Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 81 | 361 | 96 | 0 | 214 | 1923 | 95 | 65 | 318 |
N.S. |
1 | 1.16 | 5.16 | 1.37 | 0.00 | 3.06 | 27.47 | 1.36 | 0.93 | 4.54 |
time (sec) |
N/A | 0.425 | 1.420 | 0.671 | 0.000 | 0.102 | 113.176 | 0.170 | 0.165 | 40.399 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F(-2) | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 737 | 667 | 2452 | 0 | 0 | 2684 | 0 | 0 | 30 | 0 |
N.S. |
1 | 0.91 | 3.33 | 0.00 | 0.00 | 3.64 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 3.647 | 10.424 | 0.000 | 0.000 | 0.298 | 0.000 | 0.000 | 200.024 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F(-2) | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 536 | 483 | 2283 | 0 | 0 | 1779 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.90 | 4.26 | 0.00 | 0.00 | 3.32 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.361 | 5.694 | 0.000 | 0.000 | 0.250 | 0.000 | 0.000 | 10.348 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 351 | 318 | 816 | 1750 | 0 | 1037 | 0 | 0 | 1226 | 0 |
N.S. |
1 | 0.91 | 2.32 | 4.99 | 0.00 | 2.95 | 0.00 | 0.00 | 3.49 | 0.00 |
time (sec) |
N/A | 1.371 | 4.065 | 3.612 | 0.000 | 0.231 | 0.000 | 0.000 | 0.222 | 0.000 |
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 | 61 | 54 | 54 | 54 | 55 | 53 | 0 | 60 | 141 | 55 |
N.S. |
1 | 0.89 | 0.89 | 0.89 | 0.90 | 0.87 | 0.00 | 0.98 | 2.31 | 0.90 |
time (sec) |
N/A | 0.257 | 0.068 | 0.598 | 0.029 | 0.118 | 0.000 | 0.158 | 0.174 | 0.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F(-2) | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 937 | 814 | 2506 | 0 | 0 | 3069 | 0 | 0 | 316 | 0 |
N.S. |
1 | 0.87 | 2.67 | 0.00 | 0.00 | 3.28 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 3.068 | 11.804 | 0.000 | 0.000 | 0.376 | 0.000 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F(-2) | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 667 | 591 | 1461 | 0 | 0 | 2035 | 0 | 0 | 244 | 0 |
N.S. |
1 | 0.89 | 2.19 | 0.00 | 0.00 | 3.05 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 2.170 | 6.908 | 0.000 | 0.000 | 0.323 | 0.000 | 0.000 | 0.283 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 413 | 386 | 1185 | 846 | 0 | 1181 | 0 | 0 | 166 | 0 |
N.S. |
1 | 0.93 | 2.87 | 2.05 | 0.00 | 2.86 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 1.358 | 10.967 | 1.395 | 0.000 | 0.291 | 0.000 | 0.000 | 0.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 80 | 64 | 71 | 64 | 62 | 0 | 76 | 104 | 69 |
N.S. |
1 | 1.07 | 0.85 | 0.95 | 0.85 | 0.83 | 0.00 | 1.01 | 1.39 | 0.92 |
time (sec) |
N/A | 0.298 | 0.039 | 0.625 | 0.033 | 0.094 | 0.000 | 0.161 | 0.174 | 0.216 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 923 | 774 | 1438 | 0 | 0 | 4116 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.84 | 1.56 | 0.00 | 0.00 | 4.46 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.436 | 10.313 | 0.000 | 0.000 | 0.450 | 0.000 | 0.000 | 0.472 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 659 | 561 | 1122 | 0 | 0 | 2659 | 0 | 0 | 394 | 0 |
N.S. |
1 | 0.85 | 1.70 | 0.00 | 0.00 | 4.03 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 2.495 | 8.914 | 0.000 | 0.000 | 0.359 | 0.000 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 349 | 324 | 2180 | 2065 | 0 | 1267 | 0 | 0 | 251 | 0 |
N.S. |
1 | 0.93 | 6.25 | 5.92 | 0.00 | 3.63 | 0.00 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 1.555 | 16.117 | 1.773 | 0.000 | 0.266 | 0.000 | 0.000 | 0.218 | 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 | 84 | 90 | 152 | 112 | 0 | 305 | 0 | 107 | 131 | 149 |
N.S. |
1 | 1.07 | 1.81 | 1.33 | 0.00 | 3.63 | 0.00 | 1.27 | 1.56 | 1.77 |
time (sec) |
N/A | 0.357 | 0.229 | 0.647 | 0.000 | 0.129 | 0.000 | 0.172 | 0.218 | 39.284 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 28 | 30 | 30 | 26 | 30 | 30 | 30 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.07 | 1.07 | 0.93 | 1.07 | 1.07 | 1.07 |
time (sec) |
N/A | 0.239 | 14.771 | 0.680 | 0.669 | 0.081 | 16.913 | 0.175 | 0.208 | 38.927 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 26 | 28 | 28 | 24 | 28 | 226 | 28 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.08 | 0.92 | 1.08 | 8.69 | 1.08 |
time (sec) |
N/A | 0.226 | 10.163 | 0.346 | 0.339 | 0.072 | 4.995 | 0.153 | 0.218 | 39.222 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 22 | 22 | 17 | 22 | 97 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 0.85 | 1.10 | 4.85 | 1.10 |
time (sec) |
N/A | 0.230 | 0.066 | 0.015 | 0.244 | 0.113 | 1.667 | 0.178 | 0.223 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 26 | 28 | 28 | 24 | 28 | 28 | 30 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.08 | 0.92 | 1.08 | 1.08 | 1.15 |
time (sec) |
N/A | 0.215 | 161.166 | 0.479 | 2.575 | 0.078 | 26.337 | 0.204 | 0.217 | 38.846 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 28 | 30 | 30 | 26 | 30 | 30 | 30 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.07 | 1.07 | 0.93 | 1.07 | 1.07 | 1.07 |
time (sec) |
N/A | 0.241 | 26.069 | 0.487 | 18.851 | 0.076 | 106.329 | 0.206 | 0.246 | 39.139 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | A | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 83 | 73 | 194 | 0 | 339 | 0 | 0 | 158 | 0 |
N.S. |
1 | 1.08 | 0.95 | 2.52 | 0.00 | 4.40 | 0.00 | 0.00 | 2.05 | 0.00 |
time (sec) |
N/A | 0.316 | 1.507 | 4.411 | 0.000 | 0.094 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 280 | 272 | 311 | 606 | 0 | 1393 | 0 | 0 | 1574 | 0 |
N.S. |
1 | 0.97 | 1.11 | 2.16 | 0.00 | 4.98 | 0.00 | 0.00 | 5.62 | 0.00 |
time (sec) |
N/A | 0.988 | 3.634 | 4.177 | 0.000 | 0.226 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 418 | 382 | 446 | 0 | 0 | 2284 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.91 | 1.07 | 0.00 | 0.00 | 5.46 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.516 | 3.153 | 0.000 | 0.000 | 0.280 | 0.000 | 0.000 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | B | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 128 | 112 | 349 | 0 | 625 | 0 | 0 | 455 | 0 |
N.S. |
1 | 1.10 | 0.97 | 3.01 | 0.00 | 5.39 | 0.00 | 0.00 | 3.92 | 0.00 |
time (sec) |
N/A | 0.437 | 2.298 | 6.703 | 0.000 | 0.149 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 357 | 355 | 1017 | 946 | 0 | 2375 | 0 | 0 | 1145 | 0 |
N.S. |
1 | 0.99 | 2.85 | 2.65 | 0.00 | 6.65 | 0.00 | 0.00 | 3.21 | 0.00 |
time (sec) |
N/A | 1.370 | 15.867 | 6.582 | 0.000 | 0.267 | 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(-2) | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 753 | 672 | 8825 | 0 | 0 | 4917 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.89 | 11.72 | 0.00 | 0.00 | 6.53 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.086 | 20.275 | 0.000 | 0.000 | 0.426 | 0.000 | 0.000 | 2.875 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F(-2) | B | F | F(-1) | F | F(-1) |
verified |
N/A | N/A | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 765 | 0 | 1194 | 0 | 0 | 3089 | 0 | 0 | 34 | 0 |
N.S. |
1 | 0.00 | 1.56 | 0.00 | 0.00 | 4.04 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.000 | 2.448 | 0.000 | 0.000 | 0.385 | 0.000 | 0.000 | 200.021 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 557 | 627 | 607 | 0 | 0 | 2109 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.13 | 1.09 | 0.00 | 0.00 | 3.79 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 4.114 | 2.390 | 0.000 | 0.000 | 0.323 | 0.000 | 0.000 | 200.023 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 350 | 406 | 2079 | 1189 | 0 | 1273 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.16 | 5.94 | 3.40 | 0.00 | 3.64 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 2.221 | 16.125 | 1.668 | 0.000 | 0.285 | 0.000 | 0.000 | 200.024 | 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 | 75 | 87 | 90 | 94 | 0 | 262 | 0 | 94 | 67 | 896 |
N.S. |
1 | 1.16 | 1.20 | 1.25 | 0.00 | 3.49 | 0.00 | 1.25 | 0.89 | 11.95 |
time (sec) |
N/A | 0.517 | 0.110 | 0.802 | 0.000 | 0.122 | 0.000 | 0.148 | 0.176 | 40.772 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | F | F(-2) | B | F | F | F | F(-1) |
verified |
N/A | N/A | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 763 | 0 | 4052 | 0 | 0 | 3449 | 0 | 0 | 36 | 0 |
N.S. |
1 | 0.00 | 5.31 | 0.00 | 0.00 | 4.52 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.000 | 11.397 | 0.000 | 0.000 | 0.441 | 0.000 | 0.000 | 200.017 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F(-2) | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 566 | 701 | 1741 | 0 | 0 | 2260 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.24 | 3.08 | 0.00 | 0.00 | 3.99 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 4.751 | 9.939 | 0.000 | 0.000 | 0.405 | 0.000 | 0.000 | 200.024 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 379 | 463 | 868 | 1694 | 0 | 1293 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.22 | 2.29 | 4.47 | 0.00 | 3.41 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 2.804 | 5.711 | 7.575 | 0.000 | 0.307 | 0.000 | 0.000 | 200.017 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 57 | 53 | 55 | 54 | 55 | 0 | 61 | 119 | 98 |
N.S. |
1 | 0.97 | 0.90 | 0.93 | 0.92 | 0.93 | 0.00 | 1.03 | 2.02 | 1.66 |
time (sec) |
N/A | 0.306 | 0.059 | 1.427 | 0.035 | 0.104 | 0.000 | 0.117 | 4.760 | 40.233 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F(-2) | B | F | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1125 | 0 | 1181 | 0 | 0 | 4205 | 0 | 0 | 36 | 0 |
N.S. |
1 | 0.00 | 1.05 | 0.00 | 0.00 | 3.74 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 0.000 | 7.979 | 0.000 | 0.000 | 0.736 | 0.000 | 0.000 | 200.024 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F(-2) | B | F | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 825 | 0 | 1254 | 0 | 0 | 2787 | 0 | 0 | 36 | 0 |
N.S. |
1 | 0.00 | 1.52 | 0.00 | 0.00 | 3.38 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.000 | 5.630 | 0.000 | 0.000 | 0.410 | 0.000 | 0.000 | 200.024 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | F(-2) | B | F | F(-1) | F | F(-1) |
verified |
N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 512 | 0 | 2194 | 1874 | 0 | 1611 | 0 | 0 | 34 | 0 |
N.S. |
1 | 0.00 | 4.29 | 3.66 | 0.00 | 3.15 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.000 | 17.190 | 8.290 | 0.000 | 0.494 | 0.000 | 0.000 | 200.023 | 0.000 |
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 | 124 | 138 | 143 | 180 | 0 | 350 | 0 | 183 | 169 | 1320 |
N.S. |
1 | 1.11 | 1.15 | 1.45 | 0.00 | 2.82 | 0.00 | 1.48 | 1.36 | 10.65 |
time (sec) |
N/A | 0.744 | 0.252 | 2.610 | 0.000 | 0.188 | 0.000 | 0.150 | 3.597 | 42.721 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | F | F(-2) | B | F | F | F | F(-1) |
verified |
N/A | N/A | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 852 | 0 | 3039 | 0 | 0 | 3903 | 0 | 0 | 36 | 0 |
N.S. |
1 | 0.00 | 3.57 | 0.00 | 0.00 | 4.58 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.000 | 14.866 | 0.000 | 0.000 | 0.417 | 0.000 | 0.000 | 200.021 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | F | F(-2) | B | F | F | F | F(-1) |
verified |
N/A | N/A | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 616 | 0 | 1752 | 0 | 0 | 2529 | 0 | 0 | 36 | 0 |
N.S. |
1 | 0.00 | 2.84 | 0.00 | 0.00 | 4.11 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.000 | 12.271 | 0.000 | 0.000 | 0.321 | 0.000 | 0.000 | 200.029 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | F(-2) | B | F | F | F | F(-1) |
verified |
N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 386 | 0 | 1111 | 1732 | 0 | 1419 | 0 | 0 | 34 | 0 |
N.S. |
1 | 0.00 | 2.88 | 4.49 | 0.00 | 3.68 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.000 | 9.011 | 2.030 | 0.000 | 0.300 | 0.000 | 0.000 | 200.047 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 54 | 59 | 57 | 69 | 0 | 66 | 145 | 118 |
N.S. |
1 | 1.00 | 0.90 | 0.98 | 0.95 | 1.15 | 0.00 | 1.10 | 2.42 | 1.97 |
time (sec) |
N/A | 0.321 | 0.068 | 0.893 | 0.032 | 0.103 | 0.000 | 0.129 | 1.162 | 39.207 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | F | F(-2) | B | F | F(-1) | F | F(-1) |
verified |
N/A | N/A | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1144 | 0 | 3915 | 0 | 0 | 4706 | 0 | 0 | 38 | 0 |
N.S. |
1 | 0.00 | 3.42 | 0.00 | 0.00 | 4.11 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 0.000 | 9.840 | 0.000 | 0.000 | 0.554 | 0.000 | 0.000 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F(-2) | B | F | F(-1) | F | F(-1) |
verified |
N/A | N/A | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 840 | 0 | 973 | 0 | 0 | 3075 | 0 | 0 | 38 | 0 |
N.S. |
1 | 0.00 | 1.16 | 0.00 | 0.00 | 3.66 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.000 | 9.111 | 0.000 | 0.000 | 0.441 | 0.000 | 0.000 | 200.024 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | F(-2) | B | F | F(-1) | F | F(-1) |
verified |
N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 508 | 0 | 2279 | 5310 | 0 | 1751 | 0 | 0 | 36 | 0 |
N.S. |
1 | 0.00 | 4.49 | 10.45 | 0.00 | 3.45 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.000 | 18.020 | 8.188 | 0.000 | 0.330 | 0.000 | 0.000 | 200.025 | 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 | 104 | 123 | 146 | 155 | 0 | 396 | 0 | 221 | 202 | 1167 |
N.S. |
1 | 1.18 | 1.40 | 1.49 | 0.00 | 3.81 | 0.00 | 2.12 | 1.94 | 11.22 |
time (sec) |
N/A | 0.694 | 1.049 | 2.293 | 0.000 | 0.190 | 0.000 | 0.162 | 16.022 | 41.420 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | F | F(-2) | B | F | F(-1) | F | F(-1) |
verified |
N/A | N/A | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1432 | 0 | 4009 | 0 | 0 | 4916 | 0 | 0 | 38 | 0 |
N.S. |
1 | 0.00 | 2.80 | 0.00 | 0.00 | 3.43 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 0.000 | 13.604 | 0.000 | 0.000 | 0.671 | 0.000 | 0.000 | 200.025 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | F | F(-2) | B | F | F | F | F(-1) |
verified |
N/A | N/A | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1014 | 0 | 5075 | 0 | 0 | 3131 | 0 | 0 | 38 | 0 |
N.S. |
1 | 0.00 | 5.00 | 0.00 | 0.00 | 3.09 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.000 | 12.217 | 0.000 | 0.000 | 0.412 | 0.000 | 0.000 | 200.021 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | F(-2) | B | F | F | F | F(-1) |
verified |
N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 641 | 0 | 1650 | 5210 | 0 | 1707 | 0 | 0 | 36 | 0 |
N.S. |
1 | 0.00 | 2.57 | 8.13 | 0.00 | 2.66 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.000 | 10.317 | 17.613 | 0.000 | 0.341 | 0.000 | 0.000 | 200.023 | 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 | 96 | 90 | 86 | 90 | 91 | 133 | 0 | 101 | 31 | 233 |
N.S. |
1 | 0.94 | 0.90 | 0.94 | 0.95 | 1.39 | 0.00 | 1.05 | 0.32 | 2.43 |
time (sec) |
N/A | 0.352 | 0.164 | 4.477 | 0.034 | 0.111 | 0.000 | 0.145 | 200.018 | 42.898 |