.69 | 1.12 | 3.58 | 0.00 | 1.34 | 0.86 | 18.82 |
time (sec) |
N/A | 1.017 | 0.084 | 0.111 | 0.112 | 0.184 | 0.000 | 0.133 | 0.237 | 5.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 338 | 477 | 385 | 237 | 384 | 1461 | 0 | 488 | 336 | 5962 |
N.S. |
1 | 1.41 | 1.14 | 0.70 | 1.14 | 4.32 | 0.00 | 1.44 | 0.99 | 17.64 |
time (sec) |
N/A | 1.081 | 0.142 | 0.161 | 0.115 | 0.324 | 0.000 | 0.134 | 0.253 | 4.977 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 340 | 454 | 406 | 241 | 390 | 1255 | 0 | 472 | 354 | 7459 |
N.S. |
1 | 1.34 | 1.19 | 0.71 | 1.15 | 3.69 | 0.00 | 1.39 | 1.04 | 21.94 |
time (sec) |
N/A | 1.181 | 0.191 | 0.161 | 0.113 | 2.658 | 0.000 | 0.132 | 0.241 | 5.279 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 357 | 522 | 428 | 261 | 405 | 1526 | 0 | 483 | 382 | 4547 |
N.S. |
1 | 1.46 | 1.20 | 0.73 | 1.13 | 4.27 | 0.00 | 1.35 | 1.07 | 12.74 |
time (sec) |
N/A | 1.183 | 0.209 | 0.176 | 0.115 | 4.643 | 0.000 | 0.134 | 0.287 | 4.904 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 363 | 305 | 157 | 306 | 2079 | 430 | 513 | 1355 | 610 |
N.S. |
1 | 1.42 | 1.20 | 0.62 | 1.20 | 8.15 | 1.69 | 2.01 | 5.31 | 2.39 |
time (sec) |
N/A | 0.895 | 0.175 | 0.115 | 0.116 | 0.115 | 8.898 | 0.131 | 0.268 | 0.256 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 249 | 318 | 301 | 151 | 405 | 1742 | 337 | 496 | 1347 | 1615 |
N.S. |
1 | 1.28 | 1.21 | 0.61 | 1.63 | 7.00 | 1.35 | 1.99 | 5.41 | 6.49 |
time (sec) |
N/A | 0.939 | 0.168 | 0.089 | 0.120 | 0.114 | 10.400 | 0.131 | 0.227 | 0.283 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 247 | 353 | 309 | 221 | 299 | 2090 | 425 | 499 | 1356 | 651 |
N.S. |
1 | 1.43 | 1.25 | 0.89 | 1.21 | 8.46 | 1.72 | 2.02 | 5.49 | 2.64 |
time (sec) |
N/A | 0.919 | 0.176 | 0.123 | 0.118 | 0.110 | 21.434 | 0.131 | 0.206 | 3.499 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | C | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 242 | 350 | 305 | 216 | 409 | 1764 | 0 | 487 | 1388 | 1740 |
N.S. |
1 | 1.45 | 1.26 | 0.89 | 1.69 | 7.29 | 0.00 | 2.01 | 5.74 | 7.19 |
time (sec) |
N/A | 0.891 | 0.175 | 0.119 | 0.115 | 0.105 | 0.000 | 0.129 | 0.257 | 0.313 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 360 | 305 | 227 | 312 | 2096 | 440 | 502 | 1403 | 652 |
N.S. |
1 | 1.43 | 1.21 | 0.90 | 1.24 | 8.32 | 1.75 | 1.99 | 5.57 | 2.59 |
time (sec) |
N/A | 0.917 | 0.186 | 0.112 | 0.110 | 0.117 | 175.519 | 0.131 | 0.221 | 3.476 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 125 | 121 | 124 | 0 | 280 | 167 | 139 | 1108 | 196 |
N.S. |
1 | 1.00 | 0.97 | 0.99 | 0.00 | 2.24 | 1.34 | 1.11 | 8.86 | 1.57 |
time (sec) |
N/A | 0.502 | 0.224 | 0.691 | 0.000 | 0.084 | 12.168 | 0.118 | 0.221 | 3.502 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 98 | 88 | 84 | 0 | 195 | 122 | 96 | 583 | 87 |
N.S. |
1 | 1.05 | 0.95 | 0.90 | 0.00 | 2.10 | 1.31 | 1.03 | 6.27 | 0.94 |
time (sec) |
N/A | 0.391 | 0.118 | 0.193 | 0.000 | 0.089 | 8.177 | 0.130 | 0.247 | 3.246 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 69 | 62 | 0 | 156 | 92 | 66 | 218 | 54 |
N.S. |
1 | 1.00 | 0.99 | 0.89 | 0.00 | 2.23 | 1.31 | 0.94 | 3.11 | 0.77 |
time (sec) |
N/A | 0.355 | 0.078 | 0.147 | 0.000 | 0.098 | 4.354 | 0.123 | 0.238 | 3.372 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 81 | 71 | 0 | 377 | 158 | 79 | 802 | 199 |
N.S. |
1 | 1.00 | 0.95 | 0.84 | 0.00 | 4.44 | 1.86 | 0.93 | 9.44 | 2.34 |
time (sec) |
N/A | 0.395 | 0.113 | 0.166 | 0.000 | 0.104 | 7.201 | 0.127 | 0.255 | 3.685 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 121 | 107 | 96 | 0 | 507 | 0 | 107 | 2930 | 269 |
N.S. |
1 | 1.05 | 0.93 | 0.83 | 0.00 | 4.41 | 0.00 | 0.93 | 25.48 | 2.34 |
time (sec) |
N/A | 0.457 | 0.288 | 0.235 | 0.000 | 0.111 | 0.000 | 0.123 | 0.356 | 4.143 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 128 | 142 | 102 | 0 | 720 | 0 | 0 | 870 | 0 |
N.S. |
1 | 1.07 | 1.18 | 0.85 | 0.00 | 6.00 | 0.00 | 0.00 | 7.25 | 0.00 |
time (sec) |
N/A | 0.506 | 0.864 | 0.595 | 0.000 | 0.145 | 0.000 | 0.000 | 0.262 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 89 | 107 | 77 | 0 | 617 | 0 | 0 | 218 | 0 |
N.S. |
1 | 0.98 | 1.18 | 0.85 | 0.00 | 6.78 | 0.00 | 0.00 | 2.40 | 0.00 |
time (sec) |
N/A | 0.390 | 0.277 | 0.373 | 0.000 | 0.109 | 0.000 | 0.000 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 96 | 69 | 0 | 281 | 0 | 121 | 455 | 0 |
N.S. |
1 | 1.00 | 1.26 | 0.91 | 0.00 | 3.70 | 0.00 | 1.59 | 5.99 | 0.00 |
time (sec) |
N/A | 0.385 | 0.332 | 0.593 | 0.000 | 0.098 | 0.000 | 0.267 | 0.320 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 118 | 118 | 92 | 0 | 329 | 0 | 225 | 1091 | 0 |
N.S. |
1 | 1.07 | 1.07 | 0.84 | 0.00 | 2.99 | 0.00 | 2.05 | 9.92 | 0.00 |
time (sec) |
N/A | 0.517 | 0.470 | 0.994 | 0.000 | 0.116 | 0.000 | 0.266 | 0.391 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 173 | 153 | 139 | 0 | 413 | 0 | 492 | 1815 | 0 |
N.S. |
1 | 1.09 | 0.96 | 0.87 | 0.00 | 2.60 | 0.00 | 3.09 | 11.42 | 0.00 |
time (sec) |
N/A | 0.664 | 0.832 | 1.692 | 0.000 | 0.135 | 0.000 | 0.343 | 0.515 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | No | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 671 | 1002 | 241 | 303 | 0 | 0 | 0 | 0 | 139 | 0 |
N.S. |
1 | 1.49 | 0.36 | 0.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 2.637 | 10.330 | 4.010 | 0.000 | 0.000 | 0.000 | 0.000 | 0.455 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 749 | 964 | 161 | 273 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.29 | 0.21 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 2.161 | 10.128 | 0.444 | 0.000 | 0.000 | 0.000 | 0.000 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 674 | 988 | 333 | 294 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.47 | 0.49 | 0.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 2.336 | 10.196 | 5.468 | 0.000 | 0.000 | 0.000 | 0.000 | 0.798 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 857 | 1069 | 141 | 332 | 0 | 0 | 0 | 0 | 144 | 0 |
N.S. |
1 | 1.25 | 0.16 | 0.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 2.653 | 10.100 | 5.668 | 0.000 | 0.000 | 0.000 | 0.000 | 0.497 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 786 | 1096 | 65 | 299 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.39 | 0.08 | 0.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 2.550 | 10.031 | 0.457 | 0.000 | 0.000 | 0.000 | 0.000 | 0.281 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 809 | 1021 | 138 | 318 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.26 | 0.17 | 0.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 2.283 | 10.143 | 4.724 | 0.000 | 0.000 | 0.000 | 0.000 | 0.628 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 104 | 91 | 93 | 0 | 289 | 0 | 102 | 794 | 102 |
N.S. |
1 | 1.00 | 0.88 | 0.89 | 0.00 | 2.78 | 0.00 | 0.98 | 7.63 | 0.98 |
time (sec) |
N/A | 0.447 | 0.243 | 0.207 | 0.000 | 0.110 | 0.000 | 0.124 | 0.250 | 3.984 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 73 | 59 | 0 | 205 | 0 | 64 | 295 | 58 |
N.S. |
1 | 1.00 | 0.99 | 0.80 | 0.00 | 2.77 | 0.00 | 0.86 | 3.99 | 0.78 |
time (sec) |
N/A | 0.344 | 0.107 | 0.154 | 0.000 | 0.100 | 0.000 | 0.119 | 0.213 | 3.920 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 51 | 39 | 0 | 130 | 87 | 40 | 92 | 40 |
N.S. |
1 | 1.00 | 1.00 | 0.76 | 0.00 | 2.55 | 1.71 | 0.78 | 1.80 | 0.78 |
time (sec) |
N/A | 0.307 | 0.048 | 0.094 | 0.000 | 0.089 | 7.227 | 0.122 | 0.214 | 3.970 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 80 | 65 | 0 | 385 | 114 | 71 | 874 | 652 |
N.S. |
1 | 1.00 | 0.94 | 0.76 | 0.00 | 4.53 | 1.34 | 0.84 | 10.28 | 7.67 |
time (sec) |
N/A | 0.225 | 0.155 | 0.158 | 0.000 | 0.125 | 6.868 | 0.122 | 0.270 | 4.323 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 127 | 109 | 92 | 0 | 518 | 0 | 104 | 3329 | 396 |
N.S. |
1 | 1.09 | 0.93 | 0.79 | 0.00 | 4.43 | 0.00 | 0.89 | 28.45 | 3.38 |
time (sec) |
N/A | 0.272 | 0.296 | 0.230 | 0.000 | 0.130 | 0.000 | 0.116 | 0.355 | 4.925 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 134 | 136 | 98 | 0 | 745 | 0 | 0 | 1128 | 0 |
N.S. |
1 | 1.09 | 1.11 | 0.80 | 0.00 | 6.06 | 0.00 | 0.00 | 9.17 | 0.00 |
time (sec) |
N/A | 0.300 | 0.725 | 0.805 | 0.000 | 0.212 | 0.000 | 0.000 | 0.259 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 90 | 108 | 70 | 0 | 638 | 0 | 0 | 250 | 0 |
N.S. |
1 | 0.99 | 1.19 | 0.77 | 0.00 | 7.01 | 0.00 | 0.00 | 2.75 | 0.00 |
time (sec) |
N/A | 0.242 | 0.383 | 0.441 | 0.000 | 0.171 | 0.000 | 0.000 | 0.243 | 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 | 54 | 54 | 74 | 42 | 0 | 245 | 0 | 72 | 165 | 0 |
N.S. |
1 | 1.00 | 1.37 | 0.78 | 0.00 | 4.54 | 0.00 | 1.33 | 3.06 | 0.00 |
time (sec) |
N/A | 0.188 | 0.545 | 0.322 | 0.000 | 0.143 | 0.000 | 0.131 | 0.238 | 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 | 80 | 80 | 100 | 67 | 0 | 332 | 0 | 116 | 547 | 0 |
N.S. |
1 | 1.00 | 1.25 | 0.84 | 0.00 | 4.15 | 0.00 | 1.45 | 6.84 | 0.00 |
time (sec) |
N/A | 0.230 | 0.402 | 0.569 | 0.000 | 0.128 | 0.000 | 0.136 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 127 | 121 | 88 | 0 | 418 | 0 | 205 | 1240 | 0 |
N.S. |
1 | 1.10 | 1.05 | 0.77 | 0.00 | 3.63 | 0.00 | 1.78 | 10.78 | 0.00 |
time (sec) |
N/A | 0.297 | 0.755 | 1.000 | 0.000 | 0.146 | 0.000 | 0.257 | 0.362 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 660 | 1002 | 249 | 298 | 0 | 0 | 0 | 0 | 142 | 0 |
N.S. |
1 | 1.52 | 0.38 | 0.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 1.432 | 10.247 | 4.783 | 0.000 | 0.000 | 0.000 | 0.000 | 0.494 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 625 | 958 | 65 | 265 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.53 | 0.10 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 2.180 | 10.049 | 1.125 | 0.000 | 0.000 | 0.000 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 625 | 860 | 161 | 191 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.38 | 0.26 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.989 | 10.049 | 0.436 | 0.000 | 0.000 | 0.000 | 0.000 | 0.245 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 662 | 988 | 337 | 288 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.49 | 0.51 | 0.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 2.304 | 10.223 | 4.178 | 0.000 | 0.000 | 0.000 | 0.000 | 0.271 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | No | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 804 | 1089 | 65 | 292 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.35 | 0.08 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 2.472 | 10.076 | 2.116 | 0.000 | 0.000 | 0.000 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 656 | 865 | 65 | 191 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.32 | 0.10 | 0.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.870 | 10.037 | 0.436 | 0.000 | 0.000 | 0.000 | 0.000 | 0.264 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 833 | 999 | 141 | 310 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.20 | 0.17 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 2.314 | 10.093 | 3.495 | 0.000 | 0.000 | 0.000 | 0.000 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 182 | 175 | 171 | 0 | 622 | 0 | 180 | 3265 | 186 |
N.S. |
1 | 1.18 | 1.14 | 1.11 | 0.00 | 4.04 | 0.00 | 1.17 | 21.20 | 1.21 |
time (sec) |
N/A | 0.492 | 0.473 | 0.369 | 0.000 | 0.117 | 0.000 | 0.126 | 0.217 | 4.483 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 144 | 130 | 133 | 0 | 475 | 0 | 142 | 2072 | 144 |
N.S. |
1 | 1.17 | 1.06 | 1.08 | 0.00 | 3.86 | 0.00 | 1.15 | 16.85 | 1.17 |
time (sec) |
N/A | 0.459 | 0.317 | 0.257 | 0.000 | 0.123 | 0.000 | 0.124 | 0.263 | 4.466 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 98 | 100 | 83 | 0 | 348 | 0 | 116 | 1344 | 95 |
N.S. |
1 | 0.99 | 1.01 | 0.84 | 0.00 | 3.52 | 0.00 | 1.17 | 13.58 | 0.96 |
time (sec) |
N/A | 0.377 | 0.214 | 0.191 | 0.000 | 0.107 | 0.000 | 0.132 | 0.219 | 4.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 86 | 86 | 71 | 0 | 302 | 0 | 93 | 872 | 84 |
N.S. |
1 | 0.99 | 0.99 | 0.82 | 0.00 | 3.47 | 0.00 | 1.07 | 10.02 | 0.97 |
time (sec) |
N/A | 0.362 | 0.210 | 0.148 | 0.000 | 0.110 | 0.000 | 0.121 | 0.227 | 4.167 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 155 | 124 | 146 | 0 | 816 | 0 | 139 | 9123 | 3017 |
N.S. |
1 | 1.17 | 0.94 | 1.11 | 0.00 | 6.18 | 0.00 | 1.05 | 69.11 | 22.86 |
time (sec) |
N/A | 0.480 | 0.400 | 0.276 | 0.000 | 0.173 | 0.000 | 0.122 | 0.430 | 5.136 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 213 | 163 | 191 | 0 | 1189 | 0 | 257 | 15292 | 3822 |
N.S. |
1 | 1.15 | 0.88 | 1.03 | 0.00 | 6.43 | 0.00 | 1.39 | 82.66 | 20.66 |
time (sec) |
N/A | 0.602 | 1.043 | 0.391 | 0.000 | 0.180 | 0.000 | 0.124 | 1.022 | 6.207 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 213 | 189 | 143 | 0 | 1391 | 0 | 333 | 5868 | 0 |
N.S. |
1 | 1.12 | 0.99 | 0.75 | 0.00 | 7.28 | 0.00 | 1.74 | 30.72 | 0.00 |
time (sec) |
N/A | 0.734 | 2.027 | 1.743 | 0.000 | 0.564 | 0.000 | 0.217 | 0.562 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 166 | 153 | 117 | 0 | 1083 | 0 | 298 | 3238 | 0 |
N.S. |
1 | 1.18 | 1.09 | 0.83 | 0.00 | 7.68 | 0.00 | 2.11 | 22.96 | 0.00 |
time (sec) |
N/A | 0.523 | 1.389 | 0.954 | 0.000 | 0.331 | 0.000 | 0.207 | 0.350 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 97 | 112 | 81 | 0 | 426 | 0 | 244 | 1561 | 0 |
N.S. |
1 | 1.04 | 1.20 | 0.87 | 0.00 | 4.58 | 0.00 | 2.62 | 16.78 | 0.00 |
time (sec) |
N/A | 0.395 | 0.838 | 0.797 | 0.000 | 0.146 | 0.000 | 0.356 | 0.351 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 108 | 124 | 90 | 0 | 467 | 0 | 237 | 2444 | 0 |
N.S. |
1 | 1.04 | 1.19 | 0.87 | 0.00 | 4.49 | 0.00 | 2.28 | 23.50 | 0.00 |
time (sec) |
N/A | 0.383 | 1.130 | 0.783 | 0.000 | 0.170 | 0.000 | 0.148 | 0.403 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 157 | 157 | 112 | 0 | 612 | 0 | 418 | 3526 | 0 |
N.S. |
1 | 1.05 | 1.05 | 0.75 | 0.00 | 4.11 | 0.00 | 2.81 | 23.66 | 0.00 |
time (sec) |
N/A | 0.527 | 1.080 | 1.303 | 0.000 | 0.249 | 0.000 | 0.379 | 0.492 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 212 | 201 | 134 | 0 | 760 | 0 | 395 | 7920 | 0 |
N.S. |
1 | 1.02 | 0.97 | 0.64 | 0.00 | 3.65 | 0.00 | 1.90 | 38.08 | 0.00 |
time (sec) |
N/A | 0.680 | 2.115 | 2.221 | 0.000 | 0.297 | 0.000 | 0.472 | 2.106 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 852 | 1162 | 404 | 421 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.36 | 0.47 | 0.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.973 | 10.678 | 13.645 | 0.000 | 0.000 | 0.000 | 0.000 | 5.819 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 776 | 1094 | 402 | 373 | 0 | 0 | 0 | 0 | 1632 | 0 |
N.S. |
1 | 1.41 | 0.52 | 0.48 | 0.00 | 0.00 | 0.00 | 0.00 | 2.10 | 0.00 |
time (sec) |
N/A | 2.723 | 10.449 | 8.805 | 0.000 | 0.000 | 0.000 | 0.000 | 3.837 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 723 | 1032 | 253 | 337 | 0 | 0 | 0 | 0 | 62 | 0 |
N.S. |
1 | 1.43 | 0.35 | 0.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 2.383 | 10.256 | 3.243 | 0.000 | 0.000 | 0.000 | 0.000 | 1.063 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 617 | 1013 | 238 | 324 | 0 | 0 | 0 | 0 | 62 | 0 |
N.S. |
1 | 1.64 | 0.39 | 0.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 2.273 | 10.177 | 3.253 | 0.000 | 0.000 | 0.000 | 0.000 | 0.979 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 723 | 1016 | 392 | 333 | 0 | 0 | 0 | 0 | 59 | 0 |
N.S. |
1 | 1.41 | 0.54 | 0.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 2.345 | 10.299 | 1.085 | 0.000 | 0.000 | 0.000 | 0.000 | 0.255 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 778 | 1074 | 408 | 364 | 0 | 0 | 0 | 0 | 442 | 0 |
N.S. |
1 | 1.38 | 0.52 | 0.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 2.603 | 10.485 | 8.438 | 0.000 | 0.000 | 0.000 | 0.000 | 2.083 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 854 | 1144 | 383 | 405 | 0 | 0 | 0 | 0 | 778 | 0 |
N.S. |
1 | 1.34 | 0.45 | 0.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 2.787 | 10.674 | 10.155 | 0.000 | 0.000 | 0.000 | 0.000 | 4.921 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1159 | 1085 | 162 | 353 | 0 | 0 | 0 | 0 | 62 | 0 |
N.S. |
1 | 0.94 | 0.14 | 0.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 2.474 | 10.090 | 4.580 | 0.000 | 0.000 | 0.000 | 0.000 | 0.981 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1169 | 1071 | 172 | 359 | 0 | 0 | 0 | 0 | 62 | 0 |
N.S. |
1 | 0.92 | 0.15 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 2.158 | 10.128 | 1.139 | 0.000 | 0.000 | 0.000 | 0.000 | 0.253 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1248 | 1148 | 226 | 392 | 0 | 0 | 0 | 0 | 445 | 0 |
N.S. |
1 | 0.92 | 0.18 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 2.434 | 10.214 | 8.730 | 0.000 | 0.000 | 0.000 | 0.000 | 2.041 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 175 | 53 | 50 | 0 | 51 | 0 | 0 | 19 | 0 |
N.S. |
1 | 3.57 | 1.08 | 1.02 | 0.00 | 1.04 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.621 | 0.205 | 1.180 | 0.000 | 0.135 | 0.000 | 0.000 | 0.193 | 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 | 71 | 71 | 70 | 0 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.440 | 11.075 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 9.510 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 70 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.442 | 11.054 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 9.467 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 68 | 0 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.382 | 11.057 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 88.315 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 143 | 0 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 2.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.439 | 11.122 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 101.012 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 195 | 164 | 0 | 0 | 0 | 182 | 0 | 1018 | 0 |
N.S. |
1 | 1.04 | 0.87 | 0.00 | 0.00 | 0.00 | 0.97 | 0.00 | 5.41 | 0.00 |
time (sec) |
N/A | 0.624 | 9.442 | 0.000 | 0.000 | 0.000 | 6.472 | 0.000 | 0.275 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 117 | 110 | 0 | 0 | 0 | 117 | 0 | 268 | 0 |
N.S. |
1 | 1.02 | 0.96 | 0.00 | 0.00 | 0.00 | 1.02 | 0.00 | 2.33 | 0.00 |
time (sec) |
N/A | 0.405 | 1.532 | 0.000 | 0.000 | 0.000 | 2.227 | 0.000 | 0.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 66 | 0 | 0 | 0 | 56 | 0 | 27 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.82 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.300 | 0.589 | 0.000 | 0.000 | 0.000 | 0.604 | 0.000 | 0.233 | 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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 125 | 0 | 0 | 0 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.00 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.368 | 4.153 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 179 | 0 | 0 | 0 | 0 | 0 | 66 | 0 |
N.S. |
1 | 1.00 | 2.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.368 | 10.007 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.313 | 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 | 81 | 81 | 77 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.377 | 11.100 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.401 | 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 | 205 | 200 | 167 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.633 | 11.126 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.326 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 132 | 113 | 0 | 0 | 0 | 117 | 0 | 701 | 0 |
N.S. |
1 | 1.12 | 0.96 | 0.00 | 0.00 | 0.00 | 0.99 | 0.00 | 5.94 | 0.00 |
time (sec) |
N/A | 0.425 | 4.259 | 0.000 | 0.000 | 0.000 | 18.109 | 0.000 | 0.297 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 69 | 0 | 0 | 0 | 56 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.311 | 1.343 | 0.000 | 0.000 | 0.000 | 0.741 | 0.000 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 169 | 0 | 0 | 0 | 0 | 0 | 66 | 0 |
N.S. |
1 | 1.00 | 2.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.364 | 11.129 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.322 | 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 | 84 | 84 | 77 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.387 | 11.114 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.464 | 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 | 84 | 84 | 77 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.370 | 11.118 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.615 | 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 | 369 | 430 | 188 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.17 | 0.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.437 | 6.323 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.516 | 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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 214 | 265 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.660 | 97.510 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.324 | 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 | 119 | 121 | 108 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.431 | 0.024 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 64 | 0 | 0 | 0 | 54 | 0 | 174 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.82 | 0.00 | 2.64 | 0.00 |
time (sec) |
N/A | 0.297 | 0.030 | 0.000 | 0.000 | 0.000 | 85.952 | 0.000 | 0.220 | 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 | 79 | 79 | 75 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.361 | 0.169 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.302 | 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 | 79 | 79 | 75 | 0 | 0 | 0 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.366 | 0.218 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.498 | 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 | 101 | 101 | 97 | 0 | 0 | 0 | 0 | 0 | 1026 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 10.16 | 0.00 |
time (sec) |
N/A | 0.438 | 0.179 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.707 | 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 | 54 | 54 | 56 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.293 | 0.089 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.598 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 97 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.429 | 0.159 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.072 | 0.000 |