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(-1) | A | F(-1) | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 254 | 291 | 144 | 392 | 0 | 212 | 0 | 310 | 0 |
| N.S. |
1 | 1.15 | 0.57 | 1.54 | 0.00 | 0.83 | 0.00 | 1.22 | 0.00 |
| time (sec) |
N/A | 1.769 | 0.844 | 10.777 | 0.000 | 0.283 | 0.000 | 1.753 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 208 | 233 | 118 | 324 | 1624159 | 191 | 0 | 244 | 0 |
| N.S. |
1 | 1.12 | 0.57 | 1.56 | 7808.46 | 0.92 | 0.00 | 1.17 | 0.00 |
| time (sec) |
N/A | 1.402 | 0.684 | 10.096 | 33.512 | 0.282 | 0.000 | 0.867 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 164 | 178 | 98 | 318 | 946903 | 171 | 0 | 208 | 0 |
| N.S. |
1 | 1.09 | 0.60 | 1.94 | 5773.80 | 1.04 | 0.00 | 1.27 | 0.00 |
| time (sec) |
N/A | 0.942 | 0.383 | 10.771 | 17.796 | 0.278 | 0.000 | 0.518 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 118 | 126 | 79 | 233 | 38474 | 151 | 0 | 159 | 206 |
| N.S. |
1 | 1.07 | 0.67 | 1.97 | 326.05 | 1.28 | 0.00 | 1.35 | 1.75 |
| time (sec) |
N/A | 0.516 | 0.154 | 8.181 | 0.965 | 0.280 | 0.000 | 0.338 | 1.693 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 118 | 123 | 86 | 336 | 19040 | 227 | 0 | 193 | 0 |
| N.S. |
1 | 1.04 | 0.73 | 2.85 | 161.36 | 1.92 | 0.00 | 1.64 | 0.00 |
| time (sec) |
N/A | 0.744 | 0.341 | 10.588 | 0.622 | 0.282 | 0.000 | 0.493 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 120 | 129 | 96 | 799 | 18526 | 261 | 0 | 229 | 0 |
| N.S. |
1 | 1.08 | 0.80 | 6.66 | 154.38 | 2.18 | 0.00 | 1.91 | 0.00 |
| time (sec) |
N/A | 0.801 | 0.532 | 11.699 | 0.581 | 0.301 | 0.000 | 0.412 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 169 | 181 | 118 | 1383 | 76209 | 292 | 0 | 303 | 0 |
| N.S. |
1 | 1.07 | 0.70 | 8.18 | 450.94 | 1.73 | 0.00 | 1.79 | 0.00 |
| time (sec) |
N/A | 1.130 | 0.836 | 14.665 | 2.809 | 0.382 | 0.000 | 0.423 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | A | F(-1) | A | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 213 | 237 | 163 | 2041 | 0 | 314 | 0 | 362 | 0 |
| N.S. |
1 | 1.11 | 0.77 | 9.58 | 0.00 | 1.47 | 0.00 | 1.70 | 0.00 |
| time (sec) |
N/A | 1.476 | 1.345 | 15.444 | 0.000 | 0.386 | 0.000 | 0.454 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | A | F(-1) | A | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 259 | 293 | 200 | 2666 | 0 | 334 | 0 | 430 | 0 |
| N.S. |
1 | 1.13 | 0.77 | 10.29 | 0.00 | 1.29 | 0.00 | 1.66 | 0.00 |
| time (sec) |
N/A | 1.857 | 2.956 | 16.624 | 0.000 | 0.455 | 0.000 | 0.509 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | A | F(-1) | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 277 | 303 | 180 | 577 | 0 | 259 | 0 | 0 | 0 |
| N.S. |
1 | 1.09 | 0.65 | 2.08 | 0.00 | 0.94 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.865 | 1.615 | 13.235 | 0.000 | 0.297 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | A | F(-1) | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 229 | 245 | 153 | 533 | 0 | 239 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 0.67 | 2.33 | 0.00 | 1.04 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.433 | 0.773 | 11.317 | 0.000 | 0.285 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | A | F(-1) | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 181 | 190 | 131 | 407 | 0 | 217 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.72 | 2.25 | 0.00 | 1.20 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.970 | 0.504 | 11.734 | 0.000 | 0.285 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | A | F(-1) | F(-2) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 120 | 123 | 83 | 334 | 0 | 193 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 0.69 | 2.78 | 0.00 | 1.61 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.510 | 0.558 | 11.055 | 0.000 | 0.274 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 131 | 137 | 135 | 435 | 62254 | 291 | 0 | 246 | 0 |
| N.S. |
1 | 1.05 | 1.03 | 3.32 | 475.22 | 2.22 | 0.00 | 1.88 | 0.00 |
| time (sec) |
N/A | 0.760 | 1.004 | 12.164 | 2.577 | 0.284 | 0.000 | 1.842 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | B | F | B | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 173 | 181 | 196 | 992 | 63653 | 343 | 0 | 350 | 0 |
| N.S. |
1 | 1.05 | 1.13 | 5.73 | 367.94 | 1.98 | 0.00 | 2.02 | 0.00 |
| time (sec) |
N/A | 1.159 | 1.706 | 13.472 | 2.357 | 0.328 | 0.000 | 0.676 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 232 | 243 | 186 | 1663 | 0 | 382 | 0 | 374 | 0 |
| N.S. |
1 | 1.05 | 0.80 | 7.17 | 0.00 | 1.65 | 0.00 | 1.61 | 0.00 |
| time (sec) |
N/A | 1.520 | 1.636 | 16.448 | 0.000 | 0.407 | 0.000 | 0.697 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 284 | 304 | 249 | 2413 | 0 | 402 | 0 | 462 | 0 |
| N.S. |
1 | 1.07 | 0.88 | 8.50 | 0.00 | 1.42 | 0.00 | 1.63 | 0.00 |
| time (sec) |
N/A | 1.909 | 4.461 | 20.127 | 0.000 | 0.423 | 0.000 | 0.680 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | A | F(-1) | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 277 | 303 | 152 | 617 | 0 | 291 | 0 | 374 | 0 |
| N.S. |
1 | 1.09 | 0.55 | 2.23 | 0.00 | 1.05 | 0.00 | 1.35 | 0.00 |
| time (sec) |
N/A | 1.836 | 1.697 | 12.447 | 0.000 | 0.292 | 0.000 | 15.282 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | A | F(-1) | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 227 | 243 | 126 | 512 | 0 | 273 | 0 | 325 | 0 |
| N.S. |
1 | 1.07 | 0.56 | 2.26 | 0.00 | 1.20 | 0.00 | 1.43 | 0.00 |
| time (sec) |
N/A | 1.424 | 1.225 | 12.046 | 0.000 | 0.284 | 0.000 | 8.443 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | A | F(-1) | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 179 | 188 | 107 | 442 | 0 | 252 | 0 | 286 | 0 |
| N.S. |
1 | 1.05 | 0.60 | 2.47 | 0.00 | 1.41 | 0.00 | 1.60 | 0.00 |
| time (sec) |
N/A | 0.981 | 0.853 | 11.053 | 0.000 | 0.291 | 0.000 | 3.811 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 133 | 139 | 96 | 407 | 0 | 241 | 0 | 256 | 0 |
| N.S. |
1 | 1.05 | 0.72 | 3.06 | 0.00 | 1.81 | 0.00 | 1.92 | 0.00 |
| time (sec) |
N/A | 0.535 | 0.707 | 11.828 | 0.000 | 0.289 | 0.000 | 1.645 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 171 | 183 | 200 | 533 | 0 | 357 | 0 | 314 | 0 |
| N.S. |
1 | 1.07 | 1.17 | 3.12 | 0.00 | 2.09 | 0.00 | 1.84 | 0.00 |
| time (sec) |
N/A | 1.086 | 1.846 | 14.625 | 0.000 | 0.326 | 0.000 | 8.783 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 217 | 233 | 189 | 1090 | 0 | 421 | 0 | 385 | 0 |
| N.S. |
1 | 1.07 | 0.87 | 5.02 | 0.00 | 1.94 | 0.00 | 1.77 | 0.00 |
| time (sec) |
N/A | 1.502 | 4.000 | 16.278 | 0.000 | 0.336 | 0.000 | 1.785 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-2) | A | F(-1) | A | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 280 | 298 | 222 | 1760 | 0 | 457 | 0 | 446 | 0 |
| N.S. |
1 | 1.06 | 0.79 | 6.29 | 0.00 | 1.63 | 0.00 | 1.59 | 0.00 |
| time (sec) |
N/A | 1.980 | 5.801 | 17.519 | 0.000 | 0.443 | 0.000 | 1.765 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 123 | 125 | 86 | 342 | 0 | 163 | 0 | 0 | 123 |
| N.S. |
1 | 1.02 | 0.70 | 2.78 | 0.00 | 1.33 | 0.00 | 0.00 | 1.00 |
| time (sec) |
N/A | 0.564 | 0.966 | 15.219 | 0.000 | 0.108 | 0.000 | 0.000 | 1.998 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 93 | 98 | 72 | 308 | 0 | 149 | 0 | 0 | 96 |
| N.S. |
1 | 1.05 | 0.77 | 3.31 | 0.00 | 1.60 | 0.00 | 0.00 | 1.03 |
| time (sec) |
N/A | 0.504 | 0.651 | 14.377 | 0.000 | 0.096 | 0.000 | 0.000 | 1.542 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 65 | 68 | 57 | 274 | 0 | 135 | 0 | 0 | 69 |
| N.S. |
1 | 1.05 | 0.88 | 4.22 | 0.00 | 2.08 | 0.00 | 0.00 | 1.06 |
| time (sec) |
N/A | 0.411 | 0.342 | 10.341 | 0.000 | 0.092 | 0.000 | 0.000 | 0.274 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 61 | 61 | 54 | 195 | 0 | 166 | 0 | 0 | 76 |
| N.S. |
1 | 1.00 | 0.89 | 3.20 | 0.00 | 2.72 | 0.00 | 0.00 | 1.25 |
| time (sec) |
N/A | 0.415 | 0.254 | 10.315 | 0.000 | 0.100 | 0.000 | 0.000 | 1.769 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 87 | 92 | 69 | 415 | 0 | 185 | 0 | 0 | 103 |
| N.S. |
1 | 1.06 | 0.79 | 4.77 | 0.00 | 2.13 | 0.00 | 0.00 | 1.18 |
| time (sec) |
N/A | 0.510 | 0.630 | 13.177 | 0.000 | 0.107 | 0.000 | 0.000 | 2.116 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 123 | 121 | 112 | 755 | 0 | 206 | 0 | 0 | 108 |
| N.S. |
1 | 0.98 | 0.91 | 6.14 | 0.00 | 1.67 | 0.00 | 0.00 | 0.88 |
| time (sec) |
N/A | 0.559 | 0.550 | 19.553 | 0.000 | 0.110 | 0.000 | 0.000 | 2.614 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 211 | 200 | 1344 | 543 | 0 | 244 | 0 | 0 | 265 |
| N.S. |
1 | 0.95 | 6.37 | 2.57 | 0.00 | 1.16 | 0.00 | 0.00 | 1.26 |
| time (sec) |
N/A | 0.962 | 7.068 | 27.815 | 0.000 | 0.120 | 0.000 | 0.000 | 2.756 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 177 | 172 | 1292 | 512 | 0 | 223 | 0 | 0 | 254 |
| N.S. |
1 | 0.97 | 7.30 | 2.89 | 0.00 | 1.26 | 0.00 | 0.00 | 1.44 |
| time (sec) |
N/A | 0.809 | 6.931 | 20.836 | 0.000 | 0.114 | 0.000 | 0.000 | 1.773 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 144 | 144 | 1240 | 481 | 0 | 202 | 0 | 0 | 216 |
| N.S. |
1 | 1.00 | 8.61 | 3.34 | 0.00 | 1.40 | 0.00 | 0.00 | 1.50 |
| time (sec) |
N/A | 0.788 | 6.849 | 16.931 | 0.000 | 0.111 | 0.000 | 0.000 | 1.686 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 107 | 113 | 1186 | 447 | 0 | 173 | 0 | 0 | 162 |
| N.S. |
1 | 1.06 | 11.08 | 4.18 | 0.00 | 1.62 | 0.00 | 0.00 | 1.51 |
| time (sec) |
N/A | 0.678 | 7.333 | 13.848 | 0.000 | 0.097 | 0.000 | 0.000 | 0.487 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 101 | 103 | 1173 | 381 | 0 | 202 | 0 | 0 | 146 |
| N.S. |
1 | 1.02 | 11.61 | 3.77 | 0.00 | 2.00 | 0.00 | 0.00 | 1.45 |
| time (sec) |
N/A | 0.651 | 7.407 | 12.498 | 0.000 | 0.103 | 0.000 | 0.000 | 2.081 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 100 | 103 | 1180 | 488 | 0 | 208 | 0 | 0 | 184 |
| N.S. |
1 | 1.03 | 11.80 | 4.88 | 0.00 | 2.08 | 0.00 | 0.00 | 1.84 |
| time (sec) |
N/A | 0.659 | 7.382 | 13.765 | 0.000 | 0.106 | 0.000 | 0.000 | 3.041 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 139 | 136 | 1228 | 712 | 0 | 234 | 0 | 0 | 217 |
| N.S. |
1 | 0.98 | 8.83 | 5.12 | 0.00 | 1.68 | 0.00 | 0.00 | 1.56 |
| time (sec) |
N/A | 0.781 | 7.531 | 18.046 | 0.000 | 0.102 | 0.000 | 0.000 | 3.042 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 177 | 168 | 1284 | 822 | 0 | 263 | 0 | 0 | 223 |
| N.S. |
1 | 0.95 | 7.25 | 4.64 | 0.00 | 1.49 | 0.00 | 0.00 | 1.26 |
| time (sec) |
N/A | 0.837 | 7.853 | 23.614 | 0.000 | 0.117 | 0.000 | 0.000 | 3.473 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F(-1) | F | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 251 | 249 | 1374 | 545 | 0 | 264 | 0 | 0 | 404 |
| N.S. |
1 | 0.99 | 5.47 | 2.17 | 0.00 | 1.05 | 0.00 | 0.00 | 1.61 |
| time (sec) |
N/A | 1.413 | 7.519 | 25.194 | 0.000 | 0.134 | 0.000 | 0.000 | 3.047 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 215 | 221 | 1322 | 514 | 0 | 241 | 0 | 0 | 369 |
| N.S. |
1 | 1.03 | 6.15 | 2.39 | 0.00 | 1.12 | 0.00 | 0.00 | 1.72 |
| time (sec) |
N/A | 1.360 | 7.106 | 22.589 | 0.000 | 0.115 | 0.000 | 0.000 | 2.643 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 179 | 193 | 1270 | 483 | 0 | 218 | 0 | 0 | 280 |
| N.S. |
1 | 1.08 | 7.09 | 2.70 | 0.00 | 1.22 | 0.00 | 0.00 | 1.56 |
| time (sec) |
N/A | 1.232 | 8.244 | 17.200 | 0.000 | 0.103 | 0.000 | 0.000 | 2.550 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 172 | 183 | 1039 | 595 | 0 | 231 | 0 | 0 | 237 |
| N.S. |
1 | 1.06 | 6.04 | 3.46 | 0.00 | 1.34 | 0.00 | 0.00 | 1.38 |
| time (sec) |
N/A | 1.252 | 8.886 | 15.437 | 0.000 | 0.110 | 0.000 | 0.000 | 2.947 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | C | F(-1) | F | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 172 | 184 | 1025 | 771 | 0 | 237 | 0 | 0 | 245 |
| N.S. |
1 | 1.07 | 5.96 | 4.48 | 0.00 | 1.38 | 0.00 | 0.00 | 1.42 |
| time (sec) |
N/A | 1.233 | 8.585 | 17.328 | 0.000 | 0.108 | 0.000 | 0.000 | 3.303 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 174 | 184 | 1041 | 879 | 0 | 248 | 0 | 0 | 313 |
| N.S. |
1 | 1.06 | 5.98 | 5.05 | 0.00 | 1.43 | 0.00 | 0.00 | 1.80 |
| time (sec) |
N/A | 1.227 | 9.224 | 19.155 | 0.000 | 0.115 | 0.000 | 0.000 | 3.981 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 215 | 217 | 1310 | 905 | 0 | 281 | 0 | 0 | 346 |
| N.S. |
1 | 1.01 | 6.09 | 4.21 | 0.00 | 1.31 | 0.00 | 0.00 | 1.61 |
| time (sec) |
N/A | 1.381 | 9.995 | 24.642 | 0.000 | 0.124 | 0.000 | 0.000 | 4.603 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 251 | 245 | 1364 | 1154 | 0 | 304 | 0 | 0 | 688 |
| N.S. |
1 | 0.98 | 5.43 | 4.60 | 0.00 | 1.21 | 0.00 | 0.00 | 2.74 |
| time (sec) |
N/A | 1.447 | 11.147 | 31.086 | 0.000 | 0.118 | 0.000 | 0.000 | 4.722 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F(-1) | F | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 303 | 303 | 1426 | 576 | 0 | 287 | 0 | 0 | 544 |
| N.S. |
1 | 1.00 | 4.71 | 1.90 | 0.00 | 0.95 | 0.00 | 0.00 | 1.80 |
| time (sec) |
N/A | 1.835 | 7.411 | 28.118 | 0.000 | 0.140 | 0.000 | 0.000 | 3.193 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F(-1) | F | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 267 | 275 | 1374 | 545 | 0 | 264 | 0 | 0 | 507 |
| N.S. |
1 | 1.03 | 5.15 | 2.04 | 0.00 | 0.99 | 0.00 | 0.00 | 1.90 |
| time (sec) |
N/A | 1.829 | 7.394 | 25.589 | 0.000 | 0.127 | 0.000 | 0.000 | 2.974 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F(-1) | F | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 231 | 240 | 1322 | 514 | 0 | 241 | 0 | 0 | 430 |
| N.S. |
1 | 1.04 | 5.72 | 2.23 | 0.00 | 1.04 | 0.00 | 0.00 | 1.86 |
| time (sec) |
N/A | 1.601 | 8.635 | 19.882 | 0.000 | 0.119 | 0.000 | 0.000 | 2.610 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 229 | 242 | 1313 | 727 | 0 | 264 | 0 | 0 | 376 |
| N.S. |
1 | 1.06 | 5.73 | 3.17 | 0.00 | 1.15 | 0.00 | 0.00 | 1.64 |
| time (sec) |
N/A | 1.614 | 9.762 | 19.699 | 0.000 | 0.114 | 0.000 | 0.000 | 2.589 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 227 | 238 | 1297 | 950 | 0 | 267 | 0 | 0 | 358 |
| N.S. |
1 | 1.05 | 5.71 | 4.19 | 0.00 | 1.18 | 0.00 | 0.00 | 1.58 |
| time (sec) |
N/A | 1.596 | 9.622 | 19.822 | 0.000 | 0.124 | 0.000 | 0.000 | 3.116 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | C | F | C | F(-1) | F | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 230 | 242 | 1298 | 1147 | 0 | 272 | 0 | 0 | 408 |
| N.S. |
1 | 1.05 | 5.64 | 4.99 | 0.00 | 1.18 | 0.00 | 0.00 | 1.77 |
| time (sec) |
N/A | 1.635 | 11.094 | 23.334 | 0.000 | 0.128 | 0.000 | 0.000 | 4.028 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 231 | 240 | 1317 | 1070 | 0 | 281 | 0 | 0 | 436 |
| N.S. |
1 | 1.04 | 5.70 | 4.63 | 0.00 | 1.22 | 0.00 | 0.00 | 1.89 |
| time (sec) |
N/A | 1.630 | 12.640 | 25.178 | 0.000 | 0.139 | 0.000 | 0.000 | 4.972 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 267 | 264 | 1364 | 1235 | 0 | 304 | 0 | 0 | 457 |
| N.S. |
1 | 0.99 | 5.11 | 4.63 | 0.00 | 1.14 | 0.00 | 0.00 | 1.71 |
| time (sec) |
N/A | 1.758 | 12.980 | 30.675 | 0.000 | 0.114 | 0.000 | 0.000 | 5.512 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | B |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 303 | 299 | 1418 | 1397 | 0 | 327 | 0 | 0 | 893 |
| N.S. |
1 | 0.99 | 4.68 | 4.61 | 0.00 | 1.08 | 0.00 | 0.00 | 2.95 |
| time (sec) |
N/A | 1.881 | 13.196 | 37.579 | 0.000 | 0.144 | 0.000 | 0.000 | 6.087 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 210 | 185 | 1398 | 341 | 0 | 316 | 0 | 0 | 0 |
| N.S. |
1 | 0.88 | 6.66 | 1.62 | 0.00 | 1.50 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.838 | 9.064 | 11.752 | 0.000 | 0.135 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 174 | 157 | 1343 | 319 | 0 | 296 | 0 | 0 | 0 |
| N.S. |
1 | 0.90 | 7.72 | 1.83 | 0.00 | 1.70 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.714 | 8.527 | 7.369 | 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 | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 134 | 128 | 1290 | 300 | 0 | 277 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 9.63 | 2.24 | 0.00 | 2.07 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.674 | 8.211 | 7.253 | 0.000 | 0.118 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 90 | 96 | 1253 | 281 | 0 | 266 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 13.92 | 3.12 | 0.00 | 2.96 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.540 | 7.983 | 6.473 | 0.000 | 0.112 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 125 | 121 | 1288 | 353 | 0 | 315 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 10.30 | 2.82 | 0.00 | 2.52 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.664 | 8.233 | 6.784 | 0.000 | 0.115 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 165 | 151 | 1332 | 467 | 0 | 347 | 0 | 0 | 0 |
| N.S. |
1 | 0.92 | 8.07 | 2.83 | 0.00 | 2.10 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.700 | 8.372 | 8.815 | 0.000 | 0.117 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 210 | 181 | 1391 | 785 | 0 | 369 | 0 | 0 | 0 |
| N.S. |
1 | 0.86 | 6.62 | 3.74 | 0.00 | 1.76 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.816 | 8.879 | 11.971 | 0.000 | 0.129 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 214 | 206 | 1433 | 491 | 0 | 426 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 6.70 | 2.29 | 0.00 | 1.99 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.025 | 9.398 | 11.303 | 0.000 | 0.116 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 180 | 179 | 1382 | 472 | 0 | 406 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 7.68 | 2.62 | 0.00 | 2.26 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.976 | 8.641 | 8.141 | 0.000 | 0.117 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 139 | 145 | 1108 | 507 | 0 | 371 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 7.97 | 3.65 | 0.00 | 2.67 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.837 | 8.252 | 6.861 | 0.000 | 0.116 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 133 | 142 | 1101 | 507 | 0 | 375 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 8.28 | 3.81 | 0.00 | 2.82 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.837 | 8.124 | 7.496 | 0.000 | 0.108 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-1) | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 175 | 175 | 1142 | 563 | 0 | 426 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 6.53 | 3.22 | 0.00 | 2.43 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.997 | 8.249 | 8.539 | 0.000 | 0.109 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 211 | 202 | 1424 | 724 | 0 | 476 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 6.75 | 3.43 | 0.00 | 2.26 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.028 | 8.757 | 11.300 | 0.000 | 0.121 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 273 | 272 | 1534 | 666 | 0 | 552 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 5.62 | 2.44 | 0.00 | 2.02 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.427 | 11.412 | 18.908 | 0.000 | 0.145 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 232 | 239 | 1487 | 638 | 0 | 535 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 6.41 | 2.75 | 0.00 | 2.31 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.330 | 10.146 | 19.032 | 0.000 | 0.142 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 195 | 210 | 1455 | 624 | 0 | 522 | 0 | 0 | 0 |
| N.S. |
1 | 1.08 | 7.46 | 3.20 | 0.00 | 2.68 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.179 | 9.117 | 7.902 | 0.000 | 0.119 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 191 | 206 | 1445 | 624 | 0 | 522 | 0 | 0 | 0 |
| N.S. |
1 | 1.08 | 7.57 | 3.27 | 0.00 | 2.73 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.159 | 8.614 | 7.322 | 0.000 | 0.118 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-1) | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 193 | 208 | 1448 | 624 | 0 | 522 | 0 | 0 | 0 |
| N.S. |
1 | 1.08 | 7.50 | 3.23 | 0.00 | 2.70 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.185 | 8.707 | 8.105 | 0.000 | 0.117 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-2) | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 237 | 240 | 1487 | 793 | 0 | 576 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 6.27 | 3.35 | 0.00 | 2.43 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.374 | 9.042 | 9.194 | 0.000 | 0.116 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-1) | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 270 | 265 | 1529 | 1013 | 0 | 605 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 5.66 | 3.75 | 0.00 | 2.24 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.391 | 9.740 | 13.407 | 0.000 | 0.149 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 227 | 222 | 144 | 440 | 9277 | 163 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 0.63 | 1.94 | 40.87 | 0.72 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.104 | 0.983 | 28.060 | 0.973 | 0.579 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 179 | 179 | 124 | 334 | 3770 | 143 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.69 | 1.87 | 21.06 | 0.80 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.879 | 0.524 | 27.397 | 0.799 | 0.466 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 131 | 135 | 103 | 236 | 1996 | 123 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 0.79 | 1.80 | 15.24 | 0.94 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.715 | 0.379 | 32.447 | 0.604 | 0.436 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 121 | 128 | 104 | 187 | 1035 | 127 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 0.86 | 1.55 | 8.55 | 1.05 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.706 | 0.386 | 31.971 | 0.538 | 0.344 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 120 | 128 | 105 | 168 | 435 | 128 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 0.88 | 1.40 | 3.62 | 1.07 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.698 | 0.446 | 13.924 | 0.449 | 0.301 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 130 | 142 | 85 | 97 | 524 | 88 | 0 | 0 | 227 |
| N.S. |
1 | 1.09 | 0.65 | 0.75 | 4.03 | 0.68 | 0.00 | 0.00 | 1.75 |
| time (sec) |
N/A | 0.708 | 0.404 | 11.773 | 0.383 | 0.274 | 0.000 | 0.000 | 4.813 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | C | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 178 | 184 | 121 | 130 | 710 | 109 | 0 | 184411 | 503 |
| N.S. |
1 | 1.03 | 0.68 | 0.73 | 3.99 | 0.61 | 0.00 | 1036.02 | 2.83 |
| time (sec) |
N/A | 0.903 | 0.620 | 13.227 | 0.405 | 0.269 | 0.000 | 280.726 | 7.754 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 226 | 227 | 155 | 163 | 848 | 130 | 0 | 0 | 629 |
| N.S. |
1 | 1.00 | 0.69 | 0.72 | 3.75 | 0.58 | 0.00 | 0.00 | 2.78 |
| time (sec) |
N/A | 1.105 | 0.906 | 13.430 | 0.395 | 0.287 | 0.000 | 0.000 | 8.342 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 283 | 281 | 170 | 549 | 11428 | 195 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 0.60 | 1.94 | 40.38 | 0.69 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.487 | 1.707 | 29.405 | 1.200 | 0.567 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 233 | 238 | 145 | 441 | 9982 | 174 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 0.62 | 1.89 | 42.84 | 0.75 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.244 | 1.001 | 29.743 | 1.079 | 0.600 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 181 | 191 | 125 | 335 | 3824 | 153 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 0.69 | 1.85 | 21.13 | 0.85 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.033 | 0.781 | 35.204 | 0.793 | 0.429 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 181 | 188 | 127 | 297 | 2879 | 160 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 0.70 | 1.64 | 15.91 | 0.88 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.051 | 0.664 | 32.664 | 0.693 | 0.431 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 171 | 180 | 128 | 265 | 1925 | 159 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.75 | 1.55 | 11.26 | 0.93 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.046 | 0.776 | 31.477 | 0.581 | 0.337 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 172 | 185 | 134 | 242 | 1339 | 154 | 0 | 0 | 0 |
| N.S. |
1 | 1.08 | 0.78 | 1.41 | 7.78 | 0.90 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.041 | 0.914 | 12.373 | 0.498 | 0.308 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | C | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 184 | 199 | 122 | 131 | 604 | 112 | 0 | 201151 | 273 |
| N.S. |
1 | 1.08 | 0.66 | 0.71 | 3.28 | 0.61 | 0.00 | 1093.21 | 1.48 |
| time (sec) |
N/A | 1.066 | 0.759 | 13.651 | 0.382 | 0.280 | 0.000 | 287.393 | 9.968 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 232 | 241 | 157 | 164 | 788 | 134 | 0 | 0 | 308 |
| N.S. |
1 | 1.04 | 0.68 | 0.71 | 3.40 | 0.58 | 0.00 | 0.00 | 1.33 |
| time (sec) |
N/A | 1.290 | 0.957 | 12.951 | 0.372 | 0.281 | 0.000 | 0.000 | 9.697 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 284 | 286 | 187 | 197 | 927 | 156 | 0 | 0 | 368 |
| N.S. |
1 | 1.01 | 0.66 | 0.69 | 3.26 | 0.55 | 0.00 | 0.00 | 1.30 |
| time (sec) |
N/A | 1.492 | 1.018 | 13.694 | 0.387 | 0.304 | 0.000 | 0.000 | 9.417 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 333 | 333 | 205 | 659 | 45288 | 232 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.62 | 1.98 | 136.00 | 0.70 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.905 | 2.302 | 30.494 | 3.212 | 0.605 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 281 | 291 | 171 | 551 | 12004 | 209 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 0.61 | 1.96 | 42.72 | 0.74 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.617 | 1.776 | 28.896 | 1.266 | 0.585 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 233 | 248 | 146 | 443 | 10519 | 186 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 0.63 | 1.90 | 45.15 | 0.80 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.401 | 1.128 | 33.030 | 1.115 | 0.588 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 231 | 244 | 156 | 405 | 4042 | 194 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 0.68 | 1.75 | 17.50 | 0.84 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.433 | 1.128 | 34.808 | 0.804 | 0.441 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 233 | 242 | 156 | 377 | 3474 | 195 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 0.67 | 1.62 | 14.91 | 0.84 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.421 | 1.136 | 36.490 | 0.730 | 0.452 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 223 | 235 | 156 | 375 | 2519 | 192 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.70 | 1.68 | 11.30 | 0.86 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.399 | 1.379 | 35.398 | 0.636 | 0.346 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 222 | 240 | 172 | 295 | 1789 | 187 | 0 | 0 | 0 |
| N.S. |
1 | 1.08 | 0.77 | 1.33 | 8.06 | 0.84 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.384 | 1.715 | 15.639 | 0.552 | 0.302 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 234 | 250 | 158 | 166 | 682 | 143 | 0 | 0 | 713 |
| N.S. |
1 | 1.07 | 0.68 | 0.71 | 2.91 | 0.61 | 0.00 | 0.00 | 3.05 |
| time (sec) |
N/A | 1.448 | 1.212 | 14.553 | 0.407 | 0.285 | 0.000 | 0.000 | 9.604 |