Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 81 | 74 | 94 | 72 | 72 | 73 | 114 | 118 | 71 |
N.S. |
1 | 0.91 | 1.16 | 0.89 | 0.89 | 0.90 | 1.41 | 1.46 | 0.88 |
time (sec) |
N/A | 0.398 | 0.185 | 0.493 | 0.193 | 0.395 | 0.684 | 0.374 | 11.268 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 59 | 86 | 72 | 72 | 62 | 90 | 103 | 71 |
N.S. |
1 | 0.91 | 1.32 | 1.11 | 1.11 | 0.95 | 1.38 | 1.58 | 1.09 |
time (sec) |
N/A | 0.346 | 0.142 | 0.396 | 0.187 | 0.373 | 0.445 | 0.352 | 11.265 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 92 | 86 | 65 | 69 | 74 | 0 | 70 | 126 |
N.S. |
1 | 1.07 | 1.00 | 0.76 | 0.80 | 0.86 | 0.00 | 0.81 | 1.47 |
time (sec) |
N/A | 0.259 | 0.022 | 0.500 | 0.204 | 0.411 | 0.000 | 0.360 | 11.786 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 83 | 89 | 83 | 85 | 69 | 91 | 0 | 79 | 250 |
N.S. |
1 | 1.07 | 1.00 | 1.02 | 0.83 | 1.10 | 0.00 | 0.95 | 3.01 |
time (sec) |
N/A | 0.272 | 0.020 | 0.500 | 0.196 | 0.399 | 0.000 | 0.367 | 11.518 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 92 | 77 | 105 | 68 | 102 | 0 | 82 | 229 |
N.S. |
1 | 1.07 | 0.90 | 1.22 | 0.79 | 1.19 | 0.00 | 0.95 | 2.66 |
time (sec) |
N/A | 0.279 | 0.130 | 0.495 | 0.200 | 0.412 | 0.000 | 0.346 | 11.428 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 76 | 121 | 69 | 117 | 0 | 81 | 218 |
N.S. |
1 | 1.00 | 0.89 | 1.42 | 0.81 | 1.38 | 0.00 | 0.95 | 2.56 |
time (sec) |
N/A | 0.266 | 0.100 | 0.546 | 0.201 | 0.404 | 0.000 | 0.352 | 11.429 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 81 | 69 | 96 | 101 | 69 | 110 | 0 | 82 | 207 |
N.S. |
1 | 0.85 | 1.19 | 1.25 | 0.85 | 1.36 | 0.00 | 1.01 | 2.56 |
time (sec) |
N/A | 0.234 | 0.015 | 0.505 | 0.209 | 0.417 | 0.000 | 0.376 | 11.764 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 79 | 101 | 68 | 72 | 124 | 0 | 84 | 193 |
N.S. |
1 | 0.92 | 1.17 | 0.79 | 0.84 | 1.44 | 0.00 | 0.98 | 2.24 |
time (sec) |
N/A | 0.281 | 0.028 | 0.358 | 0.205 | 0.430 | 0.000 | 0.382 | 11.611 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 54 | 61 | 70 | 70 | 100 | 0 | 70 | 69 |
N.S. |
1 | 0.89 | 1.00 | 1.15 | 1.15 | 1.64 | 0.00 | 1.15 | 1.13 |
time (sec) |
N/A | 0.413 | 0.022 | 0.305 | 0.207 | 0.365 | 0.000 | 0.363 | 11.560 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 60 | 65 | 73 | 70 | 106 | 0 | 70 | 70 |
N.S. |
1 | 0.92 | 1.00 | 1.12 | 1.08 | 1.63 | 0.00 | 1.08 | 1.08 |
time (sec) |
N/A | 0.420 | 0.011 | 0.361 | 0.211 | 0.363 | 0.000 | 0.357 | 11.397 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 81 | 75 | 97 | 73 | 70 | 109 | 0 | 70 | 70 |
N.S. |
1 | 0.93 | 1.20 | 0.90 | 0.86 | 1.35 | 0.00 | 0.86 | 0.86 |
time (sec) |
N/A | 0.426 | 0.022 | 0.384 | 0.197 | 0.387 | 0.000 | 0.398 | 11.531 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 81 | 75 | 97 | 73 | 70 | 115 | 0 | 70 | 70 |
N.S. |
1 | 0.93 | 1.20 | 0.90 | 0.86 | 1.42 | 0.00 | 0.86 | 0.86 |
time (sec) |
N/A | 0.419 | 0.024 | 0.429 | 0.215 | 0.364 | 0.000 | 0.390 | 11.560 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 101 | 97 | 73 | 70 | 122 | 0 | 70 | 70 |
N.S. |
1 | 1.04 | 1.00 | 0.75 | 0.72 | 1.26 | 0.00 | 0.72 | 0.72 |
time (sec) |
N/A | 0.276 | 0.029 | 0.382 | 0.210 | 0.371 | 0.000 | 0.395 | 11.777 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 101 | 97 | 73 | 70 | 128 | 0 | 70 | 70 |
N.S. |
1 | 1.04 | 1.00 | 0.75 | 0.72 | 1.32 | 0.00 | 0.72 | 0.72 |
time (sec) |
N/A | 0.291 | 0.022 | 0.526 | 0.211 | 0.397 | 0.000 | 0.378 | 11.618 |
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 | 138 | 139 | 169 | 106 | 108 | 121 | 190 | 173 | 108 |
N.S. |
1 | 1.01 | 1.22 | 0.77 | 0.78 | 0.88 | 1.38 | 1.25 | 0.78 |
time (sec) |
N/A | 0.362 | 0.397 | 0.786 | 0.186 | 0.413 | 0.947 | 0.415 | 11.319 |
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 | 138 | 139 | 138 | 106 | 108 | 85 | 139 | 152 | 108 |
N.S. |
1 | 1.01 | 1.00 | 0.77 | 0.78 | 0.62 | 1.01 | 1.10 | 0.78 |
time (sec) |
N/A | 0.311 | 0.394 | 0.605 | 0.211 | 0.437 | 0.667 | 0.384 | 11.333 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 130 | 133 | 105 | 81 | 105 | 96 | 0 | 118 | 153 |
N.S. |
1 | 1.02 | 0.81 | 0.62 | 0.81 | 0.74 | 0.00 | 0.91 | 1.18 |
time (sec) |
N/A | 0.313 | 0.114 | 0.559 | 0.204 | 0.397 | 0.000 | 0.393 | 11.623 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 125 | 128 | 142 | 120 | 105 | 135 | 0 | 127 | 445 |
N.S. |
1 | 1.02 | 1.14 | 0.96 | 0.84 | 1.08 | 0.00 | 1.02 | 3.56 |
time (sec) |
N/A | 0.339 | 0.033 | 0.607 | 0.206 | 0.376 | 0.000 | 0.397 | 11.988 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 130 | 143 | 141 | 104 | 160 | 0 | 140 | 331 |
N.S. |
1 | 1.02 | 1.13 | 1.11 | 0.82 | 1.26 | 0.00 | 1.10 | 2.61 |
time (sec) |
N/A | 0.338 | 0.051 | 0.612 | 0.194 | 0.347 | 0.000 | 0.361 | 11.487 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 120 | 117 | 103 | 176 | 103 | 158 | 0 | 127 | 315 |
N.S. |
1 | 0.98 | 0.86 | 1.47 | 0.86 | 1.32 | 0.00 | 1.06 | 2.62 |
time (sec) |
N/A | 0.327 | 0.186 | 0.622 | 0.199 | 0.389 | 0.000 | 0.389 | 11.751 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 126 | 111 | 142 | 157 | 105 | 177 | 0 | 138 | 310 |
N.S. |
1 | 0.88 | 1.13 | 1.25 | 0.83 | 1.40 | 0.00 | 1.10 | 2.46 |
time (sec) |
N/A | 0.281 | 0.016 | 0.637 | 0.215 | 0.408 | 0.000 | 0.389 | 11.801 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 114 | 105 | 115 | 105 | 166 | 0 | 131 | 297 |
N.S. |
1 | 0.92 | 0.85 | 0.93 | 0.85 | 1.34 | 0.00 | 1.06 | 2.40 |
time (sec) |
N/A | 0.323 | 0.125 | 0.467 | 0.191 | 0.403 | 0.000 | 0.398 | 11.408 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 130 | 129 | 107 | 117 | 108 | 183 | 0 | 134 | 274 |
N.S. |
1 | 0.99 | 0.82 | 0.90 | 0.83 | 1.41 | 0.00 | 1.03 | 2.11 |
time (sec) |
N/A | 0.337 | 0.124 | 0.416 | 0.198 | 0.390 | 0.000 | 0.409 | 12.186 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 129 | 130 | 104 | 103 | 106 | 146 | 0 | 118 | 105 |
N.S. |
1 | 1.01 | 0.81 | 0.80 | 0.82 | 1.13 | 0.00 | 0.91 | 0.81 |
time (sec) |
N/A | 0.342 | 0.136 | 0.428 | 0.231 | 0.353 | 0.000 | 0.411 | 12.314 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 138 | 139 | 108 | 107 | 106 | 148 | 0 | 118 | 107 |
N.S. |
1 | 1.01 | 0.78 | 0.78 | 0.77 | 1.07 | 0.00 | 0.86 | 0.78 |
time (sec) |
N/A | 0.338 | 0.158 | 0.456 | 0.214 | 0.361 | 0.000 | 0.424 | 12.513 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 235 | 210 | 264 | 249 | 218 | 279 | 0 | 300 | 375 |
N.S. |
1 | 0.89 | 1.12 | 1.06 | 0.93 | 1.19 | 0.00 | 1.28 | 1.60 |
time (sec) |
N/A | 0.442 | 1.409 | 1.109 | 0.208 | 0.411 | 0.000 | 0.342 | 12.429 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 193 | 172 | 225 | 198 | 184 | 246 | 0 | 249 | 254 |
N.S. |
1 | 0.89 | 1.17 | 1.03 | 0.95 | 1.27 | 0.00 | 1.29 | 1.32 |
time (sec) |
N/A | 0.412 | 1.003 | 1.039 | 0.217 | 0.429 | 0.000 | 0.342 | 13.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 157 | 138 | 188 | 152 | 148 | 203 | 0 | 194 | 161 |
N.S. |
1 | 0.88 | 1.20 | 0.97 | 0.94 | 1.29 | 0.00 | 1.24 | 1.03 |
time (sec) |
N/A | 0.350 | 0.506 | 0.878 | 0.214 | 0.370 | 0.000 | 0.321 | 12.959 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 120 | 109 | 111 | 119 | 118 | 189 | 0 | 154 | 338 |
N.S. |
1 | 0.91 | 0.92 | 0.99 | 0.98 | 1.58 | 0.00 | 1.28 | 2.82 |
time (sec) |
N/A | 0.341 | 0.350 | 0.954 | 0.224 | 0.414 | 0.000 | 0.321 | 13.394 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 109 | 100 | 95 | 106 | 120 | 214 | 0 | 131 | 313 |
N.S. |
1 | 0.92 | 0.87 | 0.97 | 1.10 | 1.96 | 0.00 | 1.20 | 2.87 |
time (sec) |
N/A | 0.358 | 0.432 | 0.928 | 0.208 | 0.419 | 0.000 | 0.335 | 13.429 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 131 | 127 | 116 | 129 | 147 | 335 | 0 | 190 | 280 |
N.S. |
1 | 0.97 | 0.89 | 0.98 | 1.12 | 2.56 | 0.00 | 1.45 | 2.14 |
time (sec) |
N/A | 0.393 | 0.497 | 0.844 | 0.203 | 0.394 | 0.000 | 0.348 | 13.800 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 147 | 143 | 127 | 139 | 158 | 401 | 0 | 211 | 319 |
N.S. |
1 | 0.97 | 0.86 | 0.95 | 1.07 | 2.73 | 0.00 | 1.44 | 2.17 |
time (sec) |
N/A | 0.403 | 1.260 | 0.879 | 0.201 | 0.361 | 0.000 | 0.362 | 13.206 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 188 | 173 | 187 | 172 | 189 | 542 | 0 | 278 | 439 |
N.S. |
1 | 0.92 | 0.99 | 0.91 | 1.01 | 2.88 | 0.00 | 1.48 | 2.34 |
time (sec) |
N/A | 0.381 | 6.025 | 1.022 | 0.208 | 0.382 | 0.000 | 0.350 | 13.321 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 226 | 213 | 220 | 198 | 225 | 696 | 0 | 332 | 628 |
N.S. |
1 | 0.94 | 0.97 | 0.88 | 1.00 | 3.08 | 0.00 | 1.47 | 2.78 |
time (sec) |
N/A | 0.457 | 2.775 | 1.010 | 0.205 | 0.376 | 0.000 | 0.373 | 12.419 |
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 | 170 | 171 | 139 | 225 | 178 | 572 | 18260 | 575 | 887 |
N.S. |
1 | 1.01 | 0.82 | 1.32 | 1.05 | 3.36 | 107.41 | 3.38 | 5.22 |
time (sec) |
N/A | 0.437 | 0.463 | 9.543 | 0.205 | 0.396 | 16.502 | 0.389 | 19.750 |
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 | 123 | 127 | 97 | 170 | 109 | 282 | 8675 | 379 | 550 |
N.S. |
1 | 1.03 | 0.79 | 1.38 | 0.89 | 2.29 | 70.53 | 3.08 | 4.47 |
time (sec) |
N/A | 0.346 | 0.146 | 4.314 | 0.208 | 0.345 | 8.820 | 0.349 | 16.697 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 167 | 155 | 133 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.434 | 0.385 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 191 | 190 | 143 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.556 | 0.296 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 238 | 300 | 210 | 199 | 135 | 161 | 488 | 214 | 441 |
N.S. |
1 | 1.26 | 0.88 | 0.84 | 0.57 | 0.68 | 2.05 | 0.90 | 1.85 |
time (sec) |
N/A | 1.415 | 1.286 | 1.974 | 0.199 | 0.373 | 3.561 | 0.387 | 15.187 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 250 | 254 | 202 | 198 | 137 | 182 | 656 | 226 | 207 |
N.S. |
1 | 1.02 | 0.81 | 0.79 | 0.55 | 0.73 | 2.62 | 0.90 | 0.83 |
time (sec) |
N/A | 0.626 | 0.841 | 1.939 | 0.203 | 0.388 | 2.678 | 0.586 | 13.409 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 187 | 241 | 197 | 171 | 115 | 128 | 384 | 217 | 386 |
N.S. |
1 | 1.29 | 1.05 | 0.91 | 0.61 | 0.68 | 2.05 | 1.16 | 2.06 |
time (sec) |
N/A | 1.160 | 0.641 | 1.604 | 0.196 | 0.383 | 1.865 | 0.487 | 15.171 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 201 | 204 | 193 | 172 | 127 | 149 | 529 | 189 | 237 |
N.S. |
1 | 1.01 | 0.96 | 0.86 | 0.63 | 0.74 | 2.63 | 0.94 | 1.18 |
time (sec) |
N/A | 0.564 | 0.463 | 1.265 | 0.219 | 0.372 | 1.378 | 0.449 | 11.735 |
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 | 152 | 169 | 161 | 115 | 92 | 97 | 282 | 176 | 332 |
N.S. |
1 | 1.11 | 1.06 | 0.76 | 0.61 | 0.64 | 1.86 | 1.16 | 2.18 |
time (sec) |
N/A | 0.751 | 0.591 | 0.928 | 0.191 | 0.355 | 0.929 | 0.382 | 15.325 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 157 | 155 | 166 | 113 | 122 | 137 | 0 | 291 | 415 |
N.S. |
1 | 0.99 | 1.06 | 0.72 | 0.78 | 0.87 | 0.00 | 1.85 | 2.64 |
time (sec) |
N/A | 0.733 | 0.592 | 0.615 | 0.208 | 0.366 | 0.000 | 0.375 | 13.410 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 178 | 190 | 220 | 165 | 172 | 188 | 0 | 368 | 683 |
N.S. |
1 | 1.07 | 1.24 | 0.93 | 0.97 | 1.06 | 0.00 | 2.07 | 3.84 |
time (sec) |
N/A | 0.757 | 0.378 | 0.614 | 0.285 | 0.366 | 0.000 | 0.372 | 12.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 180 | 195 | 250 | 187 | 190 | 244 | 0 | 346 | 484 |
N.S. |
1 | 1.08 | 1.39 | 1.04 | 1.06 | 1.36 | 0.00 | 1.92 | 2.69 |
time (sec) |
N/A | 0.667 | 6.527 | 0.638 | 0.298 | 0.362 | 0.000 | 0.396 | 11.505 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 177 | 194 | 336 | 209 | 189 | 252 | 0 | 366 | 665 |
N.S. |
1 | 1.10 | 1.90 | 1.18 | 1.07 | 1.42 | 0.00 | 2.07 | 3.76 |
time (sec) |
N/A | 0.799 | 6.615 | 0.657 | 0.284 | 0.370 | 0.000 | 0.414 | 11.556 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 174 | 195 | 337 | 237 | 205 | 309 | 0 | 346 | 479 |
N.S. |
1 | 1.12 | 1.94 | 1.36 | 1.18 | 1.78 | 0.00 | 1.99 | 2.75 |
time (sec) |
N/A | 0.689 | 6.560 | 0.694 | 0.276 | 0.365 | 0.000 | 0.399 | 11.628 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 202 | 202 | 351 | 216 | 183 | 306 | 0 | 337 | 888 |
N.S. |
1 | 1.00 | 1.74 | 1.07 | 0.91 | 1.51 | 0.00 | 1.67 | 4.40 |
time (sec) |
N/A | 0.425 | 0.716 | 0.693 | 0.279 | 0.367 | 0.000 | 0.407 | 16.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 175 | 197 | 384 | 238 | 219 | 360 | 0 | 337 | 985 |
N.S. |
1 | 1.13 | 2.19 | 1.36 | 1.25 | 2.06 | 0.00 | 1.93 | 5.63 |
time (sec) |
N/A | 0.889 | 1.627 | 0.646 | 0.282 | 0.368 | 0.000 | 0.417 | 14.999 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 158 | 164 | 280 | 172 | 153 | 320 | 0 | 356 | 379 |
N.S. |
1 | 1.04 | 1.77 | 1.09 | 0.97 | 2.03 | 0.00 | 2.25 | 2.40 |
time (sec) |
N/A | 1.159 | 1.670 | 0.520 | 0.305 | 0.383 | 0.000 | 0.424 | 11.539 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 159 | 191 | 282 | 216 | 220 | 338 | 0 | 402 | 343 |
N.S. |
1 | 1.20 | 1.77 | 1.36 | 1.38 | 2.13 | 0.00 | 2.53 | 2.16 |
time (sec) |
N/A | 0.670 | 1.306 | 0.668 | 0.210 | 0.353 | 0.000 | 0.442 | 12.639 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 151 | 160 | 204 | 191 | 154 | 291 | 0 | 408 | 373 |
N.S. |
1 | 1.06 | 1.35 | 1.26 | 1.02 | 1.93 | 0.00 | 2.70 | 2.47 |
time (sec) |
N/A | 1.281 | 1.623 | 0.645 | 0.198 | 0.386 | 0.000 | 0.440 | 11.793 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 210 | 237 | 244 | 311 | 272 | 455 | 0 | 468 | 394 |
N.S. |
1 | 1.13 | 1.16 | 1.48 | 1.30 | 2.17 | 0.00 | 2.23 | 1.88 |
time (sec) |
N/A | 0.720 | 1.784 | 0.724 | 0.196 | 0.394 | 0.000 | 0.465 | 11.950 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 198 | 207 | 250 | 247 | 196 | 363 | 0 | 502 | 448 |
N.S. |
1 | 1.05 | 1.26 | 1.25 | 0.99 | 1.83 | 0.00 | 2.54 | 2.26 |
time (sec) |
N/A | 1.524 | 2.172 | 0.774 | 0.212 | 0.447 | 0.000 | 0.440 | 16.382 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 525 | 640 | 531 | 656 | 0 | 871 | 0 | 965 | 3724 |
N.S. |
1 | 1.22 | 1.01 | 1.25 | 0.00 | 1.66 | 0.00 | 1.84 | 7.09 |
time (sec) |
N/A | 4.175 | 5.854 | 4.215 | 0.000 | 0.442 | 0.000 | 0.361 | 17.953 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 471 | 569 | 462 | 611 | 0 | 814 | 0 | 835 | 4067 |
N.S. |
1 | 1.21 | 0.98 | 1.30 | 0.00 | 1.73 | 0.00 | 1.77 | 8.63 |
time (sec) |
N/A | 3.386 | 5.616 | 3.862 | 0.000 | 0.490 | 0.000 | 0.338 | 16.377 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 231 | 255 | 371 | 468 | 0 | 697 | 0 | 593 | 3135 |
N.S. |
1 | 1.10 | 1.61 | 2.03 | 0.00 | 3.02 | 0.00 | 2.57 | 13.57 |
time (sec) |
N/A | 1.116 | 2.853 | 2.437 | 0.000 | 0.430 | 0.000 | 0.339 | 14.481 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 266 | 266 | 207 | 314 | 0 | 698 | 0 | 353 | 5197 |
N.S. |
1 | 1.00 | 0.78 | 1.18 | 0.00 | 2.62 | 0.00 | 1.33 | 19.54 |
time (sec) |
N/A | 0.614 | 1.407 | 1.543 | 0.000 | 0.850 | 0.000 | 0.343 | 13.777 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 254 | 254 | 215 | 304 | 0 | 901 | 0 | 384 | 5214 |
N.S. |
1 | 1.00 | 0.85 | 1.20 | 0.00 | 3.55 | 0.00 | 1.51 | 20.53 |
time (sec) |
N/A | 0.582 | 2.218 | 1.367 | 0.000 | 0.697 | 0.000 | 0.357 | 13.569 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 251 | 251 | 315 | 290 | 0 | 1210 | 0 | 463 | 4294 |
N.S. |
1 | 1.00 | 1.25 | 1.16 | 0.00 | 4.82 | 0.00 | 1.84 | 17.11 |
time (sec) |
N/A | 0.578 | 6.473 | 1.186 | 0.000 | 0.857 | 0.000 | 0.356 | 12.658 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 287 | 287 | 428 | 327 | 0 | 1437 | 0 | 399 | 4740 |
N.S. |
1 | 1.00 | 1.49 | 1.14 | 0.00 | 5.01 | 0.00 | 1.39 | 16.52 |
time (sec) |
N/A | 0.620 | 6.538 | 0.809 | 0.000 | 0.651 | 0.000 | 0.363 | 12.798 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 303 | 377 | 487 | 370 | 0 | 1576 | 0 | 475 | 1117 |
N.S. |
1 | 1.24 | 1.61 | 1.22 | 0.00 | 5.20 | 0.00 | 1.57 | 3.69 |
time (sec) |
N/A | 2.368 | 6.434 | 0.834 | 0.000 | 0.706 | 0.000 | 0.377 | 11.830 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 424 | 506 | 361 | 465 | 0 | 2011 | 0 | 596 | 1424 |
N.S. |
1 | 1.19 | 0.85 | 1.10 | 0.00 | 4.74 | 0.00 | 1.41 | 3.36 |
time (sec) |
N/A | 3.230 | 1.056 | 0.962 | 0.000 | 0.807 | 0.000 | 0.376 | 11.863 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 480 | 579 | 447 | 572 | 0 | 2588 | 0 | 736 | 1810 |
N.S. |
1 | 1.21 | 0.93 | 1.19 | 0.00 | 5.39 | 0.00 | 1.53 | 3.77 |
time (sec) |
N/A | 3.934 | 1.978 | 1.219 | 0.000 | 1.051 | 0.000 | 0.389 | 12.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 536 | 671 | 631 | 696 | 0 | 1128 | 0 | 968 | 4362 |
N.S. |
1 | 1.25 | 1.18 | 1.30 | 0.00 | 2.10 | 0.00 | 1.81 | 8.14 |
time (sec) |
N/A | 4.413 | 11.018 | 5.787 | 0.000 | 0.522 | 0.000 | 0.406 | 48.947 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 485 | 598 | 517 | 554 | 0 | 995 | 0 | 724 | 3700 |
N.S. |
1 | 1.23 | 1.07 | 1.14 | 0.00 | 2.05 | 0.00 | 1.49 | 7.63 |
time (sec) |
N/A | 3.607 | 11.378 | 4.652 | 0.000 | 0.425 | 0.000 | 0.373 | 24.202 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F(-2) | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 237 | 259 | 1250 | 472 | 0 | 837 | 0 | 581 | 2529 |
N.S. |
1 | 1.09 | 5.27 | 1.99 | 0.00 | 3.53 | 0.00 | 2.45 | 10.67 |
time (sec) |
N/A | 1.061 | 6.654 | 2.788 | 0.000 | 0.466 | 0.000 | 0.353 | 16.762 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 399 | 399 | 243 | 359 | 0 | 1007 | 0 | 635 | 5354 |
N.S. |
1 | 1.00 | 0.61 | 0.90 | 0.00 | 2.52 | 0.00 | 1.59 | 13.42 |
time (sec) |
N/A | 0.822 | 1.711 | 2.338 | 0.000 | 0.715 | 0.000 | 0.356 | 14.304 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 314 | 314 | 241 | 326 | 0 | 1171 | 0 | 461 | 4223 |
N.S. |
1 | 1.00 | 0.77 | 1.04 | 0.00 | 3.73 | 0.00 | 1.47 | 13.45 |
time (sec) |
N/A | 0.741 | 5.577 | 1.953 | 0.000 | 0.617 | 0.000 | 0.374 | 13.750 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 395 | 395 | 384 | 357 | 0 | 1658 | 0 | 512 | 4381 |
N.S. |
1 | 1.00 | 0.97 | 0.90 | 0.00 | 4.20 | 0.00 | 1.30 | 11.09 |
time (sec) |
N/A | 0.778 | 6.537 | 1.053 | 0.000 | 0.712 | 0.000 | 0.385 | 12.880 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 329 | 415 | 490 | 359 | 0 | 1553 | 0 | 478 | 1082 |
N.S. |
1 | 1.26 | 1.49 | 1.09 | 0.00 | 4.72 | 0.00 | 1.45 | 3.29 |
time (sec) |
N/A | 2.588 | 6.523 | 1.066 | 0.000 | 0.521 | 0.000 | 0.392 | 11.978 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 355 | 463 | 363 | 455 | 0 | 2022 | 0 | 603 | 1275 |
N.S. |
1 | 1.30 | 1.02 | 1.28 | 0.00 | 5.70 | 0.00 | 1.70 | 3.59 |
time (sec) |
N/A | 3.130 | 1.210 | 1.257 | 0.000 | 0.623 | 0.000 | 0.396 | 12.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 492 | 605 | 448 | 559 | 0 | 2571 | 0 | 731 | 1614 |
N.S. |
1 | 1.23 | 0.91 | 1.14 | 0.00 | 5.23 | 0.00 | 1.49 | 3.28 |
time (sec) |
N/A | 4.118 | 1.121 | 1.282 | 0.000 | 0.836 | 0.000 | 0.428 | 12.440 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 600 | 754 | 728 | 775 | 0 | 3687 | 0 | 1018 | 2795 |
N.S. |
1 | 1.26 | 1.21 | 1.29 | 0.00 | 6.14 | 0.00 | 1.70 | 4.66 |
time (sec) |
N/A | 5.474 | 3.041 | 1.414 | 0.000 | 0.967 | 0.000 | 0.439 | 13.004 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 712 | 773 | 1906 | 37795 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 2.68 | 53.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.575 | 8.573 | 15.296 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 159 | 196 | 127 | 425 | 0 | 147 | 0 | 0 | 0 |
N.S. |
1 | 1.23 | 0.80 | 2.67 | 0.00 | 0.92 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.750 | 0.574 | 2.617 | 0.000 | 0.126 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 193 | 193 | 105 | 458 | 0 | 237 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.54 | 2.37 | 0.00 | 1.23 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.989 | 0.702 | 2.868 | 0.000 | 0.164 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 76 | 66 | 66 | 65 | 67 | 71 | 105 | 68 | 64 |
N.S. |
1 | 0.87 | 0.87 | 0.86 | 0.88 | 0.93 | 1.38 | 0.89 | 0.84 |
time (sec) |
N/A | 0.252 | 0.251 | 0.317 | 0.193 | 0.351 | 0.446 | 0.371 | 12.149 |
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 | 55 | 48 | 49 | 54 | 49 | 47 | 87 | 50 | 47 |
N.S. |
1 | 0.87 | 0.89 | 0.98 | 0.89 | 0.85 | 1.58 | 0.91 | 0.85 |
time (sec) |
N/A | 0.245 | 0.153 | 0.231 | 0.210 | 0.410 | 0.376 | 0.365 | 0.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 30 | 39 | 33 | 33 | 31 | 65 | 34 | 31 |
N.S. |
1 | 0.88 | 1.15 | 0.97 | 0.97 | 0.91 | 1.91 | 1.00 | 0.91 |
time (sec) |
N/A | 0.215 | 0.009 | 0.178 | 0.194 | 0.347 | 0.336 | 0.427 | 0.067 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 34 | 20 | 33 | 31 | 0 | 35 | 48 |
N.S. |
1 | 1.00 | 1.00 | 0.59 | 0.97 | 0.91 | 0.00 | 1.03 | 1.41 |
time (sec) |
N/A | 0.195 | 0.012 | 0.180 | 0.210 | 0.348 | 0.000 | 0.374 | 11.979 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 49 | 50 | 35 | 47 | 56 | 0 | 49 | 89 |
N.S. |
1 | 0.98 | 1.00 | 0.70 | 0.94 | 1.12 | 0.00 | 0.98 | 1.78 |
time (sec) |
N/A | 0.247 | 0.069 | 0.256 | 0.206 | 0.335 | 0.000 | 0.361 | 12.121 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 68 | 72 | 54 | 66 | 100 | 0 | 71 | 132 |
N.S. |
1 | 0.94 | 1.00 | 0.75 | 0.92 | 1.39 | 0.00 | 0.99 | 1.83 |
time (sec) |
N/A | 0.267 | 0.068 | 0.280 | 0.209 | 0.372 | 0.000 | 0.336 | 12.226 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F(-2) | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 235 | 274 | 177 | 339 | 0 | 427 | 0 | 467 | 376 |
N.S. |
1 | 1.17 | 0.75 | 1.44 | 0.00 | 1.82 | 0.00 | 1.99 | 1.60 |
time (sec) |
N/A | 1.769 | 1.638 | 0.768 | 0.000 | 0.451 | 0.000 | 0.352 | 13.737 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F(-2) | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 191 | 222 | 146 | 265 | 0 | 380 | 0 | 366 | 2616 |
N.S. |
1 | 1.16 | 0.76 | 1.39 | 0.00 | 1.99 | 0.00 | 1.92 | 13.70 |
time (sec) |
N/A | 1.325 | 0.971 | 0.589 | 0.000 | 0.506 | 0.000 | 0.343 | 13.162 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 148 | 171 | 130 | 184 | 0 | 315 | 0 | 207 | 225 |
N.S. |
1 | 1.16 | 0.88 | 1.24 | 0.00 | 2.13 | 0.00 | 1.40 | 1.52 |
time (sec) |
N/A | 0.965 | 0.360 | 0.457 | 0.000 | 0.401 | 0.000 | 0.429 | 12.087 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 111 | 104 | 146 | 0 | 275 | 0 | 159 | 190 |
N.S. |
1 | 1.11 | 1.04 | 1.46 | 0.00 | 2.75 | 0.00 | 1.59 | 1.90 |
time (sec) |
N/A | 0.469 | 0.178 | 0.361 | 0.000 | 0.365 | 0.000 | 0.383 | 11.906 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 87 | 90 | 94 | 0 | 262 | 0 | 94 | 896 |
N.S. |
1 | 1.16 | 1.20 | 1.25 | 0.00 | 3.49 | 0.00 | 1.25 | 11.95 |
time (sec) |
N/A | 0.481 | 0.052 | 0.286 | 0.000 | 0.409 | 0.000 | 0.461 | 12.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 93 | 108 | 109 | 0 | 314 | 0 | 129 | 204 |
N.S. |
1 | 1.16 | 1.35 | 1.36 | 0.00 | 3.92 | 0.00 | 1.61 | 2.55 |
time (sec) |
N/A | 0.598 | 0.148 | 0.294 | 0.000 | 0.391 | 0.000 | 0.452 | 11.895 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 114 | 132 | 181 | 144 | 0 | 472 | 0 | 198 | 790 |
N.S. |
1 | 1.16 | 1.59 | 1.26 | 0.00 | 4.14 | 0.00 | 1.74 | 6.93 |
time (sec) |
N/A | 0.909 | 1.192 | 0.362 | 0.000 | 0.423 | 0.000 | 0.413 | 12.601 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 153 | 177 | 351 | 205 | 0 | 591 | 0 | 270 | 749 |
N.S. |
1 | 1.16 | 2.29 | 1.34 | 0.00 | 3.86 | 0.00 | 1.76 | 4.90 |
time (sec) |
N/A | 1.246 | 6.804 | 0.417 | 0.000 | 0.427 | 0.000 | 0.589 | 13.444 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 194 | 226 | 430 | 252 | 0 | 808 | 0 | 336 | 873 |
N.S. |
1 | 1.16 | 2.22 | 1.30 | 0.00 | 4.16 | 0.00 | 1.73 | 4.50 |
time (sec) |
N/A | 1.695 | 6.979 | 0.492 | 0.000 | 0.579 | 0.000 | 0.382 | 11.901 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F(-2) | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 238 | 278 | 506 | 336 | 0 | 959 | 0 | 444 | 1007 |
N.S. |
1 | 1.17 | 2.13 | 1.41 | 0.00 | 4.03 | 0.00 | 1.87 | 4.23 |
time (sec) |
N/A | 2.128 | 2.112 | 0.625 | 0.000 | 0.537 | 0.000 | 0.370 | 12.175 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 149 | 133 | 127 | 147 | 131 | 127 | 0 | 149 | 133 |
N.S. |
1 | 0.89 | 0.85 | 0.99 | 0.88 | 0.85 | 0.00 | 1.00 | 0.89 |
time (sec) |
N/A | 0.356 | 0.194 | 0.549 | 0.212 | 0.386 | 0.000 | 0.355 | 0.091 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 106 | 104 | 103 | 105 | 97 | 0 | 117 | 107 |
N.S. |
1 | 0.89 | 0.87 | 0.87 | 0.88 | 0.82 | 0.00 | 0.98 | 0.90 |
time (sec) |
N/A | 0.334 | 0.227 | 0.429 | 0.193 | 0.352 | 0.000 | 0.311 | 11.484 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 79 | 79 | 83 | 79 | 78 | 0 | 85 | 78 |
N.S. |
1 | 0.89 | 0.89 | 0.93 | 0.89 | 0.88 | 0.00 | 0.96 | 0.88 |
time (sec) |
N/A | 0.280 | 0.096 | 0.329 | 0.201 | 0.413 | 0.000 | 0.322 | 11.541 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 57 | 53 | 55 | 54 | 55 | 0 | 56 | 98 |
N.S. |
1 | 0.97 | 0.90 | 0.93 | 0.92 | 0.93 | 0.00 | 0.95 | 1.66 |
time (sec) |
N/A | 0.275 | 0.026 | 0.358 | 0.208 | 0.386 | 0.000 | 0.322 | 11.719 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 54 | 59 | 57 | 69 | 0 | 59 | 118 |
N.S. |
1 | 1.00 | 0.90 | 0.98 | 0.95 | 1.15 | 0.00 | 0.98 | 1.97 |
time (sec) |
N/A | 0.293 | 0.033 | 0.344 | 0.202 | 0.382 | 0.000 | 0.331 | 11.610 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 84 | 78 | 65 | 76 | 77 | 118 | 0 | 88 | 144 |
N.S. |
1 | 0.93 | 0.77 | 0.90 | 0.92 | 1.40 | 0.00 | 1.05 | 1.71 |
time (sec) |
N/A | 0.264 | 0.082 | 0.403 | 0.188 | 0.388 | 0.000 | 0.365 | 11.543 |