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 | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 31 | 36 | 23 | 58 | 27 | 36 | 32 | 30 |
N.S. |
1 | 1.29 | 1.50 | 0.96 | 2.42 | 1.12 | 1.50 | 1.33 | 1.25 |
time (sec) |
N/A | 0.235 | 0.067 | 0.168 | 0.267 | 0.257 | 0.151 | 0.296 | 8.896 |
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 | 35 | 0 | 35 | 43 | 0 | 57 | 44 | 27917 | 56 |
N.S. |
1 | 0.00 | 1.00 | 1.23 | 0.00 | 1.63 | 1.26 | 797.63 | 1.60 |
time (sec) |
N/A | 0.000 | 0.760 | 21.908 | 0.000 | 0.256 | 0.565 | 1.455 | 12.198 |
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 | 14 | 11 | 12 | 13 | 57 | 12 | 10 | 30 | 12 |
N.S. |
1 | 0.79 | 0.86 | 0.93 | 4.07 | 0.86 | 0.71 | 2.14 | 0.86 |
time (sec) |
N/A | 0.294 | 0.105 | 0.223 | 0.370 | 0.251 | 0.053 | 0.257 | 0.305 |
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 | 27 | 0 | 30 | 26 | 11 | 26 | 22 | 30 | 23 |
N.S. |
1 | 0.00 | 1.11 | 0.96 | 0.41 | 0.96 | 0.81 | 1.11 | 0.85 |
time (sec) |
N/A | 0.000 | 12.638 | 0.149 | 0.224 | 0.251 | 0.108 | 0.276 | 9.771 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | F(-2) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 27 | 45 | 44 | 67 | 0 | 116 | 168 |
N.S. |
1 | 0.00 | 1.08 | 1.80 | 1.76 | 2.68 | 0.00 | 4.64 | 6.72 |
time (sec) |
N/A | 0.000 | 0.133 | 11.674 | 0.580 | 0.254 | 0.000 | 0.282 | 10.723 |
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 | 21 | 17 | 20 | 22 | 21 | 20 | 19 | 19 |
N.S. |
1 | 0.72 | 0.59 | 0.69 | 0.76 | 0.72 | 0.69 | 0.66 | 0.66 |
time (sec) |
N/A | 0.176 | 0.003 | 0.437 | 0.183 | 0.231 | 0.087 | 0.253 | 8.571 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | B | A | A | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 0 | 34 | 55 | 38 | 36 | 88 | 70 |
N.S. |
1 | 0.00 | 0.00 | 1.10 | 1.77 | 1.23 | 1.16 | 2.84 | 2.26 |
time (sec) |
N/A | 0.000 | 0.000 | 3.458 | 0.422 | 0.251 | 0.397 | 0.644 | 0.978 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 56 | 750 | 1343 | 1343 | 1368 | 2234 | 0 |
N.S. |
1 | 0.00 | 2.80 | 37.50 | 67.15 | 67.15 | 68.40 | 111.70 | 0.00 |
time (sec) |
N/A | 0.000 | 0.161 | 20.778 | 1.507 | 0.305 | 4.054 | 0.999 | 0.000 |
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 | 26 | 26 | 343 | 41 | 39 | 102 | 105 |
N.S. |
1 | 0.00 | 0.84 | 0.84 | 11.06 | 1.32 | 1.26 | 3.29 | 3.39 |
time (sec) |
N/A | 0.000 | 1.241 | 2.356 | 1.250 | 0.243 | 0.246 | 0.368 | 9.252 |
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 | 20 | 0 | 20 | 24 | 17 | 23 | 20 | 24 | 23 |
N.S. |
1 | 0.00 | 1.00 | 1.20 | 0.85 | 1.15 | 1.00 | 1.20 | 1.15 |
time (sec) |
N/A | 0.000 | 0.253 | 0.823 | 0.243 | 0.238 | 0.318 | 0.328 | 9.683 |
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 | 29 | 18 | 18 | 28 | 27 | 17 | 29 | 17 |
N.S. |
1 | 1.38 | 0.86 | 0.86 | 1.33 | 1.29 | 0.81 | 1.38 | 0.81 |
time (sec) |
N/A | 0.494 | 0.165 | 0.182 | 0.338 | 0.250 | 0.077 | 0.257 | 9.429 |
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 | 24 | 22 | 39 | 23 | 20 | 33 | 17 | 20 | 75 |
N.S. |
1 | 0.92 | 1.62 | 0.96 | 0.83 | 1.38 | 0.71 | 0.83 | 3.12 |
time (sec) |
N/A | 0.255 | 0.035 | 0.288 | 0.182 | 0.246 | 0.101 | 0.270 | 9.580 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 1593 | 47 | 77 | 128 | 74 | 90 | 118 | 77 |
N.S. |
1 | 54.93 | 1.62 | 2.66 | 4.41 | 2.55 | 3.10 | 4.07 | 2.66 |
time (sec) |
N/A | 5.542 | 0.117 | 1.572 | 0.317 | 0.248 | 0.322 | 0.340 | 9.840 |
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 | 20 | 20 | 18 | 17 | 19 | 17 | 17 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.85 | 0.95 | 0.85 | 0.85 | 0.85 |
time (sec) |
N/A | 0.622 | 0.126 | 0.819 | 0.329 | 0.263 | 0.221 | 0.268 | 9.608 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | F(-1) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 28 | 27 | 82 | 33 | 0 | 27 | 60 |
N.S. |
1 | 0.00 | 1.00 | 0.96 | 2.93 | 1.18 | 0.00 | 0.96 | 2.14 |
time (sec) |
N/A | 0.000 | 0.118 | 77.562 | 0.448 | 0.268 | 0.000 | 0.637 | 9.733 |
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 | 24 | 0 | 29 | 30 | 43 | 43 | 27 | 32 | 31 |
N.S. |
1 | 0.00 | 1.21 | 1.25 | 1.79 | 1.79 | 1.12 | 1.33 | 1.29 |
time (sec) |
N/A | 0.000 | 0.221 | 0.374 | 0.223 | 0.250 | 0.068 | 0.269 | 9.456 |
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 | 21 | 29 | 22 | 21 | 21 | 20 | 21 | 21 |
N.S. |
1 | 0.95 | 1.32 | 1.00 | 0.95 | 0.95 | 0.91 | 0.95 | 0.95 |
time (sec) |
N/A | 0.162 | 0.023 | 0.286 | 0.278 | 0.273 | 0.090 | 0.267 | 9.379 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | A | A | B | C | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 0 | 50 | 51 | 27 | 27 | 51 | 52 | 27 |
N.S. |
1 | 0.00 | 3.12 | 3.19 | 1.69 | 1.69 | 3.19 | 3.25 | 1.69 |
time (sec) |
N/A | 0.000 | 0.068 | 15.116 | 0.234 | 0.257 | 0.619 | 0.401 | 9.706 |
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 | 8 | 8 | 9 | 8 | 8 | 8 | 9 | 8 |
N.S. |
1 | 0.67 | 0.67 | 0.75 | 0.67 | 0.67 | 0.67 | 0.75 | 0.67 |
time (sec) |
N/A | 0.125 | 0.001 | 0.041 | 0.194 | 0.244 | 0.019 | 0.261 | 0.022 |
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 | 23 | 50 | 22 | 18 | 66 | 17 | 20 | 17 | 17 |
N.S. |
1 | 2.17 | 0.96 | 0.78 | 2.87 | 0.74 | 0.87 | 0.74 | 0.74 |
time (sec) |
N/A | 0.276 | 0.021 | 0.118 | 0.193 | 0.250 | 0.055 | 0.257 | 8.741 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 49 | 126 | 69 | 73 | 37 | 50 | 51 |
N.S. |
1 | 0.00 | 1.48 | 3.82 | 2.09 | 2.21 | 1.12 | 1.52 | 1.55 |
time (sec) |
N/A | 0.000 | 0.291 | 255.885 | 0.326 | 0.279 | 0.368 | 2.351 | 9.987 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 29 | 19 | 0 | 19 | 22 | 19 | 20 |
N.S. |
1 | 0.00 | 1.38 | 0.90 | 0.00 | 0.90 | 1.05 | 0.90 | 0.95 |
time (sec) |
N/A | 0.000 | 1.416 | 0.382 | 0.000 | 0.245 | 0.196 | 0.273 | 9.040 |
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 | 17 | 20 | 20 | 20 | 19 | 19 | 19 | 19 | 19 |
N.S. |
1 | 1.18 | 1.18 | 1.18 | 1.12 | 1.12 | 1.12 | 1.12 | 1.12 |
time (sec) |
N/A | 0.150 | 0.027 | 0.034 | 0.216 | 0.250 | 0.066 | 0.257 | 9.136 |
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 | 23 | 29 | 34 | 41 | 28 | 36 | 24 | 62 | 43 |
N.S. |
1 | 1.26 | 1.48 | 1.78 | 1.22 | 1.57 | 1.04 | 2.70 | 1.87 |
time (sec) |
N/A | 0.285 | 0.048 | 1.164 | 0.190 | 0.253 | 0.274 | 0.257 | 0.687 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 133 | 60 | 28 | 73 | 56 | 75 | 75 | 33 |
N.S. |
1 | 4.93 | 2.22 | 1.04 | 2.70 | 2.07 | 2.78 | 2.78 | 1.22 |
time (sec) |
N/A | 0.604 | 0.038 | 0.775 | 0.199 | 0.259 | 0.447 | 0.265 | 0.656 |
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 | 15 | 15 | 15 | 14 | 14 | 15 | 14 | 14 |
N.S. |
1 | 0.71 | 0.71 | 0.71 | 0.67 | 0.67 | 0.71 | 0.67 | 0.67 |
time (sec) |
N/A | 0.277 | 0.013 | 1.105 | 0.184 | 0.247 | 0.056 | 0.255 | 9.975 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 47 | 48 | 61 | 33 | 58 | 65 | 42 |
N.S. |
1 | 0.00 | 1.57 | 1.60 | 2.03 | 1.10 | 1.93 | 2.17 | 1.40 |
time (sec) |
N/A | 0.000 | 0.155 | 2.006 | 0.300 | 0.250 | 6.611 | 0.281 | 9.428 |
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 | 39 | 27 | 26 | 22 | 25 | 22 | 25 | 22 |
N.S. |
1 | 1.30 | 0.90 | 0.87 | 0.73 | 0.83 | 0.73 | 0.83 | 0.73 |
time (sec) |
N/A | 0.320 | 0.143 | 0.056 | 0.254 | 0.240 | 0.077 | 0.269 | 8.955 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 208 | 173 | 72 | 83 | 69 | 0 | 0 | 92 |
N.S. |
1 | 6.30 | 5.24 | 2.18 | 2.52 | 2.09 | 0.00 | 0.00 | 2.79 |
time (sec) |
N/A | 1.924 | 0.423 | 0.389 | 0.308 | 0.246 | 0.000 | 0.000 | 9.297 |
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 | 30 | 0 | 31 | 27 | 36 | 29 | 39 | 30 | 0 |
N.S. |
1 | 0.00 | 1.03 | 0.90 | 1.20 | 0.97 | 1.30 | 1.00 | 0.00 |
time (sec) |
N/A | 0.000 | 1.006 | 54.781 | 0.264 | 0.247 | 0.179 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 47 | 55 | 435 | 424 | 1035 | 775 | 0 |
N.S. |
1 | 0.00 | 1.57 | 1.83 | 14.50 | 14.13 | 34.50 | 25.83 | 0.00 |
time (sec) |
N/A | 0.000 | 0.285 | 0.260 | 3.858 | 0.273 | 8.017 | 2.058 | 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 | 20 | 23 | 21 | 19 | 22 | 22 | 19 | 23 | 22 |
N.S. |
1 | 1.15 | 1.05 | 0.95 | 1.10 | 1.10 | 0.95 | 1.15 | 1.10 |
time (sec) |
N/A | 0.176 | 0.009 | 0.080 | 0.186 | 0.242 | 0.241 | 0.267 | 0.332 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | C | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 62 | 50 | 49 | 61 | 48 | 51 | 52 | 51 |
N.S. |
1 | 2.38 | 1.92 | 1.88 | 2.35 | 1.85 | 1.96 | 2.00 | 1.96 |
time (sec) |
N/A | 0.310 | 0.194 | 0.219 | 0.235 | 0.239 | 0.066 | 0.259 | 9.333 |
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 | 17 | 17 | 16 | 14 | 13 | 25 | 14 | 0 | 13 |
N.S. |
1 | 1.00 | 0.94 | 0.82 | 0.76 | 1.47 | 0.82 | 0.00 | 0.76 |
time (sec) |
N/A | 0.212 | 0.154 | 0.051 | 0.181 | 0.256 | 0.068 | 0.000 | 9.034 |
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 | 14 | 0 | 12 | 12 | 25 | 18 | 19 | 11 | 11 |
N.S. |
1 | 0.00 | 0.86 | 0.86 | 1.79 | 1.29 | 1.36 | 0.79 | 0.79 |
time (sec) |
N/A | 0.000 | 0.208 | 0.116 | 0.308 | 0.252 | 0.144 | 0.257 | 9.012 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 155 | 60 | 50 | 63 | 72 | 63 | 70 | 60 |
N.S. |
1 | 5.96 | 2.31 | 1.92 | 2.42 | 2.77 | 2.42 | 2.69 | 2.31 |
time (sec) |
N/A | 2.108 | 14.323 | 0.319 | 0.238 | 0.260 | 0.117 | 0.261 | 9.040 |
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 | 11 | 12 | 12 | 12 | 11 | 11 | 8 | 11 | 11 |
N.S. |
1 | 1.09 | 1.09 | 1.09 | 1.00 | 1.00 | 0.73 | 1.00 | 1.00 |
time (sec) |
N/A | 0.128 | 0.000 | 0.017 | 0.204 | 0.232 | 0.019 | 0.257 | 0.002 |
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 | 22 | 36 | 18 | 18 | 0 | 31 | 14 | 31 | 17 |
N.S. |
1 | 1.64 | 0.82 | 0.82 | 0.00 | 1.41 | 0.64 | 1.41 | 0.77 |
time (sec) |
N/A | 0.427 | 0.060 | 0.306 | 0.000 | 0.246 | 0.064 | 0.257 | 0.126 |
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 | 22 | 36 | 19 | 27 | 62 | 24 | 22 | 87 | 35 |
N.S. |
1 | 1.64 | 0.86 | 1.23 | 2.82 | 1.09 | 1.00 | 3.95 | 1.59 |
time (sec) |
N/A | 0.271 | 0.047 | 0.232 | 0.313 | 0.240 | 0.059 | 0.261 | 9.365 |
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 | 22 | 26 | 26 | 24 | 126 | 23 | 24 | 69 | 25 |
N.S. |
1 | 1.18 | 1.18 | 1.09 | 5.73 | 1.05 | 1.09 | 3.14 | 1.14 |
time (sec) |
N/A | 0.410 | 0.133 | 0.548 | 0.323 | 0.251 | 0.111 | 0.298 | 10.244 |
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 | 31 | 26 | 31 | 68 | 42 | 24 | 26 | 25 |
N.S. |
1 | 1.19 | 1.00 | 1.19 | 2.62 | 1.62 | 0.92 | 1.00 | 0.96 |
time (sec) |
N/A | 0.978 | 0.118 | 0.599 | 0.233 | 0.248 | 0.055 | 0.260 | 9.393 |
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 | 20 | 20 | 14 | 13 | 13 | 17 | 13 | 14 |
N.S. |
1 | 1.25 | 1.25 | 0.88 | 0.81 | 0.81 | 1.06 | 0.81 | 0.88 |
time (sec) |
N/A | 0.191 | 0.070 | 0.087 | 0.192 | 0.283 | 0.056 | 0.263 | 8.961 |
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 | 25 | 49 | 18 | 19 | 61 | 19 | 19 | 19 | 19 |
N.S. |
1 | 1.96 | 0.72 | 0.76 | 2.44 | 0.76 | 0.76 | 0.76 | 0.76 |
time (sec) |
N/A | 0.223 | 0.169 | 0.110 | 0.278 | 0.253 | 0.052 | 0.256 | 9.253 |
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 | 25 | 21 | 17 | 16 | 16 | 15 | 16 | 18 |
N.S. |
1 | 1.19 | 1.00 | 0.81 | 0.76 | 0.76 | 0.71 | 0.76 | 0.86 |
time (sec) |
N/A | 0.221 | 0.109 | 0.058 | 0.194 | 0.257 | 0.044 | 0.256 | 8.880 |
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 | 28 | 26 | 15 | 26 | 26 | 29 | 27 | 15 |
N.S. |
1 | 1.65 | 1.53 | 0.88 | 1.53 | 1.53 | 1.71 | 1.59 | 0.88 |
time (sec) |
N/A | 0.156 | 0.016 | 0.077 | 0.196 | 0.248 | 0.046 | 0.247 | 0.057 |
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 | 23 | 23 | 20 | 19 | 19 | 22 | 19 | 17 |
N.S. |
1 | 1.10 | 1.10 | 0.95 | 0.90 | 0.90 | 1.05 | 0.90 | 0.81 |
time (sec) |
N/A | 0.146 | 0.002 | 0.032 | 0.204 | 0.249 | 0.042 | 0.253 | 9.270 |
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 | 26 | 17 | 21 | 20 | 21 | 15 | 20 | 14 |
N.S. |
1 | 1.53 | 1.00 | 1.24 | 1.18 | 1.24 | 0.88 | 1.18 | 0.82 |
time (sec) |
N/A | 0.175 | 0.003 | 0.069 | 0.191 | 0.264 | 0.047 | 0.255 | 8.688 |
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 | 2 | 2 | 2 | 3 | 2 | 2 | 2 | 3 | 2 |
N.S. |
1 | 1.00 | 1.00 | 1.50 | 1.00 | 1.00 | 1.00 | 1.50 | 1.00 |
time (sec) |
N/A | 0.115 | 0.000 | 0.018 | 0.191 | 0.252 | 0.033 | 0.253 | 0.007 |
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 | 15 | 15 | 12 | 11 | 15 | 12 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.73 | 1.00 | 0.80 | 0.73 | 0.73 |
time (sec) |
N/A | 0.327 | 0.008 | 0.052 | 0.197 | 0.262 | 0.041 | 0.265 | 9.008 |
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 | 24 | 43 | 34 | 26 | 26 | 56 | 26 | 31 | 28 |
N.S. |
1 | 1.79 | 1.42 | 1.08 | 1.08 | 2.33 | 1.08 | 1.29 | 1.17 |
time (sec) |
N/A | 0.405 | 0.049 | 0.091 | 0.199 | 0.247 | 0.544 | 0.254 | 0.194 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 41 | 41 | 44 | 59 | 37 | 48 | 0 |
N.S. |
1 | 0.00 | 1.37 | 1.37 | 1.47 | 1.97 | 1.23 | 1.60 | 0.00 |
time (sec) |
N/A | 0.000 | 0.342 | 0.141 | 0.310 | 0.255 | 0.394 | 0.784 | 0.000 |
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 | 24 | 0 | 29 | 30 | 28 | 35 | 29 | 29 | 31 |
N.S. |
1 | 0.00 | 1.21 | 1.25 | 1.17 | 1.46 | 1.21 | 1.21 | 1.29 |
time (sec) |
N/A | 0.000 | 0.369 | 0.379 | 0.307 | 0.253 | 0.103 | 0.261 | 8.842 |
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 | 24 | 23 | 22 | 20 | 19 | 19 | 36 | 20 |
N.S. |
1 | 0.83 | 0.79 | 0.76 | 0.69 | 0.66 | 0.66 | 1.24 | 0.69 |
time (sec) |
N/A | 0.248 | 0.017 | 0.254 | 0.187 | 0.258 | 0.189 | 0.257 | 0.164 |
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 | 24 | 28 | 19 | 19 | 19 | 21 |
N.S. |
1 | 0.00 | 1.00 | 1.14 | 1.33 | 0.90 | 0.90 | 0.90 | 1.00 |
time (sec) |
N/A | 0.000 | 0.028 | 0.297 | 0.333 | 0.255 | 0.228 | 0.279 | 9.090 |
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 | 19 | 19 | 17 | 21 | 16 | 14 | 16 | 14 |
N.S. |
1 | 0.95 | 0.95 | 0.85 | 1.05 | 0.80 | 0.70 | 0.80 | 0.70 |
time (sec) |
N/A | 0.202 | 0.009 | 0.053 | 0.218 | 0.246 | 0.044 | 0.258 | 0.062 |
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 | 24 | 9 | 13 | 7 | 9 | 9 | 8 | 9 | 6 |
N.S. |
1 | 0.38 | 0.54 | 0.29 | 0.38 | 0.38 | 0.33 | 0.38 | 0.25 |
time (sec) |
N/A | 0.122 | 0.001 | 0.021 | 0.180 | 0.232 | 0.016 | 0.251 | 0.030 |
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 | 26 | 32 | 32 | 32 | 31 | 33 | 29 | 31 | 31 |
N.S. |
1 | 1.23 | 1.23 | 1.23 | 1.19 | 1.27 | 1.12 | 1.19 | 1.19 |
time (sec) |
N/A | 0.194 | 0.007 | 0.050 | 0.187 | 0.241 | 0.037 | 0.256 | 0.041 |
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 | 22 | 22 | 68 | 18 | 17 | 17 | 22 | 23 | 22 |
N.S. |
1 | 1.00 | 3.09 | 0.82 | 0.77 | 0.77 | 1.00 | 1.05 | 1.00 |
time (sec) |
N/A | 0.273 | 0.068 | 0.189 | 0.195 | 0.253 | 0.115 | 0.257 | 9.179 |
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 | 10 | 10 | 10 | 11 | 10 | 13 | 10 | 10 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.10 | 1.00 | 1.30 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.127 | 0.002 | 0.078 | 0.191 | 0.237 | 0.022 | 0.252 | 0.058 |
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 | 18 | 16 | 14 | 16 | 44 | 18 | 17 | 26 | 12 |
N.S. |
1 | 0.89 | 0.78 | 0.89 | 2.44 | 1.00 | 0.94 | 1.44 | 0.67 |
time (sec) |
N/A | 0.452 | 0.098 | 0.027 | 0.240 | 0.237 | 0.041 | 0.262 | 9.461 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | F | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 40 | 0 | 34 | 31 | 34 | 32 | 34 | 0 |
N.S. |
1 | 2.11 | 0.00 | 1.79 | 1.63 | 1.79 | 1.68 | 1.79 | 0.00 |
time (sec) |
N/A | 1.129 | 0.000 | 0.750 | 0.316 | 0.255 | 0.344 | 0.265 | 0.000 |
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 | 25 | 0 | 24 | 27 | 31 | 26 | 32 | 26 | 26 |
N.S. |
1 | 0.00 | 0.96 | 1.08 | 1.24 | 1.04 | 1.28 | 1.04 | 1.04 |
time (sec) |
N/A | 0.000 | 0.166 | 0.117 | 0.316 | 0.243 | 0.087 | 0.255 | 0.162 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | F(-1) | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 57 | 54 | 53 | 53 | 0 | 53 | 0 |
N.S. |
1 | 0.00 | 2.19 | 2.08 | 2.04 | 2.04 | 0.00 | 2.04 | 0.00 |
time (sec) |
N/A | 0.000 | 0.143 | 44.318 | 0.350 | 0.258 | 0.000 | 0.935 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 24 | 24 | 47 | 47 | 26 | 51 | 28 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 1.96 | 1.96 | 1.08 | 2.12 | 1.17 |
time (sec) |
N/A | 0.000 | 4.618 | 0.072 | 0.247 | 0.243 | 0.065 | 0.271 | 9.245 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 29 | 22 | 29 | 44 | 20 | 255 | 0 |
N.S. |
1 | 0.00 | 1.16 | 0.88 | 1.16 | 1.76 | 0.80 | 10.20 | 0.00 |
time (sec) |
N/A | 0.000 | 5.791 | 0.137 | 0.228 | 0.246 | 0.082 | 0.272 | 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 | 25 | 44 | 25 | 24 | 39 | 20 | 22 | 23 | 23 |
N.S. |
1 | 1.76 | 1.00 | 0.96 | 1.56 | 0.80 | 0.88 | 0.92 | 0.92 |
time (sec) |
N/A | 0.588 | 0.229 | 0.198 | 0.229 | 0.234 | 0.048 | 0.256 | 9.104 |
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 | 18 | 10 | 10 | 10 | 29 | 9 | 7 | 9 | 9 |
N.S. |
1 | 0.56 | 0.56 | 0.56 | 1.61 | 0.50 | 0.39 | 0.50 | 0.50 |
time (sec) |
N/A | 0.169 | 0.046 | 0.032 | 0.223 | 0.235 | 0.036 | 0.253 | 0.059 |
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 | 28 | 0 | 34 | 33 | 32 | 32 | 29 | 32 | 0 |
N.S. |
1 | 0.00 | 1.21 | 1.18 | 1.14 | 1.14 | 1.04 | 1.14 | 0.00 |
time (sec) |
N/A | 0.000 | 0.110 | 0.534 | 0.329 | 0.244 | 0.164 | 0.327 | 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 | 30 | 32 | 31 | 29 | 30 | 36 | 26 | 56 | 31 |
N.S. |
1 | 1.07 | 1.03 | 0.97 | 1.00 | 1.20 | 0.87 | 1.87 | 1.03 |
time (sec) |
N/A | 1.038 | 0.359 | 0.846 | 0.228 | 0.251 | 0.108 | 0.262 | 10.000 |
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 | 26 | 0 | 33 | 30 | 29 | 29 | 29 | 29 | 0 |
N.S. |
1 | 0.00 | 1.27 | 1.15 | 1.12 | 1.12 | 1.12 | 1.12 | 0.00 |
time (sec) |
N/A | 0.000 | 0.079 | 0.247 | 0.245 | 0.261 | 0.290 | 0.427 | 0.000 |
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 | 17 | 16 | 19 | 15 | 15 | 20 | 16 |
N.S. |
1 | 0.00 | 0.65 | 0.62 | 0.73 | 0.58 | 0.58 | 0.77 | 0.62 |
time (sec) |
N/A | 0.000 | 0.266 | 1.603 | 0.350 | 0.250 | 0.062 | 0.261 | 9.225 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 160 | 680 | 747 | 765 | 804 | 1239 | 0 |
N.S. |
1 | 0.00 | 4.85 | 20.61 | 22.64 | 23.18 | 24.36 | 37.55 | 0.00 |
time (sec) |
N/A | 0.000 | 2.756 | 10.616 | 1.074 | 0.280 | 2.706 | 0.996 | 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 | 21 | 20 | 17 | 17 | 27 | 26 | 22 | 17 | 17 |
N.S. |
1 | 0.95 | 0.81 | 0.81 | 1.29 | 1.24 | 1.05 | 0.81 | 0.81 |
time (sec) |
N/A | 0.213 | 0.047 | 0.093 | 0.223 | 0.255 | 0.103 | 0.266 | 0.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 38 | 56 | 124 | 61 | 65 | 0 | 156 |
N.S. |
1 | 0.00 | 1.65 | 2.43 | 5.39 | 2.65 | 2.83 | 0.00 | 6.78 |
time (sec) |
N/A | 0.000 | 0.393 | 85.663 | 0.540 | 0.268 | 1.254 | 0.000 | 10.541 |
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 | 20 | 102 | 14 | 12 | 19 | 11 | 10 | 11 | 11 |
N.S. |
1 | 5.10 | 0.70 | 0.60 | 0.95 | 0.55 | 0.50 | 0.55 | 0.55 |
time (sec) |
N/A | 0.574 | 0.135 | 0.136 | 0.199 | 0.244 | 0.059 | 0.252 | 9.262 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 40 | 39 | 36 | 41 | 40 | 46 | 71 | 27 |
N.S. |
1 | 1.33 | 1.30 | 1.20 | 1.37 | 1.33 | 1.53 | 2.37 | 0.90 |
time (sec) |
N/A | 0.232 | 0.106 | 0.140 | 0.245 | 0.259 | 0.089 | 0.253 | 0.137 |
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 | 25 | 0 | 31 | 26 | 27 | 35 | 32 | 0 | 27 |
N.S. |
1 | 0.00 | 1.24 | 1.04 | 1.08 | 1.40 | 1.28 | 0.00 | 1.08 |
time (sec) |
N/A | 0.000 | 5.192 | 3.392 | 0.297 | 0.249 | 51.078 | 0.000 | 8.695 |
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 | 13 | 8 | 8 | 9 | 8 | 8 | 7 | 9 | 8 |
N.S. |
1 | 0.62 | 0.62 | 0.69 | 0.62 | 0.62 | 0.54 | 0.69 | 0.62 |
time (sec) |
N/A | 0.134 | 0.003 | 0.175 | 0.198 | 0.261 | 0.027 | 0.265 | 0.031 |
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 | 27 | 24 | 25 | 23 | 23 | 29 | 23 | 19 |
N.S. |
1 | 1.08 | 0.96 | 1.00 | 0.92 | 0.92 | 1.16 | 0.92 | 0.76 |
time (sec) |
N/A | 0.157 | 0.004 | 0.063 | 0.205 | 0.246 | 0.052 | 0.252 | 8.930 |
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 | 27 | 20 | 15 | 21 | 14 | 12 | 16 | 14 |
N.S. |
1 | 1.80 | 1.33 | 1.00 | 1.40 | 0.93 | 0.80 | 1.07 | 0.93 |
time (sec) |
N/A | 0.284 | 0.570 | 0.084 | 0.234 | 0.235 | 0.052 | 0.253 | 0.143 |
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 | 14 | 14 | 11 | 10 | 10 | 8 | 10 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.71 | 0.71 | 0.57 | 0.71 | 0.71 |
time (sec) |
N/A | 0.128 | 0.001 | 0.027 | 0.199 | 0.230 | 0.022 | 0.255 | 8.719 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 91 | 72 | 59 | 48 | 36 | 31 | 279 | 33 |
N.S. |
1 | 3.37 | 2.67 | 2.19 | 1.78 | 1.33 | 1.15 | 10.33 | 1.22 |
time (sec) |
N/A | 0.540 | 0.088 | 0.551 | 0.329 | 0.256 | 0.161 | 0.280 | 9.347 |
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 | 24 | 0 | 24 | 27 | 26 | 38 | 26 | 0 | 1482 |
N.S. |
1 | 0.00 | 1.00 | 1.12 | 1.08 | 1.58 | 1.08 | 0.00 | 61.75 |
time (sec) |
N/A | 0.000 | 0.725 | 4.109 | 0.352 | 0.244 | 0.190 | 0.000 | 12.302 |
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 | 26 | 0 | 29 | 44 | 38 | 34 | 26 | 0 | 24 |
N.S. |
1 | 0.00 | 1.12 | 1.69 | 1.46 | 1.31 | 1.00 | 0.00 | 0.92 |
time (sec) |
N/A | 0.000 | 3.519 | 0.723 | 0.340 | 0.257 | 0.159 | 0.000 | 9.494 |
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 | 33 | 34 | 39 | 32 | 98 | 29 | 31 | 44 | 39 |
N.S. |
1 | 1.03 | 1.18 | 0.97 | 2.97 | 0.88 | 0.94 | 1.33 | 1.18 |
time (sec) |
N/A | 0.197 | 0.017 | 0.097 | 0.194 | 0.241 | 0.072 | 0.265 | 9.097 |
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 | 20 | 39 | 19 | 20 | 33 | 19 | 24 | 19 | 19 |
N.S. |
1 | 1.95 | 0.95 | 1.00 | 1.65 | 0.95 | 1.20 | 0.95 | 0.95 |
time (sec) |
N/A | 0.222 | 0.025 | 0.093 | 0.200 | 0.260 | 0.074 | 0.257 | 0.077 |
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 | 28 | 28 | 28 | 27 | 27 | 26 | 27 | 27 |
N.S. |
1 | 1.12 | 1.12 | 1.12 | 1.08 | 1.08 | 1.04 | 1.08 | 1.08 |
time (sec) |
N/A | 1.101 | 0.034 | 0.465 | 0.193 | 0.260 | 0.084 | 0.320 | 9.687 |
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 | 21 | 0 | 49 | 48 | 59 | 63 | 46 | 0 | 46 |
N.S. |
1 | 0.00 | 2.33 | 2.29 | 2.81 | 3.00 | 2.19 | 0.00 | 2.19 |
time (sec) |
N/A | 0.000 | 0.105 | 0.065 | 0.281 | 0.249 | 0.097 | 0.000 | 9.296 |
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 | 35 | 34 | 34 | 31 | 34 | 34 |
N.S. |
1 | 0.00 | 1.13 | 1.13 | 1.10 | 1.10 | 1.00 | 1.10 | 1.10 |
time (sec) |
N/A | 0.000 | 0.126 | 1.422 | 0.263 | 0.272 | 0.286 | 0.342 | 9.317 |
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 | 17 | 19 | 26 | 26 | 20 | 18 | 18 |
N.S. |
1 | 1.33 | 0.81 | 0.90 | 1.24 | 1.24 | 0.95 | 0.86 | 0.86 |
time (sec) |
N/A | 0.279 | 0.033 | 0.092 | 0.190 | 0.236 | 0.050 | 0.260 | 8.741 |
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 | 22 | 0 | 22 | 21 | 20 | 20 | 19 | 20 | 22 |
N.S. |
1 | 0.00 | 1.00 | 0.95 | 0.91 | 0.91 | 0.86 | 0.91 | 1.00 |
time (sec) |
N/A | 0.000 | 5.201 | 0.331 | 0.323 | 0.237 | 0.062 | 0.267 | 9.045 |
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 | 28 | 36 | 23 | 36 | 36 | 29 | 44 | 29 | 19 |
N.S. |
1 | 1.29 | 0.82 | 1.29 | 1.29 | 1.04 | 1.57 | 1.04 | 0.68 |
time (sec) |
N/A | 0.265 | 0.041 | 0.358 | 0.224 | 0.257 | 0.086 | 0.268 | 8.953 |
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 | 19 | 19 | 19 | 19 | 38 | 18 | 14 | 18 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 2.00 | 0.95 | 0.74 | 0.95 | 0.95 |
time (sec) |
N/A | 0.593 | 0.156 | 0.262 | 0.266 | 0.240 | 0.091 | 0.251 | 9.305 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 25 | 85 | 56 | 62 | 24 | 28 | 0 |
N.S. |
1 | 0.00 | 0.89 | 3.04 | 2.00 | 2.21 | 0.86 | 1.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.262 | 7.615 | 0.255 | 0.264 | 0.139 | 0.455 | 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 | 22 | 25 | 23 | 19 | 18 | 18 | 19 | 18 | 24 |
N.S. |
1 | 1.14 | 1.05 | 0.86 | 0.82 | 0.82 | 0.86 | 0.82 | 1.09 |
time (sec) |
N/A | 0.172 | 0.135 | 0.047 | 0.189 | 0.243 | 0.070 | 0.264 | 0.120 |
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 | 24 | 24 | 23 | 20 | 37 | 21 | 20 | 21 | 23 |
N.S. |
1 | 1.00 | 0.96 | 0.83 | 1.54 | 0.88 | 0.83 | 0.88 | 0.96 |
time (sec) |
N/A | 0.347 | 0.050 | 0.238 | 0.274 | 0.236 | 0.083 | 0.263 | 0.169 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | C | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 42 | 24 | 42 | 83 | 45 | 41 | 45 | 23 |
N.S. |
1 | 1.75 | 1.00 | 1.75 | 3.46 | 1.88 | 1.71 | 1.88 | 0.96 |
time (sec) |
N/A | 0.265 | 0.051 | 0.194 | 0.238 | 0.242 | 0.078 | 0.259 | 9.247 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | B | A | A | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 0 | 39 | 71 | 32 | 26 | 426 | 26 |
N.S. |
1 | 0.00 | 0.00 | 1.30 | 2.37 | 1.07 | 0.87 | 14.20 | 0.87 |
time (sec) |
N/A | 0.000 | 0.000 | 13.194 | 0.367 | 0.256 | 0.783 | 3.866 | 9.659 |
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 | 9 | 9 | 9 | 8 | 8 | 7 | 8 | 8 |
N.S. |
1 | 0.82 | 0.82 | 0.82 | 0.73 | 0.73 | 0.64 | 0.73 | 0.73 |
time (sec) |
N/A | 0.137 | 0.002 | 0.033 | 0.196 | 0.241 | 0.042 | 0.256 | 0.037 |
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 | 23 | 23 | 22 | 23 | 23 | 22 | 24 | 21 |
N.S. |
1 | 1.05 | 1.05 | 1.00 | 1.05 | 1.05 | 1.00 | 1.09 | 0.95 |
time (sec) |
N/A | 0.177 | 0.009 | 0.019 | 0.196 | 0.248 | 0.048 | 0.258 | 0.122 |