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 | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 188 | 354 | 419 | 410 | 598 | 396 | 545 | 415 | 486 |
N.S. |
1 | 1.00 | 1.88 | 2.23 | 2.18 | 3.18 | 2.11 | 2.90 | 2.21 | 2.59 |
time (sec) |
N/A | 0.851 | 0.167 | 1.166 | 0.086 | 0.100 | 1.155 | 0.191 | 0.249 | 0.113 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 193 | 187 | 414 | 419 | 652 | 444 | 442 | 470 | 451 |
N.S. |
1 | 1.00 | 0.97 | 2.15 | 2.17 | 3.38 | 2.30 | 2.29 | 2.44 | 2.34 |
time (sec) |
N/A | 0.739 | 0.114 | 1.204 | 0.043 | 0.086 | 3.562 | 0.150 | 0.230 | 11.956 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 189 | 351 | 416 | 431 | 650 | 486 | 439 | 469 | 451 |
N.S. |
1 | 1.00 | 1.86 | 2.20 | 2.28 | 3.44 | 2.57 | 2.32 | 2.48 | 2.39 |
time (sec) |
N/A | 0.750 | 0.193 | 1.296 | 0.050 | 0.085 | 10.259 | 0.197 | 0.219 | 0.177 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 189 | 338 | 420 | 440 | 602 | 518 | 652 | 434 | 462 |
N.S. |
1 | 1.00 | 1.79 | 2.22 | 2.33 | 3.19 | 2.74 | 3.45 | 2.30 | 2.44 |
time (sec) |
N/A | 0.746 | 0.198 | 1.202 | 0.046 | 0.084 | 34.153 | 0.143 | 0.228 | 11.795 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 156 | 332 | 415 | 459 | 526 | 542 | 438 | 375 | 465 |
N.S. |
1 | 1.01 | 2.14 | 2.68 | 2.96 | 3.39 | 3.50 | 2.83 | 2.42 | 3.00 |
time (sec) |
N/A | 0.612 | 0.172 | 1.259 | 0.047 | 0.084 | 133.988 | 0.175 | 0.227 | 0.193 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 317 | 406 | 453 | 453 | 0 | 466 | 279 | 460 |
N.S. |
1 | 1.00 | 3.69 | 4.72 | 5.27 | 5.27 | 0.00 | 5.42 | 3.24 | 5.35 |
time (sec) |
N/A | 0.373 | 0.164 | 1.149 | 0.045 | 0.076 | 0.000 | 0.144 | 0.229 | 11.192 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 131 | 323 | 413 | 478 | 478 | 0 | 468 | 338 | 479 |
N.S. |
1 | 0.97 | 2.39 | 3.06 | 3.54 | 3.54 | 0.00 | 3.47 | 2.50 | 3.55 |
time (sec) |
N/A | 0.419 | 0.171 | 1.316 | 0.048 | 0.082 | 0.000 | 0.201 | 0.213 | 0.147 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 175 | 320 | 413 | 489 | 489 | 0 | 468 | 349 | 490 |
N.S. |
1 | 0.95 | 1.73 | 2.23 | 2.64 | 2.64 | 0.00 | 2.53 | 1.89 | 2.65 |
time (sec) |
N/A | 0.471 | 0.155 | 1.144 | 0.050 | 0.106 | 0.000 | 0.171 | 0.207 | 11.723 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 206 | 322 | 413 | 500 | 500 | 0 | 468 | 360 | 501 |
N.S. |
1 | 1.00 | 1.56 | 2.00 | 2.43 | 2.43 | 0.00 | 2.27 | 1.75 | 2.43 |
time (sec) |
N/A | 0.749 | 0.156 | 1.255 | 0.050 | 0.085 | 0.000 | 0.189 | 0.224 | 12.237 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 206 | 320 | 403 | 501 | 501 | 0 | 466 | 371 | 502 |
N.S. |
1 | 1.00 | 1.55 | 1.96 | 2.43 | 2.43 | 0.00 | 2.26 | 1.80 | 2.44 |
time (sec) |
N/A | 0.730 | 0.157 | 1.219 | 0.060 | 0.089 | 0.000 | 0.159 | 0.217 | 12.236 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 206 | 323 | 413 | 522 | 522 | 0 | 468 | 382 | 523 |
N.S. |
1 | 1.00 | 1.57 | 2.00 | 2.53 | 2.53 | 0.00 | 2.27 | 1.85 | 2.54 |
time (sec) |
N/A | 0.737 | 0.158 | 1.221 | 0.065 | 0.085 | 0.000 | 0.152 | 0.214 | 0.234 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 187 | 365 | 421 | 411 | 610 | 396 | 455 | 208 | 486 |
N.S. |
1 | 1.00 | 1.95 | 2.25 | 2.20 | 3.26 | 2.12 | 2.43 | 1.11 | 2.60 |
time (sec) |
N/A | 0.803 | 0.193 | 1.316 | 0.040 | 0.086 | 1.170 | 0.139 | 0.234 | 0.130 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 145 | 250 | 277 | 273 | 417 | 257 | 293 | 132 | 293 |
N.S. |
1 | 0.97 | 1.67 | 1.85 | 1.82 | 2.78 | 1.71 | 1.95 | 0.88 | 1.95 |
time (sec) |
N/A | 0.645 | 0.147 | 1.301 | 0.044 | 0.080 | 0.794 | 0.196 | 0.228 | 12.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 99 | 153 | 151 | 158 | 249 | 151 | 164 | 72 | 165 |
N.S. |
1 | 1.00 | 1.55 | 1.53 | 1.60 | 2.52 | 1.53 | 1.66 | 0.73 | 1.67 |
time (sec) |
N/A | 0.509 | 0.087 | 1.280 | 0.039 | 0.081 | 0.486 | 0.193 | 0.229 | 12.083 |
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 | 60 | 60 | 56 | 70 | 77 | 109 | 71 | 69 | 28 | 75 |
N.S. |
1 | 1.00 | 0.93 | 1.17 | 1.28 | 1.82 | 1.18 | 1.15 | 0.47 | 1.25 |
time (sec) |
N/A | 0.402 | 0.052 | 1.293 | 0.046 | 0.070 | 0.256 | 0.172 | 0.227 | 11.505 |
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 | 32 | 32 | 31 | 33 | 34 | 37 | 27 | 32 | 10 | 32 |
N.S. |
1 | 1.00 | 0.97 | 1.03 | 1.06 | 1.16 | 0.84 | 1.00 | 0.31 | 1.00 |
time (sec) |
N/A | 0.319 | 0.013 | 1.106 | 0.032 | 0.075 | 0.104 | 0.151 | 0.251 | 0.051 |
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 | 82 | 82 | 69 | 83 | 118 | 157 | 355 | 137 | 26 | 94 |
N.S. |
1 | 1.00 | 0.84 | 1.01 | 1.44 | 1.91 | 4.33 | 1.67 | 0.32 | 1.15 |
time (sec) |
N/A | 0.453 | 0.066 | 1.589 | 0.032 | 0.074 | 0.721 | 0.169 | 0.219 | 11.600 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 117 | 103 | 123 | 256 | 396 | 706 | 192 | 115 | 263 |
N.S. |
1 | 1.00 | 0.88 | 1.05 | 2.19 | 3.38 | 6.03 | 1.64 | 0.98 | 2.25 |
time (sec) |
N/A | 0.539 | 0.114 | 1.503 | 0.046 | 0.090 | 1.374 | 0.186 | 0.233 | 11.836 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 157 | 146 | 159 | 479 | 801 | 1066 | 400 | 289 | 454 |
N.S. |
1 | 1.00 | 0.93 | 1.01 | 3.05 | 5.10 | 6.79 | 2.55 | 1.84 | 2.89 |
time (sec) |
N/A | 0.652 | 0.103 | 1.537 | 0.058 | 0.105 | 2.045 | 0.177 | 0.220 | 11.922 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 186 | 362 | 416 | 434 | 671 | 486 | 437 | 330 | 451 |
N.S. |
1 | 1.00 | 1.95 | 2.24 | 2.33 | 3.61 | 2.61 | 2.35 | 1.77 | 2.42 |
time (sec) |
N/A | 0.757 | 0.224 | 1.270 | 0.061 | 0.084 | 10.041 | 0.193 | 0.208 | 0.185 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 144 | 217 | 273 | 292 | 427 | 337 | 277 | 209 | 301 |
N.S. |
1 | 1.00 | 1.51 | 1.90 | 2.03 | 2.97 | 2.34 | 1.92 | 1.45 | 2.09 |
time (sec) |
N/A | 0.628 | 0.144 | 1.319 | 0.074 | 0.084 | 5.859 | 0.159 | 0.206 | 11.798 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 104 | 138 | 161 | 189 | 226 | 211 | 163 | 113 | 178 |
N.S. |
1 | 1.03 | 1.37 | 1.59 | 1.87 | 2.24 | 2.09 | 1.61 | 1.12 | 1.76 |
time (sec) |
N/A | 0.473 | 0.083 | 1.249 | 0.043 | 0.080 | 2.604 | 0.177 | 0.210 | 0.131 |
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 | 73 | 73 | 61 | 70 | 97 | 97 | 107 | 70 | 37 | 91 |
N.S. |
1 | 1.00 | 0.84 | 0.96 | 1.33 | 1.33 | 1.47 | 0.96 | 0.51 | 1.25 |
time (sec) |
N/A | 0.422 | 0.040 | 1.306 | 0.032 | 0.074 | 0.758 | 0.136 | 0.210 | 11.667 |
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 | 38 | 38 | 27 | 33 | 50 | 50 | 53 | 25 | 23 | 52 |
N.S. |
1 | 1.00 | 0.71 | 0.87 | 1.32 | 1.32 | 1.39 | 0.66 | 0.61 | 1.37 |
time (sec) |
N/A | 0.326 | 0.013 | 1.211 | 0.032 | 0.085 | 0.181 | 0.171 | 0.214 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 146 | 136 | 143 | 452 | 643 | 818 | 376 | 288 | 398 |
N.S. |
1 | 1.00 | 0.93 | 0.98 | 3.10 | 4.40 | 5.60 | 2.58 | 1.97 | 2.73 |
time (sec) |
N/A | 0.597 | 0.096 | 1.560 | 0.054 | 0.094 | 1.610 | 0.168 | 0.236 | 11.350 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 199 | 199 | 189 | 203 | 757 | 1228 | 1445 | 431 | 821 | 711 |
N.S. |
1 | 1.00 | 0.95 | 1.02 | 3.80 | 6.17 | 7.26 | 2.17 | 4.13 | 3.57 |
time (sec) |
N/A | 0.804 | 0.144 | 2.017 | 0.078 | 0.124 | 2.956 | 0.213 | 0.229 | 11.605 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 128 | 138 | 120 | 159 | 424 | 1020 | 1804 | 342 | 115 |
N.S. |
1 | 1.00 | 1.08 | 0.94 | 1.24 | 3.31 | 7.97 | 14.09 | 2.67 | 0.90 |
time (sec) |
N/A | 0.483 | 0.209 | 2.040 | 0.038 | 0.076 | 0.684 | 0.194 | 0.227 | 11.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 128 | 138 | 120 | 159 | 356 | 857 | 1293 | 284 | 115 |
N.S. |
1 | 1.00 | 1.08 | 0.94 | 1.24 | 2.78 | 6.70 | 10.10 | 2.22 | 0.90 |
time (sec) |
N/A | 0.461 | 0.195 | 1.905 | 0.037 | 0.075 | 0.509 | 0.198 | 0.235 | 11.147 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 128 | 139 | 117 | 159 | 289 | 257 | 854 | 226 | 115 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.24 | 2.26 | 2.01 | 6.67 | 1.77 | 0.90 |
time (sec) |
N/A | 0.469 | 0.182 | 1.850 | 0.036 | 0.076 | 1.214 | 0.227 | 0.230 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 128 | 138 | 116 | 159 | 220 | 257 | 486 | 168 | 115 |
N.S. |
1 | 1.00 | 1.08 | 0.91 | 1.24 | 1.72 | 2.01 | 3.80 | 1.31 | 0.90 |
time (sec) |
N/A | 0.440 | 0.170 | 1.719 | 0.053 | 0.075 | 1.160 | 0.180 | 0.225 | 0.077 |
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 | 126 | 126 | 137 | 117 | 159 | 155 | 255 | 206 | 114 | 115 |
N.S. |
1 | 1.00 | 1.09 | 0.93 | 1.26 | 1.23 | 2.02 | 1.63 | 0.90 | 0.91 |
time (sec) |
N/A | 0.457 | 0.166 | 1.604 | 0.039 | 0.076 | 1.023 | 0.190 | 0.218 | 0.074 |
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 | 124 | 124 | 135 | 121 | 167 | 165 | 207 | 221 | 115 | 154 |
N.S. |
1 | 1.00 | 1.09 | 0.98 | 1.35 | 1.33 | 1.67 | 1.78 | 0.93 | 1.24 |
time (sec) |
N/A | 0.473 | 0.177 | 0.957 | 0.041 | 0.073 | 4.397 | 0.175 | 0.231 | 0.080 |
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 | 124 | 124 | 136 | 105 | 163 | 175 | 709 | 203 | 122 | 189 |
N.S. |
1 | 1.00 | 1.10 | 0.85 | 1.31 | 1.41 | 5.72 | 1.64 | 0.98 | 1.52 |
time (sec) |
N/A | 0.456 | 0.205 | 0.908 | 0.040 | 0.082 | 0.403 | 0.205 | 0.217 | 11.261 |
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 | 124 | 124 | 136 | 118 | 164 | 188 | 1015 | 193 | 134 | 168 |
N.S. |
1 | 1.00 | 1.10 | 0.95 | 1.32 | 1.52 | 8.19 | 1.56 | 1.08 | 1.35 |
time (sec) |
N/A | 0.478 | 0.196 | 1.134 | 0.038 | 0.081 | 0.548 | 0.166 | 0.209 | 11.438 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 218 | 218 | 339 | 283 | 409 | 894 | 2091 | 3684 | 635 | 197 |
N.S. |
1 | 1.00 | 1.56 | 1.30 | 1.88 | 4.10 | 9.59 | 16.90 | 2.91 | 0.90 |
time (sec) |
N/A | 0.707 | 0.521 | 2.127 | 0.040 | 0.081 | 0.998 | 0.218 | 0.249 | 0.104 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 218 | 218 | 340 | 283 | 409 | 772 | 624 | 2697 | 543 | 197 |
N.S. |
1 | 1.00 | 1.56 | 1.30 | 1.88 | 3.54 | 2.86 | 12.37 | 2.49 | 0.90 |
time (sec) |
N/A | 0.619 | 0.510 | 2.313 | 0.041 | 0.083 | 2.051 | 0.227 | 0.220 | 11.701 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 218 | 218 | 339 | 282 | 409 | 649 | 624 | 1830 | 451 | 197 |
N.S. |
1 | 1.00 | 1.56 | 1.29 | 1.88 | 2.98 | 2.86 | 8.39 | 2.07 | 0.90 |
time (sec) |
N/A | 0.630 | 0.501 | 2.438 | 0.047 | 0.085 | 1.851 | 0.170 | 0.254 | 11.493 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 218 | 218 | 339 | 282 | 409 | 527 | 624 | 1083 | 359 | 197 |
N.S. |
1 | 1.00 | 1.56 | 1.29 | 1.88 | 2.42 | 2.86 | 4.97 | 1.65 | 0.90 |
time (sec) |
N/A | 0.607 | 0.435 | 2.211 | 0.041 | 0.086 | 1.900 | 0.215 | 0.254 | 0.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 216 | 338 | 283 | 409 | 408 | 622 | 478 | 271 | 197 |
N.S. |
1 | 1.00 | 1.56 | 1.31 | 1.89 | 1.89 | 2.88 | 2.21 | 1.25 | 0.91 |
time (sec) |
N/A | 0.615 | 0.420 | 2.152 | 0.037 | 0.080 | 1.784 | 0.185 | 0.242 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 214 | 335 | 280 | 417 | 418 | 507 | 593 | 273 | 296 |
N.S. |
1 | 1.00 | 1.57 | 1.31 | 1.95 | 1.95 | 2.37 | 2.77 | 1.28 | 1.38 |
time (sec) |
N/A | 0.600 | 0.451 | 1.348 | 0.047 | 0.087 | 23.029 | 0.192 | 0.251 | 11.734 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 214 | 336 | 283 | 415 | 430 | 416 | 568 | 280 | 367 |
N.S. |
1 | 1.00 | 1.57 | 1.32 | 1.94 | 2.01 | 1.94 | 2.65 | 1.31 | 1.71 |
time (sec) |
N/A | 0.626 | 0.492 | 1.411 | 0.058 | 0.091 | 23.026 | 0.178 | 0.233 | 11.490 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 214 | 337 | 290 | 416 | 441 | 2440 | 563 | 291 | 413 |
N.S. |
1 | 1.00 | 1.57 | 1.36 | 1.94 | 2.06 | 11.40 | 2.63 | 1.36 | 1.93 |
time (sec) |
N/A | 0.674 | 0.467 | 1.333 | 0.046 | 0.093 | 0.688 | 0.209 | 0.247 | 0.108 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 308 | 308 | 628 | 517 | 767 | 1470 | 1127 | 6044 | 996 | 279 |
N.S. |
1 | 1.00 | 2.04 | 1.68 | 2.49 | 4.77 | 3.66 | 19.62 | 3.23 | 0.91 |
time (sec) |
N/A | 0.943 | 1.143 | 2.202 | 0.043 | 0.098 | 2.605 | 0.269 | 0.223 | 11.745 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 308 | 308 | 629 | 516 | 767 | 1293 | 1127 | 4485 | 870 | 279 |
N.S. |
1 | 1.00 | 2.04 | 1.68 | 2.49 | 4.20 | 3.66 | 14.56 | 2.82 | 0.91 |
time (sec) |
N/A | 0.814 | 0.891 | 2.204 | 0.050 | 0.098 | 2.522 | 0.268 | 0.241 | 11.285 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 308 | 308 | 629 | 513 | 767 | 1118 | 1127 | 3094 | 744 | 279 |
N.S. |
1 | 1.00 | 2.04 | 1.67 | 2.49 | 3.63 | 3.66 | 10.05 | 2.42 | 0.91 |
time (sec) |
N/A | 0.817 | 0.840 | 1.977 | 0.044 | 0.195 | 2.317 | 0.232 | 0.239 | 11.566 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 308 | 308 | 628 | 518 | 767 | 942 | 1127 | 1871 | 618 | 279 |
N.S. |
1 | 1.00 | 2.04 | 1.68 | 2.49 | 3.06 | 3.66 | 6.07 | 2.01 | 0.91 |
time (sec) |
N/A | 0.797 | 0.800 | 2.149 | 0.044 | 0.086 | 2.230 | 0.207 | 0.243 | 11.304 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 306 | 306 | 628 | 513 | 767 | 769 | 1125 | 846 | 496 | 279 |
N.S. |
1 | 1.00 | 2.05 | 1.68 | 2.51 | 2.51 | 3.68 | 2.76 | 1.62 | 0.91 |
time (sec) |
N/A | 0.790 | 0.768 | 2.248 | 0.047 | 0.093 | 2.089 | 0.180 | 0.198 | 11.173 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 300 | 300 | 624 | 514 | 775 | 778 | 942 | 1141 | 498 | 438 |
N.S. |
1 | 1.00 | 2.08 | 1.71 | 2.58 | 2.59 | 3.14 | 3.80 | 1.66 | 1.46 |
time (sec) |
N/A | 0.799 | 0.894 | 1.385 | 0.044 | 0.090 | 72.893 | 0.191 | 0.267 | 0.097 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 302 | 302 | 624 | 511 | 773 | 790 | 784 | 1108 | 505 | 569 |
N.S. |
1 | 1.00 | 2.07 | 1.69 | 2.56 | 2.62 | 2.60 | 3.67 | 1.67 | 1.88 |
time (sec) |
N/A | 0.785 | 0.904 | 1.355 | 0.057 | 0.103 | 71.207 | 0.212 | 0.271 | 11.150 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 304 | 304 | 627 | 517 | 775 | 802 | 656 | 1103 | 516 | 675 |
N.S. |
1 | 1.00 | 2.06 | 1.70 | 2.55 | 2.64 | 2.16 | 3.63 | 1.70 | 2.22 |
time (sec) |
N/A | 0.798 | 0.888 | 1.484 | 0.098 | 0.099 | 72.759 | 0.215 | 0.227 | 11.220 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 222 | 305 | 278 | 0 | 1006 | 0 | 583 | 349 | 562 |
N.S. |
1 | 1.00 | 1.38 | 1.26 | 0.00 | 4.55 | 0.00 | 2.64 | 1.58 | 2.54 |
time (sec) |
N/A | 0.642 | 1.086 | 1.534 | 0.000 | 0.106 | 0.000 | 0.188 | 0.256 | 11.192 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 193 | 210 | 212 | 0 | 666 | 0 | 382 | 223 | 363 |
N.S. |
1 | 1.08 | 1.17 | 1.18 | 0.00 | 3.72 | 0.00 | 2.13 | 1.25 | 2.03 |
time (sec) |
N/A | 0.575 | 0.860 | 1.497 | 0.000 | 0.098 | 0.000 | 0.150 | 0.255 | 0.138 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 164 | 139 | 138 | 0 | 392 | 0 | 224 | 119 | 174 |
N.S. |
1 | 1.18 | 1.00 | 0.99 | 0.00 | 2.82 | 0.00 | 1.61 | 0.86 | 1.25 |
time (sec) |
N/A | 0.517 | 0.611 | 1.519 | 0.000 | 0.094 | 0.000 | 0.162 | 0.218 | 0.199 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 134 | 96 | 103 | 0 | 393 | 0 | 114 | 51 | 108 |
N.S. |
1 | 1.25 | 0.90 | 0.96 | 0.00 | 3.67 | 0.00 | 1.07 | 0.48 | 1.01 |
time (sec) |
N/A | 0.501 | 0.525 | 1.519 | 0.000 | 0.088 | 0.000 | 0.180 | 0.253 | 11.135 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 102 | 88 | 0 | 397 | 0 | 122 | 50 | 99 |
N.S. |
1 | 1.00 | 0.99 | 0.85 | 0.00 | 3.85 | 0.00 | 1.18 | 0.49 | 0.96 |
time (sec) |
N/A | 0.449 | 0.555 | 1.467 | 0.000 | 0.087 | 0.000 | 0.192 | 0.253 | 0.147 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 141 | 122 | 130 | 0 | 775 | 0 | 189 | 84 | 156 |
N.S. |
1 | 1.10 | 0.95 | 1.02 | 0.00 | 6.05 | 0.00 | 1.48 | 0.66 | 1.22 |
time (sec) |
N/A | 0.504 | 0.717 | 1.410 | 0.000 | 0.104 | 0.000 | 0.141 | 0.231 | 11.210 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 178 | 197 | 164 | 0 | 1086 | 0 | 282 | 223 | 210 |
N.S. |
1 | 1.07 | 1.18 | 0.98 | 0.00 | 6.50 | 0.00 | 1.69 | 1.34 | 1.26 |
time (sec) |
N/A | 0.547 | 0.995 | 1.576 | 0.000 | 0.125 | 0.000 | 0.201 | 0.288 | 11.157 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 214 | 289 | 202 | 0 | 1731 | 0 | 422 | 437 | 261 |
N.S. |
1 | 1.03 | 1.39 | 0.97 | 0.00 | 8.32 | 0.00 | 2.03 | 2.10 | 1.25 |
time (sec) |
N/A | 0.591 | 1.248 | 1.513 | 0.000 | 0.205 | 0.000 | 0.173 | 0.253 | 11.185 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 277 | 257 | 419 | 364 | 0 | 1514 | 0 | 831 | 715 | 790 |
N.S. |
1 | 0.93 | 1.51 | 1.31 | 0.00 | 5.47 | 0.00 | 3.00 | 2.58 | 2.85 |
time (sec) |
N/A | 0.653 | 2.416 | 1.734 | 0.000 | 0.137 | 0.000 | 0.225 | 0.236 | 11.169 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 232 | 227 | 306 | 287 | 0 | 1026 | 0 | 577 | 464 | 513 |
N.S. |
1 | 0.98 | 1.32 | 1.24 | 0.00 | 4.42 | 0.00 | 2.49 | 2.00 | 2.21 |
time (sec) |
N/A | 0.596 | 2.459 | 1.726 | 0.000 | 0.125 | 0.000 | 0.167 | 0.219 | 11.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 198 | 211 | 214 | 0 | 1075 | 0 | 368 | 246 | 416 |
N.S. |
1 | 1.01 | 1.08 | 1.09 | 0.00 | 5.48 | 0.00 | 1.88 | 1.26 | 2.12 |
time (sec) |
N/A | 0.571 | 2.103 | 1.716 | 0.000 | 0.113 | 0.000 | 0.205 | 0.259 | 11.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 177 | 211 | 207 | 0 | 1115 | 0 | 377 | 259 | 325 |
N.S. |
1 | 0.95 | 1.13 | 1.11 | 0.00 | 5.96 | 0.00 | 2.02 | 1.39 | 1.74 |
time (sec) |
N/A | 0.535 | 2.154 | 1.428 | 0.000 | 0.122 | 0.000 | 0.212 | 0.209 | 0.274 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 183 | 213 | 202 | 0 | 1218 | 0 | 384 | 301 | 310 |
N.S. |
1 | 0.92 | 1.08 | 1.02 | 0.00 | 6.15 | 0.00 | 1.94 | 1.52 | 1.57 |
time (sec) |
N/A | 0.541 | 1.990 | 1.513 | 0.000 | 0.123 | 0.000 | 0.211 | 0.240 | 11.193 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 209 | 197 | 214 | 210 | 0 | 1337 | 0 | 429 | 352 | 331 |
N.S. |
1 | 0.94 | 1.02 | 1.00 | 0.00 | 6.40 | 0.00 | 2.05 | 1.68 | 1.58 |
time (sec) |
N/A | 0.553 | 1.554 | 1.506 | 0.000 | 0.131 | 0.000 | 0.214 | 0.265 | 11.144 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 233 | 294 | 273 | 0 | 2114 | 0 | 521 | 437 | 420 |
N.S. |
1 | 1.01 | 1.27 | 1.18 | 0.00 | 9.15 | 0.00 | 2.26 | 1.89 | 1.82 |
time (sec) |
N/A | 0.602 | 2.481 | 1.499 | 0.000 | 0.214 | 0.000 | 0.191 | 0.281 | 11.426 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 275 | 269 | 408 | 315 | 0 | 2628 | 0 | 762 | 804 | 483 |
N.S. |
1 | 0.98 | 1.48 | 1.15 | 0.00 | 9.56 | 0.00 | 2.77 | 2.92 | 1.76 |
time (sec) |
N/A | 0.667 | 3.198 | 1.467 | 0.000 | 0.373 | 0.000 | 0.180 | 0.221 | 11.558 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 325 | 306 | 547 | 354 | 0 | 3667 | 0 | 794 | 1299 | 547 |
N.S. |
1 | 0.94 | 1.68 | 1.09 | 0.00 | 11.28 | 0.00 | 2.44 | 4.00 | 1.68 |
time (sec) |
N/A | 0.688 | 4.019 | 1.578 | 0.000 | 0.943 | 0.000 | 0.207 | 0.272 | 11.877 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 318 | 292 | 558 | 487 | 0 | 1862 | 0 | 1066 | 907 | 996 |
N.S. |
1 | 0.92 | 1.75 | 1.53 | 0.00 | 5.86 | 0.00 | 3.35 | 2.85 | 3.13 |
time (sec) |
N/A | 0.684 | 4.723 | 2.725 | 0.000 | 0.236 | 0.000 | 0.208 | 0.231 | 0.484 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 280 | 262 | 421 | 372 | 0 | 1955 | 0 | 768 | 543 | 838 |
N.S. |
1 | 0.94 | 1.50 | 1.33 | 0.00 | 6.98 | 0.00 | 2.74 | 1.94 | 2.99 |
time (sec) |
N/A | 0.638 | 5.942 | 2.667 | 0.000 | 0.179 | 0.000 | 0.220 | 0.234 | 11.400 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 273 | 241 | 421 | 377 | 0 | 2041 | 0 | 777 | 583 | 594 |
N.S. |
1 | 0.88 | 1.54 | 1.38 | 0.00 | 7.48 | 0.00 | 2.85 | 2.14 | 2.18 |
time (sec) |
N/A | 0.599 | 5.875 | 2.675 | 0.000 | 0.178 | 0.000 | 0.226 | 0.237 | 0.457 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 282 | 247 | 423 | 303 | 0 | 2238 | 0 | 803 | 661 | 572 |
N.S. |
1 | 0.88 | 1.50 | 1.07 | 0.00 | 7.94 | 0.00 | 2.85 | 2.34 | 2.03 |
time (sec) |
N/A | 0.626 | 5.691 | 2.598 | 0.000 | 0.198 | 0.000 | 0.225 | 0.252 | 11.415 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 261 | 421 | 316 | 0 | 2349 | 0 | 814 | 742 | 535 |
N.S. |
1 | 0.89 | 1.44 | 1.08 | 0.00 | 8.04 | 0.00 | 2.79 | 2.54 | 1.83 |
time (sec) |
N/A | 0.597 | 4.437 | 1.539 | 0.000 | 0.198 | 0.000 | 0.193 | 0.205 | 11.274 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 302 | 275 | 425 | 368 | 0 | 2580 | 0 | 859 | 821 | 564 |
N.S. |
1 | 0.91 | 1.41 | 1.22 | 0.00 | 8.54 | 0.00 | 2.84 | 2.72 | 1.87 |
time (sec) |
N/A | 0.657 | 4.204 | 1.535 | 0.000 | 0.212 | 0.000 | 0.219 | 0.228 | 11.565 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 313 | 289 | 423 | 361 | 0 | 2715 | 0 | 885 | 903 | 567 |
N.S. |
1 | 0.92 | 1.35 | 1.15 | 0.00 | 8.67 | 0.00 | 2.83 | 2.88 | 1.81 |
time (sec) |
N/A | 0.666 | 3.302 | 1.547 | 0.000 | 0.242 | 0.000 | 0.201 | 0.223 | 11.526 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 329 | 325 | 545 | 445 | 0 | 3876 | 0 | 1005 | 1014 | 683 |
N.S. |
1 | 0.99 | 1.66 | 1.35 | 0.00 | 11.78 | 0.00 | 3.05 | 3.08 | 2.08 |
time (sec) |
N/A | 0.695 | 6.806 | 1.662 | 0.000 | 0.774 | 0.000 | 0.254 | 0.207 | 11.954 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 376 | 362 | 705 | 579 | 0 | 4644 | 0 | 1119 | 1661 | 755 |
N.S. |
1 | 0.96 | 1.88 | 1.54 | 0.00 | 12.35 | 0.00 | 2.98 | 4.42 | 2.01 |
time (sec) |
N/A | 0.731 | 8.148 | 1.628 | 0.000 | 1.722 | 0.000 | 0.247 | 0.210 | 12.386 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 428 | 397 | 884 | 618 | 0 | 6015 | 0 | 1700 | 2284 | 802 |
N.S. |
1 | 0.93 | 2.07 | 1.44 | 0.00 | 14.05 | 0.00 | 3.97 | 5.34 | 1.87 |
time (sec) |
N/A | 0.750 | 9.599 | 1.760 | 0.000 | 3.938 | 0.000 | 0.224 | 0.226 | 12.890 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 105 | 208 | 232 | 1002 | 175 | 1516 | 471 | 172 | 1400 |
N.S. |
1 | 0.66 | 1.32 | 1.47 | 6.34 | 1.11 | 9.59 | 2.98 | 1.09 | 8.86 |
time (sec) |
N/A | 0.565 | 1.095 | 1.063 | 0.052 | 0.073 | 4.192 | 0.183 | 0.229 | 13.149 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 105 | 163 | 180 | 698 | 134 | 1080 | 364 | 131 | 935 |
N.S. |
1 | 0.66 | 1.03 | 1.14 | 4.42 | 0.85 | 6.84 | 2.30 | 0.83 | 5.92 |
time (sec) |
N/A | 0.511 | 1.083 | 0.832 | 0.045 | 0.068 | 3.196 | 0.191 | 0.197 | 12.257 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 105 | 120 | 128 | 456 | 93 | 704 | 260 | 90 | 564 |
N.S. |
1 | 0.66 | 0.76 | 0.81 | 2.89 | 0.59 | 4.46 | 1.65 | 0.57 | 3.57 |
time (sec) |
N/A | 0.477 | 1.067 | 0.868 | 0.042 | 0.073 | 2.372 | 0.170 | 0.206 | 11.561 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 84 | 74 | 76 | 254 | 52 | 393 | 155 | 49 | 223 |
N.S. |
1 | 0.51 | 0.45 | 0.46 | 1.55 | 0.32 | 2.40 | 0.95 | 0.30 | 1.36 |
time (sec) |
N/A | 0.426 | 1.042 | 0.629 | 0.039 | 0.074 | 1.783 | 0.179 | 0.220 | 11.688 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 91 | 33 | 125 | 24 | 156 | 74 | 21 | 77 |
N.S. |
1 | 1.00 | 1.32 | 0.48 | 1.81 | 0.35 | 2.26 | 1.07 | 0.30 | 1.12 |
time (sec) |
N/A | 0.322 | 0.055 | 0.559 | 0.029 | 0.075 | 0.978 | 0.180 | 0.204 | 11.180 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 88 | 74 | 98 | 0 | 68 | 0 | 116 | 72 | 0 |
N.S. |
1 | 0.67 | 0.56 | 0.74 | 0.00 | 0.52 | 0.00 | 0.88 | 0.55 | 0.00 |
time (sec) |
N/A | 0.449 | 1.047 | 0.920 | 0.000 | 0.074 | 0.000 | 0.188 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 91 | 96 | 118 | 0 | 102 | 0 | 121 | 112 | 0 |
N.S. |
1 | 0.63 | 0.67 | 0.82 | 0.00 | 0.71 | 0.00 | 0.84 | 0.78 | 0.00 |
time (sec) |
N/A | 0.450 | 1.059 | 0.953 | 0.000 | 0.079 | 0.000 | 0.177 | 0.243 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 98 | 89 | 104 | 0 | 105 | 0 | 125 | 113 | 0 |
N.S. |
1 | 0.65 | 0.59 | 0.69 | 0.00 | 0.70 | 0.00 | 0.83 | 0.75 | 0.00 |
time (sec) |
N/A | 0.468 | 1.064 | 1.121 | 0.000 | 0.075 | 0.000 | 0.180 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 104 | 81 | 77 | 0 | 93 | 0 | 177 | 69 | 86 |
N.S. |
1 | 1.00 | 0.78 | 0.74 | 0.00 | 0.89 | 0.00 | 1.70 | 0.66 | 0.83 |
time (sec) |
N/A | 0.430 | 1.046 | 1.305 | 0.000 | 0.087 | 0.000 | 0.188 | 0.206 | 11.274 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 105 | 80 | 76 | 0 | 102 | 0 | 190 | 95 | 85 |
N.S. |
1 | 0.66 | 0.51 | 0.48 | 0.00 | 0.65 | 0.00 | 1.20 | 0.60 | 0.54 |
time (sec) |
N/A | 0.455 | 1.048 | 1.241 | 0.000 | 0.077 | 0.000 | 0.329 | 0.211 | 11.242 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 105 | 83 | 79 | 0 | 117 | 0 | 208 | 106 | 88 |
N.S. |
1 | 0.66 | 0.53 | 0.50 | 0.00 | 0.74 | 0.00 | 1.32 | 0.67 | 0.56 |
time (sec) |
N/A | 0.456 | 1.053 | 1.493 | 0.000 | 0.074 | 0.000 | 0.145 | 0.221 | 11.265 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 105 | 82 | 78 | 0 | 126 | 0 | 221 | 117 | 87 |
N.S. |
1 | 0.66 | 0.52 | 0.49 | 0.00 | 0.80 | 0.00 | 1.40 | 0.74 | 0.55 |
time (sec) |
N/A | 0.469 | 1.048 | 1.937 | 0.000 | 0.079 | 0.000 | 0.161 | 0.218 | 11.344 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 298 | 191 | 496 | 676 | 1330 | 518 | 28995 | 1111 | 397 | 0 |
N.S. |
1 | 0.64 | 1.66 | 2.27 | 4.46 | 1.74 | 97.30 | 3.73 | 1.33 | 0.00 |
time (sec) |
N/A | 1.007 | 1.247 | 1.576 | 0.087 | 0.077 | 1.949 | 0.213 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 298 | 191 | 410 | 552 | 1004 | 425 | 16910 | 909 | 322 | 0 |
N.S. |
1 | 0.64 | 1.38 | 1.85 | 3.37 | 1.43 | 56.74 | 3.05 | 1.08 | 0.00 |
time (sec) |
N/A | 0.948 | 1.194 | 1.428 | 0.146 | 0.082 | 1.755 | 0.178 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 259 | 187 | 320 | 428 | 698 | 325 | 9440 | 707 | 247 | 0 |
N.S. |
1 | 0.72 | 1.24 | 1.65 | 2.69 | 1.25 | 36.45 | 2.73 | 0.95 | 0.00 |
time (sec) |
N/A | 0.816 | 1.177 | 1.388 | 0.055 | 0.075 | 1.519 | 0.215 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 146 | 233 | 304 | 456 | 239 | 4842 | 506 | 172 | 0 |
N.S. |
1 | 0.74 | 1.18 | 1.54 | 2.30 | 1.21 | 24.45 | 2.56 | 0.87 | 0.00 |
time (sec) |
N/A | 0.664 | 1.128 | 1.248 | 0.045 | 0.076 | 1.349 | 0.181 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 103 | 144 | 180 | 254 | 146 | 2076 | 304 | 97 | 0 |
N.S. |
1 | 0.76 | 1.07 | 1.33 | 1.88 | 1.08 | 15.38 | 2.25 | 0.72 | 0.00 |
time (sec) |
N/A | 0.515 | 1.085 | 1.026 | 0.041 | 0.080 | 1.568 | 0.359 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 83 | 90 | 125 | 69 | 745 | 144 | 43 | 42 |
N.S. |
1 | 1.00 | 1.17 | 1.27 | 1.76 | 0.97 | 10.49 | 2.03 | 0.61 | 0.59 |
time (sec) |
N/A | 0.326 | 0.039 | 1.122 | 0.032 | 0.074 | 0.715 | 0.184 | 0.217 | 11.208 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 236 | 152 | 187 | 325 | 0 | 260 | 0 | 441 | 208 | 0 |
N.S. |
1 | 0.64 | 0.79 | 1.38 | 0.00 | 1.10 | 0.00 | 1.87 | 0.88 | 0.00 |
time (sec) |
N/A | 0.574 | 1.139 | 1.408 | 0.000 | 0.082 | 0.000 | 0.179 | 0.253 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 285 | 178 | 262 | 326 | 0 | 396 | 0 | 440 | 297 | 0 |
N.S. |
1 | 0.62 | 0.92 | 1.14 | 0.00 | 1.39 | 0.00 | 1.54 | 1.04 | 0.00 |
time (sec) |
N/A | 0.720 | 1.154 | 1.500 | 0.000 | 0.086 | 0.000 | 0.186 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 280 | 173 | 256 | 311 | 0 | 420 | 0 | 430 | 330 | 0 |
N.S. |
1 | 0.62 | 0.91 | 1.11 | 0.00 | 1.50 | 0.00 | 1.54 | 1.18 | 0.00 |
time (sec) |
N/A | 0.667 | 1.167 | 1.547 | 0.000 | 0.078 | 0.000 | 0.161 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 284 | 177 | 251 | 320 | 0 | 406 | 0 | 423 | 309 | 0 |
N.S. |
1 | 0.62 | 0.88 | 1.13 | 0.00 | 1.43 | 0.00 | 1.49 | 1.09 | 0.00 |
time (sec) |
N/A | 0.658 | 1.170 | 1.551 | 0.000 | 0.087 | 0.000 | 0.160 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 159 | 240 | 299 | 0 | 354 | 0 | 431 | 269 | 0 |
N.S. |
1 | 0.62 | 0.93 | 1.16 | 0.00 | 1.38 | 0.00 | 1.68 | 1.05 | 0.00 |
time (sec) |
N/A | 0.589 | 1.163 | 1.721 | 0.000 | 0.083 | 0.000 | 0.216 | 0.212 | 0.000 |