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 | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 37 | 20 | 18 | 251 | 20 | 19 | 25 | 17 |
N.S. |
1 | 1.61 | 0.87 | 0.78 | 10.91 | 0.87 | 0.83 | 1.09 | 0.74 |
time (sec) |
N/A | 0.204 | 0.493 | 0.071 | 0.332 | 0.243 | 0.052 | 0.266 | 0.098 |
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 | 23 | 21 | 14 | 15 | 21 | 14 | 15 | 16 |
N.S. |
1 | 1.44 | 1.31 | 0.88 | 0.94 | 1.31 | 0.88 | 0.94 | 1.00 |
time (sec) |
N/A | 0.008 | 0.008 | 0.417 | 0.194 | 0.241 | 0.049 | 0.248 | 7.891 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 30 | 67 | 68 | 86 | 67 | 75 | 64 | 67 |
N.S. |
1 | 1.30 | 2.91 | 2.96 | 3.74 | 2.91 | 3.26 | 2.78 | 2.91 |
time (sec) |
N/A | 0.090 | 0.508 | 5.555 | 0.360 | 0.244 | 0.313 | 1.034 | 7.902 |
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 | 24 | 0 | 21 | 20 | 20 | 24 | 15 | 24 | 20 |
N.S. |
1 | 0.00 | 0.88 | 0.83 | 0.83 | 1.00 | 0.62 | 1.00 | 0.83 |
time (sec) |
N/A | 0.000 | 1.248 | 0.416 | 0.256 | 0.249 | 0.154 | 0.261 | 8.520 |
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 | 30 | 0 | 36 | 41 | 35 | 41 | 34 | 104 | 72 |
N.S. |
1 | 0.00 | 1.20 | 1.37 | 1.17 | 1.37 | 1.13 | 3.47 | 2.40 |
time (sec) |
N/A | 0.000 | 0.327 | 0.477 | 0.427 | 0.249 | 0.230 | 0.904 | 8.858 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 24 | 83 | 80 | 79 | 79 | 92 | 0 | 0 |
N.S. |
1 | 1.04 | 3.61 | 3.48 | 3.43 | 3.43 | 4.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.459 | 0.090 | 22.375 | 1.882 | 0.253 | 0.336 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | C | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 36 | 40 | 47 | 48 | 3110 | 43 |
N.S. |
1 | 1.00 | 1.00 | 1.71 | 1.90 | 2.24 | 2.29 | 148.10 | 2.05 |
time (sec) |
N/A | 0.374 | 0.100 | 85.090 | 0.271 | 0.244 | 1.285 | 1.199 | 8.549 |
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 | 14 | 15 | 16 | 14 | 15 | 14 | 14 |
N.S. |
1 | 1.08 | 1.08 | 1.15 | 1.23 | 1.08 | 1.15 | 1.08 | 1.08 |
time (sec) |
N/A | 0.053 | 0.097 | 7.007 | 0.311 | 0.244 | 0.168 | 0.279 | 8.702 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 85 | 36 | 40 | 102 | 31 | 29 | 39 | 30 |
N.S. |
1 | 2.66 | 1.12 | 1.25 | 3.19 | 0.97 | 0.91 | 1.22 | 0.94 |
time (sec) |
N/A | 0.381 | 0.413 | 0.337 | 0.232 | 0.243 | 0.133 | 0.265 | 8.661 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 40 | 45 | 44 | 44 | 41 | 44 | 0 |
N.S. |
1 | 0.00 | 1.54 | 1.73 | 1.69 | 1.69 | 1.58 | 1.69 | 0.00 |
time (sec) |
N/A | 0.000 | 0.726 | 0.631 | 0.252 | 0.247 | 0.135 | 0.892 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 52 | 50 | 70 | 63 | 66 | 70 | 73 |
N.S. |
1 | 0.00 | 1.62 | 1.56 | 2.19 | 1.97 | 2.06 | 2.19 | 2.28 |
time (sec) |
N/A | 0.000 | 0.118 | 0.280 | 0.457 | 0.268 | 0.223 | 0.289 | 9.388 |
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 | 14 | 14 | 14 | 19 | 13 | 15 | 13 | 16 |
N.S. |
1 | 0.88 | 0.88 | 0.88 | 1.19 | 0.81 | 0.94 | 0.81 | 1.00 |
time (sec) |
N/A | 0.063 | 0.287 | 0.182 | 0.314 | 0.245 | 0.138 | 0.268 | 9.218 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 21 | 20 | 19 | 19 | 0 | 0 | 19 |
N.S. |
1 | 0.00 | 1.00 | 0.95 | 0.90 | 0.90 | 0.00 | 0.00 | 0.90 |
time (sec) |
N/A | 0.000 | 0.167 | 0.583 | 0.329 | 0.260 | 0.000 | 0.000 | 9.541 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 66 | 40 | 32 | 87 | 30 | 32 | 31 | 37 |
N.S. |
1 | 2.36 | 1.43 | 1.14 | 3.11 | 1.07 | 1.14 | 1.11 | 1.32 |
time (sec) |
N/A | 0.095 | 0.194 | 0.153 | 0.196 | 0.247 | 0.067 | 0.259 | 0.094 |
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 | 25 | 28 | 28 | 29 | 0 | 28 |
N.S. |
1 | 0.00 | 1.00 | 0.93 | 1.04 | 1.04 | 1.07 | 0.00 | 1.04 |
time (sec) |
N/A | 0.000 | 2.879 | 8.033 | 0.309 | 0.252 | 134.106 | 0.000 | 9.361 |
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 | 22 | 15 | 15 | 29 | 14 | 12 | 14 | 13 |
N.S. |
1 | 1.29 | 0.88 | 0.88 | 1.71 | 0.82 | 0.71 | 0.82 | 0.76 |
time (sec) |
N/A | 0.042 | 0.013 | 0.292 | 0.200 | 0.245 | 0.051 | 0.267 | 8.914 |
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 | 17 | 17 | 15 | 14 | 16 | 12 | 19 | 15 |
N.S. |
1 | 0.74 | 0.74 | 0.65 | 0.61 | 0.70 | 0.52 | 0.83 | 0.65 |
time (sec) |
N/A | 0.108 | 0.122 | 0.051 | 0.263 | 0.242 | 0.082 | 0.254 | 9.407 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | B | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 25 | 21 | 0 | 74 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 1.04 | 0.88 | 0.00 | 3.08 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.141 | 49.094 | 0.000 | 0.256 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 41 | 54 | 65 | 60 | 61 | 0 | 61 |
N.S. |
1 | 0.00 | 1.14 | 1.50 | 1.81 | 1.67 | 1.69 | 0.00 | 1.69 |
time (sec) |
N/A | 0.000 | 0.133 | 0.324 | 0.316 | 0.249 | 0.277 | 0.000 | 9.722 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 37 | 39 | 35 | 37 | 38 | 37 | 38 | 0 |
N.S. |
1 | 2.06 | 2.17 | 1.94 | 2.06 | 2.11 | 2.06 | 2.11 | 0.00 |
time (sec) |
N/A | 0.267 | 0.072 | 0.539 | 0.234 | 0.248 | 0.178 | 0.272 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F(-1) | A | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 19 | 0 | 15 | 17 | 15 | 14 | 0 |
N.S. |
1 | 0.00 | 0.90 | 0.00 | 0.71 | 0.81 | 0.71 | 0.67 | 0.00 |
time (sec) |
N/A | 0.000 | 0.043 | 0.000 | 0.223 | 0.253 | 0.152 | 0.258 | 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 | 18 | 13 | 17 | 13 | 15 | 15 | 10 | 15 | 11 |
N.S. |
1 | 0.72 | 0.94 | 0.72 | 0.83 | 0.83 | 0.56 | 0.83 | 0.61 |
time (sec) |
N/A | 0.004 | 0.000 | 0.037 | 0.198 | 0.242 | 0.020 | 0.253 | 8.895 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | B | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 41 | 53 | 60 | 84 | 70 | 67 | 49 |
N.S. |
1 | 0.00 | 1.14 | 1.47 | 1.67 | 2.33 | 1.94 | 1.86 | 1.36 |
time (sec) |
N/A | 0.000 | 1.249 | 0.649 | 0.307 | 0.242 | 0.103 | 0.257 | 8.583 |
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 | 19 | 0 | 19 | 25 | 18 | 18 | 22 | 18 | 19 |
N.S. |
1 | 0.00 | 1.00 | 1.32 | 0.95 | 0.95 | 1.16 | 0.95 | 1.00 |
time (sec) |
N/A | 0.000 | 0.122 | 1.019 | 0.258 | 0.263 | 0.122 | 0.256 | 9.247 |
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 | 37 | 22 | 22 | 21 | 21 | 22 | 21 | 22 |
N.S. |
1 | 1.61 | 0.96 | 0.96 | 0.91 | 0.91 | 0.96 | 0.91 | 0.96 |
time (sec) |
N/A | 0.011 | 0.020 | 0.050 | 0.187 | 0.242 | 0.080 | 0.248 | 9.151 |
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 | 15 | 15 | 15 | 19 | 18 | 18 | 15 | 21 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.27 | 1.20 | 1.20 | 1.00 | 1.40 | 1.13 |
time (sec) |
N/A | 0.023 | 0.012 | 0.093 | 0.218 | 0.243 | 0.060 | 0.258 | 9.132 |
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 | 12 | 12 | 12 | 11 | 15 | 8 | 11 | 11 |
N.S. |
1 | 0.63 | 0.63 | 0.63 | 0.58 | 0.79 | 0.42 | 0.58 | 0.58 |
time (sec) |
N/A | 0.022 | 0.012 | 0.056 | 0.194 | 0.243 | 0.048 | 0.252 | 0.067 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 14 | 14 | 12 | 13 | 15 | 12 | 13 | 11 |
N.S. |
1 | 0.78 | 0.78 | 0.67 | 0.72 | 0.83 | 0.67 | 0.72 | 0.61 |
time (sec) |
N/A | 0.004 | 0.002 | 0.083 | 0.188 | 0.246 | 0.037 | 0.247 | 0.053 |
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 | 23 | 23 | 24 | 23 | 47 | 22 | 19 | 22 | 22 |
N.S. |
1 | 1.00 | 1.04 | 1.00 | 2.04 | 0.96 | 0.83 | 0.96 | 0.96 |
time (sec) |
N/A | 0.319 | 0.208 | 10.595 | 0.346 | 0.257 | 0.248 | 1.053 | 9.203 |
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 | 17 | 17 | 16 | 15 | 15 | 19 | 15 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.88 | 0.88 | 1.12 | 0.88 | 1.06 |
time (sec) |
N/A | 0.012 | 0.083 | 0.079 | 0.193 | 0.248 | 0.090 | 0.247 | 9.419 |
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 | 42 | 0 | 70 | 105 | 102 | 63 | 160 | 266 | 0 |
N.S. |
1 | 0.00 | 1.67 | 2.50 | 2.43 | 1.50 | 3.81 | 6.33 | 0.00 |
time (sec) |
N/A | 0.000 | 0.126 | 0.940 | 0.365 | 0.257 | 0.749 | 0.873 | 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 | 27 | 47 | 51 | 44 | 45 | 45 | 44 | 50 | 45 |
N.S. |
1 | 1.74 | 1.89 | 1.63 | 1.67 | 1.67 | 1.63 | 1.85 | 1.67 |
time (sec) |
N/A | 0.121 | 0.043 | 0.137 | 0.189 | 0.241 | 2.254 | 0.275 | 0.231 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 37 | 36 | 32 | 33 | 33 | 41 | 33 | 21 |
N.S. |
1 | 1.85 | 1.80 | 1.60 | 1.65 | 1.65 | 2.05 | 1.65 | 1.05 |
time (sec) |
N/A | 0.009 | 0.009 | 0.066 | 0.194 | 0.254 | 0.025 | 0.248 | 0.089 |
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 | 11 | 9 | 8 | 7 | 7 | 7 | 7 | 8 |
N.S. |
1 | 0.73 | 0.60 | 0.53 | 0.47 | 0.47 | 0.47 | 0.47 | 0.53 |
time (sec) |
N/A | 0.001 | 0.001 | 0.056 | 0.186 | 0.225 | 0.018 | 0.252 | 0.038 |
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 | 30 | 20 | 21 | 26 | 26 | 17 | 20 | 20 |
N.S. |
1 | 1.76 | 1.18 | 1.24 | 1.53 | 1.53 | 1.00 | 1.18 | 1.18 |
time (sec) |
N/A | 0.115 | 0.071 | 0.284 | 0.225 | 0.247 | 0.056 | 0.267 | 9.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 32 | 22 | 38 | 21 | 19 | 0 | 23 |
N.S. |
1 | 1.00 | 1.14 | 0.79 | 1.36 | 0.75 | 0.68 | 0.00 | 0.82 |
time (sec) |
N/A | 1.551 | 3.411 | 0.772 | 0.307 | 0.247 | 0.364 | 0.000 | 9.132 |
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 | 28 | 25 | 21 | 22 | 13 | 22 | 22 | 13 |
N.S. |
1 | 1.40 | 1.25 | 1.05 | 1.10 | 0.65 | 1.10 | 1.10 | 0.65 |
time (sec) |
N/A | 0.024 | 0.016 | 0.073 | 0.189 | 0.242 | 0.078 | 0.261 | 9.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | C | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 21 | 33 | 37 | 29 | 29 | 33 | 22 |
N.S. |
1 | 0.00 | 0.95 | 1.50 | 1.68 | 1.32 | 1.32 | 1.50 | 1.00 |
time (sec) |
N/A | 0.000 | 0.444 | 0.385 | 0.347 | 0.247 | 0.411 | 0.349 | 9.006 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 81 | 77 | 68 | 108 | 59 | 73 | 77 | 0 |
N.S. |
1 | 2.79 | 2.66 | 2.34 | 3.72 | 2.03 | 2.52 | 2.66 | 0.00 |
time (sec) |
N/A | 0.508 | 0.071 | 0.950 | 0.305 | 0.247 | 0.282 | 0.277 | 0.000 |
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 | 13 | 0 | 19 | 19 | 18 | 18 | 19 | 28 | 18 |
N.S. |
1 | 0.00 | 1.46 | 1.46 | 1.38 | 1.38 | 1.46 | 2.15 | 1.38 |
time (sec) |
N/A | 0.000 | 0.390 | 0.082 | 0.228 | 0.266 | 0.085 | 0.254 | 0.120 |
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 | 12 | 6 | 6 | 7 | 10 | 6 | 5 | 10 | 6 |
N.S. |
1 | 0.50 | 0.50 | 0.58 | 0.83 | 0.50 | 0.42 | 0.83 | 0.50 |
time (sec) |
N/A | 0.002 | 0.001 | 0.038 | 0.179 | 0.238 | 0.044 | 0.258 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 72 | 34 | 27 | 0 | 61 | 31 | 37 | 28 |
N.S. |
1 | 2.32 | 1.10 | 0.87 | 0.00 | 1.97 | 1.00 | 1.19 | 0.90 |
time (sec) |
N/A | 1.954 | 6.063 | 0.212 | 0.000 | 0.250 | 0.147 | 0.254 | 0.223 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 31 | 31 | 24 | 34 | 34 | 41 | 34 | 30 |
N.S. |
1 | 1.41 | 1.41 | 1.09 | 1.55 | 1.55 | 1.86 | 1.55 | 1.36 |
time (sec) |
N/A | 0.007 | 0.023 | 0.094 | 0.193 | 0.246 | 0.027 | 0.260 | 0.461 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F(-2) | A | F(-2) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 26 | 34 | 0 | 34 | 0 | 34 | 55 |
N.S. |
1 | 0.00 | 0.96 | 1.26 | 0.00 | 1.26 | 0.00 | 1.26 | 2.04 |
time (sec) |
N/A | 0.000 | 5.105 | 2.434 | 0.000 | 0.254 | 0.000 | 0.446 | 9.571 |
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 | 32 | 0 | 28 | 29 | 28 | 28 | 24 | 35 | 28 |
N.S. |
1 | 0.00 | 0.88 | 0.91 | 0.88 | 0.88 | 0.75 | 1.09 | 0.88 |
time (sec) |
N/A | 0.000 | 0.269 | 18.720 | 0.231 | 0.268 | 0.080 | 0.272 | 9.553 |
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 | 20 | 20 | 12 | 14 | 14 | 17 | 14 | 8 |
N.S. |
1 | 1.25 | 1.25 | 0.75 | 0.88 | 0.88 | 1.06 | 0.88 | 0.50 |
time (sec) |
N/A | 0.002 | 0.001 | 0.042 | 0.195 | 0.254 | 0.019 | 0.251 | 0.029 |
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 | 24 | 22 | 21 | 30 | 21 | 30 | 27 | 53 | 47 |
N.S. |
1 | 0.92 | 0.88 | 1.25 | 0.88 | 1.25 | 1.12 | 2.21 | 1.96 |
time (sec) |
N/A | 0.907 | 0.392 | 0.960 | 0.241 | 0.247 | 0.391 | 0.311 | 0.339 |
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 | 26 | 0 | 26 | 27 | 28 | 26 | 26 | 26 | 26 |
N.S. |
1 | 0.00 | 1.00 | 1.04 | 1.08 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.000 | 0.065 | 23.012 | 0.325 | 0.255 | 1.785 | 0.741 | 10.350 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 0 | 45 | 41 | 40 | 44 | 0 | 0 | 42 |
N.S. |
1 | 0.00 | 1.18 | 1.08 | 1.05 | 1.16 | 0.00 | 0.00 | 1.11 |
time (sec) |
N/A | 0.000 | 0.173 | 0.394 | 0.322 | 0.264 | 0.000 | 0.000 | 8.985 |
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 | 38 | 23 | 19 | 19 | 21 | 17 | 21 | 20 |
N.S. |
1 | 1.65 | 1.00 | 0.83 | 0.83 | 0.91 | 0.74 | 0.91 | 0.87 |
time (sec) |
N/A | 0.044 | 0.032 | 0.115 | 0.188 | 0.250 | 0.278 | 0.252 | 0.184 |
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 | 12 | 9 | 9 | 11 | 8 | 11 | 7 | 8 | 9 |
N.S. |
1 | 0.75 | 0.75 | 0.92 | 0.67 | 0.92 | 0.58 | 0.67 | 0.75 |
time (sec) |
N/A | 0.020 | 0.008 | 0.043 | 0.187 | 0.234 | 0.042 | 0.252 | 8.886 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | F | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 98 | 66 | 74 | 0 | 77 | 87 | 92 | 76 |
N.S. |
1 | 4.26 | 2.87 | 3.22 | 0.00 | 3.35 | 3.78 | 4.00 | 3.30 |
time (sec) |
N/A | 0.843 | 1.129 | 0.133 | 0.000 | 0.256 | 0.166 | 0.320 | 9.303 |
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 | 18 | 18 | 19 | 31 | 17 | 19 | 23 | 22 |
N.S. |
1 | 0.95 | 0.95 | 1.00 | 1.63 | 0.89 | 1.00 | 1.21 | 1.16 |
time (sec) |
N/A | 0.141 | 0.210 | 0.972 | 0.324 | 0.260 | 0.187 | 0.280 | 9.387 |
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 | 18 | 22 | 14 | 13 | 13 | 15 | 13 | 13 |
N.S. |
1 | 0.95 | 1.16 | 0.74 | 0.68 | 0.68 | 0.79 | 0.68 | 0.68 |
time (sec) |
N/A | 0.004 | 0.020 | 0.070 | 0.186 | 0.244 | 0.044 | 0.260 | 0.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 55 | 166 | 12 | 162 | 19 | 19 | 29 | 12 |
N.S. |
1 | 3.44 | 10.38 | 0.75 | 10.12 | 1.19 | 1.19 | 1.81 | 0.75 |
time (sec) |
N/A | 0.166 | 0.122 | 0.131 | 0.275 | 0.246 | 0.128 | 0.259 | 0.531 |
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 | 12 | 12 | 11 | 10 | 10 | 10 | 10 | 10 |
N.S. |
1 | 0.92 | 0.92 | 0.85 | 0.77 | 0.77 | 0.77 | 0.77 | 0.77 |
time (sec) |
N/A | 0.007 | 0.005 | 0.043 | 0.180 | 0.251 | 0.047 | 0.258 | 8.935 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 42 | 35 | 36 | 52 | 36 | 0 | 39 |
N.S. |
1 | 0.00 | 1.40 | 1.17 | 1.20 | 1.73 | 1.20 | 0.00 | 1.30 |
time (sec) |
N/A | 0.000 | 0.142 | 0.271 | 0.323 | 0.268 | 0.166 | 0.000 | 8.684 |
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 | 33 | 0 | 42 | 40 | 81 | 81 | 88 | 88 | 0 |
N.S. |
1 | 0.00 | 1.27 | 1.21 | 2.45 | 2.45 | 2.67 | 2.67 | 0.00 |
time (sec) |
N/A | 0.000 | 0.180 | 0.094 | 0.744 | 0.253 | 0.297 | 0.345 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 29 | 36 | 34 | 30 | 36 | 34 | 35 |
N.S. |
1 | 0.00 | 1.00 | 1.24 | 1.17 | 1.03 | 1.24 | 1.17 | 1.21 |
time (sec) |
N/A | 0.000 | 4.426 | 0.307 | 0.248 | 0.246 | 0.128 | 0.284 | 8.498 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 27 | 21 | 22 | 25 | 31 | 0 | 39 | 0 |
N.S. |
1 | 0.93 | 0.72 | 0.76 | 0.86 | 1.07 | 0.00 | 1.34 | 0.00 |
time (sec) |
N/A | 1.277 | 5.061 | 0.347 | 0.254 | 0.257 | 0.000 | 0.267 | 0.000 |
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 | 21 | 17 | 20 | 18 | 26 | 19 | 17 | 19 | 17 |
N.S. |
1 | 0.81 | 0.95 | 0.86 | 1.24 | 0.90 | 0.81 | 0.90 | 0.81 |
time (sec) |
N/A | 0.016 | 0.019 | 0.100 | 0.224 | 0.239 | 0.047 | 0.255 | 8.708 |
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 | 28 | 124 | 42 | 109 | 88 | 92 | 100 | 116 | 103 |
N.S. |
1 | 4.43 | 1.50 | 3.89 | 3.14 | 3.29 | 3.57 | 4.14 | 3.68 |
time (sec) |
N/A | 1.367 | 0.142 | 0.395 | 0.322 | 0.253 | 0.229 | 0.268 | 10.399 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 18 | 18 | 17 | 16 | 17 | 14 | 16 | 15 |
N.S. |
1 | 0.69 | 0.69 | 0.65 | 0.62 | 0.65 | 0.54 | 0.62 | 0.58 |
time (sec) |
N/A | 0.014 | 0.003 | 0.043 | 0.188 | 0.261 | 0.057 | 0.251 | 9.909 |
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 | 26 | 0 | 29 | 31 | 33 | 27 | 31 | 33 | 38 |
N.S. |
1 | 0.00 | 1.12 | 1.19 | 1.27 | 1.04 | 1.19 | 1.27 | 1.46 |
time (sec) |
N/A | 0.000 | 0.280 | 0.288 | 0.375 | 0.253 | 0.132 | 0.299 | 11.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 175 | 64 | 23 | 138 | 25 | 19 | 25 | 22 |
N.S. |
1 | 7.29 | 2.67 | 0.96 | 5.75 | 1.04 | 0.79 | 1.04 | 0.92 |
time (sec) |
N/A | 0.371 | 0.121 | 0.312 | 0.333 | 0.256 | 0.073 | 0.294 | 10.159 |
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 | 10 | 14 | 9 | 8 | 12 | 7 | 9 | 8 |
N.S. |
1 | 0.91 | 1.27 | 0.82 | 0.73 | 1.09 | 0.64 | 0.82 | 0.73 |
time (sec) |
N/A | 0.004 | 0.003 | 0.024 | 0.188 | 0.233 | 0.031 | 0.259 | 0.025 |
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 | 36 | 0 | 32 | 29 | 48 | 49 | 27 | 49 | 38 |
N.S. |
1 | 0.00 | 0.89 | 0.81 | 1.33 | 1.36 | 0.75 | 1.36 | 1.06 |
time (sec) |
N/A | 0.000 | 0.144 | 0.498 | 0.335 | 0.254 | 0.095 | 0.294 | 9.833 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | A | A | C | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 0 | 33 | 32 | 31 | 27 | 35 | 32 |
N.S. |
1 | 0.00 | 0.00 | 1.50 | 1.45 | 1.41 | 1.23 | 1.59 | 1.45 |
time (sec) |
N/A | 0.000 | 0.000 | 16.225 | 0.349 | 0.257 | 0.339 | 0.569 | 10.834 |
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 | 13 | 12 | 12 | 14 | 12 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.30 | 1.20 | 1.20 | 1.40 | 1.20 | 1.00 |
time (sec) |
N/A | 0.010 | 0.004 | 0.102 | 0.193 | 0.260 | 0.038 | 0.266 | 5.591 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 30 | 44 | 0 | 65 | 27 | 0 | 29 |
N.S. |
1 | 0.00 | 1.25 | 1.83 | 0.00 | 2.71 | 1.12 | 0.00 | 1.21 |
time (sec) |
N/A | 0.000 | 0.241 | 3.111 | 0.000 | 0.257 | 0.181 | 0.000 | 10.734 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 204 | 35 | 34 | 69 | 67 | 48 | 58 | 139 |
N.S. |
1 | 6.80 | 1.17 | 1.13 | 2.30 | 2.23 | 1.60 | 1.93 | 4.63 |
time (sec) |
N/A | 1.388 | 0.126 | 0.548 | 0.746 | 0.251 | 0.207 | 0.868 | 10.560 |
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 | 28 | 0 | 61 | 70 | 191 | 181 | 110 | 309 | 0 |
N.S. |
1 | 0.00 | 2.18 | 2.50 | 6.82 | 6.46 | 3.93 | 11.04 | 0.00 |
time (sec) |
N/A | 0.000 | 10.469 | 1.719 | 0.310 | 0.265 | 0.282 | 0.412 | 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 | 2 | 2 | 2 | 3 | 2 | 2 | 2 | 3 | 2 |
N.S. |
1 | 1.00 | 1.00 | 1.50 | 1.00 | 1.00 | 1.00 | 1.50 | 1.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.007 | 0.186 | 0.239 | 0.034 | 0.258 | 0.008 |
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 | 24 | 0 | 25 | 29 | 26 | 25 | 24 | 25 | 0 |
N.S. |
1 | 0.00 | 1.04 | 1.21 | 1.08 | 1.04 | 1.00 | 1.04 | 0.00 |
time (sec) |
N/A | 0.000 | 10.040 | 1.186 | 0.307 | 0.247 | 0.112 | 0.286 | 0.000 |
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 | 13 | 44 | 23 | 17 | 19 | 14 | 17 | 16 | 11 |
N.S. |
1 | 3.38 | 1.77 | 1.31 | 1.46 | 1.08 | 1.31 | 1.23 | 0.85 |
time (sec) |
N/A | 0.022 | 0.008 | 0.087 | 0.186 | 0.239 | 0.057 | 0.255 | 10.593 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 20 | 65 | 43 | 24 | 385 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 2.95 | 1.95 | 1.09 | 17.50 | 0.86 |
time (sec) |
N/A | 0.130 | 0.103 | 0.121 | 0.193 | 0.247 | 0.074 | 0.255 | 0.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 24 | 38 | 24 | 23 | 33 | 20 | 23 | 23 |
N.S. |
1 | 0.83 | 1.31 | 0.83 | 0.79 | 1.14 | 0.69 | 0.79 | 0.79 |
time (sec) |
N/A | 0.027 | 0.023 | 0.471 | 0.187 | 0.233 | 0.057 | 0.253 | 10.677 |
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 | 20 | 20 | 20 | 19 | 19 | 17 | 19 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.95 | 0.95 | 0.85 | 0.95 | 0.85 |
time (sec) |
N/A | 0.220 | 0.070 | 88.371 | 0.244 | 0.239 | 0.247 | 0.370 | 10.757 |
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 | 19 | 0 | 14 | 21 | 13 | 20 | 17 | 34 | 37 |
N.S. |
1 | 0.00 | 0.74 | 1.11 | 0.68 | 1.05 | 0.89 | 1.79 | 1.95 |
time (sec) |
N/A | 0.000 | 0.259 | 0.463 | 0.281 | 0.244 | 0.074 | 0.258 | 9.998 |
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 | 33 | 31 | 34 | 30 | 26 | 27 | 30 |
N.S. |
1 | 0.00 | 1.32 | 1.24 | 1.36 | 1.20 | 1.04 | 1.08 | 1.20 |
time (sec) |
N/A | 0.000 | 0.910 | 1.379 | 0.302 | 0.269 | 0.089 | 0.290 | 10.372 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 18 | 19 | 395 | 414 | 398 | 758 | 192 |
N.S. |
1 | 0.00 | 1.00 | 1.06 | 21.94 | 23.00 | 22.11 | 42.11 | 10.67 |
time (sec) |
N/A | 0.000 | 1.362 | 0.960 | 0.462 | 0.247 | 1.391 | 0.362 | 10.713 |
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 | 39 | 39 | 35 | 33 | 35 | 39 | 39 | 37 |
N.S. |
1 | 1.77 | 1.77 | 1.59 | 1.50 | 1.59 | 1.77 | 1.77 | 1.68 |
time (sec) |
N/A | 0.523 | 0.300 | 0.500 | 0.220 | 0.261 | 0.197 | 0.269 | 11.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | C | B | B | F(-1) | F(-2) | B |
verified |
N/A | N/A | N/A | No | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 0 | 117 | 168 | 73 | 0 | 0 | 95 |
N.S. |
1 | 0.00 | 0.00 | 3.90 | 5.60 | 2.43 | 0.00 | 0.00 | 3.17 |
time (sec) |
N/A | 0.000 | 0.000 | 118.240 | 0.320 | 0.261 | 0.000 | 0.000 | 11.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | C | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 110 | 89 | 39 | 132 | 35 | 97 | 36 | 32 |
N.S. |
1 | 3.79 | 3.07 | 1.34 | 4.55 | 1.21 | 3.34 | 1.24 | 1.10 |
time (sec) |
N/A | 0.271 | 0.127 | 0.815 | 0.313 | 0.248 | 0.974 | 0.267 | 11.138 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 25 | 33 | 28 | 97 | 29 | 0 | 33 |
N.S. |
1 | 0.00 | 0.96 | 1.27 | 1.08 | 3.73 | 1.12 | 0.00 | 1.27 |
time (sec) |
N/A | 0.000 | 0.264 | 0.644 | 0.809 | 0.265 | 0.667 | 0.000 | 10.034 |
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 | 23 | 23 | 23 | 29 | 30 | 28 | 27 | 30 | 28 |
N.S. |
1 | 1.00 | 1.00 | 1.26 | 1.30 | 1.22 | 1.17 | 1.30 | 1.22 |
time (sec) |
N/A | 0.131 | 0.040 | 2.879 | 0.322 | 0.252 | 0.084 | 0.316 | 9.980 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 25 | 26 | 26 | 25 | 0 | 0 | 25 |
N.S. |
1 | 0.00 | 1.00 | 1.04 | 1.04 | 1.00 | 0.00 | 0.00 | 1.00 |
time (sec) |
N/A | 0.000 | 1.289 | 0.342 | 0.373 | 0.250 | 0.000 | 0.000 | 9.446 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | A | F(-2) | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 43 | 124 | 324 | 74 | 46 | 0 | 0 |
N.S. |
1 | 0.00 | 1.65 | 4.77 | 12.46 | 2.85 | 1.77 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.544 | 189.045 | 0.483 | 0.261 | 0.261 | 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 | 21 | 36 | 26 | 33 | 31 | 31 | 29 | 31 | 19 |
N.S. |
1 | 1.71 | 1.24 | 1.57 | 1.48 | 1.48 | 1.38 | 1.48 | 0.90 |
time (sec) |
N/A | 0.097 | 0.263 | 0.102 | 0.201 | 0.244 | 0.047 | 0.257 | 0.088 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 59 | 21 | 34 | 303 | 33 | 34 | 67 | 21 |
N.S. |
1 | 2.46 | 0.88 | 1.42 | 12.62 | 1.38 | 1.42 | 2.79 | 0.88 |
time (sec) |
N/A | 0.265 | 0.220 | 0.211 | 0.283 | 0.257 | 0.083 | 0.259 | 0.160 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | B | A | A | A | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 0 | 25 | 46 | 30 | 36 | 26 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.09 | 2.00 | 1.30 | 1.57 | 1.13 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.232 | 0.328 | 0.272 | 0.826 | 0.265 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 320 | 25 | 29 | 113 | 45 | 24 | 26 | 27 |
N.S. |
1 | 13.91 | 1.09 | 1.26 | 4.91 | 1.96 | 1.04 | 1.13 | 1.17 |
time (sec) |
N/A | 0.328 | 0.160 | 0.087 | 0.328 | 0.249 | 0.082 | 0.263 | 9.636 |
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 | 27 | 27 | 18 | 22 | 22 | 22 | 22 | 18 |
N.S. |
1 | 1.50 | 1.50 | 1.00 | 1.22 | 1.22 | 1.22 | 1.22 | 1.00 |
time (sec) |
N/A | 0.004 | 0.004 | 0.037 | 0.189 | 0.246 | 0.023 | 0.253 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 16 | 16 | 17 | 16 | 16 | 12 | 18 | 16 |
N.S. |
1 | 0.84 | 0.84 | 0.89 | 0.84 | 0.84 | 0.63 | 0.95 | 0.84 |
time (sec) |
N/A | 0.021 | 0.008 | 0.306 | 0.194 | 0.251 | 0.050 | 0.260 | 0.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 29 | 25 | 62 | 30 | 28 | 29 | 39 | 32 |
N.S. |
1 | 1.21 | 1.04 | 2.58 | 1.25 | 1.17 | 1.21 | 1.62 | 1.33 |
time (sec) |
N/A | 1.005 | 0.387 | 0.772 | 0.332 | 0.253 | 0.546 | 0.294 | 9.442 |
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 | 26 | 0 | 24 | 16 | 27 | 27 | 10 | 27 | 13 |
N.S. |
1 | 0.00 | 0.92 | 0.62 | 1.04 | 1.04 | 0.38 | 1.04 | 0.50 |
time (sec) |
N/A | 0.000 | 0.684 | 0.051 | 0.218 | 0.253 | 0.055 | 0.260 | 0.166 |
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 | 27 | 19 | 29 | 31 | 32 | 22 | 40 | 20 |
N.S. |
1 | 1.29 | 0.90 | 1.38 | 1.48 | 1.52 | 1.05 | 1.90 | 0.95 |
time (sec) |
N/A | 0.269 | 0.031 | 3.228 | 0.235 | 0.247 | 0.108 | 0.264 | 9.440 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | F(-2) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 28 | 40 | 24 | 99 | 0 | 37 | 37 |
N.S. |
1 | 0.00 | 1.00 | 1.43 | 0.86 | 3.54 | 0.00 | 1.32 | 1.32 |
time (sec) |
N/A | 0.000 | 0.210 | 15.382 | 0.266 | 0.250 | 0.000 | 0.321 | 9.476 |
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 | 21 | 0 | 41 | 94 | 100 | 90 | 102 | 120 | 0 |
N.S. |
1 | 0.00 | 1.95 | 4.48 | 4.76 | 4.29 | 4.86 | 5.71 | 0.00 |
time (sec) |
N/A | 0.000 | 5.138 | 11.061 | 0.370 | 0.258 | 0.529 | 0.437 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 47 | 48 | 91 | 47 | 46 | 65 | 0 |
N.S. |
1 | 0.00 | 1.38 | 1.41 | 2.68 | 1.38 | 1.35 | 1.91 | 0.00 |
time (sec) |
N/A | 0.000 | 0.073 | 235.503 | 0.386 | 0.247 | 0.194 | 2.005 | 0.000 |