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 | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 70 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.155 | 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 | A | C | F | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 68 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.159 | 0.019 | 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 | C | F | F | F | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 81 | 103 | 70 | 0 | 0 | 0 | 95 | 0 | 0 |
N.S. |
1 | 1.27 | 0.86 | 0.00 | 0.00 | 0.00 | 1.17 | 0.00 | 0.00 |
time (sec) |
N/A | 0.177 | 0.018 | 0.000 | 0.000 | 0.000 | 19.002 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | F | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 114 | 143 | 70 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.25 | 0.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.196 | 0.019 | 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 | C | F | F(-2) | F | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 147 | 184 | 70 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.25 | 0.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.212 | 0.020 | 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 | C | C | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 126 | 70 | 96 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.92 | 0.51 | 0.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.188 | 0.022 | 0.215 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 90 | 70 | 88 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.88 | 0.69 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.167 | 0.017 | 0.211 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 70 | 94 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.90 | 1.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.161 | 0.017 | 0.374 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 68 | 91 | 0 | 0 | 97 | 0 | 0 |
N.S. |
1 | 1.00 | 1.48 | 1.98 | 0.00 | 0.00 | 2.11 | 0.00 | 0.00 |
time (sec) |
N/A | 0.141 | 0.018 | 0.209 | 0.000 | 0.000 | 5.691 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 70 | 107 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.85 | 1.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.163 | 0.018 | 0.402 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F(-2) | F | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 123 | 70 | 113 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.61 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.176 | 0.020 | 0.408 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | A | F | F(-2) | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 287 | 270 | 70 | 478 | 0 | 233 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 0.24 | 1.67 | 0.00 | 0.81 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.337 | 1.058 | 1.245 | 0.000 | 0.238 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 264 | 239 | 70 | 479 | 0 | 296 | 0 | 0 | 0 |
N.S. |
1 | 0.91 | 0.27 | 1.81 | 0.00 | 1.12 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.336 | 0.686 | 1.037 | 0.000 | 0.243 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 36 | 31 | 0 | 31 | 0 | 0 | 27 |
N.S. |
1 | 1.00 | 1.16 | 1.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.87 |
time (sec) |
N/A | 0.138 | 0.018 | 0.144 | 0.000 | 0.227 | 0.000 | 0.000 | 0.514 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 38 | 33 | 0 | 36 | 0 | 0 | 40 |
N.S. |
1 | 1.00 | 0.57 | 0.49 | 0.00 | 0.54 | 0.00 | 0.00 | 0.60 |
time (sec) |
N/A | 0.160 | 2.462 | 0.198 | 0.000 | 0.230 | 0.000 | 0.000 | 0.658 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 108 | 50 | 43 | 0 | 56 | 0 | 0 | 46 |
N.S. |
1 | 1.08 | 0.50 | 0.43 | 0.00 | 0.56 | 0.00 | 0.00 | 0.46 |
time (sec) |
N/A | 0.178 | 6.011 | 0.387 | 0.000 | 0.226 | 0.000 | 0.000 | 0.827 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 141 | 128 | 70 | 101 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.91 | 0.50 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.199 | 0.023 | 0.218 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 116 | 70 | 107 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.61 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.193 | 0.018 | 0.213 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 70 | 105 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.85 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.166 | 0.018 | 0.565 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 119 | 68 | 107 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.45 | 0.83 | 1.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.182 | 0.021 | 0.219 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 88 | 103 | 70 | 0 | 0 | 0 | 95 | 0 | 0 |
N.S. |
1 | 1.17 | 0.80 | 0.00 | 0.00 | 0.00 | 1.08 | 0.00 | 0.00 |
time (sec) |
N/A | 0.185 | 0.022 | 0.000 | 0.000 | 0.000 | 85.822 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F(-2) | F | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 143 | 70 | 124 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.18 | 0.58 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.200 | 0.021 | 0.247 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F(-2) | F | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 154 | 184 | 70 | 130 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.19 | 0.45 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.224 | 0.023 | 0.248 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | A | F | F(-2) | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 297 | 272 | 70 | 493 | 0 | 343 | 0 | 0 | 0 |
N.S. |
1 | 0.92 | 0.24 | 1.66 | 0.00 | 1.15 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.356 | 2.414 | 0.219 | 0.000 | 0.242 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 32 | 0 | 42 | 0 | 0 | 38 |
N.S. |
1 | 1.00 | 1.00 | 0.97 | 0.00 | 1.27 | 0.00 | 0.00 | 1.15 |
time (sec) |
N/A | 0.135 | 0.969 | 0.206 | 0.000 | 0.226 | 0.000 | 0.000 | 0.796 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 45 | 37 | 0 | 44 | 0 | 0 | 38 |
N.S. |
1 | 1.00 | 0.67 | 0.55 | 0.00 | 0.66 | 0.00 | 0.00 | 0.57 |
time (sec) |
N/A | 0.154 | 2.327 | 0.384 | 0.000 | 0.230 | 0.000 | 0.000 | 0.682 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 108 | 50 | 43 | 0 | 56 | 0 | 0 | 45 |
N.S. |
1 | 1.08 | 0.50 | 0.43 | 0.00 | 0.56 | 0.00 | 0.00 | 0.45 |
time (sec) |
N/A | 0.171 | 5.185 | 0.210 | 0.000 | 0.221 | 0.000 | 0.000 | 0.599 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 133 | 149 | 57 | 48 | 0 | 54 | 0 | 0 | 56 |
N.S. |
1 | 1.12 | 0.43 | 0.36 | 0.00 | 0.41 | 0.00 | 0.00 | 0.42 |
time (sec) |
N/A | 0.187 | 7.177 | 0.402 | 0.000 | 0.227 | 0.000 | 0.000 | 0.735 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 77 | 103 | 167 | 128 | 819 | 256 | 133 |
N.S. |
1 | 1.00 | 0.93 | 1.24 | 2.01 | 1.54 | 9.87 | 3.08 | 1.60 |
time (sec) |
N/A | 0.204 | 0.056 | 0.226 | 0.203 | 0.227 | 1.025 | 0.319 | 0.614 |
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 | 53 | 53 | 43 | 47 | 81 | 58 | 245 | 103 | 66 |
N.S. |
1 | 1.00 | 0.81 | 0.89 | 1.53 | 1.09 | 4.62 | 1.94 | 1.25 |
time (sec) |
N/A | 0.184 | 0.046 | 0.218 | 0.207 | 0.231 | 0.793 | 0.293 | 0.524 |
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 | 52 | 52 | 52 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.159 | 0.040 | 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 | 52 | 52 | 52 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.155 | 0.035 | 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 | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 53 | 0 | 0 | 0 | 124 | 0 | 0 |
N.S. |
1 | 1.00 | 1.29 | 0.00 | 0.00 | 0.00 | 3.02 | 0.00 | 0.00 |
time (sec) |
N/A | 0.157 | 0.066 | 0.000 | 0.000 | 0.000 | 4.734 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 72 | 0 | 0 | 0 | 146 | 0 | 0 |
N.S. |
1 | 1.00 | 1.26 | 0.00 | 0.00 | 0.00 | 2.56 | 0.00 | 0.00 |
time (sec) |
N/A | 0.170 | 0.038 | 0.000 | 0.000 | 0.000 | 4.779 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 0 | 0 | 0 | 39 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 1.95 | 0.00 | 0.00 |
time (sec) |
N/A | 0.133 | 0.053 | 0.000 | 0.000 | 0.000 | 2.556 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 84 | 94 | 96 | 96 | 100 | 97 | 88 |
N.S. |
1 | 1.00 | 2.21 | 2.47 | 2.53 | 2.53 | 2.63 | 2.55 | 2.32 |
time (sec) |
N/A | 0.172 | 0.012 | 0.178 | 0.219 | 0.223 | 0.028 | 0.285 | 0.210 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 67 | 70 | 69 | 69 | 73 | 72 | 65 |
N.S. |
1 | 1.00 | 1.76 | 1.84 | 1.82 | 1.82 | 1.92 | 1.89 | 1.71 |
time (sec) |
N/A | 0.171 | 0.008 | 0.178 | 0.226 | 0.215 | 0.024 | 0.303 | 0.182 |
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 | 38 | 38 | 46 | 48 | 48 | 48 | 49 | 49 | 47 |
N.S. |
1 | 1.00 | 1.21 | 1.26 | 1.26 | 1.26 | 1.29 | 1.29 | 1.24 |
time (sec) |
N/A | 0.177 | 0.006 | 0.378 | 0.209 | 0.215 | 0.031 | 0.290 | 0.049 |
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 | 28 | 28 | 28 | 25 | 24 | 26 | 26 | 26 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.86 | 0.93 | 0.93 | 0.93 | 0.89 |
time (sec) |
N/A | 0.163 | 0.003 | 0.012 | 0.202 | 0.188 | 0.017 | 0.296 | 0.038 |
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 | 12 | 14 | 12 | 11 | 10 | 10 | 8 | 10 | 10 |
N.S. |
1 | 1.17 | 1.00 | 0.92 | 0.83 | 0.83 | 0.67 | 0.83 | 0.83 |
time (sec) |
N/A | 0.129 | 0.000 | 0.008 | 0.197 | 0.188 | 0.017 | 0.309 | 0.021 |
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 | 25 | 25 | 25 | 26 | 25 | 24 | 20 | 26 | 26 |
N.S. |
1 | 1.00 | 1.00 | 1.04 | 1.00 | 0.96 | 0.80 | 1.04 | 1.04 |
time (sec) |
N/A | 0.166 | 0.006 | 0.198 | 0.279 | 0.214 | 0.084 | 0.293 | 0.055 |
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 | 32 | 32 | 31 | 32 | 35 | 39 | 27 | 57 | 31 |
N.S. |
1 | 1.00 | 0.97 | 1.00 | 1.09 | 1.22 | 0.84 | 1.78 | 0.97 |
time (sec) |
N/A | 0.173 | 0.008 | 0.383 | 0.192 | 0.218 | 0.097 | 0.279 | 0.179 |
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 | 28 | 28 | 26 | 25 | 38 | 38 | 39 | 24 | 39 |
N.S. |
1 | 1.00 | 0.93 | 0.89 | 1.36 | 1.36 | 1.39 | 0.86 | 1.39 |
time (sec) |
N/A | 0.143 | 0.007 | 0.193 | 0.210 | 0.210 | 0.137 | 0.303 | 0.183 |
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 | 38 | 38 | 27 | 26 | 50 | 50 | 53 | 25 | 52 |
N.S. |
1 | 1.00 | 0.71 | 0.68 | 1.32 | 1.32 | 1.39 | 0.66 | 1.37 |
time (sec) |
N/A | 0.173 | 0.007 | 0.384 | 0.207 | 0.214 | 0.187 | 0.308 | 0.179 |
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 | 38 | 38 | 27 | 26 | 61 | 61 | 65 | 41 | 63 |
N.S. |
1 | 1.00 | 0.71 | 0.68 | 1.61 | 1.61 | 1.71 | 1.08 | 1.66 |
time (sec) |
N/A | 0.173 | 0.006 | 0.196 | 0.206 | 0.221 | 0.249 | 0.269 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 148 | 157 | 156 | 156 | 168 | 170 | 144 |
N.S. |
1 | 1.00 | 2.28 | 2.42 | 2.40 | 2.40 | 2.58 | 2.62 | 2.22 |
time (sec) |
N/A | 0.249 | 0.017 | 0.376 | 0.206 | 0.218 | 0.035 | 0.314 | 0.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 122 | 121 | 124 | 124 | 133 | 130 | 115 |
N.S. |
1 | 1.00 | 1.88 | 1.86 | 1.91 | 1.91 | 2.05 | 2.00 | 1.77 |
time (sec) |
N/A | 0.228 | 0.010 | 0.178 | 0.213 | 0.218 | 0.032 | 0.270 | 0.053 |
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 | 65 | 65 | 79 | 84 | 81 | 81 | 87 | 89 | 74 |
N.S. |
1 | 1.00 | 1.22 | 1.29 | 1.25 | 1.25 | 1.34 | 1.37 | 1.14 |
time (sec) |
N/A | 0.210 | 0.007 | 0.184 | 0.208 | 0.216 | 0.026 | 0.287 | 0.199 |
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 | 38 | 38 | 47 | 48 | 48 | 48 | 49 | 49 | 47 |
N.S. |
1 | 1.00 | 1.24 | 1.26 | 1.26 | 1.26 | 1.29 | 1.29 | 1.24 |
time (sec) |
N/A | 0.187 | 0.007 | 0.365 | 0.204 | 0.216 | 0.022 | 0.297 | 0.058 |
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 | 14 | 14 | 14 | 13 | 20 | 20 | 19 | 12 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 1.43 | 1.43 | 1.36 | 0.86 | 1.43 |
time (sec) |
N/A | 0.132 | 0.001 | 0.177 | 0.198 | 0.218 | 0.017 | 0.294 | 0.052 |
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 | 49 | 49 | 43 | 56 | 61 | 63 | 44 | 60 | 62 |
N.S. |
1 | 1.00 | 0.88 | 1.14 | 1.24 | 1.29 | 0.90 | 1.22 | 1.27 |
time (sec) |
N/A | 0.179 | 0.012 | 0.390 | 0.204 | 0.218 | 0.159 | 0.298 | 0.227 |
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 | 51 | 47 | 63 | 67 | 92 | 60 | 98 | 71 |
N.S. |
1 | 1.00 | 0.92 | 1.24 | 1.31 | 1.80 | 1.18 | 1.92 | 1.39 |
time (sec) |
N/A | 0.192 | 0.023 | 0.205 | 0.195 | 0.220 | 0.225 | 0.297 | 0.386 |
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 | 59 | 59 | 49 | 67 | 79 | 99 | 80 | 68 | 77 |
N.S. |
1 | 1.00 | 0.83 | 1.14 | 1.34 | 1.68 | 1.36 | 1.15 | 1.31 |
time (sec) |
N/A | 0.202 | 0.016 | 0.200 | 0.210 | 0.217 | 0.304 | 0.338 | 0.215 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 53 | 60 | 84 | 84 | 88 | 59 | 80 |
N.S. |
1 | 1.00 | 1.89 | 2.14 | 3.00 | 3.00 | 3.14 | 2.11 | 2.86 |
time (sec) |
N/A | 0.142 | 0.015 | 0.393 | 0.205 | 0.226 | 0.347 | 0.291 | 0.041 |
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 | 65 | 65 | 56 | 62 | 98 | 98 | 104 | 96 | 39 |
N.S. |
1 | 1.00 | 0.86 | 0.95 | 1.51 | 1.51 | 1.60 | 1.48 | 0.60 |
time (sec) |
N/A | 0.197 | 0.012 | 0.203 | 0.203 | 0.224 | 0.425 | 0.291 | 0.206 |
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 | 65 | 65 | 57 | 62 | 109 | 109 | 116 | 61 | 107 |
N.S. |
1 | 1.00 | 0.88 | 0.95 | 1.68 | 1.68 | 1.78 | 0.94 | 1.65 |
time (sec) |
N/A | 0.198 | 0.016 | 0.208 | 0.201 | 0.221 | 0.564 | 0.276 | 0.240 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 58 | 62 | 120 | 120 | 128 | 61 | 118 |
N.S. |
1 | 1.00 | 0.89 | 0.95 | 1.85 | 1.85 | 1.97 | 0.94 | 1.82 |
time (sec) |
N/A | 0.201 | 0.013 | 0.404 | 0.207 | 0.216 | 0.624 | 0.280 | 0.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 235 | 273 | 277 | 277 | 308 | 303 | 261 |
N.S. |
1 | 1.00 | 2.55 | 2.97 | 3.01 | 3.01 | 3.35 | 3.29 | 2.84 |
time (sec) |
N/A | 0.314 | 0.044 | 0.186 | 0.199 | 0.226 | 0.043 | 0.286 | 0.263 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 217 | 222 | 225 | 225 | 243 | 245 | 208 |
N.S. |
1 | 1.00 | 2.36 | 2.41 | 2.45 | 2.45 | 2.64 | 2.66 | 2.26 |
time (sec) |
N/A | 0.287 | 0.016 | 0.187 | 0.198 | 0.214 | 0.039 | 0.289 | 0.225 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 161 | 172 | 167 | 167 | 190 | 188 | 152 |
N.S. |
1 | 1.00 | 1.75 | 1.87 | 1.82 | 1.82 | 2.07 | 2.04 | 1.65 |
time (sec) |
N/A | 0.261 | 0.012 | 0.184 | 0.202 | 0.221 | 0.040 | 0.299 | 0.067 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 122 | 121 | 124 | 124 | 133 | 130 | 115 |
N.S. |
1 | 1.00 | 1.88 | 1.86 | 1.91 | 1.91 | 2.05 | 2.00 | 1.77 |
time (sec) |
N/A | 0.230 | 0.009 | 0.185 | 0.195 | 0.216 | 0.034 | 0.288 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 67 | 70 | 69 | 69 | 73 | 72 | 65 |
N.S. |
1 | 1.00 | 1.76 | 1.84 | 1.82 | 1.82 | 1.92 | 1.89 | 1.71 |
time (sec) |
N/A | 0.175 | 0.005 | 0.373 | 0.202 | 0.214 | 0.025 | 0.304 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 13 | 31 | 31 | 32 | 12 | 31 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 2.21 | 2.21 | 2.29 | 0.86 | 2.21 |
time (sec) |
N/A | 0.128 | 0.001 | 0.182 | 0.193 | 0.214 | 0.019 | 0.283 | 0.040 |
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 | 73 | 73 | 74 | 107 | 114 | 116 | 83 | 115 | 118 |
N.S. |
1 | 1.00 | 1.01 | 1.47 | 1.56 | 1.59 | 1.14 | 1.58 | 1.62 |
time (sec) |
N/A | 0.201 | 0.019 | 0.393 | 0.210 | 0.224 | 0.188 | 0.272 | 0.239 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 72 | 109 | 118 | 173 | 102 | 167 | 123 |
N.S. |
1 | 1.00 | 0.96 | 1.45 | 1.57 | 2.31 | 1.36 | 2.23 | 1.64 |
time (sec) |
N/A | 0.219 | 0.031 | 0.204 | 0.203 | 0.224 | 0.283 | 0.276 | 0.282 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 114 | 114 | 125 | 188 | 128 | 112 | 130 |
N.S. |
1 | 1.00 | 1.46 | 1.46 | 1.60 | 2.41 | 1.64 | 1.44 | 1.67 |
time (sec) |
N/A | 0.225 | 0.026 | 0.205 | 0.197 | 0.233 | 0.512 | 0.280 | 0.378 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 80 | 115 | 142 | 176 | 148 | 118 | 138 |
N.S. |
1 | 1.00 | 0.93 | 1.34 | 1.65 | 2.05 | 1.72 | 1.37 | 1.60 |
time (sec) |
N/A | 0.228 | 0.027 | 0.204 | 0.223 | 0.225 | 0.661 | 0.276 | 0.249 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 91 | 104 | 143 | 143 | 155 | 159 | 135 |
N.S. |
1 | 1.00 | 3.25 | 3.71 | 5.11 | 5.11 | 5.54 | 5.68 | 4.82 |
time (sec) |
N/A | 0.141 | 0.020 | 0.403 | 0.200 | 0.224 | 0.912 | 0.287 | 0.076 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 97 | 110 | 160 | 160 | 172 | 114 | 39 |
N.S. |
1 | 1.00 | 1.67 | 1.90 | 2.76 | 2.76 | 2.97 | 1.97 | 0.67 |
time (sec) |
N/A | 0.164 | 0.022 | 0.205 | 0.220 | 0.214 | 1.135 | 0.292 | 0.088 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 97 | 110 | 171 | 171 | 184 | 114 | 165 |
N.S. |
1 | 1.00 | 1.05 | 1.20 | 1.86 | 1.86 | 2.00 | 1.24 | 1.79 |
time (sec) |
N/A | 0.230 | 0.021 | 0.209 | 0.208 | 0.216 | 1.487 | 0.310 | 0.237 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 97 | 110 | 182 | 182 | 196 | 114 | 176 |
N.S. |
1 | 1.00 | 1.05 | 1.20 | 1.98 | 1.98 | 2.13 | 1.24 | 1.91 |
time (sec) |
N/A | 0.227 | 0.020 | 0.209 | 0.213 | 0.219 | 1.825 | 0.314 | 0.122 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 97 | 110 | 193 | 193 | 207 | 114 | 187 |
N.S. |
1 | 1.00 | 1.05 | 1.20 | 2.10 | 2.10 | 2.25 | 1.24 | 2.03 |
time (sec) |
N/A | 0.227 | 0.023 | 0.609 | 0.211 | 0.217 | 3.042 | 0.288 | 0.261 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 200 | 200 | 993 | 1017 | 1023 | 1023 | 1163 | 1175 | 997 |
N.S. |
1 | 1.00 | 4.96 | 5.08 | 5.12 | 5.12 | 5.82 | 5.88 | 4.98 |
time (sec) |
N/A | 0.767 | 0.083 | 0.201 | 0.206 | 0.231 | 0.097 | 0.317 | 0.589 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 200 | 200 | 897 | 911 | 921 | 921 | 1046 | 1050 | 892 |
N.S. |
1 | 1.00 | 4.48 | 4.56 | 4.60 | 4.60 | 5.23 | 5.25 | 4.46 |
time (sec) |
N/A | 0.680 | 0.062 | 0.598 | 0.212 | 0.227 | 0.087 | 0.308 | 0.405 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 200 | 200 | 785 | 804 | 807 | 807 | 935 | 924 | 781 |
N.S. |
1 | 1.00 | 3.92 | 4.02 | 4.04 | 4.04 | 4.68 | 4.62 | 3.90 |
time (sec) |
N/A | 0.606 | 0.047 | 0.199 | 0.218 | 0.225 | 0.075 | 0.310 | 0.621 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 173 | 173 | 684 | 697 | 706 | 706 | 796 | 798 | 683 |
N.S. |
1 | 1.00 | 3.95 | 4.03 | 4.08 | 4.08 | 4.60 | 4.61 | 3.95 |
time (sec) |
N/A | 0.571 | 0.045 | 0.210 | 0.210 | 0.219 | 0.067 | 0.288 | 0.275 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 144 | 144 | 574 | 588 | 594 | 594 | 673 | 670 | 570 |
N.S. |
1 | 1.00 | 3.99 | 4.08 | 4.12 | 4.12 | 4.67 | 4.65 | 3.96 |
time (sec) |
N/A | 0.495 | 0.039 | 0.190 | 0.204 | 0.225 | 0.061 | 0.313 | 0.229 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 119 | 473 | 483 | 489 | 489 | 549 | 546 | 470 |
N.S. |
1 | 1.00 | 3.97 | 4.06 | 4.11 | 4.11 | 4.61 | 4.59 | 3.95 |
time (sec) |
N/A | 0.433 | 0.030 | 0.194 | 0.209 | 0.213 | 0.054 | 0.285 | 0.342 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 360 | 376 | 376 | 376 | 427 | 420 | 356 |
N.S. |
1 | 1.00 | 3.91 | 4.09 | 4.09 | 4.09 | 4.64 | 4.57 | 3.87 |
time (sec) |
N/A | 0.364 | 0.025 | 0.200 | 0.192 | 0.224 | 0.048 | 0.313 | 0.308 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 261 | 269 | 273 | 273 | 303 | 294 | 249 |
N.S. |
1 | 1.00 | 4.02 | 4.14 | 4.20 | 4.20 | 4.66 | 4.52 | 3.83 |
time (sec) |
N/A | 0.296 | 0.018 | 0.206 | 0.206 | 0.220 | 0.042 | 0.314 | 0.113 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 151 | 163 | 163 | 163 | 178 | 169 | 143 |
N.S. |
1 | 1.00 | 3.97 | 4.29 | 4.29 | 4.29 | 4.68 | 4.45 | 3.76 |
time (sec) |
N/A | 0.177 | 0.010 | 0.187 | 0.215 | 0.218 | 0.037 | 0.288 | 0.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 13 | 12 | 75 | 83 | 12 | 75 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.86 | 5.36 | 5.93 | 0.86 | 5.36 |
time (sec) |
N/A | 0.132 | 0.001 | 0.192 | 0.198 | 0.215 | 0.027 | 0.287 | 0.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 169 | 169 | 304 | 435 | 460 | 462 | 408 | 497 | 509 |
N.S. |
1 | 1.00 | 1.80 | 2.57 | 2.72 | 2.73 | 2.41 | 2.94 | 3.01 |
time (sec) |
N/A | 0.297 | 0.089 | 0.613 | 0.215 | 0.227 | 0.477 | 0.292 | 0.227 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 187 | 187 | 388 | 448 | 467 | 632 | 428 | 567 | 841 |
N.S. |
1 | 1.00 | 2.07 | 2.40 | 2.50 | 3.38 | 2.29 | 3.03 | 4.50 |
time (sec) |
N/A | 0.427 | 0.075 | 0.214 | 0.215 | 0.226 | 0.890 | 0.313 | 0.295 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 185 | 185 | 389 | 445 | 473 | 703 | 447 | 477 | 690 |
N.S. |
1 | 1.00 | 2.10 | 2.41 | 2.56 | 3.80 | 2.42 | 2.58 | 3.73 |
time (sec) |
N/A | 0.406 | 0.080 | 0.214 | 0.211 | 0.221 | 1.754 | 0.288 | 0.437 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 187 | 187 | 199 | 448 | 484 | 739 | 474 | 470 | 559 |
N.S. |
1 | 1.00 | 1.06 | 2.40 | 2.59 | 3.95 | 2.53 | 2.51 | 2.99 |
time (sec) |
N/A | 0.397 | 0.061 | 0.230 | 0.218 | 0.235 | 23.230 | 0.297 | 0.308 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 187 | 187 | 173 | 452 | 494 | 754 | 0 | 660 | 512 |
N.S. |
1 | 1.00 | 0.93 | 2.42 | 2.64 | 4.03 | 0.00 | 3.53 | 2.74 |
time (sec) |
N/A | 0.395 | 0.063 | 0.219 | 0.259 | 0.224 | 0.000 | 0.300 | 0.169 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 181 | 181 | 389 | 451 | 504 | 732 | 0 | 463 | 508 |
N.S. |
1 | 1.00 | 2.15 | 2.49 | 2.78 | 4.04 | 0.00 | 2.56 | 2.81 |
time (sec) |
N/A | 0.386 | 0.097 | 0.216 | 0.237 | 0.229 | 0.000 | 0.286 | 0.348 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 186 | 186 | 390 | 452 | 516 | 692 | 0 | 459 | 517 |
N.S. |
1 | 1.00 | 2.10 | 2.43 | 2.77 | 3.72 | 0.00 | 2.47 | 2.78 |
time (sec) |
N/A | 0.377 | 0.125 | 0.217 | 0.230 | 0.226 | 0.000 | 0.286 | 0.396 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 194 | 194 | 308 | 447 | 534 | 624 | 0 | 466 | 461 |
N.S. |
1 | 1.00 | 1.59 | 2.30 | 2.75 | 3.22 | 0.00 | 2.40 | 2.38 |
time (sec) |
N/A | 0.368 | 0.101 | 0.218 | 0.231 | 0.229 | 0.000 | 0.292 | 0.371 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 353 | 410 | 509 | 509 | 0 | 489 | 571 |
N.S. |
1 | 1.00 | 12.61 | 14.64 | 18.18 | 18.18 | 0.00 | 17.46 | 20.39 |
time (sec) |
N/A | 0.141 | 0.073 | 0.216 | 0.237 | 0.219 | 0.000 | 0.280 | 0.196 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 367 | 438 | 548 | 548 | 0 | 496 | 39 |
N.S. |
1 | 1.00 | 6.33 | 7.55 | 9.45 | 9.45 | 0.00 | 8.55 | 0.67 |
time (sec) |
N/A | 0.161 | 0.073 | 0.217 | 0.228 | 0.224 | 0.000 | 0.291 | 0.180 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 102 | 371 | 438 | 559 | 559 | 0 | 496 | 600 |
N.S. |
1 | 1.15 | 4.17 | 4.92 | 6.28 | 6.28 | 0.00 | 5.57 | 6.74 |
time (sec) |
N/A | 0.183 | 0.077 | 0.222 | 0.236 | 0.231 | 0.000 | 0.277 | 0.641 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 120 | 146 | 369 | 438 | 570 | 570 | 0 | 496 | 548 |
N.S. |
1 | 1.22 | 3.08 | 3.65 | 4.75 | 4.75 | 0.00 | 4.13 | 4.57 |
time (sec) |
N/A | 0.213 | 0.077 | 0.222 | 0.248 | 0.223 | 0.000 | 0.314 | 0.545 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 151 | 190 | 371 | 438 | 581 | 581 | 0 | 496 | 559 |
N.S. |
1 | 1.26 | 2.46 | 2.90 | 3.85 | 3.85 | 0.00 | 3.28 | 3.70 |
time (sec) |
N/A | 0.241 | 0.077 | 0.237 | 0.256 | 0.223 | 0.000 | 0.293 | 0.245 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 198 | 198 | 369 | 438 | 592 | 592 | 0 | 496 | 570 |
N.S. |
1 | 1.00 | 1.86 | 2.21 | 2.99 | 2.99 | 0.00 | 2.51 | 2.88 |
time (sec) |
N/A | 0.365 | 0.084 | 0.233 | 0.237 | 0.226 | 0.000 | 0.301 | 0.423 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 200 | 200 | 371 | 438 | 603 | 603 | 0 | 496 | 581 |
N.S. |
1 | 1.00 | 1.86 | 2.19 | 3.02 | 3.02 | 0.00 | 2.48 | 2.90 |
time (sec) |
N/A | 0.364 | 0.076 | 0.230 | 0.245 | 0.225 | 0.000 | 0.303 | 1.308 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 200 | 200 | 371 | 438 | 614 | 614 | 0 | 496 | 592 |
N.S. |
1 | 1.00 | 1.86 | 2.19 | 3.07 | 3.07 | 0.00 | 2.48 | 2.96 |
time (sec) |
N/A | 0.355 | 0.075 | 0.241 | 0.254 | 0.225 | 0.000 | 0.301 | 2.347 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 275 | 275 | 1817 | 1869 | 1877 | 1877 | 2088 | 2186 | 1847 |
N.S. |
1 | 1.00 | 6.61 | 6.80 | 6.83 | 6.83 | 7.59 | 7.95 | 6.72 |
time (sec) |
N/A | 1.350 | 0.166 | 0.212 | 0.223 | 0.239 | 0.168 | 0.299 | 1.299 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 279 | 279 | 1702 | 1721 | 1740 | 1740 | 1965 | 2010 | 1702 |
N.S. |
1 | 1.00 | 6.10 | 6.17 | 6.24 | 6.24 | 7.04 | 7.20 | 6.10 |
time (sec) |
N/A | 1.243 | 0.126 | 0.413 | 0.211 | 0.241 | 0.153 | 0.289 | 1.106 |