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 | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 205 | 176 | 179 | 217 | 174 | 0 | 672 | 156 | 277 |
N.S. |
1 | 0.93 | 0.80 | 0.81 | 0.98 | 0.79 | 0.00 | 3.04 | 0.71 | 1.25 |
time (sec) |
N/A | 1.270 | 2.309 | 1.251 | 0.041 | 0.097 | 0.000 | 0.176 | 0.151 | 11.557 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 334 | 348 | 244 | 277 | 474 | 327 | 0 | 1186 | 922 | 709 |
N.S. |
1 | 1.04 | 0.73 | 0.83 | 1.42 | 0.98 | 0.00 | 3.55 | 2.76 | 2.12 |
time (sec) |
N/A | 1.908 | 1.889 | 4.608 | 0.049 | 0.108 | 0.000 | 0.220 | 0.152 | 14.643 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 266 | 203 | 237 | 379 | 281 | 0 | 850 | 773 | 555 |
N.S. |
1 | 1.06 | 0.81 | 0.95 | 1.52 | 1.12 | 0.00 | 3.40 | 3.09 | 2.22 |
time (sec) |
N/A | 1.463 | 4.281 | 1.948 | 0.047 | 0.101 | 0.000 | 0.204 | 0.154 | 14.759 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 212 | 226 | 206 | 303 | 250 | 0 | 635 | 625 | 1969 |
N.S. |
1 | 1.06 | 1.13 | 1.03 | 1.52 | 1.25 | 0.00 | 3.18 | 3.12 | 9.84 |
time (sec) |
N/A | 0.768 | 0.689 | 1.604 | 0.043 | 0.109 | 0.000 | 0.191 | 0.154 | 13.861 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 202 | 469 | 209 | 245 | 219 | 0 | 387 | 436 | 636 |
N.S. |
1 | 1.04 | 2.41 | 1.07 | 1.26 | 1.12 | 0.00 | 1.98 | 2.24 | 3.26 |
time (sec) |
N/A | 0.810 | 7.337 | 1.477 | 0.042 | 0.103 | 0.000 | 0.193 | 0.191 | 14.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 209 | 208 | 310 | 187 | 209 | 202 | 0 | 528 | 380 | 330 |
N.S. |
1 | 1.00 | 1.48 | 0.89 | 1.00 | 0.97 | 0.00 | 2.53 | 1.82 | 1.58 |
time (sec) |
N/A | 0.905 | 3.234 | 1.230 | 0.045 | 0.104 | 0.000 | 0.186 | 0.152 | 12.857 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 203 | 257 | 189 | 197 | 196 | 0 | 371 | 213 | 2523 |
N.S. |
1 | 1.03 | 1.30 | 0.95 | 0.99 | 0.99 | 0.00 | 1.87 | 1.08 | 12.74 |
time (sec) |
N/A | 1.479 | 2.676 | 1.194 | 0.040 | 0.104 | 0.000 | 0.198 | 0.152 | 12.643 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 228 | 210 | 189 | 215 | 183 | 0 | 603 | 183 | 369 |
N.S. |
1 | 1.06 | 0.97 | 0.88 | 1.00 | 0.85 | 0.00 | 2.79 | 0.85 | 1.71 |
time (sec) |
N/A | 1.484 | 1.834 | 1.083 | 0.043 | 0.107 | 0.000 | 0.190 | 0.158 | 11.707 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 271 | 263 | 201 | 246 | 197 | 0 | 791 | 168 | 307 |
N.S. |
1 | 1.05 | 1.02 | 0.78 | 0.95 | 0.76 | 0.00 | 3.07 | 0.65 | 1.19 |
time (sec) |
N/A | 1.560 | 1.540 | 1.237 | 0.042 | 0.093 | 0.000 | 0.200 | 0.156 | 11.450 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 309 | 287 | 333 | 247 | 307 | 243 | 0 | 1127 | 227 | 403 |
N.S. |
1 | 0.93 | 1.08 | 0.80 | 0.99 | 0.79 | 0.00 | 3.65 | 0.73 | 1.30 |
time (sec) |
N/A | 1.876 | 2.846 | 1.719 | 0.044 | 0.096 | 0.000 | 0.202 | 0.158 | 13.200 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 204 | 422 | 335 | 0 | 743 | 0 | 412 | 43 | 4667 |
N.S. |
1 | 1.09 | 2.26 | 1.79 | 0.00 | 3.97 | 0.00 | 2.20 | 0.23 | 24.96 |
time (sec) |
N/A | 1.470 | 2.178 | 0.588 | 0.000 | 0.496 | 0.000 | 0.183 | 0.187 | 16.787 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 155 | 300 | 229 | 0 | 609 | 0 | 269 | 95 | 4047 |
N.S. |
1 | 1.08 | 2.10 | 1.60 | 0.00 | 4.26 | 0.00 | 1.88 | 0.66 | 28.30 |
time (sec) |
N/A | 1.002 | 1.795 | 0.464 | 0.000 | 2.478 | 0.000 | 0.182 | 0.149 | 15.777 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 95 | 130 | 144 | 0 | 472 | 0 | 176 | 18 | 719 |
N.S. |
1 | 0.97 | 1.33 | 1.47 | 0.00 | 4.82 | 0.00 | 1.80 | 0.18 | 7.34 |
time (sec) |
N/A | 0.634 | 0.803 | 0.357 | 0.000 | 0.186 | 0.000 | 0.172 | 0.160 | 12.423 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 112 | 92 | 0 | 316 | 0 | 127 | 31 | 573 |
N.S. |
1 | 1.00 | 1.47 | 1.21 | 0.00 | 4.16 | 0.00 | 1.67 | 0.41 | 7.54 |
time (sec) |
N/A | 0.467 | 0.381 | 0.286 | 0.000 | 0.428 | 0.000 | 0.162 | 0.152 | 12.583 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 68 | 73 | 0 | 250 | 0 | 274 | 1 | 573 |
N.S. |
1 | 1.00 | 1.01 | 1.09 | 0.00 | 3.73 | 0.00 | 4.09 | 0.01 | 8.55 |
time (sec) |
N/A | 0.386 | 0.141 | 0.190 | 0.000 | 0.097 | 0.000 | 0.164 | 0.150 | 12.699 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 87 | 85 | 111 | 0 | 328 | 0 | 141 | 10 | 740 |
N.S. |
1 | 0.97 | 0.94 | 1.23 | 0.00 | 3.64 | 0.00 | 1.57 | 0.11 | 8.22 |
time (sec) |
N/A | 0.440 | 0.581 | 0.313 | 0.000 | 0.102 | 0.000 | 0.147 | 0.149 | 13.168 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 145 | 121 | 168 | 0 | 427 | 0 | 227 | 22 | 3740 |
N.S. |
1 | 1.08 | 0.90 | 1.25 | 0.00 | 3.19 | 0.00 | 1.69 | 0.16 | 27.91 |
time (sec) |
N/A | 0.941 | 0.704 | 0.435 | 0.000 | 0.106 | 0.000 | 0.161 | 0.149 | 15.492 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 195 | 152 | 242 | 0 | 547 | 0 | 360 | 23 | 4572 |
N.S. |
1 | 1.10 | 0.85 | 1.36 | 0.00 | 3.07 | 0.00 | 2.02 | 0.13 | 25.69 |
time (sec) |
N/A | 1.358 | 0.878 | 0.605 | 0.000 | 0.122 | 0.000 | 0.213 | 0.173 | 16.749 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 240 | 265 | 202 | 381 | 0 | 685 | 0 | 642 | 40 | 5903 |
N.S. |
1 | 1.10 | 0.84 | 1.59 | 0.00 | 2.85 | 0.00 | 2.68 | 0.17 | 24.60 |
time (sec) |
N/A | 1.971 | 1.018 | 0.855 | 0.000 | 0.130 | 0.000 | 0.241 | 0.154 | 18.503 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 272 | 286 | 438 | 330 | 0 | 1343 | 0 | 384 | 479 | 6678 |
N.S. |
1 | 1.05 | 1.61 | 1.21 | 0.00 | 4.94 | 0.00 | 1.41 | 1.76 | 24.55 |
time (sec) |
N/A | 1.835 | 6.959 | 0.830 | 0.000 | 10.787 | 0.000 | 0.226 | 0.165 | 21.128 |
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 | 164 | 194 | 240 | 245 | 0 | 1114 | 0 | 404 | 200 | 5436 |
N.S. |
1 | 1.18 | 1.46 | 1.49 | 0.00 | 6.79 | 0.00 | 2.46 | 1.22 | 33.15 |
time (sec) |
N/A | 1.237 | 1.923 | 0.622 | 0.000 | 6.731 | 0.000 | 0.254 | 0.161 | 19.523 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 158 | 191 | 185 | 0 | 694 | 0 | 231 | 136 | 3751 |
N.S. |
1 | 1.21 | 1.46 | 1.41 | 0.00 | 5.30 | 0.00 | 1.76 | 1.04 | 28.63 |
time (sec) |
N/A | 0.853 | 0.797 | 0.435 | 0.000 | 2.057 | 0.000 | 0.210 | 0.156 | 18.554 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 111 | 97 | 132 | 0 | 389 | 0 | 172 | 64 | 106 |
N.S. |
1 | 1.11 | 0.97 | 1.32 | 0.00 | 3.89 | 0.00 | 1.72 | 0.64 | 1.06 |
time (sec) |
N/A | 0.495 | 0.393 | 0.233 | 0.000 | 0.112 | 0.000 | 0.168 | 0.154 | 11.939 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 149 | 155 | 168 | 0 | 561 | 0 | 201 | 83 | 3763 |
N.S. |
1 | 1.20 | 1.25 | 1.35 | 0.00 | 4.52 | 0.00 | 1.62 | 0.67 | 30.35 |
time (sec) |
N/A | 0.703 | 0.964 | 0.260 | 0.000 | 0.119 | 0.000 | 0.216 | 0.194 | 18.661 |
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 | 180 | 199 | 221 | 213 | 0 | 789 | 0 | 1107 | 120 | 3264 |
N.S. |
1 | 1.11 | 1.23 | 1.18 | 0.00 | 4.38 | 0.00 | 6.15 | 0.67 | 18.13 |
time (sec) |
N/A | 1.139 | 1.574 | 0.487 | 0.000 | 0.129 | 0.000 | 0.296 | 0.158 | 16.585 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 261 | 275 | 184 | 270 | 0 | 971 | 0 | 340 | 174 | 6731 |
N.S. |
1 | 1.05 | 0.70 | 1.03 | 0.00 | 3.72 | 0.00 | 1.30 | 0.67 | 25.79 |
time (sec) |
N/A | 1.742 | 1.455 | 0.698 | 0.000 | 0.154 | 0.000 | 0.189 | 0.168 | 20.618 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 346 | 355 | 224 | 346 | 0 | 1167 | 0 | 473 | 210 | 7763 |
N.S. |
1 | 1.03 | 0.65 | 1.00 | 0.00 | 3.37 | 0.00 | 1.37 | 0.61 | 22.44 |
time (sec) |
N/A | 2.447 | 1.829 | 0.972 | 0.000 | 0.170 | 0.000 | 0.193 | 0.160 | 20.827 |
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 | 407 | 433 | 507 | 464 | 0 | 2444 | 0 | 1391 | 1637 | 10533 |
N.S. |
1 | 1.06 | 1.25 | 1.14 | 0.00 | 6.00 | 0.00 | 3.42 | 4.02 | 25.88 |
time (sec) |
N/A | 2.906 | 2.779 | 1.454 | 0.000 | 38.772 | 0.000 | 0.280 | 0.173 | 23.214 |
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 | 289 | 326 | 418 | 380 | 0 | 2111 | 0 | 581 | 977 | 9286 |
N.S. |
1 | 1.13 | 1.45 | 1.31 | 0.00 | 7.30 | 0.00 | 2.01 | 3.38 | 32.13 |
time (sec) |
N/A | 2.040 | 6.973 | 1.193 | 0.000 | 25.588 | 0.000 | 0.261 | 0.166 | 23.637 |
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 | 220 | 256 | 270 | 305 | 0 | 1419 | 0 | 486 | 568 | 6899 |
N.S. |
1 | 1.16 | 1.23 | 1.39 | 0.00 | 6.45 | 0.00 | 2.21 | 2.58 | 31.36 |
time (sec) |
N/A | 1.440 | 1.503 | 0.751 | 0.000 | 9.692 | 0.000 | 0.283 | 0.197 | 20.649 |
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 | 180 | 206 | 157 | 238 | 0 | 750 | 0 | 400 | 192 | 251 |
N.S. |
1 | 1.14 | 0.87 | 1.32 | 0.00 | 4.17 | 0.00 | 2.22 | 1.07 | 1.39 |
time (sec) |
N/A | 0.879 | 0.639 | 0.418 | 0.000 | 0.124 | 0.000 | 0.228 | 0.153 | 14.814 |
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 | 164 | 190 | 172 | 236 | 0 | 752 | 0 | 399 | 192 | 251 |
N.S. |
1 | 1.16 | 1.05 | 1.44 | 0.00 | 4.59 | 0.00 | 2.43 | 1.17 | 1.53 |
time (sec) |
N/A | 0.794 | 1.034 | 0.382 | 0.000 | 0.121 | 0.000 | 0.260 | 0.166 | 14.358 |
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 | 205 | 249 | 267 | 287 | 0 | 1152 | 0 | 457 | 380 | 6909 |
N.S. |
1 | 1.21 | 1.30 | 1.40 | 0.00 | 5.62 | 0.00 | 2.23 | 1.85 | 33.70 |
time (sec) |
N/A | 1.132 | 1.749 | 0.397 | 0.000 | 0.156 | 0.000 | 0.249 | 0.174 | 21.331 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 290 | 326 | 306 | 347 | 0 | 1568 | 0 | 546 | 521 | 5530 |
N.S. |
1 | 1.12 | 1.06 | 1.20 | 0.00 | 5.41 | 0.00 | 1.88 | 1.80 | 19.07 |
time (sec) |
N/A | 1.952 | 2.405 | 0.845 | 0.000 | 0.188 | 0.000 | 0.250 | 0.171 | 18.844 |
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 | 393 | 417 | 734 | 403 | 0 | 1811 | 0 | 2700 | 623 | 10586 |
N.S. |
1 | 1.06 | 1.87 | 1.03 | 0.00 | 4.61 | 0.00 | 6.87 | 1.59 | 26.94 |
time (sec) |
N/A | 2.825 | 3.302 | 1.165 | 0.000 | 0.227 | 0.000 | 0.508 | 0.174 | 24.348 |
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 | 418 | 475 | 548 | 591 | 0 | 3434 | 0 | 1005 | 2086 | 13092 |
N.S. |
1 | 1.14 | 1.31 | 1.41 | 0.00 | 8.22 | 0.00 | 2.40 | 4.99 | 31.32 |
time (sec) |
N/A | 3.101 | 3.013 | 1.402 | 0.000 | 70.768 | 0.000 | 0.260 | 0.251 | 30.084 |
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 | 310 | 365 | 369 | 482 | 0 | 2278 | 0 | 844 | 1406 | 9713 |
N.S. |
1 | 1.18 | 1.19 | 1.55 | 0.00 | 7.35 | 0.00 | 2.72 | 4.54 | 31.33 |
time (sec) |
N/A | 2.139 | 1.755 | 1.230 | 0.000 | 26.022 | 0.000 | 0.290 | 0.162 | 23.870 |
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 | 274 | 319 | 226 | 375 | 0 | 1230 | 0 | 693 | 626 | 439 |
N.S. |
1 | 1.16 | 0.82 | 1.37 | 0.00 | 4.49 | 0.00 | 2.53 | 2.28 | 1.60 |
time (sec) |
N/A | 1.453 | 1.650 | 0.682 | 0.000 | 0.163 | 0.000 | 0.251 | 0.163 | 16.431 |
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 | 263 | 302 | 252 | 388 | 0 | 1242 | 0 | 726 | 467 | 451 |
N.S. |
1 | 1.15 | 0.96 | 1.48 | 0.00 | 4.72 | 0.00 | 2.76 | 1.78 | 1.71 |
time (sec) |
N/A | 1.295 | 1.323 | 0.677 | 0.000 | 0.165 | 0.000 | 0.227 | 0.161 | 16.547 |
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 | 237 | 279 | 404 | 376 | 0 | 1238 | 0 | 693 | 633 | 439 |
N.S. |
1 | 1.18 | 1.70 | 1.59 | 0.00 | 5.22 | 0.00 | 2.92 | 2.67 | 1.85 |
time (sec) |
N/A | 1.191 | 1.798 | 0.606 | 0.000 | 0.160 | 0.000 | 0.244 | 0.160 | 16.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 356 | 769 | 464 | 0 | 1867 | 0 | 814 | 1004 | 9721 |
N.S. |
1 | 1.22 | 2.63 | 1.59 | 0.00 | 6.39 | 0.00 | 2.79 | 3.44 | 33.29 |
time (sec) |
N/A | 1.687 | 3.721 | 0.612 | 0.000 | 0.215 | 0.000 | 0.269 | 0.163 | 23.286 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 411 | 467 | 1205 | 558 | 0 | 2560 | 0 | 966 | 1271 | 7863 |
N.S. |
1 | 1.14 | 2.93 | 1.36 | 0.00 | 6.23 | 0.00 | 2.35 | 3.09 | 19.13 |
time (sec) |
N/A | 2.969 | 5.545 | 1.373 | 0.000 | 0.300 | 0.000 | 0.281 | 0.203 | 23.014 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 538 | 582 | 1452 | 615 | 0 | 2890 | 0 | 1052 | 1469 | 14438 |
N.S. |
1 | 1.08 | 2.70 | 1.14 | 0.00 | 5.37 | 0.00 | 1.96 | 2.73 | 26.84 |
time (sec) |
N/A | 4.115 | 5.893 | 2.217 | 0.000 | 0.365 | 0.000 | 0.249 | 0.171 | 25.191 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 70 | 61 | 76 | 0 | 197 | 0 | 187 | 63 | 91 |
N.S. |
1 | 1.15 | 1.00 | 1.25 | 0.00 | 3.23 | 0.00 | 3.07 | 1.03 | 1.49 |
time (sec) |
N/A | 0.406 | 0.151 | 0.228 | 0.000 | 0.095 | 0.000 | 0.206 | 0.156 | 10.974 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 6 | 6 | 6 | 7 | 0 | 6 | 3 | 13 | 1 | 6 |
N.S. |
1 | 1.00 | 1.00 | 1.17 | 0.00 | 1.00 | 0.50 | 2.17 | 0.17 | 1.00 |
time (sec) |
N/A | 0.147 | 0.000 | 0.075 | 0.000 | 0.064 | 3.063 | 0.173 | 0.157 | 11.256 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 122 | 97 | 120 | 0 | 279 | 0 | 139 | 155 | 444 |
N.S. |
1 | 1.42 | 1.13 | 1.40 | 0.00 | 3.24 | 0.00 | 1.62 | 1.80 | 5.16 |
time (sec) |
N/A | 0.639 | 0.737 | 0.259 | 0.000 | 0.102 | 0.000 | 0.169 | 0.161 | 13.346 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 33 | 39 | 37 | 80 | 84 | 0 | 58 | 50 | 26 |
N.S. |
1 | 0.38 | 0.45 | 0.43 | 0.92 | 0.97 | 0.00 | 0.67 | 0.57 | 0.30 |
time (sec) |
N/A | 0.331 | 0.217 | 0.170 | 0.111 | 0.083 | 0.000 | 0.183 | 0.160 | 13.876 |
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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 485 | 505 | 635 | 2419 | 0 | 0 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.04 | 1.31 | 4.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 2.345 | 35.121 | 74.632 | 0.000 | 0.000 | 0.000 | 0.000 | 0.232 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 397 | 414 | 530 | 1868 | 0 | 0 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.04 | 1.34 | 4.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 1.746 | 16.826 | 60.723 | 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 | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 314 | 320 | 434 | 1343 | 0 | 0 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.02 | 1.38 | 4.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 1.189 | 14.097 | 40.160 | 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 | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 256 | 257 | 408 | 941 | 0 | 0 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.00 | 1.59 | 3.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.840 | 12.249 | 31.258 | 0.000 | 0.000 | 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 | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 320 | 320 | 379 | 647 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 1.18 | 2.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.990 | 9.291 | 15.829 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 344 | 351 | 618 | 775 | 0 | 0 | 0 | 0 | 51 | 0 |
N.S. |
1 | 1.02 | 1.80 | 2.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 1.297 | 17.000 | 8.629 | 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 | B | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 429 | 427 | 1149 | 1169 | 0 | 0 | 0 | 0 | 55 | 0 |
N.S. |
1 | 1.00 | 2.68 | 2.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 1.810 | 16.832 | 7.513 | 0.000 | 0.000 | 0.000 | 0.000 | 0.240 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 509 | 515 | 1548 | 1678 | 0 | 0 | 0 | 0 | 55 | 0 |
N.S. |
1 | 1.01 | 3.04 | 3.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 2.434 | 18.684 | 10.651 | 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 | A | B | F(-1) | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 475 | 491 | 654 | 2424 | 0 | 0 | 0 | 0 | 79 | 0 |
N.S. |
1 | 1.03 | 1.38 | 5.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 2.113 | 19.454 | 81.891 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 388 | 396 | 547 | 1872 | 0 | 0 | 0 | 0 | 79 | 0 |
N.S. |
1 | 1.02 | 1.41 | 4.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 1.613 | 17.128 | 62.877 | 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 | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 312 | 318 | 502 | 1435 | 0 | 0 | 0 | 0 | 77 | 0 |
N.S. |
1 | 1.02 | 1.61 | 4.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 1.185 | 14.730 | 34.057 | 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 | B | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 381 | 382 | 6063 | 1239 | 0 | 0 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.00 | 15.91 | 3.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 1.373 | 22.377 | 34.514 | 0.000 | 0.000 | 0.000 | 0.000 | 0.219 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 361 | 368 | 971 | 1221 | 0 | 0 | 0 | 0 | 87 | 0 |
N.S. |
1 | 1.02 | 2.69 | 3.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 1.384 | 15.664 | 12.125 | 0.000 | 0.000 | 0.000 | 0.000 | 0.227 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 428 | 431 | 1197 | 1369 | 0 | 0 | 0 | 0 | 93 | 0 |
N.S. |
1 | 1.01 | 2.80 | 3.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 1.857 | 16.381 | 10.366 | 0.000 | 0.000 | 0.000 | 0.000 | 0.240 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 520 | 522 | 1535 | 1780 | 0 | 0 | 0 | 0 | 93 | 0 |
N.S. |
1 | 1.00 | 2.95 | 3.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 2.478 | 15.699 | 10.741 | 0.000 | 0.000 | 0.000 | 0.000 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-1) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 566 | 584 | 4227 | 2999 | 0 | 0 | 0 | 0 | 109 | 0 |
N.S. |
1 | 1.03 | 7.47 | 5.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 2.597 | 25.266 | 355.852 | 0.000 | 0.000 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-1) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 469 | 479 | 660 | 2424 | 0 | 0 | 0 | 0 | 109 | 0 |
N.S. |
1 | 1.02 | 1.41 | 5.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 2.034 | 20.214 | 176.485 | 0.000 | 0.000 | 0.000 | 0.000 | 0.227 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 384 | 395 | 599 | 1974 | 0 | 0 | 0 | 0 | 107 | 0 |
N.S. |
1 | 1.03 | 1.56 | 5.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 1.629 | 18.594 | 81.243 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 442 | 448 | 7138 | 1739 | 0 | 0 | 0 | 0 | 98 | 0 |
N.S. |
1 | 1.01 | 16.15 | 3.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 1.800 | 24.987 | 53.673 | 0.000 | 0.000 | 0.000 | 0.000 | 0.179 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 433 | 439 | 7745 | 1707 | 0 | 0 | 0 | 0 | 123 | 0 |
N.S. |
1 | 1.01 | 17.89 | 3.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 1.834 | 24.243 | 38.939 | 0.000 | 0.000 | 0.000 | 0.000 | 0.247 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 450 | 451 | 1326 | 1829 | 0 | 0 | 0 | 0 | 131 | 0 |
N.S. |
1 | 1.00 | 2.95 | 4.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 2.000 | 16.294 | 87.181 | 0.000 | 0.000 | 0.000 | 0.000 | 0.265 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 518 | 526 | 1551 | 1979 | 0 | 0 | 0 | 0 | 131 | 0 |
N.S. |
1 | 1.02 | 2.99 | 3.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 2.565 | 17.112 | 207.608 | 0.000 | 0.000 | 0.000 | 0.000 | 0.315 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 617 | 624 | 5172 | 2411 | 0 | 0 | 0 | 0 | 131 | 0 |
N.S. |
1 | 1.01 | 8.38 | 3.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 3.351 | 22.264 | 594.709 | 0.000 | 0.000 | 0.000 | 0.000 | 0.268 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 329 | 341 | 395 | 1337 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.04 | 1.20 | 4.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 1.269 | 14.158 | 59.117 | 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 | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 261 | 265 | 335 | 839 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.02 | 1.28 | 3.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.891 | 11.904 | 41.400 | 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 | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 210 | 356 | 470 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 1.70 | 2.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.602 | 12.082 | 26.256 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 208 | 145 | 182 | 0 | 0 | 0 | 0 | 13 | 0 |
N.S. |
1 | 1.00 | 0.70 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.500 | 3.262 | 14.453 | 0.000 | 0.000 | 0.000 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 348 | 353 | 418 | 580 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.01 | 1.20 | 1.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.257 | 12.488 | 8.792 | 0.000 | 0.000 | 0.000 | 0.000 | 0.209 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 435 | 436 | 1216 | 1070 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.00 | 2.80 | 2.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.814 | 13.511 | 10.338 | 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 | B | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 525 | 535 | 1569 | 1678 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.02 | 2.99 | 3.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 2.516 | 18.854 | 13.522 | 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 | B | F(-1) | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 329 | 362 | 527 | 1786 | 0 | 0 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.10 | 1.60 | 5.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 1.439 | 17.066 | 50.798 | 0.000 | 0.000 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-1) | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 275 | 302 | 467 | 1237 | 0 | 0 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.10 | 1.70 | 4.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 1.000 | 14.407 | 34.188 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-1) | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 254 | 277 | 346 | 904 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.09 | 1.36 | 3.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.904 | 12.314 | 19.184 | 0.000 | 0.000 | 0.000 | 0.000 | 0.151 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 376 | 405 | 1138 | 1070 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.08 | 3.03 | 2.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 1.421 | 12.823 | 13.938 | 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 | B | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 427 | 468 | 1597 | 1608 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.10 | 3.74 | 3.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 1.858 | 16.051 | 10.836 | 0.000 | 0.000 | 0.000 | 0.000 | 0.153 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 531 | 566 | 1962 | 2243 | 0 | 0 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.07 | 3.69 | 4.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 2.585 | 14.798 | 12.452 | 0.000 | 0.000 | 0.000 | 0.000 | 0.150 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 630 | 672 | 2319 | 2893 | 0 | 0 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.07 | 3.68 | 4.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 3.258 | 20.336 | 17.567 | 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 | B | F(-1) | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 510 | 526 | 4342 | 3491 | 0 | 0 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.03 | 8.51 | 6.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 2.320 | 24.395 | 60.250 | 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 | A | B | F(-1) | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 417 | 432 | 641 | 2908 | 0 | 0 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.04 | 1.54 | 6.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 1.631 | 19.424 | 45.322 | 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 | A | B | F(-1) | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 387 | 402 | 587 | 2412 | 0 | 0 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.04 | 1.52 | 6.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 1.442 | 17.006 | 32.594 | 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 | A | B | F(-1) | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 353 | 372 | 603 | 2043 | 0 | 0 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.05 | 1.71 | 5.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 1.333 | 14.721 | 25.907 | 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 | B | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 495 | 522 | 1589 | 2819 | 0 | 0 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.05 | 3.21 | 5.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 2.017 | 14.057 | 29.019 | 0.000 | 0.000 | 0.000 | 0.000 | 0.148 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 582 | 617 | 2366 | 4148 | 0 | 0 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.06 | 4.07 | 7.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 2.673 | 19.980 | 13.974 | 0.000 | 0.000 | 0.000 | 0.000 | 0.153 | 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 | 686 | 723 | 821 | 4973 | 0 | 0 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.05 | 1.20 | 7.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 3.410 | 13.186 | 17.049 | 0.000 | 0.000 | 0.000 | 0.000 | 0.163 | 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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 248 | 371 | 0 | 0 | 0 | 0 | 69 | 0 |
N.S. |
1 | 1.00 | 2.36 | 3.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.304 | 8.910 | 26.783 | 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 | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 211 | 267 | 0 | 0 | 0 | 0 | 71 | 0 |
N.S. |
1 | 1.00 | 1.97 | 2.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.306 | 7.264 | 26.763 | 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 | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 170 | 132 | 636 | 0 | 235 | 0 | 0 | 65 | 0 |
N.S. |
1 | 0.94 | 0.73 | 3.53 | 0.00 | 1.31 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.754 | 1.737 | 6.093 | 0.000 | 0.100 | 0.000 | 0.000 | 0.188 | 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 | 143 | 142 | 104 | 401 | 0 | 205 | 0 | 0 | 56 | 0 |
N.S. |
1 | 0.99 | 0.73 | 2.80 | 0.00 | 1.43 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.703 | 0.991 | 4.385 | 0.000 | 0.094 | 0.000 | 0.000 | 0.179 | 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 | 111 | 111 | 84 | 244 | 0 | 153 | 0 | 0 | 56 | 0 |
N.S. |
1 | 1.00 | 0.76 | 2.20 | 0.00 | 1.38 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.592 | 1.402 | 4.295 | 0.000 | 0.094 | 0.000 | 0.000 | 0.218 | 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 | 115 | 118 | 90 | 326 | 0 | 156 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.03 | 0.78 | 2.83 | 0.00 | 1.36 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.597 | 0.779 | 5.110 | 0.000 | 0.095 | 0.000 | 0.000 | 0.179 | 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 | 148 | 147 | 108 | 371 | 0 | 184 | 0 | 0 | 67 | 0 |
N.S. |
1 | 0.99 | 0.73 | 2.51 | 0.00 | 1.24 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.737 | 0.982 | 10.549 | 0.000 | 0.097 | 0.000 | 0.000 | 0.182 | 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 | 180 | 174 | 125 | 413 | 0 | 203 | 0 | 0 | 67 | 0 |
N.S. |
1 | 0.97 | 0.69 | 2.29 | 0.00 | 1.13 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.762 | 1.379 | 17.662 | 0.000 | 0.101 | 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(-1) | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 263 | 235 | 221 | 832 | 0 | 314 | 0 | 0 | 91 | 0 |
N.S. |
1 | 0.89 | 0.84 | 3.16 | 0.00 | 1.19 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 1.444 | 4.306 | 12.320 | 0.000 | 0.110 | 0.000 | 0.000 | 0.195 | 0.000 |