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 | A | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 28 | 25 | 43 | 50 | 24 | 86 | 27 |
N.S. |
1 | 0.00 | 0.97 | 0.86 | 1.48 | 1.72 | 0.83 | 2.97 | 0.93 |
time (sec) |
N/A | 0.000 | 0.109 | 0.772 | 0.285 | 0.251 | 0.081 | 0.272 | 9.583 |
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 | 27 | 27 | 28 | 29 | 20 | 28 | 27 | 0 | 28 |
N.S. |
1 | 1.00 | 1.04 | 1.07 | 0.74 | 1.04 | 1.00 | 0.00 | 1.04 |
time (sec) |
N/A | 1.108 | 0.179 | 3.264 | 0.280 | 0.270 | 0.151 | 0.000 | 12.953 |
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 | 26 | 27 | 29 | 25 | 24 | 29 | 21 |
N.S. |
1 | 0.00 | 0.93 | 0.96 | 1.04 | 0.89 | 0.86 | 1.04 | 0.75 |
time (sec) |
N/A | 0.000 | 0.303 | 0.757 | 0.320 | 0.247 | 0.178 | 0.253 | 9.585 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | B | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 135 | 91 | 51 | 91 | 53 | 44 | 47 | 46 |
N.S. |
1 | 4.66 | 3.14 | 1.76 | 3.14 | 1.83 | 1.52 | 1.62 | 1.59 |
time (sec) |
N/A | 0.820 | 0.122 | 0.119 | 0.248 | 0.265 | 0.117 | 0.267 | 0.496 |
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 | 18 | 16 | 16 | 14 | 0 | 13 | 10 | 13 | 13 |
N.S. |
1 | 0.89 | 0.89 | 0.78 | 0.00 | 0.72 | 0.56 | 0.72 | 0.72 |
time (sec) |
N/A | 0.363 | 0.080 | 0.227 | 0.000 | 0.260 | 0.077 | 0.265 | 9.294 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | C | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 57407 | 82 | 80 | 80 | 75 | 162 | 0 |
N.S. |
1 | 0.00 | 1979.55 | 2.83 | 2.76 | 2.76 | 2.59 | 5.59 | 0.00 |
time (sec) |
N/A | 0.000 | 15.125 | 1.277 | 0.326 | 0.265 | 0.195 | 3.861 | 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 | 18 | 18 | 16 | 15 | 15 | 12 | 15 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.83 | 0.83 | 0.67 | 0.83 | 0.83 |
time (sec) |
N/A | 1.095 | 0.025 | 0.098 | 0.366 | 0.266 | 0.075 | 0.294 | 0.654 |
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 | 23 | 0 | 24 | 37 | 22 | 39 | 34 | 84 | 53 |
N.S. |
1 | 0.00 | 1.04 | 1.61 | 0.96 | 1.70 | 1.48 | 3.65 | 2.30 |
time (sec) |
N/A | 0.000 | 3.786 | 0.826 | 0.370 | 0.247 | 0.217 | 0.277 | 9.719 |
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 | 35 | 30 | 35 | 35 | 36 | 63 | 37 |
N.S. |
1 | 0.00 | 1.17 | 1.00 | 1.17 | 1.17 | 1.20 | 2.10 | 1.23 |
time (sec) |
N/A | 0.000 | 2.107 | 0.397 | 0.243 | 0.258 | 0.216 | 0.308 | 0.417 |
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 | 38 | 26 | 26 | 18 | 19 | 33 | 24 | 19 | 19 |
N.S. |
1 | 0.68 | 0.68 | 0.47 | 0.50 | 0.87 | 0.63 | 0.50 | 0.50 |
time (sec) |
N/A | 0.440 | 0.041 | 0.697 | 0.210 | 0.261 | 0.307 | 0.258 | 0.124 |
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 | 7 | 9 | 7 | 8 | 7 | 7 | 7 | 7 | 7 |
N.S. |
1 | 1.29 | 1.00 | 1.14 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.237 | 0.027 | 0.302 | 0.196 | 0.242 | 0.087 | 0.262 | 9.426 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | B | B | B | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 0 | 45 | 109 | 108 | 65 | 134 | 99 |
N.S. |
1 | 0.00 | 0.00 | 1.32 | 3.21 | 3.18 | 1.91 | 3.94 | 2.91 |
time (sec) |
N/A | 0.000 | 0.000 | 0.223 | 0.395 | 0.268 | 0.321 | 0.293 | 9.555 |
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 | 34 | 34 | 28 | 29 | 29 | 26 | 29 | 26 |
N.S. |
1 | 1.31 | 1.31 | 1.08 | 1.12 | 1.12 | 1.00 | 1.12 | 1.00 |
time (sec) |
N/A | 0.166 | 0.036 | 0.151 | 0.209 | 0.250 | 0.072 | 0.250 | 0.084 |
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 | 13 | 16 | 19 | 19 | 12 | 18 | 13 |
N.S. |
1 | 1.11 | 0.68 | 0.84 | 1.00 | 1.00 | 0.63 | 0.95 | 0.68 |
time (sec) |
N/A | 0.194 | 0.015 | 0.329 | 0.224 | 0.248 | 0.108 | 0.262 | 9.113 |
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 | 19 | 19 | 16 | 15 | 15 | 19 | 15 | 18 |
N.S. |
1 | 0.95 | 0.95 | 0.80 | 0.75 | 0.75 | 0.95 | 0.75 | 0.90 |
time (sec) |
N/A | 0.254 | 0.179 | 0.184 | 0.195 | 0.249 | 0.105 | 0.260 | 8.929 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | B | F(-1) | A | A | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 28 | 134 | 73 | 0 | 36 | 35 | 37 |
N.S. |
1 | 0.00 | 1.17 | 5.58 | 3.04 | 0.00 | 1.50 | 1.46 | 1.54 |
time (sec) |
N/A | 0.000 | 0.662 | 0.162 | 0.522 | 0.000 | 4.889 | 1.753 | 9.172 |
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 | 9 | 15 | 9 | 11 | 11 | 15 | 11 | 9 |
N.S. |
1 | 0.56 | 0.94 | 0.56 | 0.69 | 0.69 | 0.94 | 0.69 | 0.56 |
time (sec) |
N/A | 0.127 | 0.001 | 0.072 | 0.192 | 0.235 | 0.021 | 0.249 | 0.075 |
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 | 15 | 14 | 15 | 14 | 14 | 14 | 14 | 12 |
N.S. |
1 | 0.60 | 0.56 | 0.60 | 0.56 | 0.56 | 0.56 | 0.56 | 0.48 |
time (sec) |
N/A | 0.144 | 0.016 | 0.117 | 0.187 | 0.233 | 0.041 | 0.254 | 0.082 |
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 | 28 | 0 | 28 | 29 | 31 | 52 | 37 | 43 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.04 | 1.11 | 1.86 | 1.32 | 1.54 | 0.00 |
time (sec) |
N/A | 0.000 | 5.122 | 1.149 | 0.283 | 0.240 | 0.170 | 0.340 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 18 | 15 | 14 | 13 | 13 | 10 | 23 | 13 |
N.S. |
1 | 1.20 | 1.00 | 0.93 | 0.87 | 0.87 | 0.67 | 1.53 | 0.87 |
time (sec) |
N/A | 0.256 | 0.018 | 0.671 | 0.230 | 0.257 | 2.423 | 0.267 | 8.876 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 29 | 37 | 225 | 54 | 31 | 38 | 0 |
N.S. |
1 | 0.00 | 1.16 | 1.48 | 9.00 | 2.16 | 1.24 | 1.52 | 0.00 |
time (sec) |
N/A | 0.000 | 0.363 | 1.506 | 0.372 | 0.268 | 6.261 | 0.825 | 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 | 26 | 0 | 23 | 23 | 22 | 22 | 19 | 23 | 20 |
N.S. |
1 | 0.00 | 0.88 | 0.88 | 0.85 | 0.85 | 0.73 | 0.88 | 0.77 |
time (sec) |
N/A | 0.000 | 0.127 | 0.872 | 0.227 | 0.247 | 0.567 | 0.314 | 9.384 |
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 | 21 | 17 | 16 | 16 | 17 | 16 | 16 |
N.S. |
1 | 0.00 | 1.05 | 0.85 | 0.80 | 0.80 | 0.85 | 0.80 | 0.80 |
time (sec) |
N/A | 0.000 | 0.441 | 0.172 | 0.237 | 0.249 | 0.101 | 0.274 | 9.515 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 56 | 91 | 168 | 49 | 65 | 0 | 90 |
N.S. |
1 | 0.00 | 2.15 | 3.50 | 6.46 | 1.88 | 2.50 | 0.00 | 3.46 |
time (sec) |
N/A | 0.000 | 0.260 | 0.800 | 0.331 | 0.237 | 0.151 | 0.000 | 9.411 |
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 | 23 | 0 | 26 | 21 | 26 | 21 | 24 | 26 | 26 |
N.S. |
1 | 0.00 | 1.13 | 0.91 | 1.13 | 0.91 | 1.04 | 1.13 | 1.13 |
time (sec) |
N/A | 0.000 | 2.665 | 0.133 | 0.232 | 0.262 | 0.126 | 0.253 | 9.189 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 11 | 11 | 12 | 11 | 11 | 10 | 11 | 11 |
N.S. |
1 | 0.79 | 0.79 | 0.86 | 0.79 | 0.79 | 0.71 | 0.79 | 0.79 |
time (sec) |
N/A | 0.300 | 0.037 | 0.377 | 0.234 | 0.261 | 0.064 | 0.255 | 0.188 |
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 | 15 | 15 | 16 | 14 | 15 | 14 | 14 | 15 |
N.S. |
1 | 0.75 | 0.75 | 0.80 | 0.70 | 0.75 | 0.70 | 0.70 | 0.75 |
time (sec) |
N/A | 0.134 | 0.000 | 0.071 | 0.189 | 0.266 | 0.020 | 0.253 | 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 | 24 | 28 | 39 | 29 | 52 | 28 | 31 | 28 | 25 |
N.S. |
1 | 1.17 | 1.62 | 1.21 | 2.17 | 1.17 | 1.29 | 1.17 | 1.04 |
time (sec) |
N/A | 0.367 | 0.031 | 0.372 | 0.252 | 0.267 | 0.302 | 0.259 | 9.783 |
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 | 28 | 0 | 27 | 29 | 31 | 31 | 29 | 33 | 0 |
N.S. |
1 | 0.00 | 0.96 | 1.04 | 1.11 | 1.11 | 1.04 | 1.18 | 0.00 |
time (sec) |
N/A | 0.000 | 2.147 | 0.100 | 0.252 | 0.241 | 0.139 | 0.264 | 0.000 |
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 | 36 | 0 | 51 | 50 | 63 | 49 | 42 | 0 | 50 |
N.S. |
1 | 0.00 | 1.42 | 1.39 | 1.75 | 1.36 | 1.17 | 0.00 | 1.39 |
time (sec) |
N/A | 0.000 | 0.271 | 2.216 | 0.242 | 0.248 | 0.449 | 0.000 | 10.741 |
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 | 14 | 17 | 12 | 18 | 18 | 14 | 18 | 16 |
N.S. |
1 | 1.40 | 1.70 | 1.20 | 1.80 | 1.80 | 1.40 | 1.80 | 1.60 |
time (sec) |
N/A | 0.147 | 0.000 | 0.197 | 0.197 | 0.217 | 0.019 | 0.251 | 9.265 |
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 | 31 | 30 | 26 | 32 | 31 | 34 | 32 |
N.S. |
1 | 1.04 | 1.35 | 1.30 | 1.13 | 1.39 | 1.35 | 1.48 | 1.39 |
time (sec) |
N/A | 0.448 | 0.020 | 0.138 | 0.193 | 0.250 | 1.819 | 0.258 | 0.234 |
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 | 25 | 0 | 28 | 26 | 0 | 25 | 34 | 25 | 38 |
N.S. |
1 | 0.00 | 1.12 | 1.04 | 0.00 | 1.00 | 1.36 | 1.00 | 1.52 |
time (sec) |
N/A | 0.000 | 0.946 | 0.258 | 0.000 | 0.242 | 0.092 | 0.261 | 9.687 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 17 | 15 | 16 | 15 | 22 | 10 | 16 | 15 |
N.S. |
1 | 0.94 | 0.83 | 0.89 | 0.83 | 1.22 | 0.56 | 0.89 | 0.83 |
time (sec) |
N/A | 0.215 | 0.011 | 0.026 | 0.199 | 0.235 | 0.044 | 0.247 | 0.050 |
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 | 32 | 0 | 25 | 27 | 129 | 28 | 22 | 37 | 37 |
N.S. |
1 | 0.00 | 0.78 | 0.84 | 4.03 | 0.88 | 0.69 | 1.16 | 1.16 |
time (sec) |
N/A | 0.000 | 0.071 | 0.483 | 0.363 | 0.248 | 0.098 | 0.283 | 9.655 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 48 | 55 | 54 | 55 | 48 | 62 | 0 |
N.S. |
1 | 0.00 | 1.55 | 1.77 | 1.74 | 1.77 | 1.55 | 2.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.094 | 0.919 | 0.530 | 0.237 | 0.375 | 0.430 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | F(-1) | B | B | B | F(-1) | F(-1) |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 0 | 0 | 266 | 136 | 128 | 0 | 0 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 9.85 | 5.04 | 4.74 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 14.378 | 0.265 | 0.711 | 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 | 31 | 0 | 25 | 20 | 24 | 19 | 26 | 24 | 19 |
N.S. |
1 | 0.00 | 0.81 | 0.65 | 0.77 | 0.61 | 0.84 | 0.77 | 0.61 |
time (sec) |
N/A | 0.000 | 0.370 | 2.458 | 0.341 | 0.240 | 0.677 | 0.291 | 10.184 |
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 | 26 | 41 | 26 | 26 | 35 | 25 | 20 | 25 | 25 |
N.S. |
1 | 1.58 | 1.00 | 1.00 | 1.35 | 0.96 | 0.77 | 0.96 | 0.96 |
time (sec) |
N/A | 0.203 | 0.022 | 0.090 | 0.191 | 0.249 | 0.055 | 0.266 | 0.057 |
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 | 9 | 9 | 7 | 6 | 10 | 8 | 10 | 6 |
N.S. |
1 | 0.60 | 0.60 | 0.47 | 0.40 | 0.67 | 0.53 | 0.67 | 0.40 |
time (sec) |
N/A | 0.143 | 0.005 | 0.144 | 0.188 | 0.234 | 0.039 | 0.259 | 0.033 |
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 | 31 | 25 | 34 | 21 | 67 | 25 | 20 | 28 | 20 |
N.S. |
1 | 0.81 | 1.10 | 0.68 | 2.16 | 0.81 | 0.65 | 0.90 | 0.65 |
time (sec) |
N/A | 0.209 | 0.064 | 0.109 | 0.222 | 0.252 | 0.063 | 0.268 | 0.101 |
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 | 28 | 28 | 26 | 22 | 25 | 26 | 23 | 25 |
N.S. |
1 | 0.97 | 0.97 | 0.90 | 0.76 | 0.86 | 0.90 | 0.79 | 0.86 |
time (sec) |
N/A | 0.188 | 0.013 | 0.124 | 0.193 | 0.245 | 0.053 | 0.256 | 0.071 |
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 | 14 | 16 | 14 | 13 | 33 | 12 | 12 | 15 | 15 |
N.S. |
1 | 1.14 | 1.00 | 0.93 | 2.36 | 0.86 | 0.86 | 1.07 | 1.07 |
time (sec) |
N/A | 0.177 | 0.060 | 0.540 | 0.243 | 0.249 | 0.058 | 0.249 | 0.090 |
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 | 18 | 18 | 18 | 18 | 20 | 20 | 22 | 34 | 19 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 1.11 | 1.11 | 1.22 | 1.89 | 1.06 |
time (sec) |
N/A | 0.178 | 0.013 | 0.154 | 0.190 | 0.249 | 0.121 | 0.256 | 9.939 |
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 | 20 | 20 | 20 | 19 | 15 | 29 | 19 |
N.S. |
1 | 0.00 | 0.71 | 0.71 | 0.71 | 0.68 | 0.54 | 1.04 | 0.68 |
time (sec) |
N/A | 0.000 | 0.245 | 0.637 | 0.284 | 0.239 | 0.062 | 0.252 | 8.945 |
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 | 25 | 26 | 20 | 19 | 19 | 17 | 19 | 19 |
N.S. |
1 | 1.09 | 1.13 | 0.87 | 0.83 | 0.83 | 0.74 | 0.83 | 0.83 |
time (sec) |
N/A | 0.160 | 0.012 | 0.092 | 0.195 | 0.239 | 0.068 | 0.253 | 8.740 |
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 | 20 | 0 | 20 | 19 | 0 | 18 | 15 | 18 | 17 |
N.S. |
1 | 0.00 | 1.00 | 0.95 | 0.00 | 0.90 | 0.75 | 0.90 | 0.85 |
time (sec) |
N/A | 0.000 | 0.439 | 0.355 | 0.000 | 0.236 | 1.620 | 0.260 | 8.953 |
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 | 25 | 34 | 25 | 23 | 55 | 24 | 29 | 30 | 29 |
N.S. |
1 | 1.36 | 1.00 | 0.92 | 2.20 | 0.96 | 1.16 | 1.20 | 1.16 |
time (sec) |
N/A | 0.264 | 0.081 | 0.106 | 0.314 | 0.238 | 0.104 | 0.252 | 0.106 |
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 | 24 | 0 | 22 | 23 | 25 | 22 | 0 | 25 | 25 |
N.S. |
1 | 0.00 | 0.92 | 0.96 | 1.04 | 0.92 | 0.00 | 1.04 | 1.04 |
time (sec) |
N/A | 0.000 | 0.081 | 14.408 | 0.315 | 0.247 | 0.000 | 0.293 | 9.608 |
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 | 12 | 12 | 12 | 9 | 8 | 17 | 8 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 0.67 | 1.42 | 0.67 | 0.67 | 0.67 |
time (sec) |
N/A | 0.169 | 0.012 | 0.240 | 0.187 | 0.237 | 0.057 | 0.256 | 8.798 |
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 | 18 | 20 | 30 | 30 | 17 | 22 | 31 |
N.S. |
1 | 1.21 | 0.95 | 1.05 | 1.58 | 1.58 | 0.89 | 1.16 | 1.63 |
time (sec) |
N/A | 0.616 | 0.145 | 0.773 | 0.309 | 0.252 | 0.048 | 0.260 | 9.005 |
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 | 29 | 0 | 42 | 36 | 34 | 34 | 48 | 48 | 0 |
N.S. |
1 | 0.00 | 1.45 | 1.24 | 1.17 | 1.17 | 1.66 | 1.66 | 0.00 |
time (sec) |
N/A | 0.000 | 1.286 | 3.048 | 0.325 | 0.243 | 0.236 | 0.264 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F(-1) | A | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 39 | 41 | 0 | 46 | 46 | 0 | 51 |
N.S. |
1 | 0.00 | 1.39 | 1.46 | 0.00 | 1.64 | 1.64 | 0.00 | 1.82 |
time (sec) |
N/A | 0.000 | 0.462 | 13.885 | 0.000 | 0.262 | 0.723 | 0.000 | 9.357 |
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 | 23 | 21 | 22 | 23 | 29 | 37 | 20 |
N.S. |
1 | 0.00 | 0.68 | 0.62 | 0.65 | 0.68 | 0.85 | 1.09 | 0.59 |
time (sec) |
N/A | 0.000 | 0.156 | 0.439 | 0.255 | 0.231 | 7.970 | 0.259 | 8.916 |
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 | 20 | 20 | 20 | 19 | 227 | 18 | 17 | 18 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 11.35 | 0.90 | 0.85 | 0.90 | 0.90 |
time (sec) |
N/A | 0.378 | 0.036 | 0.865 | 0.378 | 0.243 | 0.071 | 0.287 | 9.238 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 147 | 21 | 52 | 0 | 52 | 56 | 62 | 48 |
N.S. |
1 | 4.74 | 0.68 | 1.68 | 0.00 | 1.68 | 1.81 | 2.00 | 1.55 |
time (sec) |
N/A | 0.590 | 0.342 | 0.818 | 0.000 | 0.254 | 93.397 | 0.362 | 10.016 |
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 | 33 | 58 | 38 | 50 | 45 | 45 | 51 | 45 | 40 |
N.S. |
1 | 1.76 | 1.15 | 1.52 | 1.36 | 1.36 | 1.55 | 1.36 | 1.21 |
time (sec) |
N/A | 0.256 | 0.167 | 0.327 | 0.201 | 0.246 | 0.112 | 0.254 | 0.083 |
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 | 23 | 0 | 17 | 17 | 16 | 16 | 15 | 16 | 17 |
N.S. |
1 | 0.00 | 0.74 | 0.74 | 0.70 | 0.70 | 0.65 | 0.70 | 0.74 |
time (sec) |
N/A | 0.000 | 1.049 | 0.041 | 0.235 | 0.248 | 0.088 | 0.253 | 9.161 |
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 | 16 | 19 | 19 | 20 | 24 | 27 | 24 | 23 | 702 |
N.S. |
1 | 1.19 | 1.19 | 1.25 | 1.50 | 1.69 | 1.50 | 1.44 | 43.88 |
time (sec) |
N/A | 0.177 | 0.008 | 0.111 | 0.193 | 0.252 | 0.187 | 0.250 | 9.632 |
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 | 20 | 20 | 31 | 17 | 23 | 15 | 17 | 44 | 16 |
N.S. |
1 | 1.00 | 1.55 | 0.85 | 1.15 | 0.75 | 0.85 | 2.20 | 0.80 |
time (sec) |
N/A | 0.188 | 0.065 | 0.109 | 0.280 | 0.251 | 0.097 | 0.257 | 10.434 |
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 | 11 | 9 | 8 | 7 | 7 | 5 | 7 | 8 |
N.S. |
1 | 0.48 | 0.39 | 0.35 | 0.30 | 0.30 | 0.22 | 0.30 | 0.35 |
time (sec) |
N/A | 0.124 | 0.001 | 0.005 | 0.201 | 0.246 | 0.029 | 0.252 | 0.032 |
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 | 14 | 78 | 20 | 13 | 46 | 12 | 15 | 16 | 10 |
N.S. |
1 | 5.57 | 1.43 | 0.93 | 3.29 | 0.86 | 1.07 | 1.14 | 0.71 |
time (sec) |
N/A | 0.276 | 0.021 | 0.473 | 0.286 | 0.238 | 0.078 | 0.253 | 10.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 27 | 890 | 28 | 27 | 27 | 27 | 27 | 27 |
N.S. |
1 | 1.29 | 42.38 | 1.33 | 1.29 | 1.29 | 1.29 | 1.29 | 1.29 |
time (sec) |
N/A | 0.961 | 0.311 | 0.992 | 0.237 | 0.244 | 0.197 | 0.291 | 9.465 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 217 | 85 | 84 | 69 | 42 | 68 | 0 |
N.S. |
1 | 0.00 | 7.23 | 2.83 | 2.80 | 2.30 | 1.40 | 2.27 | 0.00 |
time (sec) |
N/A | 0.000 | 0.069 | 0.862 | 0.258 | 0.256 | 0.552 | 0.265 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | F(-2) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 46 | 34 | 66 | 39 | 0 | 53 | 38 |
N.S. |
1 | 0.00 | 2.00 | 1.48 | 2.87 | 1.70 | 0.00 | 2.30 | 1.65 |
time (sec) |
N/A | 0.000 | 0.813 | 1.200 | 0.318 | 0.256 | 0.000 | 0.264 | 9.780 |
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 | 11 | 11 | 9 | 9 | 9 | 8 | 9 | 8 |
N.S. |
1 | 0.69 | 0.69 | 0.56 | 0.56 | 0.56 | 0.50 | 0.56 | 0.50 |
time (sec) |
N/A | 0.132 | 0.001 | 0.005 | 0.187 | 0.225 | 0.020 | 0.256 | 0.034 |
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 | 26 | 28 | 81 | 103 | 39 | 212 | 49 |
N.S. |
1 | 0.00 | 1.00 | 1.08 | 3.12 | 3.96 | 1.50 | 8.15 | 1.88 |
time (sec) |
N/A | 0.000 | 0.224 | 11.493 | 0.263 | 0.262 | 0.146 | 0.307 | 9.697 |
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 | 27 | 26 | 52 | 58 | 29 | 927 | 60 |
N.S. |
1 | 0.00 | 1.04 | 1.00 | 2.00 | 2.23 | 1.12 | 35.65 | 2.31 |
time (sec) |
N/A | 0.000 | 5.266 | 1.394 | 0.324 | 0.254 | 0.153 | 0.346 | 9.885 |
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 | 17 | 17 | 18 | 17 | 21 | 14 | 17 | 16 |
N.S. |
1 | 0.85 | 0.85 | 0.90 | 0.85 | 1.05 | 0.70 | 0.85 | 0.80 |
time (sec) |
N/A | 0.175 | 0.006 | 0.049 | 0.193 | 0.263 | 0.067 | 0.256 | 8.964 |
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 | 22 | 22 | 21 | 19 | 21 | 27 | 32 | 20 |
N.S. |
1 | 0.92 | 0.92 | 0.88 | 0.79 | 0.88 | 1.12 | 1.33 | 0.83 |
time (sec) |
N/A | 0.545 | 0.208 | 5.449 | 0.235 | 0.270 | 0.136 | 0.286 | 9.276 |
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 | 39 | 28 | 35 | 35 | 31 | 36 | 38 | 35 |
N.S. |
1 | 1.50 | 1.08 | 1.35 | 1.35 | 1.19 | 1.38 | 1.46 | 1.35 |
time (sec) |
N/A | 0.193 | 0.013 | 0.135 | 0.198 | 0.232 | 0.250 | 0.253 | 9.394 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 10 | 10 | 8 | 7 | 7 | 8 | 7 | 7 |
N.S. |
1 | 0.83 | 0.83 | 0.67 | 0.58 | 0.58 | 0.67 | 0.58 | 0.58 |
time (sec) |
N/A | 0.124 | 0.000 | 0.116 | 0.195 | 0.238 | 0.023 | 0.250 | 0.016 |
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 | 24 | 22 | 20 | 21 | 26 | 24 | 17 | 20 | 20 |
N.S. |
1 | 0.92 | 0.83 | 0.88 | 1.08 | 1.00 | 0.71 | 0.83 | 0.83 |
time (sec) |
N/A | 0.374 | 0.079 | 0.142 | 0.229 | 0.236 | 0.038 | 0.260 | 9.395 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 21 | 12 | 17 | 20 | 16 | 17 | 16 | 13 |
N.S. |
1 | 1.50 | 0.86 | 1.21 | 1.43 | 1.14 | 1.21 | 1.14 | 0.93 |
time (sec) |
N/A | 0.153 | 0.021 | 0.072 | 0.207 | 0.247 | 0.052 | 0.257 | 9.206 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | B | A | F(-2) | B | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 42 | 10690 | 81 | 45 | 0 | 86 | 45 |
N.S. |
1 | 0.00 | 1.45 | 368.62 | 2.79 | 1.55 | 0.00 | 2.97 | 1.55 |
time (sec) |
N/A | 0.000 | 0.240 | 27.540 | 0.281 | 0.250 | 0.000 | 2.716 | 9.905 |
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 | 34 | 27 | 32 | 40 | 32 | 27 | 40 | 31 |
N.S. |
1 | 1.55 | 1.23 | 1.45 | 1.82 | 1.45 | 1.23 | 1.82 | 1.41 |
time (sec) |
N/A | 0.258 | 0.101 | 0.064 | 0.207 | 0.235 | 0.102 | 0.256 | 9.067 |
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 | 9 | 9 | 9 | 7 | 6 | 6 | 5 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 0.67 | 0.67 | 0.56 | 0.67 | 0.67 |
time (sec) |
N/A | 0.149 | 0.019 | 0.119 | 0.209 | 0.240 | 0.040 | 0.247 | 9.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 22 | 20 | 55 | 141 | 54 | 65 | 141 | 20 |
N.S. |
1 | 1.10 | 1.00 | 2.75 | 7.05 | 2.70 | 3.25 | 7.05 | 1.00 |
time (sec) |
N/A | 0.150 | 0.006 | 0.099 | 0.218 | 0.221 | 0.056 | 0.259 | 9.002 |
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 | 25 | 22 | 18 | 17 | 18 | 29 | 14 | 18 | 16 |
N.S. |
1 | 0.88 | 0.72 | 0.68 | 0.72 | 1.16 | 0.56 | 0.72 | 0.64 |
time (sec) |
N/A | 0.240 | 0.011 | 0.060 | 0.213 | 0.229 | 0.068 | 0.252 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | C | C | C | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 56 | 22 | 31 | 91 | 57 | 53 | 92 | 29 |
N.S. |
1 | 2.55 | 1.00 | 1.41 | 4.14 | 2.59 | 2.41 | 4.18 | 1.32 |
time (sec) |
N/A | 0.309 | 0.070 | 0.967 | 0.197 | 0.260 | 0.143 | 0.261 | 9.671 |
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 | 25 | 23 | 23 | 22 | 20 | 21 | 22 | 0 | 23 |
N.S. |
1 | 0.92 | 0.92 | 0.88 | 0.80 | 0.84 | 0.88 | 0.00 | 0.92 |
time (sec) |
N/A | 0.748 | 0.827 | 3.689 | 0.294 | 0.255 | 2.261 | 0.000 | 9.751 |
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 | 19 | 43 | 26 | 31 | 28 | 28 | 34 | 28 | 36 |
N.S. |
1 | 2.26 | 1.37 | 1.63 | 1.47 | 1.47 | 1.79 | 1.47 | 1.89 |
time (sec) |
N/A | 0.211 | 0.202 | 0.093 | 0.191 | 0.242 | 0.068 | 0.253 | 0.076 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 85 | 32 | 63 | 99 | 62 | 83 | 81 | 39 |
N.S. |
1 | 2.43 | 0.91 | 1.80 | 2.83 | 1.77 | 2.37 | 2.31 | 1.11 |
time (sec) |
N/A | 0.266 | 0.047 | 0.304 | 0.291 | 0.270 | 0.365 | 0.265 | 9.400 |
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 | 25 | 12 | 13 | 37 | 12 | 8 | 23 | 10 |
N.S. |
1 | 0.86 | 0.41 | 0.45 | 1.28 | 0.41 | 0.28 | 0.79 | 0.34 |
time (sec) |
N/A | 0.234 | 0.019 | 0.387 | 0.198 | 0.254 | 0.056 | 0.249 | 0.105 |
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 | 21 | 0 | 22 | 22 | 22 | 22 | 26 | 22 | 21 |
N.S. |
1 | 0.00 | 1.05 | 1.05 | 1.05 | 1.05 | 1.24 | 1.05 | 1.00 |
time (sec) |
N/A | 0.000 | 0.424 | 1.531 | 0.246 | 0.240 | 0.139 | 0.272 | 9.064 |
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 | 30 | 69 | 36 | 39 | 80 | 31 | 37 | 38 | 37 |
N.S. |
1 | 2.30 | 1.20 | 1.30 | 2.67 | 1.03 | 1.23 | 1.27 | 1.23 |
time (sec) |
N/A | 0.338 | 0.133 | 0.179 | 0.195 | 0.237 | 0.147 | 0.265 | 0.529 |
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 | 19 | 20 | 17 | 18 | 25 | 17 | 14 | 17 | 16 |
N.S. |
1 | 1.05 | 0.89 | 0.95 | 1.32 | 0.89 | 0.74 | 0.89 | 0.84 |
time (sec) |
N/A | 0.184 | 0.096 | 0.138 | 0.215 | 0.252 | 0.063 | 0.251 | 9.019 |
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 | 25 | 28 | 27 | 20 | 19 | 19 | 19 | 0 | 22 |
N.S. |
1 | 1.12 | 1.08 | 0.80 | 0.76 | 0.76 | 0.76 | 0.00 | 0.88 |
time (sec) |
N/A | 0.242 | 0.554 | 0.304 | 0.266 | 0.238 | 0.115 | 0.000 | 9.250 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 22 | 20 | 19 | 27 | 22 | 27 | 18 |
N.S. |
1 | 1.00 | 0.79 | 0.71 | 0.68 | 0.96 | 0.79 | 0.96 | 0.64 |
time (sec) |
N/A | 0.187 | 0.008 | 0.104 | 0.198 | 0.268 | 0.073 | 0.256 | 0.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 9 | 9 | 10 | 9 | 9 | 8 | 9 | 9 |
N.S. |
1 | 0.64 | 0.64 | 0.71 | 0.64 | 0.64 | 0.57 | 0.64 | 0.64 |
time (sec) |
N/A | 0.189 | 0.026 | 0.357 | 0.237 | 0.240 | 0.058 | 0.255 | 0.261 |
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 | 27 | 48 | 50 | 21 | 28 | 28 | 63 | 29 | 17 |
N.S. |
1 | 1.78 | 1.85 | 0.78 | 1.04 | 1.04 | 2.33 | 1.07 | 0.63 |
time (sec) |
N/A | 0.171 | 0.013 | 0.241 | 0.217 | 0.254 | 0.105 | 0.258 | 8.978 |
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 | 26 | 0 | 25 | 22 | 35 | 37 | 17 | 53 | 45 |
N.S. |
1 | 0.00 | 0.96 | 0.85 | 1.35 | 1.42 | 0.65 | 2.04 | 1.73 |
time (sec) |
N/A | 0.000 | 0.095 | 0.763 | 0.244 | 0.247 | 0.124 | 0.272 | 9.979 |
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 | 32 | 0 | 35 | 35 | 35 | 32 | 0 | 37 | 33 |
N.S. |
1 | 0.00 | 1.09 | 1.09 | 1.09 | 1.00 | 0.00 | 1.16 | 1.03 |
time (sec) |
N/A | 0.000 | 0.792 | 115.918 | 0.370 | 0.254 | 0.000 | 0.283 | 8.921 |
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 | 46 | 40 | 46 | 44 | 39 | 42 | 0 |
N.S. |
1 | 0.00 | 1.92 | 1.67 | 1.92 | 1.83 | 1.62 | 1.75 | 0.00 |
time (sec) |
N/A | 0.000 | 0.051 | 1.230 | 0.322 | 0.268 | 0.250 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 47 | 21 | 23 | 31 | 20 | 19 | 20 | 17 |
N.S. |
1 | 1.81 | 0.81 | 0.88 | 1.19 | 0.77 | 0.73 | 0.77 | 0.65 |
time (sec) |
N/A | 0.205 | 0.121 | 0.072 | 0.235 | 0.244 | 0.070 | 0.255 | 8.871 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | A | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 50 | 56 | 52 | 64 | 73 | 64 | 25 |
N.S. |
1 | 0.00 | 2.00 | 2.24 | 2.08 | 2.56 | 2.92 | 2.56 | 1.00 |
time (sec) |
N/A | 0.000 | 5.038 | 16.027 | 0.343 | 0.257 | 0.082 | 0.272 | 9.600 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 26 | 26 | 53 | 0 | 57 | 51 | 0 | 0 |
N.S. |
1 | 0.84 | 0.84 | 1.71 | 0.00 | 1.84 | 1.65 | 0.00 | 0.00 |
time (sec) |
N/A | 0.995 | 0.407 | 1.388 | 0.000 | 0.263 | 3.932 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 52 | 51 | 39 | 49 | 165 | 51 | 202 | 52 |
N.S. |
1 | 2.36 | 2.32 | 1.77 | 2.23 | 7.50 | 2.32 | 9.18 | 2.36 |
time (sec) |
N/A | 0.703 | 0.570 | 7.688 | 0.263 | 0.250 | 0.432 | 2.336 | 9.250 |
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 | 61 | 34 | 44 | 47 | 34 | 39 | 54 | 46 |
N.S. |
1 | 1.85 | 1.03 | 1.33 | 1.42 | 1.03 | 1.18 | 1.64 | 1.39 |
time (sec) |
N/A | 2.740 | 0.101 | 2.329 | 0.315 | 0.241 | 0.237 | 0.275 | 9.607 |
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 | 12 | 10 | 9 | 8 | 8 | 8 | 9 | 8 |
N.S. |
1 | 1.20 | 1.00 | 0.90 | 0.80 | 0.80 | 0.80 | 0.90 | 0.80 |
time (sec) |
N/A | 0.136 | 0.001 | 0.031 | 0.202 | 0.233 | 0.030 | 0.249 | 0.021 |