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 | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 102 | 104 | 81 | 81 | 192 | 197 | 252 | 73 |
N.S. |
1 | 1.00 | 1.02 | 0.79 | 0.79 | 1.88 | 1.93 | 2.47 | 0.72 |
time (sec) |
N/A | 0.624 | 0.335 | 0.202 | 0.289 | 0.241 | 0.282 | 1.668 | 4.560 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 81 | 68 | 70 | 159 | 168 | 204 | 63 |
N.S. |
1 | 1.00 | 0.98 | 0.82 | 0.84 | 1.92 | 2.02 | 2.46 | 0.76 |
time (sec) |
N/A | 0.506 | 0.218 | 0.211 | 0.285 | 0.235 | 0.216 | 0.969 | 4.816 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 74 | 60 | 59 | 120 | 121 | 156 | 51 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 0.88 | 1.79 | 1.81 | 2.33 | 0.76 |
time (sec) |
N/A | 0.414 | 0.174 | 0.229 | 0.294 | 0.246 | 0.180 | 0.653 | 4.165 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 53 | 47 | 48 | 85 | 85 | 107 | 39 |
N.S. |
1 | 1.00 | 1.08 | 0.96 | 0.98 | 1.73 | 1.73 | 2.18 | 0.80 |
time (sec) |
N/A | 0.324 | 0.116 | 0.198 | 0.302 | 0.226 | 0.168 | 0.484 | 4.706 |
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 | 34 | 34 | 43 | 37 | 37 | 47 | 44 | 58 | 25 |
N.S. |
1 | 1.00 | 1.26 | 1.09 | 1.09 | 1.38 | 1.29 | 1.71 | 0.74 |
time (sec) |
N/A | 0.237 | 0.023 | 0.126 | 0.291 | 0.234 | 0.118 | 0.336 | 4.277 |
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 | 19 | 19 | 23 | 17 | 18 | 24 | 18 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.21 | 0.89 | 0.95 | 1.26 | 0.95 | 0.89 |
time (sec) |
N/A | 0.147 | 0.001 | 0.090 | 0.214 | 0.230 | 0.095 | 0.305 | 5.095 |
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 | 21 | 31 | 27 | 37 | 17 | 20 | 34 | 19 |
N.S. |
1 | 1.11 | 1.63 | 1.42 | 1.95 | 0.89 | 1.05 | 1.79 | 1.00 |
time (sec) |
N/A | 0.238 | 0.017 | 0.338 | 0.289 | 0.238 | 0.093 | 0.350 | 4.210 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 34 | 61 | 42 | 49 | 51 | 46 | 75 | 27 |
N.S. |
1 | 1.06 | 1.91 | 1.31 | 1.53 | 1.59 | 1.44 | 2.34 | 0.84 |
time (sec) |
N/A | 0.323 | 0.035 | 0.366 | 0.292 | 0.243 | 0.151 | 0.411 | 4.624 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 52 | 68 | 50 | 58 | 83 | 80 | 102 | 47 |
N.S. |
1 | 1.04 | 1.36 | 1.00 | 1.16 | 1.66 | 1.60 | 2.04 | 0.94 |
time (sec) |
N/A | 0.434 | 0.218 | 0.378 | 0.302 | 0.240 | 0.151 | 0.445 | 4.933 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 64 | 66 | 72 | 63 | 71 | 125 | 128 | 128 | 57 |
N.S. |
1 | 1.03 | 1.12 | 0.98 | 1.11 | 1.95 | 2.00 | 2.00 | 0.89 |
time (sec) |
N/A | 0.536 | 0.209 | 0.380 | 0.308 | 0.230 | 0.179 | 0.544 | 4.435 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 83 | 85 | 93 | 73 | 83 | 156 | 158 | 158 | 70 |
N.S. |
1 | 1.02 | 1.12 | 0.88 | 1.00 | 1.88 | 1.90 | 1.90 | 0.84 |
time (sec) |
N/A | 0.641 | 0.041 | 0.403 | 0.310 | 0.236 | 0.230 | 0.544 | 4.828 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 102 | 101 | 84 | 93 | 197 | 206 | 186 | 79 |
N.S. |
1 | 1.02 | 1.01 | 0.84 | 0.93 | 1.97 | 2.06 | 1.86 | 0.79 |
time (sec) |
N/A | 0.771 | 0.041 | 0.414 | 0.284 | 0.232 | 0.285 | 0.588 | 4.761 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 112 | 108 | 82 | 95 | 217 | 219 | 274 | 86 |
N.S. |
1 | 1.00 | 0.96 | 0.73 | 0.85 | 1.94 | 1.96 | 2.45 | 0.77 |
time (sec) |
N/A | 0.706 | 0.328 | 0.202 | 0.291 | 0.242 | 0.284 | 1.001 | 5.080 |
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 | 93 | 93 | 73 | 70 | 82 | 174 | 168 | 222 | 73 |
N.S. |
1 | 1.00 | 0.78 | 0.75 | 0.88 | 1.87 | 1.81 | 2.39 | 0.78 |
time (sec) |
N/A | 0.564 | 0.225 | 0.174 | 0.295 | 0.245 | 0.334 | 0.731 | 4.155 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 76 | 61 | 68 | 137 | 136 | 170 | 60 |
N.S. |
1 | 1.00 | 1.19 | 0.95 | 1.06 | 2.14 | 2.12 | 2.66 | 0.94 |
time (sec) |
N/A | 0.355 | 0.260 | 0.238 | 0.298 | 0.235 | 0.203 | 0.539 | 4.746 |
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 | 62 | 65 | 51 | 49 | 55 | 93 | 88 | 116 | 40 |
N.S. |
1 | 1.05 | 0.82 | 0.79 | 0.89 | 1.50 | 1.42 | 1.87 | 0.65 |
time (sec) |
N/A | 0.342 | 0.175 | 0.217 | 0.635 | 0.238 | 0.170 | 0.418 | 4.393 |
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 | 38 | 38 | 34 | 40 | 41 | 56 | 53 | 66 | 29 |
N.S. |
1 | 1.00 | 0.89 | 1.05 | 1.08 | 1.47 | 1.39 | 1.74 | 0.76 |
time (sec) |
N/A | 0.246 | 0.030 | 0.108 | 0.563 | 0.234 | 0.141 | 0.311 | 4.783 |
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 | 37 | 39 | 38 | 31 | 42 | 19 | 22 | 68 | 30 |
N.S. |
1 | 1.05 | 1.03 | 0.84 | 1.14 | 0.51 | 0.59 | 1.84 | 0.81 |
time (sec) |
N/A | 0.272 | 0.036 | 0.648 | 0.298 | 0.243 | 0.118 | 0.490 | 4.482 |
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 | 38 | 43 | 48 | 43 | 56 | 58 | 51 | 85 | 29 |
N.S. |
1 | 1.13 | 1.26 | 1.13 | 1.47 | 1.53 | 1.34 | 2.24 | 0.76 |
time (sec) |
N/A | 0.357 | 0.237 | 0.536 | 0.308 | 0.234 | 0.153 | 0.557 | 4.207 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 58 | 63 | 64 | 52 | 68 | 94 | 87 | 116 | 53 |
N.S. |
1 | 1.09 | 1.10 | 0.90 | 1.17 | 1.62 | 1.50 | 2.00 | 0.91 |
time (sec) |
N/A | 0.463 | 0.217 | 0.647 | 0.299 | 0.234 | 0.234 | 0.675 | 4.918 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 79 | 105 | 63 | 83 | 139 | 136 | 146 | 68 |
N.S. |
1 | 1.07 | 1.42 | 0.85 | 1.12 | 1.88 | 1.84 | 1.97 | 0.92 |
time (sec) |
N/A | 0.588 | 0.499 | 0.511 | 0.296 | 0.236 | 0.213 | 0.809 | 4.263 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 93 | 100 | 78 | 75 | 97 | 174 | 168 | 180 | 80 |
N.S. |
1 | 1.08 | 0.84 | 0.81 | 1.04 | 1.87 | 1.81 | 1.94 | 0.86 |
time (sec) |
N/A | 0.712 | 0.699 | 0.615 | 0.446 | 0.245 | 0.704 | 0.892 | 5.337 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 119 | 145 | 86 | 109 | 219 | 218 | 212 | 92 |
N.S. |
1 | 1.06 | 1.29 | 0.77 | 0.97 | 1.96 | 1.95 | 1.89 | 0.82 |
time (sec) |
N/A | 0.847 | 0.067 | 0.652 | 0.497 | 0.233 | 0.305 | 1.033 | 4.404 |
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 | 126 | 132 | 110 | 83 | 95 | 214 | 207 | 274 | 87 |
N.S. |
1 | 1.05 | 0.87 | 0.66 | 0.75 | 1.70 | 1.64 | 2.17 | 0.69 |
time (sec) |
N/A | 0.793 | 0.554 | 0.244 | 0.704 | 0.241 | 0.313 | 0.765 | 4.499 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 90 | 94 | 67 | 72 | 82 | 177 | 173 | 222 | 73 |
N.S. |
1 | 1.04 | 0.74 | 0.80 | 0.91 | 1.97 | 1.92 | 2.47 | 0.81 |
time (sec) |
N/A | 0.454 | 0.444 | 0.244 | 0.287 | 0.243 | 0.257 | 0.631 | 4.463 |
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 | 85 | 94 | 57 | 62 | 69 | 134 | 131 | 170 | 59 |
N.S. |
1 | 1.11 | 0.67 | 0.73 | 0.81 | 1.58 | 1.54 | 2.00 | 0.69 |
time (sec) |
N/A | 0.441 | 0.363 | 0.200 | 0.290 | 0.246 | 0.203 | 0.461 | 4.121 |
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 | 63 | 67 | 46 | 51 | 76 | 97 | 94 | 118 | 41 |
N.S. |
1 | 1.06 | 0.73 | 0.81 | 1.21 | 1.54 | 1.49 | 1.87 | 0.65 |
time (sec) |
N/A | 0.325 | 0.047 | 0.139 | 0.305 | 0.227 | 0.167 | 0.366 | 5.019 |
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 | 60 | 65 | 50 | 41 | 53 | 83 | 66 | 123 | 39 |
N.S. |
1 | 1.08 | 0.83 | 0.68 | 0.88 | 1.38 | 1.10 | 2.05 | 0.65 |
time (sec) |
N/A | 0.533 | 0.283 | 0.430 | 0.293 | 0.240 | 0.219 | 0.601 | 4.455 |
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 | 69 | 71 | 48 | 43 | 56 | 91 | 71 | 119 | 38 |
N.S. |
1 | 1.03 | 0.70 | 0.62 | 0.81 | 1.32 | 1.03 | 1.72 | 0.55 |
time (sec) |
N/A | 0.564 | 0.343 | 0.455 | 0.291 | 0.247 | 0.239 | 0.712 | 4.641 |
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 | 71 | 80 | 61 | 52 | 68 | 94 | 87 | 116 | 53 |
N.S. |
1 | 1.13 | 0.86 | 0.73 | 0.96 | 1.32 | 1.23 | 1.63 | 0.75 |
time (sec) |
N/A | 0.507 | 0.200 | 0.418 | 0.440 | 0.229 | 0.205 | 0.865 | 4.605 |
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 | 101 | 115 | 80 | 64 | 83 | 139 | 136 | 146 | 68 |
N.S. |
1 | 1.14 | 0.79 | 0.63 | 0.82 | 1.38 | 1.35 | 1.45 | 0.67 |
time (sec) |
N/A | 0.668 | 0.278 | 0.440 | 0.494 | 0.246 | 0.248 | 1.060 | 4.450 |
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 | 108 | 118 | 89 | 75 | 94 | 174 | 165 | 180 | 80 |
N.S. |
1 | 1.09 | 0.82 | 0.69 | 0.87 | 1.61 | 1.53 | 1.67 | 0.74 |
time (sec) |
N/A | 0.809 | 0.384 | 0.469 | 0.303 | 0.227 | 0.336 | 1.317 | 5.136 |
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 | 126 | 136 | 110 | 85 | 109 | 219 | 218 | 212 | 92 |
N.S. |
1 | 1.08 | 0.87 | 0.67 | 0.87 | 1.74 | 1.73 | 1.68 | 0.73 |
time (sec) |
N/A | 0.944 | 0.452 | 0.530 | 0.299 | 0.231 | 0.331 | 1.473 | 4.915 |
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 | 160 | 169 | 128 | 93 | 108 | 254 | 246 | 326 | 100 |
N.S. |
1 | 1.06 | 0.80 | 0.58 | 0.68 | 1.59 | 1.54 | 2.04 | 0.62 |
time (sec) |
N/A | 1.041 | 0.462 | 0.288 | 0.298 | 0.235 | 0.817 | 0.893 | 4.884 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 116 | 123 | 82 | 82 | 95 | 217 | 218 | 274 | 87 |
N.S. |
1 | 1.06 | 0.71 | 0.71 | 0.82 | 1.87 | 1.88 | 2.36 | 0.75 |
time (sec) |
N/A | 0.565 | 0.769 | 0.295 | 0.300 | 0.237 | 0.285 | 0.702 | 4.535 |
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 | 108 | 123 | 67 | 72 | 82 | 174 | 170 | 222 | 72 |
N.S. |
1 | 1.14 | 0.62 | 0.67 | 0.76 | 1.61 | 1.57 | 2.06 | 0.67 |
time (sec) |
N/A | 0.540 | 0.272 | 0.276 | 0.302 | 0.228 | 0.281 | 0.546 | 4.806 |
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 | 89 | 96 | 58 | 61 | 108 | 137 | 138 | 170 | 59 |
N.S. |
1 | 1.08 | 0.65 | 0.69 | 1.21 | 1.54 | 1.55 | 1.91 | 0.66 |
time (sec) |
N/A | 0.430 | 0.254 | 0.175 | 0.436 | 0.238 | 0.209 | 0.387 | 4.071 |
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 | 86 | 91 | 68 | 52 | 67 | 137 | 105 | 157 | 64 |
N.S. |
1 | 1.06 | 0.79 | 0.60 | 0.78 | 1.59 | 1.22 | 1.83 | 0.74 |
time (sec) |
N/A | 0.708 | 0.361 | 0.452 | 0.438 | 0.237 | 0.258 | 0.855 | 4.729 |
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 | 71 | 74 | 58 | 49 | 67 | 58 | 51 | 163 | 63 |
N.S. |
1 | 1.04 | 0.82 | 0.69 | 0.94 | 0.82 | 0.72 | 2.30 | 0.89 |
time (sec) |
N/A | 0.408 | 0.964 | 0.742 | 0.630 | 0.235 | 0.194 | 1.003 | 4.550 |
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 | 103 | 105 | 61 | 52 | 68 | 138 | 107 | 150 | 65 |
N.S. |
1 | 1.02 | 0.59 | 0.50 | 0.66 | 1.34 | 1.04 | 1.46 | 0.63 |
time (sec) |
N/A | 0.814 | 0.829 | 0.487 | 0.292 | 0.234 | 0.491 | 1.264 | 4.136 |
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 | 103 | 117 | 78 | 63 | 83 | 139 | 136 | 146 | 68 |
N.S. |
1 | 1.14 | 0.76 | 0.61 | 0.81 | 1.35 | 1.32 | 1.42 | 0.66 |
time (sec) |
N/A | 0.665 | 0.323 | 0.572 | 0.308 | 0.232 | 0.266 | 1.497 | 5.030 |
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 | 134 | 152 | 93 | 75 | 96 | 174 | 168 | 180 | 80 |
N.S. |
1 | 1.13 | 0.69 | 0.56 | 0.72 | 1.30 | 1.25 | 1.34 | 0.60 |
time (sec) |
N/A | 0.839 | 0.403 | 0.435 | 0.306 | 0.237 | 1.272 | 1.342 | 4.571 |
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 | 142 | 157 | 108 | 85 | 109 | 219 | 218 | 212 | 92 |
N.S. |
1 | 1.11 | 0.76 | 0.60 | 0.77 | 1.54 | 1.54 | 1.49 | 0.65 |
time (sec) |
N/A | 1.089 | 0.755 | 0.503 | 0.300 | 0.254 | 0.355 | 0.750 | 5.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 162 | 178 | 123 | 94 | 123 | 254 | 246 | 245 | 107 |
N.S. |
1 | 1.10 | 0.76 | 0.58 | 0.76 | 1.57 | 1.52 | 1.51 | 0.66 |
time (sec) |
N/A | 1.247 | 0.337 | 0.411 | 0.587 | 0.253 | 4.275 | 0.858 | 5.329 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 130 | 120 | 114 | 102 | 0 | 221 | 219 | 114 | 125 |
N.S. |
1 | 0.92 | 0.88 | 0.78 | 0.00 | 1.70 | 1.68 | 0.88 | 0.96 |
time (sec) |
N/A | 0.737 | 0.654 | 0.342 | 0.000 | 0.249 | 0.293 | 2.318 | 4.869 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 109 | 104 | 106 | 101 | 0 | 175 | 197 | 102 | 106 |
N.S. |
1 | 0.95 | 0.97 | 0.93 | 0.00 | 1.61 | 1.81 | 0.94 | 0.97 |
time (sec) |
N/A | 0.604 | 0.543 | 0.299 | 0.000 | 0.250 | 0.279 | 1.614 | 4.270 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 90 | 86 | 92 | 78 | 0 | 138 | 134 | 85 | 91 |
N.S. |
1 | 0.96 | 1.02 | 0.87 | 0.00 | 1.53 | 1.49 | 0.94 | 1.01 |
time (sec) |
N/A | 0.494 | 0.391 | 0.352 | 0.000 | 0.241 | 0.229 | 0.958 | 4.769 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 72 | 85 | 72 | 0 | 93 | 114 | 68 | 73 |
N.S. |
1 | 0.97 | 1.15 | 0.97 | 0.00 | 1.26 | 1.54 | 0.92 | 0.99 |
time (sec) |
N/A | 0.380 | 0.327 | 0.271 | 0.000 | 0.235 | 0.194 | 0.683 | 4.619 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 51 | 71 | 56 | 0 | 55 | 88 | 58 | 61 |
N.S. |
1 | 1.02 | 1.42 | 1.12 | 0.00 | 1.10 | 1.76 | 1.16 | 1.22 |
time (sec) |
N/A | 0.246 | 0.215 | 0.333 | 0.000 | 0.240 | 0.178 | 0.489 | 4.156 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 46 | 26 | 0 | 32 | 65 | 55 | 29 |
N.S. |
1 | 1.00 | 1.39 | 0.79 | 0.00 | 0.97 | 1.97 | 1.67 | 0.88 |
time (sec) |
N/A | 0.202 | 0.098 | 0.229 | 0.000 | 0.239 | 0.116 | 0.413 | 4.919 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 35 | 26 | 0 | 32 | 60 | 58 | 29 |
N.S. |
1 | 1.00 | 1.06 | 0.79 | 0.00 | 0.97 | 1.82 | 1.76 | 0.88 |
time (sec) |
N/A | 0.184 | 0.060 | 0.192 | 0.000 | 0.232 | 0.101 | 0.297 | 4.400 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 54 | 71 | 55 | 0 | 55 | 92 | 70 | 72 |
N.S. |
1 | 1.15 | 1.51 | 1.17 | 0.00 | 1.17 | 1.96 | 1.49 | 1.53 |
time (sec) |
N/A | 0.320 | 0.315 | 0.371 | 0.000 | 0.241 | 0.169 | 0.411 | 4.754 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 80 | 78 | 0 | 99 | 116 | 89 | 96 |
N.S. |
1 | 1.00 | 1.14 | 1.11 | 0.00 | 1.41 | 1.66 | 1.27 | 1.37 |
time (sec) |
N/A | 0.486 | 0.677 | 0.424 | 0.000 | 0.241 | 0.199 | 0.500 | 4.447 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 90 | 88 | 89 | 77 | 0 | 134 | 138 | 103 | 110 |
N.S. |
1 | 0.98 | 0.99 | 0.86 | 0.00 | 1.49 | 1.53 | 1.14 | 1.22 |
time (sec) |
N/A | 0.618 | 1.054 | 0.394 | 0.000 | 0.240 | 0.214 | 0.566 | 5.015 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 108 | 104 | 96 | 102 | 0 | 181 | 196 | 114 | 126 |
N.S. |
1 | 0.96 | 0.89 | 0.94 | 0.00 | 1.68 | 1.81 | 1.06 | 1.17 |
time (sec) |
N/A | 0.733 | 1.318 | 0.416 | 0.000 | 0.246 | 0.286 | 0.677 | 4.639 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 142 | 147 | 169 | 120 | 0 | 198 | 262 | 111 | 132 |
N.S. |
1 | 1.04 | 1.19 | 0.85 | 0.00 | 1.39 | 1.85 | 0.78 | 0.93 |
time (sec) |
N/A | 0.860 | 0.705 | 0.437 | 0.000 | 0.241 | 0.312 | 2.341 | 4.376 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 133 | 148 | 104 | 0 | 151 | 214 | 98 | 114 |
N.S. |
1 | 1.07 | 1.19 | 0.84 | 0.00 | 1.22 | 1.73 | 0.79 | 0.92 |
time (sec) |
N/A | 0.737 | 0.572 | 0.325 | 0.000 | 0.242 | 0.768 | 1.757 | 5.401 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 111 | 147 | 90 | 0 | 113 | 177 | 79 | 100 |
N.S. |
1 | 1.07 | 1.41 | 0.87 | 0.00 | 1.09 | 1.70 | 0.76 | 0.96 |
time (sec) |
N/A | 0.610 | 0.539 | 0.328 | 0.000 | 0.238 | 0.257 | 1.046 | 4.288 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 79 | 87 | 95 | 72 | 0 | 66 | 148 | 69 | 84 |
N.S. |
1 | 1.10 | 1.20 | 0.91 | 0.00 | 0.84 | 1.87 | 0.87 | 1.06 |
time (sec) |
N/A | 0.515 | 0.477 | 0.226 | 0.000 | 0.250 | 0.283 | 0.750 | 4.947 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 61 | 52 | 44 | 0 | 43 | 117 | 68 | 39 |
N.S. |
1 | 1.03 | 0.88 | 0.75 | 0.00 | 0.73 | 1.98 | 1.15 | 0.66 |
time (sec) |
N/A | 0.335 | 0.298 | 0.240 | 0.000 | 0.235 | 0.164 | 0.534 | 4.571 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 65 | 66 | 26 | 0 | 32 | 73 | 67 | 46 |
N.S. |
1 | 1.10 | 1.12 | 0.44 | 0.00 | 0.54 | 1.24 | 1.14 | 0.78 |
time (sec) |
N/A | 0.284 | 0.114 | 0.239 | 0.000 | 0.234 | 0.139 | 0.457 | 4.601 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 65 | 52 | 44 | 0 | 43 | 117 | 68 | 39 |
N.S. |
1 | 1.07 | 0.85 | 0.72 | 0.00 | 0.70 | 1.92 | 1.11 | 0.64 |
time (sec) |
N/A | 0.263 | 0.082 | 0.206 | 0.000 | 0.232 | 0.141 | 0.341 | 4.385 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 71 | 85 | 82 | 72 | 0 | 66 | 150 | 81 | 97 |
N.S. |
1 | 1.20 | 1.15 | 1.01 | 0.00 | 0.93 | 2.11 | 1.14 | 1.37 |
time (sec) |
N/A | 0.543 | 0.869 | 0.378 | 0.000 | 0.242 | 0.223 | 0.602 | 4.865 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 106 | 102 | 96 | 0 | 114 | 180 | 103 | 125 |
N.S. |
1 | 1.09 | 1.05 | 0.99 | 0.00 | 1.18 | 1.86 | 1.06 | 1.29 |
time (sec) |
N/A | 0.739 | 1.380 | 0.494 | 0.000 | 0.248 | 0.279 | 0.755 | 4.677 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 122 | 133 | 114 | 105 | 0 | 151 | 216 | 109 | 135 |
N.S. |
1 | 1.09 | 0.93 | 0.86 | 0.00 | 1.24 | 1.77 | 0.89 | 1.11 |
time (sec) |
N/A | 0.894 | 1.589 | 0.483 | 0.000 | 0.234 | 0.401 | 1.064 | 4.312 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 161 | 176 | 195 | 126 | 0 | 167 | 257 | 109 | 140 |
N.S. |
1 | 1.09 | 1.21 | 0.78 | 0.00 | 1.04 | 1.60 | 0.68 | 0.87 |
time (sec) |
N/A | 1.010 | 0.796 | 0.414 | 0.000 | 0.236 | 0.386 | 2.430 | 5.319 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 143 | 155 | 187 | 111 | 0 | 120 | 214 | 89 | 122 |
N.S. |
1 | 1.08 | 1.31 | 0.78 | 0.00 | 0.84 | 1.50 | 0.62 | 0.85 |
time (sec) |
N/A | 0.856 | 0.586 | 0.273 | 0.000 | 0.240 | 0.414 | 1.808 | 4.400 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 135 | 130 | 92 | 0 | 77 | 184 | 78 | 110 |
N.S. |
1 | 1.13 | 1.09 | 0.77 | 0.00 | 0.65 | 1.55 | 0.66 | 0.92 |
time (sec) |
N/A | 0.750 | 0.501 | 0.358 | 0.000 | 0.242 | 0.290 | 1.191 | 4.865 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 103 | 75 | 60 | 0 | 54 | 156 | 78 | 49 |
N.S. |
1 | 1.12 | 0.82 | 0.65 | 0.00 | 0.59 | 1.70 | 0.85 | 0.53 |
time (sec) |
N/A | 0.447 | 0.274 | 0.343 | 0.000 | 0.233 | 0.253 | 0.847 | 4.644 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 95 | 91 | 62 | 0 | 54 | 151 | 78 | 49 |
N.S. |
1 | 1.08 | 1.03 | 0.70 | 0.00 | 0.61 | 1.72 | 0.89 | 0.56 |
time (sec) |
N/A | 0.419 | 0.549 | 0.331 | 0.000 | 0.228 | 0.207 | 0.720 | 4.482 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 84 | 97 | 91 | 60 | 0 | 54 | 153 | 78 | 49 |
N.S. |
1 | 1.15 | 1.08 | 0.71 | 0.00 | 0.64 | 1.82 | 0.93 | 0.58 |
time (sec) |
N/A | 0.378 | 0.517 | 0.392 | 0.000 | 0.226 | 0.219 | 0.601 | 4.441 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 97 | 65 | 62 | 0 | 54 | 155 | 78 | 50 |
N.S. |
1 | 1.10 | 0.74 | 0.70 | 0.00 | 0.61 | 1.76 | 0.89 | 0.57 |
time (sec) |
N/A | 0.358 | 0.140 | 0.293 | 0.000 | 0.230 | 0.184 | 0.367 | 4.696 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 120 | 108 | 89 | 0 | 77 | 187 | 91 | 120 |
N.S. |
1 | 1.22 | 1.10 | 0.91 | 0.00 | 0.79 | 1.91 | 0.93 | 1.22 |
time (sec) |
N/A | 0.748 | 0.641 | 0.463 | 0.000 | 0.247 | 0.296 | 0.935 | 4.724 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 133 | 147 | 148 | 114 | 0 | 125 | 218 | 115 | 145 |
N.S. |
1 | 1.11 | 1.11 | 0.86 | 0.00 | 0.94 | 1.64 | 0.86 | 1.09 |
time (sec) |
N/A | 0.983 | 1.898 | 0.474 | 0.000 | 0.247 | 0.324 | 0.848 | 4.341 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 193 | 265 | 128 | 0 | 135 | 248 | 100 | 132 |
N.S. |
1 | 1.13 | 1.55 | 0.75 | 0.00 | 0.79 | 1.45 | 0.58 | 0.77 |
time (sec) |
N/A | 1.124 | 0.818 | 0.393 | 0.000 | 0.236 | 0.401 | 2.696 | 5.310 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 147 | 170 | 134 | 107 | 0 | 88 | 219 | 89 | 128 |
N.S. |
1 | 1.16 | 0.91 | 0.73 | 0.00 | 0.60 | 1.49 | 0.61 | 0.87 |
time (sec) |
N/A | 0.990 | 0.590 | 0.427 | 0.000 | 0.232 | 1.350 | 2.089 | 4.578 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 128 | 145 | 108 | 80 | 0 | 65 | 189 | 88 | 59 |
N.S. |
1 | 1.13 | 0.84 | 0.62 | 0.00 | 0.51 | 1.48 | 0.69 | 0.46 |
time (sec) |
N/A | 0.615 | 0.250 | 0.339 | 0.000 | 0.227 | 0.275 | 1.404 | 5.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 126 | 141 | 95 | 60 | 0 | 54 | 156 | 88 | 60 |
N.S. |
1 | 1.12 | 0.75 | 0.48 | 0.00 | 0.43 | 1.24 | 0.70 | 0.48 |
time (sec) |
N/A | 0.621 | 0.621 | 0.336 | 0.000 | 0.236 | 0.482 | 1.081 | 4.775 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 116 | 127 | 69 | 44 | 0 | 43 | 117 | 83 | 92 |
N.S. |
1 | 1.09 | 0.59 | 0.38 | 0.00 | 0.37 | 1.01 | 0.72 | 0.79 |
time (sec) |
N/A | 0.524 | 0.491 | 0.396 | 0.000 | 0.233 | 0.204 | 0.902 | 4.735 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 129 | 94 | 60 | 0 | 54 | 156 | 88 | 60 |
N.S. |
1 | 1.17 | 0.85 | 0.55 | 0.00 | 0.49 | 1.42 | 0.80 | 0.55 |
time (sec) |
N/A | 0.477 | 0.167 | 0.315 | 0.000 | 0.227 | 0.286 | 0.677 | 4.460 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 116 | 129 | 113 | 80 | 0 | 65 | 189 | 88 | 60 |
N.S. |
1 | 1.11 | 0.97 | 0.69 | 0.00 | 0.56 | 1.63 | 0.76 | 0.52 |
time (sec) |
N/A | 0.457 | 0.178 | 0.268 | 0.000 | 0.227 | 0.235 | 0.430 | 4.645 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 120 | 149 | 115 | 106 | 0 | 88 | 221 | 101 | 142 |
N.S. |
1 | 1.24 | 0.96 | 0.88 | 0.00 | 0.73 | 1.84 | 0.84 | 1.18 |
time (sec) |
N/A | 0.966 | 1.199 | 0.406 | 0.000 | 0.245 | 0.382 | 1.202 | 5.014 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 159 | 182 | 150 | 132 | 0 | 136 | 252 | 123 | 165 |
N.S. |
1 | 1.14 | 0.94 | 0.83 | 0.00 | 0.86 | 1.58 | 0.77 | 1.04 |
time (sec) |
N/A | 1.293 | 1.764 | 0.563 | 0.000 | 0.237 | 0.360 | 1.153 | 4.619 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 168 | 184 | 104 | 94 | 120 | 330 | 0 | 0 | 109 |
N.S. |
1 | 1.10 | 0.62 | 0.56 | 0.71 | 1.96 | 0.00 | 0.00 | 0.65 |
time (sec) |
N/A | 0.901 | 0.780 | 1.161 | 0.301 | 0.243 | 0.000 | 0.000 | 0.371 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 132 | 90 | 93 | 120 | 285 | 0 | 0 | 100 |
N.S. |
1 | 1.04 | 0.71 | 0.73 | 0.94 | 2.24 | 0.00 | 0.00 | 0.79 |
time (sec) |
N/A | 0.637 | 0.587 | 1.047 | 0.289 | 0.251 | 0.000 | 0.000 | 5.257 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 73 | 58 | 84 | 233 | 0 | 0 | 63 |
N.S. |
1 | 1.00 | 0.96 | 0.76 | 1.11 | 3.07 | 0.00 | 0.00 | 0.83 |
time (sec) |
N/A | 0.315 | 0.367 | 1.004 | 0.295 | 0.254 | 0.000 | 0.000 | 0.322 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 67 | 53 | 83 | 187 | 0 | 0 | 54 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 1.24 | 2.79 | 0.00 | 0.00 | 0.81 |
time (sec) |
N/A | 0.300 | 0.146 | 1.084 | 0.303 | 0.241 | 0.000 | 0.000 | 4.369 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 46 | 36 | 60 | 159 | 0 | 0 | 39 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 1.30 | 3.46 | 0.00 | 0.00 | 0.85 |
time (sec) |
N/A | 0.204 | 0.064 | 0.950 | 0.295 | 0.233 | 0.000 | 0.000 | 4.866 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 71 | 211 | 107 | 336 | 0 | 0 | 61 |
N.S. |
1 | 1.00 | 0.91 | 2.71 | 1.37 | 4.31 | 0.00 | 0.00 | 0.78 |
time (sec) |
N/A | 0.511 | 0.151 | 7.395 | 0.303 | 0.245 | 0.000 | 0.000 | 0.187 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 111 | 117 | 106 | 580 | 134 | 476 | 0 | 0 | 97 |
N.S. |
1 | 1.05 | 0.95 | 5.23 | 1.21 | 4.29 | 0.00 | 0.00 | 0.87 |
time (sec) |
N/A | 0.709 | 0.405 | 7.933 | 0.313 | 0.253 | 0.000 | 0.000 | 4.603 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 145 | 158 | 116 | 669 | 179 | 519 | 0 | 0 | 124 |
N.S. |
1 | 1.09 | 0.80 | 4.61 | 1.23 | 3.58 | 0.00 | 0.00 | 0.86 |
time (sec) |
N/A | 0.978 | 0.920 | 7.425 | 0.285 | 0.253 | 0.000 | 0.000 | 5.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 199 | 220 | 103 | 111 | 138 | 354 | 0 | 0 | 120 |
N.S. |
1 | 1.11 | 0.52 | 0.56 | 0.69 | 1.78 | 0.00 | 0.00 | 0.60 |
time (sec) |
N/A | 1.169 | 0.978 | 1.097 | 0.279 | 0.250 | 0.000 | 0.000 | 4.485 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 95 | 76 | 102 | 315 | 0 | 0 | 84 |
N.S. |
1 | 1.00 | 0.94 | 0.75 | 1.01 | 3.12 | 0.00 | 0.00 | 0.83 |
time (sec) |
N/A | 0.411 | 0.612 | 0.852 | 0.284 | 0.261 | 0.000 | 0.000 | 0.323 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 101 | 81 | 70 | 102 | 258 | 0 | 0 | 74 |
N.S. |
1 | 1.10 | 0.88 | 0.76 | 1.11 | 2.80 | 0.00 | 0.00 | 0.80 |
time (sec) |
N/A | 0.392 | 0.331 | 0.870 | 0.287 | 0.237 | 0.000 | 0.000 | 5.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 69 | 54 | 83 | 215 | 0 | 0 | 61 |
N.S. |
1 | 1.00 | 0.96 | 0.75 | 1.15 | 2.99 | 0.00 | 0.00 | 0.85 |
time (sec) |
N/A | 0.276 | 0.101 | 0.671 | 0.290 | 0.244 | 0.000 | 0.000 | 0.219 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 71 | 64 | 107 | 357 | 0 | 0 | 76 |
N.S. |
1 | 1.00 | 0.90 | 0.81 | 1.35 | 4.52 | 0.00 | 0.00 | 0.96 |
time (sec) |
N/A | 0.506 | 0.168 | 1.257 | 0.286 | 0.241 | 0.000 | 0.000 | 4.397 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 141 | 151 | 107 | 99 | 132 | 501 | 0 | 0 | 112 |
N.S. |
1 | 1.07 | 0.76 | 0.70 | 0.94 | 3.55 | 0.00 | 0.00 | 0.79 |
time (sec) |
N/A | 0.980 | 0.390 | 1.039 | 0.289 | 0.249 | 0.000 | 0.000 | 4.617 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 184 | 198 | 117 | 117 | 178 | 546 | 0 | 0 | 136 |
N.S. |
1 | 1.08 | 0.64 | 0.64 | 0.97 | 2.97 | 0.00 | 0.00 | 0.74 |
time (sec) |
N/A | 1.278 | 1.028 | 1.085 | 0.284 | 0.249 | 0.000 | 0.000 | 5.070 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 204 | 224 | 116 | 131 | 156 | 412 | 0 | 0 | 142 |
N.S. |
1 | 1.10 | 0.57 | 0.64 | 0.76 | 2.02 | 0.00 | 0.00 | 0.70 |
time (sec) |
N/A | 1.149 | 1.818 | 1.126 | 0.285 | 0.255 | 0.000 | 0.000 | 4.537 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 130 | 132 | 107 | 96 | 120 | 371 | 0 | 0 | 107 |
N.S. |
1 | 1.02 | 0.82 | 0.74 | 0.92 | 2.85 | 0.00 | 0.00 | 0.82 |
time (sec) |
N/A | 0.510 | 1.107 | 0.901 | 0.274 | 0.251 | 0.000 | 0.000 | 5.092 |