Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 26 | 25 | 26 | 19 | 25 | 27 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.89 | 0.93 | 0.68 | 0.89 | 0.96 |
time (sec) |
N/A | 0.839 | 5.129 | 1.502 | 0.367 | 0.253 | 0.495 | 0.337 | 16.377 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 52 | 48 | 47 | 137 | 60 | 49 | 0 | 44 |
N.S. |
1 | 2.48 | 2.29 | 2.24 | 6.52 | 2.86 | 2.33 | 0.00 | 2.10 |
time (sec) |
N/A | 0.831 | 0.078 | 0.194 | 0.260 | 0.273 | 0.120 | 0.000 | 16.011 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 62 | 56 | 40 | 72 | 42 | 41 | 43 | 35 |
N.S. |
1 | 2.21 | 2.00 | 1.43 | 2.57 | 1.50 | 1.46 | 1.54 | 1.25 |
time (sec) |
N/A | 0.357 | 0.127 | 0.386 | 0.274 | 0.258 | 0.196 | 0.276 | 0.171 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 24 | 23 | 21 | 20 | 23 | 22 | 20 | 20 |
N.S. |
1 | 1.04 | 1.00 | 0.91 | 0.87 | 1.00 | 0.96 | 0.87 | 0.87 |
time (sec) |
N/A | 0.146 | 0.010 | 0.196 | 0.197 | 0.243 | 0.022 | 0.275 | 17.280 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 0 | 31 | 43 | 29 | 31 | 29 | 30 |
N.S. |
1 | 0.00 | 0.00 | 1.24 | 1.72 | 1.16 | 1.24 | 1.16 | 1.20 |
time (sec) |
N/A | 0.000 | 0.000 | 1.508 | 0.287 | 0.275 | 0.325 | 0.329 | 16.980 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 37 | 89 | 155 | 96 | 95 | 135 | 0 |
N.S. |
1 | 0.00 | 1.19 | 2.87 | 5.00 | 3.10 | 3.06 | 4.35 | 0.00 |
time (sec) |
N/A | 0.000 | 0.174 | 6.076 | 0.335 | 0.275 | 0.407 | 0.310 | 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 | 10 | 10 | 10 | 11 | 10 | 10 | 10 | 11 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.10 | 1.00 | 1.00 | 1.00 | 1.10 | 1.00 |
time (sec) |
N/A | 0.183 | 0.002 | 0.115 | 0.187 | 0.256 | 0.068 | 0.277 | 16.367 |
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 | 13 | 14 | 12 | 11 | 12 | 10 | 8 | 12 | 10 |
N.S. |
1 | 1.08 | 0.92 | 0.85 | 0.92 | 0.77 | 0.62 | 0.92 | 0.77 |
time (sec) |
N/A | 0.151 | 0.002 | 0.049 | 0.190 | 0.265 | 0.042 | 0.276 | 16.049 |
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 | 19 | 31 | 19 | 18 | 43 | 17 | 19 | 27 | 19 |
N.S. |
1 | 1.63 | 1.00 | 0.95 | 2.26 | 0.89 | 1.00 | 1.42 | 1.00 |
time (sec) |
N/A | 0.221 | 0.105 | 0.610 | 0.212 | 0.270 | 0.076 | 0.271 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 43 | 46 | 95 | 57 | 34 | 235 | 70 |
N.S. |
1 | 0.00 | 1.59 | 1.70 | 3.52 | 2.11 | 1.26 | 8.70 | 2.59 |
time (sec) |
N/A | 0.000 | 0.064 | 61.330 | 0.242 | 0.257 | 0.108 | 0.388 | 18.190 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | A | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 27 | 195 | 36 | 23 | 26 | 29 | 0 |
N.S. |
1 | 0.00 | 1.00 | 7.22 | 1.33 | 0.85 | 0.96 | 1.07 | 0.00 |
time (sec) |
N/A | 0.000 | 0.109 | 0.437 | 0.344 | 0.257 | 1.453 | 0.294 | 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 | 14 | 5 | 5 | 6 | 5 | 5 | 3 | 5 | 5 |
N.S. |
1 | 0.36 | 0.36 | 0.43 | 0.36 | 0.36 | 0.21 | 0.36 | 0.36 |
time (sec) |
N/A | 0.119 | 0.000 | 0.026 | 0.190 | 0.248 | 0.026 | 0.278 | 0.017 |
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 | 24 | 39 | 22 | 23 | 54 | 22 | 17 | 27 | 25 |
N.S. |
1 | 1.62 | 0.92 | 0.96 | 2.25 | 0.92 | 0.71 | 1.12 | 1.04 |
time (sec) |
N/A | 0.457 | 0.057 | 0.529 | 0.320 | 0.264 | 0.078 | 0.283 | 16.278 |
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 | 34 | 42 | 28 | 27 | 229 | 44 | 22 | 46 | 30 |
N.S. |
1 | 1.24 | 0.82 | 0.79 | 6.74 | 1.29 | 0.65 | 1.35 | 0.88 |
time (sec) |
N/A | 1.835 | 1.164 | 0.348 | 0.240 | 0.288 | 0.080 | 0.279 | 16.692 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 56 | 36 | 48 | 0 | 54 | 53 | 70 | 49 |
N.S. |
1 | 2.24 | 1.44 | 1.92 | 0.00 | 2.16 | 2.12 | 2.80 | 1.96 |
time (sec) |
N/A | 1.426 | 0.549 | 0.176 | 0.000 | 0.271 | 0.145 | 0.360 | 15.976 |
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 | 22 | 14 | 14 | 16 | 16 | 14 | 16 | 18 |
N.S. |
1 | 1.47 | 0.93 | 0.93 | 1.07 | 1.07 | 0.93 | 1.07 | 1.20 |
time (sec) |
N/A | 0.139 | 0.003 | 0.202 | 0.194 | 0.253 | 0.023 | 0.293 | 0.121 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 17 | 17 | 16 | 15 | 20 | 12 | 20 | 15 |
N.S. |
1 | 0.94 | 0.94 | 0.89 | 0.83 | 1.11 | 0.67 | 1.11 | 0.83 |
time (sec) |
N/A | 0.168 | 0.014 | 0.321 | 0.206 | 0.247 | 0.073 | 0.286 | 0.087 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | F(-1) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 38 | 37 | 0 | 29 | 0 | 0 | 118 |
N.S. |
1 | 0.00 | 1.46 | 1.42 | 0.00 | 1.12 | 0.00 | 0.00 | 4.54 |
time (sec) |
N/A | 0.000 | 0.542 | 0.145 | 0.000 | 0.274 | 0.000 | 0.000 | 16.286 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 28 | 32 | 46 | 45 | 26 | 46 | 59 |
N.S. |
1 | 0.00 | 0.82 | 0.94 | 1.35 | 1.32 | 0.76 | 1.35 | 1.74 |
time (sec) |
N/A | 0.000 | 5.486 | 0.398 | 0.249 | 0.261 | 0.111 | 0.296 | 15.691 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 14 | 15 | 14 | 14 | 10 | 14 | 14 |
N.S. |
1 | 0.00 | 0.70 | 0.75 | 0.70 | 0.70 | 0.50 | 0.70 | 0.70 |
time (sec) |
N/A | 0.000 | 0.262 | 1.399 | 0.232 | 0.239 | 0.054 | 0.282 | 0.315 |
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 | 18 | 21 | 30 | 20 | 19 | 27 | 20 |
N.S. |
1 | 1.00 | 0.95 | 1.11 | 1.58 | 1.05 | 1.00 | 1.42 | 1.05 |
time (sec) |
N/A | 1.137 | 0.319 | 2.152 | 0.220 | 0.253 | 0.438 | 0.348 | 15.318 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 18 | 18 | 27 | 20 | 19 | 20 | 17 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 1.50 | 1.11 | 1.06 | 1.11 | 0.94 |
time (sec) |
N/A | 0.000 | 0.477 | 4.781 | 0.343 | 0.253 | 0.090 | 0.303 | 17.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 29 | 24 | 23 | 23 | 24 | 33 | 23 |
N.S. |
1 | 0.00 | 1.16 | 0.96 | 0.92 | 0.92 | 0.96 | 1.32 | 0.92 |
time (sec) |
N/A | 0.000 | 0.686 | 0.556 | 0.253 | 0.259 | 0.179 | 0.288 | 19.192 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | A | A | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 0 | 21 | 23 | 20 | 19 | 42 | 17 |
N.S. |
1 | 0.00 | 0.00 | 1.05 | 1.15 | 1.00 | 0.95 | 2.10 | 0.85 |
time (sec) |
N/A | 0.000 | 0.000 | 0.896 | 0.333 | 0.255 | 0.160 | 0.268 | 18.846 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 27 | 31 | 35 | 30 | 27 | 0 | 30 |
N.S. |
1 | 0.00 | 1.00 | 1.15 | 1.30 | 1.11 | 1.00 | 0.00 | 1.11 |
time (sec) |
N/A | 0.000 | 0.098 | 16.682 | 0.260 | 0.254 | 4.970 | 0.000 | 19.902 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 140 | 76 | 70 | 70 | 73 | 76 | 73 | 68 |
N.S. |
1 | 5.19 | 2.81 | 2.59 | 2.59 | 2.70 | 2.81 | 2.70 | 2.52 |
time (sec) |
N/A | 0.312 | 0.068 | 0.267 | 0.284 | 0.266 | 0.202 | 0.275 | 18.983 |
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 | 30 | 29 | 26 | 36 | 74 | 44 | 22 | 48 | 25 |
N.S. |
1 | 0.97 | 0.87 | 1.20 | 2.47 | 1.47 | 0.73 | 1.60 | 0.83 |
time (sec) |
N/A | 1.347 | 1.621 | 0.626 | 0.223 | 0.265 | 0.100 | 0.286 | 17.715 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 210 | 18 | 18 | 224 | 17 | 17 | 139 | 17 |
N.S. |
1 | 8.08 | 0.69 | 0.69 | 8.62 | 0.65 | 0.65 | 5.35 | 0.65 |
time (sec) |
N/A | 0.985 | 0.327 | 1.380 | 0.277 | 0.264 | 0.099 | 0.272 | 0.186 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 36 | 26 | 30 | 50 | 30 | 22 | 29 | 0 |
N.S. |
1 | 1.80 | 1.30 | 1.50 | 2.50 | 1.50 | 1.10 | 1.45 | 0.00 |
time (sec) |
N/A | 0.246 | 0.128 | 0.214 | 0.234 | 0.260 | 0.147 | 0.270 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 49 | 53 | 103 | 103 | 70 | 75 | 0 |
N.S. |
1 | 0.00 | 2.04 | 2.21 | 4.29 | 4.29 | 2.92 | 3.12 | 0.00 |
time (sec) |
N/A | 0.000 | 0.078 | 1.486 | 0.239 | 0.255 | 0.126 | 0.294 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 55 | 53 | 28 | 115 | 27 | 22 | 117 | 27 |
N.S. |
1 | 1.90 | 1.83 | 0.97 | 3.97 | 0.93 | 0.76 | 4.03 | 0.93 |
time (sec) |
N/A | 0.361 | 0.052 | 2.139 | 0.237 | 0.275 | 0.169 | 0.283 | 0.263 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 44 | 17 | 16 | 15 | 15 | 14 | 17 | 16 |
N.S. |
1 | 2.10 | 0.81 | 0.76 | 0.71 | 0.71 | 0.67 | 0.81 | 0.76 |
time (sec) |
N/A | 0.252 | 0.013 | 1.434 | 0.183 | 0.250 | 0.098 | 0.280 | 0.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | A | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 18 | 42 | 199 | 34 | 37 | 56 | 0 |
N.S. |
1 | 0.00 | 1.00 | 2.33 | 11.06 | 1.89 | 2.06 | 3.11 | 0.00 |
time (sec) |
N/A | 0.000 | 0.358 | 1.705 | 0.632 | 0.257 | 0.520 | 1.143 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | F(-2) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 20 | 51 | 68 | 0 | 0 | 26 |
N.S. |
1 | 0.00 | 1.00 | 0.87 | 2.22 | 2.96 | 0.00 | 0.00 | 1.13 |
time (sec) |
N/A | 0.000 | 5.280 | 28.123 | 0.546 | 0.274 | 0.000 | 0.000 | 17.708 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 29 | 75 | 112 | 79 | 75 | 0 | 121 |
N.S. |
1 | 0.00 | 1.07 | 2.78 | 4.15 | 2.93 | 2.78 | 0.00 | 4.48 |
time (sec) |
N/A | 0.000 | 0.276 | 5.086 | 0.671 | 0.260 | 1.004 | 0.000 | 17.645 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 26 | 31 | 48 | 47 | 26 | 30 | 45 |
N.S. |
1 | 0.00 | 0.90 | 1.07 | 1.66 | 1.62 | 0.90 | 1.03 | 1.55 |
time (sec) |
N/A | 0.000 | 0.419 | 1.901 | 0.313 | 0.260 | 0.074 | 0.274 | 18.262 |
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 | 15 | 15 | 15 | 15 | 15 | 15 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 0.93 |
time (sec) |
N/A | 0.173 | 0.009 | 0.226 | 0.193 | 0.250 | 0.095 | 0.275 | 17.768 |
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 | 18 | 25 | 25 | 26 | 88 | 25 | 22 | 25 | 25 |
N.S. |
1 | 1.39 | 1.39 | 1.44 | 4.89 | 1.39 | 1.22 | 1.39 | 1.39 |
time (sec) |
N/A | 0.205 | 0.015 | 0.055 | 0.189 | 0.265 | 0.071 | 0.280 | 16.987 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | F(-1) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 23 | 78 | 18 | 0 | 22 | 21 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 3.39 | 0.78 | 0.00 | 0.96 | 0.91 |
time (sec) |
N/A | 0.000 | 0.103 | 0.562 | 0.227 | 0.246 | 0.000 | 0.278 | 18.073 |
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 | 28 | 26 | 26 | 28 | 555 | 61 | 60 | 72 | 72 |
N.S. |
1 | 0.93 | 0.93 | 1.00 | 19.82 | 2.18 | 2.14 | 2.57 | 2.57 |
time (sec) |
N/A | 4.836 | 0.137 | 32.720 | 0.625 | 0.254 | 1.942 | 3.757 | 18.390 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 28 | 32 | 23 | 24 | 22 | 24 | 23 | 22 |
N.S. |
1 | 1.04 | 1.19 | 0.85 | 0.89 | 0.81 | 0.89 | 0.85 | 0.81 |
time (sec) |
N/A | 0.218 | 0.011 | 0.102 | 0.184 | 0.250 | 0.105 | 0.276 | 18.260 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 19 | 22 | 20 | 33 | 25 | 22 | 19 | 12 |
N.S. |
1 | 1.12 | 1.29 | 1.18 | 1.94 | 1.47 | 1.29 | 1.12 | 0.71 |
time (sec) |
N/A | 0.306 | 0.072 | 0.350 | 0.208 | 0.244 | 0.103 | 0.280 | 17.620 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 31 | 30 | 43 | 37 | 29 | 29 | 44 |
N.S. |
1 | 0.00 | 1.35 | 1.30 | 1.87 | 1.61 | 1.26 | 1.26 | 1.91 |
time (sec) |
N/A | 0.000 | 0.271 | 1.750 | 0.313 | 0.259 | 0.212 | 0.286 | 15.435 |
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 | 21 | 22 | 16 | 21 | 21 | 17 | 21 | 19 |
N.S. |
1 | 1.11 | 1.16 | 0.84 | 1.11 | 1.11 | 0.89 | 1.11 | 1.00 |
time (sec) |
N/A | 0.153 | 0.000 | 0.137 | 0.184 | 0.254 | 0.025 | 0.270 | 0.032 |
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 | 20 | 27 | 17 | 17 | 34 | 19 | 12 | 19 | 17 |
N.S. |
1 | 1.35 | 0.85 | 0.85 | 1.70 | 0.95 | 0.60 | 0.95 | 0.85 |
time (sec) |
N/A | 0.209 | 0.105 | 0.074 | 0.193 | 0.279 | 0.101 | 0.288 | 15.198 |
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 | 16 | 13 | 10 | 11 | 11 | 10 | 11 | 11 |
N.S. |
1 | 0.67 | 0.54 | 0.42 | 0.46 | 0.46 | 0.42 | 0.46 | 0.46 |
time (sec) |
N/A | 0.128 | 0.001 | 0.165 | 0.187 | 0.231 | 0.029 | 0.297 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 20 | 17 | 14 | 13 | 13 | 15 | 13 | 15 |
N.S. |
1 | 0.83 | 0.71 | 0.58 | 0.54 | 0.54 | 0.62 | 0.54 | 0.62 |
time (sec) |
N/A | 0.219 | 0.032 | 0.380 | 0.191 | 0.268 | 0.053 | 0.273 | 0.097 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 17 | 17 | 18 | 30 | 17 | 19 | 30 | 15 |
N.S. |
1 | 0.94 | 0.94 | 1.00 | 1.67 | 0.94 | 1.06 | 1.67 | 0.83 |
time (sec) |
N/A | 0.150 | 0.005 | 0.149 | 0.197 | 0.266 | 0.061 | 0.273 | 15.431 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 62 | 21 | 28 | 37 | 37 | 36 | 27 | 21 |
N.S. |
1 | 3.44 | 1.17 | 1.56 | 2.06 | 2.06 | 2.00 | 1.50 | 1.17 |
time (sec) |
N/A | 0.278 | 0.010 | 0.084 | 0.203 | 0.247 | 0.070 | 0.279 | 14.986 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 27 | 27 | 26 | 25 | 25 | 26 | 25 | 25 |
N.S. |
1 | 1.69 | 1.69 | 1.62 | 1.56 | 1.56 | 1.62 | 1.56 | 1.56 |
time (sec) |
N/A | 0.774 | 0.137 | 1.358 | 0.241 | 0.245 | 0.109 | 0.286 | 15.261 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 92 | 25 | 23 | 22 | 25 | 0 |
N.S. |
1 | 1.00 | 1.00 | 4.00 | 1.09 | 1.00 | 0.96 | 1.09 | 0.00 |
time (sec) |
N/A | 2.524 | 0.090 | 0.014 | 0.260 | 0.258 | 0.622 | 5.058 | 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 | 29 | 29 | 19 | 17 | 28 | 20 | 15 | 20 | 16 |
N.S. |
1 | 1.00 | 0.66 | 0.59 | 0.97 | 0.69 | 0.52 | 0.69 | 0.55 |
time (sec) |
N/A | 0.299 | 0.021 | 0.240 | 0.191 | 0.268 | 0.093 | 0.277 | 15.591 |
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 | 20 | 26 | 19 | 11 | 18 | 18 | 17 | 18 | 10 |
N.S. |
1 | 1.30 | 0.95 | 0.55 | 0.90 | 0.90 | 0.85 | 0.90 | 0.50 |
time (sec) |
N/A | 0.143 | 0.001 | 0.235 | 0.183 | 0.236 | 0.026 | 0.280 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 24 | 22 | 30 | 22 | 33 | 24 | 26 | 20 |
N.S. |
1 | 1.09 | 1.00 | 1.36 | 1.00 | 1.50 | 1.09 | 1.18 | 0.91 |
time (sec) |
N/A | 0.193 | 0.017 | 0.502 | 0.194 | 0.252 | 0.075 | 0.277 | 15.492 |
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 | 31 | 28 | 24 | 30 | 22 | 22 | 30 | 18 |
N.S. |
1 | 1.29 | 1.17 | 1.00 | 1.25 | 0.92 | 0.92 | 1.25 | 0.75 |
time (sec) |
N/A | 0.159 | 0.060 | 0.209 | 0.192 | 0.254 | 0.063 | 0.285 | 0.154 |
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 | 17 | 16 | 22 | 16 | 15 | 20 | 12 | 25 | 20 |
N.S. |
1 | 0.94 | 1.29 | 0.94 | 0.88 | 1.18 | 0.71 | 1.47 | 1.18 |
time (sec) |
N/A | 0.442 | 0.304 | 1.633 | 0.226 | 0.262 | 0.074 | 0.285 | 0.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 28 | 26 | 37 | 23 | 36 | 36 | 72 | 47 |
N.S. |
1 | 1.08 | 1.00 | 1.42 | 0.88 | 1.38 | 1.38 | 2.77 | 1.81 |
time (sec) |
N/A | 0.799 | 0.185 | 9.300 | 1.606 | 0.261 | 0.295 | 0.436 | 16.712 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 28 | 31 | 32 | 27 | 32 | 27 |
N.S. |
1 | 1.00 | 1.00 | 0.97 | 1.07 | 1.10 | 0.93 | 1.10 | 0.93 |
time (sec) |
N/A | 0.210 | 0.031 | 0.389 | 0.240 | 0.272 | 0.052 | 0.279 | 15.694 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 69 | 34 | 41 | 49 | 49 | 48 | 48 | 53 |
N.S. |
1 | 2.56 | 1.26 | 1.52 | 1.81 | 1.81 | 1.78 | 1.78 | 1.96 |
time (sec) |
N/A | 0.446 | 0.031 | 0.226 | 0.201 | 0.249 | 0.519 | 0.293 | 15.970 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 36 | 16 | 13 | 311 | 15 | 15 | 17 | 17 |
N.S. |
1 | 1.80 | 0.80 | 0.65 | 15.55 | 0.75 | 0.75 | 0.85 | 0.85 |
time (sec) |
N/A | 0.174 | 0.403 | 0.362 | 0.345 | 0.261 | 0.061 | 0.278 | 0.133 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 30 | 27 | 28 | 27 | 29 | 24 | 27 | 30 |
N.S. |
1 | 1.20 | 1.08 | 1.12 | 1.08 | 1.16 | 0.96 | 1.08 | 1.20 |
time (sec) |
N/A | 0.540 | 0.558 | 0.673 | 0.307 | 0.247 | 0.157 | 0.347 | 17.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 28 | 25 | 28 | 23 | 26 | 24 | 23 |
N.S. |
1 | 0.00 | 0.97 | 0.86 | 0.97 | 0.79 | 0.90 | 0.83 | 0.79 |
time (sec) |
N/A | 0.000 | 0.168 | 1.205 | 0.241 | 0.261 | 0.134 | 0.280 | 16.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 9 | 13 | 9 | 7 | 6 | 6 | 7 | 6 | 6 |
N.S. |
1 | 1.44 | 1.00 | 0.78 | 0.67 | 0.67 | 0.78 | 0.67 | 0.67 |
time (sec) |
N/A | 0.135 | 0.001 | 0.176 | 0.203 | 0.262 | 0.037 | 0.270 | 15.625 |
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 | 28 | 28 | 28 | 24 | 0 | 34 | 27 | 35 | 34 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.00 | 1.21 | 0.96 | 1.25 | 1.21 |
time (sec) |
N/A | 0.553 | 0.252 | 0.589 | 0.000 | 0.273 | 0.190 | 0.298 | 16.512 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 14 | 14 | 14 | 13 | 13 | 12 | 13 | 13 |
N.S. |
1 | 0.56 | 0.56 | 0.56 | 0.52 | 0.52 | 0.48 | 0.52 | 0.52 |
time (sec) |
N/A | 0.414 | 0.181 | 1.516 | 0.259 | 0.253 | 0.194 | 0.283 | 16.396 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 62 | 36 | 33 | 0 | 27 | 48 | 39 | 39 |
N.S. |
1 | 2.30 | 1.33 | 1.22 | 0.00 | 1.00 | 1.78 | 1.44 | 1.44 |
time (sec) |
N/A | 0.495 | 0.383 | 0.387 | 0.000 | 0.268 | 0.196 | 0.273 | 16.250 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 89 | 23 | 60 | 69 | 74 | 70 | 78 | 24 |
N.S. |
1 | 3.42 | 0.88 | 2.31 | 2.65 | 2.85 | 2.69 | 3.00 | 0.92 |
time (sec) |
N/A | 0.313 | 0.069 | 0.676 | 0.287 | 0.263 | 0.134 | 0.277 | 0.233 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 20 | 19 | 27 | 19 | 19 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.90 | 1.29 | 0.90 | 0.90 | 1.00 |
time (sec) |
N/A | 0.218 | 0.038 | 0.234 | 0.197 | 0.248 | 0.081 | 0.272 | 15.674 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 19 | 19 | 18 | 17 | 17 | 15 | 19 | 17 |
N.S. |
1 | 1.19 | 1.19 | 1.12 | 1.06 | 1.06 | 0.94 | 1.19 | 1.06 |
time (sec) |
N/A | 0.246 | 0.011 | 0.113 | 0.192 | 0.260 | 0.067 | 0.267 | 16.373 |
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 | 10 | 10 | 11 | 10 | 12 | 7 | 10 | 12 |
N.S. |
1 | 0.53 | 0.53 | 0.58 | 0.53 | 0.63 | 0.37 | 0.53 | 0.63 |
time (sec) |
N/A | 0.155 | 0.001 | 0.063 | 0.199 | 0.264 | 0.039 | 0.270 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 33 | 28 | 29 | 25 | 37 | 26 | 48 | 55 |
N.S. |
1 | 1.43 | 1.22 | 1.26 | 1.09 | 1.61 | 1.13 | 2.09 | 2.39 |
time (sec) |
N/A | 1.776 | 0.321 | 1.243 | 0.292 | 0.275 | 0.150 | 0.308 | 17.243 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 0 | 24 | 39 | 23 | 24 | 30 | 51 |
N.S. |
1 | 0.00 | 0.00 | 0.86 | 1.39 | 0.82 | 0.86 | 1.07 | 1.82 |
time (sec) |
N/A | 0.000 | 0.000 | 0.208 | 0.341 | 0.252 | 0.163 | 0.439 | 22.499 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 24 | 75 | 68 | 56 | 73 | 69 | 259 |
N.S. |
1 | 0.00 | 0.92 | 2.88 | 2.62 | 2.15 | 2.81 | 2.65 | 9.96 |
time (sec) |
N/A | 0.000 | 2.698 | 1.566 | 0.343 | 0.262 | 0.144 | 0.366 | 19.189 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 193 | 62 | 46 | 58 | 53 | 58 | 58 | 53 |
N.S. |
1 | 7.72 | 2.48 | 1.84 | 2.32 | 2.12 | 2.32 | 2.32 | 2.12 |
time (sec) |
N/A | 1.394 | 0.035 | 2.007 | 0.291 | 0.252 | 0.725 | 0.282 | 17.388 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 20 | 22 | 29 | 30 | 24 | 0 | 19 |
N.S. |
1 | 0.00 | 0.87 | 0.96 | 1.26 | 1.30 | 1.04 | 0.00 | 0.83 |
time (sec) |
N/A | 0.000 | 0.390 | 2.325 | 0.328 | 0.252 | 0.144 | 0.000 | 17.584 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 31 | 21 | 49 | 40 | 34 | 54 | 44 |
N.S. |
1 | 0.00 | 1.29 | 0.88 | 2.04 | 1.67 | 1.42 | 2.25 | 1.83 |
time (sec) |
N/A | 0.000 | 1.510 | 0.966 | 0.516 | 0.274 | 0.218 | 0.318 | 17.338 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 510 | 26 | 27 | 34 | 30 | 32 | 38 | 26 |
N.S. |
1 | 16.45 | 0.84 | 0.87 | 1.10 | 0.97 | 1.03 | 1.23 | 0.84 |
time (sec) |
N/A | 1.613 | 3.599 | 1.454 | 0.258 | 0.281 | 0.117 | 0.267 | 16.733 |
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 | 9 | 12 | 10 | 11 | 12 | 12 | 8 | 10 | 10 |
N.S. |
1 | 1.33 | 1.11 | 1.22 | 1.33 | 1.33 | 0.89 | 1.11 | 1.11 |
time (sec) |
N/A | 0.175 | 0.023 | 0.224 | 0.214 | 0.244 | 0.051 | 0.269 | 16.717 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 24 | 26 | 116 | 116 | 117 | 432 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.08 | 4.83 | 4.83 | 4.88 | 18.00 | 0.00 |
time (sec) |
N/A | 0.000 | 5.075 | 13.376 | 0.419 | 0.266 | 0.300 | 1.472 | 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 | 21 | 19 | 17 | 18 | 18 | 17 | 17 | 17 | 17 |
N.S. |
1 | 0.90 | 0.81 | 0.86 | 0.86 | 0.81 | 0.81 | 0.81 | 0.81 |
time (sec) |
N/A | 0.201 | 0.074 | 0.173 | 0.200 | 0.282 | 0.092 | 0.265 | 17.424 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | A | A | A | A | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 21 | 441 | 25 | 21 | 19 | 23 | 24 |
N.S. |
1 | 0.00 | 0.91 | 19.17 | 1.09 | 0.91 | 0.83 | 1.00 | 1.04 |
time (sec) |
N/A | 0.000 | 0.111 | 51.939 | 0.351 | 0.262 | 0.365 | 0.420 | 17.327 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 33 | 29 | 42 | 28 | 29 | 0 | 28 |
N.S. |
1 | 0.00 | 1.57 | 1.38 | 2.00 | 1.33 | 1.38 | 0.00 | 1.33 |
time (sec) |
N/A | 0.000 | 0.113 | 1.134 | 0.388 | 0.262 | 0.245 | 0.000 | 17.223 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 54 | 57 | 50 | 55 | 56 | 0 | 58 |
N.S. |
1 | 0.00 | 1.80 | 1.90 | 1.67 | 1.83 | 1.87 | 0.00 | 1.93 |
time (sec) |
N/A | 0.000 | 6.192 | 10.146 | 0.484 | 0.257 | 0.334 | 0.000 | 17.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 0 | 36 | 42 | 41 | 32 | 42 | 42 |
N.S. |
1 | 0.00 | 0.00 | 1.00 | 1.17 | 1.14 | 0.89 | 1.17 | 1.17 |
time (sec) |
N/A | 0.000 | 0.000 | 1.846 | 0.486 | 0.265 | 1.452 | 0.716 | 16.263 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 24 | 23 | 37 | 37 | 26 | 22 | 22 |
N.S. |
1 | 0.00 | 1.20 | 1.15 | 1.85 | 1.85 | 1.30 | 1.10 | 1.10 |
time (sec) |
N/A | 0.000 | 2.531 | 0.101 | 0.240 | 0.262 | 0.173 | 0.265 | 0.217 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 25 | 31 | 27 | 28 | 29 | 0 | 28 |
N.S. |
1 | 0.00 | 0.81 | 1.00 | 0.87 | 0.90 | 0.94 | 0.00 | 0.90 |
time (sec) |
N/A | 0.000 | 5.149 | 0.224 | 0.309 | 0.270 | 0.168 | 0.000 | 17.365 |
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 | 22 | 30 | 32 | 24 | 24 | 22 | 31 | 23 | 24 |
N.S. |
1 | 1.36 | 1.45 | 1.09 | 1.09 | 1.00 | 1.41 | 1.05 | 1.09 |
time (sec) |
N/A | 0.164 | 0.005 | 0.124 | 0.199 | 0.254 | 0.032 | 0.276 | 0.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F(-2) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 47 | 32 | 41 | 31 | 36 | 0 | 27 |
N.S. |
1 | 0.00 | 1.42 | 0.97 | 1.24 | 0.94 | 1.09 | 0.00 | 0.82 |
time (sec) |
N/A | 0.000 | 1.257 | 0.138 | 0.257 | 0.254 | 0.442 | 0.000 | 17.449 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 18 | 17 | 21 | 16 | 19 | 65 | 29 |
N.S. |
1 | 0.00 | 0.90 | 0.85 | 1.05 | 0.80 | 0.95 | 3.25 | 1.45 |
time (sec) |
N/A | 0.000 | 0.079 | 1.736 | 0.347 | 0.281 | 0.081 | 0.276 | 17.430 |
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 | 31 | 26 | 26 | 25 | 25 | 24 | 25 | 28 |
N.S. |
1 | 1.29 | 1.08 | 1.08 | 1.04 | 1.04 | 1.00 | 1.04 | 1.17 |
time (sec) |
N/A | 0.980 | 1.901 | 3.846 | 0.376 | 0.258 | 0.336 | 0.272 | 16.125 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | C | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 74 | 32 | 72 | 86 | 205 | 165 | 197 | 30 |
N.S. |
1 | 2.00 | 0.86 | 1.95 | 2.32 | 5.54 | 4.46 | 5.32 | 0.81 |
time (sec) |
N/A | 1.242 | 3.326 | 0.362 | 0.252 | 0.254 | 0.213 | 0.281 | 16.489 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 43 | 59 | 35 | 25 | 46 | 45 | 25 |
N.S. |
1 | 0.00 | 2.05 | 2.81 | 1.67 | 1.19 | 2.19 | 2.14 | 1.19 |
time (sec) |
N/A | 0.000 | 0.215 | 1.648 | 0.253 | 0.254 | 0.373 | 0.618 | 15.850 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 32 | 33 | 31 | 39 | 39 | 33 | 0 |
N.S. |
1 | 0.00 | 1.10 | 1.14 | 1.07 | 1.34 | 1.34 | 1.14 | 0.00 |
time (sec) |
N/A | 0.000 | 0.950 | 0.229 | 0.253 | 0.269 | 0.170 | 0.296 | 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 | 23 | 19 | 19 | 17 | 18 | 16 | 12 | 16 | 15 |
N.S. |
1 | 0.83 | 0.83 | 0.74 | 0.78 | 0.70 | 0.52 | 0.70 | 0.65 |
time (sec) |
N/A | 0.360 | 0.007 | 0.141 | 0.185 | 0.258 | 0.041 | 0.264 | 13.924 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 27 | 28 | 28 | 28 | 41 | 28 | 24 |
N.S. |
1 | 1.00 | 0.96 | 1.00 | 1.00 | 1.00 | 1.46 | 1.00 | 0.86 |
time (sec) |
N/A | 0.160 | 0.003 | 0.147 | 0.195 | 0.251 | 0.027 | 0.273 | 13.768 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | A | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 46 | 194 | 47 | 172 | 178 | 202 | 178 |
N.S. |
1 | 0.00 | 1.64 | 6.93 | 1.68 | 6.14 | 6.36 | 7.21 | 6.36 |
time (sec) |
N/A | 0.000 | 0.129 | 15.135 | 9.551 | 0.261 | 3.084 | 3.505 | 16.193 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 34 | 42 | 81 | 59 | 100 | 105 | 0 |
N.S. |
1 | 0.00 | 1.48 | 1.83 | 3.52 | 2.57 | 4.35 | 4.57 | 0.00 |
time (sec) |
N/A | 0.000 | 11.861 | 1.437 | 0.278 | 0.256 | 0.305 | 0.309 | 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 | 20 | 39 | 39 | 36 | 35 | 35 | 36 | 37 | 35 |
N.S. |
1 | 1.95 | 1.95 | 1.80 | 1.75 | 1.75 | 1.80 | 1.85 | 1.75 |
time (sec) |
N/A | 0.344 | 0.017 | 0.128 | 0.217 | 0.303 | 0.087 | 0.279 | 0.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 32 | 50 | 78 | 75 | 26 | 90 | 76 |
N.S. |
1 | 0.00 | 1.19 | 1.85 | 2.89 | 2.78 | 0.96 | 3.33 | 2.81 |
time (sec) |
N/A | 0.000 | 6.704 | 0.796 | 0.300 | 0.266 | 0.160 | 0.384 | 14.938 |
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 | 8 | 8 | 8 | 6 | 5 | 5 | 5 | 5 | 5 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 0.62 | 0.62 | 0.62 | 0.62 | 0.62 |
time (sec) |
N/A | 0.122 | 0.000 | 0.052 | 0.194 | 0.249 | 0.017 | 0.278 | 0.002 |