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 | A | A | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 25 | 30 | 0 | 28 | 0 | 0 | 289 |
N.S. |
1 | 1.00 | 1.39 | 1.67 | 0.00 | 1.56 | 0.00 | 0.00 | 16.06 |
time (sec) |
N/A | 0.202 | 1.088 | 1.328 | 0.000 | 0.296 | 0.000 | 0.000 | 0.117 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F(-2) | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 37 | 4397 | 0 | 181 | 0 | 0 | 632 |
N.S. |
1 | 1.00 | 1.23 | 146.57 | 0.00 | 6.03 | 0.00 | 0.00 | 21.07 |
time (sec) |
N/A | 0.226 | 1.894 | 1.807 | 0.000 | 0.321 | 0.000 | 0.000 | 19.706 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F(-2) | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 37 | 1908 | 0 | 191 | 0 | 0 | 677 |
N.S. |
1 | 1.00 | 0.97 | 50.21 | 0.00 | 5.03 | 0.00 | 0.00 | 17.82 |
time (sec) |
N/A | 0.240 | 1.975 | 1.841 | 0.000 | 0.310 | 0.000 | 0.000 | 18.721 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F(-2) | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 35 | 4437 | 0 | 187 | 0 | 0 | 629 |
N.S. |
1 | 1.00 | 0.97 | 123.25 | 0.00 | 5.19 | 0.00 | 0.00 | 17.47 |
time (sec) |
N/A | 0.227 | 1.919 | 1.686 | 0.000 | 0.315 | 0.000 | 0.000 | 0.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F(-2) | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 39 | 1888 | 0 | 185 | 0 | 0 | 680 |
N.S. |
1 | 1.00 | 1.22 | 59.00 | 0.00 | 5.78 | 0.00 | 0.00 | 21.25 |
time (sec) |
N/A | 0.231 | 1.918 | 1.770 | 0.000 | 0.296 | 0.000 | 0.000 | 19.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 355 | 355 | 186 | 261 | 0 | 189 | 175 | 0 | 0 |
N.S. |
1 | 1.00 | 0.52 | 0.74 | 0.00 | 0.53 | 0.49 | 0.00 | 0.00 |
time (sec) |
N/A | 0.471 | 10.113 | 1.729 | 0.000 | 0.162 | 2.009 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 326 | 326 | 146 | 234 | 0 | 165 | 138 | 0 | 0 |
N.S. |
1 | 1.00 | 0.45 | 0.72 | 0.00 | 0.51 | 0.42 | 0.00 | 0.00 |
time (sec) |
N/A | 0.413 | 8.157 | 1.500 | 0.000 | 0.162 | 1.806 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 158 | 158 | 109 | 119 | 0 | 94 | 88 | 0 | 0 |
N.S. |
1 | 1.00 | 0.69 | 0.75 | 0.00 | 0.59 | 0.56 | 0.00 | 0.00 |
time (sec) |
N/A | 0.268 | 5.290 | 1.231 | 0.000 | 0.129 | 1.518 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 89 | 85 | 0 | 41 | 37 | 0 | 37 |
N.S. |
1 | 1.00 | 0.85 | 0.81 | 0.00 | 0.39 | 0.35 | 0.00 | 0.35 |
time (sec) |
N/A | 0.178 | 0.087 | 1.009 | 0.000 | 0.078 | 0.461 | 0.000 | 18.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 730 | 660 | 421 | 404 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.90 | 0.58 | 0.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.151 | 9.226 | 2.336 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 1221 | 975 | 394 | 402 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.80 | 0.32 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.770 | 11.459 | 1.023 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 295 | 295 | 157 | 218 | 0 | 152 | 141 | 0 | 0 |
N.S. |
1 | 1.00 | 0.53 | 0.74 | 0.00 | 0.52 | 0.48 | 0.00 | 0.00 |
time (sec) |
N/A | 0.416 | 10.111 | 1.599 | 0.000 | 0.137 | 1.698 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 263 | 263 | 133 | 197 | 0 | 137 | 105 | 0 | 0 |
N.S. |
1 | 1.00 | 0.51 | 0.75 | 0.00 | 0.52 | 0.40 | 0.00 | 0.00 |
time (sec) |
N/A | 0.372 | 10.085 | 1.058 | 0.000 | 0.139 | 1.420 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 79 | 96 | 0 | 72 | 61 | 0 | 0 |
N.S. |
1 | 1.00 | 0.65 | 0.79 | 0.00 | 0.60 | 0.50 | 0.00 | 0.00 |
time (sec) |
N/A | 0.264 | 10.043 | 1.036 | 0.000 | 0.117 | 1.027 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 74 | 70 | 0 | 29 | 36 | 0 | 37 |
N.S. |
1 | 1.00 | 0.84 | 0.80 | 0.00 | 0.33 | 0.41 | 0.00 | 0.42 |
time (sec) |
N/A | 0.171 | 0.038 | 0.968 | 0.000 | 0.083 | 0.420 | 0.000 | 17.623 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 405 | 431 | 200 | 169 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.49 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.723 | 0.213 | 1.036 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 610 | 634 | 448 | 421 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.73 | 0.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.371 | 0.811 | 1.008 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 659 | 677 | 614 | 483 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.93 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.781 | 11.428 | 1.129 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 298 | 295 | 126 | 245 | 0 | 160 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.42 | 0.82 | 0.00 | 0.54 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.412 | 10.075 | 1.282 | 0.000 | 0.106 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 270 | 268 | 108 | 233 | 0 | 143 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.40 | 0.86 | 0.00 | 0.53 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.381 | 10.068 | 1.109 | 0.000 | 0.118 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 114 | 114 | 59 | 115 | 0 | 76 | 61 | 0 | 57 |
N.S. |
1 | 1.00 | 0.52 | 1.01 | 0.00 | 0.67 | 0.54 | 0.00 | 0.50 |
time (sec) |
N/A | 0.229 | 10.040 | 1.003 | 0.000 | 0.098 | 2.773 | 0.000 | 18.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 108 | 108 | 55 | 94 | 0 | 64 | 36 | 0 | 37 |
N.S. |
1 | 1.00 | 0.51 | 0.87 | 0.00 | 0.59 | 0.33 | 0.00 | 0.34 |
time (sec) |
N/A | 0.192 | 4.719 | 0.919 | 0.000 | 0.082 | 0.471 | 0.000 | 18.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 818 | 727 | 455 | 496 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.89 | 0.56 | 0.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.533 | 10.646 | 0.972 | 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 | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 349 | 349 | 274 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.883 | 0.427 | 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 | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 349 | 349 | 274 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.856 | 0.283 | 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 | C | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 1605 | 1590 | 455 | 1153 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.28 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 8.073 | 11.255 | 1.363 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 161 | 87 | 132 | 200 | 119 | 233 | 0 | 355 | 234 |
N.S. |
1 | 0.54 | 0.82 | 1.24 | 0.74 | 1.45 | 0.00 | 2.20 | 1.45 |
time (sec) |
N/A | 0.244 | 0.089 | 0.041 | 0.257 | 0.294 | 0.000 | 0.340 | 18.204 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 143 | 72 | 63 | 60 | 136 | 74 | 0 | 72 | 0 |
N.S. |
1 | 0.50 | 0.44 | 0.42 | 0.95 | 0.52 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.233 | 0.835 | 0.169 | 0.238 | 0.296 | 0.000 | 0.342 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 143 | 69 | 63 | 60 | 47 | 74 | 0 | 72 | 0 |
N.S. |
1 | 0.48 | 0.44 | 0.42 | 0.33 | 0.52 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.225 | 0.084 | 0.952 | 0.255 | 0.317 | 0.000 | 0.305 | 0.000 |
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 | 66 | 63 | 63 | 60 | 98 | 74 | 0 | 48 | 50 |
N.S. |
1 | 0.95 | 0.95 | 0.91 | 1.48 | 1.12 | 0.00 | 0.73 | 0.76 |
time (sec) |
N/A | 0.222 | 0.729 | 0.127 | 0.232 | 0.304 | 0.000 | 0.470 | 17.832 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 143 | 69 | 63 | 60 | 47 | 74 | 0 | 72 | 0 |
N.S. |
1 | 0.48 | 0.44 | 0.42 | 0.33 | 0.52 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.219 | 0.078 | 0.730 | 0.206 | 0.272 | 0.000 | 0.300 | 0.000 |
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 | 32 | 29 | 29 | 26 | 60 | 73 | 0 | 25 | 40 |
N.S. |
1 | 0.91 | 0.91 | 0.81 | 1.88 | 2.28 | 0.00 | 0.78 | 1.25 |
time (sec) |
N/A | 0.161 | 0.009 | 0.136 | 0.229 | 0.264 | 0.000 | 0.339 | 18.466 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 135 | 65 | 61 | 58 | 43 | 72 | 0 | 46 | 0 |
N.S. |
1 | 0.48 | 0.45 | 0.43 | 0.32 | 0.53 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.201 | 0.076 | 0.483 | 0.233 | 0.327 | 0.000 | 0.292 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 139 | 68 | 234 | 59 | 171 | 73 | 0 | 73 | 0 |
N.S. |
1 | 0.49 | 1.68 | 0.42 | 1.23 | 0.53 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.216 | 0.525 | 0.126 | 0.191 | 0.382 | 0.000 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 134 | 60 | 62 | 60 | 48 | 72 | 0 | 69 | 0 |
N.S. |
1 | 0.45 | 0.46 | 0.45 | 0.36 | 0.54 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.209 | 0.101 | 0.657 | 0.192 | 0.246 | 0.000 | 0.309 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 140 | 67 | 237 | 61 | 176 | 76 | 0 | 91 | 0 |
N.S. |
1 | 0.48 | 1.69 | 0.44 | 1.26 | 0.54 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.219 | 0.697 | 0.138 | 0.209 | 0.284 | 0.000 | 0.327 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 253 | 215 | 142 | 155 | 0 | 433 | 0 | 177 | 0 |
N.S. |
1 | 0.85 | 0.56 | 0.61 | 0.00 | 1.71 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 0.312 | 0.104 | 2.045 | 0.000 | 0.310 | 0.000 | 0.463 | 0.000 |
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 | 32 | 29 | 29 | 26 | 70 | 87 | 0 | 28 | 62 |
N.S. |
1 | 0.91 | 0.91 | 0.81 | 2.19 | 2.72 | 0.00 | 0.88 | 1.94 |
time (sec) |
N/A | 0.167 | 0.012 | 1.564 | 0.216 | 0.278 | 0.000 | 0.309 | 18.395 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 207 | 177 | 123 | 138 | 0 | 402 | 0 | 153 | 0 |
N.S. |
1 | 0.86 | 0.59 | 0.67 | 0.00 | 1.94 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.242 | 0.066 | 1.544 | 0.000 | 0.297 | 0.000 | 0.326 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 192 | 143 | 111 | 221 | 0 | 391 | 0 | 185 | 0 |
N.S. |
1 | 0.74 | 0.58 | 1.15 | 0.00 | 2.04 | 0.00 | 0.96 | 0.00 |
time (sec) |
N/A | 0.255 | 0.073 | 1.498 | 0.000 | 0.275 | 0.000 | 0.494 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 208 | 179 | 121 | 141 | 0 | 396 | 0 | 185 | 0 |
N.S. |
1 | 0.86 | 0.58 | 0.68 | 0.00 | 1.90 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.268 | 0.047 | 2.262 | 0.000 | 0.304 | 0.000 | 0.326 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 202 | 153 | 118 | 223 | 0 | 411 | 0 | 204 | 0 |
N.S. |
1 | 0.76 | 0.58 | 1.10 | 0.00 | 2.03 | 0.00 | 1.01 | 0.00 |
time (sec) |
N/A | 0.258 | 0.055 | 2.306 | 0.000 | 0.283 | 0.000 | 0.313 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 80 | 73 | 60 | 0 | 141 | 0 | 71 | 0 |
N.S. |
1 | 1.04 | 0.95 | 0.78 | 0.00 | 1.83 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 0.197 | 0.026 | 0.070 | 0.000 | 0.287 | 0.000 | 0.336 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 20 | 19 | 19 | 42 | 28 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.90 | 0.90 | 2.00 | 1.33 | 0.90 |
time (sec) |
N/A | 0.157 | 0.004 | 0.086 | 0.193 | 0.256 | 0.255 | 0.334 | 19.465 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 20 | 0 | 19 | 46 | 28 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.00 | 0.90 | 2.19 | 1.33 | 0.90 |
time (sec) |
N/A | 0.148 | 0.005 | 0.048 | 0.000 | 0.248 | 0.297 | 0.333 | 18.460 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 59 | 64 | 80 | 138 | 0 | 59 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.90 | 1.13 | 1.94 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.209 | 0.015 | 0.064 | 0.266 | 0.268 | 0.000 | 0.320 | 0.000 |
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 | 48 | 75 | 32 | 37 | 46 | 32 | 0 | 81 | 54 |
N.S. |
1 | 1.56 | 0.67 | 0.77 | 0.96 | 0.67 | 0.00 | 1.69 | 1.12 |
time (sec) |
N/A | 0.194 | 0.010 | 0.069 | 0.197 | 0.253 | 0.000 | 0.343 | 19.487 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 99 | 78 | 81 | 121 | 175 | 0 | 103 | 0 |
N.S. |
1 | 0.95 | 0.75 | 0.78 | 1.16 | 1.68 | 0.00 | 0.99 | 0.00 |
time (sec) |
N/A | 0.227 | 0.024 | 0.091 | 0.269 | 0.268 | 0.000 | 0.445 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 138 | 132 | 63 | 58 | 85 | 75 | 144 | 137 | 109 |
N.S. |
1 | 0.96 | 0.46 | 0.42 | 0.62 | 0.54 | 1.04 | 0.99 | 0.79 |
time (sec) |
N/A | 0.266 | 0.056 | 0.046 | 0.193 | 0.296 | 11.192 | 0.311 | 18.884 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 108 | 52 | 47 | 64 | 63 | 116 | 109 | 88 |
N.S. |
1 | 1.06 | 0.51 | 0.46 | 0.63 | 0.62 | 1.14 | 1.07 | 0.86 |
time (sec) |
N/A | 0.244 | 0.038 | 0.030 | 0.199 | 0.285 | 5.864 | 0.299 | 18.945 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 66 | 84 | 41 | 36 | 43 | 51 | 87 | 81 | 67 |
N.S. |
1 | 1.27 | 0.62 | 0.55 | 0.65 | 0.77 | 1.32 | 1.23 | 1.02 |
time (sec) |
N/A | 0.222 | 0.036 | 0.032 | 0.194 | 0.267 | 3.011 | 0.325 | 18.251 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 31 | 31 | 26 | 25 | 37 | 58 | 17 | 28 |
N.S. |
1 | 0.86 | 0.86 | 0.72 | 0.69 | 1.03 | 1.61 | 0.47 | 0.78 |
time (sec) |
N/A | 0.154 | 0.006 | 0.061 | 0.189 | 0.299 | 1.427 | 0.313 | 18.868 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | F(-1) | F | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 117 | 95 | 96 | 0 | 118 | 0 | 0 | 190 | 0 |
N.S. |
1 | 0.81 | 0.82 | 0.00 | 1.01 | 0.00 | 0.00 | 1.62 | 0.00 |
time (sec) |
N/A | 0.228 | 0.084 | 0.000 | 0.269 | 0.000 | 0.000 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | F(-1) | F | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 133 | 100 | 107 | 0 | 138 | 0 | 0 | 212 | 0 |
N.S. |
1 | 0.75 | 0.80 | 0.00 | 1.04 | 0.00 | 0.00 | 1.59 | 0.00 |
time (sec) |
N/A | 0.227 | 0.129 | 0.000 | 0.279 | 0.000 | 0.000 | 0.333 | 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 | 152 | 139 | 68 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.91 | 0.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.235 | 0.052 | 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 | 119 | 105 | 52 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.88 | 0.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.192 | 0.009 | 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 | 115 | 109 | 55 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.210 | 0.011 | 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(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 154 | 139 | 57 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.90 | 0.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.231 | 10.016 | 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 | A | F(-2) | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 75 | 68 | 0 | 80 | 114 | 61 | 0 |
N.S. |
1 | 1.00 | 1.06 | 0.96 | 0.00 | 1.13 | 1.61 | 0.86 | 0.00 |
time (sec) |
N/A | 0.199 | 0.071 | 0.992 | 0.000 | 0.314 | 0.900 | 0.413 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 48 | 53 | 59 | 114 | 0 | 44 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 1.23 | 2.38 | 0.00 | 0.92 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.213 | 0.046 | 1.531 | 0.000 | 0.115 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 55 | 28 | 0 | 43 | 71 | 61 | 0 |
N.S. |
1 | 1.00 | 1.72 | 0.88 | 0.00 | 1.34 | 2.22 | 1.91 | 0.00 |
time (sec) |
N/A | 0.164 | 0.012 | 1.032 | 0.000 | 0.336 | 0.872 | 0.351 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 18 | 43 | 0 | 9 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.50 | 3.58 | 0.00 | 0.75 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.150 | 0.013 | 0.498 | 0.000 | 0.113 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 244 | 268 | 198 | 241 | 0 | 541 | 0 | 226 | 0 |
N.S. |
1 | 1.10 | 0.81 | 0.99 | 0.00 | 2.22 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.438 | 0.437 | 0.226 | 0.000 | 0.373 | 0.000 | 0.382 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 161 | 185 | 161 | 189 | 0 | 407 | 0 | 169 | 0 |
N.S. |
1 | 1.15 | 1.00 | 1.17 | 0.00 | 2.53 | 0.00 | 1.05 | 0.00 |
time (sec) |
N/A | 0.336 | 0.087 | 0.123 | 0.000 | 0.343 | 0.000 | 0.385 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 103 | 110 | 132 | 154 | 0 | 313 | 0 | 138 | 0 |
N.S. |
1 | 1.07 | 1.28 | 1.50 | 0.00 | 3.04 | 0.00 | 1.34 | 0.00 |
time (sec) |
N/A | 0.240 | 0.049 | 0.104 | 0.000 | 0.342 | 0.000 | 0.395 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 142 | 147 | 179 | 0 | 865 | 0 | 0 | 0 |
N.S. |
1 | 1.27 | 1.31 | 1.60 | 0.00 | 7.72 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.309 | 0.041 | 0.102 | 0.000 | 0.479 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | B | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 110 | 137 | 162 | 0 | 333 | 0 | 242 | 0 |
N.S. |
1 | 0.87 | 1.08 | 1.28 | 0.00 | 2.62 | 0.00 | 1.91 | 0.00 |
time (sec) |
N/A | 0.267 | 0.057 | 0.150 | 0.000 | 0.482 | 0.000 | 0.393 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | B | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 208 | 184 | 174 | 201 | 0 | 427 | 0 | 549 | 0 |
N.S. |
1 | 0.88 | 0.84 | 0.97 | 0.00 | 2.05 | 0.00 | 2.64 | 0.00 |
time (sec) |
N/A | 0.365 | 0.087 | 0.159 | 0.000 | 0.883 | 0.000 | 0.449 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | B | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 318 | 267 | 222 | 257 | 0 | 561 | 0 | 1001 | 0 |
N.S. |
1 | 0.84 | 0.70 | 0.81 | 0.00 | 1.76 | 0.00 | 3.15 | 0.00 |
time (sec) |
N/A | 0.449 | 1.486 | 0.192 | 0.000 | 2.168 | 0.000 | 0.412 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 357 | 372 | 255 | 490 | 0 | 273 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.71 | 1.37 | 0.00 | 0.76 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.539 | 1.321 | 5.207 | 0.000 | 0.122 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 266 | 294 | 208 | 350 | 0 | 182 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 0.78 | 1.32 | 0.00 | 0.68 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.418 | 1.223 | 4.720 | 0.000 | 0.106 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 194 | 248 | 86 | 184 | 0 | 150 | 0 | 0 | 0 |
N.S. |
1 | 1.28 | 0.44 | 0.95 | 0.00 | 0.77 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.332 | 1.065 | 1.151 | 0.000 | 0.107 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 239 | 287 | 111 | 192 | 0 | 132 | 0 | 0 | 0 |
N.S. |
1 | 1.20 | 0.46 | 0.80 | 0.00 | 0.55 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.396 | 1.179 | 4.665 | 0.000 | 0.108 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 321 | 348 | 238 | 378 | 0 | 199 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 0.74 | 1.18 | 0.00 | 0.62 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.500 | 1.442 | 5.432 | 0.000 | 0.113 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 424 | 432 | 302 | 539 | 0 | 289 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.71 | 1.27 | 0.00 | 0.68 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.646 | 2.786 | 6.593 | 0.000 | 0.114 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 282 | 302 | 222 | 313 | 0 | 553 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.79 | 1.11 | 0.00 | 1.96 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.553 | 4.541 | 0.224 | 0.000 | 1.287 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 199 | 215 | 177 | 252 | 0 | 417 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 0.89 | 1.27 | 0.00 | 2.10 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.408 | 2.846 | 0.184 | 0.000 | 0.681 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 141 | 123 | 136 | 231 | 0 | 328 | 0 | 0 | 0 |
N.S. |
1 | 0.87 | 0.96 | 1.64 | 0.00 | 2.33 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.255 | 1.894 | 0.161 | 0.000 | 0.462 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 151 | 183 | 187 | 401 | 0 | 1049 | 0 | 0 | 0 |
N.S. |
1 | 1.21 | 1.24 | 2.66 | 0.00 | 6.95 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.366 | 2.299 | 0.139 | 0.000 | 0.898 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 165 | 123 | 146 | 239 | 0 | 350 | 0 | 0 | 0 |
N.S. |
1 | 0.75 | 0.88 | 1.45 | 0.00 | 2.12 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.289 | 3.804 | 0.209 | 0.000 | 0.908 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 256 | 214 | 186 | 270 | 0 | 435 | 0 | 0 | 0 |
N.S. |
1 | 0.84 | 0.73 | 1.05 | 0.00 | 1.70 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.414 | 4.303 | 0.240 | 0.000 | 2.537 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 366 | 301 | 245 | 333 | 0 | 573 | 0 | 0 | 0 |
N.S. |
1 | 0.82 | 0.67 | 0.91 | 0.00 | 1.57 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.537 | 4.762 | 0.268 | 0.000 | 9.703 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 391 | 403 | 266 | 775 | 0 | 275 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.68 | 1.98 | 0.00 | 0.70 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.631 | 5.606 | 9.881 | 0.000 | 0.122 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 310 | 339 | 235 | 734 | 0 | 229 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 0.76 | 2.37 | 0.00 | 0.74 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.477 | 4.955 | 8.941 | 0.000 | 0.124 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 262 | 305 | 206 | 527 | 0 | 173 | 0 | 0 | 0 |
N.S. |
1 | 1.16 | 0.79 | 2.01 | 0.00 | 0.66 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.398 | 1.210 | 3.336 | 0.000 | 0.108 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 307 | 360 | 228 | 670 | 0 | 170 | 0 | 0 | 0 |
N.S. |
1 | 1.17 | 0.74 | 2.18 | 0.00 | 0.55 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.518 | 5.247 | 8.050 | 0.000 | 0.116 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 383 | 415 | 253 | 790 | 0 | 214 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 0.66 | 2.06 | 0.00 | 0.56 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.634 | 5.625 | 8.284 | 0.000 | 0.117 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 480 | 489 | 322 | 908 | 0 | 293 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.67 | 1.89 | 0.00 | 0.61 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.756 | 6.229 | 10.053 | 0.000 | 0.122 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 57 | 95 | 52 | 0 | 55 | 0 | 18 | 55 |
N.S. |
1 | 1.12 | 1.86 | 1.02 | 0.00 | 1.08 | 0.00 | 0.35 | 1.08 |
time (sec) |
N/A | 0.189 | 0.127 | 0.410 | 0.000 | 0.306 | 0.000 | 0.311 | 17.176 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 76 | 119 | 78 | 76 | 77 | 0 | 30 | 88 |
N.S. |
1 | 1.06 | 1.65 | 1.08 | 1.06 | 1.07 | 0.00 | 0.42 | 1.22 |
time (sec) |
N/A | 0.198 | 0.205 | 0.442 | 0.269 | 0.325 | 0.000 | 0.318 | 0.222 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 59 | 95 | 68 | 0 | 55 | 0 | 22 | 56 |
N.S. |
1 | 1.11 | 1.79 | 1.28 | 0.00 | 1.04 | 0.00 | 0.42 | 1.06 |
time (sec) |
N/A | 0.192 | 0.206 | 0.830 | 0.000 | 0.361 | 0.000 | 0.366 | 16.809 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 113 | 108 | 95 | 80 | 0 | 65 | 0 | 57 | 101 |
N.S. |
1 | 0.96 | 0.84 | 0.71 | 0.00 | 0.58 | 0.00 | 0.50 | 0.89 |
time (sec) |
N/A | 0.240 | 0.469 | 0.869 | 0.000 | 0.341 | 0.000 | 0.318 | 16.905 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 106 | 117 | 106 | 114 | 121 | 82 | 0 | 47 | 134 |
N.S. |
1 | 1.10 | 1.00 | 1.08 | 1.14 | 0.77 | 0.00 | 0.44 | 1.26 |
time (sec) |
N/A | 0.233 | 0.649 | 0.777 | 0.270 | 0.342 | 0.000 | 0.322 | 0.232 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 49 | 42 | 0 | 32 | 0 | 40 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.81 | 0.00 | 0.62 | 0.00 | 0.77 | 0.00 |
time (sec) |
N/A | 0.192 | 0.031 | 0.873 | 0.000 | 0.303 | 0.000 | 0.376 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 65 | 60 | 0 | 42 | 0 | 61 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.88 | 0.00 | 0.62 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.224 | 0.043 | 0.898 | 0.000 | 0.342 | 0.000 | 0.353 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 281 | 274 | 224 | 243 | 0 | 545 | 0 | 235 | 0 |
N.S. |
1 | 0.98 | 0.80 | 0.86 | 0.00 | 1.94 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.424 | 1.458 | 0.161 | 0.000 | 0.393 | 0.000 | 0.362 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 169 | 184 | 161 | 191 | 0 | 413 | 0 | 172 | 0 |
N.S. |
1 | 1.09 | 0.95 | 1.13 | 0.00 | 2.44 | 0.00 | 1.02 | 0.00 |
time (sec) |
N/A | 0.309 | 0.886 | 0.127 | 0.000 | 0.352 | 0.000 | 0.366 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 106 | 113 | 136 | 154 | 0 | 313 | 0 | 142 | 0 |
N.S. |
1 | 1.07 | 1.28 | 1.45 | 0.00 | 2.95 | 0.00 | 1.34 | 0.00 |
time (sec) |
N/A | 0.240 | 0.377 | 0.110 | 0.000 | 0.322 | 0.000 | 0.402 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 142 | 147 | 179 | 0 | 881 | 0 | 0 | 0 |
N.S. |
1 | 1.27 | 1.31 | 1.60 | 0.00 | 7.87 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.313 | 0.429 | 0.092 | 0.000 | 0.524 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | B | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 130 | 113 | 143 | 162 | 0 | 333 | 0 | 238 | 0 |
N.S. |
1 | 0.87 | 1.10 | 1.25 | 0.00 | 2.56 | 0.00 | 1.83 | 0.00 |
time (sec) |
N/A | 0.267 | 0.606 | 0.145 | 0.000 | 0.540 | 0.000 | 0.347 | 0.000 |