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 | B | A | A | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 152 | 152 | 313 | 157 | 155 | 291 | 0 | 324 | 357 |
N.S. |
1 | 1.00 | 2.06 | 1.03 | 1.02 | 1.91 | 0.00 | 2.13 | 2.35 |
time (sec) |
N/A | 0.221 | 6.775 | 0.526 | 0.247 | 0.283 | 0.000 | 0.424 | 10.775 |
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 | 228 | 228 | 353 | 248 | 273 | 327 | 0 | 324 | 357 |
N.S. |
1 | 1.00 | 1.55 | 1.09 | 1.20 | 1.43 | 0.00 | 1.42 | 1.57 |
time (sec) |
N/A | 0.300 | 6.674 | 0.557 | 0.282 | 0.277 | 0.000 | 0.444 | 11.301 |
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 | 194 | 194 | 187 | 179 | 197 | 360 | 0 | 388 | 433 |
N.S. |
1 | 1.00 | 0.96 | 0.92 | 1.02 | 1.86 | 0.00 | 2.00 | 2.23 |
time (sec) |
N/A | 0.254 | 7.839 | 0.638 | 0.244 | 0.303 | 0.000 | 0.445 | 12.226 |
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 | 270 | 270 | 197 | 190 | 323 | 384 | 0 | 420 | 471 |
N.S. |
1 | 1.00 | 0.73 | 0.70 | 1.20 | 1.42 | 0.00 | 1.56 | 1.74 |
time (sec) |
N/A | 0.355 | 8.878 | 0.758 | 0.262 | 0.302 | 0.000 | 0.452 | 12.634 |
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 | 224 | 224 | 146 | 155 | 184 | 150 | 748 | 225 | 612 |
N.S. |
1 | 1.00 | 0.65 | 0.69 | 0.82 | 0.67 | 3.34 | 1.00 | 2.73 |
time (sec) |
N/A | 0.352 | 1.242 | 1.452 | 0.233 | 0.305 | 3.475 | 0.366 | 14.776 |
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 | 209 | 209 | 136 | 142 | 164 | 137 | 699 | 208 | 683 |
N.S. |
1 | 1.00 | 0.65 | 0.68 | 0.78 | 0.66 | 3.34 | 1.00 | 3.27 |
time (sec) |
N/A | 0.350 | 0.850 | 1.088 | 0.219 | 0.300 | 2.650 | 0.348 | 13.302 |
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 | 183 | 183 | 126 | 133 | 164 | 124 | 597 | 191 | 543 |
N.S. |
1 | 1.00 | 0.69 | 0.73 | 0.90 | 0.68 | 3.26 | 1.04 | 2.97 |
time (sec) |
N/A | 0.275 | 0.588 | 0.895 | 0.225 | 0.293 | 1.847 | 0.539 | 15.038 |
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 | 181 | 181 | 116 | 122 | 141 | 111 | 542 | 174 | 572 |
N.S. |
1 | 1.00 | 0.64 | 0.67 | 0.78 | 0.61 | 2.99 | 0.96 | 3.16 |
time (sec) |
N/A | 0.154 | 0.455 | 0.731 | 0.224 | 0.281 | 1.300 | 0.434 | 13.409 |
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 | 185 | 185 | 122 | 112 | 171 | 154 | 0 | 277 | 429 |
N.S. |
1 | 1.00 | 0.66 | 0.61 | 0.92 | 0.83 | 0.00 | 1.50 | 2.32 |
time (sec) |
N/A | 0.208 | 5.731 | 0.472 | 0.255 | 0.281 | 0.000 | 0.443 | 13.069 |
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 | 173 | 173 | 168 | 149 | 186 | 173 | 0 | 290 | 429 |
N.S. |
1 | 1.00 | 0.97 | 0.86 | 1.08 | 1.00 | 0.00 | 1.68 | 2.48 |
time (sec) |
N/A | 0.207 | 6.741 | 0.470 | 0.305 | 0.288 | 0.000 | 0.425 | 10.867 |
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 | 181 | 181 | 664 | 179 | 239 | 212 | 0 | 306 | 438 |
N.S. |
1 | 1.00 | 3.67 | 0.99 | 1.32 | 1.17 | 0.00 | 1.69 | 2.42 |
time (sec) |
N/A | 0.221 | 11.668 | 0.490 | 0.311 | 0.293 | 0.000 | 0.439 | 11.160 |
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 | 176 | 176 | 219 | 189 | 246 | 231 | 0 | 292 | 429 |
N.S. |
1 | 1.00 | 1.24 | 1.07 | 1.40 | 1.31 | 0.00 | 1.66 | 2.44 |
time (sec) |
N/A | 0.182 | 6.484 | 0.460 | 0.434 | 0.284 | 0.000 | 0.432 | 11.156 |
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 | 178 | 235 | 186 | 268 | 258 | 0 | 313 | 419 |
N.S. |
1 | 1.00 | 1.32 | 1.04 | 1.51 | 1.45 | 0.00 | 1.76 | 2.35 |
time (sec) |
N/A | 0.178 | 6.067 | 0.479 | 0.301 | 0.281 | 0.000 | 0.465 | 10.487 |
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 | 175 | 175 | 271 | 224 | 250 | 278 | 0 | 276 | 408 |
N.S. |
1 | 1.00 | 1.55 | 1.28 | 1.43 | 1.59 | 0.00 | 1.58 | 2.33 |
time (sec) |
N/A | 0.210 | 6.622 | 0.507 | 0.392 | 0.279 | 0.000 | 0.443 | 10.575 |
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 | 182 | 182 | 289 | 231 | 275 | 316 | 0 | 307 | 396 |
N.S. |
1 | 1.00 | 1.59 | 1.27 | 1.51 | 1.74 | 0.00 | 1.69 | 2.18 |
time (sec) |
N/A | 0.205 | 7.752 | 0.520 | 0.303 | 0.286 | 0.000 | 0.491 | 10.434 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 172 | 172 | 292 | 244 | 233 | 336 | 0 | 291 | 388 |
N.S. |
1 | 1.00 | 1.70 | 1.42 | 1.35 | 1.95 | 0.00 | 1.69 | 2.26 |
time (sec) |
N/A | 0.234 | 1.673 | 0.544 | 0.307 | 0.283 | 0.000 | 0.463 | 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 | 238 | 238 | 279 | 153 | 265 | 362 | 0 | 302 | 389 |
N.S. |
1 | 1.00 | 1.17 | 0.64 | 1.11 | 1.52 | 0.00 | 1.27 | 1.63 |
time (sec) |
N/A | 0.290 | 1.175 | 0.462 | 0.301 | 0.283 | 0.000 | 0.500 | 12.653 |
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 | 200 | 200 | 459 | 157 | 246 | 291 | 0 | 324 | 357 |
N.S. |
1 | 1.00 | 2.30 | 0.78 | 1.23 | 1.46 | 0.00 | 1.62 | 1.78 |
time (sec) |
N/A | 0.281 | 0.363 | 0.507 | 0.236 | 0.274 | 0.000 | 0.493 | 11.058 |
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 | 228 | 228 | 365 | 168 | 286 | 327 | 0 | 356 | 395 |
N.S. |
1 | 1.00 | 1.60 | 0.74 | 1.25 | 1.43 | 0.00 | 1.56 | 1.73 |
time (sec) |
N/A | 0.339 | 7.349 | 0.577 | 0.229 | 0.284 | 0.000 | 0.516 | 11.197 |
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 | 246 | 246 | 187 | 179 | 308 | 360 | 0 | 388 | 433 |
N.S. |
1 | 1.00 | 0.76 | 0.73 | 1.25 | 1.46 | 0.00 | 1.58 | 1.76 |
time (sec) |
N/A | 0.327 | 8.128 | 0.678 | 0.223 | 0.307 | 0.000 | 0.524 | 11.951 |
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 | 270 | 270 | 197 | 190 | 348 | 384 | 0 | 420 | 471 |
N.S. |
1 | 1.00 | 0.73 | 0.70 | 1.29 | 1.42 | 0.00 | 1.56 | 1.74 |
time (sec) |
N/A | 0.371 | 9.127 | 0.758 | 0.231 | 0.295 | 0.000 | 0.542 | 12.105 |
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 | 286 | 286 | 206 | 201 | 368 | 417 | 0 | 452 | 509 |
N.S. |
1 | 1.00 | 0.72 | 0.70 | 1.29 | 1.46 | 0.00 | 1.58 | 1.78 |
time (sec) |
N/A | 0.386 | 10.462 | 0.904 | 0.246 | 0.306 | 0.000 | 0.556 | 12.677 |
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 | 178 | 229 | 200 | 294 | 245 | 0 | 324 | 474 |
N.S. |
1 | 1.00 | 1.29 | 1.12 | 1.65 | 1.38 | 0.00 | 1.82 | 2.66 |
time (sec) |
N/A | 0.244 | 7.199 | 0.589 | 0.296 | 0.301 | 0.000 | 0.526 | 10.667 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 159 | 159 | 429 | 89 | 502 | 90 | 4318 | 218 | 211 |
N.S. |
1 | 1.00 | 2.70 | 0.56 | 3.16 | 0.57 | 27.16 | 1.37 | 1.33 |
time (sec) |
N/A | 0.174 | 6.214 | 0.329 | 0.301 | 0.262 | 76.240 | 0.326 | 12.552 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 141 | 141 | 375 | 78 | 461 | 80 | 3580 | 205 | 199 |
N.S. |
1 | 1.00 | 2.66 | 0.55 | 3.27 | 0.57 | 25.39 | 1.45 | 1.41 |
time (sec) |
N/A | 0.159 | 6.332 | 0.290 | 0.317 | 0.264 | 49.087 | 0.332 | 13.684 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 115 | 351 | 89 | 400 | 70 | 2773 | 179 | 172 |
N.S. |
1 | 1.00 | 3.05 | 0.77 | 3.48 | 0.61 | 24.11 | 1.56 | 1.50 |
time (sec) |
N/A | 0.135 | 8.238 | 0.373 | 0.304 | 0.259 | 31.006 | 0.317 | 14.438 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 377 | 78 | 379 | 60 | 2307 | 179 | 173 |
N.S. |
1 | 1.00 | 3.89 | 0.80 | 3.91 | 0.62 | 23.78 | 1.85 | 1.78 |
time (sec) |
N/A | 0.102 | 3.502 | 0.291 | 0.311 | 0.260 | 19.242 | 0.293 | 14.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 86 | 68 | 280 | 84 | 0 | 143 | 225 |
N.S. |
1 | 1.00 | 0.85 | 0.67 | 2.77 | 0.83 | 0.00 | 1.42 | 2.23 |
time (sec) |
N/A | 0.101 | 0.772 | 0.296 | 0.304 | 0.279 | 0.000 | 0.306 | 11.582 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 95 | 95 | 122 | 97 | 277 | 104 | 0 | 147 | 229 |
N.S. |
1 | 1.00 | 1.28 | 1.02 | 2.92 | 1.09 | 0.00 | 1.55 | 2.41 |
time (sec) |
N/A | 0.129 | 1.310 | 0.285 | 0.302 | 0.267 | 0.000 | 0.322 | 9.993 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 106 | 106 | 152 | 140 | 261 | 126 | 0 | 167 | 223 |
N.S. |
1 | 1.00 | 1.43 | 1.32 | 2.46 | 1.19 | 0.00 | 1.58 | 2.10 |
time (sec) |
N/A | 0.138 | 0.977 | 0.322 | 0.300 | 0.266 | 0.000 | 0.311 | 9.484 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 138 | 125 | 240 | 148 | 0 | 157 | 212 |
N.S. |
1 | 1.00 | 1.47 | 1.33 | 2.55 | 1.57 | 0.00 | 1.67 | 2.26 |
time (sec) |
N/A | 0.116 | 1.327 | 0.292 | 0.310 | 0.266 | 0.000 | 0.317 | 10.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 102 | 232 | 126 | 217 | 171 | 0 | 167 | 317 |
N.S. |
1 | 1.00 | 2.27 | 1.24 | 2.13 | 1.68 | 0.00 | 1.64 | 3.11 |
time (sec) |
N/A | 0.106 | 1.002 | 0.296 | 0.317 | 0.261 | 0.000 | 0.346 | 10.440 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | C | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 189 | 134 | 234 | 155 | 0 | 187 | 183 |
N.S. |
1 | 1.00 | 2.30 | 1.63 | 2.85 | 1.89 | 0.00 | 2.28 | 2.23 |
time (sec) |
N/A | 0.095 | 0.513 | 0.293 | 0.224 | 0.262 | 0.000 | 0.323 | 10.308 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 135 | 135 | 418 | 89 | 416 | 80 | 3046 | 179 | 173 |
N.S. |
1 | 1.00 | 3.10 | 0.66 | 3.08 | 0.59 | 22.56 | 1.33 | 1.28 |
time (sec) |
N/A | 0.261 | 2.125 | 0.339 | 0.308 | 0.258 | 83.575 | 0.331 | 14.239 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 104 | 362 | 78 | 353 | 70 | 2271 | 153 | 146 |
N.S. |
1 | 1.00 | 3.48 | 0.75 | 3.39 | 0.67 | 21.84 | 1.47 | 1.40 |
time (sec) |
N/A | 0.203 | 1.442 | 0.291 | 0.301 | 0.256 | 54.929 | 0.325 | 13.004 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 262 | 56 | 310 | 60 | 1720 | 140 | 81 |
N.S. |
1 | 1.00 | 2.62 | 0.56 | 3.10 | 0.60 | 17.20 | 1.40 | 0.81 |
time (sec) |
N/A | 0.106 | 0.843 | 0.337 | 0.320 | 0.251 | 34.748 | 0.305 | 9.180 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 69 | 57 | 188 | 71 | 0 | 91 | 167 |
N.S. |
1 | 1.00 | 0.95 | 0.78 | 2.58 | 0.97 | 0.00 | 1.25 | 2.29 |
time (sec) |
N/A | 0.151 | 0.772 | 0.316 | 0.384 | 0.272 | 0.000 | 0.324 | 10.121 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 116 | 86 | 202 | 88 | 0 | 131 | 175 |
N.S. |
1 | 1.00 | 1.57 | 1.16 | 2.73 | 1.19 | 0.00 | 1.77 | 2.36 |
time (sec) |
N/A | 0.166 | 1.068 | 0.349 | 0.312 | 0.272 | 0.000 | 0.327 | 9.874 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 134 | 101 | 204 | 118 | 0 | 128 | 186 |
N.S. |
1 | 1.00 | 1.84 | 1.38 | 2.79 | 1.62 | 0.00 | 1.75 | 2.55 |
time (sec) |
N/A | 0.174 | 1.209 | 0.383 | 0.336 | 0.273 | 0.000 | 0.337 | 10.146 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 124 | 98 | 176 | 139 | 0 | 137 | 261 |
N.S. |
1 | 1.00 | 1.70 | 1.34 | 2.41 | 1.90 | 0.00 | 1.88 | 3.58 |
time (sec) |
N/A | 0.240 | 1.566 | 0.357 | 0.309 | 0.261 | 0.000 | 0.333 | 9.504 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 116 | 122 | 194 | 138 | 0 | 158 | 151 |
N.S. |
1 | 1.00 | 1.41 | 1.49 | 2.37 | 1.68 | 0.00 | 1.93 | 1.84 |
time (sec) |
N/A | 0.216 | 1.612 | 0.370 | 0.228 | 0.261 | 0.000 | 0.358 | 9.374 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 189 | 122 | 195 | 167 | 0 | 157 | 149 |
N.S. |
1 | 1.00 | 1.89 | 1.22 | 1.95 | 1.67 | 0.00 | 1.57 | 1.49 |
time (sec) |
N/A | 0.127 | 0.873 | 0.376 | 0.227 | 0.265 | 0.000 | 0.355 | 9.549 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 124 | 229 | 168 | 274 | 196 | 0 | 216 | 339 |
N.S. |
1 | 1.00 | 1.85 | 1.35 | 2.21 | 1.58 | 0.00 | 1.74 | 2.73 |
time (sec) |
N/A | 0.259 | 1.286 | 0.441 | 0.257 | 0.270 | 0.000 | 0.365 | 10.999 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 129 | 129 | 366 | 78 | 373 | 78 | 2404 | 166 | 160 |
N.S. |
1 | 1.00 | 2.84 | 0.60 | 2.89 | 0.60 | 18.64 | 1.29 | 1.24 |
time (sec) |
N/A | 0.202 | 1.703 | 0.348 | 0.420 | 0.276 | 133.527 | 0.363 | 13.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 310 | 67 | 290 | 68 | 1608 | 127 | 95 |
N.S. |
1 | 1.00 | 2.95 | 0.64 | 2.76 | 0.65 | 15.31 | 1.21 | 0.90 |
time (sec) |
N/A | 0.167 | 1.330 | 0.305 | 0.357 | 0.259 | 89.954 | 0.348 | 10.393 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 84 | 105 | 255 | 56 | 267 | 58 | 1246 | 127 | 78 |
N.S. |
1 | 1.25 | 3.04 | 0.67 | 3.18 | 0.69 | 14.83 | 1.51 | 0.93 |
time (sec) |
N/A | 0.121 | 0.979 | 0.267 | 0.312 | 0.264 | 58.305 | 0.336 | 10.193 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 63 | 44 | 161 | 59 | 0 | 89 | 150 |
N.S. |
1 | 1.00 | 1.05 | 0.73 | 2.68 | 0.98 | 0.00 | 1.48 | 2.50 |
time (sec) |
N/A | 0.108 | 0.705 | 0.457 | 0.306 | 0.275 | 0.000 | 0.325 | 10.501 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 106 | 66 | 158 | 82 | 0 | 111 | 151 |
N.S. |
1 | 1.00 | 2.16 | 1.35 | 3.22 | 1.67 | 0.00 | 2.27 | 3.08 |
time (sec) |
N/A | 0.127 | 1.093 | 0.538 | 0.306 | 0.263 | 0.000 | 0.349 | 10.474 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 126 | 72 | 138 | 109 | 0 | 108 | 161 |
N.S. |
1 | 1.00 | 2.10 | 1.20 | 2.30 | 1.82 | 0.00 | 1.80 | 2.68 |
time (sec) |
N/A | 0.136 | 0.988 | 0.426 | 0.310 | 0.259 | 0.000 | 0.358 | 10.370 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 115 | 94 | 153 | 123 | 0 | 128 | 119 |
N.S. |
1 | 1.00 | 1.60 | 1.31 | 2.12 | 1.71 | 0.00 | 1.78 | 1.65 |
time (sec) |
N/A | 0.147 | 1.675 | 0.424 | 0.217 | 0.254 | 0.000 | 0.374 | 9.690 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 125 | 120 | 195 | 149 | 0 | 156 | 151 |
N.S. |
1 | 1.00 | 1.34 | 1.29 | 2.10 | 1.60 | 0.00 | 1.68 | 1.62 |
time (sec) |
N/A | 0.176 | 1.999 | 0.453 | 0.228 | 0.262 | 0.000 | 0.387 | 10.082 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 114 | 114 | 189 | 146 | 234 | 179 | 0 | 187 | 291 |
N.S. |
1 | 1.00 | 1.66 | 1.28 | 2.05 | 1.57 | 0.00 | 1.64 | 2.55 |
time (sec) |
N/A | 0.159 | 1.706 | 0.492 | 0.227 | 0.266 | 0.000 | 0.371 | 10.402 |
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 | 267 | 267 | 188 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.225 | 0.448 | 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 | 200 | 200 | 164 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.182 | 0.202 | 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 | 141 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.102 | 0.819 | 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 | 129 | 129 | 117 | 88 | 94 | 128 | 184 | 163 | 93 |
N.S. |
1 | 1.00 | 0.91 | 0.68 | 0.73 | 0.99 | 1.43 | 1.26 | 0.72 |
time (sec) |
N/A | 0.077 | 0.633 | 1.278 | 0.211 | 0.281 | 4.779 | 0.467 | 0.103 |
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 | 113 | 113 | 137 | 88 | 94 | 117 | 160 | 193 | 93 |
N.S. |
1 | 1.00 | 1.21 | 0.78 | 0.83 | 1.04 | 1.42 | 1.71 | 0.82 |
time (sec) |
N/A | 0.109 | 0.412 | 0.862 | 0.219 | 0.279 | 3.570 | 0.444 | 10.008 |
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 | 113 | 113 | 127 | 88 | 94 | 106 | 160 | 178 | 93 |
N.S. |
1 | 1.00 | 1.12 | 0.78 | 0.83 | 0.94 | 1.42 | 1.58 | 0.82 |
time (sec) |
N/A | 0.107 | 0.321 | 0.724 | 0.206 | 0.280 | 2.626 | 0.395 | 0.091 |
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 | 97 | 117 | 88 | 94 | 95 | 138 | 163 | 93 |
N.S. |
1 | 1.00 | 1.21 | 0.91 | 0.97 | 0.98 | 1.42 | 1.68 | 0.96 |
time (sec) |
N/A | 0.103 | 0.361 | 0.537 | 0.224 | 0.273 | 1.797 | 0.377 | 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 | 97 | 97 | 97 | 88 | 94 | 84 | 138 | 133 | 93 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.97 | 0.87 | 1.42 | 1.37 | 0.96 |
time (sec) |
N/A | 0.102 | 0.272 | 0.449 | 0.234 | 0.272 | 1.290 | 0.352 | 10.648 |
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 | 81 | 60 | 88 | 94 | 73 | 114 | 118 | 93 |
N.S. |
1 | 1.00 | 0.74 | 1.09 | 1.16 | 0.90 | 1.41 | 1.46 | 1.15 |
time (sec) |
N/A | 0.069 | 0.234 | 0.382 | 0.218 | 0.263 | 0.924 | 0.336 | 10.258 |
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 | 118 | 118 | 118 | 85 | 91 | 96 | 0 | 92 | 160 |
N.S. |
1 | 1.00 | 1.00 | 0.72 | 0.77 | 0.81 | 0.00 | 0.78 | 1.36 |
time (sec) |
N/A | 0.057 | 0.033 | 0.399 | 0.211 | 0.276 | 0.000 | 0.328 | 10.751 |
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 | 114 | 114 | 114 | 105 | 91 | 113 | 0 | 101 | 340 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.80 | 0.99 | 0.00 | 0.89 | 2.98 |
time (sec) |
N/A | 0.073 | 0.033 | 0.328 | 0.204 | 0.284 | 0.000 | 0.341 | 11.174 |
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 | 115 | 115 | 115 | 125 | 90 | 124 | 0 | 104 | 311 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 0.78 | 1.08 | 0.00 | 0.90 | 2.70 |
time (sec) |
N/A | 0.068 | 0.035 | 0.376 | 0.233 | 0.272 | 0.000 | 0.340 | 10.715 |
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 | 118 | 118 | 118 | 143 | 92 | 139 | 0 | 104 | 300 |
N.S. |
1 | 1.00 | 1.00 | 1.21 | 0.78 | 1.18 | 0.00 | 0.88 | 2.54 |
time (sec) |
N/A | 0.069 | 0.033 | 0.385 | 0.222 | 0.279 | 0.000 | 0.338 | 10.191 |
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 | 118 | 118 | 118 | 161 | 92 | 142 | 0 | 103 | 290 |
N.S. |
1 | 1.00 | 1.00 | 1.36 | 0.78 | 1.20 | 0.00 | 0.87 | 2.46 |
time (sec) |
N/A | 0.071 | 0.038 | 0.387 | 0.222 | 0.274 | 0.000 | 0.361 | 10.408 |
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 | 115 | 115 | 115 | 179 | 91 | 157 | 0 | 103 | 281 |
N.S. |
1 | 1.00 | 1.00 | 1.56 | 0.79 | 1.37 | 0.00 | 0.90 | 2.44 |
time (sec) |
N/A | 0.061 | 0.027 | 0.381 | 0.222 | 0.274 | 0.000 | 0.351 | 10.479 |
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 | 115 | 115 | 111 | 143 | 91 | 158 | 0 | 104 | 267 |
N.S. |
1 | 1.00 | 0.97 | 1.24 | 0.79 | 1.37 | 0.00 | 0.90 | 2.32 |
time (sec) |
N/A | 0.044 | 0.248 | 0.412 | 0.217 | 0.263 | 0.000 | 0.371 | 11.726 |
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 | 119 | 119 | 115 | 83 | 94 | 172 | 0 | 106 | 270 |
N.S. |
1 | 1.00 | 0.97 | 0.70 | 0.79 | 1.45 | 0.00 | 0.89 | 2.27 |
time (sec) |
N/A | 0.062 | 0.262 | 0.320 | 0.217 | 0.262 | 0.000 | 0.357 | 10.342 |
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 | 74 | 74 | 74 | 84 | 92 | 131 | 0 | 92 | 91 |
N.S. |
1 | 1.00 | 1.00 | 1.14 | 1.24 | 1.77 | 0.00 | 1.24 | 1.23 |
time (sec) |
N/A | 0.084 | 0.017 | 0.318 | 0.217 | 0.256 | 0.000 | 0.382 | 10.367 |
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 | 81 | 81 | 81 | 88 | 92 | 139 | 0 | 92 | 92 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 1.14 | 1.72 | 0.00 | 1.14 | 1.14 |
time (sec) |
N/A | 0.091 | 0.049 | 0.344 | 0.219 | 0.251 | 0.000 | 0.361 | 10.264 |
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 | 97 | 97 | 129 | 88 | 92 | 144 | 0 | 92 | 92 |
N.S. |
1 | 1.00 | 1.33 | 0.91 | 0.95 | 1.48 | 0.00 | 0.95 | 0.95 |
time (sec) |
N/A | 0.101 | 0.053 | 0.408 | 0.219 | 0.259 | 0.000 | 0.375 | 10.814 |
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 | 97 | 97 | 129 | 88 | 92 | 152 | 0 | 92 | 92 |
N.S. |
1 | 1.00 | 1.33 | 0.91 | 0.95 | 1.57 | 0.00 | 0.95 | 0.95 |
time (sec) |
N/A | 0.091 | 0.027 | 0.475 | 0.220 | 0.264 | 0.000 | 0.382 | 10.372 |
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 | 113 | 113 | 129 | 88 | 92 | 153 | 0 | 92 | 92 |
N.S. |
1 | 1.00 | 1.14 | 0.78 | 0.81 | 1.35 | 0.00 | 0.81 | 0.81 |
time (sec) |
N/A | 0.114 | 0.025 | 0.558 | 0.210 | 0.279 | 0.000 | 0.388 | 10.065 |
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 | 113 | 113 | 129 | 88 | 92 | 161 | 0 | 92 | 92 |
N.S. |
1 | 1.00 | 1.14 | 0.78 | 0.81 | 1.42 | 0.00 | 0.81 | 0.81 |
time (sec) |
N/A | 0.107 | 0.036 | 0.599 | 0.248 | 0.278 | 0.000 | 0.371 | 10.361 |
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 | 129 | 129 | 129 | 88 | 92 | 166 | 0 | 92 | 92 |
N.S. |
1 | 1.00 | 1.00 | 0.68 | 0.71 | 1.29 | 0.00 | 0.71 | 0.71 |
time (sec) |
N/A | 0.072 | 0.027 | 0.604 | 0.208 | 0.284 | 0.000 | 0.399 | 9.958 |
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 | 109 | 109 | 68 | 70 | 69 | 109 | 0 | 69 | 83 |
N.S. |
1 | 1.00 | 0.62 | 0.64 | 0.63 | 1.00 | 0.00 | 0.63 | 0.76 |
time (sec) |
N/A | 0.096 | 0.331 | 0.384 | 0.205 | 0.281 | 0.000 | 0.332 | 0.083 |
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 | 109 | 109 | 68 | 70 | 69 | 99 | 0 | 69 | 83 |
N.S. |
1 | 1.00 | 0.62 | 0.64 | 0.63 | 0.91 | 0.00 | 0.63 | 0.76 |
time (sec) |
N/A | 0.092 | 0.235 | 0.263 | 0.223 | 0.275 | 0.000 | 0.330 | 9.851 |
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 | 109 | 109 | 68 | 70 | 69 | 89 | 2093 | 69 | 83 |
N.S. |
1 | 1.00 | 0.62 | 0.64 | 0.63 | 0.82 | 19.20 | 0.63 | 0.76 |
time (sec) |
N/A | 0.095 | 0.124 | 0.269 | 0.198 | 0.276 | 119.043 | 0.323 | 10.158 |
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 | 91 | 91 | 68 | 70 | 69 | 79 | 1906 | 69 | 83 |
N.S. |
1 | 1.00 | 0.75 | 0.77 | 0.76 | 0.87 | 20.95 | 0.76 | 0.91 |
time (sec) |
N/A | 0.122 | 0.128 | 0.212 | 0.216 | 0.258 | 78.786 | 0.311 | 0.063 |
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 | 91 | 91 | 68 | 70 | 69 | 69 | 1719 | 69 | 83 |
N.S. |
1 | 1.00 | 0.75 | 0.77 | 0.76 | 0.76 | 18.89 | 0.76 | 0.91 |
time (sec) |
N/A | 0.128 | 0.099 | 0.175 | 0.219 | 0.261 | 50.937 | 0.308 | 10.645 |
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 | 73 | 73 | 68 | 70 | 69 | 59 | 1530 | 69 | 83 |
N.S. |
1 | 1.00 | 0.93 | 0.96 | 0.95 | 0.81 | 20.96 | 0.95 | 1.14 |
time (sec) |
N/A | 0.090 | 0.090 | 0.261 | 0.211 | 0.261 | 32.284 | 0.298 | 10.013 |
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 | 68 | 68 | 66 | 68 | 67 | 49 | 1096 | 67 | 80 |
N.S. |
1 | 1.00 | 0.97 | 1.00 | 0.99 | 0.72 | 16.12 | 0.99 | 1.18 |
time (sec) |
N/A | 0.049 | 0.129 | 0.244 | 0.253 | 0.268 | 19.926 | 0.284 | 10.313 |
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 | 99 | 99 | 68 | 64 | 71 | 70 | 0 | 88 | 140 |
N.S. |
1 | 1.00 | 0.69 | 0.65 | 0.72 | 0.71 | 0.00 | 0.89 | 1.41 |
time (sec) |
N/A | 0.079 | 0.050 | 0.354 | 0.216 | 0.265 | 0.000 | 0.291 | 10.281 |
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 | 95 | 95 | 66 | 63 | 74 | 85 | 0 | 95 | 272 |
N.S. |
1 | 1.00 | 0.69 | 0.66 | 0.78 | 0.89 | 0.00 | 1.00 | 2.86 |
time (sec) |
N/A | 0.100 | 0.091 | 0.340 | 0.219 | 0.282 | 0.000 | 0.316 | 10.718 |
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 | 97 | 97 | 66 | 64 | 74 | 91 | 0 | 94 | 231 |
N.S. |
1 | 1.00 | 0.68 | 0.66 | 0.76 | 0.94 | 0.00 | 0.97 | 2.38 |
time (sec) |
N/A | 0.098 | 0.082 | 0.372 | 0.229 | 0.279 | 0.000 | 0.336 | 10.550 |
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 | 97 | 97 | 66 | 67 | 73 | 107 | 0 | 87 | 221 |
N.S. |
1 | 1.00 | 0.68 | 0.69 | 0.75 | 1.10 | 0.00 | 0.90 | 2.28 |
time (sec) |
N/A | 0.084 | 0.094 | 0.366 | 0.222 | 0.274 | 0.000 | 0.402 | 10.911 |
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 | 94 | 94 | 66 | 62 | 72 | 104 | 0 | 83 | 214 |
N.S. |
1 | 1.00 | 0.70 | 0.66 | 0.77 | 1.11 | 0.00 | 0.88 | 2.28 |
time (sec) |
N/A | 0.083 | 0.201 | 0.362 | 0.205 | 0.271 | 0.000 | 0.413 | 11.184 |
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 | 100 | 100 | 68 | 68 | 70 | 118 | 0 | 82 | 204 |
N.S. |
1 | 1.00 | 0.68 | 0.68 | 0.70 | 1.18 | 0.00 | 0.82 | 2.04 |
time (sec) |
N/A | 0.074 | 0.074 | 0.321 | 0.248 | 0.270 | 0.000 | 0.415 | 10.229 |
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 | 68 | 68 | 61 | 67 | 66 | 96 | 0 | 66 | 63 |
N.S. |
1 | 1.00 | 0.90 | 0.99 | 0.97 | 1.41 | 0.00 | 0.97 | 0.93 |
time (sec) |
N/A | 0.069 | 0.080 | 0.319 | 0.205 | 0.260 | 0.000 | 0.529 | 10.032 |
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 | 73 | 73 | 68 | 70 | 66 | 104 | 0 | 66 | 66 |
N.S. |
1 | 1.00 | 0.93 | 0.96 | 0.90 | 1.42 | 0.00 | 0.90 | 0.90 |
time (sec) |
N/A | 0.104 | 0.107 | 0.260 | 0.233 | 0.256 | 0.000 | 0.451 | 10.064 |
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 | 91 | 91 | 68 | 70 | 66 | 107 | 0 | 66 | 66 |
N.S. |
1 | 1.00 | 0.75 | 0.77 | 0.73 | 1.18 | 0.00 | 0.73 | 0.73 |
time (sec) |
N/A | 0.124 | 0.098 | 0.289 | 0.235 | 0.247 | 0.000 | 0.482 | 9.891 |
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 | 91 | 91 | 68 | 70 | 66 | 115 | 0 | 66 | 65 |
N.S. |
1 | 1.00 | 0.75 | 0.77 | 0.73 | 1.26 | 0.00 | 0.73 | 0.71 |
time (sec) |
N/A | 0.127 | 0.110 | 0.359 | 0.235 | 0.252 | 0.000 | 0.543 | 10.099 |
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 | 109 | 109 | 68 | 70 | 66 | 120 | 0 | 66 | 66 |
N.S. |
1 | 1.00 | 0.62 | 0.64 | 0.61 | 1.10 | 0.00 | 0.61 | 0.61 |
time (sec) |
N/A | 0.094 | 0.079 | 0.309 | 0.210 | 0.262 | 0.000 | 0.432 | 10.355 |
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 | 109 | 109 | 68 | 70 | 66 | 128 | 0 | 66 | 65 |
N.S. |
1 | 1.00 | 0.62 | 0.64 | 0.61 | 1.17 | 0.00 | 0.61 | 0.60 |
time (sec) |
N/A | 0.090 | 0.083 | 0.418 | 0.222 | 0.267 | 0.000 | 0.371 | 10.229 |
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 | 109 | 109 | 68 | 70 | 66 | 131 | 0 | 66 | 65 |
N.S. |
1 | 1.00 | 0.62 | 0.64 | 0.61 | 1.20 | 0.00 | 0.61 | 0.60 |
time (sec) |
N/A | 0.099 | 0.079 | 0.536 | 0.211 | 0.266 | 0.000 | 0.481 | 9.962 |
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 | 184 | 184 | 126 | 415 | 165 | 697 | 41196 | 1360 | 1130 |
N.S. |
1 | 1.00 | 0.68 | 2.26 | 0.90 | 3.79 | 223.89 | 7.39 | 6.14 |
time (sec) |
N/A | 0.140 | 0.635 | 28.819 | 0.210 | 0.341 | 83.341 | 0.570 | 17.986 |
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 | 184 | 184 | 126 | 379 | 165 | 628 | 29818 | 1019 | 1142 |
N.S. |
1 | 1.00 | 0.68 | 2.06 | 0.90 | 3.41 | 162.05 | 5.54 | 6.21 |
time (sec) |
N/A | 0.138 | 0.532 | 16.280 | 0.203 | 0.315 | 48.248 | 0.422 | 19.259 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 167 | 167 | 154 | 230 | 148 | 445 | 19968 | 674 | 901 |
N.S. |
1 | 1.00 | 0.92 | 1.38 | 0.89 | 2.66 | 119.57 | 4.04 | 5.40 |
time (sec) |
N/A | 0.107 | 1.288 | 9.142 | 0.211 | 0.320 | 27.648 | 0.361 | 17.201 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 137 | 95 | 184 | 241 | 243 | 0 | 0 | 568 |
N.S. |
1 | 1.00 | 0.69 | 1.34 | 1.76 | 1.77 | 0.00 | 0.00 | 4.15 |
time (sec) |
N/A | 0.124 | 0.211 | 3.558 | 0.239 | 0.282 | 0.000 | 0.000 | 15.315 |