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 | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 316 | 182 | 234 | 289 | 315 | 326 | 0 | 437 | 437 |
N.S. |
1 | 0.58 | 0.74 | 0.91 | 1.00 | 1.03 | 0.00 | 1.38 | 1.38 |
time (sec) |
N/A | 0.307 | 0.127 | 2.272 | 0.218 | 0.307 | 0.000 | 0.295 | 10.716 |
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 | 318 | 184 | 235 | 289 | 327 | 338 | 0 | 437 | 472 |
N.S. |
1 | 0.58 | 0.74 | 0.91 | 1.03 | 1.06 | 0.00 | 1.37 | 1.48 |
time (sec) |
N/A | 0.301 | 0.134 | 2.571 | 0.214 | 0.406 | 0.000 | 0.306 | 10.712 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 263 | 175 | 168 | 237 | 0 | 424 | 0 | 343 | 0 |
N.S. |
1 | 0.67 | 0.64 | 0.90 | 0.00 | 1.61 | 0.00 | 1.30 | 0.00 |
time (sec) |
N/A | 0.283 | 0.177 | 2.389 | 0.000 | 0.375 | 0.000 | 0.298 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 212 | 146 | 127 | 171 | 0 | 290 | 0 | 231 | 0 |
N.S. |
1 | 0.69 | 0.60 | 0.81 | 0.00 | 1.37 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.262 | 0.155 | 2.124 | 0.000 | 0.447 | 0.000 | 0.307 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 161 | 117 | 96 | 120 | 0 | 188 | 0 | 141 | 0 |
N.S. |
1 | 0.73 | 0.60 | 0.75 | 0.00 | 1.17 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.244 | 0.140 | 2.133 | 0.000 | 0.366 | 0.000 | 0.279 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 88 | 81 | 93 | 0 | 143 | 0 | 80 | 0 |
N.S. |
1 | 0.79 | 0.72 | 0.83 | 0.00 | 1.28 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.227 | 0.065 | 2.159 | 0.000 | 0.641 | 0.000 | 0.278 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 63 | 51 | 0 | 119 | 0 | 44 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.71 | 0.00 | 1.65 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.205 | 0.045 | 2.135 | 0.000 | 0.283 | 0.000 | 0.276 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 95 | 95 | 90 | 0 | 214 | 0 | 75 | 0 |
N.S. |
1 | 0.80 | 0.80 | 0.76 | 0.00 | 1.80 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.226 | 0.090 | 2.205 | 0.000 | 0.268 | 0.000 | 0.296 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 168 | 131 | 113 | 129 | 0 | 398 | 0 | 120 | 0 |
N.S. |
1 | 0.78 | 0.67 | 0.77 | 0.00 | 2.37 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.261 | 0.171 | 2.582 | 0.000 | 0.299 | 0.000 | 0.277 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 219 | 167 | 133 | 202 | 0 | 706 | 0 | 190 | 0 |
N.S. |
1 | 0.76 | 0.61 | 0.92 | 0.00 | 3.22 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.271 | 0.248 | 2.160 | 0.000 | 0.312 | 0.000 | 0.283 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 308 | 208 | 236 | 226 | 0 | 730 | 0 | 397 | 0 |
N.S. |
1 | 0.68 | 0.77 | 0.73 | 0.00 | 2.37 | 0.00 | 1.29 | 0.00 |
time (sec) |
N/A | 0.300 | 0.658 | 2.314 | 0.000 | 0.289 | 0.000 | 0.314 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 254 | 179 | 185 | 176 | 0 | 520 | 0 | 287 | 0 |
N.S. |
1 | 0.70 | 0.73 | 0.69 | 0.00 | 2.05 | 0.00 | 1.13 | 0.00 |
time (sec) |
N/A | 0.277 | 0.555 | 2.345 | 0.000 | 0.279 | 0.000 | 0.289 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 202 | 150 | 138 | 149 | 0 | 344 | 0 | 195 | 0 |
N.S. |
1 | 0.74 | 0.68 | 0.74 | 0.00 | 1.70 | 0.00 | 0.97 | 0.00 |
time (sec) |
N/A | 0.258 | 0.399 | 2.310 | 0.000 | 0.284 | 0.000 | 0.314 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 158 | 128 | 110 | 194 | 0 | 383 | 0 | 124 | 0 |
N.S. |
1 | 0.81 | 0.70 | 1.23 | 0.00 | 2.42 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.233 | 0.329 | 2.270 | 0.000 | 0.306 | 0.000 | 0.287 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 168 | 134 | 121 | 200 | 0 | 456 | 0 | 150 | 0 |
N.S. |
1 | 0.80 | 0.72 | 1.19 | 0.00 | 2.71 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.240 | 0.332 | 2.418 | 0.000 | 0.312 | 0.000 | 0.307 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 172 | 148 | 121 | 203 | 0 | 549 | 0 | 184 | 0 |
N.S. |
1 | 0.86 | 0.70 | 1.18 | 0.00 | 3.19 | 0.00 | 1.07 | 0.00 |
time (sec) |
N/A | 0.266 | 0.210 | 2.764 | 0.000 | 0.317 | 0.000 | 0.288 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 223 | 185 | 155 | 285 | 0 | 782 | 0 | 306 | 0 |
N.S. |
1 | 0.83 | 0.70 | 1.28 | 0.00 | 3.51 | 0.00 | 1.37 | 0.00 |
time (sec) |
N/A | 0.299 | 0.413 | 2.290 | 0.000 | 0.415 | 0.000 | 0.289 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 275 | 221 | 188 | 388 | 0 | 1226 | 0 | 388 | 0 |
N.S. |
1 | 0.80 | 0.68 | 1.41 | 0.00 | 4.46 | 0.00 | 1.41 | 0.00 |
time (sec) |
N/A | 0.316 | 0.596 | 2.300 | 0.000 | 0.473 | 0.000 | 0.308 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 329 | 257 | 241 | 518 | 0 | 1858 | 0 | 494 | 0 |
N.S. |
1 | 0.78 | 0.73 | 1.57 | 0.00 | 5.65 | 0.00 | 1.50 | 0.00 |
time (sec) |
N/A | 0.345 | 0.737 | 2.266 | 0.000 | 0.617 | 0.000 | 0.308 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 400 | 272 | 374 | 311 | 0 | 1286 | 0 | 651 | 0 |
N.S. |
1 | 0.68 | 0.94 | 0.78 | 0.00 | 3.22 | 0.00 | 1.63 | 0.00 |
time (sec) |
N/A | 0.349 | 1.414 | 2.319 | 0.000 | 0.567 | 0.000 | 0.307 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 346 | 243 | 300 | 260 | 0 | 968 | 0 | 498 | 0 |
N.S. |
1 | 0.70 | 0.87 | 0.75 | 0.00 | 2.80 | 0.00 | 1.44 | 0.00 |
time (sec) |
N/A | 0.334 | 1.273 | 2.314 | 0.000 | 0.389 | 0.000 | 0.321 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 294 | 214 | 232 | 233 | 0 | 680 | 0 | 364 | 0 |
N.S. |
1 | 0.73 | 0.79 | 0.79 | 0.00 | 2.31 | 0.00 | 1.24 | 0.00 |
time (sec) |
N/A | 0.305 | 0.933 | 2.441 | 0.000 | 0.317 | 0.000 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 250 | 192 | 185 | 467 | 0 | 765 | 0 | 251 | 0 |
N.S. |
1 | 0.77 | 0.74 | 1.87 | 0.00 | 3.06 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.286 | 0.814 | 2.613 | 0.000 | 0.311 | 0.000 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 260 | 198 | 194 | 477 | 0 | 894 | 0 | 283 | 0 |
N.S. |
1 | 0.76 | 0.75 | 1.83 | 0.00 | 3.44 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.287 | 0.868 | 2.249 | 0.000 | 0.326 | 0.000 | 0.304 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 270 | 212 | 194 | 477 | 0 | 1043 | 0 | 321 | 0 |
N.S. |
1 | 0.79 | 0.72 | 1.77 | 0.00 | 3.86 | 0.00 | 1.19 | 0.00 |
time (sec) |
N/A | 0.308 | 0.821 | 2.258 | 0.000 | 0.303 | 0.000 | 0.300 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 280 | 226 | 192 | 500 | 0 | 1176 | 0 | 359 | 0 |
N.S. |
1 | 0.81 | 0.69 | 1.79 | 0.00 | 4.20 | 0.00 | 1.28 | 0.00 |
time (sec) |
N/A | 0.308 | 0.848 | 2.288 | 0.000 | 0.337 | 0.000 | 0.325 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 278 | 240 | 187 | 497 | 0 | 1325 | 0 | 391 | 0 |
N.S. |
1 | 0.86 | 0.67 | 1.79 | 0.00 | 4.77 | 0.00 | 1.41 | 0.00 |
time (sec) |
N/A | 0.327 | 0.483 | 2.283 | 0.000 | 0.352 | 0.000 | 0.295 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 329 | 277 | 247 | 602 | 0 | 1734 | 0 | 553 | 0 |
N.S. |
1 | 0.84 | 0.75 | 1.83 | 0.00 | 5.27 | 0.00 | 1.68 | 0.00 |
time (sec) |
N/A | 0.355 | 1.015 | 2.289 | 0.000 | 0.542 | 0.000 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 381 | 313 | 301 | 763 | 0 | 2494 | 0 | 635 | 0 |
N.S. |
1 | 0.82 | 0.79 | 2.00 | 0.00 | 6.55 | 0.00 | 1.67 | 0.00 |
time (sec) |
N/A | 0.363 | 1.328 | 2.564 | 0.000 | 0.785 | 0.000 | 0.315 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 435 | 349 | 378 | 951 | 0 | 3368 | 0 | 743 | 0 |
N.S. |
1 | 0.80 | 0.87 | 2.19 | 0.00 | 7.74 | 0.00 | 1.71 | 0.00 |
time (sec) |
N/A | 0.404 | 1.488 | 2.567 | 0.000 | 1.432 | 0.000 | 0.324 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 206 | 206 | 175 | 1694 | 818 | 2230 | 28410 | 3878 | 1898 |
N.S. |
1 | 1.00 | 0.85 | 8.22 | 3.97 | 10.83 | 137.91 | 18.83 | 9.21 |
time (sec) |
N/A | 0.371 | 0.177 | 2.387 | 0.226 | 0.729 | 5.670 | 0.304 | 10.610 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 142 | 142 | 121 | 735 | 392 | 901 | 8719 | 1528 | 831 |
N.S. |
1 | 1.00 | 0.85 | 5.18 | 2.76 | 6.35 | 61.40 | 10.76 | 5.85 |
time (sec) |
N/A | 0.314 | 0.108 | 2.305 | 0.220 | 0.300 | 1.906 | 0.278 | 9.932 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 67 | 159 | 138 | 237 | 1506 | 385 | 226 |
N.S. |
1 | 1.00 | 0.86 | 2.04 | 1.77 | 3.04 | 19.31 | 4.94 | 2.90 |
time (sec) |
N/A | 0.229 | 0.076 | 2.046 | 0.196 | 0.308 | 0.584 | 0.276 | 9.641 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 52 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.185 | 0.045 | 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 | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 54 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.188 | 0.046 | 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 | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 54 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.189 | 0.054 | 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 | B | B | B | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 337 | 203 | 167 | 1361 | 792 | 1460 | 0 | 3197 | 0 |
N.S. |
1 | 0.60 | 0.50 | 4.04 | 2.35 | 4.33 | 0.00 | 9.49 | 0.00 |
time (sec) |
N/A | 0.352 | 0.205 | 2.324 | 0.203 | 0.392 | 0.000 | 0.352 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 219 | 139 | 113 | 402 | 305 | 496 | 0 | 1073 | 0 |
N.S. |
1 | 0.63 | 0.52 | 1.84 | 1.39 | 2.26 | 0.00 | 4.90 | 0.00 |
time (sec) |
N/A | 0.291 | 0.118 | 2.252 | 0.227 | 0.582 | 0.000 | 0.313 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 75 | 59 | 62 | 62 | 83 | 0 | 180 | 0 |
N.S. |
1 | 0.74 | 0.58 | 0.61 | 0.61 | 0.82 | 0.00 | 1.78 | 0.00 |
time (sec) |
N/A | 0.220 | 0.056 | 2.199 | 0.189 | 0.258 | 0.000 | 0.268 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 67 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.201 | 0.050 | 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(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 72 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.208 | 0.055 | 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(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 72 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.204 | 0.060 | 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(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 75 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.239 | 0.051 | 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 | B | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 181 | 175 | 107 | 405 | 276 | 516 | 0 | 1279 | 484 |
N.S. |
1 | 0.97 | 0.59 | 2.24 | 1.52 | 2.85 | 0.00 | 7.07 | 2.67 |
time (sec) |
N/A | 0.326 | 0.091 | 2.337 | 0.220 | 0.381 | 0.000 | 0.295 | 10.027 |
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 | 127 | 131 | 75 | 175 | 157 | 249 | 0 | 608 | 250 |
N.S. |
1 | 1.03 | 0.59 | 1.38 | 1.24 | 1.96 | 0.00 | 4.79 | 1.97 |
time (sec) |
N/A | 0.286 | 0.083 | 2.679 | 0.234 | 0.407 | 0.000 | 0.294 | 9.903 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 76 | 80 | 54 | 65 | 78 | 96 | 604 | 224 | 112 |
N.S. |
1 | 1.05 | 0.71 | 0.86 | 1.03 | 1.26 | 7.95 | 2.95 | 1.47 |
time (sec) |
N/A | 0.217 | 0.048 | 2.533 | 0.187 | 0.271 | 0.869 | 0.284 | 9.943 |
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 | 34 | 38 | 25 | 26 | 25 | 32 | 100 | 51 | 41 |
N.S. |
1 | 1.12 | 0.74 | 0.76 | 0.74 | 0.94 | 2.94 | 1.50 | 1.21 |
time (sec) |
N/A | 0.168 | 0.004 | 2.253 | 0.189 | 0.263 | 0.478 | 0.280 | 9.790 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 71 | 78 | 62 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.206 | 0.046 | 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 | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 72 | 75 | 63 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.198 | 0.043 | 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 | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 74 | 76 | 65 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.199 | 0.046 | 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 | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 73 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.209 | 0.120 | 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 | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 73 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.204 | 0.086 | 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 | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 71 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.212 | 0.089 | 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 | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 71 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.204 | 0.116 | 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 | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 73 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.206 | 0.144 | 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(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 87 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.237 | 0.080 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 133 | 72 | 139 | 0 | 219 | 0 | 0 | 259 |
N.S. |
1 | 1.16 | 0.63 | 1.21 | 0.00 | 1.90 | 0.00 | 0.00 | 2.25 |
time (sec) |
N/A | 0.243 | 0.058 | 2.474 | 0.000 | 0.294 | 0.000 | 0.000 | 9.763 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 48 | 43 | 65 | 64 | 321 | 148 | 87 |
N.S. |
1 | 1.00 | 0.80 | 0.72 | 1.08 | 1.07 | 5.35 | 2.47 | 1.45 |
time (sec) |
N/A | 0.197 | 0.038 | 2.187 | 0.208 | 0.314 | 0.809 | 0.283 | 0.108 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 84 | 94 | 96 | 96 | 100 | 97 | 88 |
N.S. |
1 | 1.00 | 2.21 | 2.47 | 2.53 | 2.53 | 2.63 | 2.55 | 2.32 |
time (sec) |
N/A | 0.190 | 0.013 | 2.002 | 0.202 | 0.254 | 0.028 | 0.276 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 67 | 70 | 69 | 69 | 73 | 72 | 65 |
N.S. |
1 | 1.00 | 1.76 | 1.84 | 1.82 | 1.82 | 1.92 | 1.89 | 1.71 |
time (sec) |
N/A | 0.187 | 0.010 | 2.339 | 0.201 | 0.266 | 0.024 | 0.286 | 9.663 |
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 | 38 | 38 | 46 | 48 | 48 | 48 | 49 | 49 | 47 |
N.S. |
1 | 1.00 | 1.21 | 1.26 | 1.26 | 1.26 | 1.29 | 1.29 | 1.24 |
time (sec) |
N/A | 0.194 | 0.006 | 0.227 | 0.193 | 0.311 | 0.020 | 0.271 | 0.050 |
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 | 28 | 28 | 32 | 25 | 24 | 24 | 26 | 24 | 25 |
N.S. |
1 | 1.00 | 1.14 | 0.89 | 0.86 | 0.86 | 0.93 | 0.86 | 0.89 |
time (sec) |
N/A | 0.168 | 0.000 | 0.043 | 0.186 | 0.316 | 0.017 | 0.273 | 0.037 |
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 | 12 | 14 | 12 | 11 | 10 | 10 | 8 | 10 | 10 |
N.S. |
1 | 1.17 | 1.00 | 0.92 | 0.83 | 0.83 | 0.67 | 0.83 | 0.83 |
time (sec) |
N/A | 0.154 | 0.001 | 2.033 | 0.214 | 0.298 | 0.022 | 0.265 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 26 | 25 | 24 | 20 | 117 | 26 |
N.S. |
1 | 1.00 | 1.00 | 1.04 | 1.00 | 0.96 | 0.80 | 4.68 | 1.04 |
time (sec) |
N/A | 0.183 | 0.007 | 2.014 | 0.215 | 0.274 | 0.078 | 0.262 | 0.051 |
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 | 32 | 32 | 31 | 33 | 35 | 39 | 27 | 33 | 31 |
N.S. |
1 | 1.00 | 0.97 | 1.03 | 1.09 | 1.22 | 0.84 | 1.03 | 0.97 |
time (sec) |
N/A | 0.184 | 0.009 | 2.137 | 0.195 | 0.368 | 0.096 | 0.273 | 9.680 |
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 | 28 | 28 | 26 | 25 | 38 | 38 | 39 | 24 | 39 |
N.S. |
1 | 1.00 | 0.93 | 0.89 | 1.36 | 1.36 | 1.39 | 0.86 | 1.39 |
time (sec) |
N/A | 0.160 | 0.008 | 2.417 | 0.182 | 0.430 | 0.144 | 0.272 | 9.845 |
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 | 38 | 38 | 27 | 26 | 50 | 50 | 53 | 41 | 52 |
N.S. |
1 | 1.00 | 0.71 | 0.68 | 1.32 | 1.32 | 1.39 | 1.08 | 1.37 |
time (sec) |
N/A | 0.185 | 0.006 | 2.035 | 0.220 | 0.366 | 0.192 | 0.264 | 9.746 |
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 | 38 | 38 | 27 | 26 | 61 | 61 | 65 | 25 | 63 |
N.S. |
1 | 1.00 | 0.71 | 0.68 | 1.61 | 1.61 | 1.71 | 0.66 | 1.66 |
time (sec) |
N/A | 0.185 | 0.007 | 2.009 | 0.189 | 0.368 | 0.229 | 0.275 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 189 | 195 | 197 | 197 | 218 | 212 | 181 |
N.S. |
1 | 1.00 | 2.91 | 3.00 | 3.03 | 3.03 | 3.35 | 3.26 | 2.78 |
time (sec) |
N/A | 0.290 | 0.021 | 2.371 | 0.214 | 0.355 | 0.040 | 0.263 | 0.091 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 148 | 157 | 156 | 156 | 168 | 170 | 144 |
N.S. |
1 | 1.00 | 2.28 | 2.42 | 2.40 | 2.40 | 2.58 | 2.62 | 2.22 |
time (sec) |
N/A | 0.273 | 0.013 | 2.364 | 0.207 | 0.426 | 0.035 | 0.263 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 122 | 121 | 124 | 124 | 133 | 130 | 115 |
N.S. |
1 | 1.00 | 1.88 | 1.86 | 1.91 | 1.91 | 2.05 | 2.00 | 1.77 |
time (sec) |
N/A | 0.241 | 0.010 | 2.606 | 0.191 | 0.243 | 0.034 | 0.270 | 9.748 |
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 | 65 | 77 | 79 | 69 | 72 | 81 | 87 | 89 | 74 |
N.S. |
1 | 1.18 | 1.22 | 1.06 | 1.11 | 1.25 | 1.34 | 1.37 | 1.14 |
time (sec) |
N/A | 0.254 | 0.008 | 2.482 | 0.186 | 0.238 | 0.031 | 0.259 | 0.042 |
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 | 38 | 38 | 47 | 48 | 48 | 48 | 49 | 49 | 47 |
N.S. |
1 | 1.00 | 1.24 | 1.26 | 1.26 | 1.26 | 1.29 | 1.29 | 1.24 |
time (sec) |
N/A | 0.201 | 0.007 | 2.368 | 0.213 | 0.263 | 0.041 | 0.263 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 13 | 20 | 20 | 19 | 84 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 1.43 | 1.43 | 1.36 | 6.00 | 1.43 |
time (sec) |
N/A | 0.156 | 0.002 | 2.334 | 0.209 | 0.253 | 0.040 | 0.275 | 0.033 |
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 | 49 | 49 | 43 | 56 | 61 | 63 | 44 | 60 | 62 |
N.S. |
1 | 1.00 | 0.88 | 1.14 | 1.24 | 1.29 | 0.90 | 1.22 | 1.27 |
time (sec) |
N/A | 0.205 | 0.012 | 2.325 | 0.195 | 0.242 | 0.134 | 0.286 | 0.069 |
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 | 51 | 51 | 47 | 63 | 67 | 92 | 60 | 65 | 71 |
N.S. |
1 | 1.00 | 0.92 | 1.24 | 1.31 | 1.80 | 1.18 | 1.27 | 1.39 |
time (sec) |
N/A | 0.216 | 0.023 | 2.697 | 0.204 | 0.266 | 0.197 | 0.268 | 0.079 |
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 | 59 | 59 | 49 | 67 | 79 | 99 | 80 | 110 | 77 |
N.S. |
1 | 1.00 | 0.83 | 1.14 | 1.34 | 1.68 | 1.36 | 1.86 | 1.31 |
time (sec) |
N/A | 0.220 | 0.016 | 2.520 | 0.201 | 0.297 | 0.266 | 0.282 | 9.764 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 53 | 60 | 84 | 84 | 88 | 59 | 80 |
N.S. |
1 | 1.00 | 1.89 | 2.14 | 3.00 | 3.00 | 3.14 | 2.11 | 2.86 |
time (sec) |
N/A | 0.160 | 0.016 | 2.355 | 0.225 | 0.275 | 0.348 | 0.266 | 0.043 |
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 | 65 | 65 | 56 | 62 | 98 | 98 | 104 | 61 | 96 |
N.S. |
1 | 1.00 | 0.86 | 0.95 | 1.51 | 1.51 | 1.60 | 0.94 | 1.48 |
time (sec) |
N/A | 0.216 | 0.013 | 2.376 | 0.190 | 0.261 | 0.449 | 0.278 | 0.047 |
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 | 65 | 65 | 57 | 62 | 109 | 109 | 116 | 61 | 107 |
N.S. |
1 | 1.00 | 0.88 | 0.95 | 1.68 | 1.68 | 1.78 | 0.94 | 1.65 |
time (sec) |
N/A | 0.224 | 0.017 | 2.352 | 0.197 | 0.260 | 0.627 | 0.273 | 9.786 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 58 | 62 | 120 | 120 | 128 | 61 | 118 |
N.S. |
1 | 1.00 | 0.89 | 0.95 | 1.85 | 1.85 | 1.97 | 0.94 | 1.82 |
time (sec) |
N/A | 0.217 | 0.015 | 2.525 | 0.196 | 0.277 | 1.055 | 0.270 | 9.857 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 57 | 62 | 131 | 131 | 139 | 61 | 129 |
N.S. |
1 | 1.00 | 0.88 | 0.95 | 2.02 | 2.02 | 2.14 | 0.94 | 1.98 |
time (sec) |
N/A | 0.217 | 0.018 | 2.795 | 0.194 | 0.273 | 2.870 | 0.279 | 0.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 276 | 325 | 327 | 327 | 364 | 362 | 308 |
N.S. |
1 | 1.00 | 3.00 | 3.53 | 3.55 | 3.55 | 3.96 | 3.93 | 3.35 |
time (sec) |
N/A | 0.379 | 0.055 | 2.360 | 0.232 | 0.281 | 0.055 | 0.289 | 9.859 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 235 | 273 | 277 | 277 | 308 | 303 | 261 |
N.S. |
1 | 1.00 | 2.55 | 2.97 | 3.01 | 3.01 | 3.35 | 3.29 | 2.84 |
time (sec) |
N/A | 0.340 | 0.036 | 2.359 | 0.195 | 0.269 | 0.053 | 0.282 | 0.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 217 | 222 | 225 | 225 | 243 | 245 | 208 |
N.S. |
1 | 1.00 | 2.36 | 2.41 | 2.45 | 2.45 | 2.64 | 2.66 | 2.26 |
time (sec) |
N/A | 0.311 | 0.017 | 2.281 | 0.192 | 0.303 | 0.049 | 0.280 | 0.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 104 | 161 | 172 | 140 | 167 | 190 | 188 | 152 |
N.S. |
1 | 1.13 | 1.75 | 1.87 | 1.52 | 1.82 | 2.07 | 2.04 | 1.65 |
time (sec) |
N/A | 0.318 | 0.012 | 2.417 | 0.202 | 0.260 | 0.035 | 0.299 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 122 | 121 | 124 | 124 | 133 | 130 | 115 |
N.S. |
1 | 1.00 | 1.88 | 1.86 | 1.91 | 1.91 | 2.05 | 2.00 | 1.77 |
time (sec) |
N/A | 0.253 | 0.009 | 3.263 | 0.199 | 0.266 | 0.058 | 0.282 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 67 | 73 | 69 | 69 | 73 | 155 | 65 |
N.S. |
1 | 1.00 | 1.76 | 1.92 | 1.82 | 1.82 | 1.92 | 4.08 | 1.71 |
time (sec) |
N/A | 0.196 | 0.005 | 2.579 | 0.202 | 0.308 | 0.058 | 0.279 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 13 | 31 | 31 | 32 | 31 | 31 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 2.21 | 2.21 | 2.29 | 2.21 | 2.21 |
time (sec) |
N/A | 0.150 | 0.003 | 2.347 | 0.192 | 0.276 | 0.053 | 0.285 | 0.044 |
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 | 73 | 73 | 74 | 109 | 114 | 116 | 83 | 115 | 118 |
N.S. |
1 | 1.00 | 1.01 | 1.49 | 1.56 | 1.59 | 1.14 | 1.58 | 1.62 |
time (sec) |
N/A | 0.218 | 0.022 | 2.360 | 0.191 | 0.276 | 0.199 | 0.273 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 72 | 109 | 118 | 173 | 102 | 167 | 123 |
N.S. |
1 | 1.00 | 0.96 | 1.45 | 1.57 | 2.31 | 1.36 | 2.23 | 1.64 |
time (sec) |
N/A | 0.246 | 0.032 | 2.360 | 0.203 | 0.278 | 0.305 | 0.280 | 9.736 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 114 | 114 | 125 | 188 | 128 | 112 | 130 |
N.S. |
1 | 1.00 | 1.46 | 1.46 | 1.60 | 2.41 | 1.64 | 1.44 | 1.67 |
time (sec) |
N/A | 0.249 | 0.026 | 2.759 | 0.221 | 0.303 | 0.484 | 0.295 | 0.102 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 80 | 115 | 142 | 176 | 148 | 118 | 138 |
N.S. |
1 | 1.00 | 0.93 | 1.34 | 1.65 | 2.05 | 1.72 | 1.37 | 1.60 |
time (sec) |
N/A | 0.254 | 0.025 | 2.523 | 0.215 | 0.285 | 0.795 | 0.281 | 0.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 91 | 104 | 143 | 143 | 155 | 111 | 135 |
N.S. |
1 | 1.00 | 3.25 | 3.71 | 5.11 | 5.11 | 5.54 | 3.96 | 4.82 |
time (sec) |
N/A | 0.162 | 0.020 | 2.334 | 0.206 | 0.276 | 2.597 | 0.278 | 9.739 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 58 | 90 | 97 | 110 | 160 | 160 | 172 | 114 | 154 |
N.S. |
1 | 1.55 | 1.67 | 1.90 | 2.76 | 2.76 | 2.97 | 1.97 | 2.66 |
time (sec) |
N/A | 0.252 | 0.023 | 2.381 | 0.196 | 0.269 | 10.865 | 0.279 | 9.820 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 97 | 110 | 171 | 171 | 184 | 114 | 165 |
N.S. |
1 | 1.00 | 1.05 | 1.20 | 1.86 | 1.86 | 2.00 | 1.24 | 1.79 |
time (sec) |
N/A | 0.245 | 0.022 | 2.509 | 0.207 | 0.270 | 44.480 | 0.273 | 9.794 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 97 | 110 | 182 | 182 | 196 | 114 | 176 |
N.S. |
1 | 1.00 | 1.05 | 1.20 | 1.98 | 1.98 | 2.13 | 1.24 | 1.91 |
time (sec) |
N/A | 0.252 | 0.021 | 2.842 | 0.207 | 0.280 | 156.378 | 0.269 | 9.823 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 97 | 110 | 193 | 193 | 0 | 114 | 187 |
N.S. |
1 | 1.00 | 1.05 | 1.20 | 2.10 | 2.10 | 0.00 | 1.24 | 2.03 |
time (sec) |
N/A | 0.256 | 0.027 | 2.358 | 0.206 | 0.266 | 0.000 | 0.286 | 0.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 122 | 122 | 167 | 244 | 258 | 259 | 209 | 273 | 280 |
N.S. |
1 | 1.00 | 1.37 | 2.00 | 2.11 | 2.12 | 1.71 | 2.24 | 2.30 |
time (sec) |
N/A | 0.274 | 0.045 | 2.419 | 0.198 | 0.288 | 0.285 | 0.274 | 0.061 |
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 | 98 | 98 | 115 | 168 | 177 | 179 | 136 | 184 | 189 |
N.S. |
1 | 1.00 | 1.17 | 1.71 | 1.81 | 1.83 | 1.39 | 1.88 | 1.93 |
time (sec) |
N/A | 0.252 | 0.029 | 2.485 | 0.197 | 0.451 | 0.228 | 0.288 | 0.050 |