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 | 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 |
size | 14 | 14 | 16 | 12 | 14 | 14 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.14 | 0.86 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.418 | 0.136 | 0.042 | 0.215 | 0.251 | 0.287 | 0.333 | 20.753 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 14 | 14 | 16 | 12 | 14 | 24 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.14 | 0.86 | 1.00 | 1.71 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.388 | 0.194 | 0.039 | 0.225 | 0.252 | 0.306 | 0.329 | 20.188 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 17 | 17 | 19 | 13 | 15 | 15 | 15 | 15 | 15 |
N.S. |
1 | 1.00 | 1.12 | 0.76 | 0.88 | 0.88 | 0.88 | 0.88 | 0.88 |
time (sec) |
N/A | 0.327 | 0.004 | 0.040 | 0.219 | 0.254 | 1.240 | 0.327 | 20.414 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 17 | 17 | 19 | 13 | 15 | 25 | 15 | 15 | 15 |
N.S. |
1 | 1.00 | 1.12 | 0.76 | 0.88 | 1.47 | 0.88 | 0.88 | 0.88 |
time (sec) |
N/A | 0.295 | 0.004 | 0.037 | 0.232 | 0.250 | 0.529 | 0.308 | 20.177 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 10 | 10 | 12 | 10 | 12 | 12 | 8 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 0.80 | 1.20 | 1.20 |
time (sec) |
N/A | 0.210 | 0.008 | 0.012 | 0.203 | 0.232 | 0.182 | 0.324 | 20.252 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 12 | 12 | 14 | 12 | 14 | 14 | 12 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 1.17 | 1.00 | 1.17 | 1.17 |
time (sec) |
N/A | 0.212 | 0.007 | 0.013 | 0.178 | 0.228 | 0.191 | 0.302 | 20.163 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 10 | 10 | 12 | 10 | 12 | 12 | 8 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 0.80 | 1.20 | 1.20 |
time (sec) |
N/A | 0.173 | 0.007 | 0.010 | 0.184 | 0.230 | 0.204 | 0.325 | 20.477 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 14 | 14 | 16 | 14 | 16 | 16 | 12 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 1.14 | 0.86 | 1.14 | 1.14 |
time (sec) |
N/A | 0.180 | 0.008 | 0.010 | 0.177 | 0.243 | 0.238 | 0.323 | 21.677 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 12 | 12 | 14 | 12 | 14 | 25 | 12 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 2.08 | 1.00 | 1.17 | 1.17 |
time (sec) |
N/A | 0.173 | 0.010 | 0.010 | 0.176 | 0.238 | 0.237 | 0.306 | 21.461 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 14 | 14 | 16 | 14 | 16 | 27 | 14 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 1.93 | 1.00 | 1.14 | 1.14 |
time (sec) |
N/A | 0.181 | 0.009 | 0.013 | 0.175 | 0.234 | 0.280 | 0.295 | 19.764 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 75 | 0 | 0 | 135 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.60 | 0.00 | 0.00 | 2.87 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.246 | 0.284 | 0.000 | 0.000 | 1.105 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 82 | 0 | 0 | 146 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.71 | 0.00 | 0.00 | 3.04 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.246 | 0.280 | 0.000 | 0.000 | 1.076 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 169 | 169 | 364 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.413 | 0.892 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 268 | 309 | 1464 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.15 | 5.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.501 | 3.421 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 45 | 42 | 28 | 27 | 25 | 37 | 27 | 27 |
N.S. |
1 | 1.10 | 1.02 | 0.68 | 0.66 | 0.61 | 0.90 | 0.66 | 0.66 |
time (sec) |
N/A | 0.270 | 0.032 | 1.026 | 0.264 | 0.366 | 3.136 | 0.316 | 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 | 26 | 30 | 26 | 21 | 20 | 20 | 24 | 20 | 22 |
N.S. |
1 | 1.15 | 1.00 | 0.81 | 0.77 | 0.77 | 0.92 | 0.77 | 0.85 |
time (sec) |
N/A | 0.216 | 0.032 | 0.007 | 0.268 | 0.343 | 0.951 | 0.330 | 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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 36 | 42 | 31 | 30 | 30 | 39 | 30 | 42 |
N.S. |
1 | 0.86 | 1.00 | 0.74 | 0.71 | 0.71 | 0.93 | 0.71 | 1.00 |
time (sec) |
N/A | 0.258 | 0.031 | 1.109 | 0.265 | 0.347 | 4.037 | 0.337 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 22 | 48 | 50 | 0 | 75 | 0 | 44 | 17 |
N.S. |
1 | 1.10 | 2.40 | 2.50 | 0.00 | 3.75 | 0.00 | 2.20 | 0.85 |
time (sec) |
N/A | 0.158 | 0.023 | 1.063 | 0.000 | 0.332 | 0.000 | 0.321 | 19.265 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 22 | 52 | 61 | 0 | 84 | 0 | 40 | 21 |
N.S. |
1 | 1.10 | 2.60 | 3.05 | 0.00 | 4.20 | 0.00 | 2.00 | 1.05 |
time (sec) |
N/A | 0.159 | 0.022 | 1.136 | 0.000 | 0.348 | 0.000 | 0.320 | 19.251 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 124 | 160 | 247 | 0 | 1532 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.32 | 2.04 | 0.00 | 12.66 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.362 | 0.229 | 1.104 | 0.000 | 0.766 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 181 | 184 | 186 | 397 | 0 | 2411 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.03 | 2.19 | 0.00 | 13.32 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.497 | 0.457 | 1.062 | 0.000 | 43.573 | 0.000 | 0.000 | 0.000 |
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 | 26 | 26 | 26 | 17 | 16 | 16 | 22 | 11 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.65 | 0.62 | 0.62 | 0.85 | 0.42 | 0.62 |
time (sec) |
N/A | 0.162 | 6.307 | 0.023 | 0.177 | 0.260 | 63.480 | 0.320 | 19.993 |
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 | 26 | 28 | 47 | 23 | 22 | 32 | 17 | 22 | 22 |
N.S. |
1 | 1.08 | 1.81 | 0.88 | 0.85 | 1.23 | 0.65 | 0.85 | 0.85 |
time (sec) |
N/A | 0.160 | 0.037 | 1.443 | 0.257 | 0.326 | 0.380 | 0.319 | 19.761 |
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 | 15 | 15 | 13 | 10 | 11 | 11 | 12 | 11 | 9 |
N.S. |
1 | 1.00 | 0.87 | 0.67 | 0.73 | 0.73 | 0.80 | 0.73 | 0.60 |
time (sec) |
N/A | 0.134 | 10.009 | 1.089 | 0.180 | 0.260 | 0.069 | 0.319 | 19.903 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 19 | 16 | 28 | 27 | 0 | 27 | 18 |
N.S. |
1 | 1.00 | 0.86 | 0.73 | 1.27 | 1.23 | 0.00 | 1.23 | 0.82 |
time (sec) |
N/A | 0.141 | 0.057 | 1.026 | 0.179 | 0.293 | 0.000 | 0.322 | 19.847 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 41 | 9 | 9 | 17 | 0 | 17 | 0 |
N.S. |
1 | 1.00 | 3.42 | 0.75 | 0.75 | 1.42 | 0.00 | 1.42 | 0.00 |
time (sec) |
N/A | 0.142 | 0.043 | 1.288 | 0.268 | 0.272 | 0.000 | 0.361 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 43 | 11 | 11 | 17 | 0 | 17 | 0 |
N.S. |
1 | 1.00 | 3.58 | 0.92 | 0.92 | 1.42 | 0.00 | 1.42 | 0.00 |
time (sec) |
N/A | 0.143 | 0.035 | 1.330 | 0.260 | 0.300 | 0.000 | 0.363 | 0.000 |
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 | 15 | 15 | 12 | 11 | 13 | 13 | 10 | 13 | 10 |
N.S. |
1 | 1.00 | 0.80 | 0.73 | 0.87 | 0.87 | 0.67 | 0.87 | 0.67 |
time (sec) |
N/A | 0.135 | 0.028 | 1.065 | 0.180 | 0.269 | 0.063 | 0.302 | 20.276 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 58 | 82 | 47 | 42 | 49 | 0 | 53 | 0 |
N.S. |
1 | 1.07 | 1.52 | 0.87 | 0.78 | 0.91 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 0.219 | 0.104 | 1.859 | 0.266 | 0.301 | 0.000 | 0.300 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F(-1) | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 47 | 38 | 0 | 0 | 0 | 45 | 27 |
N.S. |
1 | 1.00 | 0.80 | 0.64 | 0.00 | 0.00 | 0.00 | 0.76 | 0.46 |
time (sec) |
N/A | 0.214 | 0.319 | 3.477 | 0.000 | 0.000 | 0.000 | 1.062 | 20.191 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 64 | 39 | 28 | 0 | 30 | 0 | 33 | 27 |
N.S. |
1 | 1.08 | 0.66 | 0.47 | 0.00 | 0.51 | 0.00 | 0.56 | 0.46 |
time (sec) |
N/A | 0.196 | 0.028 | 1.047 | 0.000 | 0.374 | 0.000 | 0.306 | 19.831 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 94 | 109 | 51 | 38 | 0 | 40 | 0 | 51 | 0 |
N.S. |
1 | 1.16 | 0.54 | 0.40 | 0.00 | 0.43 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.249 | 0.032 | 1.061 | 0.000 | 0.373 | 0.000 | 0.313 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 20 | 0 | 20 | 29 | 18 | 19 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 0.00 | 1.11 | 1.61 | 1.00 | 1.06 |
time (sec) |
N/A | 0.157 | 0.047 | 1.060 | 0.000 | 0.294 | 0.329 | 0.334 | 0.143 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 107 | 91 | 82 | 47 | 0 | 62 | 0 | 60 | 0 |
N.S. |
1 | 0.85 | 0.77 | 0.44 | 0.00 | 0.58 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.220 | 0.067 | 0.345 | 0.000 | 0.284 | 0.000 | 0.332 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 24 | 25 | 24 | 14 | 64 | 0 | 14 | 25 |
N.S. |
1 | 0.96 | 1.00 | 0.96 | 0.56 | 2.56 | 0.00 | 0.56 | 1.00 |
time (sec) |
N/A | 0.157 | 0.032 | 2.705 | 0.179 | 0.344 | 0.000 | 0.325 | 21.394 |
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 | 42 | 44 | 42 | 34 | 33 | 35 | 49 | 33 | 35 |
N.S. |
1 | 1.05 | 1.00 | 0.81 | 0.79 | 0.83 | 1.17 | 0.79 | 0.83 |
time (sec) |
N/A | 0.195 | 0.031 | 0.270 | 0.268 | 0.283 | 0.109 | 0.301 | 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 | 32 | 38 | 32 | 26 | 25 | 27 | 37 | 25 | 27 |
N.S. |
1 | 1.19 | 1.00 | 0.81 | 0.78 | 0.84 | 1.16 | 0.78 | 0.84 |
time (sec) |
N/A | 0.181 | 0.022 | 0.257 | 0.274 | 0.282 | 0.101 | 0.334 | 21.127 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 76 | 83 | 49 | 53 | 0 | 95 | 0 | 45 | 0 |
N.S. |
1 | 1.09 | 0.64 | 0.70 | 0.00 | 1.25 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.191 | 0.220 | 0.027 | 0.000 | 0.304 | 0.000 | 0.327 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 41 | 43 | 0 | 64 | 48 | 79 | 46 |
N.S. |
1 | 1.00 | 0.89 | 0.93 | 0.00 | 1.39 | 1.04 | 1.72 | 1.00 |
time (sec) |
N/A | 0.275 | 0.078 | 0.115 | 0.000 | 0.351 | 1.419 | 0.311 | 20.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 18 | 0 | 14 | 0 | 13 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.00 | 0.70 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.133 | 0.266 | 1.023 | 0.000 | 0.277 | 0.000 | 0.301 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | C | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 36 | 18 | 20 | 38 | 19 | 68 | 0 | 14 |
N.S. |
1 | 1.03 | 0.51 | 0.57 | 1.09 | 0.54 | 1.94 | 0.00 | 0.40 |
time (sec) |
N/A | 0.160 | 0.157 | 1.133 | 0.303 | 0.275 | 0.658 | 0.000 | 19.876 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | A | A | C | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 111 | 0 | 13 | 16 | 122 | 0 | 13 |
N.S. |
1 | 1.00 | 7.40 | 0.00 | 0.87 | 1.07 | 8.13 | 0.00 | 0.87 |
time (sec) |
N/A | 0.153 | 0.193 | 0.000 | 0.234 | 0.300 | 5.334 | 0.000 | 20.460 |
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 | 53 | 53 | 28 | 24 | 37 | 24 | 46 | 37 | 37 |
N.S. |
1 | 1.00 | 0.53 | 0.45 | 0.70 | 0.45 | 0.87 | 0.70 | 0.70 |
time (sec) |
N/A | 0.187 | 0.014 | 1.089 | 0.180 | 0.283 | 0.496 | 0.322 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 22 | 31 | 26 | 25 | 25 | 27 | 25 | 25 |
N.S. |
1 | 0.71 | 1.00 | 0.84 | 0.81 | 0.81 | 0.87 | 0.81 | 0.81 |
time (sec) |
N/A | 0.178 | 0.015 | 0.029 | 0.175 | 0.263 | 0.129 | 0.297 | 0.072 |
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 | 11 | 11 | 11 | 10 | 9 | 9 | 8 | 9 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.82 | 0.82 | 0.73 | 0.82 | 0.82 |
time (sec) |
N/A | 0.133 | 0.025 | 1.126 | 0.181 | 0.268 | 0.056 | 0.300 | 21.206 |
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 | 6 | 6 | 6 | 5 | 4 | 4 | 5 | 4 | 4 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.67 | 0.67 | 0.83 | 0.67 | 0.67 |
time (sec) |
N/A | 0.128 | 0.009 | 1.074 | 0.265 | 0.303 | 0.085 | 0.351 | 21.159 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 17 | 14 | 16 | 16 | 0 | 25 | 16 |
N.S. |
1 | 1.00 | 0.85 | 0.70 | 0.80 | 0.80 | 0.00 | 1.25 | 0.80 |
time (sec) |
N/A | 0.140 | 0.014 | 1.076 | 0.265 | 0.254 | 0.000 | 0.310 | 21.207 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 12 | 26 | 11 | 12 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.71 | 1.53 | 0.65 | 0.71 | 0.65 | 0.65 |
time (sec) |
N/A | 0.141 | 0.001 | 0.027 | 0.188 | 0.301 | 0.066 | 0.301 | 0.025 |
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 | 19 | 19 | 19 | 12 | 11 | 11 | 15 | 11 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.63 | 0.58 | 0.58 | 0.79 | 0.58 | 0.63 |
time (sec) |
N/A | 0.147 | 0.002 | 0.056 | 0.180 | 0.279 | 0.377 | 0.316 | 0.025 |
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 | 45 | 42 | 28 | 27 | 25 | 37 | 27 | 27 |
N.S. |
1 | 1.10 | 1.02 | 0.68 | 0.66 | 0.61 | 0.90 | 0.66 | 0.66 |
time (sec) |
N/A | 0.159 | 0.024 | 1.121 | 0.260 | 0.280 | 1.700 | 0.305 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 75 | 86 | 48 | 63 | 65 | 39 | 64 | 73 |
N.S. |
1 | 1.12 | 1.28 | 0.72 | 0.94 | 0.97 | 0.58 | 0.96 | 1.09 |
time (sec) |
N/A | 0.177 | 0.043 | 1.077 | 0.263 | 0.270 | 0.637 | 0.326 | 21.538 |
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 | 11 | 11 | 11 | 8 | 7 | 7 | 8 | 7 | 7 |
N.S. |
1 | 1.00 | 1.00 | 0.73 | 0.64 | 0.64 | 0.73 | 0.64 | 0.64 |
time (sec) |
N/A | 0.131 | 0.001 | 0.030 | 0.182 | 0.279 | 0.021 | 0.309 | 0.003 |
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 | 11 | 11 | 11 | 8 | 7 | 7 | 8 | 7 | 7 |
N.S. |
1 | 1.00 | 1.00 | 0.73 | 0.64 | 0.64 | 0.73 | 0.64 | 0.64 |
time (sec) |
N/A | 0.130 | 0.001 | 0.040 | 0.174 | 0.278 | 0.021 | 0.301 | 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 | 11 | 11 | 11 | 8 | 7 | 7 | 8 | 7 | 7 |
N.S. |
1 | 1.00 | 1.00 | 0.73 | 0.64 | 0.64 | 0.73 | 0.64 | 0.64 |
time (sec) |
N/A | 0.143 | 0.000 | 1.110 | 0.179 | 0.288 | 0.460 | 0.318 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 75 | 49 | 0 | 192 | 162 | 123 | 0 |
N.S. |
1 | 1.00 | 1.23 | 0.80 | 0.00 | 3.15 | 2.66 | 2.02 | 0.00 |
time (sec) |
N/A | 0.186 | 0.061 | 1.260 | 0.000 | 0.390 | 1.070 | 0.309 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 78 | 55 | 0 | 202 | 162 | 131 | 0 |
N.S. |
1 | 1.00 | 1.20 | 0.85 | 0.00 | 3.11 | 2.49 | 2.02 | 0.00 |
time (sec) |
N/A | 0.188 | 0.087 | 1.176 | 0.000 | 0.281 | 1.133 | 0.320 | 0.000 |
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 | 13 | 23 | 13 | 10 | 21 | 21 | 26 | 22 | 9 |
N.S. |
1 | 1.77 | 1.00 | 0.77 | 1.62 | 1.62 | 2.00 | 1.69 | 0.69 |
time (sec) |
N/A | 0.147 | 0.018 | 1.048 | 0.262 | 0.288 | 0.125 | 0.415 | 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 | 13 | 23 | 13 | 10 | 21 | 21 | 26 | 22 | 9 |
N.S. |
1 | 1.77 | 1.00 | 0.77 | 1.62 | 1.62 | 2.00 | 1.69 | 0.69 |
time (sec) |
N/A | 0.142 | 0.002 | 1.071 | 0.270 | 0.301 | 0.158 | 0.311 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 77 | 72 | 58 | 77 | 131 | 202 | 80 | 233 |
N.S. |
1 | 1.07 | 1.00 | 0.81 | 1.07 | 1.82 | 2.81 | 1.11 | 3.24 |
time (sec) |
N/A | 0.234 | 0.062 | 1.194 | 0.260 | 0.302 | 0.699 | 0.331 | 20.604 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 23 | 23 | 15 | 22 | 0 | 48 | 22 |
N.S. |
1 | 1.00 | 0.62 | 0.62 | 0.41 | 0.59 | 0.00 | 1.30 | 0.59 |
time (sec) |
N/A | 0.167 | 0.012 | 1.148 | 0.189 | 0.251 | 0.000 | 0.330 | 19.204 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 41 | 9 | 9 | 17 | 0 | 17 | 0 |
N.S. |
1 | 1.00 | 3.42 | 0.75 | 0.75 | 1.42 | 0.00 | 1.42 | 0.00 |
time (sec) |
N/A | 0.146 | 0.004 | 1.076 | 0.261 | 0.301 | 0.000 | 0.331 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 95 | 107 | 71 | 67 | 0 | 89 | 56 | 51 | 0 |
N.S. |
1 | 1.13 | 0.75 | 0.71 | 0.00 | 0.94 | 0.59 | 0.54 | 0.00 |
time (sec) |
N/A | 0.245 | 0.106 | 0.028 | 0.000 | 1.124 | 0.361 | 0.318 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 25 | 28 | 24 | 23 | 21 | 184 | 23 | 16 |
N.S. |
1 | 0.71 | 0.80 | 0.69 | 0.66 | 0.60 | 5.26 | 0.66 | 0.46 |
time (sec) |
N/A | 0.160 | 0.014 | 0.127 | 0.174 | 0.289 | 0.636 | 0.287 | 19.371 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 25 | 30 | 28 | 27 | 22 | 265 | 27 | 24 |
N.S. |
1 | 0.68 | 0.81 | 0.76 | 0.73 | 0.59 | 7.16 | 0.73 | 0.65 |
time (sec) |
N/A | 0.167 | 0.014 | 0.087 | 0.183 | 0.285 | 0.625 | 0.310 | 20.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 35 | 40 | 48 | 0 | 33 | 32 | 29 | 39 |
N.S. |
1 | 1.21 | 1.38 | 1.66 | 0.00 | 1.14 | 1.10 | 1.00 | 1.34 |
time (sec) |
N/A | 0.164 | 0.082 | 1.078 | 0.000 | 0.275 | 1.378 | 0.332 | 21.865 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 33 | 42 | 48 | 0 | 36 | 42 | 32 | 40 |
N.S. |
1 | 1.32 | 1.68 | 1.92 | 0.00 | 1.44 | 1.68 | 1.28 | 1.60 |
time (sec) |
N/A | 0.163 | 0.086 | 1.100 | 0.000 | 0.308 | 1.267 | 0.326 | 22.285 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 16 | 0 | 15 | 56 | 15 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.76 | 0.00 | 0.71 | 2.67 | 0.71 | 1.05 |
time (sec) |
N/A | 0.167 | 0.052 | 1.045 | 0.000 | 0.300 | 0.170 | 0.470 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 64 | 49 | 57 | 0 | 97 | 0 | 105 | 127 |
N.S. |
1 | 0.98 | 0.75 | 0.88 | 0.00 | 1.49 | 0.00 | 1.62 | 1.95 |
time (sec) |
N/A | 0.220 | 0.109 | 0.212 | 0.000 | 0.269 | 0.000 | 0.323 | 21.672 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 38 | 50 | 28 | 0 | 41 | 0 | 63 | 64 |
N.S. |
1 | 1.23 | 1.61 | 0.90 | 0.00 | 1.32 | 0.00 | 2.03 | 2.06 |
time (sec) |
N/A | 0.205 | 0.134 | 0.227 | 0.000 | 0.286 | 0.000 | 0.323 | 0.187 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 94 | 57 | 46 | 0 | 54 | 58 | 50 | 0 |
N.S. |
1 | 1.15 | 0.70 | 0.56 | 0.00 | 0.66 | 0.71 | 0.61 | 0.00 |
time (sec) |
N/A | 0.214 | 0.085 | 1.135 | 0.000 | 0.621 | 0.271 | 0.335 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 84 | 74 | 56 | 55 | 57 | 155 | 55 | 95 |
N.S. |
1 | 1.14 | 1.00 | 0.76 | 0.74 | 0.77 | 2.09 | 0.74 | 1.28 |
time (sec) |
N/A | 0.337 | 0.047 | 1.049 | 0.279 | 0.284 | 2.480 | 0.336 | 20.542 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 124 | 115 | 81 | 80 | 80 | 221 | 80 | 130 |
N.S. |
1 | 1.08 | 1.00 | 0.70 | 0.70 | 0.70 | 1.92 | 0.70 | 1.13 |
time (sec) |
N/A | 0.397 | 0.055 | 1.067 | 0.266 | 0.274 | 2.913 | 0.348 | 0.127 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | C | F | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 4 | 4 | 22 | 29 | 0 | 20 | 0 | 4 | 4 |
N.S. |
1 | 1.00 | 5.50 | 7.25 | 0.00 | 5.00 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.175 | 0.099 | 0.142 | 0.000 | 0.270 | 0.000 | 0.337 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 39 | 50 | 40 | 0 | 31 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.77 | 2.27 | 1.82 | 0.00 | 1.41 | 0.82 |
time (sec) |
N/A | 0.160 | 0.028 | 0.111 | 0.180 | 0.284 | 0.000 | 0.333 | 21.500 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 40 | 37 | 26 | 0 | 28 | 20 |
N.S. |
1 | 1.00 | 1.00 | 1.67 | 1.54 | 1.08 | 0.00 | 1.17 | 0.83 |
time (sec) |
N/A | 0.159 | 0.020 | 0.172 | 0.271 | 0.291 | 0.000 | 0.332 | 20.532 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 28 | 34 | 39 | 51 | 40 | 0 | 35 | 24 |
N.S. |
1 | 1.17 | 1.42 | 1.62 | 2.12 | 1.67 | 0.00 | 1.46 | 1.00 |
time (sec) |
N/A | 0.164 | 0.050 | 0.109 | 0.191 | 0.308 | 0.000 | 0.360 | 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 | 24 | 24 | 24 | 39 | 38 | 38 | 32 | 38 | 20 |
N.S. |
1 | 1.00 | 1.00 | 1.62 | 1.58 | 1.58 | 1.33 | 1.58 | 0.83 |
time (sec) |
N/A | 0.175 | 0.019 | 0.092 | 0.177 | 0.274 | 1.000 | 0.496 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 51 | 45 | 51 | 42 | 0 | 35 | 35 |
N.S. |
1 | 1.00 | 2.32 | 2.05 | 2.32 | 1.91 | 0.00 | 1.59 | 1.59 |
time (sec) |
N/A | 0.154 | 0.035 | 0.096 | 0.179 | 0.278 | 0.000 | 0.313 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 27 | 52 | 44 | 35 | 25 | 0 | 35 | 23 |
N.S. |
1 | 0.93 | 1.79 | 1.52 | 1.21 | 0.86 | 0.00 | 1.21 | 0.79 |
time (sec) |
N/A | 0.172 | 0.009 | 0.189 | 0.261 | 0.279 | 0.000 | 0.344 | 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 | 33 | 35 | 49 | 27 | 36 | 35 | 22 | 25 | 26 |
N.S. |
1 | 1.06 | 1.48 | 0.82 | 1.09 | 1.06 | 0.67 | 0.76 | 0.79 |
time (sec) |
N/A | 0.168 | 0.066 | 1.159 | 0.258 | 0.295 | 0.513 | 0.304 | 21.653 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 40 | 7 | 6 | 16 | 5 | 25 | 6 |
N.S. |
1 | 1.00 | 5.00 | 0.88 | 0.75 | 2.00 | 0.62 | 3.12 | 0.75 |
time (sec) |
N/A | 0.143 | 0.026 | 1.167 | 0.262 | 0.291 | 0.497 | 0.313 | 0.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 11 | 10 | 11 | 18 | 0 | 18 | 13 |
N.S. |
1 | 1.00 | 0.85 | 0.77 | 0.85 | 1.38 | 0.00 | 1.38 | 1.00 |
time (sec) |
N/A | 0.149 | 0.014 | 1.084 | 0.182 | 0.261 | 0.000 | 0.302 | 22.393 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 41 | 0 | 33 | 0 | 73 | 17 |
N.S. |
1 | 1.00 | 1.09 | 1.86 | 0.00 | 1.50 | 0.00 | 3.32 | 0.77 |
time (sec) |
N/A | 0.185 | 0.039 | 1.079 | 0.000 | 0.273 | 0.000 | 0.342 | 22.370 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 39 | 30 | 11 | 13 | 15 | 13 | 45 |
N.S. |
1 | 1.00 | 1.62 | 1.25 | 0.46 | 0.54 | 0.62 | 0.54 | 1.88 |
time (sec) |
N/A | 0.152 | 0.018 | 1.132 | 0.265 | 0.259 | 0.375 | 0.295 | 22.709 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 55 | 23 | 27 | 62 | 75 | 59 | 28 |
N.S. |
1 | 1.00 | 1.96 | 0.82 | 0.96 | 2.21 | 2.68 | 2.11 | 1.00 |
time (sec) |
N/A | 0.147 | 0.038 | 1.122 | 0.185 | 0.287 | 0.329 | 0.306 | 21.388 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 55 | 23 | 27 | 62 | 75 | 59 | 28 |
N.S. |
1 | 1.00 | 1.96 | 0.82 | 0.96 | 2.21 | 2.68 | 2.11 | 1.00 |
time (sec) |
N/A | 0.160 | 0.001 | 1.086 | 0.186 | 0.295 | 0.707 | 0.472 | 21.322 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 55 | 29 | 27 | 62 | 75 | 59 | 28 |
N.S. |
1 | 1.00 | 1.96 | 1.04 | 0.96 | 2.21 | 2.68 | 2.11 | 1.00 |
time (sec) |
N/A | 0.158 | 0.001 | 0.040 | 0.184 | 0.296 | 0.656 | 0.312 | 21.687 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 55 | 29 | 27 | 62 | 75 | 59 | 28 |
N.S. |
1 | 1.00 | 1.96 | 1.04 | 0.96 | 2.21 | 2.68 | 2.11 | 1.00 |
time (sec) |
N/A | 0.158 | 0.001 | 0.037 | 0.185 | 0.294 | 0.705 | 0.325 | 22.675 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 55 | 29 | 27 | 62 | 75 | 59 | 28 |
N.S. |
1 | 1.00 | 1.96 | 1.04 | 0.96 | 2.21 | 2.68 | 2.11 | 1.00 |
time (sec) |
N/A | 0.159 | 0.001 | 0.041 | 0.176 | 0.278 | 0.662 | 0.351 | 22.632 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 55 | 29 | 27 | 62 | 75 | 59 | 28 |
N.S. |
1 | 1.00 | 1.96 | 1.04 | 0.96 | 2.21 | 2.68 | 2.11 | 1.00 |
time (sec) |
N/A | 0.157 | 0.001 | 0.038 | 0.178 | 0.304 | 0.686 | 0.362 | 21.136 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 56 | 28 | 36 | 87 | 97 | 76 | 33 |
N.S. |
1 | 1.00 | 1.40 | 0.70 | 0.90 | 2.18 | 2.42 | 1.90 | 0.82 |
time (sec) |
N/A | 0.153 | 0.007 | 1.189 | 0.184 | 0.271 | 0.334 | 0.324 | 21.399 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 56 | 28 | 36 | 87 | 97 | 76 | 33 |
N.S. |
1 | 1.00 | 1.40 | 0.70 | 0.90 | 2.18 | 2.42 | 1.90 | 0.82 |
time (sec) |
N/A | 0.168 | 0.001 | 1.129 | 0.187 | 0.282 | 0.657 | 0.336 | 20.973 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 56 | 28 | 36 | 87 | 97 | 76 | 33 |
N.S. |
1 | 1.00 | 1.40 | 0.70 | 0.90 | 2.18 | 2.42 | 1.90 | 0.82 |
time (sec) |
N/A | 0.161 | 0.001 | 1.095 | 0.181 | 0.335 | 0.711 | 0.301 | 22.701 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 56 | 37 | 36 | 87 | 97 | 76 | 33 |
N.S. |
1 | 1.00 | 1.40 | 0.92 | 0.90 | 2.18 | 2.42 | 1.90 | 0.82 |
time (sec) |
N/A | 0.168 | 0.001 | 0.045 | 0.181 | 0.284 | 0.691 | 0.301 | 23.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F | F | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 63 | 0 | 110 | 0 | 0 | 68 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 1.75 | 0.00 | 0.00 | 1.08 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.501 | 0.000 | 0.000 | 0.639 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 66 | 0 | 91 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 1.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.616 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | C | F | B | F | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 78 | 319 | 83 | 217 | 0 | 434 | 0 | 218 | 649 |
N.S. |
1 | 4.09 | 1.06 | 2.78 | 0.00 | 5.56 | 0.00 | 2.79 | 8.32 |
time (sec) |
N/A | 0.813 | 0.323 | 2.327 | 0.000 | 0.289 | 0.000 | 0.409 | 20.649 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 126 | 132 | 97 | 430 | 0 | 105 | 0 | 444 | 0 |
N.S. |
1 | 1.05 | 0.77 | 3.41 | 0.00 | 0.83 | 0.00 | 3.52 | 0.00 |
time (sec) |
N/A | 0.333 | 0.109 | 1.669 | 0.000 | 0.280 | 0.000 | 0.376 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 96 | 0 | 0 | 62 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 4.36 | 0.00 | 0.00 | 2.82 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.199 | 0.219 | 0.000 | 0.000 | 0.632 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 42 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.263 | 0.833 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |