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 | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 195 | 170 | 170 | 336 | 170 | 471 | 183 | 294 | 0 |
N.S. |
1 | 1.07 | 0.93 | 0.93 | 1.84 | 0.93 | 2.57 | 1.00 | 1.61 | 0.00 |
time (sec) |
N/A | 0.490 | 1.011 | 0.513 | 0.118 | 0.094 | 0.609 | 0.136 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 160 | 157 | 147 | 193 | 148 | 333 | 158 | 244 | 0 |
N.S. |
1 | 1.09 | 1.07 | 1.00 | 1.31 | 1.01 | 2.27 | 1.07 | 1.66 | 0.00 |
time (sec) |
N/A | 0.435 | 0.603 | 0.406 | 0.111 | 0.085 | 0.581 | 0.138 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 124 | 126 | 122 | 138 | 121 | 226 | 123 | 194 | 0 |
N.S. |
1 | 0.94 | 0.95 | 0.92 | 1.05 | 0.92 | 1.71 | 0.93 | 1.47 | 0.00 |
time (sec) |
N/A | 0.344 | 0.721 | 0.299 | 0.113 | 0.083 | 0.617 | 0.144 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 79 | 94 | 74 | 55 | 79 | 119 | 58 | 87 | 77 |
N.S. |
1 | 1.01 | 1.21 | 0.95 | 0.71 | 1.01 | 1.53 | 0.74 | 1.12 | 0.99 |
time (sec) |
N/A | 0.299 | 0.248 | 0.285 | 0.114 | 0.078 | 0.388 | 0.132 | 0.208 | 9.496 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 91 | 82 | 76 | 91 | 74 | 0 | 71 | 93 | 0 |
N.S. |
1 | 0.92 | 0.83 | 0.77 | 0.92 | 0.75 | 0.00 | 0.72 | 0.94 | 0.00 |
time (sec) |
N/A | 0.352 | 0.428 | 0.372 | 0.114 | 0.078 | 0.000 | 0.139 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 101 | 93 | 111 | 106 | 123 | 0 | 163 | 204 | 0 |
N.S. |
1 | 1.11 | 1.02 | 1.22 | 1.16 | 1.35 | 0.00 | 1.79 | 2.24 | 0.00 |
time (sec) |
N/A | 0.376 | 0.474 | 0.405 | 0.114 | 0.092 | 0.000 | 0.140 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 101 | 92 | 185 | 0 | 168 | 0 | 170 | 193 | 0 |
N.S. |
1 | 0.94 | 0.86 | 1.73 | 0.00 | 1.57 | 0.00 | 1.59 | 1.80 | 0.00 |
time (sec) |
N/A | 0.363 | 0.685 | 0.416 | 0.000 | 0.120 | 0.000 | 0.138 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 59 | 59 | 334 | 175 | 0 | 275 | 98 | 263 |
N.S. |
1 | 1.00 | 0.71 | 0.71 | 4.02 | 2.11 | 0.00 | 3.31 | 1.18 | 3.17 |
time (sec) |
N/A | 0.343 | 0.599 | 0.442 | 0.041 | 0.085 | 0.000 | 0.134 | 0.238 | 10.251 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | C | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 128 | 82 | 85 | 526 | 240 | 0 | 388 | 29 | 589 |
N.S. |
1 | 1.02 | 0.65 | 0.67 | 4.17 | 1.90 | 0.00 | 3.08 | 0.23 | 4.67 |
time (sec) |
N/A | 0.394 | 0.760 | 0.477 | 0.045 | 0.094 | 0.000 | 0.143 | 200.085 | 10.570 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 168 | 106 | 109 | 751 | 297 | 0 | 536 | 475 | 847 |
N.S. |
1 | 1.02 | 0.64 | 0.66 | 4.55 | 1.80 | 0.00 | 3.25 | 2.88 | 5.13 |
time (sec) |
N/A | 0.443 | 0.849 | 0.523 | 0.049 | 0.125 | 0.000 | 0.134 | 0.233 | 10.684 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 210 | 129 | 133 | 1009 | 359 | 0 | 666 | 584 | 1141 |
N.S. |
1 | 1.00 | 0.61 | 0.63 | 4.80 | 1.71 | 0.00 | 3.17 | 2.78 | 5.43 |
time (sec) |
N/A | 0.505 | 1.260 | 0.567 | 0.055 | 0.218 | 0.000 | 0.138 | 0.252 | 10.866 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 225 | 215 | 219 | 417 | 219 | 685 | 241 | 394 | 0 |
N.S. |
1 | 1.01 | 0.96 | 0.98 | 1.87 | 0.98 | 3.07 | 1.08 | 1.77 | 0.00 |
time (sec) |
N/A | 0.525 | 1.307 | 0.474 | 0.118 | 0.084 | 0.966 | 0.149 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 189 | 201 | 195 | 248 | 193 | 534 | 211 | 344 | 0 |
N.S. |
1 | 1.03 | 1.10 | 1.07 | 1.36 | 1.05 | 2.92 | 1.15 | 1.88 | 0.00 |
time (sec) |
N/A | 0.474 | 0.752 | 0.405 | 0.114 | 0.084 | 0.902 | 0.146 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 153 | 170 | 170 | 183 | 166 | 396 | 178 | 294 | 0 |
N.S. |
1 | 0.92 | 1.02 | 1.02 | 1.10 | 0.99 | 2.37 | 1.07 | 1.76 | 0.00 |
time (sec) |
N/A | 0.391 | 0.939 | 0.308 | 0.111 | 0.081 | 0.911 | 0.145 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 108 | 107 | 97 | 76 | 102 | 151 | 85 | 137 | 68 |
N.S. |
1 | 1.05 | 1.04 | 0.94 | 0.74 | 0.99 | 1.47 | 0.83 | 1.33 | 0.66 |
time (sec) |
N/A | 0.322 | 0.446 | 0.295 | 0.110 | 0.095 | 0.469 | 0.142 | 0.206 | 10.290 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 125 | 126 | 123 | 251 | 122 | 296 | 125 | 194 | 0 |
N.S. |
1 | 0.93 | 0.94 | 0.92 | 1.87 | 0.91 | 2.21 | 0.93 | 1.45 | 0.00 |
time (sec) |
N/A | 0.384 | 0.671 | 0.378 | 0.128 | 0.097 | 2.046 | 0.136 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 135 | 112 | 99 | 230 | 101 | 0 | 278 | 144 | 0 |
N.S. |
1 | 1.02 | 0.84 | 0.74 | 1.73 | 0.76 | 0.00 | 2.09 | 1.08 | 0.00 |
time (sec) |
N/A | 0.420 | 0.493 | 0.403 | 0.122 | 0.085 | 0.000 | 0.149 | 0.265 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 137 | 109 | 153 | 224 | 158 | 0 | 127 | 290 | 0 |
N.S. |
1 | 1.15 | 0.92 | 1.29 | 1.88 | 1.33 | 0.00 | 1.07 | 2.44 | 0.00 |
time (sec) |
N/A | 0.438 | 0.587 | 0.429 | 0.121 | 0.088 | 0.000 | 0.143 | 0.254 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 138 | 116 | 215 | 313 | 206 | 0 | 194 | 382 | 0 |
N.S. |
1 | 1.05 | 0.88 | 1.63 | 2.37 | 1.56 | 0.00 | 1.47 | 2.89 | 0.00 |
time (sec) |
N/A | 0.422 | 0.661 | 0.460 | 0.129 | 0.094 | 0.000 | 0.141 | 0.287 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 130 | 105 | 346 | 471 | 242 | 0 | 0 | 436 | 0 |
N.S. |
1 | 1.02 | 0.83 | 2.72 | 3.71 | 1.91 | 0.00 | 0.00 | 3.43 | 0.00 |
time (sec) |
N/A | 0.444 | 0.835 | 0.478 | 0.121 | 0.099 | 0.000 | 0.000 | 0.274 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 61 | 59 | 672 | 232 | 0 | 405 | 29 | 397 |
N.S. |
1 | 1.00 | 0.73 | 0.71 | 8.10 | 2.80 | 0.00 | 4.88 | 0.35 | 4.78 |
time (sec) |
N/A | 0.342 | 0.756 | 0.531 | 0.050 | 0.097 | 0.000 | 0.144 | 200.093 | 10.269 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 128 | 84 | 85 | 919 | 299 | 0 | 536 | 452 | 633 |
N.S. |
1 | 1.02 | 0.67 | 0.67 | 7.29 | 2.37 | 0.00 | 4.25 | 3.59 | 5.02 |
time (sec) |
N/A | 0.405 | 0.945 | 0.625 | 0.057 | 0.126 | 0.000 | 0.150 | 0.310 | 11.082 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 169 | 109 | 109 | 1199 | 359 | 0 | 666 | 584 | 912 |
N.S. |
1 | 1.01 | 0.65 | 0.65 | 7.14 | 2.14 | 0.00 | 3.96 | 3.48 | 5.43 |
time (sec) |
N/A | 0.454 | 1.075 | 0.645 | 0.063 | 0.217 | 0.000 | 0.151 | 0.224 | 11.440 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 210 | 131 | 133 | 1512 | 418 | 0 | 796 | 693 | 1237 |
N.S. |
1 | 1.00 | 0.62 | 0.63 | 7.20 | 1.99 | 0.00 | 3.79 | 3.30 | 5.89 |
time (sec) |
N/A | 0.515 | 1.572 | 0.737 | 0.068 | 0.288 | 0.000 | 0.151 | 0.225 | 11.972 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 259 | 254 | 260 | 267 | 498 | 268 | 926 | 296 | 494 | 0 |
N.S. |
1 | 0.98 | 1.00 | 1.03 | 1.92 | 1.03 | 3.58 | 1.14 | 1.91 | 0.00 |
time (sec) |
N/A | 0.566 | 1.584 | 0.510 | 0.125 | 0.087 | 0.799 | 0.151 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 218 | 246 | 243 | 303 | 244 | 762 | 268 | 444 | 0 |
N.S. |
1 | 1.00 | 1.12 | 1.11 | 1.38 | 1.11 | 3.48 | 1.22 | 2.03 | 0.00 |
time (sec) |
N/A | 0.493 | 0.893 | 0.425 | 0.122 | 0.091 | 0.742 | 0.149 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 182 | 214 | 218 | 228 | 214 | 632 | 232 | 394 | 0 |
N.S. |
1 | 0.90 | 1.06 | 1.08 | 1.13 | 1.06 | 3.13 | 1.15 | 1.95 | 0.00 |
time (sec) |
N/A | 0.429 | 1.188 | 0.322 | 0.119 | 0.095 | 0.761 | 0.146 | 0.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 137 | 119 | 120 | 97 | 127 | 182 | 111 | 187 | 68 |
N.S. |
1 | 1.07 | 0.93 | 0.94 | 0.76 | 0.99 | 1.42 | 0.87 | 1.46 | 0.53 |
time (sec) |
N/A | 0.366 | 0.558 | 0.292 | 0.112 | 0.091 | 0.503 | 0.146 | 0.211 | 9.148 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 154 | 170 | 171 | 297 | 168 | 672 | 181 | 294 | 0 |
N.S. |
1 | 0.91 | 1.01 | 1.01 | 1.76 | 0.99 | 3.98 | 1.07 | 1.74 | 0.00 |
time (sec) |
N/A | 0.426 | 0.918 | 0.382 | 0.137 | 0.086 | 2.392 | 0.151 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 168 | 157 | 147 | 297 | 148 | 481 | 409 | 244 | 0 |
N.S. |
1 | 0.98 | 0.92 | 0.86 | 1.74 | 0.87 | 2.81 | 2.39 | 1.43 | 0.00 |
time (sec) |
N/A | 0.465 | 0.613 | 0.405 | 0.132 | 0.090 | 3.020 | 0.187 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 170 | 127 | 123 | 350 | 124 | 0 | 129 | 194 | 0 |
N.S. |
1 | 1.09 | 0.81 | 0.79 | 2.24 | 0.79 | 0.00 | 0.83 | 1.24 | 0.00 |
time (sec) |
N/A | 0.481 | 0.725 | 0.431 | 0.119 | 0.084 | 0.000 | 0.161 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 164 | 143 | 176 | 379 | 185 | 0 | 154 | 370 | 0 |
N.S. |
1 | 0.96 | 0.84 | 1.04 | 2.23 | 1.09 | 0.00 | 0.91 | 2.18 | 0.00 |
time (sec) |
N/A | 0.471 | 0.682 | 0.486 | 0.134 | 0.087 | 0.000 | 0.155 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 167 | 133 | 258 | 503 | 242 | 0 | 344 | 491 | 0 |
N.S. |
1 | 1.04 | 0.83 | 1.60 | 3.12 | 1.50 | 0.00 | 2.14 | 3.05 | 0.00 |
time (sec) |
N/A | 0.604 | 0.796 | 0.556 | 0.134 | 0.085 | 0.000 | 0.185 | 0.254 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 173 | 141 | 372 | 718 | 288 | 0 | 354 | 727 | 0 |
N.S. |
1 | 1.02 | 0.83 | 2.20 | 4.25 | 1.70 | 0.00 | 2.09 | 4.30 | 0.00 |
time (sec) |
N/A | 0.481 | 0.860 | 0.660 | 0.137 | 0.114 | 0.000 | 0.164 | 0.352 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 161 | 117 | 506 | 934 | 312 | 0 | 367 | 29 | 0 |
N.S. |
1 | 1.01 | 0.74 | 3.18 | 5.87 | 1.96 | 0.00 | 2.31 | 0.18 | 0.00 |
time (sec) |
N/A | 0.459 | 1.072 | 0.790 | 0.142 | 0.101 | 0.000 | 0.166 | 200.045 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 61 | 59 | 1137 | 289 | 0 | 535 | 471 | 551 |
N.S. |
1 | 1.00 | 0.73 | 0.71 | 13.70 | 3.48 | 0.00 | 6.45 | 5.67 | 6.64 |
time (sec) |
N/A | 0.346 | 0.949 | 1.040 | 0.063 | 0.146 | 0.000 | 0.162 | 0.285 | 11.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 128 | 84 | 85 | 1439 | 358 | 0 | 666 | 574 | 808 |
N.S. |
1 | 1.02 | 0.67 | 0.67 | 11.42 | 2.84 | 0.00 | 5.29 | 4.56 | 6.41 |
time (sec) |
N/A | 0.398 | 1.273 | 1.464 | 0.067 | 0.190 | 0.000 | 0.165 | 0.232 | 11.637 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 169 | 109 | 109 | 1774 | 418 | 0 | 796 | 693 | 1112 |
N.S. |
1 | 1.01 | 0.65 | 0.65 | 10.56 | 2.49 | 0.00 | 4.74 | 4.12 | 6.62 |
time (sec) |
N/A | 0.452 | 1.269 | 1.949 | 0.078 | 0.294 | 0.000 | 0.170 | 0.222 | 12.813 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 210 | 131 | 133 | 2142 | 476 | 0 | 926 | 802 | 1457 |
N.S. |
1 | 1.00 | 0.62 | 0.63 | 10.20 | 2.27 | 0.00 | 4.41 | 3.82 | 6.94 |
time (sec) |
N/A | 0.506 | 2.122 | 2.728 | 0.080 | 0.634 | 0.000 | 0.153 | 0.244 | 13.905 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 165 | 128 | 123 | 254 | 123 | 287 | 128 | 194 | 0 |
N.S. |
1 | 1.10 | 0.85 | 0.82 | 1.69 | 0.82 | 1.91 | 0.85 | 1.29 | 0.00 |
time (sec) |
N/A | 0.461 | 0.770 | 0.480 | 0.119 | 0.084 | 0.607 | 0.150 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 129 | 104 | 99 | 137 | 99 | 202 | 97 | 144 | 0 |
N.S. |
1 | 1.17 | 0.95 | 0.90 | 1.25 | 0.90 | 1.84 | 0.88 | 1.31 | 0.00 |
time (sec) |
N/A | 0.397 | 0.638 | 0.415 | 0.109 | 0.089 | 0.588 | 0.153 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 90 | 81 | 75 | 92 | 74 | 136 | 70 | 93 | 166 |
N.S. |
1 | 1.22 | 1.09 | 1.01 | 1.24 | 1.00 | 1.84 | 0.95 | 1.26 | 2.24 |
time (sec) |
N/A | 0.331 | 0.473 | 0.311 | 0.109 | 0.080 | 0.604 | 0.157 | 0.220 | 10.273 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 61 | 51 | 33 | 53 | 97 | 38 | 31 | 55 |
N.S. |
1 | 1.00 | 1.27 | 1.06 | 0.69 | 1.10 | 2.02 | 0.79 | 0.65 | 1.15 |
time (sec) |
N/A | 0.271 | 0.244 | 0.286 | 0.110 | 0.085 | 0.361 | 0.146 | 0.201 | 9.595 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 77 | 87 | 73 | 104 | 0 | 73 | 80 | 0 |
N.S. |
1 | 1.00 | 1.20 | 1.36 | 1.14 | 1.62 | 0.00 | 1.14 | 1.25 | 0.00 |
time (sec) |
N/A | 0.304 | 0.446 | 0.372 | 0.115 | 0.082 | 0.000 | 0.140 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 53 | 53 | 190 | 117 | 0 | 145 | 88 | 52 |
N.S. |
1 | 1.00 | 0.64 | 0.64 | 2.29 | 1.41 | 0.00 | 1.75 | 1.06 | 0.63 |
time (sec) |
N/A | 0.334 | 0.471 | 0.396 | 0.120 | 0.106 | 0.000 | 0.143 | 0.203 | 8.830 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 128 | 76 | 79 | 349 | 181 | 0 | 276 | 179 | 78 |
N.S. |
1 | 1.07 | 0.63 | 0.66 | 2.91 | 1.51 | 0.00 | 2.30 | 1.49 | 0.65 |
time (sec) |
N/A | 0.390 | 0.605 | 0.421 | 0.122 | 0.094 | 0.000 | 0.147 | 0.201 | 9.154 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 169 | 101 | 103 | 541 | 241 | 0 | 406 | 134 | 153 |
N.S. |
1 | 1.04 | 0.62 | 0.64 | 3.34 | 1.49 | 0.00 | 2.51 | 0.83 | 0.94 |
time (sec) |
N/A | 0.459 | 0.783 | 0.450 | 0.119 | 0.110 | 0.000 | 0.153 | 0.273 | 9.294 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 132 | 110 | 155 | 253 | 159 | 0 | 125 | 290 | 0 |
N.S. |
1 | 1.18 | 0.98 | 1.38 | 2.26 | 1.42 | 0.00 | 1.12 | 2.59 | 0.00 |
time (sec) |
N/A | 0.566 | 0.618 | 0.496 | 0.112 | 0.093 | 0.000 | 0.153 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 94 | 93 | 113 | 135 | 126 | 0 | 96 | 202 | 0 |
N.S. |
1 | 1.07 | 1.06 | 1.28 | 1.53 | 1.43 | 0.00 | 1.09 | 2.30 | 0.00 |
time (sec) |
N/A | 0.364 | 0.453 | 0.403 | 0.112 | 0.105 | 0.000 | 0.146 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 77 | 102 | 93 | 105 | 206 | 73 | 81 | 106 |
N.S. |
1 | 1.00 | 1.24 | 1.65 | 1.50 | 1.69 | 3.32 | 1.18 | 1.31 | 1.71 |
time (sec) |
N/A | 0.314 | 0.438 | 0.296 | 0.119 | 0.089 | 4.638 | 0.151 | 0.209 | 9.793 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 35 | 34 | 40 | 66 | 87 | 43 | 34 | 27 |
N.S. |
1 | 1.00 | 1.00 | 0.97 | 1.14 | 1.89 | 2.49 | 1.23 | 0.97 | 0.77 |
time (sec) |
N/A | 0.265 | 0.330 | 0.285 | 0.028 | 0.077 | 3.138 | 0.140 | 0.209 | 9.147 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 82 | 77 | 139 | 173 | 0 | 0 | 150 | 83 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.81 | 2.25 | 0.00 | 0.00 | 1.95 | 1.08 |
time (sec) |
N/A | 0.347 | 0.470 | 0.394 | 0.038 | 0.102 | 0.000 | 0.000 | 0.220 | 9.173 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 119 | 106 | 109 | 333 | 202 | 0 | 321 | 240 | 109 |
N.S. |
1 | 0.99 | 0.88 | 0.91 | 2.78 | 1.68 | 0.00 | 2.68 | 2.00 | 0.91 |
time (sec) |
N/A | 0.368 | 0.594 | 0.398 | 0.042 | 0.096 | 0.000 | 0.157 | 0.243 | 9.821 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 160 | 128 | 132 | 604 | 294 | 0 | 0 | 325 | 244 |
N.S. |
1 | 1.03 | 0.82 | 0.85 | 3.87 | 1.88 | 0.00 | 0.00 | 2.08 | 1.56 |
time (sec) |
N/A | 0.436 | 0.803 | 0.422 | 0.046 | 0.191 | 0.000 | 0.000 | 0.233 | 9.987 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 164 | 133 | 266 | 594 | 240 | 0 | 259 | 492 | 0 |
N.S. |
1 | 1.07 | 0.87 | 1.74 | 3.88 | 1.57 | 0.00 | 1.69 | 3.22 | 0.00 |
time (sec) |
N/A | 0.567 | 0.816 | 0.735 | 0.124 | 0.092 | 0.000 | 0.160 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 133 | 118 | 223 | 405 | 203 | 0 | 191 | 383 | 0 |
N.S. |
1 | 1.06 | 0.94 | 1.77 | 3.21 | 1.61 | 0.00 | 1.52 | 3.04 | 0.00 |
time (sec) |
N/A | 0.437 | 0.676 | 0.553 | 0.120 | 0.105 | 0.000 | 0.158 | 0.279 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 99 | 91 | 300 | 308 | 172 | 0 | 170 | 193 | 0 |
N.S. |
1 | 0.97 | 0.89 | 2.94 | 3.02 | 1.69 | 0.00 | 1.67 | 1.89 | 0.00 |
time (sec) |
N/A | 0.353 | 0.668 | 0.441 | 0.121 | 0.098 | 0.000 | 0.164 | 0.254 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 54 | 56 | 168 | 119 | 0 | 145 | 88 | 53 |
N.S. |
1 | 1.00 | 0.67 | 0.69 | 2.07 | 1.47 | 0.00 | 1.79 | 1.09 | 0.65 |
time (sec) |
N/A | 0.321 | 0.459 | 0.393 | 0.031 | 0.082 | 0.000 | 0.153 | 0.254 | 10.004 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | C | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 81 | 82 | 129 | 169 | 481 | 0 | 152 | 83 |
N.S. |
1 | 1.00 | 1.09 | 1.11 | 1.74 | 2.28 | 6.50 | 0.00 | 2.05 | 1.12 |
time (sec) |
N/A | 0.302 | 0.463 | 0.302 | 0.035 | 0.090 | 5.196 | 0.000 | 0.209 | 9.783 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 66 | 48 | 63 | 102 | 296 | 59 | 62 | 47 |
N.S. |
1 | 1.00 | 1.03 | 0.75 | 0.98 | 1.59 | 4.62 | 0.92 | 0.97 | 0.73 |
time (sec) |
N/A | 0.280 | 0.401 | 0.287 | 0.033 | 0.109 | 4.089 | 0.170 | 0.229 | 10.329 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 109 | 130 | 126 | 184 | 290 | 0 | 0 | 325 | 134 |
N.S. |
1 | 0.97 | 1.16 | 1.12 | 1.64 | 2.59 | 0.00 | 0.00 | 2.90 | 1.20 |
time (sec) |
N/A | 0.339 | 0.627 | 0.385 | 0.046 | 0.110 | 0.000 | 0.000 | 0.214 | 10.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 151 | 153 | 157 | 378 | 360 | 0 | 427 | 350 | 275 |
N.S. |
1 | 0.97 | 0.98 | 1.01 | 2.42 | 2.31 | 0.00 | 2.74 | 2.24 | 1.76 |
time (sec) |
N/A | 0.413 | 0.697 | 0.405 | 0.045 | 0.147 | 0.000 | 0.173 | 0.219 | 10.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 191 | 172 | 181 | 649 | 399 | 0 | 0 | 494 | 366 |
N.S. |
1 | 1.02 | 0.91 | 0.96 | 3.45 | 2.12 | 0.00 | 0.00 | 2.63 | 1.95 |
time (sec) |
N/A | 0.462 | 1.039 | 0.424 | 0.049 | 0.277 | 0.000 | 0.000 | 0.219 | 10.818 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 192 | 117 | 115 | 150 | 144 | 0 | 492 | 118 | 170 |
N.S. |
1 | 0.94 | 0.57 | 0.56 | 0.73 | 0.70 | 0.00 | 2.40 | 0.58 | 0.83 |
time (sec) |
N/A | 0.484 | 0.299 | 0.428 | 0.059 | 0.079 | 0.000 | 0.120 | 0.195 | 10.363 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 153 | 94 | 91 | 128 | 119 | 0 | 404 | 94 | 143 |
N.S. |
1 | 0.97 | 0.59 | 0.58 | 0.81 | 0.75 | 0.00 | 2.56 | 0.59 | 0.91 |
time (sec) |
N/A | 0.430 | 0.248 | 0.418 | 0.057 | 0.085 | 0.000 | 0.125 | 0.210 | 9.741 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 115 | 72 | 67 | 106 | 96 | 0 | 164 | 70 | 116 |
N.S. |
1 | 1.00 | 0.63 | 0.58 | 0.92 | 0.83 | 0.00 | 1.43 | 0.61 | 1.01 |
time (sec) |
N/A | 0.375 | 0.207 | 0.370 | 0.049 | 0.083 | 0.000 | 0.125 | 0.213 | 9.778 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 55 | 47 | 55 | 71 | 0 | 52 | 46 | 64 |
N.S. |
1 | 1.00 | 0.74 | 0.64 | 0.74 | 0.96 | 0.00 | 0.70 | 0.62 | 0.86 |
time (sec) |
N/A | 0.324 | 0.183 | 0.352 | 0.045 | 0.079 | 0.000 | 0.120 | 0.217 | 9.554 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 130 | 104 | 126 | 0 | 281 | 0 | 80 | 111 | 0 |
N.S. |
1 | 0.98 | 0.79 | 0.95 | 0.00 | 2.13 | 0.00 | 0.61 | 0.84 | 0.00 |
time (sec) |
N/A | 0.416 | 0.491 | 0.368 | 0.000 | 0.095 | 0.000 | 0.123 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 146 | 107 | 169 | 0 | 369 | 0 | 87 | 212 | 0 |
N.S. |
1 | 1.12 | 0.82 | 1.30 | 0.00 | 2.84 | 0.00 | 0.67 | 1.63 | 0.00 |
time (sec) |
N/A | 0.438 | 0.438 | 0.375 | 0.000 | 0.096 | 0.000 | 0.121 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 144 | 119 | 268 | 0 | 461 | 0 | 109 | 276 | 0 |
N.S. |
1 | 0.98 | 0.81 | 1.82 | 0.00 | 3.14 | 0.00 | 0.74 | 1.88 | 0.00 |
time (sec) |
N/A | 0.448 | 0.523 | 0.357 | 0.000 | 0.104 | 0.000 | 0.122 | 0.427 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 189 | 142 | 374 | 0 | 579 | 0 | 157 | 397 | 0 |
N.S. |
1 | 0.99 | 0.75 | 1.97 | 0.00 | 3.05 | 0.00 | 0.83 | 2.09 | 0.00 |
time (sec) |
N/A | 0.504 | 0.653 | 0.353 | 0.000 | 0.107 | 0.000 | 0.119 | 0.257 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 236 | 233 | 166 | 478 | 0 | 709 | 0 | 205 | 518 | 0 |
N.S. |
1 | 0.99 | 0.70 | 2.03 | 0.00 | 3.00 | 0.00 | 0.87 | 2.19 | 0.00 |
time (sec) |
N/A | 0.579 | 0.690 | 0.378 | 0.000 | 0.111 | 0.000 | 0.141 | 0.367 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 192 | 119 | 115 | 172 | 167 | 0 | 870 | 142 | 191 |
N.S. |
1 | 0.94 | 0.58 | 0.56 | 0.84 | 0.81 | 0.00 | 4.24 | 0.69 | 0.93 |
time (sec) |
N/A | 0.480 | 1.021 | 0.414 | 0.062 | 0.086 | 0.000 | 0.120 | 0.214 | 9.642 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 153 | 96 | 91 | 150 | 143 | 0 | 375 | 118 | 171 |
N.S. |
1 | 0.97 | 0.61 | 0.58 | 0.95 | 0.91 | 0.00 | 2.37 | 0.75 | 1.08 |
time (sec) |
N/A | 0.429 | 0.678 | 0.426 | 0.058 | 0.083 | 0.000 | 0.112 | 0.221 | 9.457 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 115 | 74 | 67 | 100 | 118 | 0 | 192 | 94 | 107 |
N.S. |
1 | 1.00 | 0.64 | 0.58 | 0.87 | 1.03 | 0.00 | 1.67 | 0.82 | 0.93 |
time (sec) |
N/A | 0.375 | 0.654 | 0.410 | 0.047 | 0.084 | 0.000 | 0.122 | 0.282 | 9.667 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 55 | 47 | 74 | 94 | 0 | 144 | 70 | 88 |
N.S. |
1 | 1.00 | 0.73 | 0.63 | 0.99 | 1.25 | 0.00 | 1.92 | 0.93 | 1.17 |
time (sec) |
N/A | 0.332 | 0.673 | 0.382 | 0.046 | 0.084 | 0.000 | 0.124 | 0.244 | 9.958 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 166 | 125 | 162 | 0 | 335 | 0 | 119 | 152 | 0 |
N.S. |
1 | 0.96 | 0.72 | 0.94 | 0.00 | 1.94 | 0.00 | 0.69 | 0.88 | 0.00 |
time (sec) |
N/A | 0.463 | 1.113 | 0.365 | 0.000 | 0.107 | 0.000 | 0.122 | 0.284 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 182 | 126 | 183 | 0 | 399 | 0 | 118 | 241 | 0 |
N.S. |
1 | 1.07 | 0.74 | 1.08 | 0.00 | 2.35 | 0.00 | 0.69 | 1.42 | 0.00 |
time (sec) |
N/A | 0.506 | 1.232 | 0.384 | 0.000 | 0.100 | 0.000 | 0.125 | 0.263 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 181 | 125 | 192 | 0 | 487 | 0 | 116 | 365 | 0 |
N.S. |
1 | 1.03 | 0.71 | 1.09 | 0.00 | 2.77 | 0.00 | 0.66 | 2.07 | 0.00 |
time (sec) |
N/A | 0.501 | 1.354 | 0.390 | 0.000 | 0.096 | 0.000 | 0.136 | 0.796 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 181 | 142 | 374 | 0 | 581 | 0 | 157 | 397 | 0 |
N.S. |
1 | 0.96 | 0.76 | 1.99 | 0.00 | 3.09 | 0.00 | 0.84 | 2.11 | 0.00 |
time (sec) |
N/A | 0.501 | 1.717 | 0.365 | 0.000 | 0.103 | 0.000 | 0.128 | 0.292 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 227 | 166 | 478 | 0 | 705 | 0 | 205 | 518 | 0 |
N.S. |
1 | 0.97 | 0.71 | 2.05 | 0.00 | 3.03 | 0.00 | 0.88 | 2.22 | 0.00 |
time (sec) |
N/A | 0.551 | 2.348 | 0.369 | 0.000 | 0.113 | 0.000 | 0.135 | 0.504 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 191 | 118 | 115 | 194 | 192 | 0 | 674 | 166 | 217 |
N.S. |
1 | 0.95 | 0.59 | 0.57 | 0.97 | 0.96 | 0.00 | 3.35 | 0.83 | 1.08 |
time (sec) |
N/A | 0.498 | 0.778 | 0.408 | 0.060 | 0.089 | 0.000 | 0.128 | 0.241 | 10.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 153 | 96 | 91 | 144 | 165 | 0 | 422 | 142 | 144 |
N.S. |
1 | 0.97 | 0.61 | 0.58 | 0.91 | 1.04 | 0.00 | 2.67 | 0.90 | 0.91 |
time (sec) |
N/A | 0.431 | 0.706 | 0.407 | 0.050 | 0.082 | 0.000 | 0.137 | 0.230 | 9.862 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 116 | 75 | 67 | 122 | 144 | 0 | 471 | 118 | 125 |
N.S. |
1 | 0.99 | 0.64 | 0.57 | 1.04 | 1.23 | 0.00 | 4.03 | 1.01 | 1.07 |
time (sec) |
N/A | 0.390 | 0.742 | 0.409 | 0.048 | 0.082 | 0.000 | 0.132 | 0.250 | 9.890 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 55 | 47 | 99 | 119 | 0 | 286 | 94 | 106 |
N.S. |
1 | 1.00 | 0.73 | 0.63 | 1.32 | 1.59 | 0.00 | 3.81 | 1.25 | 1.41 |
time (sec) |
N/A | 0.351 | 0.772 | 0.385 | 0.046 | 0.077 | 0.000 | 0.128 | 0.231 | 9.784 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 202 | 147 | 195 | 0 | 387 | 0 | 166 | 194 | 0 |
N.S. |
1 | 0.94 | 0.68 | 0.90 | 0.00 | 1.79 | 0.00 | 0.77 | 0.90 | 0.00 |
time (sec) |
N/A | 0.530 | 1.312 | 0.371 | 0.000 | 0.153 | 0.000 | 0.126 | 0.265 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 213 | 218 | 147 | 206 | 0 | 458 | 0 | 158 | 289 | 0 |
N.S. |
1 | 1.02 | 0.69 | 0.97 | 0.00 | 2.15 | 0.00 | 0.74 | 1.36 | 0.00 |
time (sec) |
N/A | 0.554 | 1.326 | 0.388 | 0.000 | 0.107 | 0.000 | 0.131 | 0.299 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 217 | 149 | 206 | 0 | 518 | 0 | 148 | 394 | 0 |
N.S. |
1 | 0.99 | 0.68 | 0.94 | 0.00 | 2.37 | 0.00 | 0.68 | 1.80 | 0.00 |
time (sec) |
N/A | 0.565 | 1.690 | 0.389 | 0.000 | 0.111 | 0.000 | 0.151 | 1.098 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 218 | 149 | 215 | 0 | 607 | 0 | 163 | 518 | 0 |
N.S. |
1 | 1.00 | 0.69 | 0.99 | 0.00 | 2.80 | 0.00 | 0.75 | 2.39 | 0.00 |
time (sec) |
N/A | 0.555 | 2.243 | 0.389 | 0.000 | 0.116 | 0.000 | 0.130 | 0.288 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 218 | 165 | 478 | 0 | 695 | 0 | 204 | 518 | 0 |
N.S. |
1 | 0.95 | 0.72 | 2.09 | 0.00 | 3.03 | 0.00 | 0.89 | 2.26 | 0.00 |
time (sec) |
N/A | 0.569 | 2.616 | 0.370 | 0.000 | 0.112 | 0.000 | 0.144 | 0.396 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 274 | 264 | 188 | 582 | 0 | 827 | 0 | 252 | 639 | 0 |
N.S. |
1 | 0.96 | 0.69 | 2.12 | 0.00 | 3.02 | 0.00 | 0.92 | 2.33 | 0.00 |
time (sec) |
N/A | 0.614 | 4.226 | 0.371 | 0.000 | 0.130 | 0.000 | 0.142 | 0.382 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 318 | 307 | 210 | 686 | 0 | 945 | 0 | 299 | 760 | 0 |
N.S. |
1 | 0.97 | 0.66 | 2.16 | 0.00 | 2.97 | 0.00 | 0.94 | 2.39 | 0.00 |
time (sec) |
N/A | 0.696 | 4.304 | 0.377 | 0.000 | 0.159 | 0.000 | 0.136 | 0.413 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 154 | 89 | 85 | 100 | 95 | 0 | 124 | 70 | 117 |
N.S. |
1 | 0.96 | 0.55 | 0.53 | 0.62 | 0.59 | 0.00 | 0.77 | 0.43 | 0.73 |
time (sec) |
N/A | 0.439 | 0.264 | 0.447 | 0.046 | 0.088 | 0.000 | 0.121 | 0.215 | 9.753 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 116 | 65 | 61 | 76 | 71 | 0 | 77 | 46 | 91 |
N.S. |
1 | 0.99 | 0.56 | 0.52 | 0.65 | 0.61 | 0.00 | 0.66 | 0.39 | 0.78 |
time (sec) |
N/A | 0.377 | 0.221 | 0.374 | 0.048 | 0.089 | 0.000 | 0.115 | 0.232 | 9.803 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 45 | 40 | 53 | 49 | 0 | 40 | 26 | 61 |
N.S. |
1 | 1.00 | 0.61 | 0.54 | 0.72 | 0.66 | 0.00 | 0.54 | 0.35 | 0.82 |
time (sec) |
N/A | 0.314 | 0.180 | 0.349 | 0.045 | 0.077 | 0.000 | 0.127 | 0.240 | 9.640 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 89 | 99 | 0 | 263 | 0 | 53 | 108 | 0 |
N.S. |
1 | 1.00 | 0.98 | 1.09 | 0.00 | 2.89 | 0.00 | 0.58 | 1.19 | 0.00 |
time (sec) |
N/A | 0.362 | 0.351 | 0.366 | 0.000 | 0.087 | 0.000 | 0.130 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 106 | 105 | 170 | 0 | 353 | 0 | 81 | 235 | 0 |
N.S. |
1 | 1.00 | 0.99 | 1.60 | 0.00 | 3.33 | 0.00 | 0.76 | 2.22 | 0.00 |
time (sec) |
N/A | 0.376 | 0.455 | 0.365 | 0.000 | 0.092 | 0.000 | 0.118 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 153 | 119 | 270 | 0 | 467 | 0 | 110 | 402 | 0 |
N.S. |
1 | 1.01 | 0.79 | 1.79 | 0.00 | 3.09 | 0.00 | 0.73 | 2.66 | 0.00 |
time (sec) |
N/A | 0.429 | 0.532 | 0.362 | 0.000 | 0.117 | 0.000 | 0.130 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 196 | 143 | 374 | 0 | 591 | 0 | 158 | 573 | 0 |
N.S. |
1 | 1.01 | 0.73 | 1.92 | 0.00 | 3.03 | 0.00 | 0.81 | 2.94 | 0.00 |
time (sec) |
N/A | 0.492 | 0.625 | 0.365 | 0.000 | 0.113 | 0.000 | 0.121 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 163 | 96 | 91 | 77 | 99 | 0 | 120 | 72 | 124 |
N.S. |
1 | 1.06 | 0.62 | 0.59 | 0.50 | 0.64 | 0.00 | 0.78 | 0.47 | 0.81 |
time (sec) |
N/A | 0.430 | 1.008 | 0.381 | 0.049 | 0.088 | 0.000 | 0.120 | 0.229 | 10.157 |