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 | B | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 1421 | 1888 | 1875 | 1875 | 0 | 2230 | 2008 |
N.S. |
1 | 1.00 | 16.52 | 21.95 | 21.80 | 21.80 | 0.00 | 25.93 | 23.35 |
time (sec) |
N/A | 0.025 | 0.489 | 2.153 | 0.299 | 0.276 | 0.000 | 0.315 | 0.774 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 135 | 135 | 1433 | 1901 | 1951 | 1951 | 0 | 2232 | 2031 |
N.S. |
1 | 1.00 | 10.61 | 14.08 | 14.45 | 14.45 | 0.00 | 16.53 | 15.04 |
time (sec) |
N/A | 0.038 | 0.491 | 2.128 | 0.294 | 0.286 | 0.000 | 0.309 | 2.182 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 185 | 185 | 1430 | 1901 | 1962 | 1962 | 0 | 2232 | 2044 |
N.S. |
1 | 1.00 | 7.73 | 10.28 | 10.61 | 10.61 | 0.00 | 12.06 | 11.05 |
time (sec) |
N/A | 0.054 | 0.544 | 0.726 | 0.296 | 0.285 | 0.000 | 0.293 | 2.777 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 235 | 235 | 1430 | 1901 | 1973 | 1973 | 0 | 2232 | 2055 |
N.S. |
1 | 1.00 | 6.09 | 8.09 | 8.40 | 8.40 | 0.00 | 9.50 | 8.74 |
time (sec) |
N/A | 0.076 | 0.498 | 2.131 | 0.296 | 0.287 | 0.000 | 0.291 | 3.689 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 285 | 285 | 1429 | 1901 | 1984 | 1984 | 0 | 2232 | 2066 |
N.S. |
1 | 1.00 | 5.01 | 6.67 | 6.96 | 6.96 | 0.00 | 7.83 | 7.25 |
time (sec) |
N/A | 0.096 | 0.475 | 2.132 | 0.309 | 0.308 | 0.000 | 0.291 | 0.648 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 335 | 335 | 1433 | 1901 | 1995 | 1995 | 0 | 2232 | 2077 |
N.S. |
1 | 1.00 | 4.28 | 5.67 | 5.96 | 5.96 | 0.00 | 6.66 | 6.20 |
time (sec) |
N/A | 0.117 | 0.545 | 2.132 | 0.313 | 0.329 | 0.000 | 0.311 | 0.741 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 385 | 385 | 1428 | 1901 | 2006 | 2006 | 0 | 2232 | 2088 |
N.S. |
1 | 1.00 | 3.71 | 4.94 | 5.21 | 5.21 | 0.00 | 5.80 | 5.42 |
time (sec) |
N/A | 0.146 | 0.489 | 2.125 | 0.320 | 0.351 | 0.000 | 0.290 | 16.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 460 | 460 | 1433 | 1901 | 2017 | 2017 | 0 | 2232 | 2099 |
N.S. |
1 | 1.00 | 3.12 | 4.13 | 4.38 | 4.38 | 0.00 | 4.85 | 4.56 |
time (sec) |
N/A | 0.563 | 0.521 | 2.144 | 0.315 | 0.357 | 0.000 | 0.294 | 30.395 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 462 | 462 | 1428 | 1901 | 2028 | 2028 | 0 | 2232 | 2110 |
N.S. |
1 | 1.00 | 3.09 | 4.11 | 4.39 | 4.39 | 0.00 | 4.83 | 4.57 |
time (sec) |
N/A | 0.453 | 0.492 | 2.149 | 0.328 | 0.399 | 0.000 | 0.296 | 2.210 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 464 | 464 | 1431 | 1901 | 2039 | 2039 | 0 | 2232 | 2121 |
N.S. |
1 | 1.00 | 3.08 | 4.10 | 4.39 | 4.39 | 0.00 | 4.81 | 4.57 |
time (sec) |
N/A | 0.397 | 0.533 | 2.145 | 0.344 | 0.408 | 0.000 | 0.291 | 2.436 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 187 | 187 | 368 | 575 | 563 | 566 | 534 | 670 | 565 |
N.S. |
1 | 1.00 | 1.97 | 3.07 | 3.01 | 3.03 | 2.86 | 3.58 | 3.02 |
time (sec) |
N/A | 0.090 | 0.119 | 2.128 | 0.212 | 0.227 | 0.724 | 0.286 | 0.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 155 | 155 | 257 | 404 | 400 | 403 | 352 | 466 | 411 |
N.S. |
1 | 1.00 | 1.66 | 2.61 | 2.58 | 2.60 | 2.27 | 3.01 | 2.65 |
time (sec) |
N/A | 0.067 | 0.091 | 0.707 | 0.201 | 0.223 | 0.550 | 0.286 | 1.209 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 123 | 123 | 169 | 261 | 266 | 269 | 221 | 298 | 268 |
N.S. |
1 | 1.00 | 1.37 | 2.12 | 2.16 | 2.19 | 1.80 | 2.42 | 2.18 |
time (sec) |
N/A | 0.053 | 0.054 | 0.705 | 0.210 | 0.222 | 0.392 | 0.284 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 102 | 150 | 155 | 158 | 117 | 166 | 159 |
N.S. |
1 | 1.00 | 1.12 | 1.65 | 1.70 | 1.74 | 1.29 | 1.82 | 1.75 |
time (sec) |
N/A | 0.037 | 0.034 | 0.707 | 0.196 | 0.218 | 0.265 | 0.285 | 0.078 |
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 | 59 | 59 | 56 | 66 | 72 | 75 | 53 | 69 | 68 |
N.S. |
1 | 1.00 | 0.95 | 1.12 | 1.22 | 1.27 | 0.90 | 1.17 | 1.15 |
time (sec) |
N/A | 0.029 | 0.017 | 0.698 | 0.209 | 0.222 | 0.154 | 0.287 | 1.231 |
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 | 25 | 25 | 25 | 26 | 26 | 25 | 20 | 27 | 25 |
N.S. |
1 | 1.00 | 1.00 | 1.04 | 1.04 | 1.00 | 0.80 | 1.08 | 1.00 |
time (sec) |
N/A | 0.011 | 0.006 | 2.108 | 0.199 | 0.217 | 0.082 | 0.294 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 50 | 58 | 58 | 53 | 226 | 60 | 57 |
N.S. |
1 | 1.00 | 0.88 | 1.02 | 1.02 | 0.93 | 3.96 | 1.05 | 1.00 |
time (sec) |
N/A | 0.032 | 0.019 | 0.734 | 0.190 | 0.223 | 0.901 | 0.289 | 1.584 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 80 | 83 | 119 | 148 | 355 | 101 | 95 |
N.S. |
1 | 1.00 | 0.98 | 1.01 | 1.45 | 1.80 | 4.33 | 1.23 | 1.16 |
time (sec) |
N/A | 0.048 | 0.053 | 2.178 | 0.210 | 0.227 | 0.709 | 0.296 | 1.265 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 112 | 112 | 111 | 247 | 343 | 558 | 233 | 228 |
N.S. |
1 | 1.00 | 1.00 | 0.99 | 2.21 | 3.06 | 4.98 | 2.08 | 2.04 |
time (sec) |
N/A | 0.062 | 0.060 | 0.764 | 0.191 | 0.229 | 1.139 | 0.280 | 1.449 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 146 | 146 | 145 | 144 | 444 | 608 | 818 | 376 | 399 |
N.S. |
1 | 1.00 | 0.99 | 0.99 | 3.04 | 4.16 | 5.60 | 2.58 | 2.73 |
time (sec) |
N/A | 0.085 | 0.116 | 0.779 | 0.223 | 0.242 | 1.652 | 0.304 | 1.571 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 178 | 178 | 183 | 173 | 687 | 922 | 1132 | 530 | 629 |
N.S. |
1 | 1.00 | 1.03 | 0.97 | 3.86 | 5.18 | 6.36 | 2.98 | 3.53 |
time (sec) |
N/A | 0.110 | 0.060 | 0.829 | 0.259 | 0.247 | 2.320 | 0.296 | 1.709 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 227 | 227 | 500 | 593 | 579 | 832 | 573 | 741 | 766 |
N.S. |
1 | 1.00 | 2.20 | 2.61 | 2.55 | 3.67 | 2.52 | 3.26 | 3.37 |
time (sec) |
N/A | 0.250 | 0.160 | 0.717 | 0.202 | 0.232 | 1.514 | 0.285 | 1.455 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 187 | 187 | 365 | 421 | 411 | 610 | 396 | 544 | 486 |
N.S. |
1 | 1.00 | 1.95 | 2.25 | 2.20 | 3.26 | 2.12 | 2.91 | 2.60 |
time (sec) |
N/A | 0.177 | 0.108 | 0.713 | 0.207 | 0.228 | 1.083 | 0.285 | 0.122 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 145 | 145 | 250 | 277 | 273 | 417 | 257 | 370 | 293 |
N.S. |
1 | 1.00 | 1.72 | 1.91 | 1.88 | 2.88 | 1.77 | 2.55 | 2.02 |
time (sec) |
N/A | 0.115 | 0.076 | 0.706 | 0.206 | 0.225 | 0.786 | 0.292 | 0.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 99 | 99 | 153 | 151 | 158 | 249 | 151 | 229 | 165 |
N.S. |
1 | 1.00 | 1.55 | 1.53 | 1.60 | 2.52 | 1.53 | 2.31 | 1.67 |
time (sec) |
N/A | 0.072 | 0.046 | 0.716 | 0.203 | 0.232 | 0.505 | 0.275 | 1.366 |
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 | 60 | 60 | 56 | 70 | 77 | 109 | 71 | 112 | 75 |
N.S. |
1 | 1.00 | 0.93 | 1.17 | 1.28 | 1.82 | 1.18 | 1.87 | 1.25 |
time (sec) |
N/A | 0.042 | 0.028 | 0.711 | 0.211 | 0.215 | 0.258 | 0.270 | 1.232 |
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 | 32 | 32 | 31 | 33 | 34 | 37 | 27 | 57 | 32 |
N.S. |
1 | 1.00 | 0.97 | 1.03 | 1.06 | 1.16 | 0.84 | 1.78 | 1.00 |
time (sec) |
N/A | 0.015 | 0.009 | 2.134 | 0.192 | 0.217 | 0.096 | 0.312 | 0.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 69 | 83 | 118 | 157 | 355 | 100 | 94 |
N.S. |
1 | 1.00 | 0.84 | 1.01 | 1.44 | 1.91 | 4.33 | 1.22 | 1.15 |
time (sec) |
N/A | 0.043 | 0.038 | 2.206 | 0.188 | 0.240 | 0.704 | 0.305 | 1.319 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 117 | 117 | 103 | 123 | 256 | 396 | 706 | 194 | 263 |
N.S. |
1 | 1.00 | 0.88 | 1.05 | 2.19 | 3.38 | 6.03 | 1.66 | 2.25 |
time (sec) |
N/A | 0.075 | 0.065 | 0.788 | 0.206 | 0.233 | 1.357 | 0.305 | 0.374 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 157 | 157 | 146 | 159 | 479 | 801 | 1066 | 306 | 454 |
N.S. |
1 | 1.00 | 0.93 | 1.01 | 3.05 | 5.10 | 6.79 | 1.95 | 2.89 |
time (sec) |
N/A | 0.104 | 0.060 | 0.796 | 0.208 | 0.237 | 2.107 | 0.285 | 1.547 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 200 | 200 | 188 | 203 | 761 | 1219 | 1445 | 432 | 527 |
N.S. |
1 | 1.00 | 0.94 | 1.02 | 3.80 | 6.10 | 7.22 | 2.16 | 2.64 |
time (sec) |
N/A | 0.143 | 0.077 | 0.805 | 0.235 | 0.264 | 2.953 | 0.298 | 1.943 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 239 | 239 | 225 | 239 | 1090 | 1702 | 1877 | 590 | 767 |
N.S. |
1 | 1.00 | 0.94 | 1.00 | 4.56 | 7.12 | 7.85 | 2.47 | 3.21 |
time (sec) |
N/A | 0.183 | 0.106 | 0.838 | 0.269 | 0.303 | 4.159 | 0.299 | 1.981 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 230 | 230 | 254 | 587 | 592 | 912 | 615 | 633 | 681 |
N.S. |
1 | 1.00 | 1.10 | 2.55 | 2.57 | 3.97 | 2.67 | 2.75 | 2.96 |
time (sec) |
N/A | 0.236 | 0.082 | 0.710 | 0.204 | 0.242 | 4.748 | 0.288 | 0.275 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 191 | 191 | 187 | 416 | 424 | 668 | 444 | 442 | 451 |
N.S. |
1 | 1.00 | 0.98 | 2.18 | 2.22 | 3.50 | 2.32 | 2.31 | 2.36 |
time (sec) |
N/A | 0.158 | 0.065 | 0.718 | 0.199 | 0.230 | 3.305 | 0.277 | 0.147 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 141 | 141 | 245 | 268 | 282 | 442 | 299 | 283 | 290 |
N.S. |
1 | 1.00 | 1.74 | 1.90 | 2.00 | 3.13 | 2.12 | 2.01 | 2.06 |
time (sec) |
N/A | 0.116 | 0.077 | 0.753 | 0.226 | 0.229 | 2.088 | 0.282 | 1.321 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 140 | 157 | 170 | 258 | 187 | 157 | 170 |
N.S. |
1 | 1.00 | 1.36 | 1.52 | 1.65 | 2.50 | 1.82 | 1.52 | 1.65 |
time (sec) |
N/A | 0.075 | 0.045 | 0.737 | 0.188 | 0.224 | 1.151 | 0.292 | 0.141 |
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 | 69 | 69 | 75 | 72 | 92 | 110 | 94 | 72 | 82 |
N.S. |
1 | 1.00 | 1.09 | 1.04 | 1.33 | 1.59 | 1.36 | 1.04 | 1.19 |
time (sec) |
N/A | 0.043 | 0.021 | 0.693 | 0.190 | 0.225 | 0.471 | 0.267 | 1.392 |
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 | 28 | 28 | 26 | 25 | 38 | 38 | 39 | 24 | 39 |
N.S. |
1 | 1.00 | 0.93 | 0.89 | 1.36 | 1.36 | 1.39 | 0.86 | 1.39 |
time (sec) |
N/A | 0.004 | 0.006 | 2.125 | 0.193 | 0.220 | 0.141 | 0.287 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 103 | 111 | 252 | 361 | 558 | 232 | 228 |
N.S. |
1 | 1.00 | 0.91 | 0.98 | 2.23 | 3.19 | 4.94 | 2.05 | 2.02 |
time (sec) |
N/A | 0.064 | 0.040 | 0.761 | 0.210 | 0.237 | 1.102 | 0.265 | 1.355 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 158 | 158 | 146 | 161 | 477 | 803 | 1066 | 305 | 453 |
N.S. |
1 | 1.00 | 0.92 | 1.02 | 3.02 | 5.08 | 6.75 | 1.93 | 2.87 |
time (sec) |
N/A | 0.120 | 0.059 | 0.791 | 0.213 | 0.248 | 2.079 | 0.286 | 1.766 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 199 | 199 | 185 | 200 | 745 | 1215 | 1431 | 532 | 726 |
N.S. |
1 | 1.00 | 0.93 | 1.01 | 3.74 | 6.11 | 7.19 | 2.67 | 3.65 |
time (sec) |
N/A | 0.163 | 0.079 | 0.799 | 0.212 | 0.256 | 2.941 | 0.279 | 1.780 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 248 | 248 | 233 | 247 | 1126 | 1845 | 1975 | 800 | 1030 |
N.S. |
1 | 1.00 | 0.94 | 1.00 | 4.54 | 7.44 | 7.96 | 3.23 | 4.15 |
time (sec) |
N/A | 0.211 | 0.109 | 0.870 | 0.258 | 0.309 | 4.254 | 0.279 | 2.233 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 62 | 54 | 54 | 54 | 60 | 54 | 54 |
N.S. |
1 | 1.00 | 1.82 | 1.59 | 1.59 | 1.59 | 1.76 | 1.59 | 1.59 |
time (sec) |
N/A | 0.016 | 0.003 | 2.107 | 0.194 | 0.214 | 0.026 | 0.295 | 0.063 |
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 | 34 | 34 | 53 | 49 | 49 | 49 | 51 | 49 | 49 |
N.S. |
1 | 1.00 | 1.56 | 1.44 | 1.44 | 1.44 | 1.50 | 1.44 | 1.44 |
time (sec) |
N/A | 0.016 | 0.002 | 0.684 | 0.192 | 0.219 | 0.025 | 0.284 | 0.044 |
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 | 34 | 34 | 48 | 44 | 44 | 44 | 46 | 44 | 44 |
N.S. |
1 | 1.00 | 1.41 | 1.29 | 1.29 | 1.29 | 1.35 | 1.29 | 1.29 |
time (sec) |
N/A | 0.014 | 0.002 | 2.094 | 0.199 | 0.221 | 0.023 | 0.289 | 0.036 |
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 | 34 | 34 | 47 | 39 | 39 | 39 | 44 | 39 | 39 |
N.S. |
1 | 1.00 | 1.38 | 1.15 | 1.15 | 1.15 | 1.29 | 1.15 | 1.15 |
time (sec) |
N/A | 0.012 | 0.002 | 0.683 | 0.196 | 0.213 | 0.022 | 0.300 | 0.031 |
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 | 34 | 34 | 42 | 34 | 34 | 34 | 39 | 34 | 34 |
N.S. |
1 | 1.00 | 1.24 | 1.00 | 1.00 | 1.00 | 1.15 | 1.00 | 1.00 |
time (sec) |
N/A | 0.011 | 0.001 | 2.134 | 0.196 | 0.218 | 0.020 | 0.285 | 0.027 |
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 | 34 | 34 | 35 | 29 | 29 | 29 | 32 | 29 | 29 |
N.S. |
1 | 1.00 | 1.03 | 0.85 | 0.85 | 0.85 | 0.94 | 0.85 | 0.85 |
time (sec) |
N/A | 0.010 | 0.001 | 0.684 | 0.195 | 0.212 | 0.019 | 0.280 | 0.023 |
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 | 28 | 28 | 28 | 24 | 24 | 24 | 26 | 24 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.86 | 0.86 | 0.93 | 0.86 | 0.86 |
time (sec) |
N/A | 0.008 | 0.001 | 1.747 | 0.198 | 0.213 | 0.019 | 0.280 | 0.022 |
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 | 25 | 25 | 25 | 19 | 19 | 19 | 22 | 19 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.76 | 0.76 | 0.76 | 0.88 | 0.76 | 0.76 |
time (sec) |
N/A | 0.006 | 0.001 | 0.011 | 0.191 | 0.210 | 0.016 | 0.269 | 0.035 |
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 | 18 | 18 | 18 | 14 | 14 | 14 | 14 | 14 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 0.78 | 0.78 | 0.78 | 0.78 | 0.72 |
time (sec) |
N/A | 0.004 | 0.001 | 0.009 | 0.188 | 0.207 | 0.016 | 0.298 | 0.028 |
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 | 22 | 16 | 17 | 17 | 20 | 18 | 15 |
N.S. |
1 | 1.00 | 0.96 | 0.70 | 0.74 | 0.74 | 0.87 | 0.78 | 0.65 |
time (sec) |
N/A | 0.009 | 0.006 | 0.695 | 0.202 | 0.222 | 0.032 | 0.278 | 0.035 |
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 | 27 | 27 | 26 | 20 | 21 | 32 | 20 | 32 | 19 |
N.S. |
1 | 1.00 | 0.96 | 0.74 | 0.78 | 1.19 | 0.74 | 1.19 | 0.70 |
time (sec) |
N/A | 0.010 | 0.009 | 2.154 | 0.192 | 0.210 | 0.040 | 0.277 | 1.280 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 27 | 24 | 28 | 37 | 26 | 24 | 24 |
N.S. |
1 | 1.00 | 0.82 | 0.73 | 0.85 | 1.12 | 0.79 | 0.73 | 0.73 |
time (sec) |
N/A | 0.010 | 0.009 | 1.732 | 0.208 | 0.234 | 0.047 | 0.276 | 1.292 |
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 | 34 | 34 | 21 | 20 | 29 | 29 | 27 | 19 | 28 |
N.S. |
1 | 1.00 | 0.62 | 0.59 | 0.85 | 0.85 | 0.79 | 0.56 | 0.82 |
time (sec) |
N/A | 0.009 | 0.006 | 1.765 | 0.204 | 0.217 | 0.050 | 0.272 | 1.193 |
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 | 34 | 34 | 21 | 20 | 34 | 34 | 31 | 28 | 28 |
N.S. |
1 | 1.00 | 0.62 | 0.59 | 1.00 | 1.00 | 0.91 | 0.82 | 0.82 |
time (sec) |
N/A | 0.009 | 0.005 | 0.711 | 0.204 | 0.213 | 0.054 | 0.278 | 1.417 |
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 | 34 | 34 | 21 | 19 | 39 | 39 | 36 | 19 | 28 |
N.S. |
1 | 1.00 | 0.62 | 0.56 | 1.15 | 1.15 | 1.06 | 0.56 | 0.82 |
time (sec) |
N/A | 0.011 | 0.007 | 2.132 | 0.189 | 0.225 | 0.060 | 0.286 | 1.208 |
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 | 45 | 45 | 69 | 59 | 59 | 59 | 66 | 59 | 59 |
N.S. |
1 | 1.00 | 1.53 | 1.31 | 1.31 | 1.31 | 1.47 | 1.31 | 1.31 |
time (sec) |
N/A | 0.017 | 0.002 | 1.703 | 0.192 | 0.220 | 0.027 | 0.284 | 0.067 |
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 | 45 | 45 | 62 | 54 | 54 | 54 | 60 | 54 | 54 |
N.S. |
1 | 1.00 | 1.38 | 1.20 | 1.20 | 1.20 | 1.33 | 1.20 | 1.20 |
time (sec) |
N/A | 0.017 | 0.002 | 0.681 | 0.203 | 0.215 | 0.028 | 0.289 | 0.055 |
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 | 45 | 45 | 51 | 49 | 49 | 49 | 49 | 49 | 49 |
N.S. |
1 | 1.00 | 1.13 | 1.09 | 1.09 | 1.09 | 1.09 | 1.09 | 1.09 |
time (sec) |
N/A | 0.017 | 0.002 | 0.695 | 0.200 | 0.210 | 0.027 | 0.276 | 0.044 |
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 | 45 | 45 | 52 | 44 | 44 | 44 | 49 | 44 | 44 |
N.S. |
1 | 1.00 | 1.16 | 0.98 | 0.98 | 0.98 | 1.09 | 0.98 | 0.98 |
time (sec) |
N/A | 0.017 | 0.006 | 2.148 | 0.194 | 0.215 | 0.025 | 0.283 | 0.035 |
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 | 45 | 45 | 47 | 39 | 39 | 39 | 44 | 39 | 39 |
N.S. |
1 | 1.00 | 1.04 | 0.87 | 0.87 | 0.87 | 0.98 | 0.87 | 0.87 |
time (sec) |
N/A | 0.016 | 0.001 | 0.696 | 0.193 | 0.215 | 0.024 | 0.272 | 0.030 |
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 | 44 | 44 | 44 | 34 | 34 | 34 | 41 | 34 | 34 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.77 | 0.77 | 0.93 | 0.77 | 0.77 |
time (sec) |
N/A | 0.013 | 0.002 | 2.141 | 0.212 | 0.215 | 0.030 | 0.273 | 0.027 |
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 | 31 | 31 | 31 | 29 | 29 | 29 | 29 | 29 | 29 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.94 | 0.94 | 0.94 | 0.94 | 0.94 |
time (sec) |
N/A | 0.012 | 0.002 | 0.699 | 0.195 | 0.217 | 0.019 | 0.258 | 0.030 |
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 | 30 | 30 | 30 | 24 | 24 | 24 | 27 | 24 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.80 | 0.80 | 0.90 | 0.80 | 0.80 |
time (sec) |
N/A | 0.009 | 0.001 | 1.754 | 0.203 | 0.218 | 0.020 | 0.370 | 0.029 |
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 | 23 | 19 | 19 | 19 | 20 | 19 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.83 | 0.83 | 0.87 | 0.83 | 0.83 |
time (sec) |
N/A | 0.006 | 0.001 | 0.693 | 0.209 | 0.221 | 0.021 | 0.344 | 0.050 |
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 | 30 | 30 | 27 | 21 | 22 | 22 | 27 | 23 | 20 |
N.S. |
1 | 1.00 | 0.90 | 0.70 | 0.73 | 0.73 | 0.90 | 0.77 | 0.67 |
time (sec) |
N/A | 0.009 | 0.020 | 1.780 | 0.214 | 0.225 | 0.035 | 0.278 | 0.049 |
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 | 34 | 34 | 36 | 25 | 26 | 37 | 27 | 48 | 24 |
N.S. |
1 | 1.00 | 1.06 | 0.74 | 0.76 | 1.09 | 0.79 | 1.41 | 0.71 |
time (sec) |
N/A | 0.011 | 0.017 | 1.788 | 0.211 | 0.222 | 0.042 | 0.274 | 0.056 |
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 | 38 | 38 | 35 | 27 | 31 | 47 | 31 | 27 | 26 |
N.S. |
1 | 1.00 | 0.92 | 0.71 | 0.82 | 1.24 | 0.82 | 0.71 | 0.68 |
time (sec) |
N/A | 0.013 | 0.032 | 3.555 | 0.199 | 0.216 | 0.050 | 0.296 | 1.169 |
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 | 44 | 44 | 36 | 29 | 38 | 52 | 36 | 29 | 34 |
N.S. |
1 | 1.00 | 0.82 | 0.66 | 0.86 | 1.18 | 0.82 | 0.66 | 0.77 |
time (sec) |
N/A | 0.013 | 0.021 | 2.166 | 0.202 | 0.215 | 0.055 | 0.282 | 0.037 |
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 | 37 | 37 | 26 | 25 | 39 | 39 | 37 | 37 | 37 |
N.S. |
1 | 1.00 | 0.70 | 0.68 | 1.05 | 1.05 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.004 | 0.013 | 2.173 | 0.196 | 0.223 | 0.057 | 0.270 | 1.190 |
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 | 45 | 45 | 26 | 24 | 44 | 44 | 41 | 24 | 37 |
N.S. |
1 | 1.00 | 0.58 | 0.53 | 0.98 | 0.98 | 0.91 | 0.53 | 0.82 |
time (sec) |
N/A | 0.012 | 0.015 | 2.159 | 0.207 | 0.222 | 0.063 | 0.289 | 1.324 |
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 | 45 | 45 | 26 | 24 | 49 | 49 | 46 | 24 | 37 |
N.S. |
1 | 1.00 | 0.58 | 0.53 | 1.09 | 1.09 | 1.02 | 0.53 | 0.82 |
time (sec) |
N/A | 0.012 | 0.015 | 2.194 | 0.205 | 0.222 | 0.068 | 0.293 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 26 | 24 | 54 | 54 | 51 | 24 | 37 |
N.S. |
1 | 1.00 | 0.58 | 0.53 | 1.20 | 1.20 | 1.13 | 0.53 | 0.82 |
time (sec) |
N/A | 0.014 | 0.015 | 2.181 | 0.215 | 0.218 | 0.074 | 0.274 | 1.305 |
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 | 56 | 56 | 74 | 64 | 64 | 64 | 71 | 64 | 64 |
N.S. |
1 | 1.00 | 1.32 | 1.14 | 1.14 | 1.14 | 1.27 | 1.14 | 1.14 |
time (sec) |
N/A | 0.024 | 0.003 | 2.177 | 0.191 | 0.219 | 0.029 | 0.285 | 0.087 |
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 | 56 | 56 | 67 | 59 | 59 | 59 | 65 | 59 | 59 |
N.S. |
1 | 1.00 | 1.20 | 1.05 | 1.05 | 1.05 | 1.16 | 1.05 | 1.05 |
time (sec) |
N/A | 0.018 | 0.003 | 0.703 | 0.200 | 0.206 | 0.027 | 0.281 | 0.073 |
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 | 56 | 56 | 60 | 54 | 54 | 54 | 58 | 54 | 54 |
N.S. |
1 | 1.00 | 1.07 | 0.96 | 0.96 | 0.96 | 1.04 | 0.96 | 0.96 |
time (sec) |
N/A | 0.016 | 0.003 | 2.170 | 0.198 | 0.212 | 0.025 | 0.283 | 0.066 |
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 | 56 | 56 | 55 | 49 | 49 | 49 | 53 | 49 | 49 |
N.S. |
1 | 1.00 | 0.98 | 0.88 | 0.88 | 0.88 | 0.95 | 0.88 | 0.88 |
time (sec) |
N/A | 0.015 | 0.003 | 0.707 | 0.201 | 0.219 | 0.024 | 0.268 | 0.054 |
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 | 56 | 56 | 52 | 44 | 44 | 44 | 49 | 44 | 44 |
N.S. |
1 | 1.00 | 0.93 | 0.79 | 0.79 | 0.79 | 0.88 | 0.79 | 0.79 |
time (sec) |
N/A | 0.016 | 0.002 | 2.157 | 0.204 | 0.210 | 0.025 | 0.280 | 0.048 |
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 | 49 | 49 | 49 | 39 | 39 | 39 | 46 | 39 | 39 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.80 | 0.80 | 0.94 | 0.80 | 0.80 |
time (sec) |
N/A | 0.014 | 0.001 | 0.702 | 0.193 | 0.218 | 0.021 | 0.287 | 0.046 |
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 | 40 | 40 | 40 | 34 | 34 | 34 | 37 | 34 | 34 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.85 | 0.85 | 0.92 | 0.85 | 0.85 |
time (sec) |
N/A | 0.012 | 0.001 | 2.131 | 0.189 | 0.214 | 0.020 | 0.270 | 0.036 |
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 | 34 | 34 | 33 | 29 | 29 | 29 | 31 | 29 | 29 |
N.S. |
1 | 1.00 | 0.97 | 0.85 | 0.85 | 0.85 | 0.91 | 0.85 | 0.85 |
time (sec) |
N/A | 0.010 | 0.001 | 0.697 | 0.193 | 0.214 | 0.022 | 0.284 | 0.030 |
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 | 28 | 24 | 24 | 24 | 26 | 24 | 24 |
N.S. |
1 | 1.00 | 1.22 | 1.04 | 1.04 | 1.04 | 1.13 | 1.04 | 1.04 |
time (sec) |
N/A | 0.004 | 0.001 | 1.779 | 0.206 | 0.211 | 0.021 | 0.275 | 0.026 |
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 | 37 | 37 | 32 | 26 | 27 | 27 | 34 | 28 | 25 |
N.S. |
1 | 1.00 | 0.86 | 0.70 | 0.73 | 0.73 | 0.92 | 0.76 | 0.68 |
time (sec) |
N/A | 0.010 | 0.011 | 0.727 | 0.189 | 0.219 | 0.037 | 0.270 | 0.039 |
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 | 41 | 41 | 44 | 30 | 31 | 42 | 34 | 57 | 29 |
N.S. |
1 | 1.00 | 1.07 | 0.73 | 0.76 | 1.02 | 0.83 | 1.39 | 0.71 |
time (sec) |
N/A | 0.013 | 0.010 | 2.191 | 0.195 | 0.219 | 0.047 | 0.282 | 0.033 |
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 | 45 | 45 | 46 | 32 | 36 | 52 | 36 | 32 | 32 |
N.S. |
1 | 1.00 | 1.02 | 0.71 | 0.80 | 1.16 | 0.80 | 0.71 | 0.71 |
time (sec) |
N/A | 0.015 | 0.011 | 2.198 | 0.212 | 0.217 | 0.054 | 0.271 | 0.041 |
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 | 49 | 49 | 47 | 32 | 41 | 62 | 41 | 32 | 36 |
N.S. |
1 | 1.00 | 0.96 | 0.65 | 0.84 | 1.27 | 0.84 | 0.65 | 0.73 |
time (sec) |
N/A | 0.015 | 0.014 | 2.198 | 0.190 | 0.214 | 0.057 | 0.272 | 0.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 41 | 34 | 48 | 67 | 46 | 55 | 31 |
N.S. |
1 | 1.00 | 0.75 | 0.62 | 0.87 | 1.22 | 0.84 | 1.00 | 0.56 |
time (sec) |
N/A | 0.015 | 0.012 | 2.885 | 0.208 | 0.216 | 0.066 | 0.278 | 0.056 |
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 | 37 | 37 | 31 | 29 | 49 | 49 | 48 | 29 | 46 |
N.S. |
1 | 1.00 | 0.84 | 0.78 | 1.32 | 1.32 | 1.30 | 0.78 | 1.24 |
time (sec) |
N/A | 0.004 | 0.008 | 0.718 | 0.194 | 0.226 | 0.064 | 0.279 | 1.399 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 31 | 29 | 54 | 54 | 51 | 29 | 46 |
N.S. |
1 | 1.00 | 0.56 | 0.53 | 0.98 | 0.98 | 0.93 | 0.53 | 0.84 |
time (sec) |
N/A | 0.007 | 0.009 | 2.885 | 0.207 | 0.216 | 0.068 | 0.266 | 0.036 |
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 | 56 | 56 | 31 | 29 | 59 | 59 | 56 | 29 | 46 |
N.S. |
1 | 1.00 | 0.55 | 0.52 | 1.05 | 1.05 | 1.00 | 0.52 | 0.82 |
time (sec) |
N/A | 0.016 | 0.009 | 0.724 | 0.194 | 0.213 | 0.073 | 0.277 | 1.391 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 56 | 54 | 54 | 54 | 54 | 54 | 54 |
N.S. |
1 | 1.00 | 3.11 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 | 3.00 |
time (sec) |
N/A | 0.002 | 0.003 | 2.190 | 0.187 | 0.223 | 0.026 | 0.284 | 0.060 |
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 | 58 | 58 | 47 | 41 | 42 | 42 | 54 | 43 | 40 |
N.S. |
1 | 1.00 | 0.81 | 0.71 | 0.72 | 0.72 | 0.93 | 0.74 | 0.69 |
time (sec) |
N/A | 0.015 | 0.014 | 2.207 | 0.187 | 0.214 | 0.042 | 0.288 | 0.039 |
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 | 51 | 51 | 42 | 36 | 37 | 37 | 48 | 38 | 35 |
N.S. |
1 | 1.00 | 0.82 | 0.71 | 0.73 | 0.73 | 0.94 | 0.75 | 0.69 |
time (sec) |
N/A | 0.013 | 0.011 | 0.727 | 0.200 | 0.215 | 0.040 | 0.273 | 0.035 |
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 | 44 | 44 | 37 | 31 | 32 | 32 | 41 | 33 | 30 |
N.S. |
1 | 1.00 | 0.84 | 0.70 | 0.73 | 0.73 | 0.93 | 0.75 | 0.68 |
time (sec) |
N/A | 0.014 | 0.012 | 2.199 | 0.194 | 0.213 | 0.038 | 0.285 | 0.028 |
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 | 37 | 37 | 35 | 26 | 27 | 27 | 34 | 28 | 25 |
N.S. |
1 | 1.00 | 0.95 | 0.70 | 0.73 | 0.73 | 0.92 | 0.76 | 0.68 |
time (sec) |
N/A | 0.009 | 0.012 | 2.204 | 0.192 | 0.218 | 0.037 | 0.295 | 0.026 |
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 | 30 | 30 | 27 | 21 | 22 | 22 | 27 | 23 | 20 |
N.S. |
1 | 1.00 | 0.90 | 0.70 | 0.73 | 0.73 | 0.90 | 0.77 | 0.67 |
time (sec) |
N/A | 0.011 | 0.009 | 1.809 | 0.202 | 0.213 | 0.035 | 0.297 | 0.033 |
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 | 22 | 16 | 17 | 17 | 20 | 18 | 15 |
N.S. |
1 | 1.00 | 0.96 | 0.70 | 0.74 | 0.74 | 0.87 | 0.78 | 0.65 |
time (sec) |
N/A | 0.008 | 0.005 | 1.801 | 0.195 | 0.214 | 0.032 | 0.279 | 0.034 |
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 | 16 | 16 | 17 | 11 | 12 | 12 | 14 | 13 | 10 |
N.S. |
1 | 1.00 | 1.06 | 0.69 | 0.75 | 0.75 | 0.88 | 0.81 | 0.62 |
time (sec) |
N/A | 0.006 | 0.002 | 1.811 | 0.198 | 0.218 | 0.028 | 0.281 | 0.060 |
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 | 21 | 21 | 21 | 14 | 17 | 17 | 19 | 19 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.67 | 0.81 | 0.81 | 0.90 | 0.90 | 0.62 |
time (sec) |
N/A | 0.007 | 0.006 | 1.828 | 0.199 | 0.214 | 0.050 | 0.286 | 0.062 |