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 | A | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 79 | 135 | 100 | 86 | 160 | 0 | 173 | 174 |
N.S. |
1 | 1.07 | 1.82 | 1.35 | 1.16 | 2.16 | 0.00 | 2.34 | 2.35 |
time (sec) |
N/A | 0.500 | 0.111 | 0.372 | 0.189 | 0.290 | 0.000 | 0.366 | 10.397 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 107 | 175 | 118 | 106 | 187 | 0 | 201 | 205 |
N.S. |
1 | 1.09 | 1.79 | 1.20 | 1.08 | 1.91 | 0.00 | 2.05 | 2.09 |
time (sec) |
N/A | 0.657 | 0.019 | 0.438 | 0.191 | 0.292 | 0.000 | 0.345 | 11.678 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 114 | 121 | 239 | 137 | 118 | 221 | 0 | 229 | 399 |
N.S. |
1 | 1.06 | 2.10 | 1.20 | 1.04 | 1.94 | 0.00 | 2.01 | 3.50 |
time (sec) |
N/A | 0.668 | 0.116 | 0.477 | 0.190 | 0.277 | 0.000 | 0.382 | 12.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 136 | 147 | 279 | 156 | 138 | 239 | 0 | 201 | 205 |
N.S. |
1 | 1.08 | 2.05 | 1.15 | 1.01 | 1.76 | 0.00 | 1.48 | 1.51 |
time (sec) |
N/A | 0.788 | 0.117 | 0.392 | 0.194 | 0.300 | 0.000 | 0.376 | 10.433 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 301 | 310 | 144 | 142 | 100 | 116 | 335 | 142 | 309 |
N.S. |
1 | 1.03 | 0.48 | 0.47 | 0.33 | 0.39 | 1.11 | 0.47 | 1.03 |
time (sec) |
N/A | 1.747 | 0.528 | 0.894 | 0.190 | 0.297 | 1.012 | 0.435 | 15.391 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 278 | 284 | 141 | 144 | 101 | 128 | 420 | 150 | 139 |
N.S. |
1 | 1.02 | 0.51 | 0.52 | 0.36 | 0.46 | 1.51 | 0.54 | 0.50 |
time (sec) |
N/A | 1.529 | 0.347 | 0.761 | 0.194 | 0.277 | 0.729 | 0.426 | 11.994 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 129 | 143 | 132 | 105 | 81 | 85 | 223 | 141 | 256 |
N.S. |
1 | 1.11 | 1.02 | 0.81 | 0.63 | 0.66 | 1.73 | 1.09 | 1.98 |
time (sec) |
N/A | 0.639 | 0.214 | 0.638 | 0.182 | 0.274 | 0.471 | 0.377 | 14.487 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 116 | 204 | 125 | 93 | 97 | 112 | 0 | 213 | 319 |
N.S. |
1 | 1.76 | 1.08 | 0.80 | 0.84 | 0.97 | 0.00 | 1.84 | 2.75 |
time (sec) |
N/A | 1.219 | 0.734 | 0.485 | 0.195 | 0.292 | 0.000 | 0.337 | 12.358 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 181 | 202 | 167 | 131 | 127 | 155 | 0 | 274 | 578 |
N.S. |
1 | 1.12 | 0.92 | 0.72 | 0.70 | 0.86 | 0.00 | 1.51 | 3.19 |
time (sec) |
N/A | 1.263 | 0.563 | 0.480 | 0.275 | 0.289 | 0.000 | 0.347 | 10.585 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 189 | 201 | 191 | 157 | 150 | 210 | 0 | 252 | 397 |
N.S. |
1 | 1.06 | 1.01 | 0.83 | 0.79 | 1.11 | 0.00 | 1.33 | 2.10 |
time (sec) |
N/A | 1.248 | 2.154 | 0.540 | 0.277 | 0.293 | 0.000 | 0.367 | 11.229 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 133 | 133 | 293 | 145 | 138 | 218 | 0 | 241 | 584 |
N.S. |
1 | 1.00 | 2.20 | 1.09 | 1.04 | 1.64 | 0.00 | 1.81 | 4.39 |
time (sec) |
N/A | 0.369 | 6.094 | 0.574 | 0.278 | 0.286 | 0.000 | 0.498 | 12.680 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 178 | 194 | 270 | 167 | 166 | 260 | 0 | 244 | 825 |
N.S. |
1 | 1.09 | 1.52 | 0.94 | 0.93 | 1.46 | 0.00 | 1.37 | 4.63 |
time (sec) |
N/A | 1.271 | 5.181 | 0.451 | 0.339 | 0.282 | 0.000 | 0.521 | 12.774 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 209 | 224 | 285 | 129 | 123 | 241 | 0 | 263 | 346 |
N.S. |
1 | 1.07 | 1.36 | 0.62 | 0.59 | 1.15 | 0.00 | 1.26 | 1.66 |
time (sec) |
N/A | 1.315 | 1.790 | 0.385 | 0.399 | 0.310 | 0.000 | 0.542 | 10.950 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 236 | 245 | 319 | 198 | 180 | 274 | 0 | 309 | 262 |
N.S. |
1 | 1.04 | 1.35 | 0.84 | 0.76 | 1.16 | 0.00 | 1.31 | 1.11 |
time (sec) |
N/A | 1.539 | 1.173 | 0.501 | 0.203 | 0.287 | 0.000 | 0.497 | 11.139 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 261 | 276 | 322 | 163 | 134 | 248 | 0 | 347 | 302 |
N.S. |
1 | 1.06 | 1.23 | 0.62 | 0.51 | 0.95 | 0.00 | 1.33 | 1.16 |
time (sec) |
N/A | 1.807 | 1.657 | 0.550 | 0.216 | 0.301 | 0.000 | 0.690 | 10.497 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 354 | 351 | 204 | 198 | 140 | 164 | 505 | 204 | 578 |
N.S. |
1 | 0.99 | 0.58 | 0.56 | 0.40 | 0.46 | 1.43 | 0.58 | 1.63 |
time (sec) |
N/A | 2.060 | 0.752 | 0.967 | 0.246 | 0.295 | 0.995 | 0.477 | 11.851 |
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 | 194 | 197 | 189 | 177 | 117 | 136 | 456 | 184 | 552 |
N.S. |
1 | 1.02 | 0.97 | 0.91 | 0.60 | 0.70 | 2.35 | 0.95 | 2.85 |
time (sec) |
N/A | 0.918 | 0.534 | 0.839 | 0.195 | 0.312 | 0.689 | 0.430 | 11.797 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 250 | 265 | 191 | 149 | 137 | 150 | 0 | 427 | 690 |
N.S. |
1 | 1.06 | 0.76 | 0.60 | 0.55 | 0.60 | 0.00 | 1.71 | 2.76 |
time (sec) |
N/A | 1.644 | 0.782 | 0.651 | 0.215 | 0.290 | 0.000 | 0.392 | 12.231 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 229 | 252 | 194 | 152 | 143 | 179 | 0 | 345 | 674 |
N.S. |
1 | 1.10 | 0.85 | 0.66 | 0.62 | 0.78 | 0.00 | 1.51 | 2.94 |
time (sec) |
N/A | 1.602 | 1.736 | 0.590 | 0.318 | 0.308 | 0.000 | 0.400 | 11.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 231 | 255 | 252 | 198 | 186 | 260 | 0 | 400 | 718 |
N.S. |
1 | 1.10 | 1.09 | 0.86 | 0.81 | 1.13 | 0.00 | 1.73 | 3.11 |
time (sec) |
N/A | 1.628 | 6.518 | 0.650 | 0.285 | 0.283 | 0.000 | 0.425 | 10.725 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 194 | 194 | 355 | 186 | 187 | 293 | 0 | 421 | 405 |
N.S. |
1 | 1.00 | 1.83 | 0.96 | 0.96 | 1.51 | 0.00 | 2.17 | 2.09 |
time (sec) |
N/A | 0.441 | 6.108 | 0.642 | 0.288 | 0.310 | 0.000 | 0.408 | 11.757 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 187 | 204 | 381 | 226 | 212 | 331 | 0 | 343 | 699 |
N.S. |
1 | 1.09 | 2.04 | 1.21 | 1.13 | 1.77 | 0.00 | 1.83 | 3.74 |
time (sec) |
N/A | 1.490 | 7.181 | 0.676 | 0.281 | 0.299 | 0.000 | 0.468 | 10.467 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 227 | 244 | 405 | 192 | 182 | 334 | 0 | 356 | 1007 |
N.S. |
1 | 1.07 | 1.78 | 0.85 | 0.80 | 1.47 | 0.00 | 1.57 | 4.44 |
time (sec) |
N/A | 1.711 | 2.125 | 0.612 | 0.298 | 0.294 | 0.000 | 0.433 | 14.540 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 275 | 292 | 408 | 227 | 217 | 373 | 0 | 399 | 446 |
N.S. |
1 | 1.06 | 1.48 | 0.83 | 0.79 | 1.36 | 0.00 | 1.45 | 1.62 |
time (sec) |
N/A | 1.838 | 2.060 | 0.547 | 0.273 | 0.316 | 0.000 | 0.426 | 10.670 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 303 | 314 | 324 | 243 | 208 | 347 | 0 | 456 | 359 |
N.S. |
1 | 1.04 | 1.07 | 0.80 | 0.69 | 1.15 | 0.00 | 1.50 | 1.18 |
time (sec) |
N/A | 2.089 | 1.377 | 0.675 | 0.201 | 0.307 | 0.000 | 0.461 | 10.595 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 334 | 340 | 268 | 280 | 248 | 384 | 0 | 457 | 381 |
N.S. |
1 | 1.02 | 0.80 | 0.84 | 0.74 | 1.15 | 0.00 | 1.37 | 1.14 |
time (sec) |
N/A | 2.289 | 2.067 | 0.669 | 0.206 | 0.292 | 0.000 | 0.448 | 10.559 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 307 | 352 | 378 | 434 | 0 | 649 | 0 | 536 | 2390 |
N.S. |
1 | 1.15 | 1.23 | 1.41 | 0.00 | 2.11 | 0.00 | 1.75 | 7.79 |
time (sec) |
N/A | 2.049 | 3.178 | 2.417 | 0.000 | 0.329 | 0.000 | 0.347 | 14.772 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 267 | 304 | 325 | 382 | 0 | 604 | 0 | 449 | 1003 |
N.S. |
1 | 1.14 | 1.22 | 1.43 | 0.00 | 2.26 | 0.00 | 1.68 | 3.76 |
time (sec) |
N/A | 1.571 | 2.893 | 1.756 | 0.000 | 0.339 | 0.000 | 0.338 | 13.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 163 | 179 | 247 | 276 | 0 | 507 | 0 | 300 | 964 |
N.S. |
1 | 1.10 | 1.52 | 1.69 | 0.00 | 3.11 | 0.00 | 1.84 | 5.91 |
time (sec) |
N/A | 0.735 | 1.581 | 1.271 | 0.000 | 0.336 | 0.000 | 0.328 | 12.605 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 166 | 161 | 193 | 0 | 516 | 0 | 286 | 2773 |
N.S. |
1 | 1.21 | 1.18 | 1.41 | 0.00 | 3.77 | 0.00 | 2.09 | 20.24 |
time (sec) |
N/A | 0.712 | 0.758 | 0.867 | 0.000 | 0.383 | 0.000 | 0.336 | 12.754 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 154 | 175 | 182 | 201 | 0 | 675 | 0 | 260 | 6377 |
N.S. |
1 | 1.14 | 1.18 | 1.31 | 0.00 | 4.38 | 0.00 | 1.69 | 41.41 |
time (sec) |
N/A | 0.740 | 1.565 | 0.536 | 0.000 | 0.397 | 0.000 | 0.422 | 13.834 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 158 | 201 | 191 | 209 | 0 | 804 | 0 | 275 | 675 |
N.S. |
1 | 1.27 | 1.21 | 1.32 | 0.00 | 5.09 | 0.00 | 1.74 | 4.27 |
time (sec) |
N/A | 1.027 | 3.008 | 0.548 | 0.000 | 0.377 | 0.000 | 0.441 | 10.319 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 238 | 266 | 403 | 287 | 0 | 1149 | 0 | 356 | 973 |
N.S. |
1 | 1.12 | 1.69 | 1.21 | 0.00 | 4.83 | 0.00 | 1.50 | 4.09 |
time (sec) |
N/A | 1.445 | 6.150 | 0.708 | 0.000 | 0.410 | 0.000 | 0.486 | 10.672 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 292 | 330 | 496 | 365 | 0 | 1578 | 0 | 461 | 1158 |
N.S. |
1 | 1.13 | 1.70 | 1.25 | 0.00 | 5.40 | 0.00 | 1.58 | 3.97 |
time (sec) |
N/A | 2.028 | 7.023 | 0.872 | 0.000 | 0.525 | 0.000 | 0.490 | 10.643 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 331 | 378 | 1250 | 450 | 0 | 1110 | 0 | 540 | 3581 |
N.S. |
1 | 1.14 | 3.78 | 1.36 | 0.00 | 3.35 | 0.00 | 1.63 | 10.82 |
time (sec) |
N/A | 2.091 | 7.531 | 2.723 | 0.000 | 0.385 | 0.000 | 0.820 | 17.951 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 284 | 321 | 1030 | 344 | 0 | 976 | 0 | 393 | 2034 |
N.S. |
1 | 1.13 | 3.63 | 1.21 | 0.00 | 3.44 | 0.00 | 1.38 | 7.16 |
time (sec) |
N/A | 1.615 | 5.146 | 2.340 | 0.000 | 0.365 | 0.000 | 0.370 | 16.857 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 173 | 186 | 274 | 288 | 0 | 837 | 0 | 429 | 1743 |
N.S. |
1 | 1.08 | 1.58 | 1.66 | 0.00 | 4.84 | 0.00 | 2.48 | 10.08 |
time (sec) |
N/A | 0.735 | 2.418 | 1.724 | 0.000 | 0.353 | 0.000 | 0.370 | 14.669 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 175 | 199 | 176 | 240 | 0 | 1042 | 0 | 275 | 3001 |
N.S. |
1 | 1.14 | 1.01 | 1.37 | 0.00 | 5.95 | 0.00 | 1.57 | 17.15 |
time (sec) |
N/A | 0.772 | 1.662 | 0.837 | 0.000 | 0.515 | 0.000 | 0.333 | 16.361 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 182 | 222 | 184 | 214 | 0 | 1064 | 0 | 273 | 956 |
N.S. |
1 | 1.22 | 1.01 | 1.18 | 0.00 | 5.85 | 0.00 | 1.50 | 5.25 |
time (sec) |
N/A | 1.063 | 2.195 | 0.732 | 0.000 | 0.377 | 0.000 | 0.372 | 12.122 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 218 | 279 | 319 | 283 | 0 | 1560 | 0 | 395 | 1100 |
N.S. |
1 | 1.28 | 1.46 | 1.30 | 0.00 | 7.16 | 0.00 | 1.81 | 5.05 |
time (sec) |
N/A | 1.547 | 6.350 | 0.798 | 0.000 | 0.459 | 0.000 | 0.374 | 10.925 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 289 | 358 | 459 | 360 | 0 | 2027 | 0 | 451 | 1261 |
N.S. |
1 | 1.24 | 1.59 | 1.25 | 0.00 | 7.01 | 0.00 | 1.56 | 4.36 |
time (sec) |
N/A | 2.116 | 6.140 | 0.923 | 0.000 | 0.575 | 0.000 | 0.377 | 11.296 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 340 | 429 | 347 | 431 | 0 | 2592 | 0 | 550 | 1487 |
N.S. |
1 | 1.26 | 1.02 | 1.27 | 0.00 | 7.62 | 0.00 | 1.62 | 4.37 |
time (sec) |
N/A | 2.712 | 4.431 | 1.036 | 0.000 | 0.738 | 0.000 | 0.414 | 13.229 |
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 | 463 | 493 | 327 | 1619 | 0 | 633 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.71 | 3.50 | 0.00 | 1.37 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.752 | 3.959 | 2.566 | 0.000 | 0.150 | 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 | 332 | 349 | 326 | 1356 | 0 | 584 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.98 | 4.08 | 0.00 | 1.76 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.640 | 3.098 | 2.099 | 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 | F | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 338 | 349 | 435 | 1155 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 1.29 | 3.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.470 | 2.430 | 1.488 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 323 | 338 | 422 | 657 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 1.31 | 2.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.396 | 2.667 | 1.399 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 345 | 351 | 450 | 1364 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.30 | 3.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.399 | 2.444 | 1.577 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 351 | 353 | 473 | 1494 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.35 | 4.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.461 | 4.023 | 1.436 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 412 | 422 | 643 | 1761 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.56 | 4.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.163 | 6.947 | 1.620 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 484 | 502 | 545 | 2075 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.13 | 4.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.929 | 6.745 | 2.062 | 0.000 | 0.000 | 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 | 528 | 560 | 382 | 1801 | 0 | 689 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.72 | 3.41 | 0.00 | 1.30 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.321 | 10.640 | 2.936 | 0.000 | 0.223 | 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 | 394 | 416 | 382 | 1619 | 0 | 632 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.97 | 4.11 | 0.00 | 1.60 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.035 | 8.604 | 2.513 | 0.000 | 0.170 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 390 | 403 | 477 | 1405 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 1.22 | 3.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.986 | 2.696 | 1.843 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 374 | 392 | 452 | 727 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 1.21 | 1.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.866 | 3.087 | 1.762 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 383 | 401 | 434 | 1379 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 1.13 | 3.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.908 | 2.339 | 1.671 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 386 | 390 | 486 | 1511 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.26 | 3.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.823 | 4.504 | 1.832 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 408 | 413 | 641 | 1760 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.57 | 4.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.147 | 7.191 | 1.929 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 484 | 493 | 544 | 2075 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.12 | 4.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.856 | 7.213 | 2.388 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 551 | 571 | 771 | 2458 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.40 | 4.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 4.258 | 7.355 | 3.294 | 0.000 | 0.000 | 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 | 451 | 478 | 450 | 1801 | 0 | 688 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 1.00 | 3.99 | 0.00 | 1.53 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.510 | 16.056 | 38.121 | 0.000 | 0.190 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 447 | 458 | 521 | 1573 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.17 | 3.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.551 | 3.175 | 89.299 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 426 | 446 | 496 | 864 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 1.16 | 2.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.453 | 3.645 | 39.878 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 430 | 451 | 460 | 1520 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 1.07 | 3.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.483 | 4.039 | 17.615 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 429 | 445 | 466 | 1526 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.09 | 3.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.516 | 2.726 | 8.234 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 449 | 455 | 655 | 1777 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.46 | 3.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.653 | 7.331 | 21.626 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 482 | 486 | 545 | 2075 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.13 | 4.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.906 | 7.335 | 50.168 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 551 | 562 | 771 | 2458 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.40 | 4.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 4.373 | 7.499 | 121.333 | 0.000 | 0.000 | 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 | 471 | 502 | 382 | 1619 | 0 | 634 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.81 | 3.44 | 0.00 | 1.35 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.873 | 4.242 | 1.822 | 0.000 | 0.185 | 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 | 405 | 428 | 326 | 1356 | 0 | 585 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.80 | 3.35 | 0.00 | 1.44 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.330 | 3.301 | 1.419 | 0.000 | 0.162 | 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 | 283 | 295 | 275 | 1190 | 0 | 537 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.97 | 4.20 | 0.00 | 1.90 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.351 | 2.128 | 1.217 | 0.000 | 0.153 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 288 | 297 | 408 | 1018 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 1.42 | 3.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.962 | 2.603 | 1.019 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 285 | 291 | 416 | 704 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.46 | 2.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.952 | 2.630 | 1.080 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 307 | 304 | 443 | 913 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 1.44 | 2.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.983 | 2.348 | 1.495 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 353 | 361 | 475 | 1496 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.35 | 4.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.489 | 3.827 | 1.315 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 412 | 428 | 647 | 1761 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.57 | 4.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.193 | 7.139 | 1.608 | 0.000 | 0.000 | 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 | 466 | 504 | 326 | 1356 | 0 | 788 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 0.70 | 2.91 | 0.00 | 1.69 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.994 | 5.270 | 3.000 | 0.000 | 0.257 | 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 | 401 | 430 | 275 | 1190 | 0 | 723 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.69 | 2.97 | 0.00 | 1.80 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.356 | 3.942 | 2.505 | 0.000 | 0.215 | 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 | 261 | 273 | 222 | 943 | 0 | 659 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.85 | 3.61 | 0.00 | 2.52 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.242 | 2.709 | 1.759 | 0.000 | 0.187 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 296 | 303 | 419 | 1010 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.42 | 3.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.989 | 2.715 | 1.323 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-1) | F(-1) | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 294 | 302 | 433 | 620 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 1.47 | 2.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.014 | 2.617 | 1.353 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-1) | F(-1) | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 366 | 369 | 435 | 1349 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.19 | 3.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.607 | 3.508 | 1.433 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-1) | F(-1) | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 416 | 436 | 468 | 1496 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 1.12 | 3.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.208 | 3.830 | 1.701 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 469 | 508 | 1044 | 2033 | 0 | 955 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 2.23 | 4.33 | 0.00 | 2.04 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.990 | 7.535 | 2.613 | 0.000 | 0.357 | 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 | 411 | 436 | 257 | 1642 | 0 | 873 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.63 | 4.00 | 0.00 | 2.12 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.450 | 5.962 | 1.939 | 0.000 | 0.245 | 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 | 254 | 266 | 211 | 1430 | 0 | 794 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.83 | 5.63 | 0.00 | 3.13 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.212 | 4.325 | 1.861 | 0.000 | 0.183 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 313 | 317 | 443 | 1375 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.42 | 4.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.042 | 3.699 | 2.124 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 346 | 384 | 445 | 2112 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 1.29 | 6.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.662 | 4.142 | 1.509 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-1) | F(-1) | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 407 | 449 | 622 | 2617 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 1.53 | 6.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.275 | 6.629 | 1.519 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-1) | F(-1) | F | F(-1) | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 458 | 518 | 680 | 2870 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 1.48 | 6.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.933 | 6.612 | 2.004 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 510 | 549 | 1670 | 17280 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 3.27 | 33.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.720 | 7.408 | 9.723 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 35 | 29 | 31 | 31 | 32 | 31 | 31 |
N.S. |
1 | 1.00 | 1.06 | 0.88 | 0.94 | 0.94 | 0.97 | 0.94 | 0.94 |
time (sec) |
N/A | 0.287 | 91.206 | 0.312 | 1.291 | 13.562 | 23.442 | 216.549 | 15.255 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 31 | 31 | 0 | 31 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.07 | 1.07 | 0.00 | 1.07 | 1.07 |
time (sec) |
N/A | 0.257 | 5.291 | 0.435 | 6.378 | 0.601 | 0.000 | 13.956 | 18.927 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 35 | 33 | 35 | 35 | 0 | 35 | 35 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 1.06 | 0.00 | 1.06 | 1.06 |
time (sec) |
N/A | 0.267 | 4.828 | 0.928 | 5.551 | 0.499 | 0.000 | 1.927 | 16.681 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 35 | 33 | 35 | 35 | 0 | 35 | 35 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 1.06 | 0.00 | 1.06 | 1.06 |
time (sec) |
N/A | 0.273 | 4.641 | 0.796 | 15.885 | 0.441 | 0.000 | 2.470 | 15.650 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 623 | 579 | 195 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.969 | 0.590 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 487 | 466 | 167 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 0.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.100 | 0.239 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 129 | 129 | 111 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.361 | 0.115 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 101 | 105 | 72 | 72 | 106 | 136 | 133 | 71 |
N.S. |
1 | 1.04 | 1.08 | 0.74 | 0.74 | 1.09 | 1.40 | 1.37 | 0.73 |
time (sec) |
N/A | 0.294 | 0.266 | 0.878 | 0.190 | 0.429 | 1.922 | 0.420 | 0.087 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 101 | 94 | 72 | 72 | 95 | 136 | 118 | 71 |
N.S. |
1 | 1.04 | 0.97 | 0.74 | 0.74 | 0.98 | 1.40 | 1.22 | 0.73 |
time (sec) |
N/A | 0.291 | 0.169 | 0.779 | 0.208 | 0.393 | 1.333 | 0.455 | 11.466 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 81 | 74 | 105 | 72 | 72 | 84 | 114 | 133 | 71 |
N.S. |
1 | 0.91 | 1.30 | 0.89 | 0.89 | 1.04 | 1.41 | 1.64 | 0.88 |
time (sec) |
N/A | 0.412 | 0.160 | 0.619 | 0.188 | 0.369 | 0.933 | 0.390 | 0.067 |