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 | C | A | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 175 | 183 | 62 | 157 | 0 | 1220 | 0 | 1336 | 0 |
N.S. |
1 | 1.05 | 0.35 | 0.90 | 0.00 | 6.97 | 0.00 | 7.63 | 0.00 |
time (sec) |
N/A | 0.327 | 10.045 | 2.781 | 0.000 | 3.037 | 0.000 | 0.359 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 92 | 79 | 0 | 251 | 656 | 128 | 241 |
N.S. |
1 | 1.00 | 0.94 | 0.81 | 0.00 | 2.56 | 6.69 | 1.31 | 2.46 |
time (sec) |
N/A | 0.246 | 3.129 | 2.349 | 0.000 | 0.437 | 0.358 | 0.264 | 10.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 207 | 204 | 221 | 294 | 0 | 677 | 3067 | 389 | 0 |
N.S. |
1 | 0.99 | 1.07 | 1.42 | 0.00 | 3.27 | 14.82 | 1.88 | 0.00 |
time (sec) |
N/A | 0.360 | 3.247 | 2.620 | 0.000 | 0.444 | 1.008 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 44 | 41 | 0 | 149 | 371 | 58 | 58 |
N.S. |
1 | 1.00 | 0.75 | 0.69 | 0.00 | 2.53 | 6.29 | 0.98 | 0.98 |
time (sec) |
N/A | 0.197 | 1.841 | 2.324 | 0.000 | 0.659 | 0.226 | 0.348 | 10.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 165 | 165 | 153 | 193 | 0 | 473 | 1042 | 257 | 0 |
N.S. |
1 | 1.00 | 0.93 | 1.17 | 0.00 | 2.87 | 6.32 | 1.56 | 0.00 |
time (sec) |
N/A | 0.306 | 1.967 | 2.673 | 0.000 | 0.297 | 0.744 | 0.374 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 18 | 16 | 15 | 55 | 146 | 15 | 15 |
N.S. |
1 | 1.00 | 0.95 | 0.84 | 0.79 | 2.89 | 7.68 | 0.79 | 0.79 |
time (sec) |
N/A | 0.150 | 0.039 | 2.859 | 0.192 | 0.264 | 0.142 | 0.463 | 9.658 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 120 | 124 | 119 | 0 | 246 | 0 | 149 | 0 |
N.S. |
1 | 1.04 | 1.08 | 1.03 | 0.00 | 2.14 | 0.00 | 1.30 | 0.00 |
time (sec) |
N/A | 0.271 | 1.191 | 2.329 | 0.000 | 0.312 | 0.000 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 113 | 118 | 244 | 179 | 0 | 281 | 0 | 440 | 0 |
N.S. |
1 | 1.04 | 2.16 | 1.58 | 0.00 | 2.49 | 0.00 | 3.89 | 0.00 |
time (sec) |
N/A | 0.237 | 1.823 | 2.435 | 0.000 | 0.321 | 0.000 | 0.393 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 120 | 62 | 114 | 0 | 320 | 0 | 378 | 0 |
N.S. |
1 | 1.04 | 0.54 | 0.99 | 0.00 | 2.78 | 0.00 | 3.29 | 0.00 |
time (sec) |
N/A | 0.264 | 10.047 | 2.480 | 0.000 | 0.358 | 0.000 | 0.296 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 107 | 112 | 95 | 311 | 0 | 345 | 0 | 431 | 0 |
N.S. |
1 | 1.05 | 0.89 | 2.91 | 0.00 | 3.22 | 0.00 | 4.03 | 0.00 |
time (sec) |
N/A | 0.249 | 10.084 | 2.689 | 0.000 | 0.489 | 0.000 | 0.365 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 123 | 128 | 162 | 124 | 0 | 622 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.32 | 1.01 | 0.00 | 5.06 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.264 | 10.426 | 2.583 | 0.000 | 0.697 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 38 | 38 | 0 | 183 | 0 | 588 | 1156 |
N.S. |
1 | 1.00 | 0.97 | 0.97 | 0.00 | 4.69 | 0.00 | 15.08 | 29.64 |
time (sec) |
N/A | 0.171 | 10.043 | 3.246 | 0.000 | 1.383 | 0.000 | 0.376 | 10.700 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 165 | 169 | 62 | 157 | 0 | 1064 | 0 | 1312 | 0 |
N.S. |
1 | 1.02 | 0.38 | 0.95 | 0.00 | 6.45 | 0.00 | 7.95 | 0.00 |
time (sec) |
N/A | 0.330 | 10.059 | 2.752 | 0.000 | 3.341 | 0.000 | 0.398 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 62 | 70 | 0 | 398 | 0 | 997 | 1814 |
N.S. |
1 | 1.00 | 0.78 | 0.89 | 0.00 | 5.04 | 0.00 | 12.62 | 22.96 |
time (sec) |
N/A | 0.218 | 10.042 | 3.731 | 0.000 | 5.594 | 0.000 | 0.438 | 11.595 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 207 | 220 | 62 | 194 | 0 | 1646 | 0 | 2225 | 0 |
N.S. |
1 | 1.06 | 0.30 | 0.94 | 0.00 | 7.95 | 0.00 | 10.75 | 0.00 |
time (sec) |
N/A | 0.394 | 10.054 | 2.726 | 0.000 | 9.366 | 0.000 | 0.528 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 118 | 130 | 110 | 133 | 0 | 676 | 0 | 1387 | 3111 |
N.S. |
1 | 1.10 | 0.93 | 1.13 | 0.00 | 5.73 | 0.00 | 11.75 | 26.36 |
time (sec) |
N/A | 0.263 | 10.048 | 5.374 | 0.000 | 15.293 | 0.000 | 0.673 | 13.582 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 92 | 79 | 0 | 338 | 913 | 128 | 128 |
N.S. |
1 | 1.00 | 0.94 | 0.81 | 0.00 | 3.45 | 9.32 | 1.31 | 1.31 |
time (sec) |
N/A | 0.236 | 3.163 | 2.903 | 0.000 | 0.441 | 0.475 | 0.268 | 10.408 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 249 | 249 | 315 | 427 | 0 | 923 | 8670 | 545 | 0 |
N.S. |
1 | 1.00 | 1.27 | 1.71 | 0.00 | 3.71 | 34.82 | 2.19 | 0.00 |
time (sec) |
N/A | 0.419 | 3.758 | 2.907 | 0.000 | 0.443 | 1.029 | 0.306 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 44 | 41 | 0 | 215 | 559 | 58 | 58 |
N.S. |
1 | 1.00 | 0.75 | 0.69 | 0.00 | 3.64 | 9.47 | 0.98 | 0.98 |
time (sec) |
N/A | 0.196 | 2.048 | 2.595 | 0.000 | 0.371 | 0.322 | 0.278 | 10.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 207 | 210 | 223 | 294 | 0 | 675 | 2958 | 387 | 0 |
N.S. |
1 | 1.01 | 1.08 | 1.42 | 0.00 | 3.26 | 14.29 | 1.87 | 0.00 |
time (sec) |
N/A | 0.366 | 2.154 | 2.696 | 0.000 | 0.426 | 0.807 | 0.294 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 18 | 16 | 15 | 94 | 260 | 15 | 15 |
N.S. |
1 | 1.00 | 0.95 | 0.84 | 0.79 | 4.95 | 13.68 | 0.79 | 0.79 |
time (sec) |
N/A | 0.151 | 0.022 | 2.943 | 0.191 | 0.651 | 0.226 | 0.273 | 9.810 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 149 | 157 | 172 | 158 | 0 | 372 | 0 | 237 | 0 |
N.S. |
1 | 1.05 | 1.15 | 1.06 | 0.00 | 2.50 | 0.00 | 1.59 | 0.00 |
time (sec) |
N/A | 0.328 | 1.216 | 2.868 | 0.000 | 0.341 | 0.000 | 0.293 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 153 | 161 | 295 | 262 | 0 | 427 | 0 | 814 | 0 |
N.S. |
1 | 1.05 | 1.93 | 1.71 | 0.00 | 2.79 | 0.00 | 5.32 | 0.00 |
time (sec) |
N/A | 0.286 | 2.038 | 2.747 | 0.000 | 0.360 | 0.000 | 0.531 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 147 | 157 | 62 | 174 | 0 | 480 | 0 | 510 | 0 |
N.S. |
1 | 1.07 | 0.42 | 1.18 | 0.00 | 3.27 | 0.00 | 3.47 | 0.00 |
time (sec) |
N/A | 0.308 | 10.036 | 2.762 | 0.000 | 0.451 | 0.000 | 0.306 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 145 | 155 | 331 | 329 | 0 | 529 | 0 | 612 | 0 |
N.S. |
1 | 1.07 | 2.28 | 2.27 | 0.00 | 3.65 | 0.00 | 4.22 | 0.00 |
time (sec) |
N/A | 0.278 | 2.577 | 3.156 | 0.000 | 0.643 | 0.000 | 0.426 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 147 | 157 | 62 | 175 | 0 | 524 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.42 | 1.19 | 0.00 | 3.56 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.310 | 10.044 | 3.800 | 0.000 | 1.032 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 139 | 149 | 97 | 440 | 0 | 549 | 0 | 1013 | 0 |
N.S. |
1 | 1.07 | 0.70 | 3.17 | 0.00 | 3.95 | 0.00 | 7.29 | 0.00 |
time (sec) |
N/A | 0.282 | 10.056 | 4.455 | 0.000 | 1.505 | 0.000 | 0.577 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 155 | 165 | 233 | 167 | 0 | 914 | 0 | 1249 | 0 |
N.S. |
1 | 1.06 | 1.50 | 1.08 | 0.00 | 5.90 | 0.00 | 8.06 | 0.00 |
time (sec) |
N/A | 0.308 | 10.271 | 5.361 | 0.000 | 2.152 | 0.000 | 0.461 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 38 | 38 | 0 | 270 | 0 | 1241 | 3088 |
N.S. |
1 | 1.00 | 0.97 | 0.97 | 0.00 | 6.92 | 0.00 | 31.82 | 79.18 |
time (sec) |
N/A | 0.163 | 10.026 | 9.339 | 0.000 | 5.455 | 0.000 | 0.552 | 12.955 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 197 | 206 | 62 | 241 | 0 | 1448 | 0 | 2227 | 0 |
N.S. |
1 | 1.05 | 0.31 | 1.22 | 0.00 | 7.35 | 0.00 | 11.30 | 0.00 |
time (sec) |
N/A | 0.368 | 10.055 | 13.190 | 0.000 | 9.378 | 0.000 | 0.605 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 62 | 70 | 0 | 530 | 0 | 1843 | 5511 |
N.S. |
1 | 1.00 | 0.78 | 0.89 | 0.00 | 6.71 | 0.00 | 23.33 | 69.76 |
time (sec) |
N/A | 0.212 | 10.046 | 24.212 | 0.000 | 18.080 | 0.000 | 1.148 | 16.217 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 239 | 257 | 62 | 324 | 0 | 2114 | 0 | 3431 | 0 |
N.S. |
1 | 1.08 | 0.26 | 1.36 | 0.00 | 8.85 | 0.00 | 14.36 | 0.00 |
time (sec) |
N/A | 0.436 | 10.041 | 38.266 | 0.000 | 26.825 | 0.000 | 1.086 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 118 | 130 | 110 | 133 | 0 | 851 | 0 | 2365 | 9995 |
N.S. |
1 | 1.10 | 0.93 | 1.13 | 0.00 | 7.21 | 0.00 | 20.04 | 84.70 |
time (sec) |
N/A | 0.258 | 10.063 | 66.997 | 0.000 | 50.416 | 0.000 | 1.371 | 25.572 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 117 | 114 | 100 | 114 | 0 | 313 | 549 | 157 | 0 |
N.S. |
1 | 0.97 | 0.85 | 0.97 | 0.00 | 2.68 | 4.69 | 1.34 | 0.00 |
time (sec) |
N/A | 0.255 | 0.763 | 2.670 | 0.000 | 0.282 | 0.746 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 43 | 40 | 0 | 48 | 97 | 58 | 48 |
N.S. |
1 | 1.00 | 0.73 | 0.68 | 0.00 | 0.81 | 1.64 | 0.98 | 0.81 |
time (sec) |
N/A | 0.193 | 0.411 | 2.308 | 0.000 | 0.270 | 0.104 | 0.274 | 9.601 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 70 | 66 | 0 | 195 | 233 | 76 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.88 | 0.00 | 2.60 | 3.11 | 1.01 | 0.00 |
time (sec) |
N/A | 0.201 | 0.471 | 3.217 | 0.000 | 0.281 | 0.600 | 0.298 | 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 | 17 | 17 | 16 | 16 | 15 | 15 | 15 | 15 | 15 |
N.S. |
1 | 1.00 | 0.94 | 0.94 | 0.88 | 0.88 | 0.88 | 0.88 | 0.88 |
time (sec) |
N/A | 0.146 | 0.015 | 2.834 | 0.193 | 0.287 | 0.079 | 0.263 | 9.503 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 77 | 52 | 0 | 174 | 0 | 65 | 0 |
N.S. |
1 | 1.00 | 1.40 | 0.95 | 0.00 | 3.16 | 0.00 | 1.18 | 0.00 |
time (sec) |
N/A | 0.188 | 0.285 | 2.674 | 0.000 | 0.275 | 0.000 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 236 | 38 | 0 | 48 | 0 | 139 | 37 |
N.S. |
1 | 1.00 | 6.38 | 1.03 | 0.00 | 1.30 | 0.00 | 3.76 | 1.00 |
time (sec) |
N/A | 0.165 | 0.742 | 2.696 | 0.000 | 0.290 | 0.000 | 0.282 | 9.585 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 95 | 95 | 107 | 97 | 0 | 440 | 0 | 267 | 0 |
N.S. |
1 | 1.00 | 1.13 | 1.02 | 0.00 | 4.63 | 0.00 | 2.81 | 0.00 |
time (sec) |
N/A | 0.234 | 10.190 | 2.731 | 0.000 | 0.321 | 0.000 | 0.303 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 60 | 70 | 0 | 165 | 0 | 128 | 60 |
N.S. |
1 | 1.00 | 0.76 | 0.89 | 0.00 | 2.09 | 0.00 | 1.62 | 0.76 |
time (sec) |
N/A | 0.210 | 10.028 | 3.216 | 0.000 | 0.478 | 0.000 | 0.306 | 9.569 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 103 | 93 | 336 | 0 | 357 | 0 | 247 | 0 |
N.S. |
1 | 1.01 | 0.91 | 3.29 | 0.00 | 3.50 | 0.00 | 2.42 | 0.00 |
time (sec) |
N/A | 0.245 | 0.684 | 3.036 | 0.000 | 0.365 | 0.000 | 0.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 40 | 41 | 0 | 47 | 92 | 48 | 40 |
N.S. |
1 | 1.00 | 0.83 | 0.85 | 0.00 | 0.98 | 1.92 | 1.00 | 0.83 |
time (sec) |
N/A | 0.189 | 0.428 | 2.515 | 0.000 | 0.318 | 0.131 | 0.258 | 9.503 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 75 | 212 | 0 | 225 | 0 | 111 | 156 |
N.S. |
1 | 1.00 | 1.14 | 3.21 | 0.00 | 3.41 | 0.00 | 1.68 | 2.36 |
time (sec) |
N/A | 0.193 | 0.406 | 2.538 | 0.000 | 0.329 | 0.000 | 0.283 | 9.719 |
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 | 17 | 17 | 16 | 16 | 15 | 15 | 17 | 15 | 15 |
N.S. |
1 | 1.00 | 0.94 | 0.94 | 0.88 | 0.88 | 1.00 | 0.88 | 0.88 |
time (sec) |
N/A | 0.147 | 0.018 | 2.503 | 0.192 | 0.275 | 0.101 | 0.255 | 9.448 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 104 | 108 | 0 | 311 | 0 | 158 | 0 |
N.S. |
1 | 1.00 | 1.21 | 1.26 | 0.00 | 3.62 | 0.00 | 1.84 | 0.00 |
time (sec) |
N/A | 0.222 | 0.632 | 2.864 | 0.000 | 0.348 | 0.000 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 463 | 68 | 0 | 155 | 0 | 266 | 188 |
N.S. |
1 | 1.00 | 6.09 | 0.89 | 0.00 | 2.04 | 0.00 | 3.50 | 2.47 |
time (sec) |
N/A | 0.208 | 2.576 | 3.098 | 0.000 | 0.710 | 0.000 | 0.295 | 9.650 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 132 | 143 | 60 | 115 | 0 | 702 | 0 | 432 | 0 |
N.S. |
1 | 1.08 | 0.45 | 0.87 | 0.00 | 5.32 | 0.00 | 3.27 | 0.00 |
time (sec) |
N/A | 0.277 | 10.034 | 2.631 | 0.000 | 1.178 | 0.000 | 0.300 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 118 | 127 | 108 | 111 | 0 | 381 | 0 | 398 | 4588 |
N.S. |
1 | 1.08 | 0.92 | 0.94 | 0.00 | 3.23 | 0.00 | 3.37 | 38.88 |
time (sec) |
N/A | 0.256 | 10.041 | 2.933 | 0.000 | 2.244 | 0.000 | 0.306 | 11.303 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 136 | 135 | 145 | 712 | 0 | 693 | 0 | 526 | 0 |
N.S. |
1 | 0.99 | 1.07 | 5.24 | 0.00 | 5.10 | 0.00 | 3.87 | 0.00 |
time (sec) |
N/A | 0.292 | 1.116 | 3.119 | 0.000 | 0.675 | 0.000 | 0.298 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 84 | 80 | 91 | 70 | 0 | 140 | 702 | 386 | 118 |
N.S. |
1 | 0.95 | 1.08 | 0.83 | 0.00 | 1.67 | 8.36 | 4.60 | 1.40 |
time (sec) |
N/A | 0.233 | 0.774 | 2.853 | 0.000 | 0.540 | 0.604 | 0.287 | 9.703 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 96 | 96 | 88 | 1137 | 0 | 440 | 0 | 313 | 0 |
N.S. |
1 | 1.00 | 0.92 | 11.84 | 0.00 | 4.58 | 0.00 | 3.26 | 0.00 |
time (sec) |
N/A | 0.252 | 0.770 | 3.058 | 0.000 | 0.505 | 0.000 | 0.288 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 42 | 39 | 0 | 83 | 320 | 67 | 62 |
N.S. |
1 | 1.00 | 0.81 | 0.75 | 0.00 | 1.60 | 6.15 | 1.29 | 1.19 |
time (sec) |
N/A | 0.197 | 0.700 | 2.469 | 0.000 | 0.408 | 0.605 | 0.286 | 9.631 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 38 | 38 | 0 | 146 | 0 | 195 | 67 |
N.S. |
1 | 1.00 | 0.97 | 0.97 | 0.00 | 3.74 | 0.00 | 5.00 | 1.72 |
time (sec) |
N/A | 0.165 | 0.607 | 2.531 | 0.000 | 0.427 | 0.000 | 0.295 | 9.612 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 18 | 16 | 15 | 52 | 82 | 30 | 15 |
N.S. |
1 | 1.00 | 0.95 | 0.84 | 0.79 | 2.74 | 4.32 | 1.58 | 0.79 |
time (sec) |
N/A | 0.152 | 0.018 | 2.437 | 0.195 | 0.392 | 0.507 | 0.275 | 9.515 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 118 | 128 | 1624 | 132 | 0 | 620 | 0 | 906 | 0 |
N.S. |
1 | 1.08 | 13.76 | 1.12 | 0.00 | 5.25 | 0.00 | 7.68 | 0.00 |
time (sec) |
N/A | 0.278 | 5.783 | 2.792 | 0.000 | 0.566 | 0.000 | 0.313 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 122 | 128 | 108 | 132 | 0 | 374 | 0 | 374 | 110 |
N.S. |
1 | 1.05 | 0.89 | 1.08 | 0.00 | 3.07 | 0.00 | 3.07 | 0.90 |
time (sec) |
N/A | 0.259 | 10.053 | 3.156 | 0.000 | 1.209 | 0.000 | 0.332 | 10.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 176 | 195 | 62 | 194 | 0 | 1287 | 0 | 1443 | 0 |
N.S. |
1 | 1.11 | 0.35 | 1.10 | 0.00 | 7.31 | 0.00 | 8.20 | 0.00 |
time (sec) |
N/A | 0.333 | 10.036 | 2.672 | 0.000 | 2.143 | 0.000 | 0.432 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 162 | 177 | 178 | 187 | 0 | 677 | 0 | 1389 | 5604 |
N.S. |
1 | 1.09 | 1.10 | 1.15 | 0.00 | 4.18 | 0.00 | 8.57 | 34.59 |
time (sec) |
N/A | 0.307 | 10.069 | 2.868 | 0.000 | 3.953 | 0.000 | 0.352 | 11.373 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 294 | 24 | 14 | 66 | 0 | 89 | 0 |
N.S. |
1 | 1.00 | 10.89 | 0.89 | 0.52 | 2.44 | 0.00 | 3.30 | 0.00 |
time (sec) |
N/A | 0.174 | 0.404 | 2.791 | 0.280 | 0.263 | 0.000 | 0.288 | 0.000 |
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 | 55 | 55 | 45 | 46 | 46 | 122 | 289 | 567 | 39 |
N.S. |
1 | 1.00 | 0.82 | 0.84 | 0.84 | 2.22 | 5.25 | 10.31 | 0.71 |
time (sec) |
N/A | 0.201 | 0.052 | 2.281 | 0.215 | 0.252 | 0.410 | 0.273 | 0.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 45 | 46 | 46 | 87 | 73 | 376 | 39 |
N.S. |
1 | 1.00 | 0.82 | 0.84 | 0.84 | 1.58 | 1.33 | 6.84 | 0.71 |
time (sec) |
N/A | 0.200 | 0.034 | 2.395 | 0.197 | 0.267 | 0.754 | 0.266 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 42 | 45 | 46 | 58 | 73 | 228 | 39 |
N.S. |
1 | 1.00 | 0.76 | 0.82 | 0.84 | 1.05 | 1.33 | 4.15 | 0.71 |
time (sec) |
N/A | 0.200 | 0.031 | 2.059 | 0.213 | 0.248 | 0.681 | 0.264 | 9.152 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 43 | 41 | 116 | 40 | 146 | 116 | 37 |
N.S. |
1 | 1.00 | 0.78 | 0.75 | 2.11 | 0.73 | 2.65 | 2.11 | 0.67 |
time (sec) |
N/A | 0.203 | 0.030 | 2.145 | 0.198 | 0.268 | 0.534 | 0.266 | 0.045 |
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 | 55 | 43 | 39 | 51 | 52 | 73 | 47 | 37 |
N.S. |
1 | 1.00 | 0.78 | 0.71 | 0.93 | 0.95 | 1.33 | 0.85 | 0.67 |
time (sec) |
N/A | 0.192 | 0.032 | 2.006 | 0.201 | 0.252 | 0.792 | 0.262 | 9.239 |
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 | 55 | 55 | 40 | 45 | 51 | 68 | 235 | 47 | 37 |
N.S. |
1 | 1.00 | 0.73 | 0.82 | 0.93 | 1.24 | 4.27 | 0.85 | 0.67 |
time (sec) |
N/A | 0.196 | 0.036 | 2.354 | 0.192 | 0.263 | 0.316 | 0.261 | 9.205 |
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 | 55 | 55 | 40 | 43 | 45 | 81 | 298 | 47 | 37 |
N.S. |
1 | 1.00 | 0.73 | 0.78 | 0.82 | 1.47 | 5.42 | 0.85 | 0.67 |
time (sec) |
N/A | 0.203 | 0.039 | 2.317 | 0.212 | 0.257 | 0.442 | 0.265 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 42 | 44 | 46 | 96 | 360 | 48 | 39 |
N.S. |
1 | 1.00 | 0.76 | 0.80 | 0.84 | 1.75 | 6.55 | 0.87 | 0.71 |
time (sec) |
N/A | 0.199 | 0.039 | 2.074 | 0.194 | 0.252 | 0.670 | 0.273 | 9.243 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 78 | 83 | 81 | 164 | 144 | 867 | 99 |
N.S. |
1 | 1.00 | 0.89 | 0.94 | 0.92 | 1.86 | 1.64 | 9.85 | 1.12 |
time (sec) |
N/A | 0.248 | 0.069 | 2.572 | 0.193 | 0.239 | 0.993 | 0.277 | 9.214 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 78 | 83 | 81 | 121 | 144 | 580 | 99 |
N.S. |
1 | 1.00 | 0.89 | 0.94 | 0.92 | 1.38 | 1.64 | 6.59 | 1.12 |
time (sec) |
N/A | 0.241 | 0.061 | 2.505 | 0.196 | 0.238 | 0.883 | 0.274 | 9.143 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 78 | 82 | 351 | 92 | 144 | 349 | 99 |
N.S. |
1 | 1.00 | 0.89 | 0.93 | 3.99 | 1.05 | 1.64 | 3.97 | 1.12 |
time (sec) |
N/A | 0.232 | 0.054 | 2.911 | 0.199 | 0.242 | 0.856 | 0.277 | 9.280 |
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 | 88 | 88 | 78 | 91 | 89 | 105 | 134 | 109 | 99 |
N.S. |
1 | 1.00 | 0.89 | 1.03 | 1.01 | 1.19 | 1.52 | 1.24 | 1.12 |
time (sec) |
N/A | 0.233 | 0.056 | 3.044 | 0.197 | 0.248 | 1.351 | 0.281 | 9.239 |
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 | 88 | 88 | 78 | 95 | 90 | 120 | 134 | 109 | 99 |
N.S. |
1 | 1.00 | 0.89 | 1.08 | 1.02 | 1.36 | 1.52 | 1.24 | 1.12 |
time (sec) |
N/A | 0.227 | 0.058 | 2.524 | 0.219 | 0.380 | 1.377 | 0.274 | 9.219 |
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 | 88 | 88 | 78 | 84 | 93 | 134 | 688 | 99 | 92 |
N.S. |
1 | 1.00 | 0.89 | 0.95 | 1.06 | 1.52 | 7.82 | 1.12 | 1.05 |
time (sec) |
N/A | 0.237 | 0.062 | 2.577 | 0.210 | 0.370 | 0.509 | 0.280 | 9.203 |
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 | 88 | 88 | 78 | 82 | 92 | 149 | 826 | 100 | 92 |
N.S. |
1 | 1.00 | 0.89 | 0.93 | 1.05 | 1.69 | 9.39 | 1.14 | 1.05 |
time (sec) |
N/A | 0.228 | 0.061 | 2.557 | 0.203 | 0.400 | 0.728 | 0.281 | 0.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 78 | 84 | 81 | 162 | 966 | 99 | 67 |
N.S. |
1 | 1.00 | 0.89 | 0.95 | 0.92 | 1.84 | 10.98 | 1.12 | 0.76 |
time (sec) |
N/A | 0.227 | 0.063 | 2.507 | 0.201 | 0.392 | 1.036 | 0.274 | 0.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 133 | 148 | 127 | 205 | 248 | 1165 | 111 |
N.S. |
1 | 1.00 | 1.10 | 1.22 | 1.05 | 1.69 | 2.05 | 9.63 | 0.92 |
time (sec) |
N/A | 0.259 | 0.088 | 2.664 | 0.188 | 0.626 | 1.073 | 0.276 | 9.181 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 133 | 147 | 778 | 165 | 248 | 778 | 111 |
N.S. |
1 | 1.00 | 1.10 | 1.21 | 6.43 | 1.36 | 2.05 | 6.43 | 0.92 |
time (sec) |
N/A | 0.250 | 0.080 | 2.262 | 0.205 | 0.273 | 1.066 | 0.274 | 0.068 |
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 | 121 | 121 | 133 | 169 | 136 | 178 | 226 | 187 | 129 |
N.S. |
1 | 1.00 | 1.10 | 1.40 | 1.12 | 1.47 | 1.87 | 1.55 | 1.07 |
time (sec) |
N/A | 0.259 | 0.077 | 2.299 | 0.207 | 0.261 | 1.976 | 0.290 | 0.076 |
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 | 121 | 121 | 133 | 170 | 136 | 194 | 226 | 187 | 131 |
N.S. |
1 | 1.00 | 1.10 | 1.40 | 1.12 | 1.60 | 1.87 | 1.55 | 1.08 |
time (sec) |
N/A | 0.267 | 0.082 | 2.317 | 0.199 | 0.252 | 2.010 | 0.286 | 0.075 |
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 | 121 | 121 | 133 | 143 | 142 | 208 | 216 | 186 | 170 |
N.S. |
1 | 1.00 | 1.10 | 1.18 | 1.17 | 1.72 | 1.79 | 1.54 | 1.40 |
time (sec) |
N/A | 0.257 | 0.087 | 2.511 | 0.229 | 0.256 | 2.108 | 0.289 | 9.223 |
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 | 121 | 121 | 133 | 138 | 142 | 210 | 1394 | 186 | 159 |
N.S. |
1 | 1.00 | 1.10 | 1.14 | 1.17 | 1.74 | 11.52 | 1.54 | 1.31 |
time (sec) |
N/A | 0.255 | 0.083 | 2.858 | 0.196 | 0.282 | 0.842 | 0.290 | 9.225 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 133 | 132 | 138 | 238 | 1731 | 176 | 147 |
N.S. |
1 | 1.00 | 1.10 | 1.09 | 1.14 | 1.97 | 14.31 | 1.45 | 1.21 |
time (sec) |
N/A | 0.256 | 0.090 | 2.391 | 0.205 | 0.265 | 1.157 | 0.287 | 9.390 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 133 | 130 | 138 | 252 | 1975 | 176 | 147 |
N.S. |
1 | 1.00 | 1.10 | 1.07 | 1.14 | 2.08 | 16.32 | 1.45 | 1.21 |
time (sec) |
N/A | 0.261 | 0.093 | 2.383 | 0.199 | 0.290 | 1.668 | 0.292 | 0.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 175 | 199 | 254 | 372 | 0 | 1079 | 0 | 733 | 240 |
N.S. |
1 | 1.14 | 1.45 | 2.13 | 0.00 | 6.17 | 0.00 | 4.19 | 1.37 |
time (sec) |
N/A | 0.419 | 0.387 | 5.761 | 0.000 | 0.282 | 0.000 | 0.301 | 9.357 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 147 | 170 | 217 | 303 | 0 | 1005 | 0 | 531 | 168 |
N.S. |
1 | 1.16 | 1.48 | 2.06 | 0.00 | 6.84 | 0.00 | 3.61 | 1.14 |
time (sec) |
N/A | 0.361 | 0.349 | 3.160 | 0.000 | 0.278 | 0.000 | 0.293 | 9.411 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 145 | 168 | 215 | 302 | 0 | 629 | 0 | 531 | 167 |
N.S. |
1 | 1.16 | 1.48 | 2.08 | 0.00 | 4.34 | 0.00 | 3.66 | 1.15 |
time (sec) |
N/A | 0.355 | 0.325 | 3.929 | 0.000 | 0.279 | 0.000 | 0.295 | 9.362 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 139 | 214 | 257 | 0 | 472 | 0 | 354 | 97 |
N.S. |
1 | 1.17 | 1.80 | 2.16 | 0.00 | 3.97 | 0.00 | 2.97 | 0.82 |
time (sec) |
N/A | 0.307 | 0.225 | 2.680 | 0.000 | 0.273 | 0.000 | 0.299 | 0.135 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 117 | 137 | 192 | 255 | 0 | 200 | 0 | 354 | 97 |
N.S. |
1 | 1.17 | 1.64 | 2.18 | 0.00 | 1.71 | 0.00 | 3.03 | 0.83 |
time (sec) |
N/A | 0.307 | 0.193 | 2.652 | 0.000 | 0.275 | 0.000 | 0.294 | 9.248 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 110 | 151 | 228 | 0 | 237 | 0 | 393 | 83 |
N.S. |
1 | 1.09 | 1.50 | 2.26 | 0.00 | 2.35 | 0.00 | 3.89 | 0.82 |
time (sec) |
N/A | 0.263 | 0.158 | 2.835 | 0.000 | 0.262 | 0.000 | 0.291 | 0.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 110 | 153 | 228 | 0 | 407 | 0 | 393 | 161 |
N.S. |
1 | 1.09 | 1.51 | 2.26 | 0.00 | 4.03 | 0.00 | 3.89 | 1.59 |
time (sec) |
N/A | 0.261 | 0.168 | 2.804 | 0.000 | 0.265 | 0.000 | 0.296 | 9.277 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 129 | 151 | 193 | 274 | 0 | 900 | 0 | 497 | 153 |
N.S. |
1 | 1.17 | 1.50 | 2.12 | 0.00 | 6.98 | 0.00 | 3.85 | 1.19 |
time (sec) |
N/A | 0.319 | 0.220 | 2.526 | 0.000 | 0.274 | 0.000 | 0.297 | 9.434 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 131 | 153 | 242 | 274 | 0 | 1116 | 0 | 497 | 1345 |
N.S. |
1 | 1.17 | 1.85 | 2.09 | 0.00 | 8.52 | 0.00 | 3.79 | 10.27 |
time (sec) |
N/A | 0.310 | 0.263 | 2.500 | 0.000 | 0.272 | 0.000 | 0.287 | 9.529 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 159 | 196 | 219 | 301 | 0 | 1880 | 0 | 605 | 230 |
N.S. |
1 | 1.23 | 1.38 | 1.89 | 0.00 | 11.82 | 0.00 | 3.81 | 1.45 |
time (sec) |
N/A | 0.368 | 0.330 | 2.532 | 0.000 | 0.275 | 0.000 | 0.295 | 0.261 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 210 | 234 | 351 | 439 | 0 | 1293 | 0 | 876 | 1060 |
N.S. |
1 | 1.11 | 1.67 | 2.09 | 0.00 | 6.16 | 0.00 | 4.17 | 5.05 |
time (sec) |
N/A | 0.458 | 1.119 | 2.756 | 0.000 | 0.277 | 0.000 | 0.330 | 9.446 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 181 | 205 | 290 | 373 | 0 | 1211 | 0 | 646 | 249 |
N.S. |
1 | 1.13 | 1.60 | 2.06 | 0.00 | 6.69 | 0.00 | 3.57 | 1.38 |
time (sec) |
N/A | 0.410 | 0.813 | 3.160 | 0.000 | 0.285 | 0.000 | 0.313 | 9.335 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 179 | 203 | 296 | 373 | 0 | 816 | 0 | 646 | 834 |
N.S. |
1 | 1.13 | 1.65 | 2.08 | 0.00 | 4.56 | 0.00 | 3.61 | 4.66 |
time (sec) |
N/A | 0.408 | 0.787 | 2.948 | 0.000 | 0.282 | 0.000 | 0.311 | 0.203 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 152 | 174 | 254 | 315 | 0 | 659 | 0 | 441 | 165 |
N.S. |
1 | 1.14 | 1.67 | 2.07 | 0.00 | 4.34 | 0.00 | 2.90 | 1.09 |
time (sec) |
N/A | 0.361 | 0.682 | 2.676 | 0.000 | 0.278 | 0.000 | 0.318 | 9.303 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 150 | 172 | 256 | 312 | 0 | 361 | 0 | 441 | 597 |
N.S. |
1 | 1.15 | 1.71 | 2.08 | 0.00 | 2.41 | 0.00 | 2.94 | 3.98 |
time (sec) |
N/A | 0.342 | 0.742 | 2.595 | 0.000 | 0.265 | 0.000 | 0.306 | 0.197 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 131 | 142 | 230 | 277 | 0 | 376 | 0 | 439 | 131 |
N.S. |
1 | 1.08 | 1.76 | 2.11 | 0.00 | 2.87 | 0.00 | 3.35 | 1.00 |
time (sec) |
N/A | 0.301 | 0.655 | 2.909 | 0.000 | 0.274 | 0.000 | 0.297 | 0.148 |