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 | A | B | F(-2) | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 431 | 419 | 552 | 809 | 0 | 1445 | 3818 | 796 | 28 | 2712 |
N.S. |
1 | 0.97 | 1.28 | 1.88 | 0.00 | 3.35 | 8.86 | 1.85 | 0.06 | 6.29 |
time (sec) |
N/A | 0.896 | 7.983 | 1.793 | 0.000 | 0.165 | 1.317 | 0.186 | 200.038 | 23.745 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 312 | 301 | 375 | 515 | 0 | 985 | 2142 | 523 | 1195 | 1679 |
N.S. |
1 | 0.96 | 1.20 | 1.65 | 0.00 | 3.16 | 6.87 | 1.68 | 3.83 | 5.38 |
time (sec) |
N/A | 0.577 | 5.199 | 1.483 | 0.000 | 0.148 | 1.198 | 0.173 | 2.258 | 15.333 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 196 | 236 | 288 | 0 | 617 | 1136 | 309 | 685 | 876 |
N.S. |
1 | 1.01 | 1.21 | 1.48 | 0.00 | 3.16 | 5.83 | 1.58 | 3.51 | 4.49 |
time (sec) |
N/A | 0.393 | 2.610 | 1.535 | 0.000 | 0.319 | 1.200 | 0.215 | 0.373 | 14.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 127 | 174 | 141 | 0 | 343 | 508 | 159 | 318 | 395 |
N.S. |
1 | 1.04 | 1.43 | 1.16 | 0.00 | 2.81 | 4.16 | 1.30 | 2.61 | 3.24 |
time (sec) |
N/A | 0.454 | 1.810 | 1.322 | 0.000 | 0.106 | 1.104 | 0.182 | 0.255 | 13.597 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 17 | 15 | 14 | 14 | 60 | 14 | 23 | 14 |
N.S. |
1 | 1.00 | 0.94 | 0.83 | 0.78 | 0.78 | 3.33 | 0.78 | 1.28 | 0.78 |
time (sec) |
N/A | 0.251 | 0.032 | 1.264 | 0.026 | 0.077 | 0.069 | 0.184 | 0.216 | 12.275 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 199 | 205 | 227 | 296 | 0 | 1196 | 0 | 0 | 6799 | 0 |
N.S. |
1 | 1.03 | 1.14 | 1.49 | 0.00 | 6.01 | 0.00 | 0.00 | 34.17 | 0.00 |
time (sec) |
N/A | 0.849 | 1.913 | 1.855 | 0.000 | 7.091 | 0.000 | 0.000 | 0.565 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 209 | 210 | 561 | 0 | 1964 | 0 | 0 | 1409 | 0 |
N.S. |
1 | 1.03 | 1.03 | 2.76 | 0.00 | 9.67 | 0.00 | 0.00 | 6.94 | 0.00 |
time (sec) |
N/A | 0.724 | 2.384 | 1.938 | 0.000 | 11.962 | 0.000 | 0.000 | 0.402 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 266 | 319 | 389 | 1823 | 0 | 3684 | 0 | 1148 | 3284 | 0 |
N.S. |
1 | 1.20 | 1.46 | 6.85 | 0.00 | 13.85 | 0.00 | 4.32 | 12.35 | 0.00 |
time (sec) |
N/A | 1.043 | 11.334 | 2.202 | 0.000 | 148.056 | 0.000 | 0.513 | 0.412 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 237 | 214 | 2401 | 0 | 2040 | 0 | 2677 | 2669 | 0 |
N.S. |
1 | 1.09 | 0.99 | 11.06 | 0.00 | 9.40 | 0.00 | 12.34 | 12.30 | 0.00 |
time (sec) |
N/A | 0.679 | 10.483 | 2.395 | 0.000 | 1.891 | 0.000 | 0.482 | 1.382 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 307 | 341 | 290 | 3788 | 0 | 3996 | 0 | 0 | 6278 | 0 |
N.S. |
1 | 1.11 | 0.94 | 12.34 | 0.00 | 13.02 | 0.00 | 0.00 | 20.45 | 0.00 |
time (sec) |
N/A | 0.966 | 10.858 | 2.153 | 0.000 | 10.266 | 0.000 | 0.000 | 12.064 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 430 | 467 | 401 | 6447 | 0 | 6858 | 0 | 10398 | 12069 | 0 |
N.S. |
1 | 1.09 | 0.93 | 14.99 | 0.00 | 15.95 | 0.00 | 24.18 | 28.07 | 0.00 |
time (sec) |
N/A | 1.414 | 13.027 | 2.602 | 0.000 | 46.414 | 0.000 | 8.873 | 67.363 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 379 | 344 | 297 | 907 | 0 | 1587 | 6965 | 883 | 1968 | 0 |
N.S. |
1 | 0.91 | 0.78 | 2.39 | 0.00 | 4.19 | 18.38 | 2.33 | 5.19 | 0.00 |
time (sec) |
N/A | 1.078 | 10.781 | 1.898 | 0.000 | 0.202 | 1.256 | 0.230 | 166.504 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 242 | 239 | 391 | 529 | 0 | 1015 | 3582 | 536 | 1180 | 0 |
N.S. |
1 | 0.99 | 1.62 | 2.19 | 0.00 | 4.19 | 14.80 | 2.21 | 4.88 | 0.00 |
time (sec) |
N/A | 0.740 | 5.292 | 1.852 | 0.000 | 0.154 | 1.119 | 0.202 | 2.396 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 170 | 224 | 259 | 0 | 559 | 1564 | 276 | 572 | 0 |
N.S. |
1 | 1.06 | 1.40 | 1.62 | 0.00 | 3.49 | 9.78 | 1.72 | 3.58 | 0.00 |
time (sec) |
N/A | 0.520 | 3.255 | 1.513 | 0.000 | 0.114 | 1.330 | 0.198 | 1.398 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 17 | 15 | 14 | 49 | 136 | 14 | 50 | 14 |
N.S. |
1 | 1.00 | 0.94 | 0.83 | 0.78 | 2.72 | 7.56 | 0.78 | 2.78 | 0.78 |
time (sec) |
N/A | 0.245 | 0.039 | 1.509 | 0.036 | 0.083 | 0.117 | 0.169 | 0.223 | 12.392 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 360 | 377 | 353 | 538 | 0 | 0 | 0 | 0 | 14638 | 0 |
N.S. |
1 | 1.05 | 0.98 | 1.49 | 0.00 | 0.00 | 0.00 | 0.00 | 40.66 | 0.00 |
time (sec) |
N/A | 1.533 | 4.440 | 1.970 | 0.000 | 0.000 | 0.000 | 0.000 | 22.628 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 303 | 313 | 395 | 764 | 0 | 2231 | 0 | 0 | 1580 | 0 |
N.S. |
1 | 1.03 | 1.30 | 2.52 | 0.00 | 7.36 | 0.00 | 0.00 | 5.21 | 0.00 |
time (sec) |
N/A | 1.186 | 11.070 | 2.102 | 0.000 | 95.064 | 0.000 | 0.000 | 0.445 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 309 | 317 | 544 | 1314 | 0 | 3955 | 0 | 1210 | 3587 | 0 |
N.S. |
1 | 1.03 | 1.76 | 4.25 | 0.00 | 12.80 | 0.00 | 3.92 | 11.61 | 0.00 |
time (sec) |
N/A | 1.176 | 12.382 | 2.082 | 0.000 | 119.733 | 0.000 | 0.407 | 0.520 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 390 | 490 | 485 | 2272 | 0 | 0 | 0 | 2889 | 6959 | 0 |
N.S. |
1 | 1.26 | 1.24 | 5.83 | 0.00 | 0.00 | 0.00 | 7.41 | 17.84 | 0.00 |
time (sec) |
N/A | 1.650 | 13.012 | 2.407 | 0.000 | 0.000 | 0.000 | 4.364 | 1.339 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 446 | 387 | 345 | 1422 | 0 | 2343 | 21208 | 1341 | 28 | 0 |
N.S. |
1 | 0.87 | 0.77 | 3.19 | 0.00 | 5.25 | 47.55 | 3.01 | 0.06 | 0.00 |
time (sec) |
N/A | 1.182 | 11.127 | 2.031 | 0.000 | 0.380 | 1.596 | 0.201 | 200.039 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 289 | 282 | 596 | 851 | 0 | 1523 | 10924 | 827 | 1813 | 0 |
N.S. |
1 | 0.98 | 2.06 | 2.94 | 0.00 | 5.27 | 37.80 | 2.86 | 6.27 | 0.00 |
time (sec) |
N/A | 0.817 | 10.402 | 1.799 | 0.000 | 0.265 | 1.231 | 0.286 | 11.891 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 213 | 342 | 418 | 0 | 841 | 4765 | 425 | 904 | 0 |
N.S. |
1 | 1.08 | 1.73 | 2.11 | 0.00 | 4.25 | 24.07 | 2.15 | 4.57 | 0.00 |
time (sec) |
N/A | 0.603 | 5.929 | 1.665 | 0.000 | 0.146 | 1.262 | 0.179 | 7.775 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 17 | 15 | 14 | 86 | 243 | 14 | 91 | 14 |
N.S. |
1 | 1.00 | 0.94 | 0.83 | 0.78 | 4.78 | 13.50 | 0.78 | 5.06 | 0.78 |
time (sec) |
N/A | 0.236 | 0.036 | 1.500 | 0.026 | 0.089 | 0.208 | 0.189 | 0.222 | 11.783 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 627 | 658 | 607 | 998 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.05 | 0.97 | 1.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 2.630 | 11.792 | 2.019 | 0.000 | 0.000 | 0.000 | 0.000 | 200.035 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 508 | 531 | 659 | 1192 | 0 | 0 | 0 | 0 | 3512 | 0 |
N.S. |
1 | 1.05 | 1.30 | 2.35 | 0.00 | 0.00 | 0.00 | 0.00 | 6.91 | 0.00 |
time (sec) |
N/A | 1.995 | 12.505 | 2.132 | 0.000 | 0.000 | 0.000 | 0.000 | 0.456 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 464 | 481 | 535 | 1703 | 0 | 0 | 0 | 2125 | 3831 | 0 |
N.S. |
1 | 1.04 | 1.15 | 3.67 | 0.00 | 0.00 | 0.00 | 4.58 | 8.26 | 0.00 |
time (sec) |
N/A | 1.975 | 12.378 | 2.326 | 0.000 | 0.000 | 0.000 | 0.500 | 6.856 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 473 | 491 | 535 | 2650 | 0 | 0 | 0 | 3027 | 7348 | 0 |
N.S. |
1 | 1.04 | 1.13 | 5.60 | 0.00 | 0.00 | 0.00 | 6.40 | 15.53 | 0.00 |
time (sec) |
N/A | 1.794 | 13.187 | 2.462 | 0.000 | 0.000 | 0.000 | 4.675 | 1.299 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 258 | 202 | 248 | 0 | 545 | 806 | 261 | 624 | 0 |
N.S. |
1 | 1.05 | 0.82 | 1.01 | 0.00 | 2.22 | 3.29 | 1.07 | 2.55 | 0.00 |
time (sec) |
N/A | 0.875 | 1.834 | 1.915 | 0.000 | 0.144 | 1.118 | 0.168 | 0.495 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 153 | 128 | 134 | 0 | 335 | 468 | 146 | 330 | 0 |
N.S. |
1 | 1.03 | 0.86 | 0.91 | 0.00 | 2.26 | 3.16 | 0.99 | 2.23 | 0.00 |
time (sec) |
N/A | 0.545 | 1.063 | 1.714 | 0.000 | 0.114 | 1.039 | 0.200 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 84 | 73 | 0 | 197 | 236 | 78 | 143 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.00 | 2.35 | 2.81 | 0.93 | 1.70 | 0.00 |
time (sec) |
N/A | 0.389 | 0.834 | 1.472 | 0.000 | 0.110 | 1.141 | 0.199 | 0.243 | 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 | 16 | 16 | 15 | 15 | 14 | 14 | 14 | 14 | 13 | 14 |
N.S. |
1 | 1.00 | 0.94 | 0.94 | 0.88 | 0.88 | 0.88 | 0.88 | 0.81 | 0.88 |
time (sec) |
N/A | 0.247 | 0.026 | 1.540 | 0.032 | 0.087 | 0.064 | 0.161 | 0.237 | 12.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 133 | 198 | 199 | 0 | 1048 | 0 | 0 | 6657 | 0 |
N.S. |
1 | 1.00 | 1.49 | 1.50 | 0.00 | 7.88 | 0.00 | 0.00 | 50.05 | 0.00 |
time (sec) |
N/A | 0.498 | 1.076 | 1.799 | 0.000 | 1.008 | 0.000 | 0.000 | 0.350 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 141 | 150 | 437 | 0 | 686 | 0 | 0 | 632 | 0 |
N.S. |
1 | 1.00 | 1.06 | 3.10 | 0.00 | 4.87 | 0.00 | 0.00 | 4.48 | 0.00 |
time (sec) |
N/A | 0.500 | 0.891 | 1.779 | 0.000 | 0.214 | 0.000 | 0.000 | 0.486 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 225 | 245 | 220 | 842 | 0 | 1500 | 0 | 1068 | 2088 | 0 |
N.S. |
1 | 1.09 | 0.98 | 3.74 | 0.00 | 6.67 | 0.00 | 4.75 | 9.28 | 0.00 |
time (sec) |
N/A | 0.792 | 10.369 | 1.886 | 0.000 | 0.611 | 0.000 | 0.228 | 0.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 328 | 0 | 323 | 1537 | 0 | 2998 | 0 | 2742 | 4974 | 0 |
N.S. |
1 | 0.00 | 0.98 | 4.69 | 0.00 | 9.14 | 0.00 | 8.36 | 15.16 | 0.00 |
time (sec) |
N/A | 0.000 | 10.594 | 2.160 | 0.000 | 3.190 | 0.000 | 0.299 | 1.446 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 209 | 247 | 634 | 0 | 965 | 0 | 573 | 1572 | 0 |
N.S. |
1 | 1.03 | 1.22 | 3.14 | 0.00 | 4.78 | 0.00 | 2.84 | 7.78 | 0.00 |
time (sec) |
N/A | 0.690 | 4.755 | 2.171 | 0.000 | 0.349 | 0.000 | 0.226 | 5.969 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 160 | 166 | 442 | 0 | 615 | 0 | 360 | 962 | 0 |
N.S. |
1 | 1.24 | 1.29 | 3.43 | 0.00 | 4.77 | 0.00 | 2.79 | 7.46 | 0.00 |
time (sec) |
N/A | 0.566 | 1.818 | 1.953 | 0.000 | 0.271 | 0.000 | 0.260 | 0.348 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 95 | 97 | 165 | 0 | 363 | 0 | 199 | 449 | 0 |
N.S. |
1 | 1.02 | 1.04 | 1.77 | 0.00 | 3.90 | 0.00 | 2.14 | 4.83 | 0.00 |
time (sec) |
N/A | 0.387 | 0.943 | 1.688 | 0.000 | 0.200 | 0.000 | 0.204 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 60 | 211 | 0 | 211 | 0 | 96 | 198 | 161 |
N.S. |
1 | 1.00 | 1.00 | 3.52 | 0.00 | 3.52 | 0.00 | 1.60 | 3.30 | 2.68 |
time (sec) |
N/A | 0.321 | 0.605 | 1.404 | 0.000 | 0.163 | 0.000 | 0.205 | 0.221 | 13.390 |
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 | 16 | 16 | 15 | 15 | 14 | 14 | 15 | 14 | 25 | 14 |
N.S. |
1 | 1.00 | 0.94 | 0.94 | 0.88 | 0.88 | 0.94 | 0.88 | 1.56 | 0.88 |
time (sec) |
N/A | 0.243 | 0.029 | 1.457 | 0.035 | 0.089 | 0.095 | 0.199 | 0.242 | 12.013 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 166 | 133 | 445 | 0 | 918 | 0 | 515 | 28 | 0 |
N.S. |
1 | 1.20 | 0.96 | 3.22 | 0.00 | 6.65 | 0.00 | 3.73 | 0.20 | 0.00 |
time (sec) |
N/A | 0.538 | 1.506 | 2.114 | 0.000 | 0.370 | 0.000 | 0.202 | 200.034 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 220 | 267 | 215 | 1065 | 0 | 2102 | 0 | 0 | 3321 | 0 |
N.S. |
1 | 1.21 | 0.98 | 4.84 | 0.00 | 9.55 | 0.00 | 0.00 | 15.10 | 0.00 |
time (sec) |
N/A | 0.797 | 10.589 | 1.849 | 0.000 | 1.277 | 0.000 | 0.000 | 0.699 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 220 | 346 | 1960 | 0 | 1493 | 0 | 781 | 28 | 0 |
N.S. |
1 | 1.06 | 1.66 | 9.42 | 0.00 | 7.18 | 0.00 | 3.75 | 0.13 | 0.00 |
time (sec) |
N/A | 0.681 | 3.705 | 2.136 | 0.000 | 0.812 | 0.000 | 0.249 | 200.034 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 169 | 231 | 1152 | 0 | 958 | 0 | 502 | 1331 | 0 |
N.S. |
1 | 1.17 | 1.60 | 8.00 | 0.00 | 6.65 | 0.00 | 3.49 | 9.24 | 0.00 |
time (sec) |
N/A | 0.590 | 2.537 | 1.936 | 0.000 | 0.700 | 0.000 | 0.211 | 0.377 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 110 | 123 | 0 | 194 | 0 | 289 | 483 | 122 |
N.S. |
1 | 1.00 | 1.49 | 1.66 | 0.00 | 2.62 | 0.00 | 3.91 | 6.53 | 1.65 |
time (sec) |
N/A | 0.352 | 1.819 | 1.675 | 0.000 | 0.593 | 0.000 | 0.222 | 0.340 | 12.092 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 64 | 67 | 0 | 145 | 0 | 197 | 266 | 66 |
N.S. |
1 | 1.00 | 1.08 | 1.14 | 0.00 | 2.46 | 0.00 | 3.34 | 4.51 | 1.12 |
time (sec) |
N/A | 0.306 | 1.415 | 1.454 | 0.000 | 0.512 | 0.000 | 0.209 | 0.244 | 12.163 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 17 | 15 | 14 | 51 | 76 | 14 | 56 | 14 |
N.S. |
1 | 1.00 | 0.94 | 0.83 | 0.78 | 2.83 | 4.22 | 0.78 | 3.11 | 0.78 |
time (sec) |
N/A | 0.244 | 0.032 | 1.331 | 0.027 | 0.172 | 0.457 | 0.191 | 0.211 | 11.890 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 263 | 312 | 249 | 847 | 0 | 3858 | 0 | 8951 | 28 | 0 |
N.S. |
1 | 1.19 | 0.95 | 3.22 | 0.00 | 14.67 | 0.00 | 34.03 | 0.11 | 0.00 |
time (sec) |
N/A | 0.856 | 10.476 | 1.789 | 0.000 | 1.469 | 0.000 | 0.465 | 200.039 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | F(-2) | B | F(-1) | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 379 | 0 | 384 | 1919 | 0 | 7442 | 0 | 6874 | 12005 | 0 |
N.S. |
1 | 0.00 | 1.01 | 5.06 | 0.00 | 19.64 | 0.00 | 18.14 | 31.68 | 0.00 |
time (sec) |
N/A | 0.000 | 11.299 | 1.901 | 0.000 | 5.633 | 0.000 | 0.784 | 1.424 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 560 | 588 | 5323 | 1221 | 0 | 586 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.05 | 9.51 | 2.18 | 0.00 | 1.05 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.692 | 34.840 | 3.930 | 0.000 | 0.092 | 0.000 | 0.000 | 200.039 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 467 | 491 | 709 | 950 | 0 | 482 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.05 | 1.52 | 2.03 | 0.00 | 1.03 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.213 | 32.358 | 3.800 | 0.000 | 0.091 | 0.000 | 0.000 | 200.035 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 449 | 473 | 955 | 957 | 0 | 502 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.05 | 2.13 | 2.13 | 0.00 | 1.12 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.120 | 30.373 | 6.994 | 0.000 | 0.092 | 0.000 | 0.000 | 200.031 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 540 | 575 | 811 | 1092 | 0 | 835 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 1.50 | 2.02 | 0.00 | 1.55 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.430 | 34.095 | 4.449 | 0.000 | 0.101 | 0.000 | 0.000 | 41.615 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 674 | 715 | 5427 | 1311 | 0 | 1513 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.06 | 8.05 | 1.95 | 0.00 | 2.24 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.930 | 35.142 | 5.737 | 0.000 | 0.143 | 0.000 | 0.000 | 200.033 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 668 | 703 | 7917 | 1704 | 0 | 729 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.05 | 11.85 | 2.55 | 0.00 | 1.09 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.884 | 35.325 | 6.965 | 0.000 | 0.102 | 0.000 | 0.000 | 200.031 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 572 | 603 | 5373 | 1720 | 0 | 829 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.05 | 9.39 | 3.01 | 0.00 | 1.45 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.625 | 35.328 | 7.688 | 0.000 | 0.111 | 0.000 | 0.000 | 200.041 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 553 | 585 | 8929 | 1402 | 0 | 824 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 16.15 | 2.54 | 0.00 | 1.49 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.562 | 35.249 | 12.032 | 0.000 | 0.106 | 0.000 | 0.000 | 104.876 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 655 | 716 | 5450 | 1427 | 0 | 1421 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.09 | 8.32 | 2.18 | 0.00 | 2.17 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.957 | 24.431 | 17.687 | 0.000 | 0.138 | 0.000 | 0.000 | 200.034 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 580 | 617 | 5339 | 1251 | 0 | 591 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.06 | 9.21 | 2.16 | 0.00 | 1.02 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.797 | 35.024 | 5.896 | 0.000 | 0.094 | 0.000 | 0.000 | 200.043 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 487 | 516 | 693 | 956 | 0 | 483 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.06 | 1.42 | 1.96 | 0.00 | 0.99 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.304 | 32.470 | 5.255 | 0.000 | 0.094 | 0.000 | 0.000 | 200.042 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 421 | 441 | 933 | 796 | 0 | 418 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.05 | 2.22 | 1.89 | 0.00 | 0.99 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.972 | 30.549 | 3.132 | 0.000 | 0.095 | 0.000 | 0.000 | 200.032 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 371 | 391 | 793 | 746 | 0 | 358 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.05 | 2.14 | 2.01 | 0.00 | 0.96 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.799 | 26.512 | 4.165 | 0.000 | 0.095 | 0.000 | 0.000 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 438 | 483 | 625 | 914 | 0 | 537 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.10 | 1.43 | 2.09 | 0.00 | 1.23 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.074 | 25.106 | 6.134 | 0.000 | 0.090 | 0.000 | 0.000 | 200.036 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 561 | 606 | 1242 | 1097 | 0 | 949 | 0 | 0 | 255 | 0 |
N.S. |
1 | 1.08 | 2.21 | 1.96 | 0.00 | 1.69 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 1.429 | 23.435 | 8.429 | 0.000 | 0.109 | 0.000 | 0.000 | 29.521 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 520 | 549 | 943 | 1346 | 0 | 805 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.06 | 1.81 | 2.59 | 0.00 | 1.55 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.423 | 31.175 | 14.027 | 0.000 | 0.111 | 0.000 | 0.000 | 200.033 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 448 | 472 | 627 | 1023 | 0 | 598 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.05 | 1.40 | 2.28 | 0.00 | 1.33 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.111 | 27.938 | 14.147 | 0.000 | 0.102 | 0.000 | 0.000 | 200.031 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 216 | 378 | 797 | 0 | 454 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.05 | 1.83 | 3.87 | 0.00 | 2.20 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.546 | 11.928 | 5.016 | 0.000 | 0.103 | 0.000 | 0.000 | 200.042 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 216 | 318 | 363 | 0 | 173 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.05 | 1.54 | 1.76 | 0.00 | 0.84 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.551 | 13.474 | 2.177 | 0.000 | 0.081 | 0.000 | 0.000 | 200.045 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 290 | 405 | 932 | 0 | 518 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.15 | 1.61 | 3.70 | 0.00 | 2.06 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.748 | 12.158 | 6.542 | 0.000 | 0.091 | 0.000 | 0.000 | 200.055 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 511 | 584 | 672 | 1286 | 0 | 1071 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.14 | 1.32 | 2.52 | 0.00 | 2.10 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.406 | 16.268 | 11.207 | 0.000 | 0.109 | 0.000 | 0.000 | 200.047 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 553 | 585 | 1338 | 1265 | 0 | 1303 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.06 | 2.42 | 2.29 | 0.00 | 2.36 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.416 | 19.272 | 7.576 | 0.000 | 0.133 | 0.000 | 0.000 | 200.055 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 474 | 509 | 1150 | 1067 | 0 | 959 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.07 | 2.43 | 2.25 | 0.00 | 2.02 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.098 | 21.457 | 6.666 | 0.000 | 0.120 | 0.000 | 0.000 | 200.046 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 436 | 475 | 928 | 912 | 0 | 671 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.09 | 2.13 | 2.09 | 0.00 | 1.54 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.030 | 17.925 | 6.533 | 0.000 | 0.146 | 0.000 | 0.000 | 200.040 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 497 | 555 | 1151 | 1261 | 0 | 1225 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.12 | 2.32 | 2.54 | 0.00 | 2.46 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.212 | 20.776 | 2.292 | 0.000 | 0.210 | 0.000 | 0.000 | 200.033 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 617 | 704 | 3575 | 1552 | 0 | 1918 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.14 | 5.79 | 2.52 | 0.00 | 3.11 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.710 | 23.637 | 12.174 | 0.000 | 0.154 | 0.000 | 0.000 | 200.037 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 449 | 449 | 1112 | 4284 | 1772 | 4607 | 76621 | 9691 | 6725 | 4573 |
N.S. |
1 | 1.00 | 2.48 | 9.54 | 3.95 | 10.26 | 170.65 | 21.58 | 14.98 | 10.18 |
time (sec) |
N/A | 1.268 | 3.467 | 1.589 | 0.104 | 0.148 | 16.061 | 0.205 | 0.234 | 14.528 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 270 | 408 | 1668 | 802 | 1750 | 23525 | 3633 | 2444 | 1825 |
N.S. |
1 | 1.00 | 1.51 | 6.18 | 2.97 | 6.48 | 87.13 | 13.46 | 9.05 | 6.76 |
time (sec) |
N/A | 0.827 | 1.231 | 1.458 | 0.079 | 0.109 | 4.404 | 0.164 | 0.240 | 13.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 143 | 134 | 424 | 287 | 511 | 4760 | 978 | 621 | 554 |
N.S. |
1 | 1.00 | 0.94 | 2.97 | 2.01 | 3.57 | 33.29 | 6.84 | 4.34 | 3.87 |
time (sec) |
N/A | 0.533 | 0.298 | 0.823 | 0.047 | 0.086 | 1.220 | 0.119 | 0.226 | 12.150 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 167 | 152 | 0 | 0 | 0 | 0 | 0 | 285 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.71 | 0.00 |
time (sec) |
N/A | 0.760 | 0.389 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.248 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 330 | 318 | 287 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.034 | 0.749 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.402 | 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 | 73 | 73 | 73 | 58 | 57 | 57 | 70 | 57 | 59 | 57 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.78 | 0.78 | 0.96 | 0.78 | 0.81 | 0.78 |
time (sec) |
N/A | 0.362 | 0.004 | 1.108 | 0.032 | 0.068 | 0.022 | 0.134 | 0.243 | 0.071 |
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 | 60 | 60 | 60 | 47 | 46 | 46 | 56 | 46 | 47 | 46 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 0.77 | 0.77 | 0.93 | 0.77 | 0.78 | 0.77 |
time (sec) |
N/A | 0.338 | 0.003 | 1.182 | 0.031 | 0.067 | 0.021 | 0.112 | 0.242 | 0.033 |
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 | 47 | 44 | 44 | 35 | 34 | 34 | 37 | 34 | 35 | 34 |
N.S. |
1 | 0.94 | 0.94 | 0.74 | 0.72 | 0.72 | 0.79 | 0.72 | 0.74 | 0.72 |
time (sec) |
N/A | 0.318 | 0.003 | 1.149 | 0.031 | 0.073 | 0.020 | 0.135 | 0.276 | 0.024 |
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 | 31 | 28 | 28 | 23 | 22 | 22 | 22 | 22 | 23 | 22 |
N.S. |
1 | 0.90 | 0.90 | 0.74 | 0.71 | 0.71 | 0.71 | 0.71 | 0.74 | 0.71 |
time (sec) |
N/A | 0.280 | 0.002 | 0.154 | 0.027 | 0.062 | 0.018 | 0.151 | 0.252 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 49 | 53 | 47 | 47 | 201 | 53 | 71 | 78 |
N.S. |
1 | 1.00 | 0.91 | 0.98 | 0.87 | 0.87 | 3.72 | 0.98 | 1.31 | 1.44 |
time (sec) |
N/A | 0.376 | 0.030 | 1.904 | 0.108 | 0.082 | 0.237 | 0.145 | 0.226 | 11.530 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 86 | 72 | 95 | 71 | 103 | 238 | 101 | 177 | 97 |
N.S. |
1 | 1.09 | 0.91 | 1.20 | 0.90 | 1.30 | 3.01 | 1.28 | 2.24 | 1.23 |
time (sec) |
N/A | 0.509 | 0.056 | 2.070 | 0.111 | 0.077 | 0.404 | 0.178 | 0.241 | 11.486 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 113 | 94 | 111 | 92 | 160 | 292 | 88 | 284 | 114 |
N.S. |
1 | 1.12 | 0.93 | 1.10 | 0.91 | 1.58 | 2.89 | 0.87 | 2.81 | 1.13 |
time (sec) |
N/A | 0.597 | 0.069 | 2.079 | 0.120 | 0.079 | 0.397 | 0.148 | 0.202 | 0.143 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 365 | 337 | 437 | 360 | 0 | 58 | 0 | 0 | 128 | 0 |
N.S. |
1 | 0.92 | 1.20 | 0.99 | 0.00 | 0.16 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.907 | 33.174 | 3.898 | 0.000 | 0.076 | 0.000 | 0.000 | 0.377 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 326 | 308 | 423 | 345 | 0 | 46 | 0 | 0 | 90 | 0 |
N.S. |
1 | 0.94 | 1.30 | 1.06 | 0.00 | 0.14 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.762 | 32.867 | 4.470 | 0.000 | 0.081 | 0.000 | 0.000 | 0.369 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 275 | 276 | 389 | 313 | 0 | 18 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.00 | 1.41 | 1.14 | 0.00 | 0.07 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.655 | 32.349 | 4.875 | 0.000 | 0.071 | 0.000 | 0.000 | 0.277 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 304 | 298 | 417 | 341 | 0 | 62 | 0 | 0 | 62 | 0 |
N.S. |
1 | 0.98 | 1.37 | 1.12 | 0.00 | 0.20 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.797 | 32.179 | 5.611 | 0.000 | 0.084 | 0.000 | 0.000 | 0.418 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 351 | 330 | 435 | 360 | 0 | 95 | 0 | 0 | 72 | 0 |
N.S. |
1 | 0.94 | 1.24 | 1.03 | 0.00 | 0.27 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.895 | 33.016 | 5.214 | 0.000 | 0.084 | 0.000 | 0.000 | 0.398 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 166 | 169 | 168 | 168 | 192 | 186 | 185 | 160 |
N.S. |
1 | 1.00 | 1.61 | 1.64 | 1.63 | 1.63 | 1.86 | 1.81 | 1.80 | 1.55 |
time (sec) |
N/A | 0.563 | 0.047 | 0.761 | 0.035 | 0.068 | 0.036 | 0.162 | 0.249 | 0.079 |
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 | 103 | 103 | 140 | 136 | 138 | 138 | 153 | 149 | 149 | 132 |
N.S. |
1 | 1.00 | 1.36 | 1.32 | 1.34 | 1.34 | 1.49 | 1.45 | 1.45 | 1.28 |
time (sec) |
N/A | 0.505 | 0.035 | 0.754 | 0.026 | 0.064 | 0.028 | 0.152 | 0.246 | 0.058 |
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 | 103 | 103 | 109 | 105 | 105 | 105 | 116 | 114 | 113 | 104 |
N.S. |
1 | 1.00 | 1.06 | 1.02 | 1.02 | 1.02 | 1.13 | 1.11 | 1.10 | 1.01 |
time (sec) |
N/A | 0.482 | 0.031 | 0.728 | 0.033 | 0.067 | 0.025 | 0.110 | 0.203 | 0.048 |
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 | 78 | 78 | 70 | 73 | 72 | 72 | 80 | 79 | 77 | 73 |
N.S. |
1 | 1.00 | 0.90 | 0.94 | 0.92 | 0.92 | 1.03 | 1.01 | 0.99 | 0.94 |
time (sec) |
N/A | 0.418 | 0.028 | 0.737 | 0.035 | 0.065 | 0.023 | 0.136 | 0.235 | 0.036 |
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 | 47 | 47 | 41 | 40 | 39 | 39 | 42 | 43 | 41 | 41 |
N.S. |
1 | 1.00 | 0.87 | 0.85 | 0.83 | 0.83 | 0.89 | 0.91 | 0.87 | 0.87 |
time (sec) |
N/A | 0.333 | 0.016 | 0.286 | 0.034 | 0.066 | 0.020 | 0.170 | 0.236 | 0.048 |
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 | 25 | 25 | 25 | 20 | 19 | 19 | 19 | 19 | 19 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.76 | 0.76 | 0.76 | 0.76 | 0.76 | 0.76 |
time (sec) |
N/A | 0.278 | 0.003 | 0.193 | 0.027 | 0.064 | 0.017 | 0.142 | 0.202 | 0.029 |
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 | 84 | 84 | 79 | 78 | 85 | 131 | 82 | 134 | 142 | 88 |
N.S. |
1 | 1.00 | 0.94 | 0.93 | 1.01 | 1.56 | 0.98 | 1.60 | 1.69 | 1.05 |
time (sec) |
N/A | 0.439 | 0.068 | 0.934 | 0.043 | 0.069 | 0.238 | 0.154 | 0.219 | 11.501 |
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 | 89 | 89 | 80 | 83 | 96 | 147 | 97 | 83 | 168 | 96 |
N.S. |
1 | 1.00 | 0.90 | 0.93 | 1.08 | 1.65 | 1.09 | 0.93 | 1.89 | 1.08 |
time (sec) |
N/A | 0.441 | 0.061 | 0.859 | 0.040 | 0.076 | 0.407 | 0.109 | 0.226 | 11.554 |