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 | C | C | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 145 | 88 | 29 | 126 | 84 | 184 | 0 | 10 | 0 |
N.S. |
1 | 1.17 | 0.71 | 0.23 | 1.02 | 0.68 | 1.48 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.506 | 0.053 | 0.534 | 0.134 | 0.154 | 1.154 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 125 | 83 | 29 | 74 | 78 | 156 | 0 | 10 | 0 |
N.S. |
1 | 1.15 | 0.76 | 0.27 | 0.68 | 0.72 | 1.43 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.603 | 0.041 | 0.484 | 0.046 | 0.090 | 0.989 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 113 | 79 | 29 | 110 | 85 | 53 | 0 | 10 | 0 |
N.S. |
1 | 1.14 | 0.80 | 0.29 | 1.11 | 0.86 | 0.54 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.425 | 0.051 | 0.505 | 0.127 | 0.089 | 0.523 | 0.000 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 93 | 71 | 29 | 62 | 65 | 121 | 0 | 10 | 0 |
N.S. |
1 | 1.11 | 0.85 | 0.35 | 0.74 | 0.77 | 1.44 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.472 | 0.030 | 0.474 | 0.038 | 0.088 | 0.948 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 82 | 74 | 62 | 94 | 58 | 112 | 0 | 10 | 0 |
N.S. |
1 | 1.11 | 1.00 | 0.84 | 1.27 | 0.78 | 1.51 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.344 | 0.013 | 0.547 | 0.117 | 0.084 | 0.569 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 61 | 59 | 54 | 49 | 53 | 80 | 0 | 10 | 0 |
N.S. |
1 | 1.03 | 1.00 | 0.92 | 0.83 | 0.90 | 1.36 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.358 | 0.010 | 0.529 | 0.049 | 0.086 | 0.587 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 50 | 49 | 29 | 70 | 51 | 53 | 0 | 8 | 0 |
N.S. |
1 | 1.02 | 1.00 | 0.59 | 1.43 | 1.04 | 1.08 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.264 | 0.011 | 0.495 | 0.137 | 0.081 | 0.340 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 25 | 26 | 26 | 48 | 0 | 6 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 1.00 | 1.00 | 1.85 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.174 | 0.004 | 0.813 | 0.030 | 0.102 | 0.616 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 0 | 29 | 0 | 0 | 46 | 0 | 10 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.40 | 0.00 | 0.00 | 0.63 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.337 | 0.000 | 0.516 | 0.000 | 0.000 | 0.373 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 24 | 38 | 25 | 42 | 0 | 10 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 1.41 | 0.93 | 1.56 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.217 | 0.010 | 0.506 | 0.095 | 0.080 | 0.348 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 42 | 44 | 27 | 61 | 45 | 51 | 0 | 10 | 0 |
N.S. |
1 | 0.95 | 1.00 | 0.61 | 1.39 | 1.02 | 1.16 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.259 | 0.009 | 0.489 | 0.189 | 0.086 | 0.398 | 0.000 | 0.249 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 55 | 52 | 46 | 42 | 44 | 56 | 0 | 10 | 0 |
N.S. |
1 | 1.06 | 1.00 | 0.88 | 0.81 | 0.85 | 1.08 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.370 | 0.013 | 0.556 | 0.104 | 0.088 | 0.767 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 71 | 69 | 65 | 61 | 54 | 110 | 0 | 10 | 0 |
N.S. |
1 | 1.03 | 1.00 | 0.94 | 0.88 | 0.78 | 1.59 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.320 | 0.012 | 0.453 | 0.184 | 0.080 | 0.670 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 83 | 77 | 29 | 48 | 65 | 46 | 0 | 10 | 0 |
N.S. |
1 | 1.08 | 1.00 | 0.38 | 0.62 | 0.84 | 0.60 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.469 | 0.016 | 0.539 | 0.112 | 0.090 | 0.564 | 0.000 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 98 | 76 | 29 | 61 | 80 | 56 | 0 | 10 | 0 |
N.S. |
1 | 1.04 | 0.81 | 0.31 | 0.65 | 0.85 | 0.60 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.393 | 0.044 | 0.488 | 0.184 | 0.091 | 0.753 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 111 | 85 | 79 | 46 | 78 | 68 | 0 | 10 | 0 |
N.S. |
1 | 1.09 | 0.83 | 0.77 | 0.45 | 0.76 | 0.67 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.578 | 0.049 | 0.576 | 0.108 | 0.089 | 2.751 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 127 | 84 | 29 | 61 | 80 | 185 | 0 | 10 | 0 |
N.S. |
1 | 1.07 | 0.71 | 0.24 | 0.51 | 0.67 | 1.55 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.486 | 0.044 | 0.487 | 0.185 | 0.086 | 1.473 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 139 | 96 | 29 | 48 | 91 | 48 | 0 | 10 | 0 |
N.S. |
1 | 1.09 | 0.76 | 0.23 | 0.38 | 0.72 | 0.38 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.697 | 0.137 | 0.527 | 0.118 | 0.093 | 1.552 | 0.000 | 0.245 | 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 | 296 | 271 | 424 | 276 | 0 | 376 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.92 | 1.43 | 0.93 | 0.00 | 1.27 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.600 | 0.588 | 0.662 | 0.000 | 0.120 | 0.000 | 0.000 | 0.231 | 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 | 193 | 183 | 236 | 189 | 0 | 248 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.95 | 1.22 | 0.98 | 0.00 | 1.28 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.453 | 0.325 | 0.598 | 0.000 | 0.104 | 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 | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 115 | 61 | 109 | 0 | 132 | 0 | 0 | 14 | 0 |
N.S. |
1 | 0.95 | 0.50 | 0.90 | 0.00 | 1.09 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.357 | 0.170 | 0.542 | 0.000 | 0.110 | 0.000 | 0.000 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 89 | 33 | 43 | 45 | 0 | 0 | 8 | 0 |
N.S. |
1 | 1.00 | 2.47 | 0.92 | 1.19 | 1.25 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.189 | 0.023 | 0.468 | 0.033 | 0.083 | 0.000 | 0.000 | 0.196 | 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 | 14 | 14 | 16 | 14 | 16 | 16 | 12 | 16 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 1.14 | 0.86 | 1.14 | 1.14 | 1.14 |
time (sec) |
N/A | 0.199 | 0.020 | 0.449 | 0.640 | 0.076 | 0.410 | 0.103 | 0.197 | 4.172 |
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 | 14 | 14 | 16 | 14 | 16 | 27 | 14 | 16 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 1.93 | 1.00 | 1.14 | 1.14 | 1.14 |
time (sec) |
N/A | 0.197 | 2.228 | 0.451 | 0.312 | 0.083 | 0.577 | 0.107 | 0.177 | 3.718 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 197 | 166 | 189 | 503 | 175 | 0 | 0 | 12 | 0 |
N.S. |
1 | 0.86 | 0.72 | 0.83 | 2.20 | 0.76 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.433 | 0.237 | 0.525 | 0.943 | 0.101 | 0.000 | 0.000 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 133 | 115 | 121 | 424 | 147 | 0 | 0 | 12 | 0 |
N.S. |
1 | 0.90 | 0.78 | 0.82 | 2.88 | 1.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.379 | 0.171 | 0.536 | 0.655 | 0.088 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 84 | 51 | 80 | 307 | 104 | 0 | 0 | 10 | 0 |
N.S. |
1 | 0.88 | 0.53 | 0.83 | 3.20 | 1.08 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.301 | 0.130 | 0.535 | 0.552 | 0.097 | 0.000 | 0.000 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 89 | 33 | 43 | 45 | 0 | 0 | 8 | 0 |
N.S. |
1 | 1.00 | 2.47 | 0.92 | 1.19 | 1.25 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.192 | 0.019 | 0.403 | 0.026 | 0.080 | 0.000 | 0.000 | 0.207 | 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 | 10 | 10 | 12 | 10 | 12 | 12 | 8 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 0.80 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.190 | 0.013 | 0.343 | 0.590 | 0.073 | 0.321 | 0.099 | 0.256 | 3.623 |
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 | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.201 | 1.464 | 0.315 | 0.310 | 0.093 | 0.273 | 0.106 | 0.189 | 3.711 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 253 | 0 | 181 | 0 | 0 | 183 | 0 | 0 | 12 | 0 |
N.S. |
1 | 0.00 | 0.72 | 0.00 | 0.00 | 0.72 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.000 | 0.092 | 0.000 | 0.000 | 0.094 | 0.000 | 0.000 | 0.174 | 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 | 239 | 459 | 171 | 324 | 0 | 184 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.92 | 0.72 | 1.36 | 0.00 | 0.77 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 2.412 | 0.208 | 0.731 | 0.000 | 0.096 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 265 | 357 | 0 | 0 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 2.227 | 0.000 | 0.000 | 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 | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 292 | 137 | 208 | 0 | 149 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.65 | 0.77 | 1.18 | 0.00 | 0.84 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 1.262 | 0.101 | 0.613 | 0.000 | 0.093 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 180 | 113 | 0 | 0 | 117 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.29 | 0.81 | 0.00 | 0.00 | 0.84 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 1.064 | 0.040 | 0.000 | 0.000 | 0.090 | 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 | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 169 | 100 | 122 | 0 | 111 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.36 | 0.81 | 0.98 | 0.00 | 0.90 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.658 | 0.087 | 0.616 | 0.000 | 0.093 | 0.000 | 0.000 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 149 | 0 | 0 | 0 | 0 | 0 | 0 | 10 | 0 |
N.S. |
1 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.537 | 0.000 | 0.000 | 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 | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 61 | 55 | 49 | 0 | 60 | 0 | 0 | 8 | 0 |
N.S. |
1 | 1.11 | 1.00 | 0.89 | 0.00 | 1.09 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.292 | 0.012 | 0.690 | 0.000 | 0.092 | 0.000 | 0.000 | 0.181 | 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 | 10 | 10 | 12 | 10 | 12 | 12 | 8 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 0.80 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.184 | 0.014 | 0.094 | 0.059 | 0.078 | 1.066 | 0.104 | 0.186 | 3.630 |
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 | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.261 | 0.021 | 0.182 | 0.064 | 0.089 | 0.990 | 0.107 | 0.234 | 3.519 |
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 | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.261 | 0.016 | 0.182 | 0.064 | 0.092 | 1.046 | 0.104 | 0.200 | 3.586 |
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 | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.509 | 0.020 | 0.184 | 0.061 | 0.094 | 1.084 | 0.102 | 0.186 | 3.532 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 142 | 127 | 0 | 0 | 111 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.12 | 1.00 | 0.00 | 0.00 | 0.87 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.888 | 0.006 | 0.000 | 0.000 | 0.125 | 0.000 | 0.000 | 0.191 | 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 | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.940 | 0.022 | 0.178 | 0.057 | 0.086 | 1.234 | 0.105 | 0.233 | 3.503 |
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 | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 1.417 | 0.017 | 0.179 | 0.060 | 0.082 | 1.522 | 0.107 | 0.210 | 3.494 |
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 | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 1.649 | 0.021 | 0.168 | 0.076 | 0.086 | 1.570 | 0.101 | 0.204 | 3.541 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 242 | 0 | 242 | 0 | 0 | 187 | 0 | 0 | 12 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.00 | 0.00 | 0.77 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.000 | 0.008 | 0.000 | 0.000 | 0.109 | 0.000 | 0.000 | 0.249 | 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 | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 2.778 | 0.022 | 0.189 | 0.056 | 0.079 | 2.230 | 0.110 | 0.211 | 3.792 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 497 | 460 | 0 | 0 | 0 | 0 | 0 | 0 | 18 | 0 |
N.S. |
1 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.579 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 279 | 256 | 0 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.431 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 72 | 67 | 60 | 0 | 89 | 0 | 0 | 10 | 0 |
N.S. |
1 | 1.03 | 0.96 | 0.86 | 0.00 | 1.27 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.485 | 0.011 | 0.454 | 0.000 | 0.092 | 0.000 | 0.000 | 0.209 | 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 | 16 | 16 | 18 | 16 | 18 | 18 | 14 | 18 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.12 | 0.88 | 1.12 | 1.12 | 1.12 |
time (sec) |
N/A | 0.206 | 0.027 | 0.201 | 0.063 | 0.081 | 0.460 | 0.097 | 0.207 | 4.452 |
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 | 16 | 16 | 18 | 16 | 18 | 29 | 15 | 18 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.81 | 0.94 | 1.12 | 1.12 | 1.12 |
time (sec) |
N/A | 0.205 | 0.057 | 0.323 | 0.066 | 0.087 | 0.668 | 0.114 | 0.191 | 4.588 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 257 | 319 | 0 | 0 | 448 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.11 | 1.38 | 0.00 | 0.00 | 1.94 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.938 | 4.408 | 0.000 | 0.000 | 0.119 | 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 | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 253 | 319 | 0 | 0 | 448 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.11 | 1.41 | 0.00 | 0.00 | 1.97 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.844 | 4.231 | 0.000 | 0.000 | 0.111 | 0.000 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 238 | 316 | 0 | 0 | 445 | 0 | 0 | 15 | 0 |
N.S. |
1 | 1.11 | 1.48 | 0.00 | 0.00 | 2.08 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.781 | 4.258 | 0.000 | 0.000 | 0.103 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 64 | 164 | 63 | 81 | 119 | 0 | 0 | 19 | 0 |
N.S. |
1 | 0.98 | 2.52 | 0.97 | 1.25 | 1.83 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.288 | 0.071 | 1.838 | 0.032 | 0.101 | 0.000 | 0.000 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 240 | 195 | 0 | 0 | 444 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.11 | 0.90 | 0.00 | 0.00 | 2.05 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.857 | 2.529 | 0.000 | 0.000 | 0.105 | 0.000 | 0.000 | 0.268 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 254 | 200 | 0 | 0 | 460 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.11 | 0.88 | 0.00 | 0.00 | 2.02 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.850 | 2.537 | 0.000 | 0.000 | 0.120 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 280 | 343 | 244 | 0 | 0 | 691 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.22 | 0.87 | 0.00 | 0.00 | 2.47 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.066 | 3.596 | 0.000 | 0.000 | 0.120 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 0 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.401 | 0.000 | 0.000 | 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 | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 0 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.404 | 0.000 | 0.000 | 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 | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 99 | 0 | 0 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.375 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 99 | 0 | 0 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.364 | 0.000 | 0.000 | 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 | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 12 | 11 | 11 | 10 | 0 | 19 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.85 | 0.85 | 0.77 | 0.00 | 1.46 | 0.00 |
time (sec) |
N/A | 0.187 | 0.004 | 0.322 | 0.025 | 0.081 | 0.193 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 12 | 11 | 11 | 10 | 0 | 17 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.85 | 0.85 | 0.77 | 0.00 | 1.31 | 0.00 |
time (sec) |
N/A | 0.187 | 0.004 | 0.280 | 0.024 | 0.096 | 0.114 | 0.000 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 10 | 9 | 9 | 8 | 0 | 19 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 1.00 | 1.00 | 0.89 | 0.00 | 2.11 | 0.00 |
time (sec) |
N/A | 0.196 | 0.011 | 0.324 | 0.028 | 0.074 | 0.120 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 12 | 11 | 11 | 10 | 0 | 19 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 1.00 | 1.00 | 0.91 | 0.00 | 1.73 | 0.00 |
time (sec) |
N/A | 0.192 | 0.004 | 0.385 | 0.023 | 0.072 | 0.287 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 12 | 11 | 11 | 14 | 0 | 19 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.85 | 0.85 | 1.08 | 0.00 | 1.46 | 0.00 |
time (sec) |
N/A | 0.191 | 0.004 | 0.571 | 0.034 | 0.091 | 0.459 | 0.000 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 18 | 17 | 18 | 31 | 0 | 19 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.06 | 1.82 | 0.00 | 1.12 | 0.00 |
time (sec) |
N/A | 0.195 | 0.006 | 0.444 | 0.024 | 0.089 | 0.595 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | A | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 232 | 0 | 232 | 0 | 0 | 169 | 301 | 0 | 20 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.00 | 0.00 | 0.73 | 1.30 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.000 | 0.008 | 0.000 | 0.000 | 0.091 | 13.811 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 440 | 153 | 318 | 0 | 167 | 0 | 0 | 20 | 0 |
N.S. |
1 | 2.04 | 0.71 | 1.47 | 0.00 | 0.77 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 2.113 | 0.181 | 5.027 | 0.000 | 0.095 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 338 | 0 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 2.003 | 0.000 | 0.000 | 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 | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 273 | 120 | 202 | 0 | 132 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.73 | 0.76 | 1.28 | 0.00 | 0.84 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 1.136 | 0.116 | 1.783 | 0.000 | 0.103 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 161 | 120 | 0 | 0 | 105 | 151 | 0 | 20 | 0 |
N.S. |
1 | 1.34 | 1.00 | 0.00 | 0.00 | 0.88 | 1.26 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.914 | 0.006 | 0.000 | 0.000 | 0.094 | 1.325 | 0.000 | 0.188 | 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 | 105 | 150 | 83 | 115 | 0 | 94 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.43 | 0.79 | 1.10 | 0.00 | 0.90 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.539 | 0.076 | 0.862 | 0.000 | 0.087 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 132 | 0 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.443 | 0.000 | 0.000 | 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 | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 44 | 46 | 0 | 47 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.00 | 0.90 | 0.94 | 0.00 | 0.96 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.238 | 0.018 | 1.042 | 0.000 | 0.086 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 12 | 11 | 11 | 10 | 0 | 17 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.85 | 0.85 | 0.77 | 0.00 | 1.31 | 0.00 |
time (sec) |
N/A | 0.177 | 0.000 | 0.336 | 0.034 | 0.078 | 0.112 | 0.000 | 0.191 | 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 | 18 | 20 | 20 | 19 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.00 | 0.95 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.187 | 0.021 | 0.253 | 0.124 | 0.086 | 1.043 | 0.125 | 0.203 | 3.423 |
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 | 18 | 20 | 20 | 20 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.196 | 0.021 | 0.256 | 0.121 | 0.078 | 1.057 | 0.129 | 0.209 | 3.457 |
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 | 18 | 20 | 20 | 20 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.420 | 0.022 | 0.273 | 0.128 | 0.085 | 1.260 | 0.132 | 0.204 | 3.403 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 123 | 109 | 0 | 0 | 98 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.13 | 1.00 | 0.00 | 0.00 | 0.90 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.766 | 0.006 | 0.000 | 0.000 | 0.093 | 0.000 | 0.000 | 0.208 | 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 | 18 | 20 | 20 | 20 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.822 | 0.024 | 0.248 | 0.117 | 0.096 | 3.078 | 0.131 | 0.214 | 3.439 |
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 | 18 | 20 | 20 | 20 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 1.270 | 0.024 | 0.273 | 0.119 | 0.083 | 5.644 | 0.127 | 0.199 | 3.416 |
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 | 18 | 20 | 20 | 20 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 1.487 | 0.028 | 0.249 | 0.134 | 0.082 | 10.841 | 0.131 | 0.184 | 3.456 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 224 | 0 | 224 | 0 | 0 | 172 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.00 | 0.00 | 0.77 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.000 | 0.008 | 0.000 | 0.000 | 0.116 | 0.000 | 0.000 | 0.205 | 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 | 18 | 20 | 20 | 20 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 2.471 | 0.027 | 0.221 | 0.119 | 0.080 | 35.825 | 0.127 | 0.196 | 3.337 |
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 | 18 | 20 | 20 | 20 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 2.311 | 0.025 | 0.244 | 0.129 | 0.084 | 65.382 | 0.131 | 0.214 | 3.393 |
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 | 19 | 19 | 21 | 17 | 19 | 19 | 19 | 19 | 19 | 19 |
N.S. |
1 | 1.00 | 1.11 | 0.89 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.181 | 0.053 | 0.263 | 0.136 | 0.103 | 1.163 | 0.142 | 0.193 | 3.434 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 307 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 439 | 163 | 321 | 0 | 169 | 0 | 0 | 20 | 0 |
N.S. |
1 | 2.02 | 0.75 | 1.48 | 0.00 | 0.78 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 2.077 | 0.130 | 8.756 | 0.000 | 0.099 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 284 | 184 | 0 | 0 | 141 | 264 | 0 | 20 | 0 |
N.S. |
1 | 1.54 | 1.00 | 0.00 | 0.00 | 0.77 | 1.43 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 1.944 | 0.006 | 0.000 | 0.000 | 0.091 | 4.589 | 0.000 | 0.200 | 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 | 166 | 283 | 126 | 212 | 0 | 139 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.70 | 0.76 | 1.28 | 0.00 | 0.84 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 1.164 | 0.125 | 3.086 | 0.000 | 0.110 | 0.000 | 0.000 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 227 | 0 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 1.069 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.210 | 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 | 108 | 149 | 90 | 119 | 0 | 97 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.38 | 0.83 | 1.10 | 0.00 | 0.90 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.586 | 0.060 | 1.388 | 0.000 | 0.094 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 78 | 73 | 0 | 0 | 58 | 114 | 0 | 20 | 0 |
N.S. |
1 | 1.07 | 1.00 | 0.00 | 0.00 | 0.79 | 1.56 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.419 | 0.005 | 0.000 | 0.000 | 0.083 | 0.462 | 0.000 | 0.192 | 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 | 59 | 59 | 48 | 52 | 0 | 53 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.00 | 0.81 | 0.88 | 0.00 | 0.90 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.258 | 0.021 | 1.142 | 0.000 | 0.085 | 0.000 | 0.000 | 0.243 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 0 | 0 | 0 | 0 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.204 | 0.000 | 0.000 | 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 | 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 | 18 | 20 | 20 | 19 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.00 | 0.95 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.193 | 0.025 | 0.256 | 0.121 | 0.084 | 1.037 | 0.120 | 0.209 | 3.556 |