Detailed conclusion table per each integral is given by 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 just an F.
In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.06 |
time (sec) |
N/A | 0.111 | 11.735 | 0.117 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | A | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 152 | 141 | 1741 | 146 | 424 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.93 | 11.45 | 0.96 | 2.79 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.217 | 3.165 | 1.374 | 0.695 | 0.485 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | A | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 126 | 116 | 1684 | 123 | 360 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.92 | 13.37 | 0.98 | 2.86 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.185 | 4.061 | 1.111 | 0.693 | 0.499 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | A | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 90 | 1603 | 100 | 306 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.90 | 16.03 | 1.00 | 3.06 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.157 | 4.055 | 0.931 | 0.706 | 0.439 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | B | A | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 197 | 265 | 72 | 227 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 2.86 | 3.84 | 1.04 | 3.29 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.097 | 2.897 | 0.566 | 0.700 | 0.374 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A | 0.060 | 3.036 | 0.145 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | A | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 165 | 147 | 1801 | 149 | 451 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.89 | 10.92 | 0.90 | 2.73 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.208 | 3.609 | 1.365 | 0.694 | 0.407 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | A | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 137 | 121 | 1742 | 125 | 382 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.88 | 12.72 | 0.91 | 2.79 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.186 | 4.054 | 1.154 | 0.693 | 0.391 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | A | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 109 | 94 | 1659 | 101 | 323 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.86 | 15.22 | 0.93 | 2.96 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.159 | 3.512 | 0.951 | 0.708 | 0.393 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | B | A | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 208 | 299 | 73 | 240 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 2.74 | 3.93 | 0.96 | 3.16 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.095 | 3.335 | 0.561 | 0.693 | 0.367 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A | 0.066 | 3.611 | 0.142 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | C | F | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 302 | 302 | 654 | 7429 | 0 | 3041 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 2.17 | 24.60 | 0.00 | 10.07 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.167 | 0.744 | 14.719 | 0.000 | 0.484 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 234 | 234 | 409 | 5543 | 0 | 1788 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.75 | 23.69 | 0.00 | 7.64 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.120 | 0.405 | 11.053 | 0.000 | 0.530 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 162 | 295 | 2543 | 0 | 948 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.82 | 15.70 | 0.00 | 5.85 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.081 | 0.323 | 1.081 | 0.000 | 0.384 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 127 | 169 | 182 | 499 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.61 | 2.14 | 2.30 | 6.32 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.033 | 0.034 | 0.602 | 0.502 | 0.408 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.06 |
time (sec) |
N/A | 0.027 | 5.050 | 0.145 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 395 | 395 | 346 | 6895 | 0 | 2165 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.88 | 17.46 | 0.00 | 5.48 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.357 | 0.649 | 25.551 | 0.000 | 0.446 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 295 | 295 | 257 | 6521 | 0 | 1689 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.87 | 22.11 | 0.00 | 5.73 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.282 | 0.442 | 2.451 | 0.000 | 0.438 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | B | B | B | F | F | F |
verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 194 | 4654 | 563 | 372 | 1185 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 23.99 | 2.90 | 1.92 | 6.11 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.173 | 30.408 | 1.277 | 0.537 | 0.530 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.06 |
time (sec) |
N/A | 0.111 | 3.511 | 0.132 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | B | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 170 | 155 | 2346 | 343 | 345 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.91 | 13.80 | 2.02 | 2.03 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.197 | 0.449 | 1.803 | 0.281 | 0.401 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | B | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 133 | 119 | 2256 | 248 | 293 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.89 | 16.96 | 1.86 | 2.20 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.168 | 0.212 | 1.191 | 0.287 | 0.389 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 84 | 321 | 260 | 218 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.90 | 3.45 | 2.80 | 2.34 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.101 | 6.225 | 0.749 | 0.482 | 0.404 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A | 0.075 | 0.756 | 0.120 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | B | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 171 | 156 | 2456 | 342 | 345 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.91 | 14.36 | 2.00 | 2.02 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.202 | 0.297 | 1.714 | 0.289 | 0.428 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | B | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 134 | 120 | 2358 | 247 | 293 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.90 | 17.60 | 1.84 | 2.19 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.171 | 0.229 | 1.273 | 0.278 | 0.441 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 85 | 365 | 262 | 219 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.90 | 3.88 | 2.79 | 2.33 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.103 | 6.015 | 0.740 | 0.471 | 0.364 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A | 0.072 | 1.204 | 0.122 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | C | F | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 302 | 302 | 654 | 7429 | 0 | 2799 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 2.17 | 24.60 | 0.00 | 9.27 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.162 | 0.175 | 14.941 | 0.000 | 0.470 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 234 | 234 | 409 | 5543 | 0 | 1590 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.75 | 23.69 | 0.00 | 6.79 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.124 | 0.115 | 11.232 | 0.000 | 0.460 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 162 | 295 | 2544 | 0 | 794 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.82 | 15.70 | 0.00 | 4.90 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.080 | 0.206 | 1.099 | 0.000 | 0.449 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 127 | 145 | 184 | 389 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.61 | 1.84 | 2.33 | 4.92 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.033 | 0.047 | 0.589 | 0.507 | 0.444 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.06 |
time (sec) |
N/A | 0.030 | 0.621 | 0.135 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 391 | 391 | 339 | 6739 | 0 | 1799 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.87 | 17.24 | 0.00 | 4.60 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.354 | 0.663 | 28.345 | 0.000 | 0.572 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 293 | 293 | 253 | 6389 | 0 | 1463 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.86 | 21.81 | 0.00 | 4.99 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.286 | 0.410 | 2.470 | 0.000 | 0.607 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | B | B | B | F | F | F |
verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 194 | 4463 | 569 | 392 | 1099 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 23.01 | 2.93 | 2.02 | 5.66 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.170 | 29.488 | 1.359 | 0.533 | 0.593 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.06 |
time (sec) |
N/A | 0.110 | 3.882 | 0.168 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | B | A | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 168 | 155 | 2456 | 344 | 180 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.92 | 14.62 | 2.05 | 1.07 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.205 | 0.311 | 1.949 | 0.285 | 0.408 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | B | A | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 132 | 119 | 2358 | 249 | 157 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.90 | 17.86 | 1.89 | 1.19 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.171 | 0.202 | 1.342 | 0.282 | 0.410 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | A | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 83 | 321 | 288 | 122 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.89 | 3.45 | 3.10 | 1.31 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.102 | 23.927 | 0.835 | 0.476 | 0.376 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A | 0.065 | 0.760 | 0.163 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | B | A | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 169 | 155 | 2346 | 345 | 180 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.92 | 13.88 | 2.04 | 1.07 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.201 | 0.308 | 1.867 | 0.298 | 0.437 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | B | A | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 133 | 119 | 2256 | 250 | 157 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.89 | 16.96 | 1.88 | 1.18 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.177 | 0.231 | 1.331 | 0.279 | 0.355 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | A | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 84 | 365 | 286 | 122 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.89 | 3.88 | 3.04 | 1.30 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.105 | 20.188 | 0.823 | 0.489 | 0.360 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | A |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A | 0.075 | 1.172 | 0.186 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | B | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 46 | 31 | 58 | 65 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 2.19 | 1.48 | 2.76 | 3.10 | 0.00 | 0.00 | -0.05 |
time (sec) |
N/A | 0.008 | 0.181 | 0.050 | 0.259 | 0.446 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 71 | 62 | 59 | 95 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.65 | 1.44 | 1.37 | 2.21 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A | 0.032 | 0.019 | 0.039 | 0.257 | 0.390 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 93 | 79 | 76 | 120 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.60 | 1.36 | 1.31 | 2.07 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A | 0.048 | 0.021 | 0.038 | 0.256 | 0.367 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 69 | 59 | 107 | 138 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.97 | 1.69 | 3.06 | 3.94 | 0.00 | 0.00 | -0.03 |
time (sec) |
N/A | 0.011 | 0.155 | 0.057 | 0.256 | 0.371 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | A | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 113 | 178 | 108 | 199 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.59 | 2.51 | 1.52 | 2.80 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.043 | 0.031 | 0.097 | 0.270 | 0.361 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | A | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 149 | 326 | 142 | 248 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.48 | 3.23 | 1.41 | 2.46 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.069 | 0.029 | 0.112 | 0.266 | 0.383 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | F(-2) | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 168 | 108 | 160 | 202 | 284 | 0 | 0 | -1 |
N.S. |
1 | 1.00 | 0.64 | 0.95 | 1.20 | 1.69 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.096 | 0.500 | 0.306 | 0.261 | 0.360 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | A | B | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 211 | 177 | 596 | 194 | 396 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.84 | 2.82 | 0.92 | 1.88 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.112 | 0.084 | 0.065 | 0.299 | 0.401 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | A | A | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 264 | 264 | 235 | 672 | 254 | 480 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.89 | 2.55 | 0.96 | 1.82 | 0.00 | 0.00 | -0.00 |
time (sec) |
N/A | 0.143 | 0.062 | 0.069 | 0.288 | 0.439 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | B | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 153 | 868 | 184 | 234 | 0 | 157 | 179 |
N.S. | 1 | 1.00 | 1.43 | 8.11 | 1.72 | 2.19 | 0.00 | 1.47 | 1.67 |
time (sec) |
N/A | 0.126 | 0.096 | 0.388 | 0.485 | 0.423 | 0.000 | 0.534 | 1.594 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 60 | 887 | 64 | 93 | 0 | 147 | 111 |
N.S. |
1 | 1.00 | 1.22 | 18.10 | 1.31 | 1.90 | 0.00 | 3.00 | 2.27 |
time (sec) |
N/A | 0.054 | 0.045 | 0.270 | 0.262 | 0.390 | 0.000 | 0.465 | 1.517 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 46 | 68 | 43 | 46 | 58 | 35 | 28 |
N.S. | 1 | 1.00 | 1.02 | 1.51 | 0.96 | 1.02 | 1.29 | 0.78 | 0.62 |
time (sec) |
N/A | 0.039 | 0.043 | 0.158 | 0.267 | 0.331 | 0.784 | 0.393 | 0.157 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 46 | 349 | 43 | 25 | 0 | 40 | 28 |
N.S. | 1 | 1.00 | 1.02 | 7.76 | 0.96 | 0.56 | 0.00 | 0.89 | 0.62 |
time (sec) |
N/A | 0.039 | 0.042 | 0.139 | 0.260 | 0.337 | 0.000 | 0.386 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 59 | 872 | 64 | 92 | 0 | 98 | 119 |
N.S. |
1 | 1.00 | 1.20 | 17.80 | 1.31 | 1.88 | 0.00 | 2.00 | 2.43 |
time (sec) |
N/A | 0.047 | 0.046 | 0.231 | 0.277 | 0.337 | 0.000 | 0.488 | 1.711 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | B | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 150 | 842 | 184 | 233 | 0 | 167 | 187 |
N.S. | 1 | 1.00 | 1.40 | 7.87 | 1.72 | 2.18 | 0.00 | 1.56 | 1.75 |
time (sec) |
N/A | 0.117 | 0.091 | 0.316 | 0.467 | 0.379 | 0.000 | 0.529 | 1.620 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | C | F | B | F(-1) | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 136 | 114 | 668 | 0 | 461 | 0 | 0 | -1 |
N.S. |
1 | 1.00 | 0.84 | 4.91 | 0.00 | 3.39 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.385 | 0.186 | 0.224 | 0.000 | 0.350 | 0.000 | 0.000 | 0.000 |