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 | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 13 | 13 | 13 | 15 | 15 | 20 | 15 | 10 |
N.S. |
1 | 0.65 | 0.65 | 0.65 | 0.75 | 0.75 | 1.00 | 0.75 | 0.50 |
time (sec) |
N/A | 0.131 | 0.002 | 0.133 | 0.208 | 0.251 | 0.032 | 0.277 | 0.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | C | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 56 | 56 | 15 | 8 | 14 | 15 | 14 | 10 |
N.S. |
1 | 3.73 | 3.73 | 1.00 | 0.53 | 0.93 | 1.00 | 0.93 | 0.67 |
time (sec) |
N/A | 0.345 | 0.059 | 0.467 | 0.245 | 0.259 | 0.121 | 0.275 | 0.220 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 43 | 57 | 83 | 83 | 63 | 60 | 0 |
N.S. |
1 | 0.00 | 1.79 | 2.38 | 3.46 | 3.46 | 2.62 | 2.50 | 0.00 |
time (sec) |
N/A | 0.000 | 0.104 | 2.622 | 0.394 | 0.259 | 0.305 | 0.332 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 31 | 31 | 35 | 53 | 30 | 31 | 30 | 30 |
N.S. |
1 | 1.03 | 1.03 | 1.17 | 1.77 | 1.00 | 1.03 | 1.00 | 1.00 |
time (sec) |
N/A | 7.347 | 0.117 | 17.917 | 0.257 | 0.255 | 0.425 | 0.327 | 14.782 |
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 | 15 | 10 | 8 | 9 | 8 | 8 | 7 | 9 | 8 |
N.S. |
1 | 0.67 | 0.53 | 0.60 | 0.53 | 0.53 | 0.47 | 0.60 | 0.53 |
time (sec) |
N/A | 0.140 | 0.003 | 1.018 | 0.194 | 0.243 | 0.032 | 0.267 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | F(-1) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 29 | 30 | 0 | 44 | 0 | 0 | 45 |
N.S. |
1 | 0.00 | 1.04 | 1.07 | 0.00 | 1.57 | 0.00 | 0.00 | 1.61 |
time (sec) |
N/A | 0.000 | 0.503 | 17.631 | 0.000 | 0.260 | 0.000 | 0.000 | 15.636 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 44 | 45 | 82 | 49 | 49 | 51 | 95 |
N.S. |
1 | 0.00 | 1.38 | 1.41 | 2.56 | 1.53 | 1.53 | 1.59 | 2.97 |
time (sec) |
N/A | 0.000 | 0.263 | 3.878 | 0.365 | 0.252 | 4.706 | 1.357 | 15.166 |
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 | 20 | 16 | 19 | 16 | 15 | 15 | 10 | 15 | 15 |
N.S. |
1 | 0.80 | 0.95 | 0.80 | 0.75 | 0.75 | 0.50 | 0.75 | 0.75 |
time (sec) |
N/A | 0.147 | 0.006 | 0.092 | 0.193 | 0.270 | 0.049 | 0.268 | 14.317 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 33 | 29 | 0 | 26 | 34 | 56 | 32 |
N.S. |
1 | 0.00 | 1.38 | 1.21 | 0.00 | 1.08 | 1.42 | 2.33 | 1.33 |
time (sec) |
N/A | 0.000 | 0.075 | 0.214 | 0.000 | 0.270 | 31.088 | 0.280 | 15.181 |
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 | 19 | 22 | 15 | 15 | 16 | 16 | 17 | 16 | 16 |
N.S. |
1 | 1.16 | 0.79 | 0.79 | 0.84 | 0.84 | 0.89 | 0.84 | 0.84 |
time (sec) |
N/A | 0.145 | 0.003 | 0.191 | 0.191 | 0.250 | 0.028 | 0.277 | 0.407 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 35 | 33 | 32 | 34 | 31 | 34 | 34 |
N.S. |
1 | 0.00 | 1.13 | 1.06 | 1.03 | 1.10 | 1.00 | 1.10 | 1.10 |
time (sec) |
N/A | 0.000 | 0.145 | 12.360 | 0.347 | 0.261 | 0.345 | 0.578 | 0.900 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | B | B | A | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 0 | 33 | 62 | 68 | 32 | 4292 | 41 |
N.S. |
1 | 0.00 | 0.00 | 1.10 | 2.07 | 2.27 | 1.07 | 143.07 | 1.37 |
time (sec) |
N/A | 0.000 | 0.000 | 0.606 | 0.272 | 0.264 | 0.203 | 0.453 | 14.843 |
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 | 23 | 34 | 27 | 18 | 25 | 39 | 15 | 46 | 20 |
N.S. |
1 | 1.48 | 1.17 | 0.78 | 1.09 | 1.70 | 0.65 | 2.00 | 0.87 |
time (sec) |
N/A | 0.403 | 0.387 | 0.410 | 0.202 | 0.247 | 0.067 | 0.281 | 16.839 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 36 | 28 | 28 | 105 | 28 | 20 | 145 | 25 |
N.S. |
1 | 1.24 | 0.97 | 0.97 | 3.62 | 0.97 | 0.69 | 5.00 | 0.86 |
time (sec) |
N/A | 0.283 | 0.011 | 1.565 | 0.286 | 0.259 | 0.100 | 0.279 | 0.635 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 29 | 37 | 23 | 28 | 22 | 20 | 0 | 23 |
N.S. |
1 | 1.12 | 1.42 | 0.88 | 1.08 | 0.85 | 0.77 | 0.00 | 0.88 |
time (sec) |
N/A | 1.327 | 0.826 | 0.699 | 0.306 | 0.265 | 0.103 | 0.000 | 17.525 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 36 | 49 | 64 | 48 | 48 | 147 | 160 |
N.S. |
1 | 0.00 | 1.16 | 1.58 | 2.06 | 1.55 | 1.55 | 4.74 | 5.16 |
time (sec) |
N/A | 0.000 | 1.278 | 0.844 | 2.910 | 0.251 | 0.214 | 0.293 | 17.285 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | C | B | B | B | B | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 68 | 1010 | 68 | 66 | 69 | 71 | 0 | 0 |
N.S. |
1 | 2.62 | 38.85 | 2.62 | 2.54 | 2.65 | 2.73 | 0.00 | 0.00 |
time (sec) |
N/A | 0.577 | 0.892 | 0.876 | 0.220 | 0.281 | 128.688 | 0.000 | 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 | 29 | 36 | 30 | 33 | 48 | 30 | 29 | 30 | 29 |
N.S. |
1 | 1.24 | 1.03 | 1.14 | 1.66 | 1.03 | 1.00 | 1.03 | 1.00 |
time (sec) |
N/A | 0.206 | 0.026 | 0.434 | 0.193 | 0.256 | 0.097 | 0.286 | 16.694 |
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 | 11 | 11 | 11 | 10 | 9 | 9 | 7 | 9 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.82 | 0.82 | 0.64 | 0.82 | 0.82 |
time (sec) |
N/A | 0.124 | 0.000 | 0.149 | 0.184 | 0.241 | 0.026 | 0.285 | 0.054 |
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 | 14 | 17 | 15 | 16 | 14 | 16 | 15 |
N.S. |
1 | 1.17 | 1.17 | 1.42 | 1.25 | 1.33 | 1.17 | 1.33 | 1.25 |
time (sec) |
N/A | 0.146 | 0.018 | 0.250 | 0.183 | 0.264 | 0.069 | 0.272 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 21 | 20 | 24 | 20 | 27 | 30 | 60 |
N.S. |
1 | 0.00 | 0.91 | 0.87 | 1.04 | 0.87 | 1.17 | 1.30 | 2.61 |
time (sec) |
N/A | 0.000 | 2.214 | 2.884 | 0.309 | 0.252 | 0.120 | 0.276 | 1.431 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 35 | 33 | 37 | 71 | 71 | 0 | 80 | 0 |
N.S. |
1 | 1.17 | 1.10 | 1.23 | 2.37 | 2.37 | 0.00 | 2.67 | 0.00 |
time (sec) |
N/A | 1.353 | 0.873 | 2.033 | 3.854 | 0.261 | 0.000 | 0.473 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | F(-2) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 20 | 21 | 47 | 19 | 0 | 29 | 20 |
N.S. |
1 | 0.00 | 1.00 | 1.05 | 2.35 | 0.95 | 0.00 | 1.45 | 1.00 |
time (sec) |
N/A | 0.000 | 0.364 | 7.773 | 0.307 | 0.265 | 0.000 | 0.382 | 16.913 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 9038 | 21 | 22 | 91 | 89 | 110 | 216 | 0 |
N.S. |
1 | 430.38 | 1.00 | 1.05 | 4.33 | 4.24 | 5.24 | 10.29 | 0.00 |
time (sec) |
N/A | 23.686 | 2.003 | 3.013 | 0.252 | 0.255 | 0.269 | 0.366 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 42 | 76 | 71 | 93 | 156 | 76 | 0 |
N.S. |
1 | 0.00 | 1.83 | 3.30 | 3.09 | 4.04 | 6.78 | 3.30 | 0.00 |
time (sec) |
N/A | 0.000 | 0.117 | 3.829 | 0.259 | 0.281 | 0.267 | 0.289 | 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 | 12 | 12 | 12 | 10 | 14 | 9 | 10 | 9 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 1.17 | 0.75 | 0.83 | 0.75 | 0.75 |
time (sec) |
N/A | 0.362 | 0.011 | 0.296 | 0.311 | 0.254 | 2.418 | 0.298 | 15.306 |
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 | 32 | 30 | 33 | 36 | 39 | 37 | 31 | 39 | 0 |
N.S. |
1 | 0.94 | 1.03 | 1.12 | 1.22 | 1.16 | 0.97 | 1.22 | 0.00 |
time (sec) |
N/A | 0.739 | 0.067 | 3.263 | 0.237 | 0.253 | 0.150 | 0.532 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 26 | 154 | 27 | 26 | 23 | 26 | 28 | 26 |
N.S. |
1 | 1.18 | 7.00 | 1.23 | 1.18 | 1.05 | 1.18 | 1.27 | 1.18 |
time (sec) |
N/A | 0.223 | 0.147 | 0.319 | 0.192 | 0.250 | 0.451 | 0.302 | 0.248 |
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 | 28 | 28 | 28 | 27 | 26 | 26 | 22 | 146 | 91 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 0.93 | 0.93 | 0.79 | 5.21 | 3.25 |
time (sec) |
N/A | 12.130 | 0.116 | 24.159 | 0.250 | 0.259 | 0.240 | 0.517 | 16.122 |
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 | 11 | 8 | 7 | 8 | 7 | 14 | 10 | 7 | 7 |
N.S. |
1 | 0.73 | 0.64 | 0.73 | 0.64 | 1.27 | 0.91 | 0.64 | 0.64 |
time (sec) |
N/A | 0.173 | 0.021 | 0.250 | 0.180 | 0.272 | 0.096 | 0.290 | 15.453 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 25 | 51 | 76 | 25 | 27 | 148 | 29 |
N.S. |
1 | 0.00 | 1.00 | 2.04 | 3.04 | 1.00 | 1.08 | 5.92 | 1.16 |
time (sec) |
N/A | 0.000 | 0.077 | 4.489 | 0.363 | 0.273 | 0.239 | 0.360 | 16.638 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 34 | 31 | 50 | 52 | 34 | 50 | 30 |
N.S. |
1 | 0.00 | 1.00 | 0.91 | 1.47 | 1.53 | 1.00 | 1.47 | 0.88 |
time (sec) |
N/A | 0.000 | 0.305 | 10.093 | 0.469 | 0.276 | 7.640 | 0.665 | 20.770 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 27 | 27 | 25 | 31 | 29 | 26 | 29 | 23 |
N.S. |
1 | 0.87 | 0.87 | 0.81 | 1.00 | 0.94 | 0.84 | 0.94 | 0.74 |
time (sec) |
N/A | 0.210 | 0.065 | 1.131 | 0.221 | 0.267 | 0.072 | 0.302 | 16.736 |
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 | 27 | 48 | 30 | 28 | 27 | 27 | 27 | 27 | 27 |
N.S. |
1 | 1.78 | 1.11 | 1.04 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 1.052 | 0.276 | 1.325 | 0.251 | 0.264 | 0.348 | 0.289 | 17.277 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 30 | 27 | 61 | 31 | 26 | 54 | 63 |
N.S. |
1 | 0.00 | 0.94 | 0.84 | 1.91 | 0.97 | 0.81 | 1.69 | 1.97 |
time (sec) |
N/A | 0.000 | 5.235 | 2.508 | 0.403 | 0.260 | 0.340 | 0.342 | 16.215 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 0 | 13 | 25 | 19 | 11 | 15 | 0 | 11 |
N.S. |
1 | 0.00 | 1.00 | 1.92 | 1.46 | 0.85 | 1.15 | 0.00 | 0.85 |
time (sec) |
N/A | 0.000 | 0.178 | 0.808 | 0.252 | 0.262 | 9.896 | 0.000 | 15.878 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 14 | 14 | 29 | 13 | 14 | 13 | 13 |
N.S. |
1 | 1.00 | 0.88 | 0.88 | 1.81 | 0.81 | 0.88 | 0.81 | 0.81 |
time (sec) |
N/A | 0.152 | 0.010 | 0.677 | 0.197 | 0.264 | 0.076 | 0.260 | 15.666 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 24 | 17 | 20 | 61 | 19 | 15 | 19 | 12 |
N.S. |
1 | 1.60 | 1.13 | 1.33 | 4.07 | 1.27 | 1.00 | 1.27 | 0.80 |
time (sec) |
N/A | 0.207 | 0.021 | 0.662 | 0.218 | 0.256 | 0.071 | 0.281 | 15.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 36 | 27 | 21 | 0 | 26 | 29 | 29 | 25 |
N.S. |
1 | 1.57 | 1.17 | 0.91 | 0.00 | 1.13 | 1.26 | 1.26 | 1.09 |
time (sec) |
N/A | 0.638 | 0.273 | 0.229 | 0.000 | 0.258 | 0.222 | 0.279 | 15.546 |
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 | 22 | 26 | 24 | 19 | 24 | 28 | 20 | 22 | 22 |
N.S. |
1 | 1.18 | 1.09 | 0.86 | 1.09 | 1.27 | 0.91 | 1.00 | 1.00 |
time (sec) |
N/A | 0.222 | 0.292 | 0.272 | 0.195 | 0.270 | 0.162 | 0.280 | 15.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 57 | 23 | 22 | 39 | 22 | 17 | 37 | 21 |
N.S. |
1 | 2.11 | 0.85 | 0.81 | 1.44 | 0.81 | 0.63 | 1.37 | 0.78 |
time (sec) |
N/A | 1.251 | 0.090 | 2.145 | 0.321 | 0.265 | 0.177 | 0.302 | 15.549 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 16 | 40 | 18 | 33 | 41 | 32 | 26 | 25 |
N.S. |
1 | 0.94 | 2.35 | 1.06 | 1.94 | 2.41 | 1.88 | 1.53 | 1.47 |
time (sec) |
N/A | 0.179 | 0.021 | 0.454 | 0.189 | 0.264 | 0.173 | 0.269 | 15.340 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | B | B | A | B | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 0 | 61 | 63 | 62 | 68 | 124 | 65 |
N.S. |
1 | 0.00 | 0.00 | 2.03 | 2.10 | 2.07 | 2.27 | 4.13 | 2.17 |
time (sec) |
N/A | 0.000 | 0.000 | 0.953 | 0.447 | 0.270 | 0.368 | 0.493 | 15.407 |
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 | 22 | 22 | 22 | 23 | 37 | 23 | 20 | 39 | 24 |
N.S. |
1 | 1.00 | 1.00 | 1.05 | 1.68 | 1.05 | 0.91 | 1.77 | 1.09 |
time (sec) |
N/A | 1.024 | 0.093 | 13.808 | 0.322 | 0.269 | 0.718 | 0.952 | 16.986 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 57 | 26 | 29 | 23 | 31 | 29 | 0 | 26 |
N.S. |
1 | 2.19 | 1.00 | 1.12 | 0.88 | 1.19 | 1.12 | 0.00 | 1.00 |
time (sec) |
N/A | 0.366 | 0.123 | 1.863 | 0.279 | 0.262 | 0.202 | 0.000 | 15.531 |
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 | 18 | 27 | 19 | 15 | 19 | 19 | 27 | 19 | 18 |
N.S. |
1 | 1.50 | 1.06 | 0.83 | 1.06 | 1.06 | 1.50 | 1.06 | 1.00 |
time (sec) |
N/A | 0.146 | 0.002 | 0.145 | 0.197 | 0.246 | 0.028 | 0.264 | 0.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 34 | 35 | 46 | 35 | 34 | 37 | 38 |
N.S. |
1 | 0.00 | 1.21 | 1.25 | 1.64 | 1.25 | 1.21 | 1.32 | 1.36 |
time (sec) |
N/A | 0.000 | 0.254 | 3.471 | 0.325 | 0.253 | 0.159 | 0.293 | 16.828 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | A | B | F(-2) | F | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 56 | 155 | 38 | 69 | 0 | 0 | 68 |
N.S. |
1 | 0.00 | 1.75 | 4.84 | 1.19 | 2.16 | 0.00 | 0.00 | 2.12 |
time (sec) |
N/A | 0.000 | 2.116 | 90.030 | 1.068 | 0.267 | 0.000 | 0.000 | 17.840 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | C | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 56 | 34 | 48 | 63 | 37 | 48 | 47 | 0 |
N.S. |
1 | 1.87 | 1.13 | 1.60 | 2.10 | 1.23 | 1.60 | 1.57 | 0.00 |
time (sec) |
N/A | 3.246 | 0.703 | 3.171 | 0.329 | 0.326 | 0.199 | 0.285 | 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 | 33 | 38 | 44 | 34 | 35 | 34 | 29 | 32 | 32 |
N.S. |
1 | 1.15 | 1.33 | 1.03 | 1.06 | 1.03 | 0.88 | 0.97 | 0.97 |
time (sec) |
N/A | 3.528 | 1.893 | 0.674 | 0.332 | 0.289 | 0.147 | 0.287 | 0.313 |
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 | 29 | 42 | 33 | 27 | 30 | 30 | 27 | 30 | 24 |
N.S. |
1 | 1.45 | 1.14 | 0.93 | 1.03 | 1.03 | 0.93 | 1.03 | 0.83 |
time (sec) |
N/A | 0.169 | 0.018 | 2.446 | 0.185 | 0.257 | 0.030 | 0.284 | 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 | 28 | 30 | 28 | 23 | 23 | 36 | 19 | 48 | 29 |
N.S. |
1 | 1.07 | 1.00 | 0.82 | 0.82 | 1.29 | 0.68 | 1.71 | 1.04 |
time (sec) |
N/A | 0.387 | 0.035 | 0.420 | 0.240 | 0.264 | 0.144 | 0.282 | 15.491 |
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 | 24 | 22 | 20 | 23 | 23 | 20 | 23 | 23 |
N.S. |
1 | 0.96 | 0.88 | 0.80 | 0.92 | 0.92 | 0.80 | 0.92 | 0.92 |
time (sec) |
N/A | 0.147 | 0.002 | 0.110 | 0.199 | 0.253 | 0.024 | 0.277 | 15.696 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 80 | 30 | 34 | 44 | 30 | 20 | 32 | 26 |
N.S. |
1 | 2.67 | 1.00 | 1.13 | 1.47 | 1.00 | 0.67 | 1.07 | 0.87 |
time (sec) |
N/A | 0.278 | 0.196 | 1.040 | 0.223 | 0.257 | 0.131 | 0.280 | 15.177 |
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 | 27 | 20 | 21 | 20 | 19 | 20 | 22 | 22 | 21 |
N.S. |
1 | 0.74 | 0.78 | 0.74 | 0.70 | 0.74 | 0.81 | 0.81 | 0.78 |
time (sec) |
N/A | 0.195 | 0.014 | 0.257 | 0.189 | 0.245 | 0.341 | 0.276 | 14.884 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 49 | 26 | 52 | 39 | 58 | 39 | 38 | 23 |
N.S. |
1 | 2.04 | 1.08 | 2.17 | 1.62 | 2.42 | 1.62 | 1.58 | 0.96 |
time (sec) |
N/A | 0.345 | 0.029 | 11.303 | 0.274 | 0.267 | 1.405 | 0.293 | 15.298 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 32 | 32 | 108 | 40 | 32 | 0 | 32 |
N.S. |
1 | 0.00 | 0.97 | 0.97 | 3.27 | 1.21 | 0.97 | 0.00 | 0.97 |
time (sec) |
N/A | 0.000 | 0.574 | 1.340 | 0.358 | 0.278 | 0.157 | 0.000 | 0.689 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 16 | 37 | 21 | 19 | 29 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 1.85 | 1.05 | 0.95 | 1.45 | 0.75 |
time (sec) |
N/A | 0.178 | 0.027 | 1.025 | 0.249 | 0.270 | 0.074 | 0.276 | 0.087 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 131 | 32 | 48 | 67 | 35 | 42 | 44 | 63 |
N.S. |
1 | 5.04 | 1.23 | 1.85 | 2.58 | 1.35 | 1.62 | 1.69 | 2.42 |
time (sec) |
N/A | 0.332 | 0.045 | 0.219 | 0.190 | 0.277 | 0.114 | 0.287 | 14.619 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 31 | 90 | 62 | 56 | 26 | 49 | 150 |
N.S. |
1 | 0.00 | 0.97 | 2.81 | 1.94 | 1.75 | 0.81 | 1.53 | 4.69 |
time (sec) |
N/A | 0.000 | 0.813 | 190.866 | 0.332 | 0.257 | 0.190 | 0.525 | 15.222 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | F(-2) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 38 | 115 | 93 | 94 | 0 | 57 | 281 |
N.S. |
1 | 0.00 | 1.23 | 3.71 | 3.00 | 3.03 | 0.00 | 1.84 | 9.06 |
time (sec) |
N/A | 0.000 | 0.141 | 5.064 | 0.249 | 0.270 | 0.000 | 0.364 | 14.701 |
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 | 17 | 19 | 16 | 15 | 17 | 17 | 14 | 17 | 14 |
N.S. |
1 | 1.12 | 0.94 | 0.88 | 1.00 | 1.00 | 0.82 | 1.00 | 0.82 |
time (sec) |
N/A | 0.145 | 0.012 | 0.335 | 0.187 | 0.259 | 0.055 | 0.272 | 14.258 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 62 | 76 | 74 | 77 | 83 | 0 | 82 |
N.S. |
1 | 0.00 | 2.30 | 2.81 | 2.74 | 2.85 | 3.07 | 0.00 | 3.04 |
time (sec) |
N/A | 0.000 | 0.743 | 1.895 | 0.234 | 0.298 | 0.201 | 0.000 | 14.791 |
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 | 19 | 17 | 17 | 18 | 17 | 17 | 14 | 17 | 16 |
N.S. |
1 | 0.89 | 0.89 | 0.95 | 0.89 | 0.89 | 0.74 | 0.89 | 0.84 |
time (sec) |
N/A | 0.141 | 0.002 | 0.053 | 0.190 | 0.263 | 0.055 | 0.267 | 14.135 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 65 | 83 | 48 | 54 | 44 | 44 | 56 | 47 |
N.S. |
1 | 2.24 | 2.86 | 1.66 | 1.86 | 1.52 | 1.52 | 1.93 | 1.62 |
time (sec) |
N/A | 0.351 | 0.068 | 0.409 | 0.196 | 0.253 | 1.931 | 0.284 | 14.416 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 506 | 36 | 38 | 961 | 37 | 37 | 40 | 37 |
N.S. |
1 | 21.08 | 1.50 | 1.58 | 40.04 | 1.54 | 1.54 | 1.67 | 1.54 |
time (sec) |
N/A | 3.359 | 0.069 | 2.117 | 0.388 | 0.276 | 0.164 | 0.402 | 32.465 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 22 | 28 | 114 | 59 | 64 | 32 | 0 | 23 |
N.S. |
1 | 0.92 | 1.17 | 4.75 | 2.46 | 2.67 | 1.33 | 0.00 | 0.96 |
time (sec) |
N/A | 2.397 | 0.095 | 7.217 | 0.399 | 0.300 | 0.287 | 0.000 | 14.045 |
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 | 14 | 10 | 10 | 10 | 9 | 9 | 8 | 9 | 9 |
N.S. |
1 | 0.71 | 0.71 | 0.71 | 0.64 | 0.64 | 0.57 | 0.64 | 0.64 |
time (sec) |
N/A | 0.128 | 0.000 | 0.021 | 0.188 | 0.247 | 0.022 | 0.277 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 33 | 18 | 18 | 153 | 17 | 15 | 17 | 18 |
N.S. |
1 | 1.50 | 0.82 | 0.82 | 6.95 | 0.77 | 0.68 | 0.77 | 0.82 |
time (sec) |
N/A | 0.201 | 0.247 | 0.165 | 0.342 | 0.267 | 0.061 | 0.283 | 13.977 |
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 | 11 | 15 | 10 | 10 | 13 | 14 | 10 | 13 | 9 |
N.S. |
1 | 1.36 | 0.91 | 0.91 | 1.18 | 1.27 | 0.91 | 1.18 | 0.82 |
time (sec) |
N/A | 0.144 | 0.002 | 0.237 | 0.199 | 0.272 | 0.033 | 0.270 | 14.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 33 | 28 | 37 | 37 | 29 | 39 | 27 |
N.S. |
1 | 0.00 | 1.27 | 1.08 | 1.42 | 1.42 | 1.12 | 1.50 | 1.04 |
time (sec) |
N/A | 0.000 | 5.066 | 2.347 | 0.312 | 0.277 | 0.105 | 0.286 | 15.344 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 50 | 42 | 57 | 57 | 42 | 57 | 0 |
N.S. |
1 | 0.00 | 2.27 | 1.91 | 2.59 | 2.59 | 1.91 | 2.59 | 0.00 |
time (sec) |
N/A | 0.000 | 0.064 | 0.952 | 0.316 | 0.265 | 0.155 | 0.714 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 47 | 108 | 47 | 42 | 38 | 39 | 43 | 41 |
N.S. |
1 | 1.42 | 3.27 | 1.42 | 1.27 | 1.15 | 1.18 | 1.30 | 1.24 |
time (sec) |
N/A | 0.879 | 0.280 | 1.872 | 0.317 | 0.264 | 0.181 | 0.282 | 15.473 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 20 | 25 | 52 | 24 | 20 | 24 | 24 |
N.S. |
1 | 0.00 | 0.71 | 0.89 | 1.86 | 0.86 | 0.71 | 0.86 | 0.86 |
time (sec) |
N/A | 0.000 | 0.376 | 0.815 | 0.276 | 0.256 | 0.113 | 0.282 | 15.274 |
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 | 27 | 15 | 15 | 16 | 15 | 17 | 12 | 15 | 14 |
N.S. |
1 | 0.56 | 0.56 | 0.59 | 0.56 | 0.63 | 0.44 | 0.56 | 0.52 |
time (sec) |
N/A | 0.174 | 0.004 | 0.211 | 0.187 | 0.259 | 0.064 | 0.271 | 15.927 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 38 | 59 | 30 | 45 | 29 | 53 | 0 |
N.S. |
1 | 0.00 | 1.15 | 1.79 | 0.91 | 1.36 | 0.88 | 1.61 | 0.00 |
time (sec) |
N/A | 0.000 | 0.450 | 2.110 | 0.230 | 0.256 | 0.179 | 0.288 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | C | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 64 | 64 | 23 | 80 | 21 | 20 | 24 | 24 |
N.S. |
1 | 3.37 | 3.37 | 1.21 | 4.21 | 1.11 | 1.05 | 1.26 | 1.26 |
time (sec) |
N/A | 0.248 | 0.065 | 0.343 | 0.242 | 0.257 | 0.066 | 0.275 | 0.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 28 | 31 | 25 | 119 | 33 | 31 | 36 | 36 |
N.S. |
1 | 1.04 | 1.15 | 0.93 | 4.41 | 1.22 | 1.15 | 1.33 | 1.33 |
time (sec) |
N/A | 0.246 | 0.093 | 1.937 | 0.331 | 0.253 | 0.346 | 0.326 | 16.457 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 53 | 57 | 41 | 45 | 54 | 66 | 49 |
N.S. |
1 | 0.00 | 1.47 | 1.58 | 1.14 | 1.25 | 1.50 | 1.83 | 1.36 |
time (sec) |
N/A | 0.000 | 10.110 | 3.101 | 0.252 | 0.251 | 0.404 | 0.288 | 16.441 |
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 | 21 | 28 | 23 | 25 | 23 | 23 | 42 | 28 | 25 |
N.S. |
1 | 1.33 | 1.10 | 1.19 | 1.10 | 1.10 | 2.00 | 1.33 | 1.19 |
time (sec) |
N/A | 0.175 | 0.022 | 2.140 | 0.207 | 0.246 | 0.297 | 0.277 | 0.214 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 41 | 29 | 27 | 173 | 29 | 31 | 29 | 29 |
N.S. |
1 | 1.71 | 1.21 | 1.12 | 7.21 | 1.21 | 1.29 | 1.21 | 1.21 |
time (sec) |
N/A | 0.324 | 0.084 | 0.181 | 0.331 | 0.282 | 0.154 | 0.284 | 0.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 25 | 25 | 31 | 29 | 27 | 0 | 30 | 26 |
N.S. |
1 | 1.04 | 1.04 | 1.29 | 1.21 | 1.12 | 0.00 | 1.25 | 1.08 |
time (sec) |
N/A | 1.090 | 0.093 | 3.917 | 0.353 | 0.250 | 0.000 | 0.347 | 15.772 |
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 | 34 | 29 | 30 | 30 | 52 | 32 | 29 | 33 | 29 |
N.S. |
1 | 0.85 | 0.88 | 0.88 | 1.53 | 0.94 | 0.85 | 0.97 | 0.85 |
time (sec) |
N/A | 0.493 | 0.068 | 0.431 | 0.334 | 0.260 | 0.117 | 0.322 | 16.085 |
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 | 20 | 35 | 19 | 20 | 40 | 19 | 19 | 19 | 19 |
N.S. |
1 | 1.75 | 0.95 | 1.00 | 2.00 | 0.95 | 0.95 | 0.95 | 0.95 |
time (sec) |
N/A | 0.267 | 0.034 | 2.111 | 0.173 | 0.284 | 0.057 | 0.275 | 0.148 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 34 | 23 | 25 | 36 | 31 | 22 | 34 | 22 |
N.S. |
1 | 1.31 | 0.88 | 0.96 | 1.38 | 1.19 | 0.85 | 1.31 | 0.85 |
time (sec) |
N/A | 0.217 | 0.155 | 0.323 | 0.215 | 0.256 | 0.131 | 0.270 | 15.888 |
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 | 35 | 24 | 22 | 27 | 24 | 22 | 23 | 23 |
N.S. |
1 | 1.40 | 0.96 | 0.88 | 1.08 | 0.96 | 0.88 | 0.92 | 0.92 |
time (sec) |
N/A | 0.702 | 0.196 | 0.270 | 0.324 | 0.255 | 0.138 | 0.280 | 17.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 23 | 21 | 29 | 17 | 21 | 156 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 0.91 | 1.26 | 0.74 | 0.91 | 6.78 |
time (sec) |
N/A | 0.000 | 0.264 | 1.817 | 0.251 | 0.254 | 0.245 | 0.276 | 15.482 |
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 | 25 | 48 | 40 | 36 | 52 | 53 | 134 | 49 | 42 |
N.S. |
1 | 1.92 | 1.60 | 1.44 | 2.08 | 2.12 | 5.36 | 1.96 | 1.68 |
time (sec) |
N/A | 0.290 | 0.023 | 2.670 | 0.183 | 0.259 | 0.436 | 0.276 | 0.245 |
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 | 16 | 16 | 16 | 18 | 17 | 17 | 19 | 17 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.12 | 1.06 | 1.06 | 1.19 | 1.06 | 1.06 |
time (sec) |
N/A | 0.439 | 0.120 | 8.674 | 0.219 | 0.251 | 0.169 | 0.270 | 15.739 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 20 | 17841276 | 146 | 63 | 61 | 109 | 41 |
N.S. |
1 | 0.00 | 1.00 | 892063.80 | 7.30 | 3.15 | 3.05 | 5.45 | 2.05 |
time (sec) |
N/A | 0.000 | 0.068 | 691.840 | 0.325 | 0.273 | 0.336 | 0.426 | 15.441 |
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 | 34 | 32 | 32 | 20 | 19 | 19 | 29 | 19 | 19 |
N.S. |
1 | 0.94 | 0.94 | 0.59 | 0.56 | 0.56 | 0.85 | 0.56 | 0.56 |
time (sec) |
N/A | 0.146 | 0.000 | 0.136 | 0.199 | 0.233 | 0.023 | 0.264 | 0.003 |
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 | 21 | 19 | 15 | 14 | 15 | 14 | 15 | 14 |
N.S. |
1 | 0.84 | 0.76 | 0.60 | 0.56 | 0.60 | 0.56 | 0.60 | 0.56 |
time (sec) |
N/A | 0.173 | 0.029 | 0.086 | 0.183 | 0.243 | 0.060 | 0.272 | 14.617 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | F(-1) | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 22 | 32 | 36 | 0 | 34 | 121 | 35 |
N.S. |
1 | 0.00 | 1.00 | 1.45 | 1.64 | 0.00 | 1.55 | 5.50 | 1.59 |
time (sec) |
N/A | 0.000 | 5.353 | 2.743 | 0.829 | 0.000 | 35.214 | 0.430 | 15.140 |
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 | 21 | 27 | 26 | 20 | 23 | 21 | 17 | 35 | 19 |
N.S. |
1 | 1.29 | 1.24 | 0.95 | 1.10 | 1.00 | 0.81 | 1.67 | 0.90 |
time (sec) |
N/A | 0.494 | 0.608 | 162.329 | 0.229 | 0.244 | 0.098 | 0.276 | 0.310 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 21 | 21 | 31 | 22 | 19 | 35 | 20 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 1.48 | 1.05 | 0.90 | 1.67 | 0.95 |
time (sec) |
N/A | 0.000 | 0.051 | 15.400 | 0.308 | 0.252 | 0.088 | 0.291 | 14.996 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 8 | 17 | 15 | 22 | 14 | 12 | 14 | 14 |
N.S. |
1 | 0.47 | 1.00 | 0.88 | 1.29 | 0.82 | 0.71 | 0.82 | 0.82 |
time (sec) |
N/A | 0.269 | 0.010 | 1.841 | 0.281 | 0.245 | 0.057 | 0.266 | 0.263 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | B | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 209 | 42 | 39 | 44 | 36 | 41 | 0 | 46 |
N.S. |
1 | 9.50 | 1.91 | 1.77 | 2.00 | 1.64 | 1.86 | 0.00 | 2.09 |
time (sec) |
N/A | 2.481 | 0.350 | 19.983 | 0.426 | 0.253 | 14.262 | 0.000 | 14.707 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 9 | 102 | 9 | 10 | 17 | 9 | 8 | 9 | 9 |
N.S. |
1 | 11.33 | 1.00 | 1.11 | 1.89 | 1.00 | 0.89 | 1.00 | 1.00 |
time (sec) |
N/A | 0.403 | 0.085 | 0.125 | 0.224 | 0.235 | 0.049 | 0.269 | 14.781 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | B | A | F(-1) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 138 | 25 | 63 | 46 | 0 | 0 | 60 |
N.S. |
1 | 0.00 | 4.93 | 0.89 | 2.25 | 1.64 | 0.00 | 0.00 | 2.14 |
time (sec) |
N/A | 0.000 | 11.225 | 2.348 | 0.242 | 0.273 | 0.000 | 0.000 | 15.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 20 | 19 | 18 | 30 | 14 | 281 | 106 |
N.S. |
1 | 0.00 | 0.71 | 0.68 | 0.64 | 1.07 | 0.50 | 10.04 | 3.79 |
time (sec) |
N/A | 0.000 | 0.472 | 0.420 | 0.234 | 0.241 | 0.195 | 0.292 | 14.370 |