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 | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 106 | 106 | 95 | 99 | 106 | 106 | 124 | 114 | 98 |
N.S. |
1 | 1.00 | 0.90 | 0.93 | 1.00 | 1.00 | 1.17 | 1.08 | 0.92 |
time (sec) |
N/A | 0.306 | 0.029 | 0.247 | 0.191 | 0.239 | 0.026 | 0.252 | 10.602 |
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 | 45 | 45 | 60 | 51 | 50 | 50 | 58 | 50 | 50 |
N.S. |
1 | 1.00 | 1.33 | 1.13 | 1.11 | 1.11 | 1.29 | 1.11 | 1.11 |
time (sec) |
N/A | 0.184 | 0.002 | 0.221 | 0.205 | 0.245 | 0.022 | 0.259 | 0.025 |
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 | 169 | 169 | 174 | 224 | 242 | 243 | 207 | 258 | 260 |
N.S. |
1 | 1.00 | 1.03 | 1.33 | 1.43 | 1.44 | 1.22 | 1.53 | 1.54 |
time (sec) |
N/A | 0.405 | 0.064 | 0.254 | 0.203 | 0.253 | 0.298 | 0.264 | 0.067 |
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 | 180 | 180 | 175 | 233 | 249 | 354 | 246 | 328 | 311 |
N.S. |
1 | 1.00 | 0.97 | 1.29 | 1.38 | 1.97 | 1.37 | 1.82 | 1.73 |
time (sec) |
N/A | 0.414 | 0.100 | 0.247 | 0.214 | 0.272 | 0.560 | 0.278 | 0.089 |
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 | 185 | 185 | 174 | 233 | 258 | 394 | 282 | 251 | 275 |
N.S. |
1 | 1.00 | 0.94 | 1.26 | 1.39 | 2.13 | 1.52 | 1.36 | 1.49 |
time (sec) |
N/A | 0.414 | 0.102 | 0.250 | 0.200 | 0.256 | 1.353 | 0.270 | 10.496 |
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 | 189 | 189 | 232 | 233 | 270 | 411 | 294 | 251 | 268 |
N.S. |
1 | 1.00 | 1.23 | 1.23 | 1.43 | 2.17 | 1.56 | 1.33 | 1.42 |
time (sec) |
N/A | 0.425 | 0.073 | 0.255 | 0.207 | 0.271 | 4.166 | 0.267 | 10.411 |
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 | 189 | 189 | 221 | 240 | 279 | 405 | 304 | 373 | 277 |
N.S. |
1 | 1.00 | 1.17 | 1.27 | 1.48 | 2.14 | 1.61 | 1.97 | 1.47 |
time (sec) |
N/A | 0.394 | 0.071 | 0.254 | 0.211 | 0.289 | 59.710 | 0.275 | 10.491 |
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 | 197 | 197 | 212 | 234 | 298 | 365 | 0 | 252 | 243 |
N.S. |
1 | 1.00 | 1.08 | 1.19 | 1.51 | 1.85 | 0.00 | 1.28 | 1.23 |
time (sec) |
N/A | 0.398 | 0.071 | 0.274 | 0.220 | 0.269 | 0.000 | 0.272 | 10.597 |
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 | 204 | 204 | 198 | 219 | 292 | 292 | 0 | 254 | 273 |
N.S. |
1 | 1.00 | 0.97 | 1.07 | 1.43 | 1.43 | 0.00 | 1.25 | 1.34 |
time (sec) |
N/A | 0.383 | 0.060 | 0.250 | 0.227 | 0.272 | 0.000 | 0.260 | 0.112 |
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 | 206 | 206 | 202 | 233 | 317 | 317 | 0 | 258 | 299 |
N.S. |
1 | 1.00 | 0.98 | 1.13 | 1.54 | 1.54 | 0.00 | 1.25 | 1.45 |
time (sec) |
N/A | 0.394 | 0.063 | 0.253 | 0.206 | 0.274 | 0.000 | 0.262 | 10.627 |
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 | 206 | 206 | 202 | 233 | 328 | 328 | 0 | 258 | 310 |
N.S. |
1 | 1.00 | 0.98 | 1.13 | 1.59 | 1.59 | 0.00 | 1.25 | 1.50 |
time (sec) |
N/A | 0.380 | 0.062 | 0.260 | 0.212 | 0.265 | 0.000 | 0.273 | 0.118 |
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 | 206 | 206 | 202 | 233 | 339 | 339 | 0 | 258 | 321 |
N.S. |
1 | 1.00 | 0.98 | 1.13 | 1.65 | 1.65 | 0.00 | 1.25 | 1.56 |
time (sec) |
N/A | 0.385 | 0.071 | 0.247 | 0.211 | 0.293 | 0.000 | 0.266 | 10.629 |
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 | 334 | 334 | 542 | 557 | 584 | 584 | 694 | 658 | 542 |
N.S. |
1 | 1.00 | 1.62 | 1.67 | 1.75 | 1.75 | 2.08 | 1.97 | 1.62 |
time (sec) |
N/A | 0.841 | 0.133 | 0.265 | 0.215 | 0.287 | 0.057 | 0.263 | 10.778 |
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 | 334 | 334 | 436 | 455 | 478 | 478 | 564 | 536 | 438 |
N.S. |
1 | 1.00 | 1.31 | 1.36 | 1.43 | 1.43 | 1.69 | 1.60 | 1.31 |
time (sec) |
N/A | 0.731 | 0.083 | 0.253 | 0.202 | 0.262 | 0.048 | 0.266 | 0.217 |
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 | 334 | 334 | 323 | 353 | 363 | 363 | 435 | 411 | 317 |
N.S. |
1 | 1.00 | 0.97 | 1.06 | 1.09 | 1.09 | 1.30 | 1.23 | 0.95 |
time (sec) |
N/A | 0.647 | 0.063 | 0.256 | 0.222 | 0.260 | 0.043 | 0.267 | 0.176 |
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 | 334 | 334 | 238 | 251 | 262 | 262 | 306 | 287 | 227 |
N.S. |
1 | 1.00 | 0.71 | 0.75 | 0.78 | 0.78 | 0.92 | 0.86 | 0.68 |
time (sec) |
N/A | 0.607 | 0.040 | 0.262 | 0.196 | 0.256 | 0.039 | 0.265 | 10.626 |
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 | 148 | 148 | 135 | 143 | 154 | 154 | 182 | 165 | 140 |
N.S. |
1 | 1.00 | 0.91 | 0.97 | 1.04 | 1.04 | 1.23 | 1.11 | 0.95 |
time (sec) |
N/A | 0.404 | 0.034 | 0.240 | 0.192 | 0.243 | 0.032 | 0.277 | 0.068 |
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 | 56 | 55 | 85 | 74 | 73 | 73 | 85 | 73 | 73 |
N.S. |
1 | 0.98 | 1.52 | 1.32 | 1.30 | 1.30 | 1.52 | 1.30 | 1.30 |
time (sec) |
N/A | 0.197 | 0.002 | 0.220 | 0.190 | 0.234 | 0.026 | 0.262 | 0.032 |
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 | 290 | 290 | 311 | 414 | 447 | 448 | 410 | 488 | 494 |
N.S. |
1 | 1.00 | 1.07 | 1.43 | 1.54 | 1.54 | 1.41 | 1.68 | 1.70 |
time (sec) |
N/A | 0.619 | 0.110 | 0.254 | 0.200 | 0.249 | 0.476 | 0.271 | 0.079 |
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 | 309 | 309 | 405 | 433 | 456 | 621 | 454 | 563 | 826 |
N.S. |
1 | 1.00 | 1.31 | 1.40 | 1.48 | 2.01 | 1.47 | 1.82 | 2.67 |
time (sec) |
N/A | 0.655 | 0.117 | 0.240 | 0.197 | 0.257 | 0.938 | 0.306 | 10.606 |
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 | 300 | 300 | 414 | 425 | 464 | 691 | 490 | 469 | 681 |
N.S. |
1 | 1.00 | 1.38 | 1.42 | 1.55 | 2.30 | 1.63 | 1.56 | 2.27 |
time (sec) |
N/A | 0.620 | 0.132 | 0.256 | 0.197 | 0.282 | 2.468 | 0.264 | 0.147 |
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 | 310 | 310 | 294 | 431 | 478 | 732 | 530 | 464 | 548 |
N.S. |
1 | 1.00 | 0.95 | 1.39 | 1.54 | 2.36 | 1.71 | 1.50 | 1.77 |
time (sec) |
N/A | 0.643 | 0.085 | 0.262 | 0.204 | 0.276 | 47.395 | 0.263 | 10.672 |
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 | 314 | 314 | 405 | 432 | 487 | 746 | 0 | 653 | 501 |
N.S. |
1 | 1.00 | 1.29 | 1.38 | 1.55 | 2.38 | 0.00 | 2.08 | 1.60 |
time (sec) |
N/A | 0.627 | 0.134 | 0.256 | 0.206 | 0.271 | 0.000 | 0.271 | 10.727 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 313 | 313 | 388 | 433 | 499 | 730 | 0 | 458 | 494 |
N.S. |
1 | 1.00 | 1.24 | 1.38 | 1.59 | 2.33 | 0.00 | 1.46 | 1.58 |
time (sec) |
N/A | 0.606 | 0.129 | 0.292 | 0.212 | 0.272 | 0.000 | 0.269 | 0.164 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 320 | 320 | 377 | 435 | 511 | 695 | 0 | 454 | 505 |
N.S. |
1 | 1.00 | 1.18 | 1.36 | 1.60 | 2.17 | 0.00 | 1.42 | 1.58 |
time (sec) |
N/A | 0.593 | 0.133 | 0.269 | 0.211 | 0.263 | 0.000 | 0.260 | 10.765 |
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 | 327 | 327 | 366 | 426 | 527 | 624 | 0 | 459 | 448 |
N.S. |
1 | 1.00 | 1.12 | 1.30 | 1.61 | 1.91 | 0.00 | 1.40 | 1.37 |
time (sec) |
N/A | 0.588 | 0.130 | 0.283 | 0.225 | 0.277 | 0.000 | 0.264 | 10.792 |
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 | 330 | 330 | 357 | 422 | 532 | 532 | 0 | 488 | 570 |
N.S. |
1 | 1.00 | 1.08 | 1.28 | 1.61 | 1.61 | 0.00 | 1.48 | 1.73 |
time (sec) |
N/A | 0.576 | 0.118 | 0.263 | 0.221 | 0.276 | 0.000 | 0.260 | 0.157 |
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 | 334 | 359 | 425 | 546 | 546 | 0 | 488 | 513 |
N.S. |
1 | 1.00 | 1.07 | 1.27 | 1.63 | 1.63 | 0.00 | 1.46 | 1.54 |
time (sec) |
N/A | 0.570 | 0.113 | 0.254 | 0.225 | 0.263 | 0.000 | 0.266 | 10.702 |
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 | 334 | 357 | 425 | 557 | 557 | 0 | 488 | 524 |
N.S. |
1 | 1.00 | 1.07 | 1.27 | 1.67 | 1.67 | 0.00 | 1.46 | 1.57 |
time (sec) |
N/A | 0.585 | 0.129 | 0.267 | 0.223 | 0.262 | 0.000 | 0.272 | 10.852 |
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 | 240 | 240 | 217 | 232 | 230 | 550 | 908 | 257 | 249 |
N.S. |
1 | 1.00 | 0.90 | 0.97 | 0.96 | 2.29 | 3.78 | 1.07 | 1.04 |
time (sec) |
N/A | 0.448 | 0.159 | 0.399 | 0.280 | 0.276 | 2.863 | 0.265 | 0.243 |
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 | 167 | 167 | 151 | 164 | 160 | 398 | 641 | 171 | 175 |
N.S. |
1 | 1.00 | 0.90 | 0.98 | 0.96 | 2.38 | 3.84 | 1.02 | 1.05 |
time (sec) |
N/A | 0.340 | 0.101 | 0.365 | 0.281 | 0.261 | 1.030 | 0.258 | 10.811 |
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 | 108 | 108 | 99 | 97 | 100 | 235 | 425 | 102 | 114 |
N.S. |
1 | 1.00 | 0.92 | 0.90 | 0.93 | 2.18 | 3.94 | 0.94 | 1.06 |
time (sec) |
N/A | 0.264 | 0.061 | 0.347 | 0.277 | 0.276 | 0.731 | 0.260 | 0.144 |
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 | 64 | 64 | 65 | 61 | 56 | 147 | 212 | 56 | 75 |
N.S. |
1 | 1.00 | 1.02 | 0.95 | 0.88 | 2.30 | 3.31 | 0.88 | 1.17 |
time (sec) |
N/A | 0.217 | 0.036 | 0.292 | 0.273 | 0.254 | 0.383 | 0.265 | 10.739 |
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 | 42 | 42 | 42 | 32 | 31 | 98 | 124 | 31 | 32 |
N.S. |
1 | 1.00 | 1.00 | 0.76 | 0.74 | 2.33 | 2.95 | 0.74 | 0.76 |
time (sec) |
N/A | 0.162 | 0.012 | 0.267 | 0.288 | 0.255 | 0.125 | 0.270 | 0.050 |
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 | 91 | 92 | 98 | 200 | 0 | 103 | 535 |
N.S. |
1 | 1.00 | 0.83 | 0.84 | 0.90 | 1.83 | 0.00 | 0.94 | 4.91 |
time (sec) |
N/A | 0.273 | 0.041 | 0.362 | 0.283 | 0.796 | 0.000 | 0.271 | 12.241 |
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 | 148 | 157 | 216 | 562 | 0 | 237 | 810 |
N.S. |
1 | 1.00 | 0.86 | 0.91 | 1.25 | 3.25 | 0.00 | 1.37 | 4.68 |
time (sec) |
N/A | 0.367 | 0.118 | 0.322 | 0.286 | 4.156 | 0.000 | 0.265 | 12.463 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 251 | 251 | 223 | 243 | 419 | 1350 | 0 | 399 | 1680 |
N.S. |
1 | 1.00 | 0.89 | 0.97 | 1.67 | 5.38 | 0.00 | 1.59 | 6.69 |
time (sec) |
N/A | 0.507 | 0.226 | 0.461 | 0.295 | 25.745 | 0.000 | 0.265 | 12.844 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 297 | 296 | 307 | 360 | 356 | 1190 | 1091 | 366 | 370 |
N.S. |
1 | 1.00 | 1.03 | 1.21 | 1.20 | 4.01 | 3.67 | 1.23 | 1.25 |
time (sec) |
N/A | 0.530 | 0.109 | 0.398 | 0.278 | 0.454 | 14.417 | 0.268 | 0.324 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 220 | 220 | 231 | 263 | 268 | 849 | 836 | 273 | 276 |
N.S. |
1 | 1.00 | 1.05 | 1.20 | 1.22 | 3.86 | 3.80 | 1.24 | 1.25 |
time (sec) |
N/A | 0.434 | 0.137 | 0.387 | 0.282 | 0.347 | 7.783 | 0.260 | 10.793 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 161 | 161 | 171 | 188 | 188 | 609 | 583 | 185 | 193 |
N.S. |
1 | 1.00 | 1.06 | 1.17 | 1.17 | 3.78 | 3.62 | 1.15 | 1.20 |
time (sec) |
N/A | 0.361 | 0.079 | 0.364 | 0.293 | 0.342 | 2.422 | 0.255 | 0.194 |
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 | 112 | 118 | 119 | 127 | 130 | 384 | 382 | 128 | 203 |
N.S. |
1 | 1.05 | 1.06 | 1.13 | 1.16 | 3.43 | 3.41 | 1.14 | 1.81 |
time (sec) |
N/A | 0.244 | 0.068 | 0.363 | 0.281 | 0.294 | 1.292 | 0.269 | 10.731 |
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 | 79 | 90 | 78 | 75 | 72 | 225 | 133 | 71 | 70 |
N.S. |
1 | 1.14 | 0.99 | 0.95 | 0.91 | 2.85 | 1.68 | 0.90 | 0.89 |
time (sec) |
N/A | 0.195 | 0.047 | 0.277 | 0.277 | 0.321 | 0.477 | 0.255 | 10.671 |
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 | 57 | 57 | 57 | 49 | 48 | 140 | 90 | 47 | 44 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.84 | 2.46 | 1.58 | 0.82 | 0.77 |
time (sec) |
N/A | 0.169 | 0.020 | 0.275 | 0.277 | 0.275 | 0.149 | 0.253 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 195 | 213 | 158 | 215 | 243 | 795 | 0 | 280 | 1086 |
N.S. |
1 | 1.09 | 0.81 | 1.10 | 1.25 | 4.08 | 0.00 | 1.44 | 5.57 |
time (sec) |
N/A | 0.465 | 0.111 | 0.458 | 0.279 | 9.803 | 0.000 | 0.264 | 12.921 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 290 | 302 | 251 | 304 | 511 | 1940 | 0 | 518 | 2029 |
N.S. |
1 | 1.04 | 0.87 | 1.05 | 1.76 | 6.69 | 0.00 | 1.79 | 7.00 |
time (sec) |
N/A | 0.581 | 0.227 | 0.364 | 0.295 | 47.971 | 0.000 | 0.262 | 13.215 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 304 | 318 | 341 | 404 | 438 | 1403 | 0 | 422 | 424 |
N.S. |
1 | 1.05 | 1.12 | 1.33 | 1.44 | 4.62 | 0.00 | 1.39 | 1.39 |
time (sec) |
N/A | 0.610 | 0.160 | 0.395 | 0.290 | 0.524 | 0.000 | 0.255 | 0.299 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 216 | 236 | 263 | 309 | 352 | 1055 | 0 | 324 | 763 |
N.S. |
1 | 1.09 | 1.22 | 1.43 | 1.63 | 4.88 | 0.00 | 1.50 | 3.53 |
time (sec) |
N/A | 0.387 | 0.134 | 0.380 | 0.326 | 0.444 | 0.000 | 0.271 | 11.657 |
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 | 125 | 127 | 186 | 215 | 248 | 752 | 468 | 239 | 265 |
N.S. |
1 | 1.02 | 1.49 | 1.72 | 1.98 | 6.02 | 3.74 | 1.91 | 2.12 |
time (sec) |
N/A | 0.233 | 0.066 | 0.306 | 0.271 | 0.402 | 35.599 | 0.277 | 0.233 |
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 | 142 | 157 | 158 | 148 | 184 | 537 | 274 | 170 | 154 |
N.S. |
1 | 1.11 | 1.11 | 1.04 | 1.30 | 3.78 | 1.93 | 1.20 | 1.08 |
time (sec) |
N/A | 0.297 | 0.070 | 0.302 | 0.286 | 0.774 | 3.039 | 0.263 | 10.875 |
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 | 110 | 119 | 101 | 95 | 114 | 355 | 180 | 98 | 100 |
N.S. |
1 | 1.08 | 0.92 | 0.86 | 1.04 | 3.23 | 1.64 | 0.89 | 0.91 |
time (sec) |
N/A | 0.217 | 0.065 | 0.288 | 0.279 | 0.329 | 0.819 | 0.266 | 10.817 |
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 | 75 | 82 | 71 | 70 | 74 | 212 | 124 | 60 | 64 |
N.S. |
1 | 1.09 | 0.95 | 0.93 | 0.99 | 2.83 | 1.65 | 0.80 | 0.85 |
time (sec) |
N/A | 0.183 | 0.035 | 0.271 | 0.303 | 0.333 | 0.234 | 0.267 | 10.772 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 307 | 350 | 263 | 435 | 525 | 1797 | 0 | 562 | 2415 |
N.S. |
1 | 1.14 | 0.86 | 1.42 | 1.71 | 5.85 | 0.00 | 1.83 | 7.87 |
time (sec) |
N/A | 0.706 | 0.189 | 0.523 | 0.304 | 92.995 | 0.000 | 0.259 | 13.663 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 443 | 480 | 378 | 567 | 997 | 4009 | 0 | 884 | 3015 |
N.S. |
1 | 1.08 | 0.85 | 1.28 | 2.25 | 9.05 | 0.00 | 2.00 | 6.81 |
time (sec) |
N/A | 0.930 | 0.332 | 0.604 | 0.324 | 233.395 | 0.000 | 0.280 | 14.604 |
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 | 29 | 29 | 31 | 20 | 21 | 21 | 26 | 24 | 19 |
N.S. |
1 | 1.00 | 1.07 | 0.69 | 0.72 | 0.72 | 0.90 | 0.83 | 0.66 |
time (sec) |
N/A | 0.178 | 0.013 | 0.256 | 0.201 | 0.274 | 0.062 | 0.261 | 0.066 |
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 | 39 | 44 | 28 | 29 | 32 | 40 | 27 | 27 | 29 |
N.S. |
1 | 1.13 | 0.72 | 0.74 | 0.82 | 1.03 | 0.69 | 0.69 | 0.74 |
time (sec) |
N/A | 0.174 | 0.015 | 0.286 | 0.278 | 0.255 | 0.067 | 0.249 | 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 | 122 | 141 | 76 | 55 | 90 | 70 | 131 | 64 | 55 |
N.S. |
1 | 1.16 | 0.62 | 0.45 | 0.74 | 0.57 | 1.07 | 0.52 | 0.45 |
time (sec) |
N/A | 0.267 | 0.218 | 0.331 | 0.293 | 0.324 | 0.461 | 0.270 | 10.227 |
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 | 100 | 123 | 71 | 50 | 76 | 65 | 63 | 57 | 50 |
N.S. |
1 | 1.23 | 0.71 | 0.50 | 0.76 | 0.65 | 0.63 | 0.57 | 0.50 |
time (sec) |
N/A | 0.240 | 0.157 | 0.277 | 0.290 | 0.368 | 1.007 | 0.272 | 10.245 |
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 | 78 | 92 | 66 | 45 | 62 | 60 | 95 | 54 | 45 |
N.S. |
1 | 1.18 | 0.85 | 0.58 | 0.79 | 0.77 | 1.22 | 0.69 | 0.58 |
time (sec) |
N/A | 0.206 | 0.123 | 0.275 | 0.286 | 0.282 | 0.203 | 0.259 | 10.526 |
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 | 56 | 69 | 61 | 40 | 48 | 55 | 48 | 48 | 40 |
N.S. |
1 | 1.23 | 1.09 | 0.71 | 0.86 | 0.98 | 0.86 | 0.86 | 0.71 |
time (sec) |
N/A | 0.178 | 0.104 | 0.277 | 0.282 | 0.271 | 0.647 | 0.270 | 0.034 |
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 | 51 | 54 | 35 | 36 | 50 | 61 | 44 | 33 |
N.S. |
1 | 1.04 | 1.10 | 0.71 | 0.73 | 1.02 | 1.24 | 0.90 | 0.67 |
time (sec) |
N/A | 0.159 | 0.067 | 0.256 | 0.287 | 0.327 | 0.093 | 0.262 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 77 | 92 | 58 | 70 | 90 | 0 | 104 | 66 |
N.S. |
1 | 1.07 | 1.28 | 0.81 | 0.97 | 1.25 | 0.00 | 1.44 | 0.92 |
time (sec) |
N/A | 0.206 | 0.311 | 0.292 | 0.276 | 0.295 | 0.000 | 0.288 | 0.188 |
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 | 73 | 73 | 95 | 77 | 76 | 109 | 0 | 285 | 80 |
N.S. |
1 | 1.00 | 1.30 | 1.05 | 1.04 | 1.49 | 0.00 | 3.90 | 1.10 |
time (sec) |
N/A | 0.214 | 0.337 | 0.279 | 0.279 | 0.394 | 0.000 | 0.394 | 0.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 79 | 84 | 103 | 77 | 99 | 126 | 0 | 205 | 92 |
N.S. |
1 | 1.06 | 1.30 | 0.97 | 1.25 | 1.59 | 0.00 | 2.59 | 1.16 |
time (sec) |
N/A | 0.208 | 0.469 | 0.303 | 0.274 | 0.389 | 0.000 | 0.300 | 0.117 |
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 | 82 | 87 | 78 | 70 | 115 | 104 | 0 | 232 | 106 |
N.S. |
1 | 1.06 | 0.95 | 0.85 | 1.40 | 1.27 | 0.00 | 2.83 | 1.29 |
time (sec) |
N/A | 0.204 | 0.571 | 0.708 | 0.282 | 0.431 | 0.000 | 0.293 | 10.538 |
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 | 104 | 114 | 83 | 75 | 148 | 119 | 0 | 181 | 140 |
N.S. |
1 | 1.10 | 0.80 | 0.72 | 1.42 | 1.14 | 0.00 | 1.74 | 1.35 |
time (sec) |
N/A | 0.234 | 0.696 | 0.734 | 0.285 | 0.397 | 0.000 | 0.299 | 0.122 |
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 | 126 | 141 | 88 | 80 | 186 | 134 | 0 | 322 | 178 |
N.S. |
1 | 1.12 | 0.70 | 0.63 | 1.48 | 1.06 | 0.00 | 2.56 | 1.41 |
time (sec) |
N/A | 0.265 | 0.906 | 0.740 | 0.278 | 0.593 | 0.000 | 0.294 | 10.578 |
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 | 148 | 168 | 93 | 85 | 229 | 149 | 0 | 367 | 223 |
N.S. |
1 | 1.14 | 0.63 | 0.57 | 1.55 | 1.01 | 0.00 | 2.48 | 1.51 |
time (sec) |
N/A | 0.292 | 1.123 | 0.330 | 0.288 | 0.384 | 0.000 | 0.301 | 0.130 |
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 | 138 | 167 | 86 | 65 | 102 | 80 | 162 | 72 | 65 |
N.S. |
1 | 1.21 | 0.62 | 0.47 | 0.74 | 0.58 | 1.17 | 0.52 | 0.47 |
time (sec) |
N/A | 0.276 | 0.259 | 0.319 | 0.276 | 0.270 | 2.058 | 0.269 | 10.498 |
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 | 116 | 144 | 81 | 60 | 88 | 75 | 144 | 66 | 60 |
N.S. |
1 | 1.24 | 0.70 | 0.52 | 0.76 | 0.65 | 1.24 | 0.57 | 0.52 |
time (sec) |
N/A | 0.252 | 0.206 | 0.277 | 0.272 | 0.305 | 1.404 | 0.271 | 10.538 |
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 | 94 | 117 | 76 | 55 | 74 | 70 | 129 | 62 | 55 |
N.S. |
1 | 1.24 | 0.81 | 0.59 | 0.79 | 0.74 | 1.37 | 0.66 | 0.59 |
time (sec) |
N/A | 0.218 | 0.176 | 0.276 | 0.282 | 0.320 | 0.883 | 0.268 | 10.596 |
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 | 72 | 90 | 71 | 50 | 60 | 65 | 110 | 56 | 50 |
N.S. |
1 | 1.25 | 0.99 | 0.69 | 0.83 | 0.90 | 1.53 | 0.78 | 0.69 |
time (sec) |
N/A | 0.191 | 0.144 | 0.267 | 0.275 | 0.295 | 0.621 | 0.282 | 10.582 |
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 | 67 | 72 | 66 | 45 | 48 | 60 | 97 | 53 | 45 |
N.S. |
1 | 1.07 | 0.99 | 0.67 | 0.72 | 0.90 | 1.45 | 0.79 | 0.67 |
time (sec) |
N/A | 0.170 | 0.103 | 0.242 | 0.274 | 0.292 | 0.393 | 0.274 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 102 | 104 | 70 | 93 | 102 | 0 | 116 | 76 |
N.S. |
1 | 1.11 | 1.13 | 0.76 | 1.01 | 1.11 | 0.00 | 1.26 | 0.83 |
time (sec) |
N/A | 0.233 | 0.257 | 0.290 | 0.281 | 0.295 | 0.000 | 0.301 | 0.129 |
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 | 97 | 107 | 111 | 87 | 99 | 121 | 0 | 475 | 108 |
N.S. |
1 | 1.10 | 1.14 | 0.90 | 1.02 | 1.25 | 0.00 | 4.90 | 1.11 |
time (sec) |
N/A | 0.238 | 0.427 | 0.293 | 0.284 | 0.279 | 0.000 | 0.447 | 0.120 |
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 | 104 | 114 | 113 | 87 | 122 | 136 | 0 | 219 | 117 |
N.S. |
1 | 1.10 | 1.09 | 0.84 | 1.17 | 1.31 | 0.00 | 2.11 | 1.12 |
time (sec) |
N/A | 0.252 | 0.585 | 0.290 | 0.275 | 0.316 | 0.000 | 0.294 | 10.731 |
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 | 106 | 116 | 113 | 87 | 150 | 151 | 0 | 265 | 133 |
N.S. |
1 | 1.09 | 1.07 | 0.82 | 1.42 | 1.42 | 0.00 | 2.50 | 1.25 |
time (sec) |
N/A | 0.257 | 0.798 | 0.299 | 0.304 | 0.304 | 0.000 | 0.295 | 0.124 |
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 | 106 | 116 | 113 | 87 | 183 | 166 | 0 | 245 | 155 |
N.S. |
1 | 1.09 | 1.07 | 0.82 | 1.73 | 1.57 | 0.00 | 2.31 | 1.46 |
time (sec) |
N/A | 0.256 | 1.022 | 0.758 | 0.280 | 0.290 | 0.000 | 0.408 | 0.124 |
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 | 109 | 119 | 88 | 80 | 209 | 134 | 0 | 318 | 179 |
N.S. |
1 | 1.09 | 0.81 | 0.73 | 1.92 | 1.23 | 0.00 | 2.92 | 1.64 |
time (sec) |
N/A | 0.233 | 1.316 | 0.309 | 0.295 | 0.261 | 0.000 | 0.300 | 10.704 |
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 | 131 | 146 | 93 | 85 | 252 | 149 | 0 | 367 | 223 |
N.S. |
1 | 1.11 | 0.71 | 0.65 | 1.92 | 1.14 | 0.00 | 2.80 | 1.70 |
time (sec) |
N/A | 0.259 | 1.485 | 0.323 | 0.285 | 0.273 | 0.000 | 0.301 | 10.684 |
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 | 153 | 173 | 98 | 90 | 300 | 164 | 0 | 408 | 272 |
N.S. |
1 | 1.13 | 0.64 | 0.59 | 1.96 | 1.07 | 0.00 | 2.67 | 1.78 |
time (sec) |
N/A | 0.298 | 1.695 | 0.325 | 0.283 | 0.298 | 0.000 | 0.298 | 0.140 |
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 | 154 | 188 | 96 | 75 | 114 | 90 | 199 | 82 | 75 |
N.S. |
1 | 1.22 | 0.62 | 0.49 | 0.74 | 0.58 | 1.29 | 0.53 | 0.49 |
time (sec) |
N/A | 0.291 | 0.387 | 0.317 | 0.311 | 0.327 | 8.230 | 0.284 | 10.603 |
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 | 132 | 165 | 91 | 70 | 100 | 85 | 180 | 76 | 70 |
N.S. |
1 | 1.25 | 0.69 | 0.53 | 0.76 | 0.64 | 1.36 | 0.58 | 0.53 |
time (sec) |
N/A | 0.259 | 0.298 | 0.295 | 0.273 | 0.302 | 5.840 | 0.297 | 10.572 |
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 | 110 | 134 | 86 | 65 | 86 | 80 | 162 | 72 | 65 |
N.S. |
1 | 1.22 | 0.78 | 0.59 | 0.78 | 0.73 | 1.47 | 0.65 | 0.59 |
time (sec) |
N/A | 0.235 | 0.250 | 0.286 | 0.274 | 0.286 | 4.162 | 0.264 | 10.603 |
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 | 88 | 111 | 81 | 60 | 72 | 75 | 143 | 63 | 60 |
N.S. |
1 | 1.26 | 0.92 | 0.68 | 0.82 | 0.85 | 1.62 | 0.72 | 0.68 |
time (sec) |
N/A | 0.202 | 0.218 | 0.293 | 0.274 | 0.276 | 2.872 | 0.267 | 10.579 |
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 | 83 | 93 | 76 | 55 | 60 | 70 | 131 | 61 | 55 |
N.S. |
1 | 1.12 | 0.92 | 0.66 | 0.72 | 0.84 | 1.58 | 0.73 | 0.66 |
time (sec) |
N/A | 0.182 | 0.164 | 0.269 | 0.297 | 0.273 | 1.982 | 0.269 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 127 | 114 | 80 | 116 | 112 | 0 | 125 | 86 |
N.S. |
1 | 1.13 | 1.02 | 0.71 | 1.04 | 1.00 | 0.00 | 1.12 | 0.77 |
time (sec) |
N/A | 0.264 | 0.393 | 0.289 | 0.275 | 0.346 | 0.000 | 0.299 | 10.675 |
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 | 117 | 127 | 121 | 97 | 122 | 131 | 0 | 665 | 138 |
N.S. |
1 | 1.09 | 1.03 | 0.83 | 1.04 | 1.12 | 0.00 | 5.68 | 1.18 |
time (sec) |
N/A | 0.268 | 0.553 | 0.326 | 0.302 | 0.326 | 0.000 | 0.497 | 0.139 |
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 | 126 | 141 | 121 | 97 | 145 | 146 | 0 | 230 | 147 |
N.S. |
1 | 1.12 | 0.96 | 0.77 | 1.15 | 1.16 | 0.00 | 1.83 | 1.17 |
time (sec) |
N/A | 0.274 | 0.643 | 0.303 | 0.279 | 0.306 | 0.000 | 0.305 | 0.129 |
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 | 133 | 146 | 128 | 97 | 173 | 167 | 0 | 275 | 161 |
N.S. |
1 | 1.10 | 0.96 | 0.73 | 1.30 | 1.26 | 0.00 | 2.07 | 1.21 |
time (sec) |
N/A | 0.277 | 0.903 | 0.323 | 0.288 | 0.295 | 0.000 | 0.299 | 0.131 |
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 | 133 | 148 | 121 | 97 | 206 | 176 | 0 | 440 | 180 |
N.S. |
1 | 1.11 | 0.91 | 0.73 | 1.55 | 1.32 | 0.00 | 3.31 | 1.35 |
time (sec) |
N/A | 0.287 | 1.056 | 0.320 | 0.287 | 0.291 | 0.000 | 0.427 | 0.133 |
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 | 133 | 148 | 123 | 97 | 244 | 191 | 0 | 355 | 206 |
N.S. |
1 | 1.11 | 0.92 | 0.73 | 1.83 | 1.44 | 0.00 | 2.67 | 1.55 |
time (sec) |
N/A | 0.285 | 1.221 | 0.325 | 0.296 | 0.442 | 0.000 | 0.315 | 10.693 |
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 | 133 | 148 | 121 | 97 | 287 | 206 | 0 | 389 | 238 |
N.S. |
1 | 1.11 | 0.91 | 0.73 | 2.16 | 1.55 | 0.00 | 2.92 | 1.79 |
time (sec) |
N/A | 0.288 | 1.317 | 0.372 | 0.295 | 0.386 | 0.000 | 0.313 | 0.139 |
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 | 136 | 151 | 98 | 90 | 323 | 164 | 0 | 408 | 272 |
N.S. |
1 | 1.11 | 0.72 | 0.66 | 2.38 | 1.21 | 0.00 | 3.00 | 2.00 |
time (sec) |
N/A | 0.260 | 1.543 | 0.386 | 0.296 | 0.350 | 0.000 | 0.327 | 10.694 |
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 | 158 | 178 | 103 | 95 | 376 | 179 | 0 | 457 | 326 |
N.S. |
1 | 1.13 | 0.65 | 0.60 | 2.38 | 1.13 | 0.00 | 2.89 | 2.06 |
time (sec) |
N/A | 0.306 | 1.897 | 0.428 | 0.301 | 0.379 | 0.000 | 0.309 | 10.754 |
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 | 180 | 205 | 108 | 100 | 434 | 194 | 0 | 502 | 385 |
N.S. |
1 | 1.14 | 0.60 | 0.56 | 2.41 | 1.08 | 0.00 | 2.79 | 2.14 |
time (sec) |
N/A | 0.343 | 2.089 | 0.478 | 0.301 | 0.653 | 0.000 | 0.328 | 0.182 |
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 | 202 | 232 | 113 | 105 | 497 | 209 | 0 | 547 | 449 |
N.S. |
1 | 1.15 | 0.56 | 0.52 | 2.46 | 1.03 | 0.00 | 2.71 | 2.22 |
time (sec) |
N/A | 0.367 | 2.499 | 0.507 | 0.302 | 0.382 | 0.000 | 0.338 | 10.919 |
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 | 106 | 128 | 66 | 45 | 78 | 60 | 97 | 53 | 45 |
N.S. |
1 | 1.21 | 0.62 | 0.42 | 0.74 | 0.57 | 0.92 | 0.50 | 0.42 |
time (sec) |
N/A | 0.253 | 0.202 | 0.318 | 0.278 | 0.288 | 0.328 | 0.271 | 0.041 |
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 | 84 | 101 | 61 | 40 | 64 | 55 | 80 | 49 | 40 |
N.S. |
1 | 1.20 | 0.73 | 0.48 | 0.76 | 0.65 | 0.95 | 0.58 | 0.48 |
time (sec) |
N/A | 0.230 | 0.197 | 0.297 | 0.270 | 0.282 | 0.217 | 0.276 | 0.034 |
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 | 62 | 74 | 56 | 35 | 50 | 50 | 63 | 42 | 35 |
N.S. |
1 | 1.19 | 0.90 | 0.56 | 0.81 | 0.81 | 1.02 | 0.68 | 0.56 |
time (sec) |
N/A | 0.194 | 0.147 | 0.279 | 0.274 | 0.301 | 0.150 | 0.267 | 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 | 40 | 51 | 49 | 28 | 36 | 43 | 44 | 37 | 28 |
N.S. |
1 | 1.28 | 1.22 | 0.70 | 0.90 | 1.08 | 1.10 | 0.92 | 0.70 |
time (sec) |
N/A | 0.165 | 0.115 | 0.249 | 0.268 | 0.324 | 0.108 | 0.279 | 0.031 |