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 | F | A | A | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 39 | 45 | 43 | 48 | 44 | 60 | 45 |
N.S. |
1 | 0.00 | 1.77 | 2.05 | 1.95 | 2.18 | 2.00 | 2.73 | 2.05 |
time (sec) |
N/A | 0.000 | 0.378 | 0.088 | 0.237 | 0.243 | 0.189 | 1.405 | 10.777 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 47 | 30 | 39 | 68 | 37 | 104 | 44 |
N.S. |
1 | 0.00 | 1.42 | 0.91 | 1.18 | 2.06 | 1.12 | 3.15 | 1.33 |
time (sec) |
N/A | 0.000 | 0.222 | 0.416 | 0.449 | 0.250 | 0.150 | 0.345 | 11.783 |
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 | 28 | 28 | 27 | 34 | 27 | 32 | 24 | 92 | 27 |
N.S. |
1 | 1.00 | 0.96 | 1.21 | 0.96 | 1.14 | 0.86 | 3.29 | 0.96 |
time (sec) |
N/A | 0.089 | 0.254 | 0.057 | 0.258 | 0.259 | 0.147 | 0.280 | 10.988 |
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 | 39 | 23 | 23 | 22 | 23 | 19 | 26 | 26 |
N.S. |
1 | 1.62 | 0.96 | 0.96 | 0.92 | 0.96 | 0.79 | 1.08 | 1.08 |
time (sec) |
N/A | 0.158 | 0.094 | 0.313 | 0.258 | 0.273 | 0.120 | 0.267 | 0.497 |
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 | 30 | 82 | 29 | 28 | 40 | 30 | 20 | 28 | 30 |
N.S. |
1 | 2.73 | 0.97 | 0.93 | 1.33 | 1.00 | 0.67 | 0.93 | 1.00 |
time (sec) |
N/A | 0.328 | 0.073 | 0.054 | 0.257 | 0.240 | 0.103 | 0.263 | 10.307 |
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 | 10 | 9 | 9 | 8 | 11 | 9 |
N.S. |
1 | 0.63 | 0.63 | 0.53 | 0.47 | 0.47 | 0.42 | 0.58 | 0.47 |
time (sec) |
N/A | 0.006 | 0.008 | 0.017 | 0.206 | 0.246 | 0.043 | 0.255 | 0.047 |
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 | 21 | 0 | 30 | 20 | 19 | 24 | 22 | 0 | 20 |
N.S. |
1 | 0.00 | 1.43 | 0.95 | 0.90 | 1.14 | 1.05 | 0.00 | 0.95 |
time (sec) |
N/A | 0.000 | 0.362 | 234.829 | 28.005 | 0.251 | 0.128 | 0.000 | 10.544 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | F | A | F(-1) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 54 | 0 | 18 | 0 | 18 | 18 |
N.S. |
1 | 0.00 | 1.00 | 2.35 | 0.00 | 0.78 | 0.00 | 0.78 | 0.78 |
time (sec) |
N/A | 0.000 | 0.350 | 9.565 | 0.000 | 0.247 | 0.000 | 0.273 | 11.190 |
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 | 19 | 0 | 21 | 18 | 36 | 29 | 29 | 36 | 41 |
N.S. |
1 | 0.00 | 1.11 | 0.95 | 1.89 | 1.53 | 1.53 | 1.89 | 2.16 |
time (sec) |
N/A | 0.000 | 1.815 | 0.075 | 0.325 | 0.245 | 0.134 | 0.297 | 10.300 |
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 | 25 | 33 | 21 | 34 | 0 | 21 | 29 | 29 | 25 |
N.S. |
1 | 1.32 | 0.84 | 1.36 | 0.00 | 0.84 | 1.16 | 1.16 | 1.00 |
time (sec) |
N/A | 1.119 | 0.229 | 0.103 | 0.000 | 0.253 | 0.148 | 0.269 | 10.531 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | B | B | F(-2) | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 70 | 47 | 67 | 67 | 0 | 58 | 0 |
N.S. |
1 | 0.00 | 2.06 | 1.38 | 1.97 | 1.97 | 0.00 | 1.71 | 0.00 |
time (sec) |
N/A | 0.000 | 21.473 | 0.408 | 0.264 | 0.284 | 0.000 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 53 | 25 | 20 | 20 | 20 | 22 | 0 | 21 |
N.S. |
1 | 2.30 | 1.09 | 0.87 | 0.87 | 0.87 | 0.96 | 0.00 | 0.91 |
time (sec) |
N/A | 0.062 | 0.037 | 0.061 | 0.313 | 0.248 | 0.084 | 0.000 | 10.290 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 20 | 20 | 40 | 63 | 46 | 46 | 315 | 0 |
N.S. |
1 | 0.87 | 0.87 | 1.74 | 2.74 | 2.00 | 2.00 | 13.70 | 0.00 |
time (sec) |
N/A | 0.236 | 0.400 | 45.540 | 0.265 | 0.252 | 0.173 | 1.352 | 0.000 |
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 | 30 | 0 | 22 | 34 | 39 | 35 | 36 | 35 | 37 |
N.S. |
1 | 0.00 | 0.73 | 1.13 | 1.30 | 1.17 | 1.20 | 1.17 | 1.23 |
time (sec) |
N/A | 0.000 | 0.665 | 0.275 | 0.285 | 0.244 | 0.139 | 0.283 | 10.476 |
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 | 10 | 22 | 10 | 20 | 19 | 19 | 17 | 19 | 9 |
N.S. |
1 | 2.20 | 1.00 | 2.00 | 1.90 | 1.90 | 1.70 | 1.90 | 0.90 |
time (sec) |
N/A | 0.024 | 0.037 | 0.022 | 0.204 | 0.254 | 0.053 | 0.258 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 42 | 34 | 33 | 159 | 0 | 39 | 0 | 31 |
N.S. |
1 | 1.40 | 1.13 | 1.10 | 5.30 | 0.00 | 1.30 | 0.00 | 1.03 |
time (sec) |
N/A | 0.314 | 0.174 | 34.521 | 0.525 | 0.000 | 0.256 | 0.000 | 10.270 |
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 | 15 | 15 | 11 | 10 | 10 | 12 | 10 | 10 |
N.S. |
1 | 0.58 | 0.58 | 0.42 | 0.38 | 0.38 | 0.46 | 0.38 | 0.38 |
time (sec) |
N/A | 0.003 | 0.031 | 0.019 | 0.196 | 0.237 | 0.047 | 0.273 | 10.299 |
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 | 32 | 97 | 36 | 35 | 130 | 30 | 39 | 68 | 76 |
N.S. |
1 | 3.03 | 1.12 | 1.09 | 4.06 | 0.94 | 1.22 | 2.12 | 2.38 |
time (sec) |
N/A | 0.536 | 0.853 | 0.338 | 0.259 | 0.246 | 0.096 | 0.260 | 0.244 |
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 | 14 | 24 | 24 | 21 | 16 | 20 | 22 | 16 | 20 |
N.S. |
1 | 1.71 | 1.71 | 1.50 | 1.14 | 1.43 | 1.57 | 1.14 | 1.43 |
time (sec) |
N/A | 0.021 | 0.008 | 0.032 | 0.210 | 0.255 | 0.057 | 0.266 | 10.391 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 33 | 28 | 28 | 37 | 67 | 27 | 80 | 33 |
N.S. |
1 | 1.14 | 0.97 | 0.97 | 1.28 | 2.31 | 0.93 | 2.76 | 1.14 |
time (sec) |
N/A | 0.446 | 0.255 | 0.126 | 0.238 | 0.250 | 0.136 | 0.279 | 10.282 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 33 | 29 | 47 | 56 | 44 | 49 | 122 |
N.S. |
1 | 0.00 | 1.03 | 0.91 | 1.47 | 1.75 | 1.38 | 1.53 | 3.81 |
time (sec) |
N/A | 0.000 | 5.094 | 0.345 | 0.292 | 0.256 | 0.136 | 0.265 | 11.075 |
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 | 34 | 0 | 30 | 35 | 34 | 41 | 20 | 0 | 37 |
N.S. |
1 | 0.00 | 0.88 | 1.03 | 1.00 | 1.21 | 0.59 | 0.00 | 1.09 |
time (sec) |
N/A | 0.000 | 2.358 | 3.228 | 0.417 | 0.259 | 0.997 | 0.000 | 10.973 |
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 | 15 | 15 | 16 | 15 | 15 | 12 | 15 | 14 |
N.S. |
1 | 0.79 | 0.79 | 0.84 | 0.79 | 0.79 | 0.63 | 0.79 | 0.74 |
time (sec) |
N/A | 0.002 | 0.000 | 0.016 | 0.199 | 0.238 | 0.022 | 0.257 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | A | A | A | A | A | B |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 33 | 0 | 21 | 23 | 23 | 22 | 23 | 26 |
N.S. |
1 | 1.74 | 0.00 | 1.11 | 1.21 | 1.21 | 1.16 | 1.21 | 1.37 |
time (sec) |
N/A | 0.124 | 0.000 | 0.094 | 0.220 | 0.245 | 0.128 | 0.279 | 11.121 |
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 | 25 | 39 | 21 | 22 | 37 | 21 | 73 | 39 | 37 |
N.S. |
1 | 1.56 | 0.84 | 0.88 | 1.48 | 0.84 | 2.92 | 1.56 | 1.48 |
time (sec) |
N/A | 0.037 | 0.007 | 0.062 | 0.192 | 0.273 | 0.443 | 0.260 | 0.133 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 51 | 57 | 35 | 40 | 32 | 44 | 48 | 42 |
N.S. |
1 | 2.43 | 2.71 | 1.67 | 1.90 | 1.52 | 2.10 | 2.29 | 2.00 |
time (sec) |
N/A | 0.016 | 0.080 | 0.043 | 0.212 | 0.256 | 0.069 | 0.266 | 0.081 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 24 | 23 | 0 | 22 | 27 | 22 | 27 |
N.S. |
1 | 0.00 | 1.00 | 0.96 | 0.00 | 0.92 | 1.12 | 0.92 | 1.12 |
time (sec) |
N/A | 0.000 | 1.942 | 0.105 | 0.000 | 0.251 | 0.152 | 0.293 | 10.807 |
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 | 28 | 0 | 44 | 47 | 759 | 51 | 146 | 0 | 54 |
N.S. |
1 | 0.00 | 1.57 | 1.68 | 27.11 | 1.82 | 5.21 | 0.00 | 1.93 |
time (sec) |
N/A | 0.000 | 0.345 | 1.061 | 0.346 | 0.257 | 0.760 | 0.000 | 11.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 44 | 25 | 58 | 33 | 20 | 49 | 0 |
N.S. |
1 | 0.00 | 1.91 | 1.09 | 2.52 | 1.43 | 0.87 | 2.13 | 0.00 |
time (sec) |
N/A | 0.000 | 0.732 | 0.177 | 0.259 | 0.248 | 0.286 | 0.303 | 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 | 23 | 23 | 24 | 23 | 23 | 24 | 23 | 23 |
N.S. |
1 | 1.28 | 1.28 | 1.33 | 1.28 | 1.28 | 1.33 | 1.28 | 1.28 |
time (sec) |
N/A | 0.003 | 0.000 | 0.018 | 0.195 | 0.254 | 0.019 | 0.257 | 10.297 |
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 | 18 | 18 | 17 | 17 | 12 | 17 | 9 |
N.S. |
1 | 1.11 | 0.95 | 0.95 | 0.89 | 0.89 | 0.63 | 0.89 | 0.47 |
time (sec) |
N/A | 0.024 | 0.035 | 0.015 | 0.205 | 0.248 | 0.038 | 0.262 | 10.358 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 41 | 22 | 30 | 29 | 45 | 31 | 52 | 30 |
N.S. |
1 | 1.52 | 0.81 | 1.11 | 1.07 | 1.67 | 1.15 | 1.93 | 1.11 |
time (sec) |
N/A | 0.025 | 0.023 | 0.143 | 0.200 | 0.257 | 0.091 | 0.260 | 10.498 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 27 | 23 | 21 | 22 | 20 | 0 | 40 | 25 |
N.S. |
1 | 1.17 | 1.00 | 0.91 | 0.96 | 0.87 | 0.00 | 1.74 | 1.09 |
time (sec) |
N/A | 0.715 | 0.322 | 0.478 | 0.320 | 0.265 | 0.000 | 0.318 | 10.385 |
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 | 21 | 21 | 24 | 21 | 17 | 27 | 19 |
N.S. |
1 | 1.04 | 0.91 | 0.91 | 1.04 | 0.91 | 0.74 | 1.17 | 0.83 |
time (sec) |
N/A | 0.032 | 0.010 | 0.023 | 0.192 | 0.243 | 0.046 | 0.262 | 0.094 |
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 | 26 | 0 | 37 | 34 | 30 | 32 | 63 | 33 | 33 |
N.S. |
1 | 0.00 | 1.42 | 1.31 | 1.15 | 1.23 | 2.42 | 1.27 | 1.27 |
time (sec) |
N/A | 0.000 | 1.689 | 0.366 | 0.251 | 0.244 | 0.190 | 0.275 | 10.408 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | C | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 116 | 101 | 99 | 157 | 99 | 102 | 108 | 92 |
N.S. |
1 | 4.64 | 4.04 | 3.96 | 6.28 | 3.96 | 4.08 | 4.32 | 3.68 |
time (sec) |
N/A | 0.216 | 0.891 | 0.062 | 0.224 | 0.244 | 0.101 | 0.264 | 10.325 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | C | B | B | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 191 | 46 | 116 | 228 | 89 | 134 | 238 | 91 |
N.S. |
1 | 7.35 | 1.77 | 4.46 | 8.77 | 3.42 | 5.15 | 9.15 | 3.50 |
time (sec) |
N/A | 0.960 | 0.157 | 0.620 | 0.351 | 0.259 | 3.923 | 0.321 | 11.682 |
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 | 26 | 0 | 28 | 24 | 72 | 72 | 34 | 72 | 23 |
N.S. |
1 | 0.00 | 1.08 | 0.92 | 2.77 | 2.77 | 1.31 | 2.77 | 0.88 |
time (sec) |
N/A | 0.000 | 0.095 | 11.733 | 0.322 | 0.253 | 0.160 | 4.614 | 10.659 |
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 | 32 | 0 | 26 | 33 | 61 | 38 | 36 | 46 | 0 |
N.S. |
1 | 0.00 | 0.81 | 1.03 | 1.91 | 1.19 | 1.12 | 1.44 | 0.00 |
time (sec) |
N/A | 0.000 | 0.260 | 215.985 | 0.475 | 0.254 | 8.271 | 1.715 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 272 | 27 | 29 | 29 | 31 | 27 | 34 | 0 |
N.S. |
1 | 10.07 | 1.00 | 1.07 | 1.07 | 1.15 | 1.00 | 1.26 | 0.00 |
time (sec) |
N/A | 2.271 | 0.300 | 1.171 | 0.251 | 0.248 | 0.129 | 0.287 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | B | B | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 65 | 30 | 75 | 52 | 56 | 0 | 85 |
N.S. |
1 | 0.00 | 2.41 | 1.11 | 2.78 | 1.93 | 2.07 | 0.00 | 3.15 |
time (sec) |
N/A | 0.000 | 0.391 | 5.802 | 0.480 | 0.264 | 0.406 | 0.000 | 11.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | C | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 38 | 76 | 49 | 200 | 51 | 51 | 148 | 106 |
N.S. |
1 | 1.52 | 3.04 | 1.96 | 8.00 | 2.04 | 2.04 | 5.92 | 4.24 |
time (sec) |
N/A | 0.207 | 0.982 | 0.101 | 0.378 | 0.247 | 0.072 | 0.272 | 0.306 |
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 | 21 | 21 | 17 | 16 | 16 | 15 | 16 | 16 |
N.S. |
1 | 0.95 | 0.95 | 0.77 | 0.73 | 0.73 | 0.68 | 0.73 | 0.73 |
time (sec) |
N/A | 0.017 | 0.035 | 0.046 | 0.185 | 0.262 | 0.123 | 0.264 | 10.289 |
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 | 18 | 29 | 30 | 17 | 17 | 32 |
N.S. |
1 | 0.00 | 1.00 | 0.95 | 1.53 | 1.58 | 0.89 | 0.89 | 1.68 |
time (sec) |
N/A | 0.000 | 0.192 | 0.282 | 0.302 | 0.237 | 0.073 | 0.287 | 10.812 |
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 | 16 | 16 | 21 | 17 | 16 | 21 |
N.S. |
1 | 1.30 | 0.95 | 0.80 | 0.80 | 1.05 | 0.85 | 0.80 | 1.05 |
time (sec) |
N/A | 0.147 | 0.036 | 0.123 | 0.233 | 0.242 | 0.092 | 0.269 | 10.298 |
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 | 23 | 27 | 17 | 20 | 16 | 17 | 18 | 16 |
N.S. |
1 | 1.05 | 1.23 | 0.77 | 0.91 | 0.73 | 0.77 | 0.82 | 0.73 |
time (sec) |
N/A | 0.263 | 0.164 | 0.096 | 0.306 | 0.244 | 0.074 | 0.268 | 10.071 |
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 | 26 | 0 | 26 | 25 | 38 | 26 | 42 | 24 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.96 | 1.46 | 1.00 | 1.62 | 0.92 | 0.00 |
time (sec) |
N/A | 0.000 | 0.247 | 1.817 | 0.352 | 0.242 | 0.143 | 0.487 | 0.000 |
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 | 27 | 0 | 27 | 22 | 100 | 24 | 24 | 86 | 23 |
N.S. |
1 | 0.00 | 1.00 | 0.81 | 3.70 | 0.89 | 0.89 | 3.19 | 0.85 |
time (sec) |
N/A | 0.000 | 0.343 | 1.386 | 0.248 | 0.255 | 0.254 | 0.291 | 10.783 |
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 | 16 | 19 | 16 | 18 | 14 | 12 | 18 | 14 |
N.S. |
1 | 1.00 | 1.19 | 1.00 | 1.12 | 0.88 | 0.75 | 1.12 | 0.88 |
time (sec) |
N/A | 0.012 | 0.010 | 0.023 | 0.195 | 0.237 | 0.049 | 0.261 | 9.891 |
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 | 14 | 14 | 14 | 17 | 19 | 14 | 17 | 13 |
N.S. |
1 | 0.61 | 0.61 | 0.61 | 0.74 | 0.83 | 0.61 | 0.74 | 0.57 |
time (sec) |
N/A | 0.006 | 0.003 | 0.025 | 0.197 | 0.232 | 0.035 | 0.257 | 9.886 |
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 | 22 | 44 | 19 | 22 | 0 | 18 | 24 | 22 | 0 |
N.S. |
1 | 2.00 | 0.86 | 1.00 | 0.00 | 0.82 | 1.09 | 1.00 | 0.00 |
time (sec) |
N/A | 0.090 | 0.341 | 0.100 | 0.000 | 0.243 | 4.748 | 0.279 | 0.000 |
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 | 31 | 17 | 34 | 18 | 17 | 17 | 17 | 0 | 17 |
N.S. |
1 | 0.55 | 1.10 | 0.58 | 0.55 | 0.55 | 0.55 | 0.00 | 0.55 |
time (sec) |
N/A | 0.234 | 0.131 | 1.305 | 0.318 | 0.250 | 0.105 | 0.000 | 10.628 |
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 | 27 | 27 | 26 | 25 | 25 | 20 | 25 | 25 |
N.S. |
1 | 0.93 | 0.93 | 0.90 | 0.86 | 0.86 | 0.69 | 0.86 | 0.86 |
time (sec) |
N/A | 0.353 | 0.046 | 0.166 | 0.245 | 0.247 | 0.163 | 0.298 | 10.255 |
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 | 21 | 25 | 21 | 38 | 24 | 36 | 36 | 42 | 37 |
N.S. |
1 | 1.19 | 1.00 | 1.81 | 1.14 | 1.71 | 1.71 | 2.00 | 1.76 |
time (sec) |
N/A | 0.403 | 0.087 | 2.762 | 0.384 | 0.240 | 0.266 | 1.387 | 10.188 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 31 | 49 | 37 | 26 | 36 | 27 | 26 | 30 |
N.S. |
1 | 1.29 | 2.04 | 1.54 | 1.08 | 1.50 | 1.12 | 1.08 | 1.25 |
time (sec) |
N/A | 0.037 | 0.037 | 0.088 | 0.188 | 0.250 | 0.148 | 0.264 | 0.210 |
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 | 21 | 19 | 22 | 23 | 23 | 26 | 23 | 28 |
N.S. |
1 | 0.95 | 0.86 | 1.00 | 1.05 | 1.05 | 1.18 | 1.05 | 1.27 |
time (sec) |
N/A | 0.022 | 0.014 | 0.046 | 0.197 | 0.256 | 0.500 | 0.256 | 10.063 |
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 | 13 | 13 | 11 | 11 | 11 | 14 | 11 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.85 | 0.85 | 1.08 | 0.85 | 1.00 |
time (sec) |
N/A | 0.018 | 0.023 | 0.045 | 0.195 | 0.300 | 0.053 | 0.257 | 10.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F(-1) | B | F(-1) | B | B | B | F | B |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 176 | 0 | 917 | 179 | 187 | 0 | 1097 |
N.S. |
1 | 0.00 | 5.68 | 0.00 | 29.58 | 5.77 | 6.03 | 0.00 | 35.39 |
time (sec) |
N/A | 0.000 | 1.781 | 0.000 | 13.691 | 0.305 | 6.034 | 0.000 | 12.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 115 | 21 | 19 | 24 | 20 | 19 | 69 | 21 |
N.S. |
1 | 5.00 | 0.91 | 0.83 | 1.04 | 0.87 | 0.83 | 3.00 | 0.91 |
time (sec) |
N/A | 0.719 | 0.136 | 0.332 | 0.324 | 0.250 | 0.334 | 0.285 | 11.449 |
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 | 27 | 21 | 21 | 18 | 24 | 17 | 22 | 17 | 17 |
N.S. |
1 | 0.78 | 0.78 | 0.67 | 0.89 | 0.63 | 0.81 | 0.63 | 0.63 |
time (sec) |
N/A | 0.015 | 0.005 | 0.020 | 0.222 | 0.247 | 0.049 | 0.261 | 11.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 29 | 36 | 0 | 41 | 26 | 0 | 29 |
N.S. |
1 | 0.00 | 0.91 | 1.12 | 0.00 | 1.28 | 0.81 | 0.00 | 0.91 |
time (sec) |
N/A | 0.000 | 0.411 | 0.038 | 0.000 | 0.255 | 37.778 | 0.000 | 10.645 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | B | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 44 | 41 | 0 | 36 | 37 | 38 | 44 |
N.S. |
1 | 0.00 | 1.83 | 1.71 | 0.00 | 1.50 | 1.54 | 1.58 | 1.83 |
time (sec) |
N/A | 0.000 | 0.122 | 0.160 | 0.000 | 0.253 | 0.214 | 0.397 | 10.821 |
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 | 18 | 0 | 20 | 20 | 50 | 50 | 19 | 56 | 19 |
N.S. |
1 | 0.00 | 1.11 | 1.11 | 2.78 | 2.78 | 1.06 | 3.11 | 1.06 |
time (sec) |
N/A | 0.000 | 2.251 | 0.115 | 0.200 | 0.255 | 0.079 | 0.266 | 0.220 |
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 | 16 | 12 | 13 | 15 | 20 | 15 | 12 | 14 |
N.S. |
1 | 0.89 | 0.67 | 0.72 | 0.83 | 1.11 | 0.83 | 0.67 | 0.78 |
time (sec) |
N/A | 0.012 | 0.005 | 0.021 | 0.186 | 0.238 | 0.052 | 0.261 | 10.569 |
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 | 13 | 13 | 14 | 14 | 13 | 12 | 14 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.08 | 1.00 | 0.92 | 1.08 | 1.00 |
time (sec) |
N/A | 0.122 | 0.149 | 0.238 | 0.217 | 0.249 | 0.074 | 0.260 | 10.624 |
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 | 24 | 15 | 20 | 18 | 18 |
N.S. |
1 | 0.95 | 0.95 | 1.00 | 1.26 | 0.79 | 1.05 | 0.95 | 0.95 |
time (sec) |
N/A | 0.100 | 0.188 | 0.091 | 0.303 | 0.249 | 0.091 | 0.265 | 10.361 |
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 | 39 | 39 | 30 | 42 | 41 | 39 | 35 | 34 |
N.S. |
1 | 1.34 | 1.34 | 1.03 | 1.45 | 1.41 | 1.34 | 1.21 | 1.17 |
time (sec) |
N/A | 0.131 | 0.063 | 0.037 | 0.215 | 0.225 | 0.051 | 0.269 | 10.429 |
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 | 22 | 0 | 22 | 22 | 22 | 21 | 19 | 21 | 21 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 1.00 | 0.95 | 0.86 | 0.95 | 0.95 |
time (sec) |
N/A | 0.000 | 0.607 | 0.198 | 0.302 | 0.240 | 0.122 | 0.291 | 11.130 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 24 | 25 | 27 | 27 | 0 | 24 | 24 |
N.S. |
1 | 0.00 | 1.20 | 1.25 | 1.35 | 1.35 | 0.00 | 1.20 | 1.20 |
time (sec) |
N/A | 0.000 | 0.949 | 0.317 | 0.222 | 0.243 | 0.000 | 0.266 | 10.387 |
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 | 26 | 24 | 25 | 35 | 24 | 25 | 26 |
N.S. |
1 | 0.00 | 1.08 | 1.00 | 1.04 | 1.46 | 1.00 | 1.04 | 1.08 |
time (sec) |
N/A | 0.000 | 0.400 | 0.470 | 0.466 | 0.230 | 0.138 | 0.289 | 12.335 |
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 | 25 | 0 | 26 | 25 | 28 | 28 | 22 | 0 | 27 |
N.S. |
1 | 0.00 | 1.04 | 1.00 | 1.12 | 1.12 | 0.88 | 0.00 | 1.08 |
time (sec) |
N/A | 0.000 | 5.062 | 0.114 | 0.263 | 0.231 | 0.115 | 0.000 | 11.310 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F | F | A | A | F(-1) | B |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 25 | 0 | 0 | 35 | 34 | 0 | 37 |
N.S. |
1 | 0.00 | 0.89 | 0.00 | 0.00 | 1.25 | 1.21 | 0.00 | 1.32 |
time (sec) |
N/A | 0.000 | 0.124 | 0.000 | 0.000 | 0.233 | 2.311 | 0.000 | 12.972 |
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 | 14 | 9 | 9 | 12 | 8 | 7 | 8 | 8 |
N.S. |
1 | 1.27 | 0.82 | 0.82 | 1.09 | 0.73 | 0.64 | 0.73 | 0.73 |
time (sec) |
N/A | 0.006 | 0.015 | 0.013 | 0.206 | 0.224 | 0.040 | 0.276 | 10.995 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 18 | 18 | 17 | 23 | 16 | 17 | 23 | 0 |
N.S. |
1 | 0.72 | 0.72 | 0.68 | 0.92 | 0.64 | 0.68 | 0.92 | 0.00 |
time (sec) |
N/A | 0.119 | 0.034 | 10.910 | 0.296 | 0.225 | 0.139 | 0.430 | 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 | 29 | 18 | 18 | 15 | 0 | 14 | 10 | 37 | 14 |
N.S. |
1 | 0.62 | 0.62 | 0.52 | 0.00 | 0.48 | 0.34 | 1.28 | 0.48 |
time (sec) |
N/A | 0.015 | 0.085 | 0.071 | 0.000 | 0.221 | 0.075 | 0.270 | 0.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | F | F(-2) | B | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 20 | 89 | 20 | 0 | 0 | 42 | 0 | 20 | 0 |
N.S. |
1 | 4.45 | 1.00 | 0.00 | 0.00 | 2.10 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 1.064 | 0.049 | 0.000 | 0.000 | 0.226 | 0.000 | 1.123 | 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 | 22 | 24 | 24 | 21 | 22 | 27 | 22 | 25 | 23 |
N.S. |
1 | 1.09 | 1.09 | 0.95 | 1.00 | 1.23 | 1.00 | 1.14 | 1.05 |
time (sec) |
N/A | 0.072 | 0.370 | 0.102 | 0.267 | 0.233 | 0.105 | 0.267 | 9.981 |
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 | 23 | 23 | 20 | 19 | 28 | 20 | 28 | 19 |
N.S. |
1 | 0.96 | 0.96 | 0.83 | 0.79 | 1.17 | 0.83 | 1.17 | 0.79 |
time (sec) |
N/A | 0.028 | 0.022 | 0.121 | 0.198 | 0.231 | 0.080 | 0.255 | 10.018 |
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 | 20 | 17 | 15 | 21 | 16 | 15 | 16 | 16 |
N.S. |
1 | 1.18 | 1.00 | 0.88 | 1.24 | 0.94 | 0.88 | 0.94 | 0.94 |
time (sec) |
N/A | 2.281 | 0.366 | 0.725 | 0.242 | 0.225 | 3.053 | 0.334 | 10.315 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | A | F(-2) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 26 | 66 | 61 | 34 | 0 | 51 | 63 |
N.S. |
1 | 0.00 | 0.93 | 2.36 | 2.18 | 1.21 | 0.00 | 1.82 | 2.25 |
time (sec) |
N/A | 0.000 | 0.139 | 125.371 | 0.371 | 0.248 | 0.000 | 0.444 | 10.625 |
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 | 26 | 0 | 33 | 30 | 32 | 45 | 32 | 0 | 50 |
N.S. |
1 | 0.00 | 1.27 | 1.15 | 1.23 | 1.73 | 1.23 | 0.00 | 1.92 |
time (sec) |
N/A | 0.000 | 3.038 | 0.368 | 0.270 | 0.226 | 0.103 | 0.000 | 10.497 |
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 | 32 | 0 | 27 | 25 | 44 | 44 | 80 | 45 | 0 |
N.S. |
1 | 0.00 | 0.84 | 0.78 | 1.38 | 1.38 | 2.50 | 1.41 | 0.00 |
time (sec) |
N/A | 0.000 | 0.413 | 1.666 | 0.230 | 0.244 | 0.175 | 0.277 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 21 | 39 | 20 | 23 | 23 | 76 | 62 | 55 |
N.S. |
1 | 1.11 | 2.05 | 1.05 | 1.21 | 1.21 | 4.00 | 3.26 | 2.89 |
time (sec) |
N/A | 0.061 | 0.152 | 0.112 | 0.189 | 0.229 | 0.137 | 0.257 | 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 | 21 | 21 | 21 | 21 | 20 | 31 | 20 | 23 | 20 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.95 | 1.48 | 0.95 | 1.10 | 0.95 |
time (sec) |
N/A | 0.054 | 0.028 | 0.042 | 0.183 | 0.239 | 0.080 | 0.255 | 0.135 |
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 | 32 | 0 | 38 | 36 | 45 | 33 | 36 | 0 | 52 |
N.S. |
1 | 0.00 | 1.19 | 1.12 | 1.41 | 1.03 | 1.12 | 0.00 | 1.62 |
time (sec) |
N/A | 0.000 | 0.397 | 4.521 | 1.062 | 0.240 | 6.815 | 0.000 | 10.597 |
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 | 32 | 32 | 35 | 32 | 56 | 32 | 27 | 140 | 32 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.75 | 1.00 | 0.84 | 4.38 | 1.00 |
time (sec) |
N/A | 0.188 | 0.082 | 0.144 | 0.229 | 0.225 | 0.152 | 0.258 | 9.997 |
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 | 25 | 0 | 35 | 23 | 35 | 28 | 22 | 63 | 23 |
N.S. |
1 | 0.00 | 1.40 | 0.92 | 1.40 | 1.12 | 0.88 | 2.52 | 0.92 |
time (sec) |
N/A | 0.000 | 0.996 | 0.118 | 0.312 | 0.239 | 0.069 | 0.272 | 13.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F(-1) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 38 | 24 | 31 | 24 | 29 | 0 | 22 |
N.S. |
1 | 0.00 | 1.73 | 1.09 | 1.41 | 1.09 | 1.32 | 0.00 | 1.00 |
time (sec) |
N/A | 0.000 | 0.604 | 0.069 | 0.310 | 0.283 | 0.088 | 0.000 | 14.219 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 125 | 33 | 31 | 31 | 35 | 36 | 0 | 29 |
N.S. |
1 | 4.03 | 1.06 | 1.00 | 1.00 | 1.13 | 1.16 | 0.00 | 0.94 |
time (sec) |
N/A | 0.683 | 0.190 | 9.921 | 0.245 | 0.264 | 0.346 | 0.000 | 14.292 |
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 | 23 | 34 | 16 | 15 | 17 | 17 | 15 | 16 |
N.S. |
1 | 1.05 | 1.55 | 0.73 | 0.68 | 0.77 | 0.77 | 0.68 | 0.73 |
time (sec) |
N/A | 0.006 | 0.000 | 0.003 | 0.201 | 0.227 | 0.014 | 0.264 | 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 | 27 | 33 | 33 | 32 | 29 | 32 | 27 | 34 | 32 |
N.S. |
1 | 1.22 | 1.22 | 1.19 | 1.07 | 1.19 | 1.00 | 1.26 | 1.19 |
time (sec) |
N/A | 0.081 | 0.028 | 0.054 | 0.195 | 0.237 | 2.199 | 0.289 | 14.796 |
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 | 16 | 14 | 28 | 13 | 14 | 13 | 13 |
N.S. |
1 | 1.00 | 0.94 | 0.82 | 1.65 | 0.76 | 0.82 | 0.76 | 0.76 |
time (sec) |
N/A | 0.015 | 0.008 | 0.037 | 0.274 | 0.240 | 0.048 | 0.279 | 15.309 |
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 | 13 | 11 | 10 | 10 | 10 | 10 | 10 |
N.S. |
1 | 0.72 | 0.72 | 0.61 | 0.56 | 0.56 | 0.56 | 0.56 | 0.56 |
time (sec) |
N/A | 0.007 | 0.010 | 0.015 | 0.192 | 0.231 | 0.045 | 0.267 | 14.398 |
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 | 7 | 7 | 8 | 7 | 7 | 5 | 7 | 7 |
N.S. |
1 | 0.39 | 0.39 | 0.44 | 0.39 | 0.39 | 0.28 | 0.39 | 0.39 |
time (sec) |
N/A | 0.001 | 0.000 | 0.009 | 0.197 | 0.223 | 0.019 | 0.268 | 0.030 |
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 | 34 | 29 | 26 | 27 | 35 | 16 | 22 | 41 | 15 |
N.S. |
1 | 0.85 | 0.76 | 0.79 | 1.03 | 0.47 | 0.65 | 1.21 | 0.44 |
time (sec) |
N/A | 0.095 | 0.037 | 0.097 | 0.336 | 0.269 | 0.072 | 0.275 | 14.882 |
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 | 15 | 19 | 15 | 13 | 24 | 11 | 12 | 15 | 13 |
N.S. |
1 | 1.27 | 1.00 | 0.87 | 1.60 | 0.73 | 0.80 | 1.00 | 0.87 |
time (sec) |
N/A | 0.092 | 0.031 | 0.076 | 0.236 | 0.232 | 0.058 | 0.251 | 0.129 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 28 | 21 | 36 | 26 | 97 | 57 | 22 |
N.S. |
1 | 0.00 | 1.00 | 0.75 | 1.29 | 0.93 | 3.46 | 2.04 | 0.79 |
time (sec) |
N/A | 0.000 | 2.557 | 0.366 | 0.248 | 0.241 | 0.134 | 0.271 | 15.159 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 40 | 53 | 38 | 53 | 51 | 0 | 0 |
N.S. |
1 | 0.00 | 1.14 | 1.51 | 1.09 | 1.51 | 1.46 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.082 | 91.416 | 0.700 | 0.243 | 3.275 | 0.000 | 0.000 |
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 | 27 | 532 | 28 | 142 | 357 | 125 | 631 | 140 | 210 |
N.S. |
1 | 19.70 | 1.04 | 5.26 | 13.22 | 4.63 | 23.37 | 5.19 | 7.78 |
time (sec) |
N/A | 2.469 | 13.152 | 0.264 | 0.244 | 0.243 | 0.242 | 0.287 | 0.605 |
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 | 24 | 27 | 27 | 25 | 0 | 24 | 24 | 30 | 24 |
N.S. |
1 | 1.12 | 1.12 | 1.04 | 0.00 | 1.00 | 1.00 | 1.25 | 1.00 |
time (sec) |
N/A | 0.134 | 0.093 | 0.138 | 0.000 | 0.251 | 0.185 | 0.296 | 14.822 |