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 | C | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 146 | 139 | 132 | 237 | 0 | 218 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.90 | 1.62 | 0.00 | 1.49 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.437 | 0.318 | 0.178 | 0.000 | 0.287 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 139 | 166 | 166 | 897 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.19 | 1.19 | 6.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.750 | 0.491 | 0.171 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 105 | 104 | 93 | 157 | 138 | 187 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.89 | 1.50 | 1.31 | 1.78 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.374 | 0.281 | 0.170 | 0.290 | 0.301 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 74 | 88 | 729 | 137 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.92 | 1.10 | 9.11 | 1.71 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.345 | 0.256 | 0.193 | 0.223 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 74 | 72 | 121 | 0 | 165 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.96 | 1.61 | 0.00 | 2.20 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.278 | 0.215 | 0.168 | 0.000 | 0.310 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 108 | 113 | 100 | 619 | 126 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.93 | 5.73 | 1.17 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.386 | 0.150 | 0.196 | 0.211 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 148 | 169 | 209 | 208 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.14 | 1.41 | 1.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.926 | 0.703 | 0.229 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 150 | 140 | 125 | 778 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.83 | 5.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.463 | 0.409 | 0.182 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 247 | 256 | 331 | 314 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.34 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.349 | 4.107 | 0.178 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 208 | 188 | 239 | 1155 | 236 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.90 | 1.15 | 5.55 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.642 | 0.398 | 0.169 | 0.218 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 200 | 213 | 121 | 363 | 143 | 0 | 0 | 124 | 0 |
N.S. |
1 | 1.06 | 0.60 | 1.82 | 0.72 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.573 | 0.145 | 0.277 | 0.221 | 0.000 | 0.000 | 0.338 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 94 | 63 | 74 | 83 | 83 | 82 | 0 | 0 |
N.S. |
1 | 1.09 | 0.73 | 0.86 | 0.97 | 0.97 | 0.95 | 0.00 | 0.00 |
time (sec) |
N/A | 0.479 | 0.038 | 0.158 | 0.202 | 0.270 | 0.500 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 70 | 73 | 48 | 82 | 59 | 55 | 65 | 0 | 0 |
N.S. |
1 | 1.04 | 0.69 | 1.17 | 0.84 | 0.79 | 0.93 | 0.00 | 0.00 |
time (sec) |
N/A | 0.356 | 0.032 | 0.209 | 0.199 | 0.254 | 0.357 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 42 | 40 | 55 | 62 | 42 | 0 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.82 | 1.12 | 1.27 | 0.86 | 0.00 | 0.00 |
time (sec) |
N/A | 0.334 | 0.048 | 0.204 | 0.200 | 0.270 | 0.337 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 47 | 26 | 38 | 24 | 38 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.68 | 0.93 | 1.36 | 0.86 | 1.36 | 0.00 |
time (sec) |
N/A | 0.221 | 0.038 | 0.222 | 0.194 | 0.268 | 0.240 | 0.292 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 12 | 11 | 23 | 10 | 0 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.85 | 1.77 | 0.77 | 0.00 | 0.85 |
time (sec) |
N/A | 0.193 | 0.008 | 0.234 | 0.193 | 0.263 | 0.198 | 0.000 | 2.398 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 46 | 57 | 89 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.35 | 1.68 | 2.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.357 | 0.109 | 0.231 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 29 | 56 | 25 | 39 | 0 | 71 | 0 |
N.S. |
1 | 1.00 | 1.07 | 2.07 | 0.93 | 1.44 | 0.00 | 2.63 | 0.00 |
time (sec) |
N/A | 0.230 | 0.049 | 0.244 | 0.192 | 0.256 | 0.000 | 0.302 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 84 | 126 | 150 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 1.58 | 1.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.517 | 0.555 | 0.200 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 175 | 124 | 120 | 578 | 134 | 158 | 0 | 0 | 0 |
N.S. |
1 | 0.71 | 0.69 | 3.30 | 0.77 | 0.90 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.382 | 0.128 | 0.271 | 0.206 | 0.271 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 181 | 158 | 129 | 338 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.87 | 0.71 | 1.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.612 | 0.617 | 0.175 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 105 | 80 | 92 | 321 | 73 | 127 | 0 | 0 | 0 |
N.S. |
1 | 0.76 | 0.88 | 3.06 | 0.70 | 1.21 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.292 | 0.109 | 0.232 | 0.204 | 0.271 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 120 | 256 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.08 | 2.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.349 | 0.400 | 0.166 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 177 | 135 | 168 | 331 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.76 | 0.95 | 1.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.644 | 0.401 | 0.203 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 129 | 251 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.23 | 2.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.412 | 0.342 | 0.209 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 201 | 150 | 223 | 334 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.75 | 1.11 | 1.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.680 | 2.252 | 0.184 | 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 | B | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 106 | 80 | 117 | 137 | 133 | 217 | 0 | 0 | 0 |
N.S. |
1 | 0.75 | 1.10 | 1.29 | 1.25 | 2.05 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.314 | 0.330 | 0.199 | 0.199 | 0.284 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 217 | 135 | 130 | 872 | 145 | 199 | 0 | 0 | 0 |
N.S. |
1 | 0.62 | 0.60 | 4.02 | 0.67 | 0.92 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.412 | 0.194 | 0.216 | 0.205 | 0.266 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 254 | 245 | 251 | 799 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 0.99 | 3.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.906 | 0.640 | 0.219 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 146 | 91 | 102 | 559 | 85 | 167 | 0 | 0 | 0 |
N.S. |
1 | 0.62 | 0.70 | 3.83 | 0.58 | 1.14 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.296 | 0.134 | 0.204 | 0.197 | 0.275 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 180 | 196 | 200 | 496 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 1.11 | 2.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.556 | 0.696 | 0.182 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 249 | 210 | 248 | 428 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.84 | 1.00 | 1.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.973 | 0.631 | 0.270 | 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 | F(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 177 | 189 | 200 | 230 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 1.13 | 1.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.624 | 0.834 | 0.249 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 270 | 218 | 352 | 289 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.81 | 1.30 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.997 | 3.471 | 0.237 | 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 | F(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 184 | 188 | 217 | 257 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.18 | 1.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.691 | 0.634 | 0.249 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 266 | 145 | 140 | 996 | 156 | 263 | 0 | 0 | 0 |
N.S. |
1 | 0.55 | 0.53 | 3.74 | 0.59 | 0.99 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.421 | 0.229 | 0.230 | 0.220 | 0.276 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 337 | 344 | 388 | 1165 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.15 | 3.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.331 | 0.896 | 0.224 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 193 | 100 | 112 | 863 | 96 | 225 | 0 | 0 | 0 |
N.S. |
1 | 0.52 | 0.58 | 4.47 | 0.50 | 1.17 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.302 | 0.152 | 0.216 | 0.207 | 0.274 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 254 | 267 | 317 | 801 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 1.25 | 3.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.752 | 0.664 | 0.185 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 329 | 297 | 339 | 540 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.90 | 1.03 | 1.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.368 | 0.712 | 0.244 | 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 | F(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 257 | 289 | 270 | 285 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.12 | 1.05 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.891 | 1.332 | 0.201 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 355 | 306 | 424 | 339 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.86 | 1.19 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.436 | 6.407 | 0.243 | 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 | F(-2) | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 266 | 285 | 286 | 322 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 1.08 | 1.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.989 | 0.992 | 0.224 | 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 | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 28 | 26 | 28 | 40 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.81 | 0.88 | 1.25 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.241 | 0.007 | 0.232 | 0.282 | 0.255 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 215 | 226 | 119 | 625 | 174 | 161 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.55 | 2.91 | 0.81 | 0.75 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.668 | 0.173 | 0.217 | 0.212 | 0.273 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 192 | 200 | 151 | 519 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.79 | 2.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.645 | 0.691 | 0.205 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 142 | 145 | 93 | 358 | 117 | 132 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.65 | 2.52 | 0.82 | 0.93 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.449 | 0.140 | 0.196 | 0.204 | 0.272 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 119 | 121 | 273 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.02 | 2.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.405 | 0.656 | 0.211 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 74 | 148 | 55 | 96 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.16 | 2.31 | 0.86 | 1.50 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.246 | 0.152 | 0.236 | 0.207 | 0.283 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 76 | 77 | 28 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.62 | 1.64 | 0.60 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.210 | 0.078 | 0.206 | 0.208 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 122 | 79 | 129 | 233 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.65 | 1.06 | 1.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.421 | 0.292 | 0.249 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 77 | 169 | 101 | 132 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.22 | 2.68 | 1.60 | 2.10 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.277 | 0.192 | 0.235 | 0.209 | 0.284 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 203 | 153 | 229 | 333 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.75 | 1.13 | 1.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.667 | 2.285 | 0.203 | 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 | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 141 | 139 | 131 | 166 | 121 | 222 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.93 | 1.18 | 0.86 | 1.57 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.471 | 0.235 | 0.221 | 0.205 | 0.300 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 212 | 154 | 174 | 238 | 0 | 197 | 0 | 0 | 0 |
N.S. |
1 | 0.73 | 0.82 | 1.12 | 0.00 | 0.93 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.461 | 0.398 | 0.230 | 0.000 | 0.307 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 206 | 222 | 161 | 274 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 0.78 | 1.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.762 | 0.550 | 0.244 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 136 | 105 | 130 | 176 | 119 | 166 | 0 | 0 | 0 |
N.S. |
1 | 0.77 | 0.96 | 1.29 | 0.88 | 1.22 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.369 | 0.355 | 0.231 | 0.280 | 0.288 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 130 | 130 | 146 | 232 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.12 | 1.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.436 | 0.331 | 0.195 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 86 | 125 | 0 | 128 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.23 | 1.79 | 0.00 | 1.83 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.272 | 0.264 | 0.240 | 0.000 | 0.300 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 100 | 143 | 58 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.32 | 1.88 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.241 | 0.174 | 0.177 | 0.209 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 194 | 146 | 231 | 271 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.75 | 1.19 | 1.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.684 | 0.683 | 0.237 | 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 | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 143 | 113 | 163 | 239 | 119 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.79 | 1.14 | 1.67 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.381 | 0.605 | 0.194 | 0.202 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 287 | 235 | 369 | 342 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.82 | 1.29 | 1.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.059 | 6.182 | 0.224 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 228 | 167 | 216 | 968 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.73 | 0.95 | 4.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.481 | 0.324 | 0.224 | 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 | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 281 | 345 | 222 | 410 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.23 | 0.79 | 1.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.203 | 0.936 | 0.253 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 210 | 164 | 177 | 400 | 0 | 219 | 0 | 0 | 0 |
N.S. |
1 | 0.78 | 0.84 | 1.90 | 0.00 | 1.04 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.452 | 0.417 | 0.262 | 0.000 | 0.298 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 203 | 241 | 191 | 345 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.19 | 0.94 | 1.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.812 | 0.576 | 0.217 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 144 | 129 | 136 | 263 | 138 | 188 | 0 | 0 | 0 |
N.S. |
1 | 0.90 | 0.94 | 1.83 | 0.96 | 1.31 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.390 | 0.363 | 0.190 | 0.278 | 0.299 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 99 | 118 | 413 | 137 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.83 | 0.99 | 3.47 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.356 | 0.281 | 0.255 | 0.204 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 114 | 99 | 103 | 198 | 0 | 166 | 0 | 0 | 0 |
N.S. |
1 | 0.87 | 0.90 | 1.74 | 0.00 | 1.46 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.293 | 0.286 | 0.192 | 0.000 | 0.286 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 147 | 152 | 143 | 425 | 126 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.97 | 2.89 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.402 | 0.188 | 0.276 | 0.203 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 262 | 244 | 247 | 364 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.94 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.045 | 1.001 | 0.245 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 214 | 165 | 227 | 1257 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.77 | 1.06 | 5.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.490 | 0.329 | 0.248 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 400 | 356 | 409 | 406 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.89 | 1.02 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.583 | 5.360 | 0.231 | 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 | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 297 | 213 | 267 | 372 | 236 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.72 | 0.90 | 1.25 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.642 | 0.360 | 0.216 | 0.216 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 200 | 213 | 121 | 363 | 143 | 0 | 0 | 124 | 0 |
N.S. |
1 | 1.06 | 0.60 | 1.82 | 0.72 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.533 | 0.083 | 0.184 | 0.203 | 0.000 | 0.000 | 0.330 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 94 | 63 | 74 | 83 | 83 | 82 | 0 | 0 |
N.S. |
1 | 1.09 | 0.73 | 0.86 | 0.97 | 0.97 | 0.95 | 0.00 | 0.00 |
time (sec) |
N/A | 0.468 | 0.023 | 0.209 | 0.203 | 0.272 | 0.417 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 70 | 73 | 48 | 82 | 59 | 55 | 65 | 0 | 0 |
N.S. |
1 | 1.04 | 0.69 | 1.17 | 0.84 | 0.79 | 0.93 | 0.00 | 0.00 |
time (sec) |
N/A | 0.355 | 0.020 | 0.232 | 0.191 | 0.271 | 0.351 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 42 | 40 | 55 | 62 | 42 | 0 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.82 | 1.12 | 1.27 | 0.86 | 0.00 | 0.00 |
time (sec) |
N/A | 0.321 | 0.013 | 0.199 | 0.192 | 0.258 | 0.299 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 47 | 26 | 38 | 24 | 38 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.68 | 0.93 | 1.36 | 0.86 | 1.36 | 0.00 |
time (sec) |
N/A | 0.212 | 0.010 | 0.243 | 0.196 | 0.267 | 0.232 | 0.284 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 12 | 11 | 23 | 10 | 0 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.85 | 1.77 | 0.77 | 0.00 | 0.85 |
time (sec) |
N/A | 0.184 | 0.001 | 0.228 | 0.193 | 0.277 | 0.204 | 0.000 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 46 | 57 | 89 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.35 | 1.68 | 2.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.350 | 0.092 | 0.201 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 29 | 56 | 25 | 39 | 0 | 71 | 0 |
N.S. |
1 | 1.00 | 1.07 | 2.07 | 0.93 | 1.44 | 0.00 | 2.63 | 0.00 |
time (sec) |
N/A | 0.228 | 0.011 | 0.211 | 0.216 | 0.274 | 0.000 | 0.300 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 84 | 126 | 150 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 1.58 | 1.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.510 | 0.114 | 0.250 | 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 | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 313 | 320 | 257 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.809 | 0.352 | 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 | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 217 | 215 | 188 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.515 | 0.013 | 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 | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 128 | 126 | 118 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.336 | 0.033 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 26 | 26 | 36 | 26 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.08 | 1.50 | 1.08 | 1.08 |
time (sec) |
N/A | 0.248 | 3.334 | 0.260 | 0.298 | 0.280 | 2.258 | 0.287 | 2.577 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 26 | 41 | 54 | 26 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.71 | 2.25 | 1.08 | 1.08 |
time (sec) |
N/A | 0.448 | 4.911 | 0.283 | 0.283 | 0.269 | 16.142 | 0.278 | 2.735 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 26 | 52 | 71 | 26 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 2.17 | 2.96 | 1.08 | 1.08 |
time (sec) |
N/A | 0.660 | 5.239 | 0.286 | 0.283 | 0.284 | 117.915 | 0.291 | 2.706 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 618 | 442 | 332 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.72 | 0.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.312 | 0.904 | 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(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 390 | 320 | 233 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.82 | 0.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.873 | 0.370 | 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 | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 240 | 215 | 179 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.90 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.530 | 0.049 | 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 | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 161 | 161 | 129 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.337 | 0.044 | 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 | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 268 | 267 | 206 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.600 | 0.161 | 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 | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 402 | 384 | 286 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.900 | 0.273 | 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 | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 102 | 102 | 97 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.273 | 0.026 | 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 | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 283 | 324 | 201 | 329 | 441 | 260 | 388 | 0 | 0 |
N.S. |
1 | 1.14 | 0.71 | 1.16 | 1.56 | 0.92 | 1.37 | 0.00 | 0.00 |
time (sec) |
N/A | 1.488 | 0.197 | 0.166 | 0.230 | 0.268 | 0.921 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 198 | 328 | 186 | 266 | 442 | 240 | 332 | 0 | 0 |
N.S. |
1 | 1.66 | 0.94 | 1.34 | 2.23 | 1.21 | 1.68 | 0.00 | 0.00 |
time (sec) |
N/A | 1.475 | 0.192 | 0.109 | 0.221 | 0.282 | 0.786 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 206 | 236 | 177 | 247 | 346 | 225 | 313 | 0 | 0 |
N.S. |
1 | 1.15 | 0.86 | 1.20 | 1.68 | 1.09 | 1.52 | 0.00 | 0.00 |
time (sec) |
N/A | 1.135 | 0.179 | 0.114 | 0.222 | 0.275 | 0.548 | 0.000 | 0.000 |