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 | F | B | F | A | F | B |
verified | N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 174 | 120 | 1278 | 0 | 512 | 0 | 246 | 90 | 200 |
N.S. |
1 | 1.16 | 0.80 | 8.52 | 0.00 | 3.41 | 0.00 | 1.64 | 0.60 | 1.33 |
time (sec) |
N/A | 0.922 | 1.366 | 0.659 | 0.000 | 0.157 | 0.000 | 0.585 | 0.285 | 5.845 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F | B |
verified | N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 112 | 87 | 1223 | 0 | 397 | 0 | 210 | 65 | 90 |
N.S. |
1 | 1.12 | 0.87 | 12.23 | 0.00 | 3.97 | 0.00 | 2.10 | 0.65 | 0.90 |
time (sec) |
N/A | 0.605 | 0.570 | 0.413 | 0.000 | 0.115 | 0.000 | 0.499 | 0.236 | 3.830 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 74 | 63 | 805 | 4432 | 306 | 0 | 179 | 38 | 854 |
N.S. |
1 | 1.07 | 0.91 | 11.67 | 64.23 | 4.43 | 0.00 | 2.59 | 0.55 | 12.38 |
time (sec) |
N/A | 0.441 | 0.194 | 0.365 | 0.341 | 0.119 | 0.000 | 0.471 | 0.211 | 3.979 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | F | B |
verified | N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 149 | 162 | 126 | 0 | 686 | 0 | 355 | 30 | 763 |
N.S. |
1 | 1.06 | 1.16 | 0.90 | 0.00 | 4.90 | 0.00 | 2.54 | 0.21 | 5.45 |
time (sec) |
N/A | 0.748 | 0.519 | 0.724 | 0.000 | 0.143 | 0.000 | 0.531 | 0.205 | 4.489 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F(-2) | B | F | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 0 | 201 | 269 | 0 | 1086 | 0 | 457 | 40 | 14675 |
N.S. |
1 | 0.00 | 0.95 | 1.27 | 0.00 | 5.15 | 0.00 | 2.17 | 0.19 | 69.55 |
time (sec) |
N/A | 0.000 | 1.707 | 0.417 | 0.000 | 0.246 | 0.000 | 0.533 | 0.193 | 4.955 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F(-2) | B | F | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 280 | 0 | 238 | 382 | 0 | 1448 | 0 | 600 | 52 | 35270 |
N.S. |
1 | 0.00 | 0.85 | 1.36 | 0.00 | 5.17 | 0.00 | 2.14 | 0.19 | 125.96 |
time (sec) |
N/A | 0.000 | 4.195 | 0.448 | 0.000 | 0.408 | 0.000 | 0.538 | 0.237 | 7.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | F | B |
verified | N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 192 | 159 | 908 | 0 | 786 | 0 | 289 | 194 | 309 |
N.S. |
1 | 1.06 | 0.88 | 5.02 | 0.00 | 4.34 | 0.00 | 1.60 | 1.07 | 1.71 |
time (sec) |
N/A | 1.187 | 2.151 | 0.475 | 0.000 | 0.235 | 0.000 | 0.668 | 0.297 | 11.319 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F | B |
verified | N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 129 | 125 | 872 | 0 | 646 | 0 | 254 | 142 | 196 |
N.S. |
1 | 0.98 | 0.95 | 6.66 | 0.00 | 4.93 | 0.00 | 1.94 | 1.08 | 1.50 |
time (sec) |
N/A | 0.796 | 0.962 | 0.405 | 0.000 | 0.152 | 0.000 | 0.600 | 0.275 | 7.546 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-1) | B | F | B | F | B |
verified | N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 89 | 86 | 852 | 0 | 504 | 0 | 222 | 88 | 2869 |
N.S. |
1 | 0.91 | 0.88 | 8.69 | 0.00 | 5.14 | 0.00 | 2.27 | 0.90 | 29.28 |
time (sec) |
N/A | 0.583 | 0.402 | 0.364 | 0.000 | 0.109 | 0.000 | 0.521 | 0.223 | 13.425 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | F | B |
verified | N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 133 | 135 | 140 | 0 | 780 | 0 | 397 | 67 | 847 |
N.S. |
1 | 0.87 | 0.88 | 0.92 | 0.00 | 5.10 | 0.00 | 2.59 | 0.44 | 5.54 |
time (sec) |
N/A | 0.763 | 0.620 | 0.366 | 0.000 | 0.147 | 0.000 | 0.482 | 0.206 | 4.460 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | F | B |
verified | N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 209 | 219 | 248 | 284 | 0 | 983 | 0 | 453 | 87 | 1580 |
N.S. |
1 | 1.05 | 1.19 | 1.36 | 0.00 | 4.70 | 0.00 | 2.17 | 0.42 | 7.56 |
time (sec) |
N/A | 1.214 | 1.274 | 0.428 | 0.000 | 0.240 | 0.000 | 0.541 | 0.197 | 4.487 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | F | B |
verified | N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 274 | 289 | 343 | 362 | 0 | 1238 | 0 | 600 | 111 | 16296 |
N.S. |
1 | 1.05 | 1.25 | 1.32 | 0.00 | 4.52 | 0.00 | 2.19 | 0.41 | 59.47 |
time (sec) |
N/A | 1.725 | 2.804 | 0.415 | 0.000 | 0.356 | 0.000 | 0.672 | 0.238 | 6.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-1) | B | F | A | F | B |
verified | N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 245 | 266 | 1047 | 0 | 1087 | 0 | 350 | 316 | 400 |
N.S. |
1 | 1.13 | 1.23 | 4.85 | 0.00 | 5.03 | 0.00 | 1.62 | 1.46 | 1.85 |
time (sec) |
N/A | 1.443 | 3.617 | 0.530 | 0.000 | 0.633 | 0.000 | 0.853 | 0.264 | 25.262 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F | B |
verified | N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 182 | 159 | 1003 | 0 | 917 | 0 | 315 | 233 | 257 |
N.S. |
1 | 1.10 | 0.96 | 6.04 | 0.00 | 5.52 | 0.00 | 1.90 | 1.40 | 1.55 |
time (sec) |
N/A | 1.017 | 1.705 | 0.424 | 0.000 | 0.310 | 0.000 | 0.763 | 0.303 | 16.713 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-1) | B | F | B | F | B |
verified | N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 140 | 117 | 970 | 0 | 732 | 0 | 278 | 149 | 3899 |
N.S. |
1 | 1.07 | 0.89 | 7.40 | 0.00 | 5.59 | 0.00 | 2.12 | 1.14 | 29.76 |
time (sec) |
N/A | 0.790 | 0.747 | 0.382 | 0.000 | 0.173 | 0.000 | 0.548 | 0.230 | 25.433 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | F | B |
verified | N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 161 | 166 | 237 | 0 | 1025 | 0 | 450 | 109 | 4857 |
N.S. |
1 | 0.87 | 0.90 | 1.28 | 0.00 | 5.54 | 0.00 | 2.43 | 0.59 | 26.25 |
time (sec) |
N/A | 0.936 | 0.800 | 0.321 | 0.000 | 0.275 | 0.000 | 0.535 | 0.220 | 6.343 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | F | B |
verified | N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 205 | 234 | 302 | 0 | 1083 | 0 | 507 | 138 | 9787 |
N.S. |
1 | 0.94 | 1.08 | 1.39 | 0.00 | 4.99 | 0.00 | 2.34 | 0.64 | 45.10 |
time (sec) |
N/A | 1.209 | 1.431 | 0.387 | 0.000 | 0.257 | 0.000 | 0.638 | 0.207 | 6.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | F | B |
verified | N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 285 | 309 | 324 | 452 | 0 | 1252 | 0 | 583 | 174 | 9472 |
N.S. |
1 | 1.08 | 1.14 | 1.59 | 0.00 | 4.39 | 0.00 | 2.05 | 0.61 | 33.24 |
time (sec) |
N/A | 1.761 | 3.848 | 0.362 | 0.000 | 0.436 | 0.000 | 0.786 | 0.255 | 6.424 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F | B |
verified | N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 133 | 92 | 793 | 0 | 427 | 0 | 222 | 138 | 119 |
N.S. |
1 | 1.06 | 0.73 | 6.29 | 0.00 | 3.39 | 0.00 | 1.76 | 1.10 | 0.94 |
time (sec) |
N/A | 0.712 | 1.470 | 0.514 | 0.000 | 0.118 | 0.000 | 0.504 | 0.220 | 3.584 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F | B |
verified | N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 72 | 70 | 766 | 0 | 341 | 0 | 181 | 97 | 67 |
N.S. |
1 | 0.97 | 0.95 | 10.35 | 0.00 | 4.61 | 0.00 | 2.45 | 1.31 | 0.91 |
time (sec) |
N/A | 0.462 | 0.894 | 0.460 | 0.000 | 0.100 | 0.000 | 0.520 | 0.250 | 2.792 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | F | B |
verified | N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 37 | 46 | 733 | 6484 | 275 | 0 | 160 | 96 | 2947 |
N.S. |
1 | 0.80 | 1.00 | 15.93 | 140.96 | 5.98 | 0.00 | 3.48 | 2.09 | 64.07 |
time (sec) |
N/A | 0.270 | 0.241 | 0.511 | 0.365 | 0.091 | 0.000 | 0.495 | 0.219 | 3.517 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | F | B |
verified | N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 157 | 145 | 150 | 0 | 990 | 0 | 370 | 29 | 12379 |
N.S. |
1 | 1.01 | 0.94 | 0.97 | 0.00 | 6.39 | 0.00 | 2.39 | 0.19 | 79.86 |
time (sec) |
N/A | 0.760 | 0.666 | 0.414 | 0.000 | 0.174 | 0.000 | 0.512 | 200.027 | 5.425 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | F | B |
verified | N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 239 | 203 | 232 | 0 | 1400 | 0 | 471 | 63 | 32178 |
N.S. |
1 | 1.08 | 0.92 | 1.05 | 0.00 | 6.33 | 0.00 | 2.13 | 0.29 | 145.60 |
time (sec) |
N/A | 1.195 | 1.123 | 0.480 | 0.000 | 0.257 | 0.000 | 0.593 | 0.204 | 6.172 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | F | B |
verified | N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 298 | 338 | 266 | 357 | 0 | 1747 | 0 | 625 | 29 | 60949 |
N.S. |
1 | 1.13 | 0.89 | 1.20 | 0.00 | 5.86 | 0.00 | 2.10 | 0.10 | 204.53 |
time (sec) |
N/A | 1.671 | 2.284 | 0.477 | 0.000 | 0.480 | 0.000 | 0.571 | 200.027 | 8.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F | B |
verified | N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 145 | 114 | 2588 | 0 | 604 | 0 | 232 | 387 | 182 |
N.S. |
1 | 1.04 | 0.82 | 18.62 | 0.00 | 4.35 | 0.00 | 1.67 | 2.78 | 1.31 |
time (sec) |
N/A | 0.749 | 1.503 | 0.502 | 0.000 | 0.118 | 0.000 | 0.607 | 0.234 | 3.698 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 115 | 98 | 2528 | 0 | 584 | 0 | 203 | 267 | 142 |
N.S. |
1 | 1.25 | 1.07 | 27.48 | 0.00 | 6.35 | 0.00 | 2.21 | 2.90 | 1.54 |
time (sec) |
N/A | 0.563 | 0.858 | 0.406 | 0.000 | 0.108 | 0.000 | 0.569 | 0.272 | 3.539 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | B | F | B | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 99 | 59 | 2440 | 0 | 534 | 0 | 189 | 264 | 4612 |
N.S. |
1 | 1.30 | 0.78 | 32.11 | 0.00 | 7.03 | 0.00 | 2.49 | 3.47 | 60.68 |
time (sec) |
N/A | 0.475 | 0.310 | 0.395 | 0.000 | 0.098 | 0.000 | 0.515 | 0.257 | 11.368 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | B | F | B |
verified | N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 214 | 143 | 257 | 0 | 1555 | 0 | 463 | 29 | 35674 |
N.S. |
1 | 1.04 | 0.70 | 1.25 | 0.00 | 7.59 | 0.00 | 2.26 | 0.14 | 174.02 |
time (sec) |
N/A | 1.034 | 0.684 | 0.332 | 0.000 | 0.346 | 0.000 | 0.627 | 200.044 | 12.672 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | B | F | B |
verified | N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 281 | 306 | 187 | 399 | 0 | 2263 | 0 | 535 | 130 | 66456 |
N.S. |
1 | 1.09 | 0.67 | 1.42 | 0.00 | 8.05 | 0.00 | 1.90 | 0.46 | 236.50 |
time (sec) |
N/A | 1.545 | 0.887 | 0.383 | 0.000 | 0.958 | 0.000 | 0.653 | 0.195 | 12.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | B | F | B |
verified | N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 368 | 415 | 294 | 596 | 0 | 2638 | 0 | 708 | 29 | 106340 |
N.S. |
1 | 1.13 | 0.80 | 1.62 | 0.00 | 7.17 | 0.00 | 1.92 | 0.08 | 288.97 |
time (sec) |
N/A | 2.196 | 1.300 | 0.382 | 0.000 | 2.657 | 0.000 | 0.808 | 200.017 | 10.551 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-1) | B | F | B | F | B |
verified | N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 189 | 124 | 2758 | 0 | 963 | 0 | 286 | 749 | 255 |
N.S. |
1 | 1.20 | 0.78 | 17.46 | 0.00 | 6.09 | 0.00 | 1.81 | 4.74 | 1.61 |
time (sec) |
N/A | 0.878 | 1.904 | 0.504 | 0.000 | 0.164 | 0.000 | 0.783 | 0.221 | 5.716 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-1) | B | F | B | F | B |
verified | N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 166 | 106 | 2685 | 0 | 909 | 0 | 240 | 514 | 221 |
N.S. |
1 | 1.31 | 0.83 | 21.14 | 0.00 | 7.16 | 0.00 | 1.89 | 4.05 | 1.74 |
time (sec) |
N/A | 0.779 | 1.733 | 0.431 | 0.000 | 0.170 | 0.000 | 0.699 | 0.213 | 5.431 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | B | F | B | F | B |
verified | N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 145 | 61 | 2597 | 0 | 823 | 0 | 222 | 512 | 7068 |
N.S. |
1 | 1.33 | 0.56 | 23.83 | 0.00 | 7.55 | 0.00 | 2.04 | 4.70 | 64.84 |
time (sec) |
N/A | 0.698 | 0.357 | 0.409 | 0.000 | 0.191 | 0.000 | 0.665 | 0.209 | 21.710 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F(-2) | B | F | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 267 | 0 | 143 | 364 | 0 | 2659 | 0 | 519 | 29 | 69981 |
N.S. |
1 | 0.00 | 0.54 | 1.36 | 0.00 | 9.96 | 0.00 | 1.94 | 0.11 | 262.10 |
time (sec) |
N/A | 0.000 | 0.782 | 0.324 | 0.000 | 1.619 | 0.000 | 0.697 | 200.023 | 90.262 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F | B | F | F(-1) |
verified | N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 351 | 380 | 188 | 518 | 0 | 3246 | 0 | 623 | 212 | 0 |
N.S. |
1 | 1.08 | 0.54 | 1.48 | 0.00 | 9.25 | 0.00 | 1.77 | 0.60 | 0.00 |
time (sec) |
N/A | 1.898 | 0.898 | 0.388 | 0.000 | 5.369 | 0.000 | 0.674 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | B | F(-1) | B | F | F(-1) |
verified | N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 446 | 497 | 243 | 743 | 0 | 3803 | 0 | 978 | 29 | 0 |
N.S. |
1 | 1.11 | 0.54 | 1.67 | 0.00 | 8.53 | 0.00 | 2.19 | 0.07 | 0.00 |
time (sec) |
N/A | 2.601 | 1.687 | 0.399 | 0.000 | 16.919 | 0.000 | 0.867 | 200.019 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 263 | 274 | 295 | 1079 | 0 | 1039 | 0 | 0 | 101 | 0 |
N.S. |
1 | 1.04 | 1.12 | 4.10 | 0.00 | 3.95 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 1.639 | 6.132 | 0.518 | 0.000 | 0.132 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 260 | 236 | 866 | 0 | 745 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.04 | 0.94 | 3.46 | 0.00 | 2.98 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 1.534 | 3.074 | 0.424 | 0.000 | 0.110 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-1) | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 151 | 194 | 866 | 0 | 485 | 0 | 0 | 28 | 2101 |
N.S. |
1 | 1.00 | 1.28 | 5.74 | 0.00 | 3.21 | 0.00 | 0.00 | 0.19 | 13.91 |
time (sec) |
N/A | 0.755 | 0.497 | 0.432 | 0.000 | 0.099 | 0.000 | 0.000 | 0.188 | 17.487 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-1) | B | F | F(-2) | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 121 | 877 | 0 | 352 | 0 | 0 | 0 | 1724 |
N.S. |
1 | 1.00 | 1.00 | 7.25 | 0.00 | 2.91 | 0.00 | 0.00 | 0.00 | 14.25 |
time (sec) |
N/A | 0.477 | 0.708 | 0.987 | 0.000 | 0.132 | 0.000 | 0.000 | 0.679 | 16.797 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 178 | 175 | 1180 | 0 | 419 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.01 | 0.99 | 6.67 | 0.00 | 2.37 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.678 | 1.149 | 0.568 | 0.000 | 0.123 | 0.000 | 0.000 | 200.019 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | F(-2) | B | F | F(-2) | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 254 | 0 | 294 | 2226 | 0 | 502 | 0 | 0 | 79 | 0 |
N.S. |
1 | 0.00 | 1.16 | 8.76 | 0.00 | 1.98 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.000 | 3.247 | 0.533 | 0.000 | 0.117 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | F(-1) | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 329 | 344 | 1526 | 1518 | 0 | 1472 | 0 | 0 | 211 | 0 |
N.S. |
1 | 1.05 | 4.64 | 4.61 | 0.00 | 4.47 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 2.090 | 6.846 | 0.414 | 0.000 | 0.169 | 0.000 | 0.000 | 0.248 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 315 | 328 | 998 | 1234 | 0 | 1108 | 0 | 0 | 135 | 0 |
N.S. |
1 | 1.04 | 3.17 | 3.92 | 0.00 | 3.52 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 2.045 | 6.502 | 0.401 | 0.000 | 0.136 | 0.000 | 0.000 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-1) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 202 | 265 | 1702 | 0 | 768 | 0 | 0 | 64 | 0 |
N.S. |
1 | 1.03 | 1.35 | 8.68 | 0.00 | 3.92 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 1.176 | 2.810 | 0.434 | 0.000 | 0.110 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 203 | 276 | 1169 | 0 | 895 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.42 | 5.99 | 0.00 | 4.59 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.194 | 3.252 | 0.411 | 0.000 | 0.212 | 0.000 | 0.000 | 0.507 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 176 | 235 | 1275 | 0 | 488 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.02 | 1.36 | 7.37 | 0.00 | 2.82 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.673 | 2.201 | 0.528 | 0.000 | 0.128 | 0.000 | 0.000 | 200.017 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 225 | 233 | 282 | 1657 | 0 | 571 | 0 | 0 | 161 | 0 |
N.S. |
1 | 1.04 | 1.25 | 7.36 | 0.00 | 2.54 | 0.00 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 0.925 | 3.377 | 0.533 | 0.000 | 0.120 | 0.000 | 0.000 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | F(-1) | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 415 | 435 | 1609 | 1851 | 0 | 1919 | 0 | 0 | 335 | 0 |
N.S. |
1 | 1.05 | 3.88 | 4.46 | 0.00 | 4.62 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 2.698 | 7.155 | 0.440 | 0.000 | 0.243 | 0.000 | 0.000 | 0.403 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | F(-1) | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 378 | 404 | 1078 | 1503 | 0 | 1493 | 0 | 0 | 218 | 0 |
N.S. |
1 | 1.07 | 2.85 | 3.98 | 0.00 | 3.95 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 2.704 | 6.627 | 0.415 | 0.000 | 0.176 | 0.000 | 0.000 | 0.307 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-1) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 271 | 326 | 2130 | 0 | 1117 | 0 | 0 | 105 | 0 |
N.S. |
1 | 1.05 | 1.27 | 8.29 | 0.00 | 4.35 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 1.631 | 1.970 | 0.439 | 0.000 | 0.130 | 0.000 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 262 | 335 | 2647 | 0 | 1163 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 1.34 | 10.59 | 0.00 | 4.65 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.625 | 3.627 | 0.415 | 0.000 | 0.205 | 0.000 | 0.000 | 0.613 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 266 | 400 | 3161 | 0 | 1071 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.04 | 1.56 | 12.30 | 0.00 | 4.17 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 1.609 | 3.789 | 0.392 | 0.000 | 0.209 | 0.000 | 0.000 | 200.039 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 225 | 231 | 306 | 2559 | 0 | 655 | 0 | 0 | 247 | 0 |
N.S. |
1 | 1.03 | 1.36 | 11.37 | 0.00 | 2.91 | 0.00 | 0.00 | 1.10 | 0.00 |
time (sec) |
N/A | 0.926 | 3.461 | 0.528 | 0.000 | 0.121 | 0.000 | 0.000 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 212 | 255 | 1295 | 0 | 781 | 0 | 0 | 842 | 0 |
N.S. |
1 | 1.06 | 1.28 | 6.48 | 0.00 | 3.90 | 0.00 | 0.00 | 4.21 | 0.00 |
time (sec) |
N/A | 1.131 | 3.976 | 0.648 | 0.000 | 0.132 | 0.000 | 0.000 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 151 | 202 | 983 | 0 | 533 | 0 | 0 | 736 | 0 |
N.S. |
1 | 1.00 | 1.34 | 6.51 | 0.00 | 3.53 | 0.00 | 0.00 | 4.87 | 0.00 |
time (sec) |
N/A | 0.752 | 1.173 | 0.629 | 0.000 | 0.090 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F(-1) | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 84 | 212 | 3634 | 259 | 0 | 0 | 637 | 473 |
N.S. |
1 | 1.00 | 1.02 | 2.59 | 44.32 | 3.16 | 0.00 | 0.00 | 7.77 | 5.77 |
time (sec) |
N/A | 0.296 | 0.238 | 0.781 | 0.342 | 0.104 | 0.000 | 0.000 | 0.231 | 7.615 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 178 | 129 | 1738 | 0 | 381 | 0 | 0 | 0 | 1508 |
N.S. |
1 | 1.02 | 0.74 | 9.99 | 0.00 | 2.19 | 0.00 | 0.00 | 0.00 | 8.67 |
time (sec) |
N/A | 0.682 | 0.733 | 0.785 | 0.000 | 0.129 | 0.000 | 0.000 | 0.521 | 17.580 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 226 | 198 | 2946 | 0 | 488 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.17 | 1.03 | 15.26 | 0.00 | 2.53 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.849 | 0.935 | 0.772 | 0.000 | 0.117 | 0.000 | 0.000 | 200.029 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 262 | 304 | 274 | 5218 | 0 | 571 | 0 | 0 | 100 | 0 |
N.S. |
1 | 1.16 | 1.05 | 19.92 | 0.00 | 2.18 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 1.344 | 2.349 | 0.796 | 0.000 | 0.169 | 0.000 | 0.000 | 0.242 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 209 | 229 | 1510 | 1815 | 0 | 940 | 0 | 0 | 625 | 0 |
N.S. |
1 | 1.10 | 7.22 | 8.68 | 0.00 | 4.50 | 0.00 | 0.00 | 2.99 | 0.00 |
time (sec) |
N/A | 1.237 | 6.760 | 0.632 | 0.000 | 0.117 | 0.000 | 0.000 | 0.273 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-1) | B | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 129 | 981 | 2564 | 0 | 551 | 0 | 0 | 336 | 0 |
N.S. |
1 | 1.00 | 7.60 | 19.88 | 0.00 | 4.27 | 0.00 | 0.00 | 2.60 | 0.00 |
time (sec) |
N/A | 0.479 | 6.562 | 0.604 | 0.000 | 0.098 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F(-1) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 129 | 131 | 1291 | 8488 | 599 | 0 | 0 | 56 | 0 |
N.S. |
1 | 1.00 | 1.02 | 10.01 | 65.80 | 4.64 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.474 | 0.703 | 0.642 | 0.672 | 0.090 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 220 | 171 | 3196 | 0 | 673 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 0.88 | 16.47 | 0.00 | 3.47 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.865 | 0.826 | 0.660 | 0.000 | 0.171 | 0.000 | 0.000 | 15.058 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 269 | 309 | 257 | 4835 | 0 | 982 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.15 | 0.96 | 17.97 | 0.00 | 3.65 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 1.391 | 3.325 | 0.645 | 0.000 | 0.189 | 0.000 | 0.000 | 200.020 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 349 | 404 | 345 | 7870 | 0 | 1074 | 0 | 0 | 200 | 0 |
N.S. |
1 | 1.16 | 0.99 | 22.55 | 0.00 | 3.08 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 1.967 | 3.698 | 0.681 | 0.000 | 0.234 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-1) | B | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 190 | 1618 | 2968 | 0 | 849 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 8.94 | 16.40 | 0.00 | 4.69 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.759 | 7.250 | 0.619 | 0.000 | 0.105 | 0.000 | 0.000 | 2.037 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 188 | 1047 | 2907 | 0 | 1006 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 5.85 | 16.24 | 0.00 | 5.62 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.709 | 6.655 | 0.630 | 0.000 | 0.106 | 0.000 | 0.000 | 1.945 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-1) | B | F | F(-1) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 222 | 186 | 2448 | 0 | 968 | 0 | 0 | 72 | 0 |
N.S. |
1 | 1.18 | 0.99 | 13.02 | 0.00 | 5.15 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.852 | 1.652 | 0.654 | 0.000 | 0.120 | 0.000 | 0.000 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | F | B | F | F(-2) | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 277 | 0 | 278 | 4889 | 0 | 1300 | 0 | 0 | 29 | 0 |
N.S. |
1 | 0.00 | 1.00 | 17.65 | 0.00 | 4.69 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.000 | 2.484 | 0.657 | 0.000 | 0.170 | 0.000 | 0.000 | 200.022 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 354 | 402 | 326 | 7061 | 0 | 1546 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.14 | 0.92 | 19.95 | 0.00 | 4.37 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.949 | 5.559 | 0.637 | 0.000 | 0.231 | 0.000 | 0.000 | 200.023 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 444 | 513 | 436 | 10145 | 0 | 1774 | 0 | 0 | 315 | 0 |
N.S. |
1 | 1.16 | 0.98 | 22.85 | 0.00 | 4.00 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 2.684 | 5.808 | 0.667 | 0.000 | 0.242 | 0.000 | 0.000 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 128 | 0 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.341 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.253 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 183 | 111 | 0 | 0 | 0 | 0 | 0 | 94 | 0 |
N.S. |
1 | 1.17 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.750 | 1.192 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.294 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 112 | 78 | 0 | 0 | 0 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.18 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 0.407 | 0.802 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 70 | 64 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.15 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.264 | 0.233 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 222 | 158 | 0 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.15 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.698 | 0.716 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 273 | 313 | 207 | 0 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.15 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 1.155 | 1.451 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 381 | 444 | 294 | 0 | 0 | 0 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.17 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 1.870 | 2.982 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 200 | 146 | 0 | 0 | 0 | 0 | 0 | 148 | 0 |
N.S. |
1 | 1.04 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.77 | 0.00 |
time (sec) |
N/A | 0.974 | 1.412 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 123 | 94 | 0 | 0 | 0 | 0 | 0 | 114 | 0 |
N.S. |
1 | 1.03 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.96 | 0.00 |
time (sec) |
N/A | 0.502 | 0.500 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 84 | 60 | 0 | 0 | 0 | 0 | 0 | 78 | 0 |
N.S. |
1 | 1.08 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.316 | 0.176 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 141 | 108 | 0 | 0 | 0 | 0 | 0 | 689 | 0 |
N.S. |
1 | 1.16 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 5.65 | 0.00 |
time (sec) |
N/A | 0.597 | 0.321 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 217 | 140 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.21 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.962 | 0.743 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 65.085 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-1) | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 264 | 321 | 215 | 0 | 0 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.22 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 1.605 | 2.236 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.036 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F(-1) | F | F(-1) |
verified | N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 137 | 0 | 0 | 0 | 0 | 0 | 0 | 65 | 0 |
N.S. |
1 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.365 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.324 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F(-1) | F | F(-1) |
verified | N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 130 | 0 | 0 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.359 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.319 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F(-1) | F | F(-1) |
verified | N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 130 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.354 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.369 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F(-1) | F | F(-1) |
verified | N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 139 | 0 | 0 | 0 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.352 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.025 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F(-1) | F | F(-1) |
verified | N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 139 | 0 | 0 | 0 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.350 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 140 | 130 | 141 | 148 | 147 | 240 | 182 | 191 | 141 |
N.S. |
1 | 1.00 | 0.93 | 1.01 | 1.06 | 1.05 | 1.71 | 1.30 | 1.36 | 1.01 |
time (sec) |
N/A | 0.608 | 0.734 | 0.151 | 0.110 | 0.094 | 0.195 | 0.279 | 0.259 | 2.313 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 87 | 96 | 90 | 92 | 92 | 143 | 105 | 114 | 91 |
N.S. |
1 | 1.00 | 1.10 | 1.03 | 1.06 | 1.06 | 1.64 | 1.21 | 1.31 | 1.05 |
time (sec) |
N/A | 0.406 | 0.325 | 0.121 | 0.115 | 0.093 | 0.113 | 0.224 | 0.211 | 2.222 |
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 | 42 | 42 | 59 | 47 | 50 | 50 | 73 | 53 | 56 | 55 |
N.S. |
1 | 1.00 | 1.40 | 1.12 | 1.19 | 1.19 | 1.74 | 1.26 | 1.33 | 1.31 |
time (sec) |
N/A | 0.258 | 0.023 | 0.098 | 0.289 | 0.100 | 0.084 | 0.193 | 0.243 | 2.172 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 66 | 83 | 89 | 75 | 524 | 99 | 86 | 94 |
N.S. |
1 | 1.00 | 1.14 | 1.43 | 1.53 | 1.29 | 9.03 | 1.71 | 1.48 | 1.62 |
time (sec) |
N/A | 0.335 | 0.092 | 0.125 | 0.122 | 0.121 | 0.467 | 0.211 | 0.230 | 2.734 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | C | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 122 | 190 | 141 | 180 | 225 | 2878 | 205 | 447 | 152 |
N.S. |
1 | 1.10 | 1.71 | 1.27 | 1.62 | 2.03 | 25.93 | 1.85 | 4.03 | 1.37 |
time (sec) |
N/A | 0.547 | 1.760 | 0.174 | 0.120 | 0.100 | 0.896 | 0.253 | 0.212 | 2.461 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F(-2) | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 197 | 243 | 206 | 333 | 501 | 0 | 316 | 998 | 279 |
N.S. |
1 | 1.13 | 1.39 | 1.18 | 1.90 | 2.86 | 0.00 | 1.81 | 5.70 | 1.59 |
time (sec) |
N/A | 0.837 | 3.239 | 0.223 | 0.127 | 0.134 | 0.000 | 0.258 | 0.236 | 2.695 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | B | A | B | B |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 215 | 215 | 221 | 232 | 253 | 252 | 445 | 350 | 366 | 259 |
N.S. |
1 | 1.00 | 1.03 | 1.08 | 1.18 | 1.17 | 2.07 | 1.63 | 1.70 | 1.20 |
time (sec) |
N/A | 0.900 | 1.699 | 0.183 | 0.119 | 0.090 | 0.231 | 0.337 | 0.230 | 2.349 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | B | A | B | B |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 131 | 185 | 161 | 159 | 158 | 258 | 215 | 225 | 230 |
N.S. |
1 | 1.00 | 1.41 | 1.23 | 1.21 | 1.21 | 1.97 | 1.64 | 1.72 | 1.76 |
time (sec) |
N/A | 0.625 | 0.785 | 0.141 | 0.117 | 0.098 | 0.142 | 0.327 | 0.228 | 2.333 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 96 | 90 | 91 | 91 | 143 | 105 | 114 | 91 |
N.S. |
1 | 1.00 | 1.08 | 1.01 | 1.02 | 1.02 | 1.61 | 1.18 | 1.28 | 1.02 |
time (sec) |
N/A | 0.423 | 0.318 | 0.118 | 0.112 | 0.110 | 0.112 | 0.290 | 0.222 | 2.211 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | C | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 93 | 108 | 117 | 123 | 129 | 1025 | 128 | 154 | 115 |
N.S. |
1 | 0.90 | 1.05 | 1.14 | 1.19 | 1.25 | 9.95 | 1.24 | 1.50 | 1.12 |
time (sec) |
N/A | 0.494 | 0.110 | 0.154 | 0.119 | 0.104 | 0.595 | 0.178 | 0.186 | 2.858 |