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 | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 67 | 52 | 67 | 0 | 163 | 170 | 73 | 42 | 94 |
N.S. |
1 | 1.24 | 0.96 | 1.24 | 0.00 | 3.02 | 3.15 | 1.35 | 0.78 | 1.74 |
time (sec) |
N/A | 0.321 | 0.086 | 0.569 | 0.000 | 0.093 | 15.708 | 0.321 | 0.209 | 17.722 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 6 | 6 | 6 | 7 | 0 | 6 | 3 | 6 | 1 | 6 |
N.S. |
1 | 1.00 | 1.00 | 1.17 | 0.00 | 1.00 | 0.50 | 1.00 | 0.17 | 1.00 |
time (sec) |
N/A | 0.149 | 0.000 | 0.207 | 0.000 | 0.070 | 0.105 | 0.363 | 0.197 | 17.428 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 26 | 0 | 12 | 0 | 32 | 12 | 24 |
N.S. |
1 | 1.00 | 1.00 | 2.17 | 0.00 | 1.00 | 0.00 | 2.67 | 1.00 | 2.00 |
time (sec) |
N/A | 0.199 | 0.066 | 0.779 | 0.000 | 0.071 | 0.000 | 0.369 | 0.200 | 17.510 |
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 | 34 | 36 | 28 | 28 | 36 | 27 | 42 | 51 | 22 | 36 |
N.S. |
1 | 1.06 | 0.82 | 0.82 | 1.06 | 0.79 | 1.24 | 1.50 | 0.65 | 1.06 |
time (sec) |
N/A | 0.244 | 0.040 | 0.309 | 0.110 | 0.079 | 0.332 | 0.340 | 0.208 | 17.511 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 258 | 203 | 375 | 0 | 795 | 0 | 450 | 825 | 8720 |
N.S. |
1 | 1.10 | 0.86 | 1.60 | 0.00 | 3.38 | 0.00 | 1.91 | 3.51 | 37.11 |
time (sec) |
N/A | 1.365 | 10.936 | 20.738 | 0.000 | 0.122 | 0.000 | 0.350 | 0.244 | 23.902 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 171 | 138 | 229 | 0 | 566 | 0 | 244 | 466 | 5902 |
N.S. |
1 | 1.10 | 0.88 | 1.47 | 0.00 | 3.63 | 0.00 | 1.56 | 2.99 | 37.83 |
time (sec) |
N/A | 0.837 | 2.697 | 3.166 | 0.000 | 0.118 | 0.000 | 0.359 | 0.201 | 22.390 |
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 | 93 | 104 | 90 | 117 | 0 | 368 | 4032 | 130 | 219 | 2628 |
N.S. |
1 | 1.12 | 0.97 | 1.26 | 0.00 | 3.96 | 43.35 | 1.40 | 2.35 | 28.26 |
time (sec) |
N/A | 0.486 | 0.910 | 1.039 | 0.000 | 0.102 | 144.454 | 0.341 | 0.204 | 20.742 |
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 | 65 | 71 | 67 | 76 | 0 | 253 | 425 | 83 | 116 | 343 |
N.S. |
1 | 1.09 | 1.03 | 1.17 | 0.00 | 3.89 | 6.54 | 1.28 | 1.78 | 5.28 |
time (sec) |
N/A | 0.319 | 0.155 | 0.625 | 0.000 | 0.118 | 15.512 | 0.365 | 0.191 | 18.792 |
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 | 47 | 53 | 47 | 47 | 0 | 190 | 144 | 60 | 53 | 42 |
N.S. |
1 | 1.13 | 1.00 | 1.00 | 0.00 | 4.04 | 3.06 | 1.28 | 1.13 | 0.89 |
time (sec) |
N/A | 0.229 | 0.025 | 0.369 | 0.000 | 0.084 | 2.627 | 0.363 | 0.205 | 17.633 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 129 | 104 | 114 | 0 | 1057 | 0 | 141 | 247 | 3281 |
N.S. |
1 | 1.10 | 0.89 | 0.97 | 0.00 | 9.03 | 0.00 | 1.21 | 2.11 | 28.04 |
time (sec) |
N/A | 0.416 | 0.342 | 1.329 | 0.000 | 0.955 | 0.000 | 0.344 | 0.216 | 18.963 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 230 | 165 | 234 | 0 | 2882 | 0 | 301 | 1480 | 24122 |
N.S. |
1 | 1.24 | 0.89 | 1.26 | 0.00 | 15.58 | 0.00 | 1.63 | 8.00 | 130.39 |
time (sec) |
N/A | 0.835 | 0.996 | 2.167 | 0.000 | 88.210 | 0.000 | 0.367 | 0.217 | 28.232 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 284 | 355 | 263 | 625 | 0 | 0 | 0 | 766 | 4848 | 62873 |
N.S. |
1 | 1.25 | 0.93 | 2.20 | 0.00 | 0.00 | 0.00 | 2.70 | 17.07 | 221.38 |
time (sec) |
N/A | 1.662 | 2.052 | 3.979 | 0.000 | 0.000 | 0.000 | 0.372 | 0.282 | 32.914 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 306 | 327 | 199 | 456 | 0 | 1451 | 0 | 502 | 1783 | 13700 |
N.S. |
1 | 1.07 | 0.65 | 1.49 | 0.00 | 4.74 | 0.00 | 1.64 | 5.83 | 44.77 |
time (sec) |
N/A | 1.764 | 7.909 | 21.130 | 0.000 | 0.158 | 0.000 | 0.398 | 0.236 | 27.584 |
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 | 205 | 233 | 151 | 303 | 0 | 1006 | 0 | 558 | 1138 | 8953 |
N.S. |
1 | 1.14 | 0.74 | 1.48 | 0.00 | 4.91 | 0.00 | 2.72 | 5.55 | 43.67 |
time (sec) |
N/A | 1.036 | 2.895 | 3.822 | 0.000 | 0.146 | 0.000 | 0.386 | 0.198 | 24.801 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 162 | 133 | 220 | 0 | 665 | 0 | 241 | 627 | 5776 |
N.S. |
1 | 1.26 | 1.03 | 1.71 | 0.00 | 5.16 | 0.00 | 1.87 | 4.86 | 44.78 |
time (sec) |
N/A | 0.614 | 0.947 | 1.197 | 0.000 | 0.119 | 0.000 | 0.373 | 0.209 | 22.595 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 103 | 96 | 144 | 0 | 399 | 0 | 151 | 289 | 215 |
N.S. |
1 | 1.06 | 0.99 | 1.48 | 0.00 | 4.11 | 0.00 | 1.56 | 2.98 | 2.22 |
time (sec) |
N/A | 0.368 | 0.449 | 1.022 | 0.000 | 0.102 | 0.000 | 0.371 | 0.197 | 17.765 |
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 | 83 | 89 | 82 | 122 | 0 | 336 | 1943 | 122 | 170 | 174 |
N.S. |
1 | 1.07 | 0.99 | 1.47 | 0.00 | 4.05 | 23.41 | 1.47 | 2.05 | 2.10 |
time (sec) |
N/A | 0.330 | 0.194 | 0.718 | 0.000 | 0.099 | 43.762 | 0.363 | 0.225 | 17.676 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 225 | 178 | 236 | 0 | 2871 | 0 | 297 | 1480 | 24123 |
N.S. |
1 | 1.24 | 0.98 | 1.30 | 0.00 | 15.86 | 0.00 | 1.64 | 8.18 | 133.28 |
time (sec) |
N/A | 0.812 | 0.939 | 2.154 | 0.000 | 71.471 | 0.000 | 0.362 | 0.243 | 27.398 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 290 | 355 | 227 | 331 | 0 | 0 | 0 | 975 | 7318 | 71320 |
N.S. |
1 | 1.22 | 0.78 | 1.14 | 0.00 | 0.00 | 0.00 | 3.36 | 25.23 | 245.93 |
time (sec) |
N/A | 1.615 | 2.466 | 7.652 | 0.000 | 0.000 | 0.000 | 0.528 | 0.381 | 32.736 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 458 | 538 | 346 | 760 | 0 | 0 | 0 | 1086 | 27 | 137274 |
N.S. |
1 | 1.17 | 0.76 | 1.66 | 0.00 | 0.00 | 0.00 | 2.37 | 0.06 | 299.72 |
time (sec) |
N/A | 2.871 | 5.694 | 16.596 | 0.000 | 0.000 | 0.000 | 0.444 | 200.026 | 42.975 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 534 | 566 | 341 | 1123 | 0 | 3174 | 0 | 3043 | 27 | 23910 |
N.S. |
1 | 1.06 | 0.64 | 2.10 | 0.00 | 5.94 | 0.00 | 5.70 | 0.05 | 44.78 |
time (sec) |
N/A | 3.535 | 12.549 | 183.451 | 0.000 | 0.261 | 0.000 | 0.436 | 200.030 | 31.760 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 318 | 362 | 894 | 854 | 0 | 2335 | 0 | 1120 | 3794 | 16958 |
N.S. |
1 | 1.14 | 2.81 | 2.69 | 0.00 | 7.34 | 0.00 | 3.52 | 11.93 | 53.33 |
time (sec) |
N/A | 1.905 | 13.591 | 22.525 | 0.000 | 0.205 | 0.000 | 0.412 | 0.222 | 27.750 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 307 | 524 | 671 | 0 | 1631 | 0 | 856 | 2592 | 11848 |
N.S. |
1 | 1.24 | 2.11 | 2.71 | 0.00 | 6.58 | 0.00 | 3.45 | 10.45 | 47.77 |
time (sec) |
N/A | 1.186 | 7.233 | 3.589 | 0.000 | 0.172 | 0.000 | 0.415 | 0.178 | 26.889 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 217 | 204 | 465 | 0 | 1025 | 0 | 586 | 1590 | 641 |
N.S. |
1 | 1.11 | 1.04 | 2.37 | 0.00 | 5.23 | 0.00 | 2.99 | 8.11 | 3.27 |
time (sec) |
N/A | 0.725 | 1.344 | 1.753 | 0.000 | 0.198 | 0.000 | 0.379 | 0.161 | 19.305 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 182 | 157 | 349 | 0 | 799 | 0 | 412 | 973 | 477 |
N.S. |
1 | 1.12 | 0.97 | 2.15 | 0.00 | 4.93 | 0.00 | 2.54 | 6.01 | 2.94 |
time (sec) |
N/A | 0.620 | 0.692 | 1.434 | 0.000 | 0.118 | 0.000 | 0.395 | 0.170 | 18.799 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 152 | 114 | 282 | 0 | 618 | 0 | 273 | 580 | 395 |
N.S. |
1 | 1.16 | 0.87 | 2.15 | 0.00 | 4.72 | 0.00 | 2.08 | 4.43 | 3.02 |
time (sec) |
N/A | 0.529 | 0.362 | 1.015 | 0.000 | 0.110 | 0.000 | 1.284 | 0.159 | 19.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 285 | 355 | 275 | 625 | 0 | 0 | 0 | 768 | 4848 | 62873 |
N.S. |
1 | 1.25 | 0.96 | 2.19 | 0.00 | 0.00 | 0.00 | 2.69 | 17.01 | 220.61 |
time (sec) |
N/A | 1.655 | 2.073 | 4.157 | 0.000 | 0.000 | 0.000 | 0.433 | 0.242 | 32.210 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 454 | 543 | 346 | 736 | 0 | 0 | 0 | 1088 | 27 | 137273 |
N.S. |
1 | 1.20 | 0.76 | 1.62 | 0.00 | 0.00 | 0.00 | 2.40 | 0.06 | 302.36 |
time (sec) |
N/A | 3.138 | 4.745 | 17.391 | 0.000 | 0.000 | 0.000 | 0.479 | 200.033 | 42.194 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | F(-1) | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 669 | 769 | 1815 | 1157 | 0 | 0 | 0 | 6885 | 27 | 571173 |
N.S. |
1 | 1.15 | 2.71 | 1.73 | 0.00 | 0.00 | 0.00 | 10.29 | 0.04 | 853.77 |
time (sec) |
N/A | 5.145 | 8.814 | 26.209 | 0.000 | 0.000 | 0.000 | 2.594 | 200.031 | 67.813 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 298 | 309 | 275 | 1835 | 0 | 567 | 0 | 0 | 150 | 0 |
N.S. |
1 | 1.04 | 0.92 | 6.16 | 0.00 | 1.90 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 1.603 | 2.094 | 6.668 | 0.000 | 0.127 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 241 | 218 | 1448 | 0 | 497 | 0 | 0 | 88 | 0 |
N.S. |
1 | 1.03 | 0.93 | 6.16 | 0.00 | 2.11 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 1.157 | 1.071 | 3.960 | 0.000 | 0.116 | 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 | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 182 | 152 | 701 | 0 | 431 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.01 | 0.84 | 3.87 | 0.00 | 2.38 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.823 | 0.657 | 2.735 | 0.000 | 0.129 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 140 | 101 | 243 | 0 | 369 | 0 | 0 | 63 | 176 |
N.S. |
1 | 1.00 | 0.72 | 1.74 | 0.00 | 2.64 | 0.00 | 0.00 | 0.45 | 1.26 |
time (sec) |
N/A | 0.605 | 3.409 | 2.895 | 0.000 | 0.097 | 0.000 | 0.000 | 0.155 | 18.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 206 | 159 | 564 | 0 | 582 | 0 | 0 | 95 | 0 |
N.S. |
1 | 1.06 | 0.82 | 2.89 | 0.00 | 2.98 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.936 | 0.620 | 2.144 | 0.000 | 0.103 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 285 | 296 | 199 | 883 | 0 | 981 | 0 | 0 | 127 | 0 |
N.S. |
1 | 1.04 | 0.70 | 3.10 | 0.00 | 3.44 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 1.334 | 1.279 | 3.096 | 0.000 | 0.120 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 369 | 395 | 297 | 1045 | 0 | 1507 | 0 | 0 | 159 | 0 |
N.S. |
1 | 1.07 | 0.80 | 2.83 | 0.00 | 4.08 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 1.844 | 2.819 | 4.069 | 0.000 | 0.167 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 451 | 461 | 382 | 2090 | 0 | 777 | 0 | 0 | 248 | 0 |
N.S. |
1 | 1.02 | 0.85 | 4.63 | 0.00 | 1.72 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 2.495 | 3.184 | 20.029 | 0.000 | 0.146 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 347 | 355 | 292 | 1556 | 0 | 659 | 0 | 0 | 150 | 0 |
N.S. |
1 | 1.02 | 0.84 | 4.48 | 0.00 | 1.90 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 1.806 | 2.683 | 5.700 | 0.000 | 0.132 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 254 | 260 | 214 | 1090 | 0 | 551 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.02 | 0.84 | 4.29 | 0.00 | 2.17 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 1.258 | 1.713 | 4.231 | 0.000 | 0.109 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 207 | 173 | 691 | 0 | 463 | 0 | 0 | 105 | 0 |
N.S. |
1 | 1.02 | 0.85 | 3.40 | 0.00 | 2.28 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.915 | 1.844 | 2.490 | 0.000 | 0.106 | 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 | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 242 | 172 | 883 | 0 | 763 | 0 | 0 | 153 | 0 |
N.S. |
1 | 1.06 | 0.75 | 3.87 | 0.00 | 3.35 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 1.053 | 1.536 | 3.984 | 0.000 | 0.118 | 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 | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 329 | 340 | 302 | 1038 | 0 | 1356 | 0 | 0 | 201 | 0 |
N.S. |
1 | 1.03 | 0.92 | 3.16 | 0.00 | 4.12 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 1.596 | 2.287 | 4.326 | 0.000 | 0.148 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 460 | 0 | 424 | 1444 | 0 | 2227 | 0 | 0 | 249 | 0 |
N.S. |
1 | 0.00 | 0.92 | 3.14 | 0.00 | 4.84 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.000 | 4.635 | 5.996 | 0.000 | 0.193 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 642 | 660 | 545 | 2695 | 0 | 1039 | 0 | 0 | 346 | 0 |
N.S. |
1 | 1.03 | 0.85 | 4.20 | 0.00 | 1.62 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 3.501 | 6.455 | 83.651 | 0.000 | 0.165 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 496 | 512 | 410 | 2090 | 0 | 869 | 0 | 0 | 212 | 0 |
N.S. |
1 | 1.03 | 0.83 | 4.21 | 0.00 | 1.75 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 2.632 | 6.122 | 10.603 | 0.000 | 0.145 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 375 | 389 | 306 | 1544 | 0 | 718 | 0 | 0 | 98 | 0 |
N.S. |
1 | 1.04 | 0.82 | 4.12 | 0.00 | 1.91 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 1.962 | 4.877 | 8.076 | 0.000 | 0.120 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 302 | 314 | 219 | 1079 | 0 | 581 | 0 | 0 | 147 | 0 |
N.S. |
1 | 1.04 | 0.73 | 3.57 | 0.00 | 1.92 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 1.456 | 4.647 | 4.925 | 0.000 | 0.111 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 361 | 369 | 311 | 1386 | 0 | 1034 | 0 | 0 | 211 | 0 |
N.S. |
1 | 1.02 | 0.86 | 3.84 | 0.00 | 2.86 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 1.873 | 3.711 | 7.758 | 0.000 | 0.140 | 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 | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 391 | 408 | 357 | 1372 | 0 | 1848 | 0 | 0 | 275 | 0 |
N.S. |
1 | 1.04 | 0.91 | 3.51 | 0.00 | 4.73 | 0.00 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 2.083 | 5.117 | 8.378 | 0.000 | 0.183 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 532 | 565 | 584 | 1614 | 0 | 2984 | 0 | 0 | 339 | 0 |
N.S. |
1 | 1.06 | 1.10 | 3.03 | 0.00 | 5.61 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 2.942 | 6.319 | 9.678 | 0.000 | 0.322 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 716 | 768 | 1127 | 2103 | 0 | 4617 | 0 | 0 | 403 | 0 |
N.S. |
1 | 1.07 | 1.57 | 2.94 | 0.00 | 6.45 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 3.998 | 10.093 | 13.378 | 0.000 | 0.394 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 296 | 312 | 606 | 1178 | 0 | 0 | 0 | 0 | 105 | 0 |
N.S. |
1 | 1.05 | 2.05 | 3.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 2.613 | 29.509 | 4.932 | 0.000 | 0.000 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 232 | 242 | 391 | 0 | 0 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.01 | 1.06 | 1.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 1.418 | 20.525 | 2.185 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 153 | 114 | 181 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 0.75 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.887 | 5.035 | 1.449 | 0.000 | 0.000 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 74 | 151 | 0 | 0 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.00 | 0.99 | 2.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.456 | 0.312 | 0.774 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 220 | 222 | 617 | 607 | 0 | 0 | 0 | 0 | 83 | 0 |
N.S. |
1 | 1.01 | 2.80 | 2.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 1.420 | 5.070 | 1.659 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 399 | 431 | 1079 | 1067 | 0 | 0 | 0 | 0 | 117 | 0 |
N.S. |
1 | 1.08 | 2.70 | 2.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 3.891 | 6.963 | 2.579 | 0.000 | 0.000 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 534 | 528 | 1109 | 1871 | 0 | 0 | 0 | 0 | 211 | 0 |
N.S. |
1 | 0.99 | 2.08 | 3.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 4.677 | 10.823 | 22.977 | 0.000 | 0.000 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 390 | 393 | 986 | 1357 | 0 | 0 | 0 | 0 | 153 | 0 |
N.S. |
1 | 1.01 | 2.53 | 3.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 3.083 | 10.646 | 21.450 | 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 | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 351 | 352 | 891 | 1022 | 0 | 0 | 0 | 0 | 95 | 0 |
N.S. |
1 | 1.00 | 2.54 | 2.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 2.655 | 6.887 | 2.660 | 0.000 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 307 | 300 | 606 | 869 | 0 | 0 | 0 | 0 | 42 | 0 |
N.S. |
1 | 0.98 | 1.97 | 2.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 2.225 | 5.173 | 2.310 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 325 | 324 | 621 | 687 | 0 | 0 | 0 | 0 | 83 | 0 |
N.S. |
1 | 1.00 | 1.91 | 2.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 2.486 | 5.332 | 1.098 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-1) | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 449 | 460 | 1057 | 1260 | 0 | 0 | 0 | 0 | 139 | 0 |
N.S. |
1 | 1.02 | 2.35 | 2.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 3.962 | 7.096 | 2.882 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-1) | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 661 | 668 | 1319 | 1723 | 0 | 0 | 0 | 0 | 195 | 0 |
N.S. |
1 | 1.01 | 2.00 | 2.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 6.263 | 8.218 | 4.645 | 0.000 | 0.000 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-1) | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 816 | 824 | 1526 | 2759 | 0 | 0 | 0 | 0 | 349 | 0 |
N.S. |
1 | 1.01 | 1.87 | 3.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 7.438 | 14.248 | 128.959 | 0.000 | 0.000 | 0.000 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 605 | 615 | 1323 | 2227 | 0 | 0 | 0 | 0 | 275 | 0 |
N.S. |
1 | 1.02 | 2.19 | 3.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 5.307 | 11.615 | 126.270 | 0.000 | 0.000 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 549 | 0 | 1149 | 1881 | 0 | 0 | 0 | 0 | 201 | 0 |
N.S. |
1 | 0.00 | 2.09 | 3.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.000 | 11.715 | 124.019 | 0.000 | 0.000 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 472 | 506 | 1001 | 1711 | 0 | 0 | 0 | 0 | 127 | 0 |
N.S. |
1 | 1.07 | 2.12 | 3.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 4.068 | 7.024 | 4.382 | 0.000 | 0.000 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 487 | 483 | 1038 | 1520 | 0 | 0 | 0 | 0 | 58 | 0 |
N.S. |
1 | 0.99 | 2.13 | 3.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 3.932 | 6.997 | 3.589 | 0.000 | 0.000 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 503 | 508 | 1069 | 864 | 0 | 0 | 0 | 0 | 117 | 0 |
N.S. |
1 | 1.01 | 2.13 | 1.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 4.128 | 7.157 | 1.506 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-1) | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 682 | 705 | 1318 | 2090 | 0 | 0 | 0 | 0 | 195 | 0 |
N.S. |
1 | 1.03 | 1.93 | 3.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 6.521 | 7.938 | 4.927 | 0.000 | 0.000 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 888 | 903 | 1978 | 262752 | 0 | 0 | 0 | 0 | 102 | 0 |
N.S. |
1 | 1.02 | 2.23 | 295.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 4.560 | 10.045 | 21.034 | 0.000 | 0.000 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 784 | 845 | 1879 | 178911 | 0 | 0 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.08 | 2.40 | 228.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 4.330 | 14.293 | 15.086 | 0.000 | 0.000 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 628 | 681 | 224699 | 101901 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.08 | 357.80 | 162.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 2.159 | 34.719 | 7.549 | 0.000 | 0.000 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 198 | 197 | 227899 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.00 | 0.99 | 1151.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.360 | 0.172 | 12.582 | 0.000 | 0.000 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 409 | 409 | 263 | 41873 | 0 | 0 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.00 | 0.64 | 102.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.983 | 11.359 | 4.898 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 489 | 501 | 2067 | 98425 | 0 | 0 | 0 | 0 | 69 | 0 |
N.S. |
1 | 1.02 | 4.23 | 201.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 1.479 | 6.557 | 10.733 | 0.000 | 0.000 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1080 | 1108 | 2091 | 366216 | 0 | 0 | 0 | 0 | 217 | 0 |
N.S. |
1 | 1.03 | 1.94 | 339.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 6.336 | 9.987 | 35.073 | 0.000 | 0.000 | 0.000 | 0.000 | 0.270 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 870 | 881 | 1952 | 262405 | 0 | 0 | 0 | 0 | 133 | 0 |
N.S. |
1 | 1.01 | 2.24 | 301.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 4.460 | 6.482 | 22.312 | 0.000 | 0.000 | 0.000 | 0.000 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 740 | 745 | 1879 | 179138 | 0 | 0 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.01 | 2.54 | 242.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 3.336 | 14.259 | 13.493 | 0.000 | 0.000 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 644 | 656 | 219398 | 355287 | 0 | 0 | 0 | 0 | 85 | 0 |
N.S. |
1 | 1.02 | 340.68 | 551.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 2.435 | 36.433 | 17.719 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 600 | 629 | 1896 | 553258 | 0 | 0 | 0 | 0 | 117 | 0 |
N.S. |
1 | 1.05 | 3.16 | 922.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 1.794 | 14.437 | 23.217 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 497 | 509 | 2012 | 92145 | 0 | 0 | 0 | 0 | 149 | 0 |
N.S. |
1 | 1.02 | 4.05 | 185.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 1.539 | 6.509 | 10.730 | 0.000 | 0.000 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1295 | 1329 | 2276 | 477743 | 0 | 0 | 0 | 0 | 348 | 0 |
N.S. |
1 | 1.03 | 1.76 | 368.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 7.932 | 13.247 | 58.568 | 0.000 | 0.000 | 0.000 | 0.000 | 0.352 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1071 | 1105 | 2091 | 366209 | 0 | 0 | 0 | 0 | 217 | 0 |
N.S. |
1 | 1.03 | 1.95 | 341.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 5.990 | 9.513 | 40.539 | 0.000 | 0.000 | 0.000 | 0.000 | 0.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 894 | 908 | 1979 | 265389 | 0 | 0 | 0 | 0 | 102 | 0 |
N.S. |
1 | 1.02 | 2.21 | 296.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 4.495 | 10.042 | 20.524 | 0.000 | 0.000 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 745 | 758 | 1894 | 473575 | 0 | 0 | 0 | 0 | 138 | 0 |
N.S. |
1 | 1.02 | 2.54 | 635.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 3.421 | 17.729 | 29.137 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 780 | 819 | 2006 | 562817 | 0 | 0 | 0 | 0 | 186 | 0 |
N.S. |
1 | 1.05 | 2.57 | 721.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 3.980 | 9.372 | 36.773 | 0.000 | 0.000 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 737 | 795 | 2169 | 709455 | 0 | 0 | 0 | 0 | 234 | 0 |
N.S. |
1 | 1.08 | 2.94 | 962.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 3.164 | 9.651 | 56.631 | 0.000 | 0.000 | 0.000 | 0.000 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 772 | 786 | 1894 | 480579 | 0 | 0 | 0 | 0 | 138 | 0 |
N.S. |
1 | 1.02 | 2.45 | 622.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 3.460 | 18.273 | 26.695 | 0.000 | 0.000 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 644 | 658 | 219398 | 357709 | 0 | 0 | 0 | 0 | 85 | 0 |
N.S. |
1 | 1.02 | 340.68 | 555.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 2.445 | 36.657 | 19.512 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 198 | 197 | 227847 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.00 | 0.99 | 1150.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.347 | 0.194 | 12.756 | 0.000 | 0.000 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 192 | 191 | 1084 | 0 | 0 | 0 | 0 | 60 | 0 |
N.S. |
1 | 1.00 | 0.99 | 5.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.345 | 0.161 | 10.088 | 0.000 | 0.000 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 405 | 405 | 88729 | 37684 | 0 | 0 | 0 | 0 | 94 | 0 |
N.S. |
1 | 1.00 | 219.08 | 93.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.931 | 36.110 | 11.973 | 0.000 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 521 | 543 | 2102 | 105868 | 0 | 0 | 0 | 0 | 128 | 0 |
N.S. |
1 | 1.04 | 4.03 | 203.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 1.521 | 6.569 | 15.402 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 822 | 835 | 2005 | 625429 | 0 | 0 | 0 | 0 | 186 | 0 |
N.S. |
1 | 1.02 | 2.44 | 760.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 3.722 | 9.447 | 46.710 | 0.000 | 0.000 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 600 | 628 | 1896 | 631467 | 0 | 0 | 0 | 0 | 117 | 0 |
N.S. |
1 | 1.05 | 3.16 | 1052.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 1.723 | 14.291 | 22.859 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 409 | 409 | 226 | 42557 | 0 | 0 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.00 | 0.55 | 104.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.976 | 8.809 | 4.995 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 405 | 405 | 88729 | 36512 | 0 | 0 | 0 | 0 | 94 | 0 |
N.S. |
1 | 1.00 | 219.08 | 90.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.958 | 39.076 | 11.822 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 495 | 528 | 2082 | 107309 | 0 | 0 | 0 | 0 | 150 | 0 |
N.S. |
1 | 1.07 | 4.21 | 216.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 1.509 | 6.765 | 14.810 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 0.000 |