Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 40 | 39 | 36 | 35 | 29 | 72 | 51 |
N.S. |
1 | 1.00 | 1.00 | 0.98 | 0.90 | 0.88 | 0.72 | 1.80 | 1.28 |
time (sec) |
N/A | 0.203 | 0.017 | 0.225 | 0.181 | 0.262 | 0.112 | 0.276 | 0.559 |
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 | 23 | 23 | 32 | 22 | 19 | 22 | 15 | 37 | 21 |
N.S. |
1 | 1.00 | 1.39 | 0.96 | 0.83 | 0.96 | 0.65 | 1.61 | 0.91 |
time (sec) |
N/A | 0.179 | 0.008 | 0.221 | 0.173 | 0.255 | 0.079 | 0.275 | 0.064 |
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 | 41 | 41 | 34 | 42 | 47 | 27 | 99 | 68 | 34 |
N.S. |
1 | 1.00 | 0.83 | 1.02 | 1.15 | 0.66 | 2.41 | 1.66 | 0.83 |
time (sec) |
N/A | 0.211 | 0.017 | 0.252 | 0.176 | 0.261 | 0.408 | 0.278 | 0.800 |
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 | 62 | 62 | 42 | 69 | 110 | 40 | 158 | 95 | 100 |
N.S. |
1 | 1.00 | 0.68 | 1.11 | 1.77 | 0.65 | 2.55 | 1.53 | 1.61 |
time (sec) |
N/A | 0.227 | 0.021 | 0.303 | 0.177 | 0.261 | 0.310 | 0.281 | 0.735 |
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 | 83 | 81 | 66 | 109 | 160 | 69 | 226 | 142 | 156 |
N.S. |
1 | 0.98 | 0.80 | 1.31 | 1.93 | 0.83 | 2.72 | 1.71 | 1.88 |
time (sec) |
N/A | 0.245 | 0.028 | 0.290 | 0.189 | 0.269 | 0.441 | 0.269 | 0.797 |
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 | 104 | 102 | 91 | 150 | 218 | 94 | 286 | 183 | 199 |
N.S. |
1 | 0.98 | 0.88 | 1.44 | 2.10 | 0.90 | 2.75 | 1.76 | 1.91 |
time (sec) |
N/A | 0.262 | 0.036 | 0.296 | 0.191 | 0.266 | 0.573 | 0.280 | 0.863 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 324 | 342 | 299 | 445 | 1368 | 264 | 0 | 334 | 0 |
N.S. |
1 | 1.06 | 0.92 | 1.37 | 4.22 | 0.81 | 0.00 | 1.03 | 0.00 |
time (sec) |
N/A | 0.475 | 0.501 | 1.166 | 0.296 | 0.284 | 0.000 | 0.303 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 249 | 264 | 244 | 351 | 979 | 216 | 0 | 285 | 0 |
N.S. |
1 | 1.06 | 0.98 | 1.41 | 3.93 | 0.87 | 0.00 | 1.14 | 0.00 |
time (sec) |
N/A | 0.415 | 0.313 | 0.924 | 0.283 | 0.276 | 0.000 | 0.306 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 229 | 232 | 198 | 268 | 624 | 174 | 0 | 241 | 0 |
N.S. |
1 | 1.01 | 0.86 | 1.17 | 2.72 | 0.76 | 0.00 | 1.05 | 0.00 |
time (sec) |
N/A | 0.361 | 0.244 | 0.914 | 0.278 | 0.269 | 0.000 | 0.303 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 163 | 172 | 157 | 195 | 293 | 136 | 0 | 210 | 0 |
N.S. |
1 | 1.06 | 0.96 | 1.20 | 1.80 | 0.83 | 0.00 | 1.29 | 0.00 |
time (sec) |
N/A | 0.292 | 0.239 | 0.832 | 0.263 | 0.278 | 0.000 | 0.321 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 94 | 109 | 45 | 129 | 103 | 99 | 0 | 180 | 0 |
N.S. |
1 | 1.16 | 0.48 | 1.37 | 1.10 | 1.05 | 0.00 | 1.91 | 0.00 |
time (sec) |
N/A | 0.235 | 0.035 | 0.852 | 0.265 | 0.266 | 0.000 | 0.306 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 134 | 163 | 189 | 1067 | 0 | 356 | 0 | 252 | 0 |
N.S. |
1 | 1.22 | 1.41 | 7.96 | 0.00 | 2.66 | 0.00 | 1.88 | 0.00 |
time (sec) |
N/A | 0.327 | 0.478 | 0.814 | 0.000 | 0.269 | 0.000 | 0.405 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 178 | 187 | 145 | 194 | 0 | 389 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.81 | 1.09 | 0.00 | 2.19 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.281 | 0.129 | 1.335 | 0.000 | 0.271 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 264 | 255 | 194 | 282 | 0 | 574 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 0.73 | 1.07 | 0.00 | 2.17 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.336 | 0.193 | 1.275 | 0.000 | 0.279 | 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(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 339 | 363 | 275 | 392 | 0 | 839 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.81 | 1.16 | 0.00 | 2.47 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.461 | 0.320 | 2.114 | 0.000 | 0.299 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 494 | 414 | 121 | 0 | 0 | 554 | 0 | 0 | 0 |
N.S. |
1 | 0.84 | 0.24 | 0.00 | 0.00 | 1.12 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.508 | 0.064 | 0.000 | 0.000 | 0.292 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 410 | 355 | 81 | 0 | 0 | 415 | 0 | 0 | 0 |
N.S. |
1 | 0.87 | 0.20 | 0.00 | 0.00 | 1.01 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.471 | 0.032 | 0.000 | 0.000 | 0.283 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 338 | 299 | 45 | 0 | 0 | 255 | 0 | 0 | 0 |
N.S. |
1 | 0.88 | 0.13 | 0.00 | 0.00 | 0.75 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.398 | 0.012 | 0.000 | 0.000 | 0.265 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 395 | 437 | 124 | 0 | 0 | 414 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 0.31 | 0.00 | 0.00 | 1.05 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.534 | 0.075 | 0.000 | 0.000 | 0.285 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | B | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 205 | 261 | 110 | 0 | 0 | 598 | 0 | 0 | 0 |
N.S. |
1 | 1.27 | 0.54 | 0.00 | 0.00 | 2.92 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.300 | 0.025 | 0.000 | 0.000 | 0.272 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 494 | 414 | 121 | 0 | 0 | 561 | 0 | 0 | 0 |
N.S. |
1 | 0.84 | 0.24 | 0.00 | 0.00 | 1.14 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.514 | 0.067 | 0.000 | 0.000 | 0.298 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 410 | 355 | 79 | 0 | 0 | 431 | 0 | 0 | 0 |
N.S. |
1 | 0.87 | 0.19 | 0.00 | 0.00 | 1.05 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.444 | 0.033 | 0.000 | 0.000 | 0.280 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 338 | 299 | 45 | 0 | 0 | 268 | 0 | 0 | 0 |
N.S. |
1 | 0.88 | 0.13 | 0.00 | 0.00 | 0.79 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.396 | 0.012 | 0.000 | 0.000 | 0.279 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | B | F(-1) | F(-2) | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 427 | 427 | 122 | 0 | 0 | 690 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.29 | 0.00 | 0.00 | 1.62 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.560 | 0.058 | 0.000 | 0.000 | 0.292 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | B | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 211 | 224 | 106 | 0 | 0 | 694 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.50 | 0.00 | 0.00 | 3.29 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.323 | 0.020 | 0.000 | 0.000 | 0.273 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 494 | 414 | 99 | 0 | 0 | 561 | 0 | 0 | 0 |
N.S. |
1 | 0.84 | 0.20 | 0.00 | 0.00 | 1.14 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.555 | 0.066 | 0.000 | 0.000 | 0.285 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 410 | 355 | 84 | 0 | 0 | 421 | 0 | 0 | 0 |
N.S. |
1 | 0.87 | 0.20 | 0.00 | 0.00 | 1.03 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.479 | 0.029 | 0.000 | 0.000 | 0.284 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 338 | 299 | 45 | 0 | 0 | 266 | 0 | 0 | 0 |
N.S. |
1 | 0.88 | 0.13 | 0.00 | 0.00 | 0.79 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.394 | 0.012 | 0.000 | 0.000 | 0.273 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 395 | 437 | 126 | 0 | 0 | 470 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 0.32 | 0.00 | 0.00 | 1.19 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.517 | 0.026 | 0.000 | 0.000 | 0.285 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | B | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 210 | 261 | 107 | 0 | 0 | 707 | 0 | 0 | 0 |
N.S. |
1 | 1.24 | 0.51 | 0.00 | 0.00 | 3.37 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.298 | 0.022 | 0.000 | 0.000 | 0.277 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 494 | 414 | 98 | 0 | 0 | 555 | 0 | 0 | 0 |
N.S. |
1 | 0.84 | 0.20 | 0.00 | 0.00 | 1.12 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.528 | 0.065 | 0.000 | 0.000 | 0.297 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 410 | 355 | 84 | 0 | 0 | 433 | 0 | 0 | 0 |
N.S. |
1 | 0.87 | 0.20 | 0.00 | 0.00 | 1.06 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.499 | 0.028 | 0.000 | 0.000 | 0.269 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 338 | 299 | 43 | 0 | 0 | 255 | 0 | 0 | 0 |
N.S. |
1 | 0.88 | 0.13 | 0.00 | 0.00 | 0.75 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.430 | 0.012 | 0.000 | 0.000 | 0.273 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | B | F(-1) | F(-2) | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 427 | 427 | 128 | 0 | 0 | 629 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.30 | 0.00 | 0.00 | 1.47 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.596 | 0.024 | 0.000 | 0.000 | 0.276 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | B | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 211 | 226 | 107 | 0 | 0 | 613 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.51 | 0.00 | 0.00 | 2.91 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.359 | 0.023 | 0.000 | 0.000 | 0.276 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 140 | 140 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.301 | 0.000 | 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(-1) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 260 | 266 | 272 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.428 | 0.260 | 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(-1) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 220 | 226 | 160 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.354 | 0.125 | 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 | 147 | 147 | 128 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.263 | 0.112 | 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 | 91 | 91 | 60 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.207 | 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 | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 191 | 203 | 170 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.295 | 0.029 | 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(-1) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 128 | 128 | 125 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.248 | 0.018 | 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(-1) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 207 | 205 | 173 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.340 | 0.055 | 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 | 102 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.329 | 0.025 | 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 | 63 | 63 | 63 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.222 | 0.012 | 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 | 61 | 61 | 61 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.206 | 0.011 | 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 | 60 | 60 | 45 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.184 | 0.018 | 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 | C | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 35 | 13 | 12 | 12 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 2.69 | 1.00 | 0.92 | 0.92 | 0.92 | 0.92 | 0.92 |
time (sec) |
N/A | 0.197 | 0.007 | 0.493 | 0.267 | 0.261 | 0.407 | 0.285 | 0.628 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 60 | 39 | 0 | 39 | 95 | 0 | 44 |
N.S. |
1 | 1.00 | 1.20 | 0.78 | 0.00 | 0.78 | 1.90 | 0.00 | 0.88 |
time (sec) |
N/A | 0.292 | 0.015 | 2.411 | 0.000 | 0.261 | 1.038 | 0.000 | 0.662 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 83 | 85 | 89 | 55 | 0 | 66 | 223 | 0 | 74 |
N.S. |
1 | 1.02 | 1.07 | 0.66 | 0.00 | 0.80 | 2.69 | 0.00 | 0.89 |
time (sec) |
N/A | 0.396 | 0.106 | 10.336 | 0.000 | 0.266 | 2.872 | 0.000 | 0.714 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 116 | 120 | 123 | 71 | 0 | 93 | 398 | 0 | 104 |
N.S. |
1 | 1.03 | 1.06 | 0.61 | 0.00 | 0.80 | 3.43 | 0.00 | 0.90 |
time (sec) |
N/A | 0.512 | 0.187 | 32.036 | 0.000 | 0.263 | 7.512 | 0.000 | 0.804 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 149 | 155 | 153 | 87 | 0 | 120 | 620 | 0 | 134 |
N.S. |
1 | 1.04 | 1.03 | 0.58 | 0.00 | 0.81 | 4.16 | 0.00 | 0.90 |
time (sec) |
N/A | 0.665 | 0.211 | 85.375 | 0.000 | 0.284 | 21.896 | 0.000 | 0.860 |
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 | 98 | 98 | 98 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.324 | 0.018 | 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 | 97 | 97 | 97 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.314 | 0.015 | 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 | 93 | 93 | 93 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.316 | 0.015 | 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 | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 35 | 37 | 0 | 42 | 0 | 0 | 33 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 0.00 | 1.20 | 0.00 | 0.00 | 0.94 |
time (sec) |
N/A | 0.213 | 0.012 | 0.207 | 0.000 | 0.262 | 0.000 | 0.000 | 0.693 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 60 | 54 | 0 | 70 | 0 | 0 | 78 |
N.S. |
1 | 1.00 | 0.83 | 0.75 | 0.00 | 0.97 | 0.00 | 0.00 | 1.08 |
time (sec) |
N/A | 0.323 | 0.025 | 0.202 | 0.000 | 0.273 | 0.000 | 0.000 | 0.729 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 108 | 116 | 79 | 70 | 0 | 97 | 0 | 0 | 120 |
N.S. |
1 | 1.07 | 0.73 | 0.65 | 0.00 | 0.90 | 0.00 | 0.00 | 1.11 |
time (sec) |
N/A | 0.440 | 0.027 | 0.200 | 0.000 | 0.261 | 0.000 | 0.000 | 0.778 |
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 | 90 | 90 | 90 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.322 | 0.018 | 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 | 53 | 53 | 53 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.232 | 0.015 | 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 | 51 | 51 | 51 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.211 | 0.010 | 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 | 46 | 46 | 37 | 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 | 0.186 | 0.020 | 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 | C | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 34 | 16 | 15 | 15 | 15 | 15 | 15 |
N.S. |
1 | 1.00 | 1.89 | 0.89 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 |
time (sec) |
N/A | 0.203 | 0.007 | 0.520 | 0.279 | 0.269 | 0.418 | 0.300 | 0.606 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 55 | 40 | 0 | 40 | 99 | 0 | 46 |
N.S. |
1 | 1.00 | 1.04 | 0.75 | 0.00 | 0.75 | 1.87 | 0.00 | 0.87 |
time (sec) |
N/A | 0.296 | 0.015 | 2.392 | 0.000 | 0.260 | 1.057 | 0.000 | 0.654 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 90 | 86 | 57 | 0 | 68 | 231 | 0 | 79 |
N.S. |
1 | 1.02 | 0.98 | 0.65 | 0.00 | 0.77 | 2.62 | 0.00 | 0.90 |
time (sec) |
N/A | 0.407 | 0.101 | 10.279 | 0.000 | 0.267 | 2.865 | 0.000 | 0.699 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 123 | 127 | 122 | 73 | 0 | 95 | 410 | 0 | 111 |
N.S. |
1 | 1.03 | 0.99 | 0.59 | 0.00 | 0.77 | 3.33 | 0.00 | 0.90 |
time (sec) |
N/A | 0.529 | 0.203 | 31.910 | 0.000 | 0.290 | 7.639 | 0.000 | 0.778 |
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 | 88 | 88 | 88 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.338 | 0.018 | 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 | 87 | 87 | 87 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.312 | 0.015 | 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(-1) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 87 | 87 | 87 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.321 | 0.017 | 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 | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 37 | 39 | 0 | 44 | 0 | 0 | 35 |
N.S. |
1 | 1.00 | 1.00 | 1.05 | 0.00 | 1.19 | 0.00 | 0.00 | 0.95 |
time (sec) |
N/A | 0.226 | 0.014 | 0.223 | 0.000 | 0.265 | 0.000 | 0.000 | 0.677 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 62 | 56 | 0 | 72 | 0 | 0 | 80 |
N.S. |
1 | 1.00 | 0.82 | 0.74 | 0.00 | 0.95 | 0.00 | 0.00 | 1.05 |
time (sec) |
N/A | 0.337 | 0.029 | 0.215 | 0.000 | 0.264 | 0.000 | 0.000 | 0.241 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 114 | 122 | 81 | 72 | 0 | 99 | 0 | 0 | 122 |
N.S. |
1 | 1.07 | 0.71 | 0.63 | 0.00 | 0.87 | 0.00 | 0.00 | 1.07 |
time (sec) |
N/A | 0.478 | 0.028 | 0.211 | 0.000 | 0.279 | 0.000 | 0.000 | 0.770 |
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 | 101 | 101 | 102 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.325 | 0.020 | 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 | 63 | 63 | 63 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.222 | 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 | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 61 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.223 | 0.011 | 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 | 60 | 60 | 45 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.196 | 0.022 | 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 | C | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 36 | 16 | 23 | 15 | 15 | 15 | 15 |
N.S. |
1 | 1.00 | 2.25 | 1.00 | 1.44 | 0.94 | 0.94 | 0.94 | 0.94 |
time (sec) |
N/A | 0.200 | 0.008 | 0.658 | 0.200 | 0.261 | 2.946 | 0.287 | 0.624 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 60 | 41 | 0 | 41 | 116 | 0 | 47 |
N.S. |
1 | 1.00 | 1.11 | 0.76 | 0.00 | 0.76 | 2.15 | 0.00 | 0.87 |
time (sec) |
N/A | 0.310 | 0.017 | 3.331 | 0.000 | 0.284 | 19.288 | 0.000 | 0.642 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 91 | 91 | 57 | 0 | 68 | 291 | 0 | 80 |
N.S. |
1 | 1.02 | 1.02 | 0.64 | 0.00 | 0.76 | 3.27 | 0.00 | 0.90 |
time (sec) |
N/A | 0.414 | 0.121 | 12.617 | 0.000 | 0.257 | 87.600 | 0.000 | 0.723 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 128 | 127 | 73 | 0 | 95 | 0 | 0 | 112 |
N.S. |
1 | 1.03 | 1.02 | 0.59 | 0.00 | 0.77 | 0.00 | 0.00 | 0.90 |
time (sec) |
N/A | 0.562 | 0.269 | 40.229 | 0.000 | 0.268 | 0.000 | 0.000 | 0.772 |
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 | 98 | 98 | 98 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.327 | 0.018 | 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 | 97 | 97 | 97 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.325 | 0.016 | 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 | 93 | 93 | 93 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.322 | 0.016 | 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 | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 37 | 39 | 0 | 44 | 0 | 0 | 35 |
N.S. |
1 | 1.00 | 0.97 | 1.03 | 0.00 | 1.16 | 0.00 | 0.00 | 0.92 |
time (sec) |
N/A | 0.218 | 0.017 | 0.200 | 0.000 | 0.270 | 0.000 | 0.000 | 0.702 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 62 | 56 | 0 | 72 | 0 | 0 | 81 |
N.S. |
1 | 1.00 | 0.81 | 0.73 | 0.00 | 0.94 | 0.00 | 0.00 | 1.05 |
time (sec) |
N/A | 0.331 | 0.031 | 0.212 | 0.000 | 0.265 | 0.000 | 0.000 | 0.733 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 123 | 81 | 72 | 0 | 99 | 0 | 0 | 123 |
N.S. |
1 | 1.07 | 0.70 | 0.63 | 0.00 | 0.86 | 0.00 | 0.00 | 1.07 |
time (sec) |
N/A | 0.466 | 0.039 | 0.212 | 0.000 | 0.291 | 0.000 | 0.000 | 0.763 |
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 | 90 | 90 | 90 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.325 | 0.019 | 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 | 53 | 53 | 53 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.218 | 0.014 | 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 | 51 | 51 | 51 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.207 | 0.011 | 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 | 46 | 46 | 37 | 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 | 0.182 | 0.021 | 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 | C | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 34 | 18 | 23 | 15 | 19 | 15 | 15 |
N.S. |
1 | 1.00 | 1.89 | 1.00 | 1.28 | 0.83 | 1.06 | 0.83 | 0.83 |
time (sec) |
N/A | 0.199 | 0.007 | 0.730 | 0.197 | 0.250 | 6.375 | 0.275 | 0.622 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 55 | 42 | 0 | 40 | 124 | 0 | 47 |
N.S. |
1 | 1.00 | 1.02 | 0.78 | 0.00 | 0.74 | 2.30 | 0.00 | 0.87 |
time (sec) |
N/A | 0.298 | 0.017 | 3.461 | 0.000 | 0.258 | 39.108 | 0.000 | 0.643 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 91 | 85 | 59 | 0 | 68 | 316 | 0 | 79 |
N.S. |
1 | 1.02 | 0.96 | 0.66 | 0.00 | 0.76 | 3.55 | 0.00 | 0.89 |
time (sec) |
N/A | 0.402 | 0.133 | 13.843 | 0.000 | 0.267 | 163.452 | 0.000 | 0.710 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 128 | 121 | 75 | 0 | 95 | 0 | 0 | 111 |
N.S. |
1 | 1.03 | 0.98 | 0.60 | 0.00 | 0.77 | 0.00 | 0.00 | 0.90 |
time (sec) |
N/A | 0.526 | 0.283 | 42.191 | 0.000 | 0.263 | 0.000 | 0.000 | 0.765 |
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 | 88 | 88 | 88 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.326 | 0.018 | 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 | 87 | 87 | 87 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.319 | 0.015 | 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(-1) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 87 | 87 | 87 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.322 | 0.016 | 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 | F | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 37 | 41 | 0 | 44 | 0 | 0 | 35 |
N.S. |
1 | 1.00 | 0.97 | 1.08 | 0.00 | 1.16 | 0.00 | 0.00 | 0.92 |
time (sec) |
N/A | 0.218 | 0.016 | 0.223 | 0.000 | 0.278 | 0.000 | 0.000 | 0.197 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 62 | 58 | 0 | 72 | 0 | 0 | 81 |
N.S. |
1 | 1.00 | 0.81 | 0.75 | 0.00 | 0.94 | 0.00 | 0.00 | 1.05 |
time (sec) |
N/A | 0.322 | 0.030 | 0.194 | 0.000 | 0.275 | 0.000 | 0.000 | 0.752 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 123 | 81 | 74 | 0 | 99 | 0 | 0 | 123 |
N.S. |
1 | 1.07 | 0.70 | 0.64 | 0.00 | 0.86 | 0.00 | 0.00 | 1.07 |
time (sec) |
N/A | 0.470 | 0.034 | 0.219 | 0.000 | 0.260 | 0.000 | 0.000 | 0.769 |