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 | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 194 | 123 | 130 | 302 | 169 | 0 | 0 | 174 | 0 |
N.S. |
1 | 1.02 | 0.64 | 0.68 | 1.58 | 0.88 | 0.00 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 1.071 | 0.172 | 0.142 | 0.037 | 0.246 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 155 | 99 | 99 | 194 | 133 | 0 | 0 | 133 | 0 |
N.S. |
1 | 1.08 | 0.69 | 0.69 | 1.36 | 0.93 | 0.00 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.474 | 0.101 | 0.129 | 0.039 | 0.206 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 89 | 71 | 71 | 97 | 83 | 0 | 0 | 89 | 0 |
N.S. |
1 | 1.03 | 0.83 | 0.83 | 1.13 | 0.97 | 0.00 | 0.00 | 1.03 | 0.00 |
time (sec) |
N/A | 0.280 | 0.057 | 0.073 | 0.026 | 0.303 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 58 | 64 | 180 | 0 | 0 | 0 | 0 | 54 | 0 |
N.S. |
1 | 0.98 | 1.08 | 3.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 0.369 | 0.051 | 0.661 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 118 | 189 | 192 | 0 | 0 | 0 | 0 | 148 | 0 |
N.S. |
1 | 0.98 | 1.58 | 1.60 | 0.00 | 0.00 | 0.00 | 0.00 | 1.23 | 0.00 |
time (sec) |
N/A | 0.554 | 1.034 | 0.218 | 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 | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 174 | 316 | 256 | 0 | 0 | 0 | 0 | 262 | 0 |
N.S. |
1 | 0.97 | 1.76 | 1.42 | 0.00 | 0.00 | 0.00 | 0.00 | 1.46 | 0.00 |
time (sec) |
N/A | 0.743 | 0.825 | 0.301 | 0.000 | 0.000 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 314 | 366 | 249 | 356 | 714 | 354 | 0 | 0 | 265 | 0 |
N.S. |
1 | 1.17 | 0.79 | 1.13 | 2.27 | 1.13 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 2.852 | 1.425 | 0.382 | 0.061 | 0.253 | 0.000 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 256 | 201 | 264 | 457 | 278 | 0 | 0 | 200 | 0 |
N.S. |
1 | 1.11 | 0.87 | 1.14 | 1.98 | 1.20 | 0.00 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 2.171 | 1.252 | 0.181 | 0.042 | 0.280 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 148 | 146 | 171 | 230 | 178 | 0 | 0 | 133 | 0 |
N.S. |
1 | 1.09 | 1.07 | 1.26 | 1.69 | 1.31 | 0.00 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 0.865 | 0.212 | 0.134 | 0.039 | 0.197 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 104 | 119 | 355 | 0 | 0 | 0 | 0 | 85 | 0 |
N.S. |
1 | 0.88 | 1.01 | 3.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 0.544 | 0.088 | 0.175 | 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 | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 185 | 359 | 428 | 0 | 0 | 0 | 0 | 233 | 0 |
N.S. |
1 | 0.95 | 1.84 | 2.19 | 0.00 | 0.00 | 0.00 | 0.00 | 1.19 | 0.00 |
time (sec) |
N/A | 1.890 | 5.432 | 0.221 | 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 | C | B | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 302 | 294 | 660 | 558 | 0 | 0 | 0 | 0 | 417 | 0 |
N.S. |
1 | 0.97 | 2.19 | 1.85 | 0.00 | 0.00 | 0.00 | 0.00 | 1.38 | 0.00 |
time (sec) |
N/A | 4.372 | 7.561 | 0.260 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 510 | 749 | 427 | 668 | 1353 | 582 | 0 | 0 | 361 | 0 |
N.S. |
1 | 1.47 | 0.84 | 1.31 | 2.65 | 1.14 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 6.508 | 1.710 | 0.237 | 0.100 | 0.250 | 0.000 | 0.000 | 0.274 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 386 | 488 | 347 | 492 | 861 | 455 | 0 | 0 | 271 | 0 |
N.S. |
1 | 1.26 | 0.90 | 1.27 | 2.23 | 1.18 | 0.00 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 3.019 | 1.368 | 0.230 | 0.070 | 0.188 | 0.000 | 0.000 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 213 | 257 | 256 | 313 | 437 | 296 | 0 | 0 | 178 | 0 |
N.S. |
1 | 1.21 | 1.20 | 1.47 | 2.05 | 1.39 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 2.122 | 0.354 | 0.199 | 0.053 | 0.228 | 0.000 | 0.000 | 0.241 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 154 | 167 | 590 | 0 | 0 | 0 | 0 | 114 | 0 |
N.S. |
1 | 0.87 | 0.94 | 3.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.988 | 0.128 | 0.254 | 0.000 | 0.000 | 0.000 | 0.000 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | B | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 316 | 286 | 708 | 811 | 0 | 0 | 0 | 0 | 312 | 0 |
N.S. |
1 | 0.91 | 2.24 | 2.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.99 | 0.00 |
time (sec) |
N/A | 3.098 | 7.518 | 0.267 | 0.000 | 0.000 | 0.000 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 61 | 45 | 44 | 0 | 0 | 0 | 0 | 64 | 0 |
N.S. |
1 | 0.91 | 0.67 | 0.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.96 | 0.00 |
time (sec) |
N/A | 0.363 | 0.327 | 0.096 | 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 | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 48 | 34 | 33 | 0 | 0 | 0 | 0 | 46 | 0 |
N.S. |
1 | 0.96 | 0.68 | 0.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 0.340 | 0.131 | 0.070 | 0.000 | 0.000 | 0.000 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 33 | 25 | 24 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.14 | 0.86 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.97 | 0.00 |
time (sec) |
N/A | 0.509 | 0.085 | 0.047 | 0.000 | 0.000 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 25 | 24 | 22 | 24 | 27 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.25 | 1.20 | 1.10 | 1.20 | 1.35 | 1.10 |
time (sec) |
N/A | 0.305 | 1.376 | 0.163 | 0.106 | 0.183 | 1.185 | 0.128 | 0.200 | 3.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 23 | 36 | 36 | 23 | 36 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.15 | 1.80 | 1.80 | 1.15 | 1.80 | 1.10 |
time (sec) |
N/A | 0.340 | 4.534 | 0.085 | 0.108 | 0.171 | 3.855 | 0.129 | 0.222 | 3.076 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 83 | 257 | 107 | 0 | 0 | 0 | 0 | 64 | 0 |
N.S. |
1 | 0.85 | 2.62 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.948 | 0.446 | 0.086 | 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 | B | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 73 | 194 | 87 | 0 | 0 | 0 | 0 | 46 | 0 |
N.S. |
1 | 0.89 | 2.37 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.783 | 0.322 | 0.075 | 0.000 | 0.000 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 57 | 65 | 61 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 0.98 | 1.12 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.638 | 0.225 | 0.053 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 259 | 24 | 26 | 24 | 31 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 12.95 | 1.20 | 1.30 | 1.20 | 1.55 | 1.10 |
time (sec) |
N/A | 0.526 | 2.588 | 0.155 | 0.248 | 0.184 | 2.402 | 0.127 | 0.189 | 3.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 351 | 36 | 41 | 23 | 42 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 17.55 | 1.80 | 2.05 | 1.15 | 2.10 | 1.10 |
time (sec) |
N/A | 0.556 | 8.119 | 0.082 | 0.289 | 0.168 | 10.283 | 0.133 | 0.192 | 3.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 269 | 226 | 183 | 242 | 0 | 0 | 0 | 0 | 80 | 0 |
N.S. |
1 | 0.84 | 0.68 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.688 | 1.415 | 0.451 | 0.000 | 0.000 | 0.000 | 0.000 | 0.259 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 172 | 139 | 182 | 0 | 0 | 0 | 0 | 58 | 0 |
N.S. |
1 | 0.86 | 0.69 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.538 | 0.504 | 0.197 | 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 | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 116 | 93 | 114 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 0.93 | 0.74 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.445 | 0.164 | 0.159 | 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 | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 29 | 39 | 36 | 28 | 40 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.21 | 1.62 | 1.50 | 1.17 | 1.67 | 1.08 |
time (sec) |
N/A | 0.227 | 2.536 | 0.133 | 0.111 | 0.167 | 2.300 | 0.131 | 0.204 | 3.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 27 | 67 | 61 | 27 | 58 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.12 | 2.79 | 2.54 | 1.12 | 2.42 | 1.08 |
time (sec) |
N/A | 0.228 | 20.632 | 0.160 | 0.114 | 0.232 | 10.519 | 0.133 | 0.195 | 3.085 |
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 | 307 | 247 | 573 | 908 | 0 | 0 | 0 | 0 | 136 | 0 |
N.S. |
1 | 0.80 | 1.87 | 2.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 1.317 | 2.058 | 0.369 | 0.000 | 0.000 | 0.000 | 0.000 | 0.258 | 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 | 240 | 198 | 261 | 591 | 0 | 0 | 0 | 0 | 100 | 0 |
N.S. |
1 | 0.82 | 1.09 | 2.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 1.451 | 1.489 | 0.217 | 0.000 | 0.000 | 0.000 | 0.000 | 0.254 | 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 | 161 | 143 | 132 | 318 | 0 | 0 | 0 | 0 | 64 | 0 |
N.S. |
1 | 0.89 | 0.82 | 1.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.785 | 0.494 | 0.187 | 0.000 | 0.000 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 447 | 71 | 73 | 28 | 74 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 18.62 | 2.96 | 3.04 | 1.17 | 3.08 | 1.08 |
time (sec) |
N/A | 0.612 | 9.369 | 0.141 | 0.300 | 0.200 | 9.119 | 0.143 | 0.219 | 3.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 644 | 119 | 121 | 27 | 112 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 26.83 | 4.96 | 5.04 | 1.12 | 4.67 | 1.08 |
time (sec) |
N/A | 0.632 | 23.638 | 0.149 | 0.366 | 0.201 | 100.070 | 0.152 | 0.208 | 2.978 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 254 | 306 | 300 | 871 | 0 | 0 | 0 | 0 | 150 | 0 |
N.S. |
1 | 1.20 | 1.18 | 3.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.971 | 1.670 | 0.374 | 0.000 | 0.000 | 0.000 | 0.000 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 216 | 192 | 546 | 0 | 0 | 0 | 0 | 101 | 0 |
N.S. |
1 | 1.21 | 1.07 | 3.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.659 | 1.262 | 0.237 | 0.000 | 0.000 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 124 | 110 | 281 | 0 | 0 | 0 | 0 | 51 | 0 |
N.S. |
1 | 1.17 | 1.04 | 2.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.428 | 0.352 | 0.214 | 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 | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 53 | 53 | 88 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.20 | 1.20 | 2.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.230 | 0.034 | 0.154 | 0.000 | 0.000 | 0.000 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 84 | 73 | 174 | 70 | 0 | 0 | 0 | 80 | 0 |
N.S. |
1 | 1.17 | 1.01 | 2.42 | 0.97 | 0.00 | 0.00 | 0.00 | 1.11 | 0.00 |
time (sec) |
N/A | 0.349 | 0.026 | 0.274 | 0.038 | 0.000 | 0.000 | 0.000 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 179 | 122 | 475 | 157 | 0 | 0 | 0 | 197 | 0 |
N.S. |
1 | 1.19 | 0.81 | 3.17 | 1.05 | 0.00 | 0.00 | 0.00 | 1.31 | 0.00 |
time (sec) |
N/A | 0.683 | 0.070 | 0.284 | 0.042 | 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 | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 225 | 274 | 168 | 2225 | 0 | 0 | 0 | 0 | 355 | 0 |
N.S. |
1 | 1.22 | 0.75 | 9.89 | 0.00 | 0.00 | 0.00 | 0.00 | 1.58 | 0.00 |
time (sec) |
N/A | 0.938 | 0.088 | 0.322 | 0.000 | 0.000 | 0.000 | 0.000 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 301 | 356 | 333 | 1061 | 0 | 0 | 0 | 0 | 166 | 0 |
N.S. |
1 | 1.18 | 1.11 | 3.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 1.701 | 2.821 | 0.273 | 0.000 | 0.000 | 0.000 | 0.000 | 0.283 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 181 | 202 | 533 | 0 | 0 | 0 | 0 | 82 | 0 |
N.S. |
1 | 0.97 | 1.09 | 2.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.805 | 1.011 | 0.253 | 0.000 | 0.000 | 0.000 | 0.000 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 53 | 53 | 147 | 0 | 0 | 0 | 0 | 69 | 0 |
N.S. |
1 | 1.20 | 1.20 | 3.34 | 0.00 | 0.00 | 0.00 | 0.00 | 1.57 | 0.00 |
time (sec) |
N/A | 0.244 | 0.041 | 0.194 | 0.000 | 0.000 | 0.000 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 140 | 127 | 560 | 0 | 0 | 0 | 0 | 142 | 0 |
N.S. |
1 | 0.86 | 0.78 | 3.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.666 | 0.330 | 0.312 | 0.000 | 0.000 | 0.000 | 0.000 | 0.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 289 | 278 | 288 | 2373 | 0 | 0 | 0 | 0 | 361 | 0 |
N.S. |
1 | 0.96 | 1.00 | 8.21 | 0.00 | 0.00 | 0.00 | 0.00 | 1.25 | 0.00 |
time (sec) |
N/A | 1.912 | 1.971 | 0.359 | 0.000 | 0.000 | 0.000 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 54 | 152 | 0 | 0 | 0 | 0 | 13 | 0 |
N.S. |
1 | 1.00 | 0.82 | 2.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.479 | 0.109 | 0.300 | 0.000 | 0.000 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 45 | 51 | 0 | 56 | 0 | 0 | 22 | 48 |
N.S. |
1 | 1.00 | 1.41 | 1.59 | 0.00 | 1.75 | 0.00 | 0.00 | 0.69 | 1.50 |
time (sec) |
N/A | 0.330 | 0.022 | 0.100 | 0.000 | 0.162 | 0.000 | 0.000 | 0.185 | 3.129 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 278 | 306 | 347 | 885 | 0 | 0 | 0 | 0 | 150 | 0 |
N.S. |
1 | 1.10 | 1.25 | 3.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 1.358 | 1.801 | 0.264 | 0.000 | 0.000 | 0.000 | 0.000 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 216 | 235 | 546 | 0 | 0 | 0 | 0 | 101 | 0 |
N.S. |
1 | 1.10 | 1.19 | 2.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.638 | 0.899 | 0.195 | 0.000 | 0.000 | 0.000 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 124 | 144 | 278 | 0 | 0 | 0 | 0 | 51 | 0 |
N.S. |
1 | 1.00 | 1.16 | 2.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.427 | 0.447 | 0.163 | 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 | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 53 | 53 | 89 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 0.95 | 0.95 | 1.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.232 | 0.032 | 0.137 | 0.000 | 0.000 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 72 | 180 | 70 | 0 | 0 | 0 | 80 | 0 |
N.S. |
1 | 1.00 | 0.86 | 2.14 | 0.83 | 0.00 | 0.00 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 0.252 | 0.027 | 0.218 | 0.038 | 0.000 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 179 | 132 | 477 | 157 | 0 | 0 | 0 | 197 | 0 |
N.S. |
1 | 1.10 | 0.81 | 2.94 | 0.97 | 0.00 | 0.00 | 0.00 | 1.22 | 0.00 |
time (sec) |
N/A | 0.444 | 0.067 | 0.250 | 0.045 | 0.000 | 0.000 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 237 | 274 | 178 | 2283 | 0 | 0 | 0 | 0 | 355 | 0 |
N.S. |
1 | 1.16 | 0.75 | 9.63 | 0.00 | 0.00 | 0.00 | 0.00 | 1.50 | 0.00 |
time (sec) |
N/A | 0.647 | 0.087 | 0.269 | 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 | B | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 324 | 356 | 374 | 1061 | 0 | 0 | 0 | 0 | 166 | 0 |
N.S. |
1 | 1.10 | 1.15 | 3.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 1.735 | 3.204 | 0.213 | 0.000 | 0.000 | 0.000 | 0.000 | 0.255 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 181 | 235 | 527 | 0 | 0 | 0 | 0 | 82 | 0 |
N.S. |
1 | 0.89 | 1.15 | 2.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 1.067 | 1.069 | 0.178 | 0.000 | 0.000 | 0.000 | 0.000 | 0.213 | 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 | 56 | 53 | 53 | 149 | 0 | 0 | 0 | 0 | 69 | 0 |
N.S. |
1 | 0.95 | 0.95 | 2.66 | 0.00 | 0.00 | 0.00 | 0.00 | 1.23 | 0.00 |
time (sec) |
N/A | 0.396 | 0.038 | 0.151 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 140 | 126 | 578 | 0 | 0 | 0 | 0 | 142 | 0 |
N.S. |
1 | 0.71 | 0.64 | 2.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 0.685 | 0.307 | 0.280 | 0.000 | 0.000 | 0.000 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 319 | 278 | 289 | 2435 | 0 | 0 | 0 | 0 | 361 | 0 |
N.S. |
1 | 0.87 | 0.91 | 7.63 | 0.00 | 0.00 | 0.00 | 0.00 | 1.13 | 0.00 |
time (sec) |
N/A | 1.675 | 1.562 | 0.321 | 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 | C | A | B | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 405 | 407 | 220 | 794 | 0 | 0 | 0 | 0 | 90 | 0 |
N.S. |
1 | 1.00 | 0.54 | 1.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 2.460 | 1.046 | 0.476 | 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 | A | F(-2) | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 387 | 390 | 148 | 536 | 0 | 0 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.01 | 0.38 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 4.648 | 0.403 | 0.319 | 0.000 | 0.000 | 0.000 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 182 | 98 | 256 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 0.79 | 0.42 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 1.320 | 0.200 | 0.240 | 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 | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 46 | 46 | 55 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 0.94 | 0.94 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.232 | 0.022 | 0.210 | 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 | C | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 241 | 143 | 162 | 548 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 0.59 | 0.67 | 2.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.801 | 0.221 | 0.383 | 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 | C | C | B | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 401 | 292 | 258 | 955 | 0 | 0 | 0 | 0 | 68 | 0 |
N.S. |
1 | 0.73 | 0.64 | 2.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 3.118 | 0.794 | 0.454 | 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 | A | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 458 | 207 | 195 | 302 | 0 | 0 | 0 | 0 | 94 | 0 |
N.S. |
1 | 0.45 | 0.43 | 0.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.594 | 0.917 | 0.256 | 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 | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 314 | 156 | 149 | 234 | 0 | 0 | 0 | 0 | 61 | 0 |
N.S. |
1 | 0.50 | 0.47 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.520 | 0.620 | 0.128 | 0.000 | 0.000 | 0.000 | 0.000 | 0.236 | 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 | 181 | 104 | 106 | 167 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 0.57 | 0.59 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.454 | 0.426 | 0.109 | 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 | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 49 | 55 | 60 | 0 | 68 | 0 | 0 | 54 | 0 |
N.S. |
1 | 0.92 | 1.04 | 1.13 | 0.00 | 1.28 | 0.00 | 0.00 | 1.02 | 0.00 |
time (sec) |
N/A | 0.259 | 0.283 | 0.152 | 0.000 | 0.225 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 24 | 26 | 81 | 27 | 26 | 88 | 26 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 3.12 | 1.04 | 1.00 | 3.38 | 1.00 |
time (sec) |
N/A | 0.256 | 8.873 | 0.196 | 0.131 | 0.165 | 7.304 | 0.174 | 0.208 | 3.011 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 24 | 26 | 108 | 27 | 26 | 129 | 26 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 4.15 | 1.04 | 1.00 | 4.96 | 1.00 |
time (sec) |
N/A | 0.246 | 3.630 | 0.295 | 0.133 | 0.181 | 38.797 | 0.183 | 0.211 | 3.013 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 454 | 247 | 271 | 628 | 0 | 0 | 0 | 0 | 136 | 0 |
N.S. |
1 | 0.54 | 0.60 | 1.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 1.030 | 1.368 | 0.273 | 0.000 | 0.000 | 0.000 | 0.000 | 0.289 | 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 | 307 | 195 | 170 | 448 | 0 | 0 | 0 | 0 | 89 | 0 |
N.S. |
1 | 0.64 | 0.55 | 1.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 1.204 | 0.798 | 0.182 | 0.000 | 0.000 | 0.000 | 0.000 | 0.242 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 146 | 122 | 271 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 0.83 | 0.70 | 1.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 1.252 | 0.386 | 0.159 | 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 | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 51 | 51 | 61 | 0 | 80 | 0 | 0 | 65 | 63 |
N.S. |
1 | 0.96 | 0.96 | 1.15 | 0.00 | 1.51 | 0.00 | 0.00 | 1.23 | 1.19 |
time (sec) |
N/A | 0.402 | 0.037 | 0.098 | 0.000 | 0.270 | 0.000 | 0.000 | 0.194 | 2.907 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 24 | 597 | 133 | 29 | 26 | 144 | 26 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 22.96 | 5.12 | 1.12 | 1.00 | 5.54 | 1.00 |
time (sec) |
N/A | 0.693 | 6.325 | 0.179 | 0.790 | 0.196 | 50.185 | 0.188 | 0.210 | 3.206 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 24 | 735 | 178 | 0 | 26 | 216 | 26 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 28.27 | 6.85 | 0.00 | 1.00 | 8.31 | 1.00 |
time (sec) |
N/A | 0.678 | 12.707 | 0.263 | 1.214 | 0.207 | 0.000 | 0.197 | 0.227 | 3.204 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | F | F | F(-2) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 351 | 352 | 154 | 0 | 0 | 0 | 0 | 0 | 51 | 0 |
N.S. |
1 | 1.00 | 0.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 2.965 | 0.226 | 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 | C | A | F | F | F(-2) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 180 | 117 | 0 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 0.88 | 0.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 1.971 | 0.142 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.284 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 48 | 48 | 41 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 0.94 | 0.94 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.382 | 0.027 | 0.101 | 0.000 | 0.000 | 0.000 | 0.000 | 0.245 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 20 | 22 | 0 | 26 | 22 | 44 | 22 |
N.S. |
1 | 1.00 | 1.08 | 0.83 | 0.92 | 0.00 | 1.08 | 0.92 | 1.83 | 0.92 |
time (sec) |
N/A | 0.601 | 5.012 | 0.289 | 0.407 | 0.000 | 4.660 | 1.644 | 0.508 | 2.851 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 20 | 22 | 0 | 26 | 22 | 278 | 22 |
N.S. |
1 | 1.00 | 1.08 | 0.83 | 0.92 | 0.00 | 1.08 | 0.92 | 11.58 | 0.92 |
time (sec) |
N/A | 1.090 | 5.542 | 0.326 | 0.432 | 0.000 | 90.569 | 1.621 | 0.615 | 2.802 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 302 | 203 | 136 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 0.67 | 0.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 1.507 | 0.325 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.392 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 48 | 48 | 41 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 0.94 | 0.94 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.228 | 0.027 | 0.098 | 0.000 | 0.000 | 0.000 | 0.000 | 0.263 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 20 | 22 | 0 | 26 | 22 | 48 | 22 |
N.S. |
1 | 1.00 | 1.08 | 0.83 | 0.92 | 0.00 | 1.08 | 0.92 | 2.00 | 0.92 |
time (sec) |
N/A | 0.365 | 4.784 | 0.237 | 0.351 | 0.000 | 43.181 | 3.017 | 0.571 | 2.787 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 20 | 22 | 0 | 0 | 22 | 296 | 22 |
N.S. |
1 | 1.00 | 1.08 | 0.83 | 0.92 | 0.00 | 0.00 | 0.92 | 12.33 | 0.92 |
time (sec) |
N/A | 1.398 | 5.597 | 0.303 | 0.364 | 0.000 | 0.000 | 3.012 | 0.760 | 2.825 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | F | F | F(-2) | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 330 | 256 | 148 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 0.78 | 0.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 3.659 | 0.413 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.432 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F(-2) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 48 | 48 | 41 | 0 | 0 | 0 | 0 | 43 | 0 |
N.S. |
1 | 0.94 | 0.94 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.259 | 0.026 | 0.100 | 0.000 | 0.000 | 0.000 | 0.000 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 20 | 22 | 0 | 0 | 22 | 50 | 22 |
N.S. |
1 | 1.00 | 1.08 | 0.83 | 0.92 | 0.00 | 0.00 | 0.92 | 2.08 | 0.92 |
time (sec) |
N/A | 0.363 | 4.384 | 0.227 | 0.377 | 0.000 | 0.000 | 3.049 | 0.626 | 2.873 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 20 | 22 | 0 | 0 | 22 | 304 | 22 |
N.S. |
1 | 1.00 | 1.08 | 0.83 | 0.92 | 0.00 | 0.00 | 0.92 | 12.67 | 0.92 |
time (sec) |
N/A | 1.541 | 3.828 | 0.295 | 0.374 | 0.000 | 0.000 | 3.040 | 0.779 | 2.807 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 368 | 369 | 165 | 0 | 0 | 0 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.00 | 0.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 3.419 | 0.325 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.438 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 186 | 121 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.88 | 0.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 2.768 | 0.203 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.279 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 50 | 50 | 44 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 0.96 | 0.96 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.221 | 0.041 | 0.131 | 0.000 | 0.000 | 0.000 | 0.000 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 20 | 22 | 0 | 20 | 22 | 37 | 22 |
N.S. |
1 | 1.00 | 1.08 | 0.83 | 0.92 | 0.00 | 0.83 | 0.92 | 1.54 | 0.92 |
time (sec) |
N/A | 0.368 | 6.514 | 0.519 | 0.407 | 0.000 | 4.611 | 1.011 | 0.441 | 2.748 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 20 | 22 | 0 | 20 | 22 | 275 | 22 |
N.S. |
1 | 1.00 | 1.08 | 0.83 | 0.92 | 0.00 | 0.83 | 0.92 | 11.46 | 0.92 |
time (sec) |
N/A | 0.959 | 3.186 | 0.470 | 0.454 | 0.000 | 91.914 | 1.024 | 0.643 | 2.666 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 316 | 217 | 144 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 0.69 | 0.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.835 | 0.421 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.319 | 0.000 |