Detailed conclusion table per each integral is given by 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 just an F.
In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 49 | 51 | 47 | 72 | 0 | 47 | 77 |
N.S. | 1 | 1.00 | 0.89 | 0.93 | 0.85 | 1.31 | 0.00 | 0.85 | 1.40 |
time (sec) |
N/A | 0.044 | 0.242 | 0.248 | 0.278 | 0.392 | 0.000 | 0.526 | 3.342 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 35 | 30 | 27 | 33 | 0 | 27 | 25 |
N.S. | 1 | 1.00 | 1.03 | 0.88 | 0.79 | 0.97 | 0.00 | 0.79 | 0.74 |
time (sec) |
N/A | 0.033 | 0.236 | 0.722 | 0.291 | 0.355 | 0.000 | 0.495 | 3.331 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 31 | 23 | 20 | 26 | 0 | 57 | 19 |
N.S. | 1 | 1.00 | 1.35 | 1.00 | 0.87 | 1.13 | 0.00 | 2.48 | 0.83 |
time (sec) |
N/A | 0.032 | 0.140 | 0.355 | 0.284 | 0.361 | 0.000 | 0.517 | 3.354 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | A | A | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 45 | 48 | 0 | 32 | 60 | 60 | 29 |
N.S. |
1 | 1.00 | 1.36 | 1.45 | 0.00 | 0.97 | 1.82 | 1.82 | 0.88 |
time (sec) |
N/A | 0.011 | 0.134 | 0.088 | 0.000 | 0.357 | 0.082 | 0.467 | 3.363 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 78 | 75 | 0 | 54 | 151 | 99 | 60 |
N.S. |
1 | 1.00 | 0.95 | 0.91 | 0.00 | 0.66 | 1.84 | 1.21 | 0.73 |
time (sec) |
N/A | 0.057 | 0.330 | 0.418 | 0.000 | 0.346 | 0.160 | 0.541 | 3.445 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 134 | 109 | 102 | 0 | 76 | 219 | 116 | 123 |
N.S. |
1 | 1.00 | 0.81 | 0.76 | 0.00 | 0.57 | 1.63 | 0.87 | 0.92 |
time (sec) |
N/A | 0.075 | 0.292 | 0.730 | 0.000 | 0.355 | 0.221 | 0.511 | 3.722 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 60 | 206 | 288 | 266 | 0 | 138 | 193 |
N.S. | 1 | 1.00 | 0.71 | 2.45 | 3.43 | 3.17 | 0.00 | 1.64 | 2.30 |
time (sec) |
N/A | 0.057 | 0.434 | 0.305 | 0.303 | 0.398 | 0.000 | 0.576 | 7.005 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 50 | 138 | 186 | 174 | 0 | 99 | 116 |
N.S. | 1 | 1.00 | 0.83 | 2.30 | 3.10 | 2.90 | 0.00 | 1.65 | 1.93 |
time (sec) |
N/A | 0.044 | 0.279 | 0.296 | 0.289 | 0.355 | 0.000 | 0.545 | 5.377 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 34 | 70 | 83 | 80 | 0 | 58 | 43 |
N.S. | 1 | 1.00 | 1.10 | 2.26 | 2.68 | 2.58 | 0.00 | 1.87 | 1.39 |
time (sec) |
N/A | 0.036 | 0.186 | 0.532 | 0.296 | 0.370 | 0.000 | 0.559 | 3.441 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 25 | 23 | 29 | 17 | 34 | 21 | 25 |
N.S. | 1 | 1.00 | 0.89 | 0.82 | 1.04 | 0.61 | 1.21 | 0.75 | 0.89 |
time (sec) |
N/A | 0.019 | 0.036 | 0.163 | 0.287 | 0.430 | 0.349 | 0.538 | 3.351 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 50 | 75 | 0 | 41 | 126 | 67 | 78 |
N.S. |
1 | 1.00 | 1.06 | 1.60 | 0.00 | 0.87 | 2.68 | 1.43 | 1.66 |
time (sec) |
N/A | 0.031 | 0.154 | 0.348 | 0.000 | 0.343 | 0.151 | 0.492 | 3.549 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F(-2) | A | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 72 | 141 | 0 | 63 | 196 | 119 | 134 |
N.S. |
1 | 1.00 | 1.07 | 2.10 | 0.00 | 0.94 | 2.93 | 1.78 | 2.00 |
time (sec) |
N/A | 0.042 | 0.212 | 0.600 | 0.000 | 0.349 | 0.239 | 0.515 | 4.789 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F(-2) | A | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 94 | 207 | 0 | 85 | 264 | 171 | 188 |
N.S. |
1 | 1.00 | 1.11 | 2.44 | 0.00 | 1.00 | 3.11 | 2.01 | 2.21 |
time (sec) |
N/A | 0.045 | 0.250 | 0.295 | 0.000 | 0.361 | 0.333 | 0.504 | 7.097 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 90 | 78 | 77 | 138 | 0 | 77 | 93 |
N.S. | 1 | 1.00 | 1.10 | 0.95 | 0.94 | 1.68 | 0.00 | 0.94 | 1.13 |
time (sec) |
N/A | 0.051 | 0.595 | 0.289 | 0.285 | 0.354 | 0.000 | 0.572 | 3.461 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 77 | 47 | 47 | 97 | 0 | 47 | 77 |
N.S. | 1 | 1.00 | 1.40 | 0.85 | 0.85 | 1.76 | 0.00 | 0.85 | 1.40 |
time (sec) |
N/A | 0.040 | 0.453 | 0.263 | 0.279 | 0.369 | 0.000 | 0.568 | 3.360 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 68 | 20 | 35 | 54 | 0 | 35 | 33 |
N.S. | 1 | 1.00 | 2.52 | 0.74 | 1.30 | 2.00 | 0.00 | 1.30 | 1.22 |
time (sec) |
N/A | 0.032 | 0.286 | 0.253 | 0.282 | 0.359 | 0.000 | 0.575 | 3.341 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 71 | 30 | 32 | 70 | 0 | 100 | 28 |
N.S. | 1 | 1.00 | 1.87 | 0.79 | 0.84 | 1.84 | 0.00 | 2.63 | 0.74 |
time (sec) |
N/A | 0.037 | 0.487 | 0.272 | 0.280 | 0.381 | 0.000 | 0.587 | 3.350 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 32 | 24 | 21 | 17 | 65 | 30 | 22 |
N.S. | 1 | 1.00 | 1.23 | 0.92 | 0.81 | 0.65 | 2.50 | 1.15 | 0.85 |
time (sec) |
N/A | 0.032 | 0.065 | 0.612 | 0.285 | 0.371 | 0.554 | 0.555 | 3.335 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 68 | 62 | 0 | 43 | 117 | 72 | 39 |
N.S. |
1 | 1.00 | 1.11 | 1.02 | 0.00 | 0.70 | 1.92 | 1.18 | 0.64 |
time (sec) |
N/A | 0.022 | 0.247 | 0.096 | 0.000 | 0.374 | 0.131 | 0.471 | 3.401 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 114 | 95 | 88 | 0 | 65 | 189 | 103 | 71 |
N.S. |
1 | 1.00 | 0.83 | 0.77 | 0.00 | 0.57 | 1.66 | 0.90 | 0.62 |
time (sec) |
N/A | 0.066 | 0.337 | 0.820 | 0.000 | 0.374 | 0.212 | 0.569 | 3.467 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 165 | 120 | 116 | 0 | 87 | 258 | 127 | 149 |
N.S. |
1 | 1.00 | 0.73 | 0.70 | 0.00 | 0.53 | 1.56 | 0.77 | 0.90 |
time (sec) |
N/A | 0.083 | 0.372 | 0.267 | 0.000 | 0.355 | 0.270 | 0.587 | 4.183 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | B | B | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 124 | 294 | 238 | 421 | 326 | 0 | 203 | 191 |
N.S. | 1 | 1.00 | 2.37 | 1.92 | 3.40 | 2.63 | 0.00 | 1.64 | 1.54 |
time (sec) |
N/A | 0.068 | 2.296 | 0.270 | 0.309 | 0.429 | 0.000 | 0.594 | 6.309 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 215 | 170 | 295 | 230 | 0 | 151 | 136 |
N.S. | 1 | 1.00 | 2.15 | 1.70 | 2.95 | 2.30 | 0.00 | 1.51 | 1.36 |
time (sec) |
N/A | 0.056 | 1.191 | 0.259 | 0.299 | 0.377 | 0.000 | 0.845 | 5.924 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 146 | 102 | 167 | 134 | 0 | 95 | 104 |
N.S. | 1 | 1.00 | 1.97 | 1.38 | 2.26 | 1.81 | 0.00 | 1.28 | 1.41 |
time (sec) |
N/A | 0.045 | 0.524 | 0.245 | 0.325 | 0.374 | 0.000 | 0.603 | 3.927 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 184 | 54 | 117 | 64 | 0 | 57 | 44 |
N.S. | 1 | 1.00 | 3.83 | 1.12 | 2.44 | 1.33 | 0.00 | 1.19 | 0.92 |
time (sec) |
N/A | 0.038 | 0.223 | 0.263 | 0.517 | 0.385 | 0.000 | 0.624 | 3.498 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 38 | 57 | 45 | 30 | 112 | 47 | 79 |
N.S. | 1 | 1.00 | 0.58 | 0.88 | 0.69 | 0.46 | 1.72 | 0.72 | 1.22 |
time (sec) |
N/A | 0.038 | 0.127 | 0.365 | 0.297 | 0.351 | 0.556 | 0.632 | 3.507 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 68 | 108 | 0 | 52 | 163 | 93 | 90 |
N.S. |
1 | 1.00 | 0.96 | 1.52 | 0.00 | 0.73 | 2.30 | 1.31 | 1.27 |
time (sec) |
N/A | 0.036 | 0.375 | 0.468 | 0.000 | 0.356 | 0.224 | 0.679 | 3.892 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 95 | 174 | 0 | 74 | 231 | 145 | 161 |
N.S. |
1 | 1.00 | 1.07 | 1.96 | 0.00 | 0.83 | 2.60 | 1.63 | 1.81 |
time (sec) |
N/A | 0.048 | 0.277 | 0.260 | 0.000 | 0.383 | 0.319 | 0.638 | 6.873 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F(-2) | A | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 117 | 240 | 0 | 96 | 299 | 197 | 216 |
N.S. |
1 | 1.00 | 1.09 | 2.24 | 0.00 | 0.90 | 2.79 | 1.84 | 2.02 |
time (sec) |
N/A | 0.049 | 0.533 | 0.267 | 0.000 | 0.355 | 0.411 | 0.778 | 5.650 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 109 | 117 | 91 | 87 | 194 | 0 | 87 | 119 |
N.S. | 1 | 1.00 | 1.07 | 0.83 | 0.80 | 1.78 | 0.00 | 0.80 | 1.09 |
time (sec) |
N/A | 0.061 | 1.075 | 0.301 | 0.300 | 0.371 | 0.000 | 0.719 | 3.605 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 106 | 93 | 87 | 153 | 0 | 87 | 103 |
N.S. | 1 | 1.00 | 1.29 | 1.13 | 1.06 | 1.87 | 0.00 | 1.06 | 1.26 |
time (sec) |
N/A | 0.051 | 0.711 | 0.300 | 0.285 | 0.371 | 0.000 | 0.813 | 3.487 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 97 | 72 | 67 | 112 | 0 | 67 | 114 |
N.S. | 1 | 1.00 | 1.76 | 1.31 | 1.22 | 2.04 | 0.00 | 1.22 | 2.07 |
time (sec) |
N/A | 0.044 | 0.656 | 0.291 | 0.286 | 0.382 | 0.000 | 1.008 | 3.342 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 84 | 21 | 47 | 69 | 0 | 47 | 77 |
N.S. | 1 | 1.00 | 3.11 | 0.78 | 1.74 | 2.56 | 0.00 | 1.74 | 2.85 |
time (sec) |
N/A | 0.031 | 0.520 | 0.280 | 0.293 | 0.357 | 0.000 | 0.747 | 3.340 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 113 | 41 | 45 | 113 | 0 | 128 | 41 |
N.S. | 1 | 1.00 | 1.95 | 0.71 | 0.78 | 1.95 | 0.00 | 2.21 | 0.71 |
time (sec) |
N/A | 0.038 | 0.530 | 0.296 | 0.292 | 0.366 | 0.000 | 0.870 | 3.371 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 88 | 35 | 66 | 55 | 0 | 100 | 42 |
N.S. | 1 | 1.00 | 1.76 | 0.70 | 1.32 | 1.10 | 0.00 | 2.00 | 0.84 |
time (sec) |
N/A | 0.039 | 0.292 | 0.296 | 0.290 | 0.371 | 0.000 | 0.968 | 3.407 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 42 | 24 | 21 | 30 | 153 | 57 | 20 |
N.S. | 1 | 1.00 | 1.56 | 0.89 | 0.78 | 1.11 | 5.67 | 2.11 | 0.74 |
time (sec) |
N/A | 0.033 | 0.119 | 0.186 | 0.287 | 0.348 | 0.837 | 0.914 | 3.350 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 93 | 75 | 0 | 54 | 155 | 80 | 50 |
N.S. |
1 | 1.00 | 1.06 | 0.85 | 0.00 | 0.61 | 1.76 | 0.91 | 0.57 |
time (sec) |
N/A | 0.038 | 0.304 | 0.120 | 0.000 | 0.368 | 0.164 | 0.671 | 3.490 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 141 | 115 | 102 | 0 | 76 | 224 | 119 | 124 |
N.S. |
1 | 1.00 | 0.82 | 0.72 | 0.00 | 0.54 | 1.59 | 0.84 | 0.88 |
time (sec) |
N/A | 0.073 | 0.340 | 0.289 | 0.000 | 0.362 | 0.281 | 0.807 | 3.678 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 195 | 137 | 129 | 0 | 98 | 292 | 136 | 173 |
N.S. |
1 | 1.00 | 0.70 | 0.66 | 0.00 | 0.50 | 1.50 | 0.70 | 0.89 |
time (sec) |
N/A | 0.100 | 0.595 | 0.269 | 0.000 | 0.367 | 0.315 | 0.741 | 5.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 119 | 113 | 206 | 341 | 278 | 0 | 164 | 150 |
N.S. | 1 | 1.00 | 0.95 | 1.73 | 2.87 | 2.34 | 0.00 | 1.38 | 1.26 |
time (sec) |
N/A | 0.090 | 0.537 | 0.297 | 0.311 | 0.372 | 0.000 | 0.742 | 6.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 63 | 138 | 215 | 182 | 0 | 112 | 135 |
N.S. | 1 | 1.00 | 0.68 | 1.48 | 2.31 | 1.96 | 0.00 | 1.20 | 1.45 |
time (sec) |
N/A | 0.077 | 0.491 | 0.284 | 0.302 | 0.379 | 0.000 | 0.724 | 5.443 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 108 | 86 | 319 | 112 | 0 | 110 | 105 |
N.S. | 1 | 1.00 | 1.66 | 1.32 | 4.91 | 1.72 | 0.00 | 1.69 | 1.62 |
time (sec) |
N/A | 0.064 | 0.384 | 0.283 | 0.516 | 0.408 | 0.000 | 0.732 | 3.770 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 32 | 57 | 29 | 17 | 80 | 36 | 68 |
N.S. | 1 | 1.00 | 1.00 | 1.78 | 0.91 | 0.53 | 2.50 | 1.12 | 2.12 |
time (sec) |
N/A | 0.030 | 0.074 | 0.306 | 0.302 | 0.364 | 0.898 | 0.660 | 3.444 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 54 | 90 | 69 | 41 | 219 | 73 | 133 |
N.S. | 1 | 1.00 | 0.55 | 0.92 | 0.70 | 0.42 | 2.23 | 0.74 | 1.36 |
time (sec) |
N/A | 0.064 | 0.229 | 0.151 | 0.309 | 0.379 | 0.912 | 0.590 | 3.680 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 76 | 141 | 0 | 63 | 197 | 119 | 134 |
N.S. |
1 | 1.00 | 0.75 | 1.40 | 0.00 | 0.62 | 1.95 | 1.18 | 1.33 |
time (sec) |
N/A | 0.066 | 0.261 | 0.307 | 0.000 | 0.364 | 0.306 | 0.772 | 5.899 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 98 | 207 | 0 | 85 | 265 | 171 | 188 |
N.S. |
1 | 1.00 | 0.81 | 1.71 | 0.00 | 0.70 | 2.19 | 1.41 | 1.55 |
time (sec) |
N/A | 0.084 | 0.329 | 0.293 | 0.000 | 0.369 | 0.384 | 0.750 | 6.609 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 139 | 120 | 273 | 0 | 107 | 333 | 223 | 136 |
N.S. |
1 | 1.00 | 0.86 | 1.96 | 0.00 | 0.77 | 2.40 | 1.60 | 0.98 |
time (sec) |
N/A | 0.093 | 0.760 | 0.296 | 0.000 | 0.372 | 0.532 | 0.806 | 5.517 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 136 | 99 | 97 | 168 | 0 | 97 | 120 |
N.S. | 1 | 1.00 | 1.66 | 1.21 | 1.18 | 2.05 | 0.00 | 1.18 | 1.46 |
time (sec) |
N/A | 0.052 | 0.870 | 0.301 | 0.299 | 0.393 | 0.000 | 0.695 | 3.517 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 127 | 67 | 67 | 127 | 0 | 67 | 113 |
N.S. | 1 | 1.00 | 2.31 | 1.22 | 1.22 | 2.31 | 0.00 | 1.22 | 2.05 |
time (sec) |
N/A | 0.038 | 0.564 | 0.277 | 0.295 | 0.369 | 0.000 | 0.897 | 3.336 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 116 | 20 | 55 | 84 | 0 | 55 | 93 |
N.S. | 1 | 1.00 | 4.30 | 0.74 | 2.04 | 3.11 | 0.00 | 2.04 | 3.44 |
time (sec) |
N/A | 0.030 | 0.494 | 0.273 | 0.297 | 0.372 | 0.000 | 0.876 | 3.389 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 168 | 51 | 53 | 156 | 0 | 154 | 60 |
N.S. | 1 | 1.00 | 1.87 | 0.57 | 0.59 | 1.73 | 0.00 | 1.71 | 0.67 |
time (sec) |
N/A | 0.043 | 0.842 | 0.293 | 0.299 | 0.392 | 0.000 | 0.832 | 3.385 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 214 | 41 | 95 | 102 | 0 | 146 | 55 |
N.S. | 1 | 1.00 | 3.40 | 0.65 | 1.51 | 1.62 | 0.00 | 2.32 | 0.87 |
time (sec) |
N/A | 0.041 | 0.792 | 0.288 | 0.296 | 0.399 | 0.000 | 0.775 | 3.357 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 32 | 36 | 66 | 17 | 95 | 44 | 25 |
N.S. | 1 | 1.00 | 1.10 | 1.24 | 2.28 | 0.59 | 3.28 | 1.52 | 0.86 |
time (sec) |
N/A | 0.031 | 0.070 | 0.311 | 0.291 | 0.378 | 1.369 | 0.766 | 3.388 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 56 | 24 | 21 | 41 | 272 | 85 | 19 |
N.S. | 1 | 1.00 | 2.07 | 0.89 | 0.78 | 1.52 | 10.07 | 3.15 | 0.70 |
time (sec) |
N/A | 0.035 | 0.225 | 0.215 | 0.292 | 0.413 | 1.547 | 0.733 | 3.398 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 116 | 98 | 89 | 0 | 65 | 189 | 92 | 60 |
N.S. |
1 | 1.00 | 0.84 | 0.77 | 0.00 | 0.56 | 1.63 | 0.79 | 0.52 |
time (sec) |
N/A | 0.052 | 0.273 | 0.163 | 0.000 | 0.381 | 0.235 | 0.517 | 3.502 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 169 | 120 | 115 | 0 | 87 | 258 | 123 | 90 |
N.S. |
1 | 1.00 | 0.71 | 0.68 | 0.00 | 0.51 | 1.53 | 0.73 | 0.53 |
time (sec) |
N/A | 0.081 | 0.376 | 0.288 | 0.000 | 0.421 | 0.327 | 0.855 | 4.132 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 224 | 224 | 142 | 143 | 0 | 109 | 326 | 147 | 197 |
N.S. |
1 | 1.00 | 0.63 | 0.64 | 0.00 | 0.49 | 1.46 | 0.66 | 0.88 |
time (sec) |
N/A | 0.106 | 0.805 | 0.295 | 0.000 | 0.388 | 0.423 | 0.853 | 4.939 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 133 | 237 | 170 | 295 | 230 | 0 | 151 | 197 |
N.S. | 1 | 1.00 | 1.78 | 1.28 | 2.22 | 1.73 | 0.00 | 1.14 | 1.48 |
time (sec) |
N/A | 0.096 | 1.312 | 0.298 | 0.313 | 0.372 | 0.000 | 0.838 | 6.874 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 988 | 118 | 457 | 160 | 0 | 113 | 162 |
N.S. | 1 | 1.00 | 9.23 | 1.10 | 4.27 | 1.50 | 0.00 | 1.06 | 1.51 |
time (sec) |
N/A | 0.083 | 6.233 | 0.285 | 0.539 | 0.387 | 0.000 | 0.776 | 5.518 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 247 | 71 | 141 | 76 | 0 | 71 | 88 |
N.S. | 1 | 1.00 | 3.01 | 0.87 | 1.72 | 0.93 | 0.00 | 0.87 | 1.07 |
time (sec) |
N/A | 0.070 | 0.361 | 0.312 | 0.533 | 0.428 | 0.000 | 0.729 | 3.675 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 40 | 90 | 53 | 30 | 182 | 73 | 133 |
N.S. | 1 | 1.00 | 0.59 | 1.32 | 0.78 | 0.44 | 2.68 | 1.07 | 1.96 |
time (sec) |
N/A | 0.063 | 0.123 | 0.309 | 0.304 | 0.399 | 1.378 | 0.733 | 3.658 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 132 | 73 | 123 | 91 | 52 | 354 | 99 | 64 |
N.S. | 1 | 1.00 | 0.55 | 0.93 | 0.69 | 0.39 | 2.68 | 0.75 | 0.48 |
time (sec) |
N/A | 0.089 | 0.276 | 0.148 | 0.309 | 0.374 | 1.402 | 0.665 | 3.740 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 134 | 95 | 174 | 0 | 74 | 231 | 145 | 161 |
N.S. |
1 | 1.00 | 0.71 | 1.30 | 0.00 | 0.55 | 1.72 | 1.08 | 1.20 |
time (sec) |
N/A | 0.096 | 0.280 | 0.306 | 0.000 | 0.393 | 0.348 | 0.818 | 7.413 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 156 | 117 | 240 | 0 | 96 | 299 | 197 | 216 |
N.S. |
1 | 1.00 | 0.75 | 1.54 | 0.00 | 0.62 | 1.92 | 1.26 | 1.38 |
time (sec) |
N/A | 0.117 | 0.549 | 0.299 | 0.000 | 0.371 | 0.457 | 0.863 | 5.611 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 174 | 139 | 306 | 0 | 118 | 367 | 249 | 262 |
N.S. |
1 | 1.00 | 0.80 | 1.76 | 0.00 | 0.68 | 2.11 | 1.43 | 1.51 |
time (sec) |
N/A | 0.120 | 0.968 | 0.315 | 0.000 | 0.376 | 0.554 | 0.859 | 6.967 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 134 | 599 | 85 | 229 | 273 | 0 | 250 | 105 |
N.S. | 1 | 1.00 | 4.47 | 0.63 | 1.71 | 2.04 | 0.00 | 1.87 | 0.78 |
time (sec) |
N/A | 0.069 | 3.055 | 0.371 | 0.311 | 0.482 | 0.000 | 1.162 | 3.449 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 126 | 537 | 78 | 212 | 199 | 0 | 224 | 114 |
N.S. | 1 | 1.00 | 4.26 | 0.62 | 1.68 | 1.58 | 0.00 | 1.78 | 0.90 |
time (sec) |
N/A | 0.063 | 1.655 | 0.338 | 0.317 | 0.399 | 0.000 | 1.844 | 3.440 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 116 | 397 | 68 | 191 | 124 | 0 | 199 | 104 |
N.S. | 1 | 1.00 | 3.42 | 0.59 | 1.65 | 1.07 | 0.00 | 1.72 | 0.90 |
time (sec) |
N/A | 0.055 | 1.123 | 0.327 | 0.310 | 0.400 | 0.000 | 1.674 | 3.498 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 32 | 63 | 158 | 17 | 160 | 70 | 73 |
N.S. | 1 | 1.00 | 0.74 | 1.47 | 3.67 | 0.40 | 3.72 | 1.63 | 1.70 |
time (sec) |
N/A | 0.036 | 0.092 | 0.337 | 0.306 | 0.387 | 10.732 | 1.616 | 3.507 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 56 | 49 | 141 | 41 | 466 | 137 | 85 |
N.S. | 1 | 1.00 | 0.69 | 0.60 | 1.74 | 0.51 | 5.75 | 1.69 | 1.05 |
time (sec) |
N/A | 0.045 | 0.308 | 0.330 | 0.295 | 0.362 | 10.851 | 1.460 | 3.499 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 78 | 36 | 121 | 63 | 774 | 163 | 85 |
N.S. | 1 | 1.00 | 1.42 | 0.65 | 2.20 | 1.15 | 14.07 | 2.96 | 1.55 |
time (sec) |
N/A | 0.041 | 0.303 | 0.341 | 0.288 | 0.365 | 10.901 | 1.374 | 3.503 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 100 | 24 | 21 | 85 | 1081 | 189 | 19 |
N.S. | 1 | 1.00 | 3.70 | 0.89 | 0.78 | 3.15 | 40.04 | 7.00 | 0.70 |
time (sec) |
N/A | 0.030 | 0.330 | 0.212 | 0.299 | 0.379 | 11.013 | 1.245 | 3.562 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 229 | 148 | 143 | 0 | 109 | 325 | 132 | 198 |
N.S. |
1 | 1.00 | 0.65 | 0.62 | 0.00 | 0.48 | 1.42 | 0.58 | 0.86 |
time (sec) |
N/A | 0.129 | 0.781 | 0.324 | 0.000 | 0.424 | 0.447 | 0.877 | 4.956 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 278 | 278 | 170 | 169 | 0 | 131 | 394 | 163 | 235 |
N.S. |
1 | 1.00 | 0.61 | 0.61 | 0.00 | 0.47 | 1.42 | 0.59 | 0.85 |
time (sec) |
N/A | 0.129 | 1.280 | 0.293 | 0.000 | 0.364 | 0.493 | 1.281 | 5.292 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 333 | 333 | 192 | 197 | 0 | 153 | 462 | 188 | 294 |
N.S. |
1 | 1.00 | 0.58 | 0.59 | 0.00 | 0.46 | 1.39 | 0.56 | 0.88 |
time (sec) |
N/A | 0.154 | 1.799 | 0.303 | 0.000 | 0.380 | 0.632 | 1.333 | 5.704 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | B | A | F | A | B |
verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 205 | 1704 | 219 | 786 | 267 | 0 | 195 | 344 |
N.S. | 1 | 1.00 | 8.31 | 1.07 | 3.83 | 1.30 | 0.00 | 0.95 | 1.68 |
time (sec) |
N/A | 0.179 | 6.476 | 0.368 | 0.640 | 0.428 | 0.000 | 2.175 | 7.566 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | B | A | F | A | B |
verified |
N/A | Yes | NO | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 183 | 1244 | 184 | 531 | 182 | 0 | 165 | 284 |
N.S. | 1 | 1.00 | 6.80 | 1.01 | 2.90 | 0.99 | 0.00 | 0.90 | 1.55 |
time (sec) |
N/A | 0.157 | 6.305 | 0.341 | 0.573 | 0.410 | 0.000 | 2.361 | 7.438 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 156 | 304 | 137 | 185 | 98 | 0 | 123 | 207 |
N.S. | 1 | 1.00 | 1.95 | 0.88 | 1.19 | 0.63 | 0.00 | 0.79 | 1.33 |
time (sec) |
N/A | 0.143 | 1.130 | 0.346 | 0.560 | 0.384 | 0.000 | 1.594 | 6.936 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 40 | 156 | 53 | 30 | 311 | 125 | 37 |
N.S. | 1 | 1.00 | 0.59 | 2.29 | 0.78 | 0.44 | 4.57 | 1.84 | 0.54 |
time (sec) |
N/A | 0.062 | 0.153 | 0.339 | 0.325 | 0.376 | 11.310 | 1.414 | 3.745 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 138 | 73 | 189 | 97 | 52 | 620 | 151 | 64 |
N.S. | 1 | 1.00 | 0.53 | 1.37 | 0.70 | 0.38 | 4.49 | 1.09 | 0.46 |
time (sec) |
N/A | 0.131 | 0.371 | 0.344 | 0.320 | 0.358 | 11.004 | 1.434 | 3.915 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 213 | 213 | 95 | 222 | 141 | 74 | 928 | 177 | 159 |
N.S. | 1 | 1.00 | 0.45 | 1.04 | 0.66 | 0.35 | 4.36 | 0.83 | 0.75 |
time (sec) |
N/A | 0.208 | 0.364 | 0.344 | 0.327 | 0.383 | 10.910 | 1.276 | 4.222 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 269 | 269 | 117 | 255 | 179 | 96 | 1221 | 203 | 224 |
N.S. | 1 | 1.00 | 0.43 | 0.95 | 0.67 | 0.36 | 4.54 | 0.75 | 0.83 |
time (sec) |
N/A | 0.207 | 0.640 | 0.153 | 0.320 | 0.399 | 11.212 | 1.238 | 5.360 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 271 | 271 | 139 | 306 | 0 | 118 | 367 | 249 | 262 |
N.S. |
1 | 1.00 | 0.51 | 1.13 | 0.00 | 0.44 | 1.35 | 0.92 | 0.97 |
time (sec) |
N/A | 0.250 | 1.197 | 0.307 | 0.000 | 0.366 | 0.602 | 1.251 | 6.665 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 301 | 301 | 161 | 372 | 0 | 140 | 435 | 301 | 308 |
N.S. |
1 | 1.00 | 0.53 | 1.24 | 0.00 | 0.47 | 1.45 | 1.00 | 1.02 |
time (sec) |
N/A | 0.281 | 1.595 | 0.305 | 0.000 | 0.356 | 0.719 | 1.230 | 9.524 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | B | F | C | F(-2) | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 123 | 156 | 365 | 0 | 195 | 0 | 0 | -1 |
N.S. |
1 | 1.00 | 1.27 | 2.97 | 0.00 | 1.59 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.075 | 2.161 | 6.696 | 0.000 | 0.113 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 57 | 192 | 0 | 143 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.61 | 2.04 | 0.00 | 1.52 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.053 | 0.459 | 0.463 | 0.000 | 0.088 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | B | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 102 | 351 | 0 | 113 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.13 | 3.90 | 0.00 | 1.26 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.050 | 0.816 | 0.523 | 0.000 | 0.087 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | F | C | F | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 44 | 164 | 0 | 55 | 0 | 0 | 40 |
N.S. | 1 | 1.00 | 0.73 | 2.73 | 0.00 | 0.92 | 0.00 | 0.00 | 0.67 |
time (sec) |
N/A | 0.037 | 0.215 | 0.924 | 0.000 | 0.108 | 0.000 | 0.000 | 3.784 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | B | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 73 | 910 | 0 | 26 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.22 | 15.17 | 0.00 | 0.43 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A | 0.036 | 0.335 | 0.586 | 0.000 | 0.098 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 96 | 62 | 170 | 0 | 68 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.65 | 1.77 | 0.00 | 0.71 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.053 | 0.398 | 0.476 | 0.000 | 0.096 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | B | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 96 | 99 | 339 | 0 | 100 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.03 | 3.53 | 0.00 | 1.04 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.055 | 0.783 | 0.465 | 0.000 | 0.111 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 125 | 121 | 187 | 0 | 109 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.97 | 1.50 | 0.00 | 0.87 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.068 | 0.742 | 0.484 | 0.000 | 0.098 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | B | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 138 | 267 | 374 | 0 | 166 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.93 | 2.71 | 0.00 | 1.20 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.095 | 2.570 | 0.489 | 0.000 | 0.121 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 106 | 67 | 201 | 0 | 110 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.63 | 1.90 | 0.00 | 1.04 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.070 | 0.561 | 0.487 | 0.000 | 0.108 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | B | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 132 | 1099 | 0 | 61 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.23 | 10.27 | 0.00 | 0.57 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.063 | 1.007 | 0.509 | 0.000 | 0.097 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 114 | 173 | 0 | 74 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.34 | 2.04 | 0.00 | 0.87 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.065 | 0.432 | 0.471 | 0.000 | 0.101 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | B | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 114 | 343 | 0 | 86 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.34 | 4.04 | 0.00 | 1.01 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.057 | 0.965 | 0.449 | 0.000 | 0.142 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 116 | 133 | 188 | 0 | 88 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.15 | 1.62 | 0.00 | 0.76 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.069 | 0.813 | 0.897 | 0.000 | 0.094 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | B | F | C | F(-2) | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 116 | 133 | 351 | 0 | 122 | 0 | 0 | -1 |
N.S. |
1 | 1.00 | 1.15 | 3.03 | 0.00 | 1.05 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.073 | 1.759 | 0.532 | 0.000 | 0.100 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | C | F(-1) | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 147 | 155 | 205 | 0 | 133 | 0 | 0 | -1 |
N.S. |
1 | 1.00 | 1.05 | 1.39 | 0.00 | 0.90 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.083 | 1.208 | 0.582 | 0.000 | 0.103 | 0.000 | 0.000 | 0.000 |