Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 113 | 68 | 120 | 168 | 0 | 96 | 89 |
N.S. |
1 | 1.00 | 2.05 | 1.24 | 2.18 | 3.05 | 0.00 | 1.75 | 1.62 |
time (sec) |
N/A | 0.450 | 1.095 | 0.482 | 0.229 | 0.255 | 0.000 | 0.267 | 17.689 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 44 | 46 | 83 | 54 | 97 | 134 | 0 | 73 | 69 |
N.S. |
1 | 1.05 | 1.89 | 1.23 | 2.20 | 3.05 | 0.00 | 1.66 | 1.57 |
time (sec) |
N/A | 0.432 | 0.481 | 0.409 | 0.223 | 0.243 | 0.000 | 0.272 | 19.437 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 63 | 36 | 68 | 91 | 0 | 53 | 49 |
N.S. |
1 | 1.00 | 2.33 | 1.33 | 2.52 | 3.37 | 0.00 | 1.96 | 1.81 |
time (sec) |
N/A | 0.380 | 0.290 | 0.350 | 0.221 | 0.243 | 0.000 | 0.270 | 18.414 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 44 | 21 | 31 | 53 | 0 | 24 | 23 |
N.S. |
1 | 1.00 | 2.20 | 1.05 | 1.55 | 2.65 | 0.00 | 1.20 | 1.15 |
time (sec) |
N/A | 0.293 | 0.143 | 0.195 | 0.241 | 0.248 | 0.000 | 0.274 | 18.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 26 | 14 | 16 | 22 | 0 | 13 | 13 |
N.S. |
1 | 1.00 | 2.17 | 1.17 | 1.33 | 1.83 | 0.00 | 1.08 | 1.08 |
time (sec) |
N/A | 0.179 | 0.089 | 0.122 | 0.227 | 0.230 | 0.000 | 0.269 | 17.550 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 47 | 29 | 50 | 54 | 0 | 32 | 27 |
N.S. |
1 | 1.00 | 1.68 | 1.04 | 1.79 | 1.93 | 0.00 | 1.14 | 0.96 |
time (sec) |
N/A | 0.182 | 0.261 | 0.284 | 0.309 | 0.241 | 0.000 | 0.275 | 18.400 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 26 | 32 | 20 | 78 | 35 | 0 | 44 | 46 |
N.S. |
1 | 1.04 | 1.28 | 0.80 | 3.12 | 1.40 | 0.00 | 1.76 | 1.84 |
time (sec) |
N/A | 0.304 | 0.190 | 0.335 | 0.317 | 0.240 | 0.000 | 0.265 | 18.344 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 41 | 42 | 29 | 128 | 53 | 0 | 56 | 59 |
N.S. |
1 | 1.02 | 1.05 | 0.72 | 3.20 | 1.32 | 0.00 | 1.40 | 1.48 |
time (sec) |
N/A | 0.352 | 0.252 | 0.398 | 0.337 | 0.255 | 0.000 | 0.272 | 18.303 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 52 | 49 | 33 | 180 | 70 | 0 | 67 | 78 |
N.S. |
1 | 0.98 | 0.92 | 0.62 | 3.40 | 1.32 | 0.00 | 1.26 | 1.47 |
time (sec) |
N/A | 0.388 | 0.323 | 0.462 | 0.355 | 0.255 | 0.000 | 0.268 | 19.655 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 66 | 67 | 57 | 45 | 230 | 81 | 0 | 91 | 93 |
N.S. |
1 | 1.02 | 0.86 | 0.68 | 3.48 | 1.23 | 0.00 | 1.38 | 1.41 |
time (sec) |
N/A | 0.448 | 0.385 | 0.593 | 0.326 | 0.243 | 0.000 | 0.288 | 18.678 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 61 | 108 | 54 | 142 | 124 | 0 | 60 | 52 |
N.S. |
1 | 1.07 | 1.89 | 0.95 | 2.49 | 2.18 | 0.00 | 1.05 | 0.91 |
time (sec) |
N/A | 0.389 | 0.602 | 0.449 | 0.345 | 0.252 | 0.000 | 0.282 | 18.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 98 | 123 | 77 | 228 | 181 | 0 | 86 | 78 |
N.S. |
1 | 1.11 | 1.40 | 0.88 | 2.59 | 2.06 | 0.00 | 0.98 | 0.89 |
time (sec) |
N/A | 0.557 | 1.052 | 0.576 | 0.321 | 0.248 | 0.000 | 0.291 | 19.655 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 69 | 80 | 275 | 417 | 318 | 0 | 250 | 0 |
N.S. |
1 | 1.06 | 1.23 | 4.23 | 6.42 | 4.89 | 0.00 | 3.85 | 0.00 |
time (sec) |
N/A | 0.447 | 2.229 | 0.876 | 0.348 | 0.268 | 0.000 | 0.462 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 69 | 245 | 200 | 212 | 0 | 195 | 0 |
N.S. |
1 | 1.00 | 1.57 | 5.57 | 4.55 | 4.82 | 0.00 | 4.43 | 0.00 |
time (sec) |
N/A | 0.257 | 0.130 | 0.552 | 0.330 | 0.259 | 0.000 | 0.424 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 32 | 166 | 148 | 120 | 0 | 353 | 0 |
N.S. |
1 | 1.00 | 1.23 | 6.38 | 5.69 | 4.62 | 0.00 | 13.58 | 0.00 |
time (sec) |
N/A | 0.175 | 0.085 | 1.065 | 0.323 | 0.256 | 0.000 | 0.482 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 54 | 185 | 83 | 219 | 0 | 205 | 0 |
N.S. |
1 | 1.00 | 0.87 | 2.98 | 1.34 | 3.53 | 0.00 | 3.31 | 0.00 |
time (sec) |
N/A | 0.328 | 0.179 | 0.532 | 0.333 | 0.263 | 0.000 | 0.430 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 81 | 87 | 129 | 642 | 150 | 427 | 0 | 243 | 0 |
N.S. |
1 | 1.07 | 1.59 | 7.93 | 1.85 | 5.27 | 0.00 | 3.00 | 0.00 |
time (sec) |
N/A | 0.460 | 0.495 | 0.539 | 0.329 | 0.278 | 0.000 | 0.356 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 100 | 112 | 139 | 1104 | 0 | 546 | 0 | 286 | 0 |
N.S. |
1 | 1.12 | 1.39 | 11.04 | 0.00 | 5.46 | 0.00 | 2.86 | 0.00 |
time (sec) |
N/A | 0.645 | 0.596 | 0.589 | 0.000 | 0.273 | 0.000 | 0.360 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F | B | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 108 | 98 | 0 | 283 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.92 | 2.65 | 0.00 | 7.65 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.238 | 0.887 | 2.512 | 0.000 | 0.275 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 101 | 127 | 0 | 296 | 0 | 101 | 0 |
N.S. |
1 | 1.00 | 2.66 | 3.34 | 0.00 | 7.79 | 0.00 | 2.66 | 0.00 |
time (sec) |
N/A | 0.237 | 3.136 | 2.749 | 0.000 | 0.261 | 0.000 | 0.661 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 254 | 266 | 102 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.345 | 8.587 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 213 | 213 | 46 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.303 | 3.078 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 254 | 266 | 110 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.323 | 3.380 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 514 | 510 | 120 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.477 | 21.349 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 470 | 474 | 109 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.475 | 15.581 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 508 | 508 | 46 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.479 | 15.297 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 552 | 545 | 72 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.498 | 15.881 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 48 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.257 | 1.180 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 73 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.260 | 2.903 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 156 | 158 | 178 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.669 | 5.541 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 109 | 109 | 126 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.433 | 0.970 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 60 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.302 | 0.384 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.285 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.327 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.331 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 107 | 114 | 568 | 112 | 125 | 217 | 0 | 205 | 314 |
N.S. |
1 | 1.07 | 5.31 | 1.05 | 1.17 | 2.03 | 0.00 | 1.92 | 2.93 |
time (sec) |
N/A | 0.397 | 12.920 | 1.200 | 0.221 | 0.252 | 0.000 | 0.290 | 18.003 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 75 | 152 | 85 | 95 | 155 | 0 | 134 | 234 |
N.S. |
1 | 1.03 | 2.08 | 1.16 | 1.30 | 2.12 | 0.00 | 1.84 | 3.21 |
time (sec) |
N/A | 0.246 | 3.441 | 0.717 | 0.228 | 0.246 | 0.000 | 0.286 | 18.594 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 76 | 42 | 43 | 77 | 0 | 74 | 105 |
N.S. |
1 | 1.00 | 2.24 | 1.24 | 1.26 | 2.26 | 0.00 | 2.18 | 3.09 |
time (sec) |
N/A | 0.273 | 0.709 | 0.649 | 0.223 | 0.247 | 0.000 | 0.278 | 18.673 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 139 | 125 | 156 | 0 | 607 | 0 | 194 | 588 |
N.S. |
1 | 1.24 | 1.12 | 1.39 | 0.00 | 5.42 | 0.00 | 1.73 | 5.25 |
time (sec) |
N/A | 1.001 | 2.097 | 0.750 | 0.000 | 0.350 | 0.000 | 0.282 | 19.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 84 | 105 | 144 | 112 | 0 | 524 | 0 | 141 | 515 |
N.S. |
1 | 1.25 | 1.71 | 1.33 | 0.00 | 6.24 | 0.00 | 1.68 | 6.13 |
time (sec) |
N/A | 0.705 | 0.718 | 0.568 | 0.000 | 0.359 | 0.000 | 0.275 | 17.917 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 62 | 76 | 106 | 77 | 0 | 308 | 0 | 98 | 135 |
N.S. |
1 | 1.23 | 1.71 | 1.24 | 0.00 | 4.97 | 0.00 | 1.58 | 2.18 |
time (sec) |
N/A | 0.488 | 0.367 | 0.467 | 0.000 | 0.300 | 0.000 | 0.288 | 18.108 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 62 | 62 | 53 | 0 | 245 | 0 | 63 | 129 |
N.S. |
1 | 1.17 | 1.17 | 1.00 | 0.00 | 4.62 | 0.00 | 1.19 | 2.43 |
time (sec) |
N/A | 0.401 | 0.143 | 0.350 | 0.000 | 0.294 | 0.000 | 0.284 | 18.291 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 49 | 40 | 39 | 0 | 154 | 0 | 48 | 36 |
N.S. |
1 | 1.22 | 1.00 | 0.98 | 0.00 | 3.85 | 0.00 | 1.20 | 0.90 |
time (sec) |
N/A | 0.270 | 0.033 | 0.181 | 0.000 | 0.267 | 0.000 | 0.282 | 18.126 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 66 | 59 | 68 | 0 | 238 | 0 | 77 | 184 |
N.S. |
1 | 1.16 | 1.04 | 1.19 | 0.00 | 4.18 | 0.00 | 1.35 | 3.23 |
time (sec) |
N/A | 0.279 | 0.206 | 0.349 | 0.000 | 0.265 | 0.000 | 0.274 | 18.592 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 73 | 56 | 73 | 0 | 235 | 0 | 77 | 766 |
N.S. |
1 | 1.20 | 0.92 | 1.20 | 0.00 | 3.85 | 0.00 | 1.26 | 12.56 |
time (sec) |
N/A | 0.358 | 0.272 | 0.463 | 0.000 | 0.278 | 0.000 | 0.274 | 18.997 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 103 | 78 | 112 | 0 | 285 | 0 | 112 | 1147 |
N.S. |
1 | 1.26 | 0.95 | 1.37 | 0.00 | 3.48 | 0.00 | 1.37 | 13.99 |
time (sec) |
N/A | 0.667 | 0.362 | 0.543 | 0.000 | 0.265 | 0.000 | 0.268 | 20.241 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 136 | 98 | 145 | 0 | 329 | 0 | 149 | 1218 |
N.S. |
1 | 1.24 | 0.89 | 1.32 | 0.00 | 2.99 | 0.00 | 1.35 | 11.07 |
time (sec) |
N/A | 0.915 | 0.791 | 0.721 | 0.000 | 0.264 | 0.000 | 0.272 | 19.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 144 | 178 | 129 | 234 | 0 | 410 | 0 | 252 | 1639 |
N.S. |
1 | 1.24 | 0.90 | 1.62 | 0.00 | 2.85 | 0.00 | 1.75 | 11.38 |
time (sec) |
N/A | 1.271 | 1.452 | 0.981 | 0.000 | 0.284 | 0.000 | 0.276 | 19.318 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 108 | 142 | 139 | 168 | 0 | 493 | 0 | 158 | 2677 |
N.S. |
1 | 1.31 | 1.29 | 1.56 | 0.00 | 4.56 | 0.00 | 1.46 | 24.79 |
time (sec) |
N/A | 0.633 | 0.650 | 0.550 | 0.000 | 0.275 | 0.000 | 0.268 | 22.691 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 170 | 225 | 216 | 314 | 0 | 933 | 0 | 297 | 5917 |
N.S. |
1 | 1.32 | 1.27 | 1.85 | 0.00 | 5.49 | 0.00 | 1.75 | 34.81 |
time (sec) |
N/A | 0.993 | 1.971 | 1.050 | 0.000 | 0.300 | 0.000 | 0.286 | 27.173 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 239 | 314 | 279 | 545 | 0 | 1554 | 0 | 535 | 8167 |
N.S. |
1 | 1.31 | 1.17 | 2.28 | 0.00 | 6.50 | 0.00 | 2.24 | 34.17 |
time (sec) |
N/A | 1.412 | 5.557 | 2.092 | 0.000 | 0.342 | 0.000 | 0.297 | 31.996 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 41 | 66 | 34 | 49 | 33 | 0 | 49 | 39 |
N.S. |
1 | 1.32 | 2.13 | 1.10 | 1.58 | 1.06 | 0.00 | 1.58 | 1.26 |
time (sec) |
N/A | 0.219 | 0.157 | 0.559 | 0.325 | 0.254 | 0.000 | 0.265 | 19.319 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 68 | 50 | 67 | 41 | 71 | 52 | 0 | 45 | 27 |
N.S. |
1 | 0.74 | 0.99 | 0.60 | 1.04 | 0.76 | 0.00 | 0.66 | 0.40 |
time (sec) |
N/A | 0.258 | 0.147 | 0.313 | 0.315 | 0.250 | 0.000 | 0.272 | 18.570 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 274 | 274 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.693 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 220 | 220 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.447 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 104 | 104 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.253 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 12 | 12 | 14 | 12 | 14 | 14 | 12 | 14 | 16 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 1.17 | 1.00 | 1.17 | 1.33 |
time (sec) |
N/A | 0.165 | 3.158 | 0.613 | 1.236 | 0.256 | 0.495 | 0.324 | 18.725 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 19 | 19 | 21 | 19 | 21 | 21 | 19 | 21 | 23 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.11 | 1.00 | 1.11 | 1.21 |
time (sec) |
N/A | 0.194 | 8.296 | 0.677 | 1.655 | 0.259 | 4.478 | 0.396 | 18.431 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 21 | 21 | 23 | 21 | 23 | 26 | 20 | 23 | 25 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.24 | 0.95 | 1.10 | 1.19 |
time (sec) |
N/A | 0.201 | 6.528 | 1.039 | 2.105 | 0.255 | 21.256 | 0.396 | 19.495 |