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 | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 189 | 151 | 1229 | 338 | 911 | 5992 | 1708 | 747 | 469 |
N.S. |
1 | 1.00 | 0.80 | 6.50 | 1.79 | 4.82 | 31.70 | 9.04 | 3.95 | 2.48 |
time (sec) |
N/A | 0.546 | 0.429 | 0.514 | 0.076 | 0.122 | 0.924 | 0.156 | 0.284 | 0.586 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 144 | 113 | 711 | 242 | 532 | 3271 | 1009 | 475 | 305 |
N.S. |
1 | 1.00 | 0.78 | 4.94 | 1.68 | 3.69 | 22.72 | 7.01 | 3.30 | 2.12 |
time (sec) |
N/A | 0.300 | 0.103 | 0.457 | 0.064 | 0.114 | 0.702 | 0.138 | 0.201 | 0.232 |
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 | 97 | 97 | 73 | 96 | 146 | 235 | 1460 | 478 | 263 | 185 |
N.S. |
1 | 1.00 | 0.75 | 0.99 | 1.51 | 2.42 | 15.05 | 4.93 | 2.71 | 1.91 |
time (sec) |
N/A | 0.230 | 0.055 | 0.105 | 0.047 | 0.092 | 0.459 | 0.133 | 0.219 | 0.169 |
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 | 60 | 60 | 43 | 59 | 70 | 94 | 439 | 167 | 111 | 97 |
N.S. |
1 | 1.00 | 0.72 | 0.98 | 1.17 | 1.57 | 7.32 | 2.78 | 1.85 | 1.62 |
time (sec) |
N/A | 0.200 | 0.038 | 0.066 | 0.040 | 0.083 | 0.309 | 0.118 | 0.192 | 0.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 93 | 0 | 0 | 0 | 418 | 0 | 36 | 0 |
N.S. |
1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 3.54 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.253 | 0.123 | 0.000 | 0.000 | 0.000 | 3.449 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 174 | 108 | 0 | 0 | 0 | 2069 | 0 | 95 | 0 |
N.S. |
1 | 1.14 | 0.71 | 0.00 | 0.00 | 0.00 | 13.52 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.342 | 0.177 | 0.000 | 0.000 | 0.000 | 30.583 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 220 | 133 | 0 | 0 | 0 | 6411 | 0 | 613 | 0 |
N.S. |
1 | 1.07 | 0.65 | 0.00 | 0.00 | 0.00 | 31.12 | 0.00 | 2.98 | 0.00 |
time (sec) |
N/A | 0.384 | 0.381 | 0.000 | 0.000 | 0.000 | 103.008 | 0.000 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 292 | 247 | 2443 | 550 | 1711 | 11914 | 3283 | 1484 | 694 |
N.S. |
1 | 1.00 | 0.85 | 8.37 | 1.88 | 5.86 | 40.80 | 11.24 | 5.08 | 2.38 |
time (sec) |
N/A | 0.499 | 0.620 | 0.638 | 0.110 | 0.119 | 1.354 | 0.180 | 0.211 | 0.599 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 216 | 178 | 1471 | 396 | 1043 | 6836 | 2010 | 977 | 499 |
N.S. |
1 | 1.00 | 0.82 | 6.81 | 1.83 | 4.83 | 31.65 | 9.31 | 4.52 | 2.31 |
time (sec) |
N/A | 0.415 | 0.209 | 0.546 | 0.084 | 0.100 | 0.972 | 0.161 | 0.197 | 0.377 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 144 | 113 | 711 | 242 | 495 | 3271 | 1009 | 570 | 305 |
N.S. |
1 | 1.00 | 0.78 | 4.94 | 1.68 | 3.44 | 22.72 | 7.01 | 3.96 | 2.12 |
time (sec) |
N/A | 0.310 | 0.106 | 0.453 | 0.078 | 0.092 | 0.710 | 0.143 | 0.236 | 0.242 |
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 | 91 | 91 | 67 | 90 | 116 | 217 | 1096 | 380 | 263 | 179 |
N.S. |
1 | 1.00 | 0.74 | 0.99 | 1.27 | 2.38 | 12.04 | 4.18 | 2.89 | 1.97 |
time (sec) |
N/A | 0.224 | 0.050 | 0.416 | 0.043 | 0.080 | 0.572 | 0.130 | 0.194 | 0.150 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 178 | 146 | 0 | 0 | 0 | 649 | 0 | 94 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 3.65 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.365 | 0.194 | 0.000 | 0.000 | 0.000 | 6.004 | 0.000 | 0.205 | 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 | 200 | 245 | 156 | 0 | 0 | 0 | 0 | 0 | 292 | 0 |
N.S. |
1 | 1.22 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.46 | 0.00 |
time (sec) |
N/A | 0.517 | 0.511 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.214 | 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 | 290 | 305 | 165 | 0 | 0 | 0 | 0 | 0 | 1569 | 0 |
N.S. |
1 | 1.05 | 0.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 5.41 | 0.00 |
time (sec) |
N/A | 0.510 | 0.697 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 379 | 379 | 327 | 3953 | 762 | 2657 | 20086 | 5234 | 2401 | 933 |
N.S. |
1 | 1.00 | 0.86 | 10.43 | 2.01 | 7.01 | 53.00 | 13.81 | 6.34 | 2.46 |
time (sec) |
N/A | 0.612 | 0.891 | 0.867 | 0.129 | 0.130 | 1.854 | 0.200 | 0.209 | 0.840 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 284 | 284 | 239 | 2443 | 550 | 1690 | 11914 | 3283 | 1619 | 694 |
N.S. |
1 | 1.00 | 0.84 | 8.60 | 1.94 | 5.95 | 41.95 | 11.56 | 5.70 | 2.44 |
time (sec) |
N/A | 0.505 | 0.528 | 0.630 | 0.106 | 0.109 | 1.331 | 0.180 | 0.236 | 0.593 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 189 | 151 | 1229 | 338 | 837 | 5992 | 1708 | 977 | 469 |
N.S. |
1 | 1.00 | 0.80 | 6.50 | 1.79 | 4.43 | 31.70 | 9.04 | 5.17 | 2.48 |
time (sec) |
N/A | 0.368 | 0.354 | 0.507 | 0.081 | 0.095 | 0.923 | 0.157 | 0.236 | 0.413 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 90 | 475 | 162 | 381 | 2152 | 673 | 475 | 280 |
N.S. |
1 | 1.00 | 0.74 | 3.93 | 1.34 | 3.15 | 17.79 | 5.56 | 3.93 | 2.31 |
time (sec) |
N/A | 0.262 | 0.084 | 0.450 | 0.047 | 0.086 | 0.592 | 0.136 | 0.269 | 0.214 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 258 | 217 | 0 | 0 | 0 | 887 | 0 | 179 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.00 | 3.44 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.505 | 0.523 | 0.000 | 0.000 | 0.000 | 9.074 | 0.000 | 0.217 | 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 | 260 | 340 | 209 | 0 | 0 | 0 | 0 | 0 | 693 | 0 |
N.S. |
1 | 1.31 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.67 | 0.00 |
time (sec) |
N/A | 0.646 | 0.745 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.218 | 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 | 340 | 489 | 218 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.44 | 0.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.017 | 0.737 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 363 | 363 | 315 | 0 | 0 | 0 | 1102 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 3.04 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.645 | 0.606 | 0.000 | 0.000 | 0.000 | 13.934 | 0.000 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 260 | 260 | 219 | 0 | 0 | 0 | 887 | 0 | 1357 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.00 | 3.41 | 0.00 | 5.22 | 0.00 |
time (sec) |
N/A | 0.496 | 0.510 | 0.000 | 0.000 | 0.000 | 9.509 | 0.000 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 180 | 147 | 0 | 0 | 0 | 649 | 0 | 693 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 3.61 | 0.00 | 3.85 | 0.00 |
time (sec) |
N/A | 0.367 | 0.219 | 0.000 | 0.000 | 0.000 | 6.130 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 120 | 93 | 0 | 0 | 0 | 418 | 0 | 292 | 0 |
N.S. |
1 | 1.00 | 0.78 | 0.00 | 0.00 | 0.00 | 3.48 | 0.00 | 2.43 | 0.00 |
time (sec) |
N/A | 0.250 | 0.104 | 0.000 | 0.000 | 0.000 | 3.672 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 56 | 0 | 0 | 0 | 201 | 0 | 95 | 0 |
N.S. |
1 | 1.00 | 0.73 | 0.00 | 0.00 | 0.00 | 2.61 | 0.00 | 1.23 | 0.00 |
time (sec) |
N/A | 0.193 | 0.055 | 0.000 | 0.000 | 0.000 | 2.019 | 0.000 | 0.224 | 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 | 125 | 125 | 100 | 0 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.00 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.282 | 0.138 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.216 | 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 | 206 | 223 | 149 | 0 | 0 | 0 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.08 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.462 | 0.316 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 342 | 0 | 195 | 0 | 0 | 0 | 0 | 0 | 58 | 0 |
N.S. |
1 | 0.00 | 0.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.000 | 0.853 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.199 | 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 | 264 | 333 | 212 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.26 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.680 | 0.755 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.268 | 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 | 202 | 245 | 158 | 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 | 0.500 | 0.578 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 174 | 108 | 0 | 0 | 0 | 2069 | 0 | 1569 | 0 |
N.S. |
1 | 1.14 | 0.71 | 0.00 | 0.00 | 0.00 | 13.52 | 0.00 | 10.25 | 0.00 |
time (sec) |
N/A | 0.323 | 0.180 | 0.000 | 0.000 | 0.000 | 28.269 | 0.000 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 81 | 0 | 0 | 0 | 954 | 0 | 613 | 0 |
N.S. |
1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 9.26 | 0.00 | 5.95 | 0.00 |
time (sec) |
N/A | 0.206 | 0.067 | 0.000 | 0.000 | 0.000 | 14.120 | 0.000 | 0.220 | 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 | 205 | 222 | 147 | 0 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.08 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.468 | 0.295 | 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(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 304 | 329 | 207 | 0 | 0 | 0 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.08 | 0.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.738 | 0.884 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 491 | 0 | 265 | 0 | 0 | 0 | 0 | 0 | 99 | 0 |
N.S. |
1 | 0.00 | 0.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.000 | 1.133 | 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 | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 326 | 443 | 222 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.36 | 0.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.008 | 0.764 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.303 | 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 | 270 | 304 | 169 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 0.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.514 | 0.712 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 219 | 133 | 0 | 0 | 0 | 6411 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.65 | 0.00 | 0.00 | 0.00 | 31.12 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.387 | 0.390 | 0.000 | 0.000 | 0.000 | 92.256 | 0.000 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 81 | 0 | 0 | 0 | 3199 | 0 | 1550 | 0 |
N.S. |
1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 31.06 | 0.00 | 15.05 | 0.00 |
time (sec) |
N/A | 0.204 | 0.075 | 0.000 | 0.000 | 0.000 | 50.867 | 0.000 | 0.246 | 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 | 333 | 370 | 197 | 0 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.11 | 0.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.739 | 0.814 | 0.000 | 0.000 | 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 | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 452 | 500 | 266 | 0 | 0 | 0 | 0 | 0 | 82 | 0 |
N.S. |
1 | 1.11 | 0.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 1.081 | 1.129 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 665 | 0 | 329 | 0 | 0 | 0 | 0 | 0 | 140 | 0 |
N.S. |
1 | 0.00 | 0.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.000 | 1.417 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.260 | 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 | 688 | 1020 | 248 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.48 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.675 | 0.265 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.418 | 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 | 399 | 455 | 198 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.14 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.807 | 0.163 | 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 | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 241 | 147 | 0 | 0 | 0 | 236 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 0.68 | 0.00 | 0.00 | 0.00 | 1.09 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.433 | 0.094 | 0.000 | 0.000 | 0.000 | 177.905 | 0.000 | 0.235 | 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 | 162 | 162 | 118 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.326 | 0.362 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.302 | 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 | 295 | 286 | 128 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 0.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.497 | 0.340 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.727 | 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 | 483 | 491 | 128 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.896 | 0.492 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.696 | 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 | 94 | 89 | 91 | 95 | 100 | 234 | 151 | 113 | 141 | 101 |
N.S. |
1 | 0.95 | 0.97 | 1.01 | 1.06 | 2.49 | 1.61 | 1.20 | 1.50 | 1.07 |
time (sec) |
N/A | 0.229 | 0.101 | 0.525 | 0.040 | 0.095 | 10.611 | 0.124 | 0.217 | 0.784 |
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 | 95 | 89 | 91 | 95 | 100 | 220 | 151 | 113 | 170 | 101 |
N.S. |
1 | 0.94 | 0.96 | 1.00 | 1.05 | 2.32 | 1.59 | 1.19 | 1.79 | 1.06 |
time (sec) |
N/A | 0.221 | 0.109 | 0.503 | 0.039 | 0.094 | 10.522 | 0.123 | 0.272 | 0.689 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1522 | 1802 | 1001 | 2627 | 0 | 1561 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.18 | 0.66 | 1.73 | 0.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.329 | 6.671 | 19.832 | 0.000 | 0.191 | 0.000 | 0.000 | 2.052 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1130 | 1430 | 777 | 1668 | 0 | 1199 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.27 | 0.69 | 1.48 | 0.00 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.668 | 5.609 | 9.787 | 0.000 | 0.112 | 0.000 | 0.000 | 1.626 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 841 | 1103 | 570 | 1075 | 0 | 873 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.31 | 0.68 | 1.28 | 0.00 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.957 | 4.231 | 7.883 | 0.000 | 0.117 | 0.000 | 0.000 | 1.295 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 609 | 1043 | 422 | 704 | 0 | 593 | 0 | 0 | 1140 | 0 |
N.S. |
1 | 1.71 | 0.69 | 1.16 | 0.00 | 0.97 | 0.00 | 0.00 | 1.87 | 0.00 |
time (sec) |
N/A | 1.400 | 2.390 | 6.022 | 0.000 | 0.103 | 0.000 | 0.000 | 0.984 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 692 | 670 | 324 | 516 | 0 | 0 | 0 | 0 | 921 | 0 |
N.S. |
1 | 0.97 | 0.47 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 1.33 | 0.00 |
time (sec) |
N/A | 1.107 | 2.350 | 5.377 | 0.000 | 0.000 | 0.000 | 0.000 | 1.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 694 | 639 | 308 | 444 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.92 | 0.44 | 0.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.124 | 2.397 | 5.918 | 0.000 | 0.000 | 0.000 | 0.000 | 1.992 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1067 | 751 | 383 | 547 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.70 | 0.36 | 0.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.368 | 2.628 | 7.292 | 0.000 | 0.000 | 0.000 | 0.000 | 4.370 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1641 | 1012 | 520 | 755 | 0 | 589 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.62 | 0.32 | 0.46 | 0.00 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.904 | 4.156 | 8.572 | 0.000 | 0.099 | 0.000 | 0.000 | 7.782 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 689 | 623 | 471 | 893 | 0 | 691 | 0 | 0 | 1358 | 0 |
N.S. |
1 | 0.90 | 0.68 | 1.30 | 0.00 | 1.00 | 0.00 | 0.00 | 1.97 | 0.00 |
time (sec) |
N/A | 1.046 | 3.454 | 6.783 | 0.000 | 0.108 | 0.000 | 0.000 | 1.031 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 530 | 472 | 367 | 604 | 0 | 485 | 0 | 0 | 906 | 0 |
N.S. |
1 | 0.89 | 0.69 | 1.14 | 0.00 | 0.92 | 0.00 | 0.00 | 1.71 | 0.00 |
time (sec) |
N/A | 0.794 | 1.709 | 5.480 | 0.000 | 0.098 | 0.000 | 0.000 | 0.820 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 381 | 350 | 269 | 431 | 0 | 313 | 0 | 0 | 520 | 0 |
N.S. |
1 | 0.92 | 0.71 | 1.13 | 0.00 | 0.82 | 0.00 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 0.478 | 1.480 | 4.023 | 0.000 | 0.096 | 0.000 | 0.000 | 0.658 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 324 | 312 | 225 | 345 | 0 | 0 | 0 | 0 | 413 | 0 |
N.S. |
1 | 0.96 | 0.69 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 1.27 | 0.00 |
time (sec) |
N/A | 0.461 | 1.465 | 3.998 | 0.000 | 0.000 | 0.000 | 0.000 | 0.874 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 332 | 319 | 251 | 369 | 0 | 0 | 0 | 0 | 1284 | 0 |
N.S. |
1 | 0.96 | 0.76 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 3.87 | 0.00 |
time (sec) |
N/A | 0.483 | 1.589 | 5.265 | 0.000 | 0.000 | 0.000 | 0.000 | 1.682 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 391 | 424 | 324 | 477 | 0 | 314 | 0 | 0 | 1114 | 0 |
N.S. |
1 | 1.08 | 0.83 | 1.22 | 0.00 | 0.80 | 0.00 | 0.00 | 2.85 | 0.00 |
time (sec) |
N/A | 0.695 | 1.933 | 6.417 | 0.000 | 0.091 | 0.000 | 0.000 | 3.268 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 536 | 580 | 446 | 636 | 0 | 483 | 0 | 0 | 1029 | 0 |
N.S. |
1 | 1.08 | 0.83 | 1.19 | 0.00 | 0.90 | 0.00 | 0.00 | 1.92 | 0.00 |
time (sec) |
N/A | 0.984 | 3.260 | 7.563 | 0.000 | 0.095 | 0.000 | 0.000 | 4.641 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 695 | 752 | 571 | 833 | 0 | 686 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 0.82 | 1.20 | 0.00 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.338 | 3.938 | 8.628 | 0.000 | 0.105 | 0.000 | 0.000 | 5.281 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1113 | 0 | 829 | 1105 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 0.00 | 0.74 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 0.000 | 8.833 | 18.342 | 0.000 | 0.000 | 0.000 | 0.000 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 787 | 0 | 596 | 785 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 0.00 | 0.76 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.000 | 4.642 | 8.973 | 0.000 | 0.000 | 0.000 | 0.000 | 200.018 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 558 | 0 | 426 | 565 | 0 | 0 | 0 | 0 | 1494 | 0 |
N.S. |
1 | 0.00 | 0.76 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 2.68 | 0.00 |
time (sec) |
N/A | 0.000 | 3.495 | 7.647 | 0.000 | 0.000 | 0.000 | 0.000 | 12.271 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 401 | 0 | 320 | 699 | 0 | 0 | 0 | 0 | 600 | 0 |
N.S. |
1 | 0.00 | 0.80 | 1.74 | 0.00 | 0.00 | 0.00 | 0.00 | 1.50 | 0.00 |
time (sec) |
N/A | 0.000 | 2.249 | 9.052 | 0.000 | 0.000 | 0.000 | 0.000 | 4.999 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 322 | 326 | 185 | 340 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.01 | 0.57 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.473 | 1.584 | 1.203 | 0.000 | 0.000 | 0.000 | 0.000 | 0.528 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 415 | 0 | 533 | 412 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 0.00 | 1.28 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.000 | 2.219 | 8.295 | 0.000 | 0.000 | 0.000 | 0.000 | 8.013 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 528 | 0 | 348 | 461 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 0.00 | 0.66 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.000 | 3.440 | 8.494 | 0.000 | 0.000 | 0.000 | 0.000 | 27.332 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 741 | 0 | 1206 | 813 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 0.00 | 1.63 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.000 | 4.095 | 9.385 | 0.000 | 0.000 | 0.000 | 0.000 | 52.806 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 771 | 0 | 505 | 1538 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 0.00 | 0.65 | 1.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.000 | 4.787 | 20.293 | 0.000 | 0.000 | 0.000 | 0.000 | 200.029 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 587 | 0 | 378 | 1265 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.64 | 2.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 3.598 | 21.960 | 0.000 | 0.000 | 0.000 | 0.000 | 49.287 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 531 | 0 | 874 | 849 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 1.65 | 1.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 2.505 | 5.072 | 0.000 | 0.000 | 0.000 | 0.000 | 26.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 413 | 378 | 401 | 559 | 0 | 0 | 0 | 0 | 39 | 0 |
N.S. |
1 | 0.92 | 0.97 | 1.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.563 | 2.834 | 1.458 | 0.000 | 0.000 | 0.000 | 0.000 | 9.241 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 651 | 0 | 244 | 791 | 0 | 0 | 0 | 0 | 43 | 0 |
N.S. |
1 | 0.00 | 0.37 | 1.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.000 | 2.958 | 19.706 | 0.000 | 0.000 | 0.000 | 0.000 | 27.952 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 771 | 0 | 416 | 1135 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 0.00 | 0.54 | 1.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.000 | 4.573 | 20.697 | 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 | F | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1095 | 0 | 470 | 1785 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 0.00 | 0.43 | 1.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 0.000 | 4.532 | 22.803 | 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 | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1902 | 2236 | 1265 | 3327 | 0 | 1964 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.18 | 0.67 | 1.75 | 0.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 4.208 | 8.944 | 21.655 | 0.000 | 0.137 | 0.000 | 0.000 | 2.643 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1435 | 1816 | 1012 | 2657 | 0 | 1561 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.27 | 0.71 | 1.85 | 0.00 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.243 | 7.822 | 20.766 | 0.000 | 0.124 | 0.000 | 0.000 | 2.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1120 | 1435 | 782 | 2046 | 0 | 1199 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.28 | 0.70 | 1.83 | 0.00 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.587 | 6.646 | 10.452 | 0.000 | 0.108 | 0.000 | 0.000 | 1.729 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 849 | 1352 | 584 | 1300 | 0 | 881 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.59 | 0.69 | 1.53 | 0.00 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.987 | 5.630 | 8.128 | 0.000 | 0.101 | 0.000 | 0.000 | 1.355 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 927 | 894 | 451 | 854 | 0 | 0 | 0 | 0 | 1520 | 0 |
N.S. |
1 | 0.96 | 0.49 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 1.64 | 0.00 |
time (sec) |
N/A | 1.541 | 4.086 | 6.832 | 0.000 | 0.000 | 0.000 | 0.000 | 1.660 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1035 | 794 | 392 | 644 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.77 | 0.38 | 0.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.492 | 4.000 | 6.460 | 0.000 | 0.000 | 0.000 | 0.000 | 2.505 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1343 | 798 | 415 | 629 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.59 | 0.31 | 0.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.571 | 4.205 | 6.770 | 0.000 | 0.000 | 0.000 | 0.000 | 5.691 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 684 | 624 | 480 | 1060 | 0 | 688 | 0 | 0 | 1358 | 0 |
N.S. |
1 | 0.91 | 0.70 | 1.55 | 0.00 | 1.01 | 0.00 | 0.00 | 1.99 | 0.00 |
time (sec) |
N/A | 1.044 | 4.484 | 7.523 | 0.000 | 0.106 | 0.000 | 0.000 | 1.047 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 526 | 471 | 368 | 695 | 0 | 494 | 0 | 0 | 906 | 0 |
N.S. |
1 | 0.90 | 0.70 | 1.32 | 0.00 | 0.94 | 0.00 | 0.00 | 1.72 | 0.00 |
time (sec) |
N/A | 0.663 | 3.034 | 5.756 | 0.000 | 0.097 | 0.000 | 0.000 | 0.814 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 430 | 415 | 288 | 509 | 0 | 0 | 0 | 0 | 749 | 0 |
N.S. |
1 | 0.97 | 0.67 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 | 1.74 | 0.00 |
time (sec) |
N/A | 0.632 | 2.911 | 5.246 | 0.000 | 0.000 | 0.000 | 0.000 | 0.965 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 396 | 371 | 272 | 433 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 0.69 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.638 | 3.044 | 5.710 | 0.000 | 0.000 | 0.000 | 0.000 | 1.641 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 453 | 419 | 349 | 502 | 0 | 0 | 0 | 0 | 1555 | 0 |
N.S. |
1 | 0.92 | 0.77 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 3.43 | 0.00 |
time (sec) |
N/A | 0.712 | 3.477 | 7.315 | 0.000 | 0.000 | 0.000 | 0.000 | 3.447 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 526 | 580 | 429 | 643 | 0 | 489 | 0 | 0 | 1405 | 0 |
N.S. |
1 | 1.10 | 0.82 | 1.22 | 0.00 | 0.93 | 0.00 | 0.00 | 2.67 | 0.00 |
time (sec) |
N/A | 1.025 | 4.680 | 9.002 | 0.000 | 0.088 | 0.000 | 0.000 | 5.791 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 690 | 755 | 560 | 832 | 0 | 684 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 0.81 | 1.21 | 0.00 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.346 | 5.448 | 9.965 | 0.000 | 0.102 | 0.000 | 0.000 | 8.121 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 790 | 0 | 609 | 826 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 0.00 | 0.77 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.000 | 6.068 | 18.555 | 0.000 | 0.000 | 0.000 | 0.000 | 200.020 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 547 | 0 | 437 | 601 | 0 | 0 | 0 | 0 | 1492 | 0 |
N.S. |
1 | 0.00 | 0.80 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 2.73 | 0.00 |
time (sec) |
N/A | 0.000 | 4.542 | 8.976 | 0.000 | 0.000 | 0.000 | 0.000 | 12.967 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 402 | 382 | 742 | 831 | 0 | 0 | 0 | 0 | 779 | 0 |
N.S. |
1 | 0.95 | 1.85 | 2.07 | 0.00 | 0.00 | 0.00 | 0.00 | 1.94 | 0.00 |
time (sec) |
N/A | 0.585 | 3.472 | 9.448 | 0.000 | 0.000 | 0.000 | 0.000 | 6.884 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 516 | 0 | 739 | 636 | 0 | 0 | 0 | 0 | 818 | 0 |
N.S. |
1 | 0.00 | 1.43 | 1.23 | 0.00 | 0.00 | 0.00 | 0.00 | 1.59 | 0.00 |
time (sec) |
N/A | 0.000 | 3.974 | 9.846 | 0.000 | 0.000 | 0.000 | 0.000 | 12.451 | 0.000 |