Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 422 | 526 | 593 | 4040 | 0 | 0 | 0 | 0 | 8880 | 0 |
N.S. |
1 | 1.25 | 1.41 | 9.57 | 0.00 | 0.00 | 0.00 | 0.00 | 21.04 | 0.00 |
time (sec) |
N/A | 1.029 | 12.685 | 1.583 | 0.000 | 0.000 | 0.000 | 0.000 | 26.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | F(-1) | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 482 | 660 | 6043 | 12286 | 0 | 0 | 0 | 0 | 14173 | 0 |
N.S. |
1 | 1.37 | 12.54 | 25.49 | 0.00 | 0.00 | 0.00 | 0.00 | 29.40 | 0.00 |
time (sec) |
N/A | 1.181 | 16.368 | 1.868 | 0.000 | 0.000 | 0.000 | 0.000 | 147.090 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 36 | 23 | 41 | 32 | 85 | 25 | 31 | 22 |
N.S. |
1 | 1.00 | 0.95 | 0.61 | 1.08 | 0.84 | 2.24 | 0.66 | 0.82 | 0.58 |
time (sec) |
N/A | 0.172 | 0.127 | 0.815 | 0.121 | 0.084 | 0.122 | 0.497 | 0.486 | 0.046 |
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 | 54 | 59 | 53 | 34 | 52 | 45 | 36 | 45 | 64 | 84 |
N.S. |
1 | 1.09 | 0.98 | 0.63 | 0.96 | 0.83 | 0.67 | 0.83 | 1.19 | 1.56 |
time (sec) |
N/A | 0.201 | 0.084 | 0.842 | 0.111 | 0.083 | 0.841 | 2.051 | 0.490 | 0.142 |
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 | 56 | 59 | 56 | 43 | 52 | 47 | 41 | 32 | 53 | 74 |
N.S. |
1 | 1.05 | 1.00 | 0.77 | 0.93 | 0.84 | 0.73 | 0.57 | 0.95 | 1.32 |
time (sec) |
N/A | 0.199 | 0.121 | 0.747 | 0.104 | 0.085 | 0.580 | 0.175 | 0.648 | 5.496 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 66 | 57 | 50 | 62 | 64 | 0 | 67 | 79 | 0 |
N.S. |
1 | 1.08 | 0.93 | 0.82 | 1.02 | 1.05 | 0.00 | 1.10 | 1.30 | 0.00 |
time (sec) |
N/A | 0.238 | 0.118 | 0.852 | 0.028 | 0.094 | 0.000 | 0.163 | 0.697 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 66 | 59 | 46 | 58 | 51 | 0 | 52 | 51 | 0 |
N.S. |
1 | 1.02 | 0.91 | 0.71 | 0.89 | 0.78 | 0.00 | 0.80 | 0.78 | 0.00 |
time (sec) |
N/A | 0.244 | 0.099 | 0.858 | 0.107 | 0.091 | 0.000 | 0.190 | 0.582 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 296 | 312 | 247 | 276 | 0 | 599 | 622 | 291 | 22 | 0 |
N.S. |
1 | 1.05 | 0.83 | 0.93 | 0.00 | 2.02 | 2.10 | 0.98 | 0.07 | 0.00 |
time (sec) |
N/A | 0.583 | 0.821 | 1.177 | 0.000 | 0.165 | 1.024 | 0.210 | 200.059 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 182 | 150 | 162 | 0 | 391 | 393 | 176 | 433 | 0 |
N.S. |
1 | 1.05 | 0.86 | 0.93 | 0.00 | 2.25 | 2.26 | 1.01 | 2.49 | 0.00 |
time (sec) |
N/A | 0.357 | 0.547 | 1.101 | 0.000 | 0.122 | 0.959 | 0.183 | 2.718 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 133 | 106 | 94 | 0 | 247 | 243 | 105 | 243 | 0 |
N.S. |
1 | 1.29 | 1.03 | 0.91 | 0.00 | 2.40 | 2.36 | 1.02 | 2.36 | 0.00 |
time (sec) |
N/A | 0.291 | 0.448 | 1.023 | 0.000 | 0.099 | 0.812 | 0.187 | 0.563 | 0.000 |
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 | 68 | 68 | 66 | 57 | 0 | 165 | 146 | 61 | 105 | 80 |
N.S. |
1 | 1.00 | 0.97 | 0.84 | 0.00 | 2.43 | 2.15 | 0.90 | 1.54 | 1.18 |
time (sec) |
N/A | 0.195 | 0.368 | 0.940 | 0.000 | 0.094 | 0.544 | 0.199 | 0.600 | 5.877 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 35 | 30 | 0 | 106 | 85 | 66 | 42 | 29 |
N.S. |
1 | 1.00 | 0.97 | 0.83 | 0.00 | 2.94 | 2.36 | 1.83 | 1.17 | 0.81 |
time (sec) |
N/A | 0.159 | 0.091 | 0.878 | 0.000 | 0.097 | 0.644 | 0.147 | 0.478 | 5.766 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 92 | 157 | 0 | 343 | 0 | 71 | 3755 | 0 |
N.S. |
1 | 1.00 | 1.16 | 1.99 | 0.00 | 4.34 | 0.00 | 0.90 | 47.53 | 0.00 |
time (sec) |
N/A | 0.199 | 0.330 | 1.101 | 0.000 | 0.129 | 0.000 | 0.178 | 0.712 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 134 | 125 | 271 | 0 | 652 | 0 | 0 | 578 | 0 |
N.S. |
1 | 1.00 | 0.93 | 2.02 | 0.00 | 4.87 | 0.00 | 0.00 | 4.31 | 0.00 |
time (sec) |
N/A | 0.264 | 0.567 | 1.112 | 0.000 | 0.230 | 0.000 | 0.000 | 0.962 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 209 | 230 | 205 | 561 | 0 | 1362 | 0 | 795 | 1920 | 0 |
N.S. |
1 | 1.10 | 0.98 | 2.68 | 0.00 | 6.52 | 0.00 | 3.80 | 9.19 | 0.00 |
time (sec) |
N/A | 0.420 | 10.232 | 1.240 | 0.000 | 0.951 | 0.000 | 0.214 | 0.714 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 286 | 294 | 317 | 443 | 0 | 1173 | 0 | 395 | 2028 | 0 |
N.S. |
1 | 1.03 | 1.11 | 1.55 | 0.00 | 4.10 | 0.00 | 1.38 | 7.09 | 0.00 |
time (sec) |
N/A | 0.541 | 1.709 | 1.226 | 0.000 | 0.299 | 0.000 | 0.212 | 1.485 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 189 | 194 | 303 | 0 | 755 | 0 | 240 | 1171 | 0 |
N.S. |
1 | 1.07 | 1.10 | 1.71 | 0.00 | 4.27 | 0.00 | 1.36 | 6.62 | 0.00 |
time (sec) |
N/A | 0.347 | 0.921 | 1.206 | 0.000 | 0.229 | 0.000 | 0.208 | 0.526 | 0.000 |
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 | 117 | 140 | 118 | 207 | 0 | 461 | 0 | 132 | 619 | 150 |
N.S. |
1 | 1.20 | 1.01 | 1.77 | 0.00 | 3.94 | 0.00 | 1.13 | 5.29 | 1.28 |
time (sec) |
N/A | 0.290 | 0.710 | 1.016 | 0.000 | 0.187 | 0.000 | 0.215 | 0.579 | 6.370 |
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 | 45 | 45 | 43 | 45 | 0 | 74 | 0 | 55 | 169 | 45 |
N.S. |
1 | 1.00 | 0.96 | 1.00 | 0.00 | 1.64 | 0.00 | 1.22 | 3.76 | 1.00 |
time (sec) |
N/A | 0.170 | 0.361 | 0.888 | 0.000 | 0.130 | 0.000 | 0.207 | 0.591 | 6.088 |
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 | 32 | 32 | 32 | 33 | 0 | 61 | 0 | 41 | 95 | 31 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 0.00 | 1.91 | 0.00 | 1.28 | 2.97 | 0.97 |
time (sec) |
N/A | 0.154 | 0.268 | 0.880 | 0.000 | 0.096 | 0.000 | 0.207 | 0.554 | 0.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 155 | 190 | 400 | 0 | 1349 | 0 | 461 | 22 | 0 |
N.S. |
1 | 1.00 | 1.23 | 2.58 | 0.00 | 8.70 | 0.00 | 2.97 | 0.14 | 0.00 |
time (sec) |
N/A | 0.303 | 1.072 | 1.154 | 0.000 | 0.359 | 0.000 | 0.236 | 200.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 254 | 281 | 250 | 655 | 0 | 3004 | 0 | 0 | 4195 | 0 |
N.S. |
1 | 1.11 | 0.98 | 2.58 | 0.00 | 11.83 | 0.00 | 0.00 | 16.52 | 0.00 |
time (sec) |
N/A | 0.468 | 10.266 | 1.165 | 0.000 | 0.964 | 0.000 | 0.000 | 1.606 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 364 | 0 | 353 | 1189 | 0 | 5732 | 0 | 2718 | 9369 | 0 |
N.S. |
1 | 0.00 | 0.97 | 3.27 | 0.00 | 15.75 | 0.00 | 7.47 | 25.74 | 0.00 |
time (sec) |
N/A | 0.000 | 10.886 | 1.316 | 0.000 | 4.326 | 0.000 | 0.289 | 0.922 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 428 | 417 | 566 | 1931 | 0 | 2249 | 0 | 820 | 22 | 0 |
N.S. |
1 | 0.97 | 1.32 | 4.51 | 0.00 | 5.25 | 0.00 | 1.92 | 0.05 | 0.00 |
time (sec) |
N/A | 0.756 | 3.424 | 1.376 | 0.000 | 0.830 | 0.000 | 0.192 | 200.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 298 | 323 | 401 | 1132 | 0 | 1515 | 0 | 564 | 2476 | 0 |
N.S. |
1 | 1.08 | 1.35 | 3.80 | 0.00 | 5.08 | 0.00 | 1.89 | 8.31 | 0.00 |
time (sec) |
N/A | 0.621 | 2.323 | 1.196 | 0.000 | 0.683 | 0.000 | 0.204 | 1.017 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 190 | 287 | 0 | 366 | 0 | 333 | 1237 | 528 |
N.S. |
1 | 1.00 | 1.61 | 2.43 | 0.00 | 3.10 | 0.00 | 2.82 | 10.48 | 4.47 |
time (sec) |
N/A | 0.236 | 1.238 | 1.108 | 0.000 | 0.566 | 0.000 | 0.225 | 0.970 | 6.271 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 167 | 206 | 0 | 305 | 0 | 263 | 863 | 321 |
N.S. |
1 | 1.00 | 1.70 | 2.10 | 0.00 | 3.11 | 0.00 | 2.68 | 8.81 | 3.28 |
time (sec) |
N/A | 0.220 | 1.085 | 1.023 | 0.000 | 0.589 | 0.000 | 0.207 | 0.782 | 6.356 |
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 | 91 | 91 | 110 | 122 | 0 | 247 | 0 | 197 | 511 | 121 |
N.S. |
1 | 1.00 | 1.21 | 1.34 | 0.00 | 2.71 | 0.00 | 2.16 | 5.62 | 1.33 |
time (sec) |
N/A | 0.204 | 0.867 | 0.947 | 0.000 | 0.495 | 0.000 | 0.196 | 0.731 | 6.336 |
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 | 70 | 70 | 55 | 67 | 0 | 192 | 0 | 144 | 320 | 57 |
N.S. |
1 | 1.00 | 0.79 | 0.96 | 0.00 | 2.74 | 0.00 | 2.06 | 4.57 | 0.81 |
time (sec) |
N/A | 0.185 | 0.644 | 0.865 | 0.000 | 0.145 | 0.000 | 0.161 | 0.487 | 5.966 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 307 | 350 | 309 | 766 | 0 | 4612 | 0 | 8447 | 22 | 0 |
N.S. |
1 | 1.14 | 1.01 | 2.50 | 0.00 | 15.02 | 0.00 | 27.51 | 0.07 | 0.00 |
time (sec) |
N/A | 0.538 | 10.354 | 1.096 | 0.000 | 1.463 | 0.000 | 0.454 | 200.131 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 497 | 532 | 482 | 1143 | 0 | 8874 | 0 | 5572 | 12526 | 0 |
N.S. |
1 | 1.07 | 0.97 | 2.30 | 0.00 | 17.86 | 0.00 | 11.21 | 25.20 | 0.00 |
time (sec) |
N/A | 0.871 | 11.321 | 1.165 | 0.000 | 5.270 | 0.000 | 0.661 | 1.989 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 40 | 22 | 23 | 44 | 19 | 21 | 20 | 46 |
N.S. |
1 | 1.00 | 1.38 | 0.76 | 0.79 | 1.52 | 0.66 | 0.72 | 0.69 | 1.59 |
time (sec) |
N/A | 0.170 | 0.102 | 0.722 | 0.108 | 0.074 | 0.443 | 0.167 | 0.424 | 6.223 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 29 | 38 | 24 | 23 | 47 | 20 | 23 | 22 | 46 |
N.S. |
1 | 1.16 | 1.52 | 0.96 | 0.92 | 1.88 | 0.80 | 0.92 | 0.88 | 1.84 |
time (sec) |
N/A | 0.167 | 0.095 | 0.816 | 0.113 | 0.082 | 0.534 | 0.153 | 0.596 | 6.085 |
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 | 23 | 25 | 35 | 20 | 19 | 31 | 20 | 31 | 29 | 27 |
N.S. |
1 | 1.09 | 1.52 | 0.87 | 0.83 | 1.35 | 0.87 | 1.35 | 1.26 | 1.17 |
time (sec) |
N/A | 0.165 | 0.081 | 0.747 | 0.115 | 0.076 | 0.438 | 0.146 | 0.350 | 6.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 20 | 23 | 27 | 18 | 0 | 18 | 15 | 0 |
N.S. |
1 | 1.00 | 1.05 | 1.21 | 1.42 | 0.95 | 0.00 | 0.95 | 0.79 | 0.00 |
time (sec) |
N/A | 0.157 | 0.079 | 0.800 | 0.119 | 0.073 | 0.000 | 0.150 | 0.567 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 561 | 596 | 1289 | 1212 | 0 | 590 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.06 | 2.30 | 2.16 | 0.00 | 1.05 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.037 | 34.485 | 3.248 | 0.000 | 0.100 | 0.000 | 0.000 | 200.047 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 493 | 522 | 1144 | 892 | 0 | 481 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.06 | 2.32 | 1.81 | 0.00 | 0.98 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.722 | 32.519 | 2.837 | 0.000 | 0.092 | 0.000 | 0.000 | 200.042 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 424 | 447 | 936 | 811 | 0 | 417 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.05 | 2.21 | 1.91 | 0.00 | 0.98 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.553 | 27.838 | 1.987 | 0.000 | 0.101 | 0.000 | 0.000 | 200.040 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 399 | 424 | 865 | 795 | 0 | 418 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.06 | 2.17 | 1.99 | 0.00 | 1.05 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.531 | 25.462 | 1.234 | 0.000 | 0.110 | 0.000 | 0.000 | 200.049 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 477 | 521 | 962 | 967 | 0 | 662 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 2.02 | 2.03 | 0.00 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.662 | 29.911 | 1.375 | 0.000 | 0.103 | 0.000 | 0.000 | 20.389 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 597 | 644 | 1252 | 1149 | 0 | 1188 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 2.10 | 1.92 | 0.00 | 1.99 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.910 | 34.003 | 1.796 | 0.000 | 0.140 | 0.000 | 0.000 | 99.843 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 683 | 734 | 7541 | 1665 | 0 | 727 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.07 | 11.04 | 2.44 | 0.00 | 1.06 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 1.177 | 34.972 | 4.911 | 0.000 | 0.101 | 0.000 | 0.000 | 200.036 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 559 | 594 | 831 | 1182 | 0 | 585 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.06 | 1.49 | 2.11 | 0.00 | 1.05 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.862 | 33.402 | 3.896 | 0.000 | 0.093 | 0.000 | 0.000 | 200.033 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 495 | 525 | 1193 | 1177 | 0 | 630 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.06 | 2.41 | 2.38 | 0.00 | 1.27 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.762 | 33.174 | 5.747 | 0.000 | 0.104 | 0.000 | 0.000 | 200.050 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 479 | 508 | 978 | 1043 | 0 | 614 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 2.04 | 2.18 | 0.00 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.707 | 28.413 | 10.449 | 0.000 | 0.102 | 0.000 | 0.000 | 56.533 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 570 | 613 | 1269 | 1153 | 0 | 1032 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.08 | 2.23 | 2.02 | 0.00 | 1.81 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.895 | 33.068 | 7.417 | 0.000 | 0.114 | 0.000 | 0.000 | 200.040 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 704 | 753 | 5469 | 1372 | 0 | 1838 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.07 | 7.77 | 1.95 | 0.00 | 2.61 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 1.265 | 35.128 | 8.750 | 0.000 | 0.163 | 0.000 | 0.000 | 200.046 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 827 | 884 | 10879 | 2544 | 0 | 914 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.07 | 13.15 | 3.08 | 0.00 | 1.11 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 1.471 | 35.419 | 8.994 | 0.000 | 0.108 | 0.000 | 0.000 | 200.049 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 696 | 737 | 7946 | 2072 | 0 | 1057 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.06 | 11.42 | 2.98 | 0.00 | 1.52 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 1.213 | 35.194 | 9.786 | 0.000 | 0.112 | 0.000 | 0.000 | 200.043 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 602 | 641 | 5407 | 1870 | 0 | 1091 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.06 | 8.98 | 3.11 | 0.00 | 1.81 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.015 | 34.918 | 10.821 | 0.000 | 0.113 | 0.000 | 0.000 | 200.032 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 583 | 620 | 1283 | 1497 | 0 | 1018 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.06 | 2.20 | 2.57 | 0.00 | 1.75 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.954 | 33.213 | 15.309 | 0.000 | 0.113 | 0.000 | 0.000 | 200.034 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 685 | 754 | 1446 | 1524 | 0 | 1719 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.10 | 2.11 | 2.22 | 0.00 | 2.51 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 1.202 | 23.505 | 21.018 | 0.000 | 0.153 | 0.000 | 0.000 | 200.040 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 889 | 966 | 8108 | 1744 | 0 | 2808 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.09 | 9.12 | 1.96 | 0.00 | 3.16 | 0.00 | 0.00 | 0.02 | 0.00 |
time (sec) |
N/A | 1.574 | 35.745 | 13.198 | 0.000 | 0.271 | 0.000 | 0.000 | 200.049 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 580 | 620 | 1318 | 1221 | 0 | 589 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.07 | 2.27 | 2.11 | 0.00 | 1.02 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.097 | 34.554 | 5.860 | 0.000 | 0.093 | 0.000 | 0.000 | 200.066 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 489 | 520 | 734 | 967 | 0 | 487 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.06 | 1.50 | 1.98 | 0.00 | 1.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.817 | 29.129 | 4.928 | 0.000 | 0.090 | 0.000 | 0.000 | 200.032 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 419 | 443 | 609 | 819 | 0 | 418 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.06 | 1.45 | 1.95 | 0.00 | 1.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.604 | 25.646 | 2.461 | 0.000 | 0.088 | 0.000 | 0.000 | 200.042 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 188 | 365 | 746 | 0 | 359 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.06 | 2.05 | 4.19 | 0.00 | 2.02 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.270 | 21.575 | 1.327 | 0.000 | 0.091 | 0.000 | 0.000 | 200.043 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 189 | 308 | 287 | 0 | 128 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.06 | 1.72 | 1.60 | 0.00 | 0.72 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.288 | 22.532 | 2.957 | 0.000 | 0.079 | 0.000 | 0.000 | 200.035 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 238 | 248 | 408 | 872 | 0 | 459 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.04 | 1.71 | 3.66 | 0.00 | 1.93 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.342 | 11.554 | 5.428 | 0.000 | 0.092 | 0.000 | 0.000 | 200.031 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 503 | 547 | 643 | 990 | 0 | 774 | 0 | 0 | 124 | 0 |
N.S. |
1 | 1.09 | 1.28 | 1.97 | 0.00 | 1.54 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.762 | 15.697 | 9.254 | 0.000 | 0.097 | 0.000 | 0.000 | 14.913 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 609 | 675 | 983 | 1158 | 0 | 1403 | 0 | 0 | 160 | 0 |
N.S. |
1 | 1.11 | 1.61 | 1.90 | 0.00 | 2.30 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 1.056 | 30.036 | 11.920 | 0.000 | 0.154 | 0.000 | 0.000 | 32.083 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 621 | 653 | 890 | 1364 | 0 | 1060 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.05 | 1.43 | 2.20 | 0.00 | 1.71 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.061 | 22.318 | 13.251 | 0.000 | 0.117 | 0.000 | 0.000 | 200.028 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 513 | 552 | 1207 | 1092 | 0 | 793 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.08 | 2.35 | 2.13 | 0.00 | 1.55 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.807 | 21.774 | 5.102 | 0.000 | 0.110 | 0.000 | 0.000 | 200.045 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 437 | 476 | 964 | 953 | 0 | 621 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.09 | 2.21 | 2.18 | 0.00 | 1.42 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.630 | 17.032 | 2.029 | 0.000 | 0.098 | 0.000 | 0.000 | 200.039 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 406 | 445 | 879 | 842 | 0 | 488 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.10 | 2.17 | 2.07 | 0.00 | 1.20 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.555 | 28.116 | 2.002 | 0.000 | 0.089 | 0.000 | 0.000 | 200.031 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 460 | 522 | 976 | 1197 | 0 | 768 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.13 | 2.12 | 2.60 | 0.00 | 1.67 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.644 | 16.865 | 5.895 | 0.000 | 0.103 | 0.000 | 0.000 | 200.034 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 594 | 642 | 1172 | 1849 | 0 | 1614 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.08 | 1.97 | 3.11 | 0.00 | 2.72 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.913 | 18.290 | 9.566 | 0.000 | 0.130 | 0.000 | 0.000 | 200.033 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 723 | 785 | 1525 | 1964 | 0 | 3059 | 0 | 0 | 274 | 0 |
N.S. |
1 | 1.09 | 2.11 | 2.72 | 0.00 | 4.23 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 1.299 | 23.594 | 12.080 | 0.000 | 0.232 | 0.000 | 0.000 | 14.542 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 804 | 821 | 7889 | 1836 | 0 | 2336 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.02 | 9.81 | 2.28 | 0.00 | 2.91 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 1.456 | 28.766 | 9.060 | 0.000 | 0.155 | 0.000 | 0.000 | 200.030 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 672 | 690 | 5598 | 1502 | 0 | 1802 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.03 | 8.33 | 2.24 | 0.00 | 2.68 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 1.100 | 25.254 | 8.227 | 0.000 | 0.128 | 0.000 | 0.000 | 200.029 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 570 | 619 | 1343 | 1229 | 0 | 1364 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.09 | 2.36 | 2.16 | 0.00 | 2.39 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.890 | 33.036 | 6.144 | 0.000 | 0.115 | 0.000 | 0.000 | 200.030 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 522 | 570 | 1141 | 1064 | 0 | 1005 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.09 | 2.19 | 2.04 | 0.00 | 1.93 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.858 | 19.882 | 1.895 | 0.000 | 0.178 | 0.000 | 0.000 | 200.028 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 585 | 657 | 1323 | 1486 | 0 | 1722 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.12 | 2.26 | 2.54 | 0.00 | 2.94 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.878 | 21.429 | 1.927 | 0.000 | 0.150 | 0.000 | 0.000 | 200.035 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 705 | 776 | 5566 | 1789 | 0 | 2574 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.10 | 7.90 | 2.54 | 0.00 | 3.65 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 1.152 | 23.584 | 10.432 | 0.000 | 0.178 | 0.000 | 0.000 | 200.039 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 86 | 65 | 0 | 26 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.00 | 2.87 | 2.17 | 0.00 | 0.87 | 0.00 | 0.00 | 1.13 | 0.00 |
time (sec) |
N/A | 0.164 | 30.112 | 1.000 | 0.000 | 0.077 | 0.000 | 0.000 | 0.471 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 63 | 51 | 0 | 120 | 0 | 44 | 50 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.71 | 0.00 | 1.67 | 0.00 | 0.61 | 0.69 | 0.00 |
time (sec) |
N/A | 0.221 | 0.026 | 0.960 | 0.000 | 0.082 | 0.000 | 0.123 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 63 | 63 | 51 | 0 | 120 | 0 | 44 | 50 | 0 |
N.S. |
1 | 0.88 | 0.88 | 0.71 | 0.00 | 1.67 | 0.00 | 0.61 | 0.69 | 0.00 |
time (sec) |
N/A | 0.196 | 0.003 | 0.788 | 0.000 | 0.076 | 0.000 | 0.107 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 564 | 376 | 473 | 0 | 0 | 0 | 0 | 0 | 96 | 0 |
N.S. |
1 | 0.67 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.520 | 1.638 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.243 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 683 | 206 | 0 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 3.06 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.671 | 10.467 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.039 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 634 | 164 | 0 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 4.17 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.561 | 10.299 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.040 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 572 | 113 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 4.77 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.447 | 10.189 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.047 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 533 | 95 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 6.06 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.429 | 0.031 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.037 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 180 | 0 | 0 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.397 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.035 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F(-1) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 189 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.315 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 96.022 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 187 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.312 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 5.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 546 | 165 | 0 | 0 | 0 | 0 | 0 | 61 | 0 |
N.S. |
1 | 3.62 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.505 | 10.180 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.455 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 483 | 111 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 4.13 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.374 | 10.104 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.309 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 451 | 84 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 5.31 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.346 | 0.020 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 182 | 180 | 0 | 0 | 0 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.375 | 8.957 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 4.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 189 | 187 | 0 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.313 | 9.772 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 1143 | 172 | 0 | 0 | 0 | 0 | 0 | 172 | 0 |
N.S. |
1 | 7.78 | 1.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.17 | 0.00 |
time (sec) |
N/A | 0.972 | 10.314 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.327 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 1083 | 167 | 0 | 0 | 0 | 0 | 0 | 109 | 0 |
N.S. |
1 | 9.26 | 1.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.825 | 11.195 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 1062 | 102 | 0 | 0 | 0 | 0 | 0 | 51 | 0 |
N.S. |
1 | 12.35 | 1.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.762 | 0.044 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 182 | 180 | 0 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.317 | 10.420 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.044 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 189 | 187 | 0 | 0 | 0 | 0 | 0 | 178 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.94 | 0.00 |
time (sec) |
N/A | 0.314 | 11.610 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.353 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 1211 | 299 | 0 | 0 | 0 | 0 | 0 | 361 | 0 |
N.S. |
1 | 8.07 | 1.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.41 | 0.00 |
time (sec) |
N/A | 1.009 | 10.857 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.336 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 1133 | 200 | 0 | 0 | 0 | 0 | 0 | 235 | 0 |
N.S. |
1 | 9.60 | 1.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.99 | 0.00 |
time (sec) |
N/A | 0.827 | 11.528 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.322 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 1112 | 138 | 0 | 0 | 0 | 0 | 0 | 114 | 0 |
N.S. |
1 | 12.93 | 1.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.33 | 0.00 |
time (sec) |
N/A | 0.800 | 10.165 | 0.000 | 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 | A | A | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 182 | 180 | 0 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.317 | 11.592 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.044 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 189 | 190 | 0 | 0 | 0 | 0 | 0 | 391 | 0 |
N.S. |
1 | 1.00 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.07 | 0.00 |
time (sec) |
N/A | 0.305 | 11.758 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.807 | 0.000 |