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(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 263 | 277 | 184 | 267 | 0 | 964 | 0 | 338 | 1140 | 6743 |
N.S. |
1 | 1.05 | 0.70 | 1.02 | 0.00 | 3.67 | 0.00 | 1.29 | 4.33 | 25.64 |
time (sec) |
N/A | 1.445 | 2.321 | 0.717 | 0.000 | 0.145 | 0.000 | 0.152 | 0.177 | 6.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 185 | 147 | 205 | 0 | 789 | 0 | 1116 | 942 | 3276 |
N.S. |
1 | 1.19 | 0.95 | 1.32 | 0.00 | 5.09 | 0.00 | 7.20 | 6.08 | 21.14 |
time (sec) |
N/A | 0.964 | 1.794 | 0.530 | 0.000 | 0.133 | 0.000 | 0.252 | 0.206 | 3.655 |
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 | 122 | 149 | 119 | 160 | 0 | 551 | 0 | 199 | 530 | 3775 |
N.S. |
1 | 1.22 | 0.98 | 1.31 | 0.00 | 4.52 | 0.00 | 1.63 | 4.34 | 30.94 |
time (sec) |
N/A | 0.547 | 1.183 | 0.273 | 0.000 | 0.111 | 0.000 | 0.141 | 0.232 | 5.083 |
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 | 100 | 111 | 97 | 127 | 0 | 379 | 0 | 157 | 334 | 113 |
N.S. |
1 | 1.11 | 0.97 | 1.27 | 0.00 | 3.79 | 0.00 | 1.57 | 3.34 | 1.13 |
time (sec) |
N/A | 0.483 | 0.584 | 0.273 | 0.000 | 0.107 | 0.000 | 0.165 | 0.276 | 0.758 |
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 | 133 | 158 | 191 | 182 | 0 | 684 | 0 | 225 | 718 | 3763 |
N.S. |
1 | 1.19 | 1.44 | 1.37 | 0.00 | 5.14 | 0.00 | 1.69 | 5.40 | 28.29 |
time (sec) |
N/A | 0.854 | 1.174 | 0.530 | 0.000 | 2.516 | 0.000 | 0.170 | 0.170 | 5.097 |
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 | 189 | 208 | 240 | 241 | 0 | 1088 | 0 | 404 | 1823 | 5464 |
N.S. |
1 | 1.10 | 1.27 | 1.28 | 0.00 | 5.76 | 0.00 | 2.14 | 9.65 | 28.91 |
time (sec) |
N/A | 1.345 | 2.659 | 0.722 | 0.000 | 6.385 | 0.000 | 0.175 | 0.164 | 5.510 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 398 | 424 | 734 | 402 | 0 | 1812 | 0 | 2712 | 2686 | 10598 |
N.S. |
1 | 1.07 | 1.84 | 1.01 | 0.00 | 4.55 | 0.00 | 6.81 | 6.75 | 26.63 |
time (sec) |
N/A | 2.281 | 5.457 | 1.356 | 0.000 | 0.235 | 0.000 | 0.415 | 0.207 | 7.550 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 280 | 317 | 232 | 341 | 0 | 1561 | 0 | 543 | 2354 | 5542 |
N.S. |
1 | 1.13 | 0.83 | 1.22 | 0.00 | 5.58 | 0.00 | 1.94 | 8.41 | 19.79 |
time (sec) |
N/A | 1.565 | 3.483 | 0.937 | 0.000 | 0.213 | 0.000 | 0.177 | 0.165 | 4.865 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 247 | 204 | 282 | 0 | 1152 | 0 | 455 | 1529 | 6923 |
N.S. |
1 | 1.17 | 0.97 | 1.34 | 0.00 | 5.46 | 0.00 | 2.16 | 7.25 | 32.81 |
time (sec) |
N/A | 1.090 | 2.488 | 0.471 | 0.000 | 0.159 | 0.000 | 0.177 | 0.163 | 6.286 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 206 | 172 | 234 | 0 | 740 | 0 | 391 | 971 | 248 |
N.S. |
1 | 1.14 | 0.96 | 1.30 | 0.00 | 4.11 | 0.00 | 2.17 | 5.39 | 1.38 |
time (sec) |
N/A | 0.622 | 1.567 | 0.381 | 0.000 | 0.123 | 0.000 | 0.170 | 0.171 | 2.504 |
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 | 164 | 190 | 157 | 232 | 0 | 742 | 0 | 390 | 964 | 248 |
N.S. |
1 | 1.16 | 0.96 | 1.41 | 0.00 | 4.52 | 0.00 | 2.38 | 5.88 | 1.51 |
time (sec) |
N/A | 0.708 | 0.955 | 0.490 | 0.000 | 0.129 | 0.000 | 0.182 | 0.172 | 2.451 |
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 | 214 | 258 | 269 | 302 | 0 | 1400 | 0 | 481 | 1921 | 6911 |
N.S. |
1 | 1.21 | 1.26 | 1.41 | 0.00 | 6.54 | 0.00 | 2.25 | 8.98 | 32.29 |
time (sec) |
N/A | 1.368 | 2.043 | 0.898 | 0.000 | 11.610 | 0.000 | 0.196 | 0.199 | 6.196 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 299 | 335 | 352 | 376 | 0 | 2100 | 0 | 574 | 3951 | 9312 |
N.S. |
1 | 1.12 | 1.18 | 1.26 | 0.00 | 7.02 | 0.00 | 1.92 | 13.21 | 31.14 |
time (sec) |
N/A | 2.139 | 7.238 | 1.269 | 0.000 | 24.698 | 0.000 | 0.208 | 0.186 | 8.011 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 303 | 317 | 232 | 1305 | 0 | 561 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.05 | 0.77 | 4.31 | 0.00 | 1.85 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 1.761 | 1.572 | 14.717 | 0.000 | 0.112 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 237 | 179 | 993 | 0 | 492 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.03 | 0.77 | 4.30 | 0.00 | 2.13 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 1.190 | 3.139 | 4.883 | 0.000 | 0.107 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 172 | 146 | 600 | 0 | 437 | 0 | 0 | 59 | 0 |
N.S. |
1 | 1.01 | 0.85 | 3.51 | 0.00 | 2.56 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.984 | 0.810 | 3.380 | 0.000 | 0.099 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 179 | 107 | 247 | 0 | 0 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.01 | 0.60 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 1.381 | 12.707 | 2.195 | 0.000 | 0.000 | 0.000 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 213 | 227 | 372 | 746 | 0 | 0 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.07 | 1.75 | 3.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 1.979 | 17.870 | 3.104 | 0.000 | 0.000 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 298 | 420 | 1290 | 0 | 0 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.02 | 1.44 | 4.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 2.669 | 4.793 | 5.122 | 0.000 | 0.000 | 0.000 | 0.000 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 378 | 394 | 291 | 1635 | 0 | 639 | 0 | 0 | 102 | 0 |
N.S. |
1 | 1.04 | 0.77 | 4.33 | 0.00 | 1.69 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 2.178 | 2.780 | 14.994 | 0.000 | 0.140 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 297 | 305 | 233 | 1305 | 0 | 562 | 0 | 0 | 100 | 0 |
N.S. |
1 | 1.03 | 0.78 | 4.39 | 0.00 | 1.89 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 1.491 | 4.534 | 7.005 | 0.000 | 0.127 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 225 | 231 | 203 | 993 | 0 | 493 | 0 | 0 | 124 | 0 |
N.S. |
1 | 1.03 | 0.90 | 4.41 | 0.00 | 2.19 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 1.289 | 1.548 | 4.594 | 0.000 | 0.124 | 0.000 | 0.000 | 0.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 236 | 244 | 406 | 701 | 0 | 0 | 0 | 0 | 132 | 0 |
N.S. |
1 | 1.03 | 1.72 | 2.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 2.159 | 3.371 | 2.661 | 0.000 | 0.000 | 0.000 | 0.000 | 0.301 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 232 | 246 | 398 | 991 | 0 | 0 | 0 | 0 | 132 | 0 |
N.S. |
1 | 1.06 | 1.72 | 4.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 2.124 | 3.235 | 2.746 | 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 | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 295 | 309 | 422 | 1403 | 0 | 0 | 0 | 0 | 132 | 0 |
N.S. |
1 | 1.05 | 1.43 | 4.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 2.802 | 5.622 | 4.292 | 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 | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 375 | 390 | 634 | 2327 | 0 | 0 | 0 | 0 | 132 | 0 |
N.S. |
1 | 1.04 | 1.69 | 6.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 3.482 | 6.948 | 7.428 | 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 | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 462 | 480 | 357 | 1983 | 0 | 726 | 0 | 0 | 163 | 0 |
N.S. |
1 | 1.04 | 0.77 | 4.29 | 0.00 | 1.57 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 2.688 | 3.484 | 58.302 | 0.000 | 0.158 | 0.000 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 372 | 382 | 291 | 1635 | 0 | 639 | 0 | 0 | 161 | 0 |
N.S. |
1 | 1.03 | 0.78 | 4.40 | 0.00 | 1.72 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 1.922 | 5.370 | 16.082 | 0.000 | 0.152 | 0.000 | 0.000 | 0.298 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 288 | 299 | 254 | 1305 | 0 | 562 | 0 | 0 | 197 | 0 |
N.S. |
1 | 1.04 | 0.88 | 4.53 | 0.00 | 1.95 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 1.671 | 2.176 | 9.005 | 0.000 | 0.120 | 0.000 | 0.000 | 0.473 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 305 | 453 | 1067 | 0 | 0 | 0 | 0 | 209 | 0 |
N.S. |
1 | 1.04 | 1.55 | 3.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 2.740 | 3.951 | 7.881 | 0.000 | 0.000 | 0.000 | 0.000 | 0.371 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 296 | 310 | 442 | 1490 | 0 | 0 | 0 | 0 | 209 | 0 |
N.S. |
1 | 1.05 | 1.49 | 5.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 2.850 | 4.387 | 24.607 | 0.000 | 0.000 | 0.000 | 0.000 | 0.382 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 315 | 323 | 451 | 1742 | 0 | 0 | 0 | 0 | 209 | 0 |
N.S. |
1 | 1.03 | 1.43 | 5.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 2.815 | 6.270 | 92.674 | 0.000 | 0.000 | 0.000 | 0.000 | 0.359 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 376 | 395 | 486 | 2438 | 0 | 0 | 0 | 0 | 209 | 0 |
N.S. |
1 | 1.05 | 1.29 | 6.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 3.548 | 6.360 | 240.004 | 0.000 | 0.000 | 0.000 | 0.000 | 0.390 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 465 | 485 | 729 | 3548 | 0 | 0 | 0 | 0 | 209 | 0 |
N.S. |
1 | 1.04 | 1.57 | 7.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 4.407 | 7.227 | 453.699 | 0.000 | 0.000 | 0.000 | 0.000 | 0.357 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 258 | 180 | 993 | 0 | 493 | 0 | 0 | 73 | 0 |
N.S. |
1 | 1.05 | 0.73 | 4.04 | 0.00 | 2.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 1.405 | 1.707 | 6.778 | 0.000 | 0.105 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 187 | 154 | 671 | 0 | 437 | 0 | 0 | 71 | 199 |
N.S. |
1 | 1.02 | 0.84 | 3.67 | 0.00 | 2.39 | 0.00 | 0.00 | 0.39 | 1.09 |
time (sec) |
N/A | 0.878 | 1.996 | 3.083 | 0.000 | 0.101 | 0.000 | 0.000 | 0.163 | 0.766 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 130 | 93 | 249 | 0 | 371 | 0 | 0 | 83 | 135 |
N.S. |
1 | 1.00 | 0.72 | 1.92 | 0.00 | 2.85 | 0.00 | 0.00 | 0.64 | 1.04 |
time (sec) |
N/A | 0.760 | 4.759 | 1.750 | 0.000 | 0.114 | 0.000 | 0.000 | 0.177 | 0.840 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 81 | 194 | 0 | 0 | 0 | 0 | 87 | 0 |
N.S. |
1 | 1.00 | 0.69 | 1.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.954 | 0.597 | 0.736 | 0.000 | 0.000 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 227 | 320 | 639 | 0 | 0 | 0 | 0 | 87 | 0 |
N.S. |
1 | 1.05 | 1.48 | 2.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 1.972 | 14.350 | 1.664 | 0.000 | 0.000 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 299 | 305 | 420 | 1182 | 0 | 0 | 0 | 0 | 87 | 0 |
N.S. |
1 | 1.02 | 1.40 | 3.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 2.723 | 6.398 | 2.101 | 0.000 | 0.000 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 387 | 391 | 304 | 1312 | 0 | 890 | 0 | 0 | 105 | 0 |
N.S. |
1 | 1.01 | 0.79 | 3.39 | 0.00 | 2.30 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 2.226 | 2.755 | 8.155 | 0.000 | 0.179 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 262 | 280 | 189 | 1275 | 0 | 767 | 0 | 0 | 105 | 0 |
N.S. |
1 | 1.07 | 0.72 | 4.87 | 0.00 | 2.93 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 1.595 | 2.266 | 5.481 | 0.000 | 0.150 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 219 | 170 | 519 | 0 | 663 | 0 | 0 | 103 | 0 |
N.S. |
1 | 1.07 | 0.83 | 2.54 | 0.00 | 3.25 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 1.023 | 1.396 | 2.804 | 0.000 | 0.127 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 196 | 151 | 432 | 0 | 588 | 0 | 0 | 115 | 0 |
N.S. |
1 | 1.06 | 0.82 | 2.34 | 0.00 | 3.18 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 1.069 | 0.741 | 0.917 | 0.000 | 0.123 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 198 | 460 | 433 | 0 | 0 | 0 | 0 | 119 | 0 |
N.S. |
1 | 1.04 | 2.42 | 2.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 1.439 | 4.301 | 2.660 | 0.000 | 0.000 | 0.000 | 0.000 | 0.266 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-1) | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 303 | 335 | 482 | 912 | 0 | 0 | 0 | 0 | 119 | 0 |
N.S. |
1 | 1.11 | 1.59 | 3.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 2.916 | 5.971 | 12.035 | 0.000 | 0.000 | 0.000 | 0.000 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 413 | 421 | 334 | 1412 | 0 | 1316 | 0 | 0 | 137 | 0 |
N.S. |
1 | 1.02 | 0.81 | 3.42 | 0.00 | 3.19 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 2.437 | 3.905 | 20.640 | 0.000 | 0.212 | 0.000 | 0.000 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 331 | 338 | 274 | 954 | 0 | 1159 | 0 | 0 | 137 | 0 |
N.S. |
1 | 1.02 | 0.83 | 2.88 | 0.00 | 3.50 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 1.779 | 3.134 | 8.863 | 0.000 | 0.171 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 307 | 317 | 224 | 864 | 0 | 1044 | 0 | 0 | 135 | 0 |
N.S. |
1 | 1.03 | 0.73 | 2.81 | 0.00 | 3.40 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 1.453 | 2.586 | 6.679 | 0.000 | 0.137 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 275 | 285 | 193 | 754 | 0 | 924 | 0 | 0 | 147 | 0 |
N.S. |
1 | 1.04 | 0.70 | 2.74 | 0.00 | 3.36 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 1.458 | 1.816 | 5.743 | 0.000 | 0.130 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 349 | 375 | 743 | 858 | 0 | 0 | 0 | 0 | 151 | 0 |
N.S. |
1 | 1.07 | 2.13 | 2.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 3.152 | 7.020 | 7.612 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 437 | 471 | 750 | 1346 | 0 | 0 | 0 | 0 | 151 | 0 |
N.S. |
1 | 1.08 | 1.72 | 3.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 4.011 | 7.296 | 17.580 | 0.000 | 0.000 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 162 | 125 | 451 | 0 | 211 | 0 | 0 | 86 | 177 |
N.S. |
1 | 0.95 | 0.74 | 2.65 | 0.00 | 1.24 | 0.00 | 0.00 | 0.51 | 1.04 |
time (sec) |
N/A | 0.904 | 2.614 | 23.253 | 0.000 | 0.132 | 0.000 | 0.000 | 0.176 | 0.562 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 134 | 103 | 413 | 0 | 192 | 0 | 0 | 84 | 166 |
N.S. |
1 | 0.96 | 0.74 | 2.95 | 0.00 | 1.37 | 0.00 | 0.00 | 0.60 | 1.19 |
time (sec) |
N/A | 0.758 | 2.117 | 15.561 | 0.000 | 0.111 | 0.000 | 0.000 | 0.210 | 0.970 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 107 | 86 | 371 | 0 | 175 | 0 | 0 | 73 | 128 |
N.S. |
1 | 0.99 | 0.80 | 3.44 | 0.00 | 1.62 | 0.00 | 0.00 | 0.68 | 1.19 |
time (sec) |
N/A | 0.727 | 1.621 | 9.956 | 0.000 | 0.097 | 0.000 | 0.000 | 0.178 | 0.935 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 78 | 67 | 326 | 0 | 156 | 0 | 0 | 66 | 85 |
N.S. |
1 | 1.04 | 0.89 | 4.35 | 0.00 | 2.08 | 0.00 | 0.00 | 0.88 | 1.13 |
time (sec) |
N/A | 0.634 | 1.072 | 5.849 | 0.000 | 0.096 | 0.000 | 0.000 | 0.170 | 0.895 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 64 | 246 | 0 | 185 | 0 | 0 | 77 | 96 |
N.S. |
1 | 1.00 | 0.90 | 3.46 | 0.00 | 2.61 | 0.00 | 0.00 | 1.08 | 1.35 |
time (sec) |
N/A | 0.635 | 0.648 | 4.699 | 0.000 | 0.105 | 0.000 | 0.000 | 0.160 | 1.180 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 102 | 107 | 401 | 0 | 213 | 0 | 0 | 86 | 150 |
N.S. |
1 | 0.99 | 1.04 | 3.89 | 0.00 | 2.07 | 0.00 | 0.00 | 0.83 | 1.46 |
time (sec) |
N/A | 0.749 | 0.833 | 4.936 | 0.000 | 0.102 | 0.000 | 0.000 | 0.167 | 1.443 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 130 | 134 | 636 | 0 | 235 | 0 | 0 | 86 | 177 |
N.S. |
1 | 0.93 | 0.96 | 4.54 | 0.00 | 1.68 | 0.00 | 0.00 | 0.61 | 1.26 |
time (sec) |
N/A | 0.778 | 1.152 | 7.598 | 0.000 | 0.101 | 0.000 | 0.000 | 0.174 | 1.682 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 264 | 231 | 196 | 666 | 0 | 299 | 0 | 0 | 139 | 275 |
N.S. |
1 | 0.88 | 0.74 | 2.52 | 0.00 | 1.13 | 0.00 | 0.00 | 0.53 | 1.04 |
time (sec) |
N/A | 1.231 | 3.111 | 35.497 | 0.000 | 0.158 | 0.000 | 0.000 | 0.178 | 1.196 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 203 | 167 | 610 | 0 | 271 | 0 | 0 | 137 | 264 |
N.S. |
1 | 0.91 | 0.75 | 2.74 | 0.00 | 1.22 | 0.00 | 0.00 | 0.61 | 1.18 |
time (sec) |
N/A | 1.077 | 2.721 | 25.334 | 0.000 | 0.115 | 0.000 | 0.000 | 0.186 | 1.104 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 175 | 139 | 548 | 0 | 243 | 0 | 0 | 126 | 229 |
N.S. |
1 | 0.96 | 0.76 | 3.01 | 0.00 | 1.34 | 0.00 | 0.00 | 0.69 | 1.26 |
time (sec) |
N/A | 1.021 | 2.296 | 17.367 | 0.000 | 0.098 | 0.000 | 0.000 | 0.195 | 1.133 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 146 | 106 | 487 | 0 | 216 | 0 | 0 | 117 | 177 |
N.S. |
1 | 1.04 | 0.76 | 3.48 | 0.00 | 1.54 | 0.00 | 0.00 | 0.84 | 1.26 |
time (sec) |
N/A | 0.920 | 1.776 | 10.590 | 0.000 | 0.159 | 0.000 | 0.000 | 0.185 | 1.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 124 | 102 | 405 | 0 | 240 | 0 | 0 | 119 | 158 |
N.S. |
1 | 1.02 | 0.84 | 3.35 | 0.00 | 1.98 | 0.00 | 0.00 | 0.98 | 1.31 |
time (sec) |
N/A | 0.839 | 1.478 | 7.070 | 0.000 | 0.103 | 0.000 | 0.000 | 0.180 | 1.237 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 129 | 105 | 574 | 0 | 255 | 0 | 0 | 130 | 194 |
N.S. |
1 | 1.02 | 0.83 | 4.56 | 0.00 | 2.02 | 0.00 | 0.00 | 1.03 | 1.54 |
time (sec) |
N/A | 0.886 | 1.929 | 6.757 | 0.000 | 0.104 | 0.000 | 0.000 | 0.167 | 1.637 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 161 | 175 | 723 | 0 | 286 | 0 | 0 | 139 | 227 |
N.S. |
1 | 0.94 | 1.02 | 4.20 | 0.00 | 1.66 | 0.00 | 0.00 | 0.81 | 1.32 |
time (sec) |
N/A | 1.017 | 2.091 | 8.066 | 0.000 | 0.124 | 0.000 | 0.000 | 0.169 | 1.807 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 190 | 191 | 832 | 0 | 314 | 0 | 0 | 139 | 233 |
N.S. |
1 | 0.89 | 0.89 | 3.89 | 0.00 | 1.47 | 0.00 | 0.00 | 0.65 | 1.09 |
time (sec) |
N/A | 1.033 | 6.069 | 11.259 | 0.000 | 0.111 | 0.000 | 0.000 | 0.190 | 2.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 305 | 272 | 235 | 825 | 0 | 358 | 0 | 0 | 190 | 364 |
N.S. |
1 | 0.89 | 0.77 | 2.70 | 0.00 | 1.17 | 0.00 | 0.00 | 0.62 | 1.19 |
time (sec) |
N/A | 1.475 | 3.370 | 38.507 | 0.000 | 0.201 | 0.000 | 0.000 | 0.195 | 1.317 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 244 | 197 | 745 | 0 | 321 | 0 | 0 | 179 | 328 |
N.S. |
1 | 0.96 | 0.77 | 2.92 | 0.00 | 1.26 | 0.00 | 0.00 | 0.70 | 1.29 |
time (sec) |
N/A | 1.446 | 2.499 | 26.716 | 0.000 | 0.114 | 0.000 | 0.000 | 0.199 | 1.249 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 216 | 158 | 664 | 0 | 284 | 0 | 0 | 170 | 275 |
N.S. |
1 | 1.05 | 0.77 | 3.24 | 0.00 | 1.39 | 0.00 | 0.00 | 0.83 | 1.34 |
time (sec) |
N/A | 1.301 | 3.062 | 17.901 | 0.000 | 0.104 | 0.000 | 0.000 | 0.191 | 1.157 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 208 | 150 | 641 | 0 | 302 | 0 | 0 | 170 | 248 |
N.S. |
1 | 1.03 | 0.74 | 3.17 | 0.00 | 1.50 | 0.00 | 0.00 | 0.84 | 1.23 |
time (sec) |
N/A | 1.303 | 2.728 | 9.027 | 0.000 | 0.132 | 0.000 | 0.000 | 0.178 | 1.164 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 191 | 165 | 771 | 0 | 306 | 0 | 0 | 172 | 255 |
N.S. |
1 | 0.99 | 0.86 | 4.02 | 0.00 | 1.59 | 0.00 | 0.00 | 0.90 | 1.33 |
time (sec) |
N/A | 1.270 | 2.695 | 9.316 | 0.000 | 0.135 | 0.000 | 0.000 | 0.182 | 1.684 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 208 | 176 | 950 | 0 | 326 | 0 | 0 | 183 | 291 |
N.S. |
1 | 1.02 | 0.86 | 4.66 | 0.00 | 1.60 | 0.00 | 0.00 | 0.90 | 1.43 |
time (sec) |
N/A | 1.288 | 3.948 | 10.163 | 0.000 | 0.164 | 0.000 | 0.000 | 0.175 | 2.383 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 240 | 221 | 917 | 0 | 364 | 0 | 0 | 192 | 311 |
N.S. |
1 | 0.94 | 0.87 | 3.60 | 0.00 | 1.43 | 0.00 | 0.00 | 0.75 | 1.22 |
time (sec) |
N/A | 1.442 | 5.836 | 12.243 | 0.000 | 0.106 | 0.000 | 0.000 | 0.184 | 2.524 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 305 | 268 | 266 | 1166 | 0 | 401 | 0 | 0 | 192 | 304 |
N.S. |
1 | 0.88 | 0.87 | 3.82 | 0.00 | 1.31 | 0.00 | 0.00 | 0.63 | 1.00 |
time (sec) |
N/A | 1.490 | 7.317 | 15.676 | 0.000 | 0.133 | 0.000 | 0.000 | 0.176 | 2.887 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 272 | 305 | 1375 | 0 | 0 | 0 | 0 | 65 | 0 |
N.S. |
1 | 1.11 | 1.24 | 5.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 2.203 | 2.959 | 18.313 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 200 | 260 | 1074 | 0 | 0 | 0 | 0 | 65 | 0 |
N.S. |
1 | 1.10 | 1.43 | 5.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 1.636 | 2.612 | 5.163 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 148 | 207 | 822 | 0 | 0 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.08 | 1.51 | 6.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 1.179 | 1.705 | 6.599 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 86 | 128 | 295 | 0 | 0 | 0 | 0 | 55 | 0 |
N.S. |
1 | 0.97 | 1.44 | 3.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.706 | 1.109 | 4.118 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 58 | 217 | 0 | 0 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.00 | 0.95 | 3.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 0.563 | 0.531 | 1.899 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 206 | 300 | 0 | 0 | 0 | 0 | 69 | 0 |
N.S. |
1 | 1.00 | 2.40 | 3.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.804 | 2.678 | 2.688 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 162 | 260 | 441 | 0 | 0 | 0 | 0 | 71 | 0 |
N.S. |
1 | 1.08 | 1.73 | 2.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 1.604 | 2.462 | 4.080 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 232 | 309 | 760 | 0 | 0 | 0 | 0 | 71 | 0 |
N.S. |
1 | 1.07 | 1.42 | 3.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 2.128 | 4.549 | 6.031 | 0.000 | 0.000 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 389 | 375 | 369 | 1348 | 0 | 0 | 0 | 0 | 97 | 0 |
N.S. |
1 | 0.96 | 0.95 | 3.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 2.683 | 5.312 | 20.260 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 303 | 295 | 318 | 1066 | 0 | 0 | 0 | 0 | 97 | 0 |
N.S. |
1 | 0.97 | 1.05 | 3.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 2.012 | 3.682 | 8.708 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 224 | 220 | 280 | 849 | 0 | 0 | 0 | 0 | 95 | 0 |
N.S. |
1 | 0.98 | 1.25 | 3.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 1.473 | 3.106 | 6.178 | 0.000 | 0.000 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 192 | 260 | 808 | 0 | 0 | 0 | 0 | 87 | 0 |
N.S. |
1 | 0.97 | 1.31 | 4.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 1.364 | 2.834 | 4.773 | 0.000 | 0.000 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-1) | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 185 | 274 | 721 | 0 | 0 | 0 | 0 | 90 | 0 |
N.S. |
1 | 0.92 | 1.37 | 3.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 1.483 | 3.020 | 4.393 | 0.000 | 0.000 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-1) | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 256 | 242 | 316 | 856 | 0 | 0 | 0 | 0 | 101 | 0 |
N.S. |
1 | 0.95 | 1.23 | 3.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 2.092 | 5.001 | 5.101 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-1) | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 345 | 327 | 427 | 1005 | 0 | 0 | 0 | 0 | 103 | 0 |
N.S. |
1 | 0.95 | 1.24 | 2.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 2.761 | 7.241 | 6.563 | 0.000 | 0.000 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-1) | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 461 | 463 | 462 | 2195 | 0 | 0 | 0 | 0 | 129 | 0 |
N.S. |
1 | 1.00 | 1.00 | 4.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 3.000 | 6.066 | 112.249 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 367 | 372 | 390 | 1977 | 0 | 0 | 0 | 0 | 129 | 0 |
N.S. |
1 | 1.01 | 1.06 | 5.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 2.295 | 5.773 | 8.664 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 344 | 349 | 360 | 1937 | 0 | 0 | 0 | 0 | 127 | 0 |
N.S. |
1 | 1.01 | 1.05 | 5.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 2.251 | 4.044 | 7.251 | 0.000 | 0.000 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-1) | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 337 | 334 | 365 | 1850 | 0 | 0 | 0 | 0 | 119 | 0 |
N.S. |
1 | 0.99 | 1.08 | 5.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 2.188 | 4.813 | 6.919 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 345 | 336 | 383 | 1744 | 0 | 0 | 0 | 0 | 122 | 0 |
N.S. |
1 | 0.97 | 1.11 | 5.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 2.392 | 5.259 | 5.728 | 0.000 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-1) | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 420 | 412 | 458 | 1975 | 0 | 0 | 0 | 0 | 133 | 0 |
N.S. |
1 | 0.98 | 1.09 | 4.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 3.221 | 5.697 | 7.470 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 560 | 563 | 1224 | 1700 | 0 | 0 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.01 | 2.19 | 3.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 2.863 | 6.821 | 25.804 | 0.000 | 0.000 | 0.000 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 473 | 471 | 1175 | 1184 | 0 | 0 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.00 | 2.48 | 2.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 2.163 | 21.559 | 10.982 | 0.000 | 0.000 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 385 | 391 | 408 | 666 | 0 | 0 | 0 | 0 | 55 | 0 |
N.S. |
1 | 1.02 | 1.06 | 1.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 1.666 | 12.285 | 11.317 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 351 | 351 | 273 | 654 | 0 | 0 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.00 | 0.78 | 1.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 1.319 | 13.121 | 22.738 | 0.000 | 0.000 | 0.000 | 0.000 | 0.186 | 0.000 |