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 | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 136 | 133 | 319 | 138 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 2.35 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.285 | 0.104 | 0.053 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 90 | 95 | 154 | 83 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 1.71 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.251 | 0.043 | 0.051 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 96 | 101 | 211 | 95 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 2.20 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.250 | 0.063 | 0.049 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 91 | 43 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.65 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.274 | 0.025 | 0.043 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 87 | 65 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.47 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.355 | 0.078 | 0.042 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 10 | 0 | 0 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.156 | 0.186 | 0.060 | 0.000 | 0.000 | 0.855 | 0.383 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 251 | 418 | 173 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.47 | 2.44 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.729 | 0.228 | 0.079 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 126 | 167 | 200 | 109 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.33 | 1.59 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.821 | 0.278 | 0.061 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 125 | 176 | 277 | 117 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.41 | 2.22 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.869 | 0.157 | 0.055 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 94 | 112 | 56 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 1.26 | 0.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.694 | 0.148 | 0.044 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 76 | 81 | 138 | 83 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 1.82 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.424 | 0.105 | 0.039 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 10 | 0 | 0 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.158 | 0.194 | 0.059 | 0.000 | 0.000 | 6.304 | 0.411 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 264 | 327 | 417 | 225 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.24 | 1.58 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.672 | 0.572 | 0.084 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 190 | 247 | 272 | 139 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.30 | 1.43 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.831 | 0.859 | 0.063 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 191 | 253 | 280 | 154 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.32 | 1.47 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.070 | 0.307 | 0.056 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 132 | 146 | 73 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 1.23 | 0.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.677 | 0.272 | 0.047 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 105 | 118 | 143 | 110 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.12 | 1.36 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.565 | 0.196 | 0.040 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 10 | 0 | 0 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.158 | 0.173 | 0.055 | 0.000 | 0.000 | 60.723 | 0.423 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 12 | 12 | 14 | 12 | 115 | 14 | 12 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 9.58 | 1.17 | 1.00 | 1.17 | 1.17 |
time (sec) |
N/A | 0.325 | 0.643 | 0.606 | 0.684 | 0.251 | 5.242 | 0.589 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 12 | 12 | 14 | 12 | 115 | 14 | 12 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 9.58 | 1.17 | 1.00 | 1.17 | 1.17 |
time (sec) |
N/A | 0.313 | 0.551 | 0.460 | 0.696 | 0.263 | 2.712 | 0.565 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 150 | 148 | 122 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.339 | 0.038 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 56 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.193 | 0.018 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 12 | 12 | 14 | 12 | 14 | 14 | 10 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 1.17 | 0.83 | 1.17 | 1.17 |
time (sec) |
N/A | 0.161 | 0.299 | 0.319 | 0.347 | 0.241 | 0.404 | 0.434 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 12 | 12 | 14 | 12 | 157 | 14 | 12 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 13.08 | 1.17 | 1.00 | 1.17 | 1.17 |
time (sec) |
N/A | 0.161 | 0.324 | 0.348 | 0.956 | 0.247 | 0.705 | 0.435 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 12 | 0 | 0 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.14 | 0.86 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.160 | 0.557 | 0.049 | 0.000 | 0.000 | 57.059 | 1.874 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 12 | 0 | 0 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.14 | 0.86 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.162 | 0.792 | 0.049 | 0.000 | 0.000 | 1.100 | 1.209 | 0.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 12 | 0 | 0 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.14 | 0.86 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.162 | 0.700 | 0.048 | 0.000 | 0.000 | 0.521 | 1.060 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 12 | 0 | 0 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.14 | 0.86 | 0.00 | 0.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.165 | 0.631 | 0.052 | 0.000 | 0.000 | 3.786 | 0.967 | 0.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 12 | 12 | 14 | 12 | 0 | 14 | 12 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 0.00 | 1.17 | 1.00 | 1.17 | 1.17 |
time (sec) |
N/A | 0.165 | 0.439 | 0.607 | 0.000 | 0.259 | 3.488 | 0.824 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 167 | 159 | 132 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.357 | 0.067 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 171 | 163 | 137 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.354 | 0.053 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 86 | 75 | 138 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.88 | 1.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.316 | 0.016 | 0.121 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 79 | 77 | 73 | 240 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 0.92 | 3.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.265 | 0.038 | 0.073 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 10 | 10 | 12 | 10 | 0 | 12 | 8 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 0.00 | 1.20 | 0.80 | 1.20 | 1.20 |
time (sec) |
N/A | 0.162 | 0.251 | 0.069 | 0.000 | 0.263 | 0.372 | 0.320 | 0.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 10 | 10 | 12 | 10 | 0 | 12 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 0.00 | 1.20 | 1.00 | 1.20 | 1.20 |
time (sec) |
N/A | 0.164 | 0.550 | 0.046 | 0.000 | 0.250 | 0.537 | 0.318 | 0.084 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 14 | 14 | 16 | 12 | 0 | 16 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.14 | 0.86 | 0.00 | 1.14 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.169 | 1.964 | 0.076 | 0.000 | 0.253 | 151.119 | 0.558 | 0.092 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 14 | 14 | 16 | 12 | 0 | 14 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.14 | 0.86 | 0.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.165 | 3.007 | 0.058 | 0.000 | 0.246 | 3.534 | 0.572 | 0.088 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 14 | 14 | 16 | 12 | 0 | 20 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.14 | 0.86 | 0.00 | 1.43 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.163 | 1.263 | 0.055 | 0.000 | 0.278 | 1.520 | 0.449 | 0.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 14 | 14 | 16 | 12 | 0 | 20 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.14 | 0.86 | 0.00 | 1.43 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.169 | 1.143 | 0.059 | 0.000 | 0.265 | 12.301 | 0.479 | 0.087 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 76 | 88 | 81 | 68 | 70 | 61 | 80 | 95 | 0 |
N.S. |
1 | 1.16 | 1.07 | 0.89 | 0.92 | 0.80 | 1.05 | 1.25 | 0.00 |
time (sec) |
N/A | 0.214 | 0.025 | 0.022 | 0.289 | 0.267 | 0.265 | 0.279 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 60 | 63 | 49 | 60 | 59 | 53 | 65 | 74 | 0 |
N.S. |
1 | 1.05 | 0.82 | 1.00 | 0.98 | 0.88 | 1.08 | 1.23 | 0.00 |
time (sec) |
N/A | 0.219 | 0.028 | 0.014 | 0.283 | 0.246 | 0.205 | 0.277 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 56 | 56 | 48 | 49 | 49 | 54 | 64 | 45 |
N.S. |
1 | 1.10 | 1.10 | 0.94 | 0.96 | 0.96 | 1.06 | 1.25 | 0.88 |
time (sec) |
N/A | 0.189 | 0.015 | 0.013 | 0.291 | 0.244 | 0.161 | 0.265 | 0.158 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 30 | 29 | 31 | 26 | 29 | 28 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.97 | 1.03 | 0.87 | 0.97 | 0.93 |
time (sec) |
N/A | 0.155 | 0.010 | 0.010 | 0.304 | 0.260 | 0.069 | 0.259 | 0.179 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 71 | 52 | 118 | 0 | 0 | 0 | 0 | 48 |
N.S. |
1 | 1.13 | 0.83 | 1.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.76 |
time (sec) |
N/A | 0.349 | 0.072 | 0.094 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 36 | 39 | 47 | 55 | 39 | 325 | 34 |
N.S. |
1 | 1.00 | 1.09 | 1.18 | 1.42 | 1.67 | 1.18 | 9.85 | 1.03 |
time (sec) |
N/A | 0.194 | 0.005 | 0.012 | 0.278 | 0.260 | 0.959 | 0.303 | 0.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 44 | 46 | 36 | 35 | 61 | 163 | 0 |
N.S. |
1 | 1.00 | 1.13 | 1.18 | 0.92 | 0.90 | 1.56 | 4.18 | 0.00 |
time (sec) |
N/A | 0.180 | 0.012 | 0.011 | 0.290 | 0.252 | 0.743 | 0.279 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 67 | 61 | 69 | 80 | 117 | 284 | 0 |
N.S. |
1 | 1.00 | 1.08 | 0.98 | 1.11 | 1.29 | 1.89 | 4.58 | 0.00 |
time (sec) |
N/A | 0.207 | 0.014 | 0.013 | 0.312 | 0.280 | 1.562 | 0.442 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 109 | 95 | 125 | 142 | 111 | 170 | 194 | 0 |
N.S. |
1 | 1.07 | 0.93 | 1.23 | 1.39 | 1.09 | 1.67 | 1.90 | 0.00 |
time (sec) |
N/A | 0.411 | 0.118 | 0.053 | 0.293 | 0.241 | 0.276 | 0.276 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 76 | 84 | 73 | 119 | 0 | 99 | 126 | 155 | 0 |
N.S. |
1 | 1.11 | 0.96 | 1.57 | 0.00 | 1.30 | 1.66 | 2.04 | 0.00 |
time (sec) |
N/A | 0.374 | 0.050 | 0.045 | 0.000 | 0.251 | 0.208 | 0.275 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 51 | 47 | 72 | 72 | 65 | 82 | 75 | 142 |
N.S. |
1 | 1.09 | 1.00 | 1.53 | 1.53 | 1.38 | 1.74 | 1.60 | 3.02 |
time (sec) |
N/A | 0.259 | 0.027 | 0.042 | 0.285 | 0.250 | 0.105 | 0.287 | 0.377 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 90 | 105 | 143 | 294 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.17 | 1.59 | 3.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.483 | 0.122 | 0.072 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 81 | 78 | 126 | 165 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 1.56 | 2.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.429 | 0.209 | 0.045 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 178 | 201 | 163 | 235 | 273 | 194 | 328 | 368 | 0 |
N.S. |
1 | 1.13 | 0.92 | 1.32 | 1.53 | 1.09 | 1.84 | 2.07 | 0.00 |
time (sec) |
N/A | 0.778 | 0.297 | 0.046 | 0.319 | 0.252 | 0.373 | 0.293 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 125 | 138 | 114 | 219 | 0 | 169 | 264 | 285 | 0 |
N.S. |
1 | 1.10 | 0.91 | 1.75 | 0.00 | 1.35 | 2.11 | 2.28 | 0.00 |
time (sec) |
N/A | 0.600 | 0.094 | 0.049 | 0.000 | 0.242 | 0.285 | 0.283 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 83 | 77 | 132 | 141 | 108 | 160 | 150 | 242 |
N.S. |
1 | 1.01 | 0.94 | 1.61 | 1.72 | 1.32 | 1.95 | 1.83 | 2.95 |
time (sec) |
N/A | 0.324 | 0.063 | 0.043 | 0.311 | 0.247 | 0.142 | 0.275 | 0.439 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 123 | 141 | 244 | 530 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.15 | 1.98 | 4.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.604 | 0.174 | 0.079 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 134 | 283 | 349 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 2.07 | 2.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.636 | 0.235 | 0.099 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 104 | 91 | 102 | 0 | 0 | 0 | 173 | 0 |
N.S. |
1 | 0.86 | 0.75 | 0.84 | 0.00 | 0.00 | 0.00 | 1.43 | 0.00 |
time (sec) |
N/A | 0.402 | 0.217 | 0.037 | 0.000 | 0.000 | 0.000 | 0.274 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 56 | 56 | 58 | 0 | 0 | 0 | 86 | 0 |
N.S. |
1 | 0.89 | 0.89 | 0.92 | 0.00 | 0.00 | 0.00 | 1.37 | 0.00 |
time (sec) |
N/A | 0.456 | 0.077 | 0.033 | 0.000 | 0.000 | 0.000 | 0.273 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 48 | 44 | 48 | 0 | 0 | 0 | 49 | 0 |
N.S. |
1 | 0.91 | 0.83 | 0.91 | 0.00 | 0.00 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 0.366 | 0.057 | 0.033 | 0.000 | 0.000 | 0.000 | 0.287 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 14 | 16 | 15 | 12 | 0 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 1.07 | 0.86 | 0.00 | 1.14 |
time (sec) |
N/A | 0.176 | 0.206 | 0.074 | 0.352 | 0.243 | 0.655 | 0.000 | 0.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 14 | 14 | 16 | 14 | 16 | 19 | 14 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 1.36 | 1.00 | 1.14 | 1.14 |
time (sec) |
N/A | 0.180 | 1.919 | 0.095 | 0.356 | 0.231 | 0.591 | 0.546 | 0.108 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 156 | 140 | 125 | 149 | 0 | 0 | 0 | 646 | 0 |
N.S. |
1 | 0.90 | 0.80 | 0.96 | 0.00 | 0.00 | 0.00 | 4.14 | 0.00 |
time (sec) |
N/A | 0.345 | 0.562 | 0.042 | 0.000 | 0.000 | 0.000 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 90 | 86 | 79 | 77 | 0 | 0 | 0 | 326 | 0 |
N.S. |
1 | 0.96 | 0.88 | 0.86 | 0.00 | 0.00 | 0.00 | 3.62 | 0.00 |
time (sec) |
N/A | 0.433 | 0.319 | 0.030 | 0.000 | 0.000 | 0.000 | 0.284 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 83 | 72 | 76 | 0 | 0 | 0 | 192 | 0 |
N.S. |
1 | 0.97 | 0.84 | 0.88 | 0.00 | 0.00 | 0.00 | 2.23 | 0.00 |
time (sec) |
N/A | 0.551 | 0.210 | 0.036 | 0.000 | 0.000 | 0.000 | 0.280 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 14 | 14 | 16 | 14 | 165 | 30 | 14 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 11.79 | 2.14 | 1.00 | 1.14 | 1.14 |
time (sec) |
N/A | 0.177 | 5.007 | 0.067 | 0.613 | 0.236 | 1.068 | 0.527 | 0.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 14 | 14 | 16 | 14 | 182 | 36 | 15 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 13.00 | 2.57 | 1.07 | 1.14 | 1.14 |
time (sec) |
N/A | 0.179 | 34.229 | 0.091 | 0.766 | 0.236 | 0.970 | 0.842 | 0.116 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 197 | 248 | 168 | 290 | 0 | 0 | 0 | 1539 | 0 |
N.S. |
1 | 1.26 | 0.85 | 1.47 | 0.00 | 0.00 | 0.00 | 7.81 | 0.00 |
time (sec) |
N/A | 1.370 | 0.572 | 0.043 | 0.000 | 0.000 | 0.000 | 0.363 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 130 | 137 | 108 | 157 | 0 | 0 | 0 | 864 | 0 |
N.S. |
1 | 1.05 | 0.83 | 1.21 | 0.00 | 0.00 | 0.00 | 6.65 | 0.00 |
time (sec) |
N/A | 1.036 | 0.292 | 0.033 | 0.000 | 0.000 | 0.000 | 0.340 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 93 | 138 | 0 | 0 | 0 | 482 | 0 |
N.S. |
1 | 1.00 | 0.84 | 1.24 | 0.00 | 0.00 | 0.00 | 4.34 | 0.00 |
time (sec) |
N/A | 0.654 | 0.316 | 0.033 | 0.000 | 0.000 | 0.000 | 0.325 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 14 | 14 | 16 | 14 | 254 | 45 | 14 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 18.14 | 3.21 | 1.00 | 1.14 | 1.14 |
time (sec) |
N/A | 0.176 | 1.713 | 0.069 | 2.279 | 0.246 | 1.657 | 0.824 | 0.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 14 | 14 | 16 | 14 | 283 | 53 | 15 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 20.21 | 3.79 | 1.07 | 1.14 | 1.14 |
time (sec) |
N/A | 0.180 | 15.533 | 0.092 | 2.669 | 0.246 | 1.550 | 1.392 | 0.123 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 242 | 238 | 227 | 361 | 0 | 0 | 0 | 1057 | 0 |
N.S. |
1 | 0.98 | 0.94 | 1.49 | 0.00 | 0.00 | 0.00 | 4.37 | 0.00 |
time (sec) |
N/A | 0.772 | 0.206 | 0.131 | 0.000 | 0.000 | 0.000 | 0.930 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 132 | 127 | 186 | 0 | 0 | 0 | 448 | 0 |
N.S. |
1 | 0.96 | 0.93 | 1.36 | 0.00 | 0.00 | 0.00 | 3.27 | 0.00 |
time (sec) |
N/A | 0.572 | 0.049 | 0.062 | 0.000 | 0.000 | 0.000 | 0.696 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 120 | 118 | 119 | 187 | 0 | 0 | 0 | 531 | 0 |
N.S. |
1 | 0.98 | 0.99 | 1.56 | 0.00 | 0.00 | 0.00 | 4.42 | 0.00 |
time (sec) |
N/A | 0.647 | 0.095 | 0.053 | 0.000 | 0.000 | 0.000 | 0.552 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 14 | 16 | 0 | 14 | 16 | 16 |
N.S. |
1 | 1.00 | 1.12 | 0.88 | 1.00 | 0.00 | 0.88 | 1.00 | 1.00 |
time (sec) |
N/A | 0.185 | 1.848 | 0.084 | 0.612 | 0.000 | 0.395 | 0.887 | 0.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 14 | 16 | 0 | 15 | 16 | 16 |
N.S. |
1 | 1.00 | 1.12 | 0.88 | 1.00 | 0.00 | 0.94 | 1.00 | 1.00 |
time (sec) |
N/A | 0.187 | 5.648 | 0.103 | 0.613 | 0.000 | 0.361 | 0.959 | 0.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 313 | 422 | 245 | 547 | 0 | 0 | 0 | 1967 | 0 |
N.S. |
1 | 1.35 | 0.78 | 1.75 | 0.00 | 0.00 | 0.00 | 6.28 | 0.00 |
time (sec) |
N/A | 2.097 | 0.215 | 0.097 | 0.000 | 0.000 | 0.000 | 1.682 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 172 | 178 | 126 | 281 | 0 | 0 | 0 | 845 | 0 |
N.S. |
1 | 1.03 | 0.73 | 1.63 | 0.00 | 0.00 | 0.00 | 4.91 | 0.00 |
time (sec) |
N/A | 1.518 | 0.052 | 0.069 | 0.000 | 0.000 | 0.000 | 0.953 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 159 | 155 | 289 | 278 | 0 | 0 | 0 | 993 | 0 |
N.S. |
1 | 0.97 | 1.82 | 1.75 | 0.00 | 0.00 | 0.00 | 6.25 | 0.00 |
time (sec) |
N/A | 0.764 | 2.594 | 0.056 | 0.000 | 0.000 | 0.000 | 1.124 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 14 | 16 | 0 | 14 | 16 | 16 |
N.S. |
1 | 1.00 | 1.12 | 0.88 | 1.00 | 0.00 | 0.88 | 1.00 | 1.00 |
time (sec) |
N/A | 0.189 | 0.479 | 0.082 | 0.768 | 0.000 | 13.988 | 1.006 | 0.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 14 | 16 | 0 | 15 | 16 | 16 |
N.S. |
1 | 1.00 | 1.12 | 0.88 | 1.00 | 0.00 | 0.94 | 1.00 | 1.00 |
time (sec) |
N/A | 0.191 | 4.112 | 0.105 | 0.722 | 0.000 | 2.701 | 1.097 | 0.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 358 | 474 | 228 | 819 | 0 | 0 | 0 | 2466 | 0 |
N.S. |
1 | 1.32 | 0.64 | 2.29 | 0.00 | 0.00 | 0.00 | 6.89 | 0.00 |
time (sec) |
N/A | 2.606 | 0.203 | 0.122 | 0.000 | 0.000 | 0.000 | 2.397 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 216 | 223 | 129 | 408 | 0 | 0 | 0 | 1307 | 0 |
N.S. |
1 | 1.03 | 0.60 | 1.89 | 0.00 | 0.00 | 0.00 | 6.05 | 0.00 |
time (sec) |
N/A | 1.252 | 0.051 | 0.079 | 0.000 | 0.000 | 0.000 | 1.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 179 | 179 | 366 | 401 | 0 | 0 | 0 | 1179 | 0 |
N.S. |
1 | 1.00 | 2.04 | 2.24 | 0.00 | 0.00 | 0.00 | 6.59 | 0.00 |
time (sec) |
N/A | 0.994 | 2.766 | 0.070 | 0.000 | 0.000 | 0.000 | 1.492 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 14 | 16 | 0 | 14 | 16 | 16 |
N.S. |
1 | 1.00 | 1.12 | 0.88 | 1.00 | 0.00 | 0.88 | 1.00 | 1.00 |
time (sec) |
N/A | 0.187 | 0.561 | 0.088 | 0.821 | 0.000 | 31.593 | 1.058 | 0.092 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 14 | 16 | 0 | 15 | 16 | 16 |
N.S. |
1 | 1.00 | 1.12 | 0.88 | 1.00 | 0.00 | 0.94 | 1.00 | 1.00 |
time (sec) |
N/A | 0.188 | 4.267 | 0.105 | 0.820 | 0.000 | 22.368 | 1.129 | 0.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 223 | 218 | 228 | 196 | 0 | 0 | 0 | 317 | 0 |
N.S. |
1 | 0.98 | 1.02 | 0.88 | 0.00 | 0.00 | 0.00 | 1.42 | 0.00 |
time (sec) |
N/A | 0.498 | 0.195 | 0.080 | 0.000 | 0.000 | 0.000 | 0.463 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 99 | 98 | 123 | 91 | 0 | 0 | 0 | 132 | 0 |
N.S. |
1 | 0.99 | 1.24 | 0.92 | 0.00 | 0.00 | 0.00 | 1.33 | 0.00 |
time (sec) |
N/A | 0.540 | 0.050 | 0.054 | 0.000 | 0.000 | 0.000 | 0.396 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F(-2) | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 102 | 121 | 90 | 0 | 0 | 0 | 159 | 0 |
N.S. |
1 | 1.01 | 1.20 | 0.89 | 0.00 | 0.00 | 0.00 | 1.57 | 0.00 |
time (sec) |
N/A | 0.465 | 0.081 | 0.040 | 0.000 | 0.000 | 0.000 | 0.348 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 14 | 16 | 0 | 15 | 16 | 16 |
N.S. |
1 | 1.00 | 1.12 | 0.88 | 1.00 | 0.00 | 0.94 | 1.00 | 1.00 |
time (sec) |
N/A | 0.180 | 1.044 | 0.078 | 0.631 | 0.000 | 0.424 | 0.592 | 0.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 14 | 16 | 0 | 17 | 16 | 16 |
N.S. |
1 | 1.00 | 1.12 | 0.88 | 1.00 | 0.00 | 1.06 | 1.00 | 1.00 |
time (sec) |
N/A | 0.185 | 4.547 | 0.099 | 0.625 | 0.000 | 0.526 | 0.648 | 0.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 250 | 257 | 343 | 301 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 1.37 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.474 | 0.324 | 0.079 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 130 | 131 | 155 | 156 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.19 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.571 | 0.119 | 0.067 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 139 | 167 | 158 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 1.22 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.698 | 0.241 | 0.055 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 14 | 16 | 0 | 15 | 0 | 16 |
N.S. |
1 | 1.00 | 1.12 | 0.88 | 1.00 | 0.00 | 0.94 | 0.00 | 1.00 |
time (sec) |
N/A | 0.188 | 0.870 | 0.075 | 0.593 | 0.000 | 1.648 | 0.000 | 0.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 14 | 16 | 0 | 17 | 16 | 16 |
N.S. |
1 | 1.00 | 1.12 | 0.88 | 1.00 | 0.00 | 1.06 | 1.00 | 1.00 |
time (sec) |
N/A | 0.190 | 4.529 | 0.102 | 0.628 | 0.000 | 2.316 | 1.149 | 0.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 291 | 424 | 370 | 672 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.46 | 1.27 | 2.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.901 | 1.526 | 0.100 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 180 | 188 | 173 | 340 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.96 | 1.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.311 | 0.939 | 0.069 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 163 | 170 | 214 | 340 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.31 | 2.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.849 | 0.674 | 0.059 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |