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 | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 230 | 220 | 489 | 1352 | 0 | 4961 | 0 | 0 | 102 | 0 |
N.S. |
1 | 0.96 | 2.13 | 5.88 | 0.00 | 21.57 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 1.253 | 0.916 | 0.286 | 0.000 | 0.512 | 0.000 | 0.000 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 230 | 220 | 489 | 1352 | 0 | 4961 | 0 | 0 | 102 | 0 |
N.S. |
1 | 0.96 | 2.13 | 5.88 | 0.00 | 21.57 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 1.182 | 0.003 | 0.110 | 0.000 | 0.525 | 0.000 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 276 | 462 | 222 | 264 | 304 | 574 | 418 | 297 | 481 | 0 |
N.S. |
1 | 1.67 | 0.80 | 0.96 | 1.10 | 2.08 | 1.51 | 1.08 | 1.74 | 0.00 |
time (sec) |
N/A | 2.716 | 1.142 | 0.195 | 0.036 | 0.099 | 0.602 | 0.243 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 349 | 197 | 233 | 255 | 472 | 367 | 252 | 413 | 0 |
N.S. |
1 | 1.49 | 0.84 | 0.99 | 1.09 | 2.01 | 1.56 | 1.07 | 1.76 | 0.00 |
time (sec) |
N/A | 1.808 | 1.022 | 0.185 | 0.039 | 0.101 | 0.578 | 0.248 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 199 | 253 | 175 | 186 | 208 | 419 | 309 | 217 | 358 | 0 |
N.S. |
1 | 1.27 | 0.88 | 0.93 | 1.05 | 2.11 | 1.55 | 1.09 | 1.80 | 0.00 |
time (sec) |
N/A | 1.071 | 0.802 | 0.139 | 0.034 | 0.094 | 0.568 | 0.224 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 180 | 145 | 155 | 169 | 325 | 258 | 173 | 290 | 0 |
N.S. |
1 | 1.13 | 0.91 | 0.97 | 1.06 | 2.04 | 1.62 | 1.09 | 1.82 | 0.00 |
time (sec) |
N/A | 0.636 | 0.644 | 0.142 | 0.037 | 0.089 | 0.506 | 0.226 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 166 | 156 | 211 | 159 | 693 | 389 | 0 | 297 | 0 |
N.S. |
1 | 1.00 | 0.94 | 1.27 | 0.96 | 4.17 | 2.34 | 0.00 | 1.79 | 0.00 |
time (sec) |
N/A | 0.920 | 0.819 | 0.129 | 0.037 | 0.468 | 3.870 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 167 | 162 | 202 | 130 | 603 | 386 | 166 | 344 | 0 |
N.S. |
1 | 0.99 | 0.96 | 1.20 | 0.77 | 3.59 | 2.30 | 0.99 | 2.05 | 0.00 |
time (sec) |
N/A | 0.918 | 0.922 | 0.120 | 0.037 | 0.285 | 3.075 | 0.187 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 182 | 174 | 206 | 170 | 683 | 389 | 255 | 384 | 0 |
N.S. |
1 | 0.90 | 0.86 | 1.02 | 0.84 | 3.38 | 1.93 | 1.26 | 1.90 | 0.00 |
time (sec) |
N/A | 1.036 | 0.964 | 0.111 | 0.037 | 0.483 | 4.226 | 0.207 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 176 | 181 | 159 | 163 | 618 | 350 | 385 | 623 | 0 |
N.S. |
1 | 0.98 | 1.01 | 0.88 | 0.91 | 3.43 | 1.94 | 2.14 | 3.46 | 0.00 |
time (sec) |
N/A | 0.915 | 0.985 | 0.134 | 0.035 | 0.181 | 4.356 | 0.234 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 171 | 194 | 159 | 221 | 734 | 371 | 716 | 408 | 0 |
N.S. |
1 | 0.97 | 1.10 | 0.90 | 1.26 | 4.17 | 2.11 | 4.07 | 2.32 | 0.00 |
time (sec) |
N/A | 0.905 | 1.599 | 0.139 | 0.036 | 0.189 | 4.963 | 0.233 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 160 | 192 | 171 | 234 | 350 | 440 | 751 | 453 | 0 |
N.S. |
1 | 0.94 | 1.13 | 1.01 | 1.38 | 2.06 | 2.59 | 4.42 | 2.66 | 0.00 |
time (sec) |
N/A | 0.848 | 1.644 | 0.203 | 0.041 | 0.117 | 6.291 | 0.223 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 203 | 214 | 203 | 271 | 443 | 558 | 947 | 494 | 0 |
N.S. |
1 | 0.98 | 1.03 | 0.98 | 1.31 | 2.14 | 2.70 | 4.57 | 2.39 | 0.00 |
time (sec) |
N/A | 0.986 | 1.925 | 0.187 | 0.040 | 0.158 | 9.582 | 0.181 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 243 | 244 | 249 | 318 | 498 | 916 | 1028 | 580 | 0 |
N.S. |
1 | 0.98 | 0.98 | 1.00 | 1.28 | 2.01 | 3.69 | 4.15 | 2.34 | 0.00 |
time (sec) |
N/A | 1.108 | 2.311 | 0.275 | 0.046 | 0.190 | 12.842 | 0.226 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 288 | 290 | 265 | 282 | 367 | 593 | 1278 | 1266 | 630 | 0 |
N.S. |
1 | 1.01 | 0.92 | 0.98 | 1.27 | 2.06 | 4.44 | 4.40 | 2.19 | 0.00 |
time (sec) |
N/A | 1.249 | 2.714 | 0.262 | 0.043 | 0.286 | 29.038 | 0.206 | 0.268 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 406 | 0 | 366 | 406 | 484 | 922 | 762 | 494 | 807 | 0 |
N.S. |
1 | 0.00 | 0.90 | 1.00 | 1.19 | 2.27 | 1.88 | 1.22 | 1.99 | 0.00 |
time (sec) |
N/A | 0.000 | 2.057 | 0.203 | 0.039 | 0.118 | 0.625 | 0.189 | 9.344 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 378 | 0 | 370 | 382 | 440 | 832 | 670 | 439 | 32 | 0 |
N.S. |
1 | 0.00 | 0.98 | 1.01 | 1.16 | 2.20 | 1.77 | 1.16 | 0.08 | 0.00 |
time (sec) |
N/A | 0.000 | 3.345 | 0.207 | 0.042 | 0.117 | 0.650 | 0.197 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 300 | 351 | 284 | 290 | 340 | 681 | 576 | 369 | 609 | 0 |
N.S. |
1 | 1.17 | 0.95 | 0.97 | 1.13 | 2.27 | 1.92 | 1.23 | 2.03 | 0.00 |
time (sec) |
N/A | 1.404 | 1.484 | 0.147 | 0.037 | 0.104 | 0.603 | 0.185 | 2.446 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 264 | 269 | 246 | 268 | 305 | 593 | 484 | 314 | 29 | 0 |
N.S. |
1 | 1.02 | 0.93 | 1.02 | 1.16 | 2.25 | 1.83 | 1.19 | 0.11 | 0.00 |
time (sec) |
N/A | 0.886 | 1.244 | 0.147 | 0.037 | 0.103 | 0.547 | 0.175 | 200.035 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 238 | 249 | 240 | 340 | 259 | 1049 | 620 | 0 | 477 | 0 |
N.S. |
1 | 1.05 | 1.01 | 1.43 | 1.09 | 4.41 | 2.61 | 0.00 | 2.00 | 0.00 |
time (sec) |
N/A | 1.489 | 1.178 | 0.128 | 0.040 | 0.819 | 5.247 | 0.000 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 261 | 241 | 331 | 239 | 1015 | 629 | 270 | 559 | 0 |
N.S. |
1 | 1.02 | 0.94 | 1.29 | 0.93 | 3.95 | 2.45 | 1.05 | 2.18 | 0.00 |
time (sec) |
N/A | 1.618 | 1.407 | 0.160 | 0.037 | 3.789 | 3.498 | 0.229 | 15.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 261 | 243 | 291 | 238 | 975 | 617 | 336 | 578 | 0 |
N.S. |
1 | 1.04 | 0.97 | 1.16 | 0.95 | 3.90 | 2.47 | 1.34 | 2.31 | 0.00 |
time (sec) |
N/A | 1.627 | 1.257 | 0.138 | 0.037 | 1.150 | 5.308 | 0.208 | 0.293 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 283 | 269 | 213 | 259 | 248 | 975 | 600 | 522 | 676 | 0 |
N.S. |
1 | 0.95 | 0.75 | 0.92 | 0.88 | 3.45 | 2.12 | 1.84 | 2.39 | 0.00 |
time (sec) |
N/A | 1.534 | 1.127 | 0.164 | 0.039 | 1.175 | 6.002 | 0.247 | 22.791 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 241 | 288 | 258 | 262 | 312 | 1030 | 600 | 1017 | 668 | 0 |
N.S. |
1 | 1.20 | 1.07 | 1.09 | 1.29 | 4.27 | 2.49 | 4.22 | 2.77 | 0.00 |
time (sec) |
N/A | 1.675 | 1.798 | 0.159 | 0.042 | 0.704 | 7.289 | 0.268 | 0.255 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 256 | 249 | 281 | 340 | 1094 | 648 | 1212 | 694 | 0 |
N.S. |
1 | 1.02 | 0.99 | 1.12 | 1.35 | 4.34 | 2.57 | 4.81 | 2.75 | 0.00 |
time (sec) |
N/A | 1.545 | 2.042 | 0.239 | 0.038 | 0.296 | 7.508 | 0.232 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 273 | 248 | 293 | 309 | 409 | 618 | 819 | 1541 | 765 | 0 |
N.S. |
1 | 0.91 | 1.07 | 1.13 | 1.50 | 2.26 | 3.00 | 5.64 | 2.80 | 0.00 |
time (sec) |
N/A | 1.556 | 2.596 | 0.255 | 0.040 | 0.236 | 12.556 | 0.229 | 0.270 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 313 | 302 | 303 | 357 | 419 | 702 | 1216 | 1642 | 864 | 0 |
N.S. |
1 | 0.96 | 0.97 | 1.14 | 1.34 | 2.24 | 3.88 | 5.25 | 2.76 | 0.00 |
time (sec) |
N/A | 1.756 | 2.958 | 0.589 | 0.039 | 0.333 | 15.031 | 0.212 | 1.732 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 386 | 369 | 381 | 441 | 542 | 853 | 1678 | 2046 | 994 | 0 |
N.S. |
1 | 0.96 | 0.99 | 1.14 | 1.40 | 2.21 | 4.35 | 5.30 | 2.58 | 0.00 |
time (sec) |
N/A | 2.131 | 4.596 | 0.570 | 0.041 | 0.522 | 36.012 | 0.234 | 0.344 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 428 | 423 | 387 | 473 | 563 | 942 | 2518 | 2041 | 1064 | 0 |
N.S. |
1 | 0.99 | 0.90 | 1.11 | 1.32 | 2.20 | 5.88 | 4.77 | 2.49 | 0.00 |
time (sec) |
N/A | 2.221 | 3.999 | 0.860 | 0.045 | 0.719 | 50.465 | 0.239 | 4.825 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 367 | 391 | 342 | 520 | 624 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.07 | 0.93 | 1.42 | 1.70 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 2.162 | 1.811 | 0.274 | 0.164 | 0.000 | 0.000 | 0.000 | 200.022 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 280 | 299 | 273 | 399 | 491 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.07 | 0.98 | 1.42 | 1.75 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 1.344 | 1.344 | 0.217 | 0.100 | 0.000 | 0.000 | 0.000 | 200.021 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 217 | 212 | 312 | 362 | 0 | 0 | 0 | 3439 | 0 |
N.S. |
1 | 1.06 | 1.03 | 1.52 | 1.77 | 0.00 | 0.00 | 0.00 | 16.78 | 0.00 |
time (sec) |
N/A | 0.859 | 0.909 | 0.188 | 0.086 | 0.000 | 0.000 | 0.000 | 0.245 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | F(-1) | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 280 | 228 | 365 | 349 | 0 | 0 | 0 | 527 | 0 |
N.S. |
1 | 1.36 | 1.11 | 1.77 | 1.69 | 0.00 | 0.00 | 0.00 | 2.56 | 0.00 |
time (sec) |
N/A | 1.156 | 1.372 | 0.183 | 0.092 | 0.000 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F(-1) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 267 | 200 | 306 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.44 | 1.08 | 1.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.960 | 0.850 | 0.251 | 0.000 | 0.000 | 0.000 | 0.000 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F(-1) | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 284 | 245 | 300 | 0 | 0 | 0 | 0 | 539 | 0 |
N.S. |
1 | 1.35 | 1.16 | 1.42 | 0.00 | 0.00 | 0.00 | 0.00 | 2.55 | 0.00 |
time (sec) |
N/A | 1.012 | 1.851 | 0.267 | 0.000 | 0.000 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 240 | 246 | 258 | 334 | 0 | 1094 | 0 | 571 | 32 | 0 |
N.S. |
1 | 1.02 | 1.08 | 1.39 | 0.00 | 4.56 | 0.00 | 2.38 | 0.13 | 0.00 |
time (sec) |
N/A | 0.998 | 1.573 | 0.331 | 0.000 | 3.249 | 0.000 | 0.177 | 200.025 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 318 | 354 | 319 | 424 | 0 | 1514 | 0 | 1249 | 853 | 0 |
N.S. |
1 | 1.11 | 1.00 | 1.33 | 0.00 | 4.76 | 0.00 | 3.93 | 2.68 | 0.00 |
time (sec) |
N/A | 1.204 | 2.259 | 0.344 | 0.000 | 6.432 | 0.000 | 0.238 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 492 | 605 | 421 | 790 | 882 | 0 | 0 | 0 | 3172 | 0 |
N.S. |
1 | 1.23 | 0.86 | 1.61 | 1.79 | 0.00 | 0.00 | 0.00 | 6.45 | 0.00 |
time (sec) |
N/A | 3.499 | 3.341 | 0.325 | 0.198 | 0.000 | 0.000 | 0.000 | 37.473 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | F(-1) | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 396 | 501 | 355 | 669 | 751 | 0 | 0 | 0 | 2801 | 0 |
N.S. |
1 | 1.27 | 0.90 | 1.69 | 1.90 | 0.00 | 0.00 | 0.00 | 7.07 | 0.00 |
time (sec) |
N/A | 2.302 | 4.142 | 0.306 | 0.150 | 0.000 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | F(-1) | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 309 | 399 | 280 | 579 | 617 | 0 | 0 | 0 | 2296 | 0 |
N.S. |
1 | 1.29 | 0.91 | 1.87 | 2.00 | 0.00 | 0.00 | 0.00 | 7.43 | 0.00 |
time (sec) |
N/A | 1.578 | 1.824 | 0.250 | 0.098 | 0.000 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | F(-1) | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 234 | 322 | 217 | 512 | 478 | 0 | 0 | 0 | 1847 | 0 |
N.S. |
1 | 1.38 | 0.93 | 2.19 | 2.04 | 0.00 | 0.00 | 0.00 | 7.89 | 0.00 |
time (sec) |
N/A | 1.128 | 1.451 | 0.225 | 0.103 | 0.000 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 271 | 241 | 876 | 0 | 0 | 0 | 0 | 1420 | 0 |
N.S. |
1 | 1.25 | 1.11 | 4.04 | 0.00 | 0.00 | 0.00 | 0.00 | 6.54 | 0.00 |
time (sec) |
N/A | 1.207 | 1.457 | 0.223 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 357 | 265 | 514 | 0 | 0 | 0 | 0 | 1470 | 0 |
N.S. |
1 | 1.49 | 1.11 | 2.15 | 0.00 | 0.00 | 0.00 | 0.00 | 6.15 | 0.00 |
time (sec) |
N/A | 1.178 | 2.057 | 0.305 | 0.000 | 0.000 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 274 | 450 | 259 | 528 | 0 | 2240 | 0 | 0 | 1862 | 0 |
N.S. |
1 | 1.64 | 0.95 | 1.93 | 0.00 | 8.18 | 0.00 | 0.00 | 6.80 | 0.00 |
time (sec) |
N/A | 1.380 | 2.188 | 0.332 | 0.000 | 9.243 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 349 | 500 | 327 | 589 | 0 | 2786 | 0 | 0 | 2409 | 0 |
N.S. |
1 | 1.43 | 0.94 | 1.69 | 0.00 | 7.98 | 0.00 | 0.00 | 6.90 | 0.00 |
time (sec) |
N/A | 1.439 | 2.690 | 0.426 | 0.000 | 10.010 | 0.000 | 0.000 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 436 | 619 | 404 | 690 | 0 | 3650 | 0 | 0 | 2853 | 0 |
N.S. |
1 | 1.42 | 0.93 | 1.58 | 0.00 | 8.37 | 0.00 | 0.00 | 6.54 | 0.00 |
time (sec) |
N/A | 1.753 | 4.571 | 0.473 | 0.000 | 30.321 | 0.000 | 0.000 | 0.329 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 311 | 483 | 268 | 332 | 349 | 716 | 790 | 377 | 604 | 0 |
N.S. |
1 | 1.55 | 0.86 | 1.07 | 1.12 | 2.30 | 2.54 | 1.21 | 1.94 | 0.00 |
time (sec) |
N/A | 2.726 | 1.407 | 0.263 | 0.046 | 0.122 | 0.668 | 0.178 | 0.360 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 275 | 370 | 244 | 284 | 300 | 632 | 699 | 339 | 536 | 0 |
N.S. |
1 | 1.35 | 0.89 | 1.03 | 1.09 | 2.30 | 2.54 | 1.23 | 1.95 | 0.00 |
time (sec) |
N/A | 1.834 | 1.119 | 0.265 | 0.037 | 0.113 | 0.653 | 0.161 | 0.277 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 242 | 277 | 223 | 240 | 253 | 573 | 598 | 299 | 481 | 0 |
N.S. |
1 | 1.14 | 0.92 | 0.99 | 1.05 | 2.37 | 2.47 | 1.24 | 1.99 | 0.00 |
time (sec) |
N/A | 1.209 | 1.136 | 0.189 | 0.045 | 0.103 | 0.630 | 0.148 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 202 | 197 | 194 | 211 | 473 | 507 | 255 | 413 | 0 |
N.S. |
1 | 1.03 | 1.00 | 0.98 | 1.07 | 2.40 | 2.57 | 1.29 | 2.10 | 0.00 |
time (sec) |
N/A | 0.658 | 1.034 | 0.188 | 0.036 | 0.107 | 0.552 | 0.155 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 211 | 210 | 273 | 215 | 987 | 901 | 0 | 424 | 0 |
N.S. |
1 | 0.95 | 0.95 | 1.24 | 0.97 | 4.47 | 4.08 | 0.00 | 1.92 | 0.00 |
time (sec) |
N/A | 1.123 | 1.219 | 0.174 | 0.037 | 0.627 | 11.750 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 222 | 218 | 202 | 264 | 188 | 891 | 826 | 259 | 479 | 0 |
N.S. |
1 | 0.98 | 0.91 | 1.19 | 0.85 | 4.01 | 3.72 | 1.17 | 2.16 | 0.00 |
time (sec) |
N/A | 1.045 | 1.065 | 0.229 | 0.036 | 0.310 | 4.045 | 0.172 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 267 | 253 | 222 | 278 | 242 | 907 | 782 | 348 | 513 | 0 |
N.S. |
1 | 0.95 | 0.83 | 1.04 | 0.91 | 3.40 | 2.93 | 1.30 | 1.92 | 0.00 |
time (sec) |
N/A | 1.201 | 1.349 | 0.207 | 0.038 | 0.535 | 5.669 | 0.179 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 277 | 253 | 223 | 307 | 272 | 795 | 716 | 491 | 500 | 0 |
N.S. |
1 | 0.91 | 0.81 | 1.11 | 0.98 | 2.87 | 2.58 | 1.77 | 1.81 | 0.00 |
time (sec) |
N/A | 1.201 | 1.394 | 0.266 | 0.036 | 0.634 | 7.012 | 0.169 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 282 | 257 | 229 | 269 | 331 | 906 | 712 | 754 | 514 | 0 |
N.S. |
1 | 0.91 | 0.81 | 0.95 | 1.17 | 3.21 | 2.52 | 2.67 | 1.82 | 0.00 |
time (sec) |
N/A | 1.257 | 1.705 | 0.259 | 0.035 | 0.610 | 8.850 | 0.202 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 243 | 228 | 236 | 235 | 307 | 906 | 685 | 761 | 532 | 0 |
N.S. |
1 | 0.94 | 0.97 | 0.97 | 1.26 | 3.73 | 2.82 | 3.13 | 2.19 | 0.00 |
time (sec) |
N/A | 1.050 | 2.065 | 0.367 | 0.039 | 0.221 | 9.790 | 0.231 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 236 | 216 | 249 | 233 | 357 | 1032 | 682 | 1084 | 535 | 0 |
N.S. |
1 | 0.92 | 1.06 | 0.99 | 1.51 | 4.37 | 2.89 | 4.59 | 2.27 | 0.00 |
time (sec) |
N/A | 1.050 | 2.659 | 0.348 | 0.038 | 0.348 | 14.375 | 0.176 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 184 | 235 | 249 | 328 | 498 | 1027 | 1109 | 580 | 0 |
N.S. |
1 | 0.88 | 1.12 | 1.19 | 1.56 | 2.37 | 4.89 | 5.28 | 2.76 | 0.00 |
time (sec) |
N/A | 0.893 | 1.279 | 0.536 | 0.037 | 0.228 | 18.362 | 0.194 | 0.257 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 229 | 266 | 282 | 363 | 593 | 1447 | 1295 | 630 | 0 |
N.S. |
1 | 0.92 | 1.06 | 1.13 | 1.45 | 2.37 | 5.79 | 5.18 | 2.52 | 0.00 |
time (sec) |
N/A | 1.040 | 2.931 | 0.475 | 0.036 | 0.308 | 38.879 | 0.225 | 0.306 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 288 | 271 | 295 | 329 | 410 | 654 | 2387 | 1378 | 703 | 0 |
N.S. |
1 | 0.94 | 1.02 | 1.14 | 1.42 | 2.27 | 8.29 | 4.78 | 2.44 | 0.00 |
time (sec) |
N/A | 1.198 | 3.622 | 0.710 | 0.039 | 0.494 | 56.081 | 0.180 | 0.359 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 455 | 616 | 448 | 438 | 542 | 1152 | 1406 | 620 | 1005 | 0 |
N.S. |
1 | 1.35 | 0.98 | 0.96 | 1.19 | 2.53 | 3.09 | 1.36 | 2.21 | 0.00 |
time (sec) |
N/A | 3.487 | 2.332 | 0.366 | 0.041 | 0.132 | 0.740 | 0.198 | 24.357 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 437 | 0 | 451 | 430 | 518 | 1068 | 1253 | 565 | 32 | 0 |
N.S. |
1 | 0.00 | 1.03 | 0.98 | 1.19 | 2.44 | 2.87 | 1.29 | 0.07 | 0.00 |
time (sec) |
N/A | 0.000 | 4.771 | 0.390 | 0.044 | 0.138 | 0.695 | 0.213 | 200.029 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 349 | 374 | 368 | 322 | 398 | 923 | 1086 | 496 | 807 | 0 |
N.S. |
1 | 1.07 | 1.05 | 0.92 | 1.14 | 2.64 | 3.11 | 1.42 | 2.31 | 0.00 |
time (sec) |
N/A | 1.515 | 1.719 | 0.260 | 0.035 | 0.158 | 0.651 | 0.200 | 9.750 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 331 | 295 | 333 | 316 | 380 | 833 | 933 | 441 | 29 | 0 |
N.S. |
1 | 0.89 | 1.01 | 0.95 | 1.15 | 2.52 | 2.82 | 1.33 | 0.09 | 0.00 |
time (sec) |
N/A | 0.931 | 1.730 | 0.274 | 0.048 | 0.153 | 0.603 | 0.199 | 200.029 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 305 | 305 | 324 | 418 | 330 | 1519 | 1442 | 0 | 679 | 0 |
N.S. |
1 | 1.00 | 1.06 | 1.37 | 1.08 | 4.98 | 4.73 | 0.00 | 2.23 | 0.00 |
time (sec) |
N/A | 1.674 | 2.107 | 0.238 | 0.037 | 0.880 | 18.916 | 0.000 | 0.735 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 341 | 337 | 325 | 425 | 334 | 1479 | 1382 | 402 | 32 | 0 |
N.S. |
1 | 0.99 | 0.95 | 1.25 | 0.98 | 4.34 | 4.05 | 1.18 | 0.09 | 0.00 |
time (sec) |
N/A | 1.884 | 3.211 | 0.324 | 0.038 | 4.524 | 4.865 | 0.184 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 333 | 353 | 331 | 367 | 334 | 1331 | 1251 | 478 | 783 | 0 |
N.S. |
1 | 1.06 | 0.99 | 1.10 | 1.00 | 4.00 | 3.76 | 1.44 | 2.35 | 0.00 |
time (sec) |
N/A | 1.892 | 1.991 | 0.273 | 0.037 | 1.670 | 7.250 | 0.206 | 0.672 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 426 | 412 | 328 | 402 | 404 | 1339 | 1216 | 688 | 32 | 0 |
N.S. |
1 | 0.97 | 0.77 | 0.94 | 0.95 | 3.14 | 2.85 | 1.62 | 0.08 | 0.00 |
time (sec) |
N/A | 2.203 | 2.300 | 0.314 | 0.042 | 3.766 | 8.935 | 0.240 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 367 | 412 | 324 | 413 | 471 | 1338 | 1151 | 1102 | 835 | 0 |
N.S. |
1 | 1.12 | 0.88 | 1.13 | 1.28 | 3.65 | 3.14 | 3.00 | 2.28 | 0.00 |
time (sec) |
N/A | 2.107 | 2.067 | 0.312 | 0.037 | 2.336 | 12.183 | 0.228 | 0.753 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 383 | 362 | 302 | 415 | 455 | 1330 | 1120 | 1236 | 32 | 0 |
N.S. |
1 | 0.95 | 0.79 | 1.08 | 1.19 | 3.47 | 2.92 | 3.23 | 0.08 | 0.00 |
time (sec) |
N/A | 1.849 | 2.094 | 0.437 | 0.037 | 1.661 | 13.037 | 0.237 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 330 | 368 | 348 | 382 | 531 | 1494 | 1114 | 1711 | 876 | 0 |
N.S. |
1 | 1.12 | 1.05 | 1.16 | 1.61 | 4.53 | 3.38 | 5.18 | 2.65 | 0.00 |
time (sec) |
N/A | 2.013 | 3.861 | 0.416 | 0.039 | 0.969 | 19.196 | 0.242 | 0.275 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 323 | 312 | 337 | 409 | 506 | 1568 | 1435 | 1784 | 898 | 0 |
N.S. |
1 | 0.97 | 1.04 | 1.27 | 1.57 | 4.85 | 4.44 | 5.52 | 2.78 | 0.00 |
time (sec) |
N/A | 1.706 | 3.573 | 0.638 | 0.046 | 0.517 | 22.108 | 0.177 | 0.268 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 338 | 275 | 383 | 441 | 570 | 855 | 1889 | 2107 | 994 | 0 |
N.S. |
1 | 0.81 | 1.13 | 1.30 | 1.69 | 2.53 | 5.59 | 6.23 | 2.94 | 0.00 |
time (sec) |
N/A | 1.656 | 4.310 | 0.570 | 0.039 | 0.654 | 47.890 | 0.174 | 0.353 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 365 | 328 | 389 | 433 | 537 | 944 | 3181 | 2195 | 1064 | 0 |
N.S. |
1 | 0.90 | 1.07 | 1.19 | 1.47 | 2.59 | 8.72 | 6.01 | 2.92 | 0.00 |
time (sec) |
N/A | 1.850 | 4.514 | 0.856 | 0.039 | 0.796 | 64.337 | 0.184 | 23.692 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 450 | 392 | 462 | 573 | 701 | 1097 | 0 | 2598 | 1192 | 0 |
N.S. |
1 | 0.87 | 1.03 | 1.27 | 1.56 | 2.44 | 0.00 | 5.77 | 2.65 | 0.00 |
time (sec) |
N/A | 2.119 | 6.083 | 0.822 | 0.039 | 1.064 | 0.000 | 0.239 | 0.701 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 529 | 548 | 522 | 849 | 971 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.04 | 0.99 | 1.60 | 1.84 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 2.631 | 3.907 | 0.243 | 0.246 | 0.000 | 0.000 | 0.000 | 200.013 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 452 | 447 | 426 | 699 | 811 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 0.99 | 0.94 | 1.55 | 1.79 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 1.795 | 2.660 | 0.222 | 0.187 | 0.000 | 0.000 | 0.000 | 200.021 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 349 | 343 | 340 | 559 | 632 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 0.98 | 0.97 | 1.60 | 1.81 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.344 | 1.875 | 0.195 | 0.120 | 0.000 | 0.000 | 0.000 | 200.023 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | F(-1) | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 345 | 453 | 332 | 630 | 578 | 0 | 0 | 0 | 1157 | 0 |
N.S. |
1 | 1.31 | 0.96 | 1.83 | 1.68 | 0.00 | 0.00 | 0.00 | 3.35 | 0.00 |
time (sec) |
N/A | 1.747 | 2.187 | 0.187 | 0.140 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 296 | 394 | 280 | 551 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.33 | 0.95 | 1.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 1.333 | 1.238 | 0.253 | 0.000 | 0.000 | 0.000 | 0.000 | 200.019 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F(-1) | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 287 | 441 | 305 | 491 | 0 | 0 | 0 | 0 | 1074 | 0 |
N.S. |
1 | 1.54 | 1.06 | 1.71 | 0.00 | 0.00 | 0.00 | 0.00 | 3.74 | 0.00 |
time (sec) |
N/A | 1.370 | 1.470 | 0.282 | 0.000 | 0.000 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F(-1) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 296 | 561 | 283 | 449 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.90 | 0.96 | 1.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 1.571 | 1.334 | 0.338 | 0.000 | 0.000 | 0.000 | 0.000 | 200.032 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F(-1) | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 346 | 687 | 360 | 493 | 0 | 0 | 0 | 0 | 1183 | 0 |
N.S. |
1 | 1.99 | 1.04 | 1.42 | 0.00 | 0.00 | 0.00 | 0.00 | 3.42 | 0.00 |
time (sec) |
N/A | 1.752 | 2.566 | 0.354 | 0.000 | 0.000 | 0.000 | 0.000 | 0.307 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 404 | 763 | 449 | 596 | 0 | 1974 | 0 | 1819 | 32 | 0 |
N.S. |
1 | 1.89 | 1.11 | 1.48 | 0.00 | 4.89 | 0.00 | 4.50 | 0.08 | 0.00 |
time (sec) |
N/A | 1.932 | 2.736 | 0.450 | 0.000 | 14.677 | 0.000 | 0.175 | 200.015 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 510 | 912 | 501 | 739 | 0 | 2562 | 0 | 3056 | 32 | 0 |
N.S. |
1 | 1.79 | 0.98 | 1.45 | 0.00 | 5.02 | 0.00 | 5.99 | 0.06 | 0.00 |
time (sec) |
N/A | 2.265 | 5.461 | 0.454 | 0.000 | 29.494 | 0.000 | 0.235 | 200.025 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 614 | 673 | 538 | 1014 | 1072 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.10 | 0.88 | 1.65 | 1.75 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 2.804 | 9.447 | 0.320 | 0.199 | 0.000 | 0.000 | 0.000 | 200.020 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 496 | 549 | 435 | 870 | 890 | 0 | 0 | 0 | 2398 | 0 |
N.S. |
1 | 1.11 | 0.88 | 1.75 | 1.79 | 0.00 | 0.00 | 0.00 | 4.83 | 0.00 |
time (sec) |
N/A | 2.091 | 3.052 | 0.264 | 0.152 | 0.000 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | F(-1) | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 391 | 454 | 347 | 733 | 708 | 0 | 0 | 0 | 1949 | 0 |
N.S. |
1 | 1.16 | 0.89 | 1.87 | 1.81 | 0.00 | 0.00 | 0.00 | 4.98 | 0.00 |
time (sec) |
N/A | 1.590 | 2.292 | 0.240 | 0.126 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 350 | 524 | 342 | 1461 | 0 | 0 | 0 | 0 | 1681 | 0 |
N.S. |
1 | 1.50 | 0.98 | 4.17 | 0.00 | 0.00 | 0.00 | 0.00 | 4.80 | 0.00 |
time (sec) |
N/A | 1.889 | 1.849 | 0.230 | 0.000 | 0.000 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 359 | 533 | 335 | 744 | 0 | 0 | 0 | 0 | 1680 | 0 |
N.S. |
1 | 1.48 | 0.93 | 2.07 | 0.00 | 0.00 | 0.00 | 0.00 | 4.68 | 0.00 |
time (sec) |
N/A | 1.689 | 2.021 | 0.331 | 0.000 | 0.000 | 0.000 | 0.000 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F(-1) | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 402 | 669 | 350 | 690 | 0 | 0 | 0 | 0 | 1727 | 0 |
N.S. |
1 | 1.66 | 0.87 | 1.72 | 0.00 | 0.00 | 0.00 | 0.00 | 4.30 | 0.00 |
time (sec) |
N/A | 1.882 | 1.691 | 0.361 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F(-1) | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 466 | 799 | 408 | 692 | 0 | 0 | 0 | 0 | 1779 | 0 |
N.S. |
1 | 1.71 | 0.88 | 1.48 | 0.00 | 0.00 | 0.00 | 0.00 | 3.82 | 0.00 |
time (sec) |
N/A | 2.073 | 2.489 | 0.421 | 0.000 | 0.000 | 0.000 | 0.000 | 11.495 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 527 | 929 | 410 | 765 | 0 | 2437 | 0 | 0 | 1962 | 0 |
N.S. |
1 | 1.76 | 0.78 | 1.45 | 0.00 | 4.62 | 0.00 | 0.00 | 3.72 | 0.00 |
time (sec) |
N/A | 2.360 | 4.019 | 0.461 | 0.000 | 14.859 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 234 | 435 | 173 | 186 | 259 | 432 | 248 | 223 | 358 | 0 |
N.S. |
1 | 1.86 | 0.74 | 0.79 | 1.11 | 1.85 | 1.06 | 0.95 | 1.53 | 0.00 |
time (sec) |
N/A | 2.719 | 0.844 | 0.261 | 0.046 | 0.112 | 0.575 | 0.214 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 325 | 155 | 155 | 210 | 338 | 214 | 183 | 290 | 0 |
N.S. |
1 | 1.69 | 0.81 | 0.81 | 1.09 | 1.76 | 1.11 | 0.95 | 1.51 | 0.00 |
time (sec) |
N/A | 1.707 | 1.240 | 0.268 | 0.042 | 0.097 | 0.542 | 0.171 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 226 | 124 | 112 | 162 | 285 | 184 | 146 | 235 | 0 |
N.S. |
1 | 1.42 | 0.78 | 0.70 | 1.02 | 1.79 | 1.16 | 0.92 | 1.48 | 0.00 |
time (sec) |
N/A | 1.093 | 0.580 | 0.187 | 0.031 | 0.125 | 0.545 | 0.133 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 152 | 96 | 89 | 126 | 195 | 150 | 105 | 171 | 227 |
N.S. |
1 | 1.27 | 0.80 | 0.74 | 1.05 | 1.62 | 1.25 | 0.88 | 1.42 | 1.89 |
time (sec) |
N/A | 0.589 | 0.493 | 0.178 | 0.048 | 0.083 | 0.489 | 0.165 | 0.157 | 18.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 119 | 112 | 147 | 114 | 486 | 253 | 0 | 186 | 0 |
N.S. |
1 | 1.04 | 0.98 | 1.29 | 1.00 | 4.26 | 2.22 | 0.00 | 1.63 | 0.00 |
time (sec) |
N/A | 0.843 | 0.580 | 0.162 | 0.041 | 0.476 | 3.976 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 112 | 110 | 115 | 103 | 443 | 196 | 117 | 370 | 0 |
N.S. |
1 | 1.09 | 1.07 | 1.12 | 1.00 | 4.30 | 1.90 | 1.14 | 3.59 | 0.00 |
time (sec) |
N/A | 0.803 | 0.554 | 0.211 | 0.038 | 0.128 | 2.237 | 0.144 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 123 | 145 | 106 | 131 | 527 | 190 | 225 | 280 | 0 |
N.S. |
1 | 1.03 | 1.22 | 0.89 | 1.10 | 4.43 | 1.60 | 1.89 | 2.35 | 0.00 |
time (sec) |
N/A | 0.837 | 0.918 | 0.188 | 0.044 | 0.166 | 3.537 | 0.182 | 0.160 | 0.000 |