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 | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 299 | 299 | 239 | 1190 | 0 | 536 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.80 | 3.98 | 0.00 | 1.79 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.430 | 0.720 | 4.089 | 0.000 | 0.144 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 203 | 203 | 203 | 1039 | 0 | 474 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 5.12 | 0.00 | 2.33 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.188 | 0.659 | 6.272 | 0.000 | 0.137 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 238 | 238 | 259 | 1249 | 0 | 522 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.09 | 5.25 | 0.00 | 2.19 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.268 | 2.404 | 99.783 | 0.000 | 0.137 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 322 | 322 | 351 | 1259 | 0 | 561 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.09 | 3.91 | 0.00 | 1.74 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.445 | 6.327 | 4.219 | 0.000 | 0.146 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 439 | 439 | 338 | 1887 | 0 | 697 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.77 | 4.30 | 0.00 | 1.59 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.885 | 3.867 | 6439.010 | 0.000 | 0.176 | 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) | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 152 | 152 | 118 | 149 | 160 | 111 | 0 | 161 | 0 |
| N.S. |
1 | 1.00 | 0.78 | 0.98 | 1.05 | 0.73 | 0.00 | 1.06 | 0.00 |
| time (sec) |
N/A | 0.076 | 0.224 | 0.398 | 0.219 | 0.317 | 0.000 | 0.377 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | F(-1) | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 81 | 81 | 58 | 60 | 75 | 54 | 0 | 72 | 0 |
| N.S. |
1 | 1.00 | 0.72 | 0.74 | 0.93 | 0.67 | 0.00 | 0.89 | 0.00 |
| time (sec) |
N/A | 0.058 | 0.062 | 0.366 | 0.211 | 0.296 | 0.000 | 0.366 | 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 | 22 | 22 | 22 | 21 | 20 | 20 | 54 | 20 | 20 |
| N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.91 | 0.91 | 2.45 | 0.91 | 0.91 |
| time (sec) |
N/A | 0.025 | 0.011 | 0.191 | 0.258 | 0.304 | 0.340 | 0.371 | 5.555 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 74 | 74 | 74 | 60 | 0 | 1805 | 0 | 75 | 0 |
| N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.00 | 24.39 | 0.00 | 1.01 | 0.00 |
| time (sec) |
N/A | 0.067 | 0.039 | 0.462 | 0.000 | 0.558 | 0.000 | 0.354 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 144 | 144 | 176 | 167 | 0 | 2245 | 0 | 212 | 0 |
| N.S. |
1 | 1.00 | 1.22 | 1.16 | 0.00 | 15.59 | 0.00 | 1.47 | 0.00 |
| time (sec) |
N/A | 0.203 | 0.351 | 0.819 | 0.000 | 0.630 | 0.000 | 0.425 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 230 | 230 | 244 | 270 | 0 | 2721 | 0 | 419 | 0 |
| N.S. |
1 | 1.00 | 1.06 | 1.17 | 0.00 | 11.83 | 0.00 | 1.82 | 0.00 |
| time (sec) |
N/A | 0.257 | 1.247 | 1.570 | 0.000 | 0.872 | 0.000 | 0.392 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 247 | 247 | 219 | 942 | 0 | 493 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.89 | 3.81 | 0.00 | 2.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.262 | 0.733 | 1.470 | 0.000 | 0.133 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 175 | 175 | 145 | 462 | 0 | 408 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.83 | 2.64 | 0.00 | 2.33 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.136 | 0.468 | 1.022 | 0.000 | 0.116 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 183 | 183 | 177 | 640 | 0 | 458 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.97 | 3.50 | 0.00 | 2.50 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.156 | 0.478 | 1.221 | 0.000 | 0.110 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 291 | 291 | 306 | 1313 | 0 | 571 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.05 | 4.51 | 0.00 | 1.96 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.324 | 2.895 | 2.016 | 0.000 | 0.132 | 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) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 150 | 150 | 116 | 137 | 124 | 125 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.77 | 0.91 | 0.83 | 0.83 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.097 | 0.176 | 0.267 | 0.193 | 0.344 | 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) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 79 | 79 | 57 | 62 | 67 | 67 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.72 | 0.78 | 0.85 | 0.85 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.062 | 0.047 | 0.287 | 0.251 | 0.283 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 22 | 22 | 22 | 21 | 20 | 32 | 56 | 0 | 51 |
| N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.91 | 1.45 | 2.55 | 0.00 | 2.32 |
| time (sec) |
N/A | 0.028 | 0.012 | 0.181 | 0.211 | 0.288 | 0.656 | 0.000 | 5.993 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 105 | 105 | 91 | 94 | 0 | 2301 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.87 | 0.90 | 0.00 | 21.91 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.113 | 0.056 | 0.602 | 0.000 | 0.594 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 186 | 186 | 221 | 233 | 0 | 3117 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.19 | 1.25 | 0.00 | 16.76 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.234 | 0.747 | 0.850 | 0.000 | 0.767 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-2) | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 284 | 284 | 324 | 602 | 0 | 3861 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.14 | 2.12 | 0.00 | 13.60 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.345 | 1.384 | 0.933 | 0.000 | 1.049 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 313 | 313 | 273 | 1195 | 0 | 723 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.87 | 3.82 | 0.00 | 2.31 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.379 | 1.044 | 3.497 | 0.000 | 0.171 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 229 | 229 | 187 | 797 | 0 | 598 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.82 | 3.48 | 0.00 | 2.61 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.225 | 0.789 | 1.759 | 0.000 | 0.148 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 160 | 160 | 125 | 433 | 0 | 470 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.78 | 2.71 | 0.00 | 2.94 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.136 | 2.648 | 1.361 | 0.000 | 0.109 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 251 | 251 | 205 | 1064 | 0 | 685 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.82 | 4.24 | 0.00 | 2.73 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.262 | 1.222 | 1.560 | 0.000 | 0.124 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 359 | 359 | 348 | 1648 | 0 | 878 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.97 | 4.59 | 0.00 | 2.45 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.414 | 2.172 | 3.110 | 0.000 | 0.166 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-1) | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 150 | 150 | 117 | 126 | 0 | 147 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.78 | 0.84 | 0.00 | 0.98 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.079 | 0.206 | 0.266 | 0.000 | 0.305 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 79 | 79 | 56 | 60 | 64 | 91 | 304 | 0 | 1402 |
| N.S. |
1 | 1.00 | 0.71 | 0.76 | 0.81 | 1.15 | 3.85 | 0.00 | 17.75 |
| time (sec) |
N/A | 0.058 | 0.042 | 0.281 | 0.186 | 0.270 | 2.305 | 0.000 | 12.141 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | B | B | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 24 | 24 | 24 | 21 | 20 | 55 | 87 | 0 | 157 |
| N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.83 | 2.29 | 3.62 | 0.00 | 6.54 |
| time (sec) |
N/A | 0.027 | 0.016 | 0.195 | 0.183 | 0.271 | 2.308 | 0.000 | 6.575 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 139 | 139 | 94 | 122 | 0 | 3225 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.68 | 0.88 | 0.00 | 23.20 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.169 | 0.053 | 0.694 | 0.000 | 0.677 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F(-2) | B | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 231 | 231 | 245 | 263 | 0 | 4329 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.06 | 1.14 | 0.00 | 18.74 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.288 | 0.573 | 1.033 | 0.000 | 0.870 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-2) | B | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 339 | 339 | 296 | 632 | 0 | 5313 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.87 | 1.86 | 0.00 | 15.67 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.447 | 2.114 | 1.016 | 0.000 | 1.357 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 384 | 384 | 356 | 2253 | 0 | 1043 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.93 | 5.87 | 0.00 | 2.72 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.515 | 1.209 | 4.439 | 0.000 | 0.283 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 293 | 293 | 244 | 1642 | 0 | 874 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.83 | 5.60 | 0.00 | 2.98 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.364 | 0.811 | 3.500 | 0.000 | 0.188 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 221 | 221 | 174 | 1046 | 0 | 705 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.79 | 4.73 | 0.00 | 3.19 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.230 | 0.740 | 1.948 | 0.000 | 0.156 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 219 | 219 | 167 | 864 | 0 | 711 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.76 | 3.95 | 0.00 | 3.25 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.184 | 0.740 | 1.430 | 0.000 | 0.124 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 325 | 325 | 241 | 1653 | 0 | 993 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.74 | 5.09 | 0.00 | 3.06 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.388 | 1.310 | 3.369 | 0.000 | 0.161 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 425 | 425 | 341 | 2585 | 0 | 1242 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.80 | 6.08 | 0.00 | 2.92 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.590 | 1.693 | 4.394 | 0.000 | 0.220 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 124 | 124 | 104 | 231 | 0 | 116 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.84 | 1.86 | 0.00 | 0.94 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.069 | 0.775 | 4.937 | 0.000 | 0.100 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 95 | 95 | 79 | 222 | 0 | 111 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.83 | 2.34 | 0.00 | 1.17 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.060 | 0.497 | 3.926 | 0.000 | 0.095 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 95 | 95 | 79 | 185 | 0 | 95 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.83 | 1.95 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.061 | 0.457 | 2.553 | 0.000 | 0.097 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 63 | 63 | 56 | 123 | 0 | 85 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.89 | 1.95 | 0.00 | 1.35 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.037 | 0.203 | 1.991 | 0.000 | 0.096 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | C | F | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 61 | 61 | 50 | 75 | 0 | 75 | 0 | 0 | 47 |
| N.S. |
1 | 1.00 | 0.82 | 1.23 | 0.00 | 1.23 | 0.00 | 0.00 | 0.77 |
| time (sec) |
N/A | 0.033 | 0.283 | 1.231 | 0.000 | 0.093 | 0.000 | 0.000 | 6.074 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 91 | 91 | 54 | 119 | 0 | 110 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.59 | 1.31 | 0.00 | 1.21 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.047 | 0.241 | 2.100 | 0.000 | 0.103 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 97 | 97 | 55 | 193 | 0 | 109 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.57 | 1.99 | 0.00 | 1.12 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.058 | 0.285 | 2.325 | 0.000 | 0.094 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 126 | 126 | 70 | 309 | 0 | 127 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.56 | 2.45 | 0.00 | 1.01 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.075 | 0.435 | 3.685 | 0.000 | 0.101 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 188 | 188 | 160 | 472 | 0 | 173 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.85 | 2.51 | 0.00 | 0.92 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.139 | 1.726 | 16.839 | 0.000 | 0.114 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 149 | 149 | 113 | 408 | 0 | 161 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.76 | 2.74 | 0.00 | 1.08 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.115 | 0.966 | 13.064 | 0.000 | 0.110 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 149 | 149 | 115 | 343 | 0 | 143 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.77 | 2.30 | 0.00 | 0.96 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.115 | 1.044 | 6.969 | 0.000 | 0.111 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 109 | 109 | 80 | 251 | 0 | 126 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.73 | 2.30 | 0.00 | 1.16 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.090 | 0.521 | 5.221 | 0.000 | 0.105 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 109 | 109 | 75 | 210 | 0 | 108 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.69 | 1.93 | 0.00 | 0.99 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.090 | 0.786 | 3.519 | 0.000 | 0.095 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 113 | 113 | 71 | 198 | 0 | 137 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.63 | 1.75 | 0.00 | 1.21 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.099 | 0.720 | 4.684 | 0.000 | 0.097 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 119 | 119 | 72 | 333 | 0 | 136 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.61 | 2.80 | 0.00 | 1.14 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.108 | 0.724 | 4.520 | 0.000 | 0.112 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 160 | 160 | 105 | 564 | 0 | 162 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.66 | 3.52 | 0.00 | 1.01 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.121 | 0.972 | 7.342 | 0.000 | 0.097 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 237 | 237 | 205 | 514 | 0 | 202 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.86 | 2.17 | 0.00 | 0.85 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.231 | 1.940 | 40.983 | 0.000 | 0.132 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 197 | 197 | 150 | 504 | 0 | 189 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.76 | 2.56 | 0.00 | 0.96 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.203 | 1.399 | 38.954 | 0.000 | 0.113 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 197 | 197 | 153 | 450 | 0 | 169 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.78 | 2.28 | 0.00 | 0.86 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.194 | 1.395 | 7.447 | 0.000 | 0.113 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 156 | 156 | 101 | 339 | 0 | 150 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.65 | 2.17 | 0.00 | 0.96 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.177 | 0.820 | 5.341 | 0.000 | 0.105 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 152 | 152 | 94 | 279 | 0 | 133 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.62 | 1.84 | 0.00 | 0.88 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.178 | 1.095 | 3.495 | 0.000 | 0.097 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 160 | 160 | 98 | 248 | 0 | 165 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.61 | 1.55 | 0.00 | 1.03 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.185 | 0.862 | 4.632 | 0.000 | 0.102 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 164 | 164 | 103 | 384 | 0 | 159 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.63 | 2.34 | 0.00 | 0.97 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.170 | 1.188 | 4.970 | 0.000 | 0.098 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 187 | 187 | 126 | 618 | 0 | 190 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.67 | 3.30 | 0.00 | 1.02 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.185 | 1.202 | 8.388 | 0.000 | 0.096 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 188 | 188 | 140 | 750 | 0 | 185 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.74 | 3.99 | 0.00 | 0.98 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.189 | 1.465 | 9.538 | 0.000 | 0.109 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 305 | 305 | 251 | 781 | 0 | 258 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.82 | 2.56 | 0.00 | 0.85 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.387 | 4.414 | 153.524 | 0.000 | 0.144 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 258 | 258 | 209 | 758 | 0 | 237 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.81 | 2.94 | 0.00 | 0.92 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.351 | 2.531 | 151.023 | 0.000 | 0.139 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 258 | 258 | 189 | 639 | 0 | 215 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.73 | 2.48 | 0.00 | 0.83 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.353 | 2.798 | 12.334 | 0.000 | 0.114 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 210 | 210 | 137 | 525 | 0 | 192 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.65 | 2.50 | 0.00 | 0.91 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.300 | 1.673 | 9.961 | 0.000 | 0.110 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 210 | 210 | 130 | 412 | 0 | 172 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.62 | 1.96 | 0.00 | 0.82 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.306 | 1.649 | 6.902 | 0.000 | 0.112 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 218 | 218 | 135 | 378 | 0 | 203 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.62 | 1.73 | 0.00 | 0.93 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.583 | 1.263 | 8.510 | 0.000 | 0.117 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 216 | 216 | 137 | 575 | 0 | 194 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.63 | 2.66 | 0.00 | 0.90 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.564 | 1.767 | 8.523 | 0.000 | 0.115 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 237 | 237 | 152 | 874 | 0 | 219 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.64 | 3.69 | 0.00 | 0.92 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.590 | 1.482 | 11.411 | 0.000 | 0.119 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 241 | 241 | 177 | 1067 | 0 | 215 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.73 | 4.43 | 0.00 | 0.89 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.343 | 2.166 | 13.286 | 0.000 | 0.105 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 264 | 264 | 219 | 1315 | 0 | 252 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.83 | 4.98 | 0.00 | 0.95 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.341 | 2.910 | 18.691 | 0.000 | 0.107 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 531 | 531 | 2035 | 1256 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.83 | 2.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.299 | 53.604 | 9.179 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 446 | 446 | 757 | 1203 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.70 | 2.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.880 | 37.443 | 6.347 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 461 | 461 | 1955 | 1000 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 4.24 | 2.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.819 | 23.472 | 5.338 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 384 | 384 | 709 | 1025 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.85 | 2.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.566 | 15.131 | 5.285 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 397 | 397 | 219 | 844 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.55 | 2.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.607 | 11.923 | 2.931 | 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 | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 292 | 292 | 361 | 825 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.24 | 2.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.393 | 13.011 | 2.391 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 299 | 299 | 558 | 845 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.87 | 2.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.403 | 11.310 | 2.350 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 411 | 411 | 791 | 1202 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.92 | 2.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.661 | 19.422 | 4.391 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 434 | 434 | 1192 | 1061 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.75 | 2.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.711 | 20.698 | 6.733 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 486 | 486 | 881 | 1723 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.81 | 3.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.858 | 6.552 | 9.448 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 543 | 543 | 2030 | 2195 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.74 | 4.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.030 | 22.349 | 21.561 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 459 | 459 | 835 | 2107 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.82 | 4.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.722 | 20.592 | 17.402 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 473 | 473 | 1956 | 1962 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 4.14 | 4.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.711 | 20.709 | 16.279 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 390 | 390 | 371 | 1869 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.95 | 4.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.548 | 15.176 | 15.573 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 404 | 404 | 562 | 1803 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.39 | 4.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.594 | 8.823 | 7.732 | 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 | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 422 | 422 | 787 | 1495 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.86 | 3.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.568 | 13.532 | 6.731 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 429 | 429 | 1181 | 1346 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.75 | 3.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.610 | 20.091 | 7.039 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 492 | 492 | 777 | 2128 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.58 | 4.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.823 | 4.407 | 8.677 | 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(-2) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 514 | 514 | 1258 | 2063 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.45 | 4.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.980 | 20.680 | 11.583 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 574 | 574 | 949 | 2891 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.65 | 5.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.393 | 6.637 | 15.517 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 575 | 575 | 932 | 3556 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.62 | 6.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.949 | 19.277 | 71.914 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 589 | 589 | 2024 | 3346 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.44 | 5.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.983 | 23.130 | 66.513 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 483 | 483 | 777 | 3373 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.61 | 6.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.704 | 16.565 | 64.670 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 497 | 497 | 1954 | 3151 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 3.93 | 6.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.724 | 19.943 | 64.168 | 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 | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 505 | 505 | 831 | 3270 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.65 | 6.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.729 | 19.726 | 65.543 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 519 | 519 | 1211 | 2986 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.33 | 5.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.787 | 20.482 | 10.642 | 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(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 514 | 514 | 748 | 2562 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.46 | 4.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.778 | 18.430 | 10.439 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |