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 | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 156 | 144 | 296 | 882 | 457 | 998 | 487 | 663 | 1024 |
N.S. |
1 | 0.86 | 0.79 | 1.63 | 4.85 | 2.51 | 5.48 | 2.68 | 3.64 | 5.63 |
time (sec) |
N/A | 0.351 | 0.108 | 1.288 | 0.076 | 0.119 | 3.467 | 35.739 | 0.157 | 26.381 |
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 | 151 | 132 | 122 | 233 | 645 | 343 | 707 | 358 | 502 | 567 |
N.S. |
1 | 0.87 | 0.81 | 1.54 | 4.27 | 2.27 | 4.68 | 2.37 | 3.32 | 3.75 |
time (sec) |
N/A | 0.318 | 0.092 | 1.052 | 0.062 | 0.099 | 2.181 | 5.915 | 0.166 | 26.188 |
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 | 120 | 108 | 98 | 185 | 436 | 245 | 517 | 243 | 354 | 296 |
N.S. |
1 | 0.90 | 0.82 | 1.54 | 3.63 | 2.04 | 4.31 | 2.02 | 2.95 | 2.47 |
time (sec) |
N/A | 0.289 | 0.055 | 0.955 | 0.057 | 0.089 | 1.507 | 1.093 | 0.156 | 26.454 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 77 | 72 | 113 | 250 | 149 | 250 | 132 | 226 | 120 |
N.S. |
1 | 0.99 | 0.92 | 1.45 | 3.21 | 1.91 | 3.21 | 1.69 | 2.90 | 1.54 |
time (sec) |
N/A | 0.257 | 0.045 | 0.819 | 0.042 | 0.110 | 0.958 | 0.288 | 0.152 | 25.749 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 87 | 162 | 0 | 0 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.00 | 1.05 | 1.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.529 | 0.047 | 1.115 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
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 | 102 | 76 | 89 | 93 | 187 | 110 | 253 | 187 | 198 | 108 |
N.S. |
1 | 0.75 | 0.87 | 0.91 | 1.83 | 1.08 | 2.48 | 1.83 | 1.94 | 1.06 |
time (sec) |
N/A | 0.232 | 0.062 | 1.096 | 0.041 | 0.090 | 0.719 | 0.142 | 0.154 | 27.466 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 138 | 128 | 162 | 306 | 240 | 418 | 268 | 692 | 206 |
N.S. |
1 | 0.99 | 0.92 | 1.17 | 2.20 | 1.73 | 3.01 | 1.93 | 4.98 | 1.48 |
time (sec) |
N/A | 0.329 | 0.104 | 1.296 | 0.045 | 0.081 | 1.179 | 0.190 | 0.155 | 27.218 |
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 | 177 | 165 | 140 | 211 | 480 | 432 | 677 | 477 | 698 | 341 |
N.S. |
1 | 0.93 | 0.79 | 1.19 | 2.71 | 2.44 | 3.82 | 2.69 | 3.94 | 1.93 |
time (sec) |
N/A | 0.355 | 0.132 | 1.425 | 0.052 | 0.088 | 1.838 | 0.154 | 0.169 | 27.828 |
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 | 208 | 188 | 162 | 232 | 699 | 658 | 947 | 424 | 1015 | 579 |
N.S. |
1 | 0.90 | 0.78 | 1.12 | 3.36 | 3.16 | 4.55 | 2.04 | 4.88 | 2.78 |
time (sec) |
N/A | 0.383 | 0.170 | 2.082 | 0.064 | 0.087 | 2.552 | 0.181 | 0.156 | 29.193 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 515 | 709 | 524 | 0 | 2660 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.38 | 1.02 | 0.00 | 5.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.978 | 0.536 | 0.000 | 0.201 | 0.000 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 422 | 523 | 402 | 0 | 1950 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.24 | 0.95 | 0.00 | 4.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.454 | 0.378 | 0.000 | 0.184 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 343 | 369 | 298 | 0 | 1333 | 0 | 0 | 0 | 1441 | 0 |
N.S. |
1 | 1.08 | 0.87 | 0.00 | 3.89 | 0.00 | 0.00 | 0.00 | 4.20 | 0.00 |
time (sec) |
N/A | 1.004 | 0.264 | 0.000 | 0.168 | 0.000 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 235 | 195 | 0 | 730 | 0 | 0 | 0 | 852 | 0 |
N.S. |
1 | 1.11 | 0.92 | 0.00 | 3.46 | 0.00 | 0.00 | 0.00 | 4.04 | 0.00 |
time (sec) |
N/A | 0.671 | 0.184 | 0.000 | 0.166 | 0.000 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 125 | 624 | 0 | 0 | 0 | 0 | 0 | 130 | 0 |
N.S. |
1 | 0.95 | 4.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 0.443 | 1.694 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 116 | 322 | 188 | 573 | 200 | 450 | 388 | 472 | 227 |
N.S. |
1 | 0.74 | 2.05 | 1.20 | 3.65 | 1.27 | 2.87 | 2.47 | 3.01 | 1.45 |
time (sec) |
N/A | 0.284 | 0.522 | 1.247 | 0.077 | 0.074 | 1.246 | 0.266 | 0.158 | 27.495 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 299 | 222 | 452 | 490 | 1001 | 413 | 877 | 0 | 1157 | 504 |
N.S. |
1 | 0.74 | 1.51 | 1.64 | 3.35 | 1.38 | 2.93 | 0.00 | 3.87 | 1.69 |
time (sec) |
N/A | 0.356 | 0.529 | 1.543 | 0.103 | 0.086 | 2.291 | 0.000 | 0.168 | 27.930 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 407 | 325 | 595 | 694 | 1576 | 721 | 1561 | 0 | 1896 | 1069 |
N.S. |
1 | 0.80 | 1.46 | 1.71 | 3.87 | 1.77 | 3.84 | 0.00 | 4.66 | 2.63 |
time (sec) |
N/A | 0.492 | 0.697 | 1.792 | 0.158 | 0.098 | 12.894 | 0.000 | 0.165 | 30.149 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 501 | 388 | 680 | 886 | 2278 | 1088 | 2383 | 883 | 2755 | 1882 |
N.S. |
1 | 0.77 | 1.36 | 1.77 | 4.55 | 2.17 | 4.76 | 1.76 | 5.50 | 3.76 |
time (sec) |
N/A | 0.528 | 0.935 | 2.547 | 0.220 | 0.093 | 105.939 | 0.336 | 0.172 | 33.637 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 36 | 34 | 36 | 75 | 258 | 36 | 2306 | 36 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 2.21 | 7.59 | 1.06 | 67.82 | 1.06 |
time (sec) |
N/A | 0.217 | 0.163 | 1.316 | 0.071 | 0.072 | 3.444 | 0.245 | 0.212 | 27.670 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 34 | 32 | 34 | 57 | 165 | 34 | 1852 | 34 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 1.78 | 5.16 | 1.06 | 57.88 | 1.06 |
time (sec) |
N/A | 0.195 | 0.141 | 1.213 | 0.065 | 0.078 | 2.664 | 0.229 | 0.193 | 28.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 36 | 34 | 36 | 65 | 170 | 36 | 506 | 36 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 1.91 | 5.00 | 1.06 | 14.88 | 1.06 |
time (sec) |
N/A | 0.215 | 0.166 | 1.386 | 0.070 | 0.070 | 3.630 | 0.221 | 0.161 | 29.539 |
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 | 91 | 91 | 0 | 0 | 0 | 0 | 0 | 0 | 1108 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 12.18 | 0.00 |
time (sec) |
N/A | 0.310 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 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 | 151 | 139 | 0 | 0 | 0 | 0 | 0 | 0 | 228 | 0 |
N.S. |
1 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.51 | 0.00 |
time (sec) |
N/A | 0.408 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 36 | 34 | 312 | 125 | 792 | 36 | 9212 | 36 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 9.18 | 3.68 | 23.29 | 1.06 | 270.94 | 1.06 |
time (sec) |
N/A | 0.222 | 0.507 | 1.211 | 0.069 | 0.071 | 15.334 | 0.346 | 0.261 | 34.265 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 34 | 32 | 234 | 107 | 559 | 34 | 7388 | 34 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 7.31 | 3.34 | 17.47 | 1.06 | 230.88 | 1.06 |
time (sec) |
N/A | 0.207 | 0.387 | 1.171 | 0.069 | 0.078 | 10.103 | 0.329 | 0.227 | 37.571 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 36 | 34 | 170 | 129 | 158 | 36 | 1955 | 36 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 5.00 | 3.79 | 4.65 | 1.06 | 57.50 | 1.06 |
time (sec) |
N/A | 0.216 | 0.247 | 1.181 | 0.077 | 0.075 | 2.311 | 0.281 | 0.166 | 38.432 |
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 | 147 | 136 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.372 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 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 | 206 | 282 | 0 | 0 | 0 | 0 | 0 | 0 | 435 | 0 |
N.S. |
1 | 1.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.11 | 0.00 |
time (sec) |
N/A | 0.641 | 0.000 | 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 | F | F | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 94 | 0 | 0 | 0 | 62 | 0 | 0 | 715 | 0 |
N.S. |
1 | 0.98 | 0.00 | 0.00 | 0.00 | 0.65 | 0.00 | 0.00 | 7.45 | 0.00 |
time (sec) |
N/A | 0.465 | 0.000 | 0.000 | 0.000 | 0.082 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 355 | 343 | 279 | 594 | 593 | 636 | 1436 | 10664 | 918 | 1392 |
N.S. |
1 | 0.97 | 0.79 | 1.67 | 1.67 | 1.79 | 4.05 | 30.04 | 2.59 | 3.92 |
time (sec) |
N/A | 0.723 | 0.632 | 1.193 | 0.045 | 0.400 | 12.102 | 0.933 | 0.149 | 26.232 |
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 | 227 | 223 | 215 | 412 | 415 | 445 | 998 | 6073 | 644 | 741 |
N.S. |
1 | 0.98 | 0.95 | 1.81 | 1.83 | 1.96 | 4.40 | 26.75 | 2.84 | 3.26 |
time (sec) |
N/A | 0.530 | 0.284 | 1.079 | 0.044 | 0.211 | 5.829 | 0.582 | 0.161 | 25.859 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 155 | 142 | 265 | 262 | 280 | 658 | 3076 | 409 | 356 |
N.S. |
1 | 1.03 | 0.95 | 1.77 | 1.75 | 1.87 | 4.39 | 20.51 | 2.73 | 2.37 |
time (sec) |
N/A | 0.378 | 0.147 | 1.023 | 0.044 | 0.114 | 3.021 | 0.428 | 0.157 | 25.701 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 123 | 114 | 122 | 140 | 150 | 318 | 1145 | 208 | 144 |
N.S. |
1 | 1.13 | 1.05 | 1.12 | 1.28 | 1.38 | 2.92 | 10.50 | 1.91 | 1.32 |
time (sec) |
N/A | 0.349 | 0.112 | 0.921 | 0.036 | 0.095 | 1.394 | 0.259 | 0.150 | 25.483 |
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 | 52 | 52 | 52 | 51 | 54 | 56 | 83 | 406 | 69 | 47 |
N.S. |
1 | 1.00 | 1.00 | 0.98 | 1.04 | 1.08 | 1.60 | 7.81 | 1.33 | 0.90 |
time (sec) |
N/A | 0.205 | 0.010 | 0.744 | 0.029 | 0.075 | 0.413 | 0.171 | 0.170 | 25.297 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 149 | 115 | 372 | 0 | 0 | 0 | 0 | 43 | 0 |
N.S. |
1 | 1.06 | 0.82 | 2.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.524 | 0.068 | 5.718 | 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 | B | A | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 137 | 105 | 242 | 138 | 255 | 0 | 511 | 372 | 166 |
N.S. |
1 | 1.57 | 1.21 | 2.78 | 1.59 | 2.93 | 0.00 | 5.87 | 4.28 | 1.91 |
time (sec) |
N/A | 0.304 | 0.141 | 1.278 | 0.035 | 3.057 | 0.000 | 0.231 | 0.169 | 26.179 |
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 | 183 | 186 | 169 | 694 | 351 | 1017 | 0 | 2969 | 2285 | 417 |
N.S. |
1 | 1.02 | 0.92 | 3.79 | 1.92 | 5.56 | 0.00 | 16.22 | 12.49 | 2.28 |
time (sec) |
N/A | 0.452 | 0.472 | 1.675 | 0.046 | 43.318 | 0.000 | 0.274 | 0.167 | 28.430 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | F(-1) | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 275 | 270 | 260 | 1504 | 848 | 0 | 0 | 9339 | 6360 | 1154 |
N.S. |
1 | 0.98 | 0.95 | 5.47 | 3.08 | 0.00 | 0.00 | 33.96 | 23.13 | 4.20 |
time (sec) |
N/A | 0.628 | 0.676 | 2.415 | 0.089 | 0.000 | 0.000 | 0.450 | 0.191 | 31.974 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | F(-1) | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 379 | 367 | 355 | 2850 | 1757 | 0 | 0 | 20791 | 6836 | 2518 |
N.S. |
1 | 0.97 | 0.94 | 7.52 | 4.64 | 0.00 | 0.00 | 54.86 | 18.04 | 6.64 |
time (sec) |
N/A | 0.873 | 0.925 | 4.500 | 0.158 | 0.000 | 0.000 | 0.611 | 0.211 | 38.694 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 874 | 1069 | 733 | 0 | 2140 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.22 | 0.84 | 0.00 | 2.45 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.742 | 1.060 | 0.000 | 0.158 | 0.000 | 0.000 | 0.000 | 200.018 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 532 | 682 | 486 | 0 | 1300 | 0 | 0 | 0 | 1446 | 0 |
N.S. |
1 | 1.28 | 0.91 | 0.00 | 2.44 | 0.00 | 0.00 | 0.00 | 2.72 | 0.00 |
time (sec) |
N/A | 1.263 | 0.577 | 0.000 | 0.138 | 0.000 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 392 | 346 | 0 | 673 | 0 | 0 | 0 | 671 | 0 |
N.S. |
1 | 1.45 | 1.28 | 0.00 | 2.49 | 0.00 | 0.00 | 0.00 | 2.49 | 0.00 |
time (sec) |
N/A | 0.886 | 0.325 | 0.000 | 0.121 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 120 | 214 | 0 | 0 | 0 | 0 | 0 | 203 | 0 |
N.S. |
1 | 0.92 | 1.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.56 | 0.00 |
time (sec) |
N/A | 0.674 | 0.185 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 277 | 347 | 1348 | 818 | 0 | 0 | 0 | 0 | 81 | 0 |
N.S. |
1 | 1.25 | 4.87 | 2.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.760 | 0.608 | 5.808 | 0.000 | 0.000 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 212 | 402 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 2.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.515 | 0.510 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.414 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 369 | 499 | 595 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.35 | 1.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.068 | 1.301 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.551 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 714 | 885 | 894 | 0 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.24 | 1.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.629 | 2.811 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.032 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1159 | 1398 | 1301 | 0 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.21 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 2.414 | 6.543 | 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 | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 61 | 30 | 29 | 32 | 29 | 20 | 55 | 42 | 28 |
N.S. |
1 | 1.74 | 0.86 | 0.83 | 0.91 | 0.83 | 0.57 | 1.57 | 1.20 | 0.80 |
time (sec) |
N/A | 0.226 | 0.013 | 0.301 | 0.025 | 0.067 | 0.064 | 0.123 | 0.169 | 0.179 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 31 | 42 | 31 | 31 | 2174 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.07 | 1.45 | 1.07 | 1.07 | 74.97 | 1.07 |
time (sec) |
N/A | 0.208 | 0.271 | 1.961 | 0.072 | 0.071 | 2.542 | 13.614 | 0.216 | 26.320 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 29 | 27 | 29 | 31 | 29 | 29 | 1352 | 29 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.07 | 1.15 | 1.07 | 1.07 | 50.07 | 1.07 |
time (sec) |
N/A | 0.197 | 0.189 | 1.833 | 0.063 | 0.067 | 2.026 | 10.717 | 0.195 | 26.155 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 23 | 21 | 23 | 25 | 19 | 23 | 560 | 23 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.19 | 0.90 | 1.10 | 26.67 | 1.10 |
time (sec) |
N/A | 0.167 | 0.020 | 1.500 | 0.054 | 0.073 | 0.851 | 11.495 | 0.171 | 25.204 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 31 | 38 | 31 | 31 | 1685 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.07 | 1.31 | 1.07 | 1.07 | 58.10 | 1.07 |
time (sec) |
N/A | 0.203 | 1.080 | 1.772 | 0.067 | 0.075 | 2.719 | 17.927 | 0.239 | 26.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 31 | 62 | 32 | 31 | 3669 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.07 | 2.14 | 1.10 | 1.07 | 126.52 | 1.07 |
time (sec) |
N/A | 0.196 | 2.359 | 1.717 | 0.068 | 0.088 | 32.302 | 27.622 | 0.332 | 29.373 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 31 | 86 | 0 | 31 | 135 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.07 | 2.97 | 0.00 | 1.07 | 4.66 | 1.07 |
time (sec) |
N/A | 0.198 | 26.160 | 3.198 | 0.073 | 0.076 | 0.000 | 37.289 | 0.193 | 32.097 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 318 | 69 | 559 | 31 | 8359 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 10.97 | 2.38 | 19.28 | 1.07 | 288.24 | 1.07 |
time (sec) |
N/A | 0.189 | 1.101 | 3.878 | 0.067 | 0.109 | 16.716 | 0.559 | 0.247 | 28.450 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 29 | 27 | 225 | 58 | 337 | 29 | 5211 | 29 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 8.33 | 2.15 | 12.48 | 1.07 | 193.00 | 1.07 |
time (sec) |
N/A | 0.185 | 0.677 | 1.993 | 0.067 | 0.082 | 9.068 | 0.972 | 0.230 | 28.904 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 23 | 21 | 171 | 52 | 158 | 23 | 2122 | 23 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 8.14 | 2.48 | 7.52 | 1.10 | 101.05 | 1.10 |
time (sec) |
N/A | 0.180 | 0.364 | 2.095 | 0.064 | 0.074 | 4.288 | 0.796 | 0.184 | 26.350 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 452 | 77 | 0 | 31 | 6413 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 15.59 | 2.66 | 0.00 | 1.07 | 221.14 | 1.07 |
time (sec) |
N/A | 0.198 | 2.468 | 3.213 | 0.073 | 0.083 | 0.000 | 0.716 | 0.271 | 29.918 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 688 | 118 | 0 | 31 | 13919 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 23.72 | 4.07 | 0.00 | 1.07 | 479.97 | 1.07 |
time (sec) |
N/A | 0.194 | 3.237 | 2.164 | 0.085 | 0.072 | 0.000 | 0.884 | 0.368 | 46.121 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 921 | 159 | 0 | 31 | 264 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 31.76 | 5.48 | 0.00 | 1.07 | 9.10 | 1.07 |
time (sec) |
N/A | 0.194 | 63.106 | 3.218 | 0.096 | 0.079 | 0.000 | 1.497 | 0.196 | 56.234 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 357 | 345 | 282 | 599 | 855 | 660 | 1477 | 0 | 1148 | 1403 |
N.S. |
1 | 0.97 | 0.79 | 1.68 | 2.39 | 1.85 | 4.14 | 0.00 | 3.22 | 3.93 |
time (sec) |
N/A | 0.705 | 0.678 | 1.244 | 0.080 | 0.474 | 12.664 | 0.000 | 0.165 | 26.547 |
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 | 229 | 225 | 217 | 416 | 623 | 468 | 998 | 410 | 828 | 743 |
N.S. |
1 | 0.98 | 0.95 | 1.82 | 2.72 | 2.04 | 4.36 | 1.79 | 3.62 | 3.24 |
time (sec) |
N/A | 0.486 | 0.304 | 1.062 | 0.064 | 0.182 | 5.844 | 43.361 | 0.161 | 26.154 |
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 | 152 | 157 | 142 | 270 | 419 | 301 | 692 | 257 | 544 | 362 |
N.S. |
1 | 1.03 | 0.93 | 1.78 | 2.76 | 1.98 | 4.55 | 1.69 | 3.58 | 2.38 |
time (sec) |
N/A | 0.380 | 0.157 | 1.017 | 0.060 | 0.113 | 3.190 | 3.654 | 0.167 | 25.944 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 123 | 118 | 123 | 246 | 174 | 314 | 139 | 302 | 133 |
N.S. |
1 | 1.18 | 1.13 | 1.18 | 2.37 | 1.67 | 3.02 | 1.34 | 2.90 | 1.28 |
time (sec) |
N/A | 0.332 | 0.129 | 0.881 | 0.044 | 0.086 | 1.378 | 0.457 | 0.167 | 25.513 |
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 | 54 | 54 | 54 | 54 | 57 | 80 | 104 | 82 | 116 | 50 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 1.06 | 1.48 | 1.93 | 1.52 | 2.15 | 0.93 |
time (sec) |
N/A | 0.197 | 0.030 | 0.787 | 0.028 | 0.076 | 0.449 | 0.147 | 0.167 | 25.466 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 152 | 119 | 396 | 0 | 0 | 0 | 0 | 66 | 0 |
N.S. |
1 | 1.06 | 0.83 | 2.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.495 | 0.074 | 7.354 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 140 | 108 | 245 | 192 | 279 | 0 | 172 | 470 | 191 |
N.S. |
1 | 1.56 | 1.20 | 2.72 | 2.13 | 3.10 | 0.00 | 1.91 | 5.22 | 2.12 |
time (sec) |
N/A | 0.298 | 0.150 | 1.365 | 0.041 | 3.088 | 0.000 | 0.305 | 0.173 | 26.447 |
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 | 175 | 185 | 172 | 629 | 405 | 1036 | 0 | 486 | 2695 | 412 |
N.S. |
1 | 1.06 | 0.98 | 3.59 | 2.31 | 5.92 | 0.00 | 2.78 | 15.40 | 2.35 |
time (sec) |
N/A | 0.457 | 0.502 | 1.891 | 0.056 | 43.449 | 0.000 | 0.325 | 0.169 | 28.233 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | F(-1) | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 277 | 272 | 263 | 1293 | 900 | 0 | 0 | 1359 | 7464 | 1147 |
N.S. |
1 | 0.98 | 0.95 | 4.67 | 3.25 | 0.00 | 0.00 | 4.91 | 26.95 | 4.14 |
time (sec) |
N/A | 0.625 | 0.699 | 2.750 | 0.095 | 0.000 | 0.000 | 0.577 | 0.202 | 32.562 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | F(-1) | F(-1) | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 381 | 369 | 358 | 2299 | 1809 | 0 | 0 | 2059 | 7411 | 2520 |
N.S. |
1 | 0.97 | 0.94 | 6.03 | 4.75 | 0.00 | 0.00 | 5.40 | 19.45 | 6.61 |
time (sec) |
N/A | 0.859 | 0.984 | 5.898 | 0.158 | 0.000 | 0.000 | 2.156 | 0.226 | 39.973 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 869 | 1074 | 746 | 0 | 2351 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.24 | 0.86 | 0.00 | 2.71 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.690 | 1.076 | 0.000 | 0.198 | 0.000 | 0.000 | 0.000 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 542 | 686 | 497 | 0 | 1458 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.27 | 0.92 | 0.00 | 2.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.271 | 0.619 | 0.000 | 0.186 | 0.000 | 0.000 | 0.000 | 0.245 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 281 | 401 | 351 | 0 | 786 | 0 | 0 | 0 | 1016 | 0 |
N.S. |
1 | 1.43 | 1.25 | 0.00 | 2.80 | 0.00 | 0.00 | 0.00 | 3.62 | 0.00 |
time (sec) |
N/A | 0.868 | 0.343 | 0.000 | 0.167 | 0.000 | 0.000 | 0.000 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 124 | 220 | 0 | 0 | 0 | 0 | 0 | 318 | 0 |
N.S. |
1 | 0.93 | 1.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.37 | 0.00 |
time (sec) |
N/A | 0.662 | 0.192 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 285 | 355 | 1370 | 0 | 0 | 0 | 0 | 0 | 127 | 0 |
N.S. |
1 | 1.25 | 4.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.775 | 0.736 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 216 | 409 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 2.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.518 | 0.531 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.555 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 381 | 510 | 603 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.34 | 1.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.084 | 1.376 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.806 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 724 | 889 | 909 | 0 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.23 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.750 | 2.809 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.031 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1154 | 1400 | 1317 | 0 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.21 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 2.434 | 7.202 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.030 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 33 | 31 | 33 | 65 | 85 | 33 | 3675 | 33 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 2.10 | 2.74 | 1.06 | 118.55 | 1.06 |
time (sec) |
N/A | 0.210 | 0.177 | 1.533 | 0.086 | 0.065 | 5.705 | 0.268 | 0.314 | 26.853 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 31 | 54 | 83 | 31 | 2301 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.07 | 1.86 | 2.86 | 1.07 | 79.34 | 1.07 |
time (sec) |
N/A | 0.197 | 0.144 | 1.395 | 0.083 | 0.075 | 3.490 | 0.239 | 0.259 | 26.843 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 25 | 48 | 22 | 25 | 954 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 2.09 | 0.96 | 1.09 | 41.48 | 1.09 |
time (sec) |
N/A | 0.185 | 0.040 | 1.348 | 0.095 | 0.066 | 1.140 | 0.241 | 0.218 | 25.471 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 33 | 31 | 33 | 61 | 85 | 33 | 2839 | 33 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 1.97 | 2.74 | 1.06 | 91.58 | 1.06 |
time (sec) |
N/A | 0.212 | 0.104 | 1.628 | 0.091 | 0.070 | 3.597 | 0.257 | 0.311 | 26.600 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 33 | 31 | 33 | 85 | 87 | 33 | 5904 | 33 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 2.74 | 2.81 | 1.06 | 190.45 | 1.06 |
time (sec) |
N/A | 0.212 | 0.102 | 1.626 | 0.076 | 0.071 | 33.583 | 0.487 | 0.407 | 31.860 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 33 | 31 | 33 | 109 | 0 | 33 | 227 | 33 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 1.06 | 3.52 | 0.00 | 1.06 | 7.32 | 1.06 |
time (sec) |
N/A | 0.203 | 0.106 | 1.706 | 0.087 | 0.073 | 0.000 | 0.298 | 0.229 | 36.561 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 33 | 31 | 321 | 115 | 0 | 33 | 14696 | 33 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 10.35 | 3.71 | 0.00 | 1.06 | 474.06 | 1.06 |
time (sec) |
N/A | 0.205 | 0.805 | 1.499 | 0.076 | 0.076 | 0.000 | 0.375 | 0.371 | 30.342 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 228 | 104 | 729 | 31 | 9202 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 7.86 | 3.59 | 25.14 | 1.07 | 317.31 | 1.07 |
time (sec) |
N/A | 0.191 | 0.413 | 1.381 | 0.068 | 0.069 | 18.577 | 0.324 | 0.316 | 30.748 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 174 | 98 | 333 | 25 | 3761 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 7.57 | 4.26 | 14.48 | 1.09 | 163.52 | 1.09 |
time (sec) |
N/A | 0.172 | 0.226 | 1.292 | 0.065 | 0.071 | 8.058 | 0.249 | 0.257 | 26.886 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 33 | 31 | 455 | 123 | 0 | 33 | 11066 | 33 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 14.68 | 3.97 | 0.00 | 1.06 | 356.97 | 1.06 |
time (sec) |
N/A | 0.207 | 0.493 | 1.345 | 0.074 | 0.076 | 0.000 | 0.522 | 0.363 | 32.330 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 33 | 31 | 690 | 164 | 0 | 33 | 23059 | 33 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 22.26 | 5.29 | 0.00 | 1.06 | 743.84 | 1.06 |
time (sec) |
N/A | 0.218 | 0.595 | 1.379 | 0.089 | 0.076 | 0.000 | 0.792 | 0.501 | 56.092 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 33 | 31 | 924 | 205 | 0 | 33 | 448 | 33 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 29.81 | 6.61 | 0.00 | 1.06 | 14.45 | 1.06 |
time (sec) |
N/A | 0.200 | 0.624 | 3.231 | 0.107 | 0.086 | 0.000 | 0.773 | 0.249 | 72.315 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F(-2) | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 365 | 348 | 463 | 1170 | 671 | 805 | 0 | 0 | 968 | 1434 |
N.S. |
1 | 0.95 | 1.27 | 3.21 | 1.84 | 2.21 | 0.00 | 0.00 | 2.65 | 3.93 |
time (sec) |
N/A | 0.745 | 1.110 | 97.786 | 0.067 | 0.087 | 0.000 | 0.000 | 0.201 | 26.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-2) | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 236 | 228 | 314 | 984 | 467 | 571 | 0 | 0 | 680 | 767 |
N.S. |
1 | 0.97 | 1.33 | 4.17 | 1.98 | 2.42 | 0.00 | 0.00 | 2.88 | 3.25 |
time (sec) |
N/A | 0.539 | 0.648 | 37.585 | 0.057 | 0.080 | 0.000 | 0.000 | 0.217 | 25.808 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F(-2) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 160 | 204 | 623 | 294 | 365 | 0 | 304 | 433 | 372 |
N.S. |
1 | 1.01 | 1.29 | 3.94 | 1.86 | 2.31 | 0.00 | 1.92 | 2.74 | 2.35 |
time (sec) |
N/A | 0.411 | 0.403 | 11.805 | 0.050 | 0.084 | 0.000 | 26.701 | 0.201 | 25.641 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F(-2) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 128 | 124 | 371 | 154 | 192 | 0 | 153 | 222 | 154 |
N.S. |
1 | 1.10 | 1.07 | 3.20 | 1.33 | 1.66 | 0.00 | 1.32 | 1.91 | 1.33 |
time (sec) |
N/A | 0.321 | 0.199 | 3.504 | 0.040 | 0.078 | 0.000 | 1.350 | 0.209 | 25.677 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-2) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 57 | 83 | 59 | 59 | 0 | 58 | 75 | 53 |
N.S. |
1 | 1.00 | 1.00 | 1.46 | 1.04 | 1.04 | 0.00 | 1.02 | 1.32 | 0.93 |
time (sec) |
N/A | 0.201 | 0.014 | 0.593 | 0.034 | 0.075 | 0.000 | 0.112 | 0.218 | 25.122 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 155 | 150 | 521 | 0 | 0 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.05 | 1.01 | 3.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.483 | 0.109 | 3.152 | 0.000 | 0.000 | 0.000 | 0.000 | 0.235 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 136 | 117 | 368 | 151 | 250 | 0 | 169 | 392 | 141 |
N.S. |
1 | 1.13 | 0.98 | 3.07 | 1.26 | 2.08 | 0.00 | 1.41 | 3.27 | 1.18 |
time (sec) |
N/A | 0.353 | 0.209 | 9.310 | 0.038 | 2.906 | 0.000 | 0.154 | 0.288 | 25.857 |
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 | 191 | 191 | 178 | 1385 | 382 | 1127 | 0 | 531 | 2381 | 431 |
N.S. |
1 | 1.00 | 0.93 | 7.25 | 2.00 | 5.90 | 0.00 | 2.78 | 12.47 | 2.26 |
time (sec) |
N/A | 0.442 | 0.593 | 33.437 | 0.055 | 44.086 | 0.000 | 0.286 | 0.307 | 27.851 |