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 | 31 | 53 | 53 | 42 | 41 | 41 | 49 | 41 | 46 |
N.S. |
1 | 1.71 | 1.71 | 1.35 | 1.32 | 1.32 | 1.58 | 1.32 | 1.48 |
time (sec) |
N/A | 0.011 | 0.013 | 0.051 | 0.188 | 0.247 | 0.051 | 0.292 | 10.394 |
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 | 14 | 12 | 12 | 12 | 31 | 11 | 12 | 11 | 11 |
N.S. |
1 | 0.86 | 0.86 | 0.86 | 2.21 | 0.79 | 0.86 | 0.79 | 0.79 |
time (sec) |
N/A | 0.036 | 0.004 | 0.038 | 0.194 | 0.238 | 0.065 | 0.275 | 0.059 |
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 | 29 | 32 | 27 | 31 | 35 | 30 | 31 | 30 | 0 |
N.S. |
1 | 1.10 | 0.93 | 1.07 | 1.21 | 1.03 | 1.07 | 1.03 | 0.00 |
time (sec) |
N/A | 0.263 | 2.233 | 0.214 | 0.301 | 0.249 | 0.156 | 0.293 | 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 | 13 | 11 | 10 | 12 | 10 | 14 | 10 |
N.S. |
1 | 0.72 | 0.72 | 0.61 | 0.56 | 0.67 | 0.56 | 0.78 | 0.56 |
time (sec) |
N/A | 0.003 | 0.010 | 0.053 | 0.177 | 0.240 | 0.048 | 0.262 | 9.695 |
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 | 14 | 13 | 14 | 21 | 13 | 14 | 15 | 11 |
N.S. |
1 | 0.67 | 0.62 | 0.67 | 1.00 | 0.62 | 0.67 | 0.71 | 0.52 |
time (sec) |
N/A | 0.025 | 0.017 | 0.107 | 0.202 | 0.235 | 0.057 | 0.265 | 9.790 |
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 | 26 | 45 | 24 | 36 | 153 | 27 | 44 | 27 | 20 |
N.S. |
1 | 1.73 | 0.92 | 1.38 | 5.88 | 1.04 | 1.69 | 1.04 | 0.77 |
time (sec) |
N/A | 0.043 | 2.546 | 0.158 | 0.243 | 0.249 | 0.166 | 0.270 | 0.185 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | F | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 87 | 104 | 0 | 103 | 104 | 163 | 338 |
N.S. |
1 | 0.00 | 3.78 | 4.52 | 0.00 | 4.48 | 4.52 | 7.09 | 14.70 |
time (sec) |
N/A | 0.000 | 0.394 | 0.515 | 0.000 | 0.259 | 0.463 | 2.276 | 10.985 |
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 | 33 | 0 | 25 | 26 | 25 | 27 | 26 | 27 | 0 |
N.S. |
1 | 0.00 | 0.76 | 0.79 | 0.76 | 0.82 | 0.79 | 0.82 | 0.00 |
time (sec) |
N/A | 0.000 | 5.038 | 0.479 | 0.297 | 0.252 | 0.099 | 0.308 | 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 | 25 | 109 | 22 | 83 | 262 | 57 | 104 | 130 | 21 |
N.S. |
1 | 4.36 | 0.88 | 3.32 | 10.48 | 2.28 | 4.16 | 5.20 | 0.84 |
time (sec) |
N/A | 0.514 | 0.948 | 0.529 | 0.205 | 0.240 | 0.179 | 0.282 | 10.781 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | B | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 88 | 57 | 83 | 51 | 48 | 96 | 44 |
N.S. |
1 | 0.00 | 2.67 | 1.73 | 2.52 | 1.55 | 1.45 | 2.91 | 1.33 |
time (sec) |
N/A | 0.000 | 0.232 | 28.199 | 0.220 | 0.251 | 3.111 | 0.292 | 10.834 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 20 | 22 | 85 | 25 | 26 | 45 | 16 |
N.S. |
1 | 1.00 | 0.91 | 1.00 | 3.86 | 1.14 | 1.18 | 2.05 | 0.73 |
time (sec) |
N/A | 0.119 | 0.012 | 0.273 | 0.231 | 0.250 | 0.139 | 0.271 | 10.279 |
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 | 25 | 69 | 18 | 25 | 17 | 25 | 20 | 24 | 17 |
N.S. |
1 | 2.76 | 0.72 | 1.00 | 0.68 | 1.00 | 0.80 | 0.96 | 0.68 |
time (sec) |
N/A | 0.041 | 0.028 | 0.536 | 0.313 | 0.243 | 0.086 | 0.286 | 12.278 |
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 | 18 | 20 | 20 | 27 | 27 | 26 | 27 | 21 |
N.S. |
1 | 0.90 | 1.00 | 1.00 | 1.35 | 1.35 | 1.30 | 1.35 | 1.05 |
time (sec) |
N/A | 0.017 | 0.010 | 0.060 | 0.183 | 0.259 | 0.049 | 0.269 | 0.063 |
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 | 42 | 22 | 27 | 0 | 27 | 17 | 39 | 22 |
N.S. |
1 | 1.68 | 0.88 | 1.08 | 0.00 | 1.08 | 0.68 | 1.56 | 0.88 |
time (sec) |
N/A | 0.227 | 0.117 | 0.238 | 0.000 | 0.242 | 0.091 | 0.267 | 10.763 |
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 | 18 | 37 | 16 | 16 | 21 | 21 | 19 | 25 | 15 |
N.S. |
1 | 2.06 | 0.89 | 0.89 | 1.17 | 1.17 | 1.06 | 1.39 | 0.83 |
time (sec) |
N/A | 0.287 | 0.153 | 0.055 | 0.217 | 0.241 | 0.063 | 0.263 | 10.986 |
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 | 21 | 39 | 30 | 37 | 46 | 52 | 54 | 52 | 44 |
N.S. |
1 | 1.86 | 1.43 | 1.76 | 2.19 | 2.48 | 2.57 | 2.48 | 2.10 |
time (sec) |
N/A | 1.574 | 0.749 | 0.322 | 0.222 | 0.242 | 0.092 | 0.273 | 10.147 |
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 | 23 | 0 | 23 | 34 | 58 | 33 | 31 | 48 | 62 |
N.S. |
1 | 0.00 | 1.00 | 1.48 | 2.52 | 1.43 | 1.35 | 2.09 | 2.70 |
time (sec) |
N/A | 0.000 | 0.332 | 0.527 | 0.327 | 0.253 | 0.182 | 0.490 | 10.894 |
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 | 3 | 3 | 4 | 3 | 3 | 2 | 3 | 3 |
N.S. |
1 | 0.20 | 0.20 | 0.27 | 0.20 | 0.20 | 0.13 | 0.20 | 0.20 |
time (sec) |
N/A | 0.000 | 0.000 | 0.003 | 0.177 | 0.248 | 0.018 | 0.270 | 0.013 |
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 | 30 | 0 | 50 | 40 | 61 | 53 | 44 | 66 | 281 |
N.S. |
1 | 0.00 | 1.67 | 1.33 | 2.03 | 1.77 | 1.47 | 2.20 | 9.37 |
time (sec) |
N/A | 0.000 | 0.258 | 6.524 | 0.226 | 0.239 | 0.201 | 0.351 | 11.825 |
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 | 15 | 15 | 13 | 12 | 12 | 10 | 12 | 12 |
N.S. |
1 | 0.54 | 0.54 | 0.46 | 0.43 | 0.43 | 0.36 | 0.43 | 0.43 |
time (sec) |
N/A | 0.004 | 0.007 | 0.026 | 0.190 | 0.234 | 0.036 | 0.263 | 10.842 |
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 | 16 | 16 | 16 | 16 | 15 | 15 | 17 | 0 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.94 | 0.94 | 1.06 | 0.00 | 0.94 |
time (sec) |
N/A | 0.053 | 0.025 | 0.184 | 0.336 | 0.249 | 0.067 | 0.000 | 10.785 |
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 | 17 | 17 | 17 | 18 | 74 | 74 | 78 | 134 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 4.35 | 4.35 | 4.59 | 7.88 | 1.00 |
time (sec) |
N/A | 0.163 | 0.015 | 0.244 | 0.231 | 0.267 | 0.117 | 0.289 | 11.466 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 160 | 40 | 144 | 110 | 90 | 139 | 186 |
N.S. |
1 | 0.00 | 5.00 | 1.25 | 4.50 | 3.44 | 2.81 | 4.34 | 5.81 |
time (sec) |
N/A | 0.000 | 0.558 | 1.702 | 0.545 | 11.532 | 0.668 | 0.682 | 11.470 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 62 | 29 | 47 | 70 | 63 | 41 | 75 | 0 |
N.S. |
1 | 2.14 | 1.00 | 1.62 | 2.41 | 2.17 | 1.41 | 2.59 | 0.00 |
time (sec) |
N/A | 2.374 | 0.175 | 1.390 | 0.329 | 0.263 | 0.220 | 0.292 | 0.000 |
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 | 28 | 98 | 76 | 52 | 128 | 48 | 53 | 87 | 65 |
N.S. |
1 | 3.50 | 2.71 | 1.86 | 4.57 | 1.71 | 1.89 | 3.11 | 2.32 |
time (sec) |
N/A | 0.229 | 0.090 | 0.163 | 0.185 | 0.249 | 0.105 | 0.268 | 10.415 |
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 | 23 | 24 | 22 | 24 | 22 | 23 | 24 | 0 | 23 |
N.S. |
1 | 1.04 | 0.96 | 1.04 | 0.96 | 1.00 | 1.04 | 0.00 | 1.00 |
time (sec) |
N/A | 0.158 | 0.182 | 0.394 | 0.304 | 0.252 | 0.178 | 0.000 | 10.897 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | B | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 39 | 39 | 76 | 76 | 42 | 46 | 284 |
N.S. |
1 | 0.00 | 1.44 | 1.44 | 2.81 | 2.81 | 1.56 | 1.70 | 10.52 |
time (sec) |
N/A | 0.000 | 0.063 | 0.316 | 0.219 | 0.244 | 0.068 | 0.276 | 10.704 |
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 | 19 | 18 | 18 | 19 | 20 | 19 | 17 |
N.S. |
1 | 0.83 | 0.66 | 0.62 | 0.62 | 0.66 | 0.69 | 0.66 | 0.59 |
time (sec) |
N/A | 0.075 | 0.263 | 0.159 | 0.184 | 0.250 | 0.268 | 0.280 | 10.127 |
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 | 5 | 5 | 5 | 5 | 4 | 4 | 3 | 4 | 4 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.80 | 0.80 | 0.60 | 0.80 | 0.80 |
time (sec) |
N/A | 0.001 | 0.000 | 0.038 | 0.185 | 0.248 | 0.028 | 0.275 | 0.007 |
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 | 10 | 14 | 8 | 7 | 9 | 8 | 7 | 8 |
N.S. |
1 | 0.67 | 0.93 | 0.53 | 0.47 | 0.60 | 0.53 | 0.47 | 0.53 |
time (sec) |
N/A | 0.001 | 0.000 | 0.012 | 0.186 | 0.229 | 0.015 | 0.269 | 0.002 |
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 | 25 | 23 | 26 | 25 | 25 | 20 | 25 | 24 |
N.S. |
1 | 0.93 | 0.85 | 0.96 | 0.93 | 0.93 | 0.74 | 0.93 | 0.89 |
time (sec) |
N/A | 0.505 | 0.497 | 1.078 | 0.281 | 0.255 | 0.127 | 0.455 | 11.918 |
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 | 34 | 32 | 51 | 53 | 34 | 38 | 45 |
N.S. |
1 | 0.00 | 1.00 | 0.94 | 1.50 | 1.56 | 1.00 | 1.12 | 1.32 |
time (sec) |
N/A | 0.000 | 0.084 | 0.939 | 0.314 | 0.251 | 0.156 | 0.285 | 10.190 |
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 | 27 | 0 | 38 | 43 | 119 | 119 | 61 | 65 | 0 |
N.S. |
1 | 0.00 | 1.41 | 1.59 | 4.41 | 4.41 | 2.26 | 2.41 | 0.00 |
time (sec) |
N/A | 0.000 | 0.068 | 0.379 | 0.239 | 0.260 | 0.085 | 0.285 | 0.000 |
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 | 27 | 0 | 26 | 32 | 78 | 29 | 36 | 41 | 22 |
N.S. |
1 | 0.00 | 0.96 | 1.19 | 2.89 | 1.07 | 1.33 | 1.52 | 0.81 |
time (sec) |
N/A | 0.000 | 0.441 | 10.061 | 0.233 | 0.259 | 106.491 | 0.342 | 11.180 |
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 | 18 | 16 | 18 | 21 | 26 | 21 | 23 |
N.S. |
1 | 1.00 | 0.90 | 0.80 | 0.90 | 1.05 | 1.30 | 1.05 | 1.15 |
time (sec) |
N/A | 0.030 | 0.044 | 0.093 | 0.185 | 0.252 | 0.084 | 0.269 | 0.290 |
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 | 18 | 18 | 15 | 14 | 14 | 15 | 14 | 12 |
N.S. |
1 | 0.67 | 0.67 | 0.56 | 0.52 | 0.52 | 0.56 | 0.52 | 0.44 |
time (sec) |
N/A | 0.003 | 0.004 | 0.023 | 0.189 | 0.244 | 0.045 | 0.268 | 10.685 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 75 | 18 | 38 | 41 | 36 | 41 | 41 | 13 |
N.S. |
1 | 3.41 | 0.82 | 1.73 | 1.86 | 1.64 | 1.86 | 1.86 | 0.59 |
time (sec) |
N/A | 0.057 | 0.092 | 0.127 | 0.301 | 0.258 | 0.129 | 0.264 | 10.804 |
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 | 56 | 23 | 19 | 18 | 34 | 20 | 0 | 19 |
N.S. |
1 | 2.43 | 1.00 | 0.83 | 0.78 | 1.48 | 0.87 | 0.00 | 0.83 |
time (sec) |
N/A | 0.101 | 0.049 | 3.429 | 0.392 | 0.257 | 0.099 | 0.000 | 11.280 |
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 | 37 | 0 | 37 | 48 | 57 | 55 | 53 | 59 | 63 |
N.S. |
1 | 0.00 | 1.00 | 1.30 | 1.54 | 1.49 | 1.43 | 1.59 | 1.70 |
time (sec) |
N/A | 0.000 | 0.165 | 0.294 | 0.484 | 0.255 | 0.526 | 0.569 | 11.762 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 57 | 40 | 51 | 67 | 43 | 34 | 44 | 46 |
N.S. |
1 | 2.59 | 1.82 | 2.32 | 3.05 | 1.95 | 1.55 | 2.00 | 2.09 |
time (sec) |
N/A | 0.132 | 0.067 | 0.142 | 0.224 | 0.248 | 0.098 | 0.285 | 0.225 |
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 | 25 | 0 | 28 | 34 | 44 | 35 | 36 | 59 | 142 |
N.S. |
1 | 0.00 | 1.12 | 1.36 | 1.76 | 1.40 | 1.44 | 2.36 | 5.68 |
time (sec) |
N/A | 0.000 | 0.857 | 1.405 | 0.321 | 0.243 | 0.137 | 0.346 | 11.580 |
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 | 18 | 42 | 22 | 21 | 20 | 20 | 22 | 20 | 16 |
N.S. |
1 | 2.33 | 1.22 | 1.17 | 1.11 | 1.11 | 1.22 | 1.11 | 0.89 |
time (sec) |
N/A | 0.014 | 0.017 | 0.052 | 0.177 | 0.243 | 0.070 | 0.274 | 10.827 |
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 | 23 | 20 | 23 | 22 | 28 | 20 | 22 | 20 |
N.S. |
1 | 0.88 | 0.77 | 0.88 | 0.85 | 1.08 | 0.77 | 0.85 | 0.77 |
time (sec) |
N/A | 0.025 | 0.014 | 0.072 | 0.185 | 0.256 | 0.221 | 0.273 | 0.070 |
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 | 10 | 10 | 11 | 12 | 10 | 7 | 10 | 10 |
N.S. |
1 | 0.59 | 0.59 | 0.65 | 0.71 | 0.59 | 0.41 | 0.59 | 0.59 |
time (sec) |
N/A | 0.030 | 0.060 | 0.296 | 0.212 | 0.234 | 0.040 | 0.269 | 10.843 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | B | A | F(-2) | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 82 | 45 | 111 | 53 | 0 | 75 | 0 |
N.S. |
1 | 0.00 | 2.56 | 1.41 | 3.47 | 1.66 | 0.00 | 2.34 | 0.00 |
time (sec) |
N/A | 0.000 | 0.912 | 3.069 | 0.272 | 0.261 | 0.000 | 0.413 | 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 | 28 | 0 | 26 | 25 | 60 | 25 | 22 | 52 | 56 |
N.S. |
1 | 0.00 | 0.93 | 0.89 | 2.14 | 0.89 | 0.79 | 1.86 | 2.00 |
time (sec) |
N/A | 0.000 | 5.284 | 8.440 | 0.380 | 0.257 | 0.609 | 0.436 | 11.659 |
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 | 44 | 29 | 28 | 71 | 43 | 44 | 71 | 78 |
N.S. |
1 | 1.52 | 1.00 | 0.97 | 2.45 | 1.48 | 1.52 | 2.45 | 2.69 |
time (sec) |
N/A | 2.527 | 3.688 | 0.406 | 0.489 | 0.252 | 0.144 | 0.279 | 10.743 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 57 | 39 | 35 | 27 | 39 | 22 | 0 | 0 |
N.S. |
1 | 1.97 | 1.34 | 1.21 | 0.93 | 1.34 | 0.76 | 0.00 | 0.00 |
time (sec) |
N/A | 0.695 | 0.235 | 0.102 | 0.246 | 0.254 | 0.097 | 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 | 19 | 26 | 24 | 19 | 19 | 19 | 20 | 19 | 19 |
N.S. |
1 | 1.37 | 1.26 | 1.00 | 1.00 | 1.00 | 1.05 | 1.00 | 1.00 |
time (sec) |
N/A | 0.068 | 0.742 | 0.091 | 0.198 | 0.250 | 0.122 | 0.267 | 11.303 |
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 | 15 | 11 | 11 | 11 | 10 | 10 | 12 | 10 | 10 |
N.S. |
1 | 0.73 | 0.73 | 0.73 | 0.67 | 0.67 | 0.80 | 0.67 | 0.67 |
time (sec) |
N/A | 0.007 | 0.015 | 0.052 | 0.183 | 0.254 | 0.042 | 0.253 | 0.030 |
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 | 23 | 0 | 21 | 21 | 194 | 194 | 92 | 212 | 0 |
N.S. |
1 | 0.00 | 0.91 | 0.91 | 8.43 | 8.43 | 4.00 | 9.22 | 0.00 |
time (sec) |
N/A | 0.000 | 0.097 | 0.384 | 0.248 | 0.261 | 0.145 | 0.305 | 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 | 20 | 20 | 26 | 26 | 22 | 20 | 20 |
N.S. |
1 | 0.83 | 0.87 | 0.87 | 1.13 | 1.13 | 0.96 | 0.87 | 0.87 |
time (sec) |
N/A | 0.211 | 0.224 | 0.335 | 0.224 | 0.243 | 0.151 | 0.271 | 11.012 |
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 | 20 | 55 | 40 | 35 | 50 | 33 | 36 | 45 | 31 |
N.S. |
1 | 2.75 | 2.00 | 1.75 | 2.50 | 1.65 | 1.80 | 2.25 | 1.55 |
time (sec) |
N/A | 0.015 | 0.009 | 0.097 | 0.180 | 0.247 | 0.059 | 0.261 | 11.405 |
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 | 27 | 28 | 22 | 20 | 28 | 27 | 20 | 21 |
N.S. |
1 | 1.08 | 1.12 | 0.88 | 0.80 | 1.12 | 1.08 | 0.80 | 0.84 |
time (sec) |
N/A | 0.011 | 0.025 | 0.060 | 0.191 | 0.263 | 0.056 | 0.258 | 0.135 |
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 | 21 | 12 | 12 | 23 | 12 | 10 | 11 | 9 |
N.S. |
1 | 1.75 | 1.00 | 1.00 | 1.92 | 1.00 | 0.83 | 0.92 | 0.75 |
time (sec) |
N/A | 0.012 | 0.032 | 0.031 | 0.190 | 0.276 | 0.038 | 0.271 | 11.114 |
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 | 21 | 21 | 21 | 27 | 30 | 23 | 19 | 23 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.29 | 1.43 | 1.10 | 0.90 | 1.10 | 0.00 |
time (sec) |
N/A | 0.353 | 0.067 | 0.879 | 0.308 | 0.248 | 0.121 | 0.310 | 0.000 |
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 | 21 | 55 | 15 | 45 | 45 | 48 | 51 | 48 | 16 |
N.S. |
1 | 2.62 | 0.71 | 2.14 | 2.14 | 2.29 | 2.43 | 2.29 | 0.76 |
time (sec) |
N/A | 0.031 | 0.018 | 0.052 | 0.272 | 0.246 | 0.070 | 0.275 | 0.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 25 | 25 | 29 | 31 | 28 | 26 | 28 | 25 |
N.S. |
1 | 0.78 | 0.78 | 0.91 | 0.97 | 0.88 | 0.81 | 0.88 | 0.78 |
time (sec) |
N/A | 0.195 | 0.475 | 0.413 | 0.309 | 0.235 | 0.178 | 0.321 | 10.914 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 39 | 65 | 43 | 66 | 42 | 41 | 48 | 41 |
N.S. |
1 | 1.56 | 2.60 | 1.72 | 2.64 | 1.68 | 1.64 | 1.92 | 1.64 |
time (sec) |
N/A | 0.535 | 0.213 | 0.975 | 0.223 | 0.244 | 0.160 | 0.276 | 10.382 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | F | B | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 26 | 52 | 0 | 56 | 54 | 0 | 60 |
N.S. |
1 | 0.00 | 1.04 | 2.08 | 0.00 | 2.24 | 2.16 | 0.00 | 2.40 |
time (sec) |
N/A | 0.000 | 5.250 | 0.282 | 0.000 | 0.260 | 0.274 | 0.000 | 10.658 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 123 | 88 | 60 | 54 | 97 | 58 | 0 | 0 |
N.S. |
1 | 4.39 | 3.14 | 2.14 | 1.93 | 3.46 | 2.07 | 0.00 | 0.00 |
time (sec) |
N/A | 9.049 | 0.621 | 0.528 | 0.201 | 0.257 | 3.533 | 0.000 | 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 | 27 | 0 | 18 | 17 | 16 | 16 | 15 | 16 | 17 |
N.S. |
1 | 0.00 | 0.67 | 0.63 | 0.59 | 0.59 | 0.56 | 0.59 | 0.63 |
time (sec) |
N/A | 0.000 | 0.368 | 0.301 | 0.219 | 0.246 | 0.087 | 0.276 | 0.285 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 47 | 47 | 40 | 39 | 68 | 48 | 39 | 45 |
N.S. |
1 | 1.52 | 1.52 | 1.29 | 1.26 | 2.19 | 1.55 | 1.26 | 1.45 |
time (sec) |
N/A | 0.278 | 1.799 | 0.134 | 0.188 | 0.237 | 0.070 | 0.282 | 0.421 |
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 | 12 | 13 | 13 | 12 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.87 | 0.87 | 0.80 | 0.87 | 0.87 |
time (sec) |
N/A | 0.232 | 0.246 | 0.243 | 0.298 | 0.244 | 0.057 | 0.265 | 11.032 |
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 | 27 | 33 | 33 | 28 | 27 | 29 | 29 | 29 | 27 |
N.S. |
1 | 1.22 | 1.22 | 1.04 | 1.00 | 1.07 | 1.07 | 1.07 | 1.00 |
time (sec) |
N/A | 0.496 | 0.401 | 0.091 | 0.236 | 0.240 | 0.092 | 0.277 | 11.337 |
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 | 18 | 23 | 16 | 0 | 0 | 17 |
N.S. |
1 | 0.00 | 1.00 | 0.86 | 1.10 | 0.76 | 0.00 | 0.00 | 0.81 |
time (sec) |
N/A | 0.000 | 0.665 | 26.414 | 0.394 | 0.243 | 0.000 | 0.000 | 11.727 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | F(-1) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 124 | 61 | 78 | 70 | 70 | 0 | 72 |
N.S. |
1 | 0.00 | 4.13 | 2.03 | 2.60 | 2.33 | 2.33 | 0.00 | 2.40 |
time (sec) |
N/A | 0.000 | 1.935 | 27.898 | 0.250 | 0.254 | 0.504 | 0.000 | 12.057 |
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 | 20 | 19 | 32 | 28 | 15 | 18 | 37 |
N.S. |
1 | 0.00 | 1.00 | 0.95 | 1.60 | 1.40 | 0.75 | 0.90 | 1.85 |
time (sec) |
N/A | 0.000 | 0.215 | 0.269 | 0.303 | 0.264 | 0.062 | 0.302 | 11.961 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | B | B | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 1653 | 28 | 61 | 898 | 42 | 26 | 53 | 0 |
N.S. |
1 | 61.22 | 1.04 | 2.26 | 33.26 | 1.56 | 0.96 | 1.96 | 0.00 |
time (sec) |
N/A | 5.655 | 5.070 | 0.381 | 0.371 | 0.255 | 0.148 | 0.306 | 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 | 17 | 11 | 19 | 10 | 11 | 11 | 8 | 13 | 8 |
N.S. |
1 | 0.65 | 1.12 | 0.59 | 0.65 | 0.65 | 0.47 | 0.76 | 0.47 |
time (sec) |
N/A | 0.003 | 0.005 | 0.119 | 0.193 | 0.237 | 0.043 | 0.286 | 0.114 |
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 | 45 | 38 | 35 | 37 | 37 | 39 | 37 | 36 |
N.S. |
1 | 1.73 | 1.46 | 1.35 | 1.42 | 1.42 | 1.50 | 1.42 | 1.38 |
time (sec) |
N/A | 0.009 | 0.016 | 0.045 | 0.190 | 0.233 | 0.027 | 0.292 | 0.070 |
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 | 33 | 0 | 38 | 32 | 161 | 33 | 32 | 0 | 48 |
N.S. |
1 | 0.00 | 1.15 | 0.97 | 4.88 | 1.00 | 0.97 | 0.00 | 1.45 |
time (sec) |
N/A | 0.000 | 0.644 | 5.567 | 0.378 | 0.242 | 0.352 | 0.000 | 11.489 |
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 | 25 | 53 | 27 | 25 | 42 | 44 | 27 |
N.S. |
1 | 0.00 | 0.86 | 1.83 | 0.93 | 0.86 | 1.45 | 1.52 | 0.93 |
time (sec) |
N/A | 0.000 | 0.059 | 0.494 | 0.315 | 0.239 | 0.389 | 0.348 | 11.481 |
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 | 15 | 15 | 17 | 17 | 16 | 14 | 47 | 17 |
N.S. |
1 | 0.71 | 0.71 | 0.81 | 0.81 | 0.76 | 0.67 | 2.24 | 0.81 |
time (sec) |
N/A | 0.113 | 0.068 | 0.315 | 0.305 | 0.239 | 0.094 | 0.275 | 11.843 |
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 | 21 | 0 | 21 | 20 | 0 | 31 | 20 | 0 | 30 |
N.S. |
1 | 0.00 | 1.00 | 0.95 | 0.00 | 1.48 | 0.95 | 0.00 | 1.43 |
time (sec) |
N/A | 0.000 | 0.874 | 0.235 | 0.000 | 0.262 | 0.124 | 0.000 | 12.160 |
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 | 201 | 47 | 39 | 49 | 37 | 44 | 37 | 41 |
N.S. |
1 | 7.18 | 1.68 | 1.39 | 1.75 | 1.32 | 1.57 | 1.32 | 1.46 |
time (sec) |
N/A | 0.215 | 0.128 | 0.303 | 0.312 | 0.243 | 0.080 | 0.277 | 0.303 |
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 | 22 | 45 | 26 | 23 | 71 | 21 | 22 | 26 | 22 |
N.S. |
1 | 2.05 | 1.18 | 1.05 | 3.23 | 0.95 | 1.00 | 1.18 | 1.00 |
time (sec) |
N/A | 0.064 | 0.214 | 0.055 | 0.196 | 0.237 | 0.057 | 0.268 | 12.153 |
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 | 8 | 8 | 8 | 7 | 7 | 5 | 7 | 7 |
N.S. |
1 | 0.47 | 0.47 | 0.47 | 0.41 | 0.41 | 0.29 | 0.41 | 0.41 |
time (sec) |
N/A | 0.003 | 0.003 | 0.021 | 0.183 | 0.235 | 0.044 | 0.271 | 0.039 |
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 | 29 | 27 | 29 | 26 | 24 | 26 | 26 |
N.S. |
1 | 0.00 | 1.21 | 1.12 | 1.21 | 1.08 | 1.00 | 1.08 | 1.08 |
time (sec) |
N/A | 0.000 | 3.766 | 1.704 | 0.307 | 0.242 | 0.388 | 0.362 | 11.965 |
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 | 28 | 0 | 19 | 20 | 25 | 27 | 24 | 27 | 27 |
N.S. |
1 | 0.00 | 0.68 | 0.71 | 0.89 | 0.96 | 0.86 | 0.96 | 0.96 |
time (sec) |
N/A | 0.000 | 0.618 | 2.722 | 0.319 | 0.248 | 0.061 | 0.276 | 0.252 |
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 | 24 | 0 | 24 | 22 | 18 | 49 | 17 | 0 | 18 |
N.S. |
1 | 0.00 | 1.00 | 0.92 | 0.75 | 2.04 | 0.71 | 0.00 | 0.75 |
time (sec) |
N/A | 0.000 | 0.331 | 0.260 | 0.345 | 0.259 | 0.156 | 0.000 | 12.473 |
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 | 17 | 19 | 16 | 19 | 16 | 20 |
N.S. |
1 | 0.00 | 1.00 | 0.89 | 1.00 | 0.84 | 1.00 | 0.84 | 1.05 |
time (sec) |
N/A | 0.000 | 0.689 | 1.409 | 0.369 | 0.249 | 0.169 | 0.391 | 12.397 |
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 | 17 | 16 | 20 | 19 | 20 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.80 | 1.00 | 0.95 | 1.00 | 0.80 |
time (sec) |
N/A | 0.130 | 0.232 | 0.212 | 0.213 | 0.267 | 0.110 | 0.278 | 12.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 27 | 43 | 19 | 33 | 17 | 114 | 33 | 18 |
N.S. |
1 | 1.08 | 1.72 | 0.76 | 1.32 | 0.68 | 4.56 | 1.32 | 0.72 |
time (sec) |
N/A | 0.027 | 0.015 | 0.254 | 0.196 | 0.253 | 0.160 | 0.271 | 0.165 |
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 | 122 | 122 | 100 | 325 | 107 | 129 | 154 | 151 |
N.S. |
1 | 4.88 | 4.88 | 4.00 | 13.00 | 4.28 | 5.16 | 6.16 | 6.04 |
time (sec) |
N/A | 0.277 | 10.511 | 0.410 | 0.363 | 0.271 | 0.180 | 0.286 | 12.083 |
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 | 30 | 0 | 25 | 21 | 24 | 19 | 26 | 0 | 23 |
N.S. |
1 | 0.00 | 0.83 | 0.70 | 0.80 | 0.63 | 0.87 | 0.00 | 0.77 |
time (sec) |
N/A | 0.000 | 0.073 | 0.404 | 0.311 | 0.253 | 0.230 | 0.000 | 13.701 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 24 | 49 | 59 | 43 | 42 | 43 | 55 |
N.S. |
1 | 0.00 | 0.96 | 1.96 | 2.36 | 1.72 | 1.68 | 1.72 | 2.20 |
time (sec) |
N/A | 0.000 | 0.331 | 1.785 | 0.301 | 0.264 | 0.192 | 0.428 | 0.237 |
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 | 29 | 150 | 23 | 40 | 0 | 36 | 37 | 87 | 47 |
N.S. |
1 | 5.17 | 0.79 | 1.38 | 0.00 | 1.24 | 1.28 | 3.00 | 1.62 |
time (sec) |
N/A | 0.440 | 0.115 | 0.498 | 0.000 | 0.247 | 0.557 | 0.342 | 12.756 |
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 | 25 | 53 | 22 | 25 | 28 | 23 | 27 | 0 | 20 |
N.S. |
1 | 2.12 | 0.88 | 1.00 | 1.12 | 0.92 | 1.08 | 0.00 | 0.80 |
time (sec) |
N/A | 0.578 | 0.627 | 3.349 | 0.300 | 0.245 | 0.201 | 0.000 | 12.459 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | F | A | A | F(-1) | A | F(-1) |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 0 | 0 | 32 | 27 | 0 | 31 | 0 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 1.33 | 1.12 | 0.00 | 1.29 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.347 | 0.254 | 0.000 | 3.093 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 34 | 18 | 33 | 84 | 32 | 31 | 32 | 23 |
N.S. |
1 | 1.89 | 1.00 | 1.83 | 4.67 | 1.78 | 1.72 | 1.78 | 1.28 |
time (sec) |
N/A | 0.172 | 0.058 | 0.078 | 0.184 | 0.243 | 0.105 | 0.277 | 10.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 26 | 26 | 23 | 22 | 22 | 22 | 22 | 22 |
N.S. |
1 | 0.79 | 0.79 | 0.70 | 0.67 | 0.67 | 0.67 | 0.67 | 0.67 |
time (sec) |
N/A | 0.004 | 0.011 | 0.062 | 0.183 | 0.253 | 0.039 | 0.276 | 0.073 |
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 | 23 | 14 | 15 | 11 | 22 | 20 | 16 | 17 |
N.S. |
1 | 1.21 | 0.74 | 0.79 | 0.58 | 1.16 | 1.05 | 0.84 | 0.89 |
time (sec) |
N/A | 0.007 | 0.007 | 0.233 | 0.185 | 0.246 | 0.059 | 0.271 | 10.109 |
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 | 11 | 11 | 10 | 11 | 11 | 8 | 11 | 12 |
N.S. |
1 | 1.22 | 1.22 | 1.11 | 1.22 | 1.22 | 0.89 | 1.22 | 1.33 |
time (sec) |
N/A | 0.001 | 0.000 | 0.049 | 0.185 | 0.234 | 0.019 | 0.273 | 0.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | A | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 52 | 68 | 47 | 51 | 26 | 30 | 0 |
N.S. |
1 | 0.00 | 1.44 | 1.89 | 1.31 | 1.42 | 0.72 | 0.83 | 0.00 |
time (sec) |
N/A | 0.000 | 0.054 | 0.735 | 0.239 | 0.254 | 0.143 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 38 | 25 | 37 | 0 | 39 | 48 | 36 | 0 |
N.S. |
1 | 2.00 | 1.32 | 1.95 | 0.00 | 2.05 | 2.53 | 1.89 | 0.00 |
time (sec) |
N/A | 2.707 | 0.077 | 0.341 | 0.000 | 0.251 | 8.214 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 66 | 23 | 17 | 22 | 16 | 19 | 52 | 18 |
N.S. |
1 | 2.87 | 1.00 | 0.74 | 0.96 | 0.70 | 0.83 | 2.26 | 0.78 |
time (sec) |
N/A | 0.201 | 0.738 | 0.235 | 0.240 | 0.279 | 0.048 | 0.283 | 10.257 |
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 | 21 | 35 | 21 | 19 | 36 | 17 | 20 | 18 | 18 |
N.S. |
1 | 1.67 | 1.00 | 0.90 | 1.71 | 0.81 | 0.95 | 0.86 | 0.86 |
time (sec) |
N/A | 0.019 | 0.041 | 0.045 | 0.187 | 0.252 | 0.057 | 0.284 | 0.076 |
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 | 18 | 16 | 18 | 21 | 19 | 15 | 19 | 22 |
N.S. |
1 | 0.86 | 0.76 | 0.86 | 1.00 | 0.90 | 0.71 | 0.90 | 1.05 |
time (sec) |
N/A | 0.027 | 0.091 | 0.119 | 0.218 | 0.265 | 0.047 | 0.272 | 10.403 |
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 | 22 | 32 | 26 | 30 | 60 | 29 | 27 | 29 | 29 |
N.S. |
1 | 1.45 | 1.18 | 1.36 | 2.73 | 1.32 | 1.23 | 1.32 | 1.32 |
time (sec) |
N/A | 0.018 | 0.011 | 0.114 | 0.180 | 0.247 | 0.068 | 0.285 | 10.153 |