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 | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 37 | 26 | 28 | 69 | 24 | 26 | 24 | 23 |
N.S. |
1 | 1.68 | 1.18 | 1.27 | 3.14 | 1.09 | 1.18 | 1.09 | 1.05 |
time (sec) |
N/A | 0.245 | 0.180 | 0.072 | 0.199 | 0.257 | 0.083 | 0.282 | 0.059 |
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 | 17 | 0 | 15 | 15 | 14 | 14 | 14 | 14 | 14 |
N.S. |
1 | 0.00 | 0.88 | 0.88 | 0.82 | 0.82 | 0.82 | 0.82 | 0.82 |
time (sec) |
N/A | 0.000 | 0.370 | 0.169 | 0.324 | 0.255 | 0.085 | 0.284 | 0.578 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | F(-2) | A | A | A | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 23 | 129 | 0 | 21 | 20 | 24 | 24 |
N.S. |
1 | 0.00 | 0.96 | 5.38 | 0.00 | 0.88 | 0.83 | 1.00 | 1.00 |
time (sec) |
N/A | 0.000 | 2.365 | 0.147 | 0.000 | 0.249 | 5.638 | 0.923 | 12.371 |
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 | 28 | 25 | 21 | 22 | 21 | 21 | 20 | 28 | 0 |
N.S. |
1 | 0.89 | 0.75 | 0.79 | 0.75 | 0.75 | 0.71 | 1.00 | 0.00 |
time (sec) |
N/A | 0.556 | 0.069 | 3.260 | 0.304 | 0.257 | 0.073 | 0.300 | 0.000 |
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 | 19 | 64 | 17 | 18 | 44 | 16 | 15 | 22 | 46 |
N.S. |
1 | 3.37 | 0.89 | 0.95 | 2.32 | 0.84 | 0.79 | 1.16 | 2.42 |
time (sec) |
N/A | 0.277 | 0.153 | 0.092 | 0.365 | 0.282 | 0.157 | 0.372 | 12.138 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 164 | 33 | 31 | 50 | 52 | 31 | 78 | 0 |
N.S. |
1 | 4.56 | 0.92 | 0.86 | 1.39 | 1.44 | 0.86 | 2.17 | 0.00 |
time (sec) |
N/A | 1.737 | 0.110 | 5.678 | 0.321 | 0.263 | 0.082 | 0.285 | 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 | 24 | 25 | 25 | 25 | 24 | 24 | 20 | 24 | 24 |
N.S. |
1 | 1.04 | 1.04 | 1.04 | 1.00 | 1.00 | 0.83 | 1.00 | 1.00 |
time (sec) |
N/A | 0.718 | 0.163 | 0.489 | 0.352 | 0.246 | 0.115 | 0.268 | 11.648 |
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 | 27 | 27 | 18 | 15 | 15 | 27 | 15 | 22 |
N.S. |
1 | 1.17 | 1.17 | 0.78 | 0.65 | 0.65 | 1.17 | 0.65 | 0.96 |
time (sec) |
N/A | 0.159 | 0.004 | 0.071 | 0.189 | 0.242 | 0.122 | 0.259 | 0.047 |
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 | 17 | 17 | 17 | 16 | 16 | 15 | 16 | 16 |
N.S. |
1 | 1.06 | 1.06 | 1.06 | 1.00 | 1.00 | 0.94 | 1.00 | 1.00 |
time (sec) |
N/A | 0.141 | 0.004 | 0.037 | 0.195 | 0.254 | 0.043 | 0.256 | 11.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 51 | 18 | 21 | 372 | 21 | 20 | 35 | 16 |
N.S. |
1 | 2.83 | 1.00 | 1.17 | 20.67 | 1.17 | 1.11 | 1.94 | 0.89 |
time (sec) |
N/A | 0.522 | 1.417 | 0.086 | 0.279 | 0.268 | 0.097 | 0.277 | 11.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 29 | 29 | 22 | 31 | 20 | 19 | 20 | 20 |
N.S. |
1 | 1.45 | 1.45 | 1.10 | 1.55 | 1.00 | 0.95 | 1.00 | 1.00 |
time (sec) |
N/A | 0.233 | 0.114 | 0.137 | 0.215 | 0.255 | 0.081 | 0.291 | 11.174 |
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 | 30 | 28 | 29 | 37 | 27 | 36 | 34 | 0 | 29 |
N.S. |
1 | 0.93 | 0.97 | 1.23 | 0.90 | 1.20 | 1.13 | 0.00 | 0.97 |
time (sec) |
N/A | 1.894 | 1.669 | 131.604 | 0.294 | 0.267 | 0.334 | 0.000 | 11.316 |
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 | 14 | 0 | 14 | 15 | 15 | 18 | 15 | 18 | 18 |
N.S. |
1 | 0.00 | 1.00 | 1.07 | 1.07 | 1.29 | 1.07 | 1.29 | 1.29 |
time (sec) |
N/A | 0.000 | 0.122 | 3.024 | 0.322 | 0.252 | 0.059 | 0.277 | 11.311 |
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 | 35 | 0 | 43 | 48 | 44 | 42 | 60 | 54 | 179 |
N.S. |
1 | 0.00 | 1.23 | 1.37 | 1.26 | 1.20 | 1.71 | 1.54 | 5.11 |
time (sec) |
N/A | 0.000 | 0.109 | 0.235 | 0.239 | 0.253 | 0.127 | 0.287 | 11.157 |
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 | 19 | 19 | 20 | 19 | 21 | 17 | 19 | 19 |
N.S. |
1 | 0.86 | 0.86 | 0.91 | 0.86 | 0.95 | 0.77 | 0.86 | 0.86 |
time (sec) |
N/A | 0.176 | 0.002 | 0.049 | 0.186 | 0.256 | 0.033 | 0.262 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 28 | 25 | 585 | 42 | 24 | 44 | 0 |
N.S. |
1 | 0.00 | 1.08 | 0.96 | 22.50 | 1.62 | 0.92 | 1.69 | 0.00 |
time (sec) |
N/A | 0.000 | 1.909 | 0.500 | 0.343 | 0.280 | 0.102 | 0.348 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 55 | 24 | 23 | 42 | 21 | 27 | 21 | 22 |
N.S. |
1 | 2.39 | 1.04 | 1.00 | 1.83 | 0.91 | 1.17 | 0.91 | 0.96 |
time (sec) |
N/A | 1.160 | 1.511 | 0.299 | 0.226 | 0.249 | 0.352 | 0.275 | 10.991 |
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 | 21 | 20 | 20 | 19 | 22 | 20 |
N.S. |
1 | 0.95 | 0.95 | 0.95 | 0.91 | 0.91 | 0.86 | 1.00 | 0.91 |
time (sec) |
N/A | 0.357 | 0.023 | 0.108 | 0.194 | 0.250 | 0.505 | 0.278 | 11.206 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 82 | 68 | 99 | 189 | 152 | 104 | 205 | 170 |
N.S. |
1 | 3.73 | 3.09 | 4.50 | 8.59 | 6.91 | 4.73 | 9.32 | 7.73 |
time (sec) |
N/A | 1.441 | 0.122 | 0.751 | 0.233 | 0.276 | 0.132 | 0.306 | 11.612 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | B | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 20 | 27 | 107 | 26 | 39 | 38 | 41 |
N.S. |
1 | 0.00 | 1.00 | 1.35 | 5.35 | 1.30 | 1.95 | 1.90 | 2.05 |
time (sec) |
N/A | 0.000 | 0.600 | 0.489 | 0.258 | 0.262 | 0.210 | 0.302 | 11.214 |
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 | 15 | 12 | 15 | 14 | 25 | 10 | 14 | 28 |
N.S. |
1 | 1.15 | 0.92 | 1.15 | 1.08 | 1.92 | 0.77 | 1.08 | 2.15 |
time (sec) |
N/A | 0.227 | 0.210 | 0.518 | 0.187 | 0.268 | 0.057 | 0.280 | 11.228 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 54 | 22 | 20 | 0 | 23 | 19 | 27 | 18 |
N.S. |
1 | 2.45 | 1.00 | 0.91 | 0.00 | 1.05 | 0.86 | 1.23 | 0.82 |
time (sec) |
N/A | 0.369 | 0.082 | 0.102 | 0.000 | 0.260 | 0.122 | 0.272 | 11.328 |
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 | 28 | 0 | 42 | 28 | 0 | 40 | 34 | 0 | 73 |
N.S. |
1 | 0.00 | 1.50 | 1.00 | 0.00 | 1.43 | 1.21 | 0.00 | 2.61 |
time (sec) |
N/A | 0.000 | 0.242 | 4.853 | 0.000 | 0.265 | 6.118 | 0.000 | 12.041 |
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 | 25 | 0 | 25 | 24 | 26 | 22 | 20 | 0 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.96 | 1.04 | 0.88 | 0.80 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.116 | 2.669 | 0.266 | 0.257 | 0.155 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | B | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 42 | 42 | 63 | 42 | 41 | 42 | 121 |
N.S. |
1 | 0.00 | 1.40 | 1.40 | 2.10 | 1.40 | 1.37 | 1.40 | 4.03 |
time (sec) |
N/A | 0.000 | 0.079 | 3.027 | 0.452 | 0.282 | 6.819 | 1.021 | 13.668 |
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 | 99 | 32 | 37 | 147 | 44 | 32 | 42 | 40 |
N.S. |
1 | 3.54 | 1.14 | 1.32 | 5.25 | 1.57 | 1.14 | 1.50 | 1.43 |
time (sec) |
N/A | 0.583 | 0.122 | 0.186 | 0.234 | 0.285 | 0.132 | 0.265 | 12.132 |
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 | 35 | 101 | 41 | 27 | 30 | 28 | 26 | 29 | 33 |
N.S. |
1 | 2.89 | 1.17 | 0.77 | 0.86 | 0.80 | 0.74 | 0.83 | 0.94 |
time (sec) |
N/A | 0.488 | 2.524 | 0.168 | 0.474 | 0.263 | 0.242 | 0.314 | 12.495 |
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 | 15 | 54 | 13 | 13 | 12 | 12 | 12 | 0 | 12 |
N.S. |
1 | 3.60 | 0.87 | 0.87 | 0.80 | 0.80 | 0.80 | 0.00 | 0.80 |
time (sec) |
N/A | 0.303 | 0.146 | 0.165 | 0.231 | 0.281 | 7.346 | 0.000 | 12.421 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | F | A | A | A | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 0 | 35 | 0 | 32 | 27 | 53 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.09 | 0.00 | 1.00 | 0.84 | 1.66 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 1.941 | 0.000 | 0.259 | 0.498 | 0.303 | 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 | 24 | 0 | 31 | 23 | 26 | 28 | 22 | 26 | 46 |
N.S. |
1 | 0.00 | 1.29 | 0.96 | 1.08 | 1.17 | 0.92 | 1.08 | 1.92 |
time (sec) |
N/A | 0.000 | 0.347 | 2.623 | 0.205 | 0.255 | 0.087 | 0.304 | 12.740 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 34 | 43 | 43 | 78 | 62 | 60 | 48 | 32 |
N.S. |
1 | 1.31 | 1.65 | 1.65 | 3.00 | 2.38 | 2.31 | 1.85 | 1.23 |
time (sec) |
N/A | 1.543 | 0.149 | 0.288 | 0.289 | 0.265 | 0.243 | 0.314 | 12.456 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | F | A | F(-1) | A | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 0 | 19 | 0 | 18 | 0 | 18 | 19 |
N.S. |
1 | 0.00 | 0.00 | 0.73 | 0.00 | 0.69 | 0.00 | 0.69 | 0.73 |
time (sec) |
N/A | 0.000 | 0.000 | 0.463 | 0.000 | 0.262 | 0.000 | 0.290 | 12.694 |
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 | 24 | 25 | 22 | 21 | 22 | 22 | 21 | 20 |
N.S. |
1 | 0.86 | 0.89 | 0.79 | 0.75 | 0.79 | 0.79 | 0.75 | 0.71 |
time (sec) |
N/A | 0.155 | 0.009 | 0.079 | 0.190 | 0.250 | 0.051 | 0.285 | 0.052 |
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 | 5 | 5 | 6 | 5 | 5 | 3 | 5 | 5 |
N.S. |
1 | 0.45 | 0.45 | 0.55 | 0.45 | 0.45 | 0.27 | 0.45 | 0.45 |
time (sec) |
N/A | 0.121 | 0.000 | 0.032 | 0.180 | 0.249 | 0.020 | 0.284 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 30 | 31 | 25 | 26 | 26 | 34 | 26 | 24 |
N.S. |
1 | 0.83 | 0.86 | 0.69 | 0.72 | 0.72 | 0.94 | 0.72 | 0.67 |
time (sec) |
N/A | 0.176 | 0.015 | 0.156 | 0.184 | 0.266 | 0.088 | 0.263 | 0.060 |
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 | 18 | 18 | 17 | 17 | 14 | 17 | 17 |
N.S. |
1 | 0.90 | 0.90 | 0.90 | 0.85 | 0.85 | 0.70 | 0.85 | 0.85 |
time (sec) |
N/A | 0.180 | 0.012 | 0.107 | 0.177 | 0.266 | 0.059 | 0.261 | 11.778 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 28 | 24 | 33 | 29 | 31 | 56 | 35 | 31 |
N.S. |
1 | 1.27 | 1.09 | 1.50 | 1.32 | 1.41 | 2.55 | 1.59 | 1.41 |
time (sec) |
N/A | 1.401 | 0.061 | 0.848 | 0.222 | 0.269 | 0.409 | 0.328 | 12.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 52 | 45 | 58 | 38 | 51 | 36 | 60 | 36 |
N.S. |
1 | 1.58 | 1.36 | 1.76 | 1.15 | 1.55 | 1.09 | 1.82 | 1.09 |
time (sec) |
N/A | 4.102 | 0.188 | 87.266 | 0.323 | 0.260 | 0.579 | 0.328 | 11.663 |
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 | 23 | 0 | 32 | 35 | 44 | 44 | 29 | 78 | 32 |
N.S. |
1 | 0.00 | 1.39 | 1.52 | 1.91 | 1.91 | 1.26 | 3.39 | 1.39 |
time (sec) |
N/A | 0.000 | 0.044 | 2.258 | 0.310 | 0.251 | 0.070 | 0.754 | 11.946 |
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 | 21 | 36 | 32 | 22 | 31 | 43 | 29 | 24 | 24 |
N.S. |
1 | 1.71 | 1.52 | 1.05 | 1.48 | 2.05 | 1.38 | 1.14 | 1.14 |
time (sec) |
N/A | 0.244 | 0.024 | 0.082 | 0.183 | 0.250 | 0.101 | 0.280 | 0.093 |
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 | 29 | 28 | 28 | 28 | 25 | 42 | 24 | 59 | 27 |
N.S. |
1 | 0.97 | 0.97 | 0.97 | 0.86 | 1.45 | 0.83 | 2.03 | 0.93 |
time (sec) |
N/A | 0.398 | 0.109 | 1.445 | 0.211 | 0.256 | 0.062 | 0.296 | 11.271 |
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 | 26 | 25 | 24 | 26 | 23 |
N.S. |
1 | 0.93 | 0.93 | 0.90 | 0.90 | 0.86 | 0.83 | 0.90 | 0.79 |
time (sec) |
N/A | 0.451 | 0.065 | 3.835 | 0.229 | 0.240 | 0.140 | 0.310 | 11.310 |
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 | 25 | 26 | 25 | 31 | 27 | 25 | 0 |
N.S. |
1 | 0.00 | 0.96 | 1.00 | 0.96 | 1.19 | 1.04 | 0.96 | 0.00 |
time (sec) |
N/A | 0.000 | 0.470 | 0.391 | 0.232 | 0.269 | 0.109 | 0.300 | 0.000 |
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 | 31 | 86 | 35 | 89 | 71 | 43 | 76 | 88 | 46 |
N.S. |
1 | 2.77 | 1.13 | 2.87 | 2.29 | 1.39 | 2.45 | 2.84 | 1.48 |
time (sec) |
N/A | 3.524 | 0.101 | 0.731 | 0.305 | 0.284 | 0.277 | 0.329 | 11.625 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | F(-1) | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 29 | 22 | 90 | 76 | 0 | 103 | 0 |
N.S. |
1 | 0.00 | 1.12 | 0.85 | 3.46 | 2.92 | 0.00 | 3.96 | 0.00 |
time (sec) |
N/A | 0.000 | 2.675 | 1.331 | 0.238 | 0.297 | 0.000 | 0.281 | 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 | 29 | 31 | 35 | 30 | 34 | 30 | 23 |
N.S. |
1 | 0.00 | 1.12 | 1.19 | 1.35 | 1.15 | 1.31 | 1.15 | 0.88 |
time (sec) |
N/A | 0.000 | 4.612 | 0.352 | 0.233 | 0.274 | 0.093 | 0.300 | 11.398 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 82 | 13 | 12 | 22 | 11 | 0 | 19 | 78 |
N.S. |
1 | 6.31 | 1.00 | 0.92 | 1.69 | 0.85 | 0.00 | 1.46 | 6.00 |
time (sec) |
N/A | 0.589 | 0.765 | 0.086 | 0.220 | 0.244 | 0.000 | 0.281 | 11.451 |
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 | 16 | 16 | 13 | 57 | 16 | 12 | 14 | 14 |
N.S. |
1 | 0.76 | 0.76 | 0.62 | 2.71 | 0.76 | 0.57 | 0.67 | 0.67 |
time (sec) |
N/A | 0.179 | 0.115 | 0.210 | 0.254 | 0.256 | 0.063 | 0.276 | 11.618 |
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 | 27 | 30 | 23 | 22 | 22 | 19 | 22 | 24 |
N.S. |
1 | 1.17 | 1.30 | 1.00 | 0.96 | 0.96 | 0.83 | 0.96 | 1.04 |
time (sec) |
N/A | 0.152 | 0.010 | 0.048 | 0.175 | 0.239 | 0.050 | 0.273 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 55 | 30 | 26 | 25 | 32 | 31 | 25 | 21 |
N.S. |
1 | 2.29 | 1.25 | 1.08 | 1.04 | 1.33 | 1.29 | 1.04 | 0.88 |
time (sec) |
N/A | 0.184 | 0.038 | 0.112 | 0.174 | 0.247 | 0.076 | 0.273 | 11.583 |
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 | 8 | 8 | 9 | 8 | 8 | 7 | 9 | 8 |
N.S. |
1 | 0.73 | 0.73 | 0.82 | 0.73 | 0.73 | 0.64 | 0.82 | 0.73 |
time (sec) |
N/A | 0.128 | 0.001 | 0.014 | 0.179 | 0.248 | 0.037 | 0.265 | 0.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 10 | 10 | 10 | 9 | 9 | 10 | 9 | 9 |
N.S. |
1 | 0.53 | 0.53 | 0.53 | 0.47 | 0.47 | 0.53 | 0.47 | 0.47 |
time (sec) |
N/A | 0.120 | 0.000 | 0.009 | 0.198 | 0.239 | 0.019 | 0.260 | 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 | 23 | 25 | 23 | 19 | 18 | 24 | 15 | 18 | 21 |
N.S. |
1 | 1.09 | 1.00 | 0.83 | 0.78 | 1.04 | 0.65 | 0.78 | 0.91 |
time (sec) |
N/A | 0.286 | 0.056 | 0.282 | 0.173 | 0.256 | 0.136 | 0.276 | 12.004 |
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 | 6 | 6 | 7 | 6 | 6 | 5 | 7 | 6 |
N.S. |
1 | 0.46 | 0.46 | 0.54 | 0.46 | 0.46 | 0.38 | 0.54 | 0.46 |
time (sec) |
N/A | 0.129 | 0.002 | 0.060 | 0.176 | 0.237 | 0.031 | 0.289 | 0.016 |
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 | 34 | 32 | 357 | 30 | 27 | 0 | 46 |
N.S. |
1 | 0.00 | 1.03 | 0.97 | 10.82 | 0.91 | 0.82 | 0.00 | 1.39 |
time (sec) |
N/A | 0.000 | 0.255 | 1.213 | 0.404 | 0.263 | 13.110 | 0.000 | 12.175 |
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 | 17 | 16 | 14 | 14 | 14 | 14 | 14 | 14 |
N.S. |
1 | 0.77 | 0.73 | 0.64 | 0.64 | 0.64 | 0.64 | 0.64 | 0.64 |
time (sec) |
N/A | 0.283 | 0.030 | 0.083 | 0.185 | 0.256 | 0.051 | 0.295 | 0.069 |
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 | 16 | 22 | 22 | 16 | 79 | 21 | 15 | 25 | 21 |
N.S. |
1 | 1.38 | 1.38 | 1.00 | 4.94 | 1.31 | 0.94 | 1.56 | 1.31 |
time (sec) |
N/A | 0.378 | 0.031 | 0.048 | 0.193 | 0.259 | 0.084 | 0.281 | 11.256 |
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 | 33 | 98 | 51 | 44 | 81 | 40 | 48 | 41 | 42 |
N.S. |
1 | 2.97 | 1.55 | 1.33 | 2.45 | 1.21 | 1.45 | 1.24 | 1.27 |
time (sec) |
N/A | 0.316 | 0.021 | 0.126 | 0.177 | 0.243 | 0.139 | 0.283 | 12.491 |
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 | 19 | 58 | 24 | 16 | 15 | 30 | 15 | 34 | 19 |
N.S. |
1 | 3.05 | 1.26 | 0.84 | 0.79 | 1.58 | 0.79 | 1.79 | 1.00 |
time (sec) |
N/A | 0.355 | 0.452 | 0.727 | 0.311 | 0.245 | 0.074 | 0.272 | 0.188 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 21 | 21 | 30 | 34 | 19 | 30 | 20 |
N.S. |
1 | 0.00 | 0.84 | 0.84 | 1.20 | 1.36 | 0.76 | 1.20 | 0.80 |
time (sec) |
N/A | 0.000 | 0.203 | 1.259 | 0.202 | 0.258 | 0.080 | 0.270 | 13.877 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 42 | 40 | 28 | 40 | 23 | 27 | 28 | 16 |
N.S. |
1 | 2.62 | 2.50 | 1.75 | 2.50 | 1.44 | 1.69 | 1.75 | 1.00 |
time (sec) |
N/A | 0.211 | 0.021 | 0.117 | 0.193 | 0.259 | 0.068 | 0.273 | 12.405 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | F | A | A | F | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 0 | 40 | 0 | 42 | 34 | 0 | 38 |
N.S. |
1 | 0.00 | 0.00 | 1.54 | 0.00 | 1.62 | 1.31 | 0.00 | 1.46 |
time (sec) |
N/A | 0.000 | 0.000 | 3.612 | 0.000 | 0.281 | 0.444 | 0.000 | 12.964 |
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 | 22 | 22 | 28 | 51 | 28 | 54 | 25 | 29 |
N.S. |
1 | 1.22 | 1.22 | 1.56 | 2.83 | 1.56 | 3.00 | 1.39 | 1.61 |
time (sec) |
N/A | 0.263 | 0.035 | 1.015 | 0.303 | 0.259 | 0.465 | 0.291 | 13.171 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 61 | 51 | 24 | 183 | 16 | 31 | 58 | 16 |
N.S. |
1 | 2.77 | 2.32 | 1.09 | 8.32 | 0.73 | 1.41 | 2.64 | 0.73 |
time (sec) |
N/A | 0.352 | 0.062 | 0.484 | 0.264 | 0.255 | 0.141 | 0.302 | 12.850 |
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 | 28 | 36 | 36 | 29 | 64 | 36 | 42 | 35 | 192 |
N.S. |
1 | 1.29 | 1.29 | 1.04 | 2.29 | 1.29 | 1.50 | 1.25 | 6.86 |
time (sec) |
N/A | 1.179 | 1.116 | 1.036 | 0.304 | 0.256 | 0.167 | 0.278 | 13.083 |
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 | 21 | 20 | 23 | 14 | 23 | 20 |
N.S. |
1 | 0.95 | 0.95 | 0.95 | 0.91 | 1.05 | 0.64 | 1.05 | 0.91 |
time (sec) |
N/A | 0.176 | 0.018 | 0.251 | 0.181 | 0.255 | 0.046 | 0.284 | 13.005 |
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 | 18 | 11 | 11 | 16 | 10 | 14 | 10 | 14 |
N.S. |
1 | 1.50 | 0.92 | 0.92 | 1.33 | 0.83 | 1.17 | 0.83 | 1.17 |
time (sec) |
N/A | 0.145 | 0.044 | 0.066 | 0.190 | 0.249 | 0.053 | 0.270 | 0.064 |
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 | 33 | 31 | 28 | 28 | 42 | 43 | 0 |
N.S. |
1 | 0.00 | 1.03 | 0.97 | 0.88 | 0.88 | 1.31 | 1.34 | 0.00 |
time (sec) |
N/A | 0.000 | 5.097 | 0.178 | 0.236 | 0.280 | 0.141 | 0.899 | 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 | 23 | 28 | 23 | 23 | 24 | 23 | 26 |
N.S. |
1 | 0.00 | 0.77 | 0.93 | 0.77 | 0.77 | 0.80 | 0.77 | 0.87 |
time (sec) |
N/A | 0.000 | 2.438 | 1.233 | 0.273 | 0.261 | 0.286 | 0.290 | 13.257 |
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 | 22 | 0 | 20 | 20 | 18 | 18 | 17 | 18 | 0 |
N.S. |
1 | 0.00 | 0.91 | 0.91 | 0.82 | 0.82 | 0.77 | 0.82 | 0.00 |
time (sec) |
N/A | 0.000 | 0.324 | 10.940 | 0.232 | 0.253 | 0.132 | 0.309 | 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 | 14 | 12 | 13 | 13 | 13 | 10 | 13 | 12 |
N.S. |
1 | 0.82 | 0.71 | 0.76 | 0.76 | 0.76 | 0.59 | 0.76 | 0.71 |
time (sec) |
N/A | 0.124 | 0.000 | 0.065 | 0.216 | 0.253 | 0.019 | 0.279 | 13.291 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 30 | 24 | 23 | 36 | 22 | 45 | 0 |
N.S. |
1 | 0.00 | 1.03 | 0.83 | 0.79 | 1.24 | 0.76 | 1.55 | 0.00 |
time (sec) |
N/A | 0.000 | 4.209 | 0.237 | 0.242 | 0.254 | 0.085 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 0 | 46 | 43 | 28 | 31 | 40 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.70 | 1.59 | 1.04 | 1.15 | 1.48 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.763 | 0.260 | 0.265 | 0.128 | 0.287 | 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 | 11 | 9 | 9 | 8 | 7 | 7 | 5 | 7 | 8 |
N.S. |
1 | 0.82 | 0.82 | 0.73 | 0.64 | 0.64 | 0.45 | 0.64 | 0.73 |
time (sec) |
N/A | 0.165 | 0.012 | 0.085 | 0.191 | 0.254 | 0.049 | 0.258 | 0.042 |
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 | 26 | 33 | 20 | 29 | 40 | 26 | 34 | 32 | 33 |
N.S. |
1 | 1.27 | 0.77 | 1.12 | 1.54 | 1.00 | 1.31 | 1.23 | 1.27 |
time (sec) |
N/A | 0.229 | 0.034 | 0.530 | 0.218 | 0.247 | 0.090 | 0.268 | 13.625 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F(-2) | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 29 | 30 | 0 | 29 | 26 | 29 | 31 |
N.S. |
1 | 0.00 | 0.88 | 0.91 | 0.00 | 0.88 | 0.79 | 0.88 | 0.94 |
time (sec) |
N/A | 0.000 | 0.123 | 0.606 | 0.000 | 0.257 | 0.140 | 0.313 | 13.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 69 | 12 | 11 | 39 | 13 | 10 | 13 | 13 |
N.S. |
1 | 3.45 | 0.60 | 0.55 | 1.95 | 0.65 | 0.50 | 0.65 | 0.65 |
time (sec) |
N/A | 0.363 | 0.028 | 0.457 | 0.170 | 0.243 | 0.053 | 0.279 | 13.710 |
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 | 24 | 21 | 22 | 148 | 21 | 24 | 21 | 21 |
N.S. |
1 | 1.71 | 1.50 | 1.57 | 10.57 | 1.50 | 1.71 | 1.50 | 1.50 |
time (sec) |
N/A | 0.365 | 0.070 | 0.718 | 0.331 | 0.268 | 0.077 | 0.294 | 0.656 |
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 | 27 | 24 | 26 | 25 | 26 | 19 | 25 | 27 |
N.S. |
1 | 0.84 | 0.75 | 0.81 | 0.78 | 0.81 | 0.59 | 0.78 | 0.84 |
time (sec) |
N/A | 0.181 | 0.010 | 0.103 | 0.177 | 0.244 | 0.052 | 0.277 | 13.629 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 0 | 0 | 42 | 53 | 45 | 36 | 51 | 48 |
N.S. |
1 | 0.00 | 0.00 | 1.14 | 1.43 | 1.22 | 0.97 | 1.38 | 1.30 |
time (sec) |
N/A | 0.000 | 0.000 | 26.733 | 0.315 | 0.262 | 0.518 | 0.401 | 14.255 |
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 | 15 | 15 | 9 | 14 | 14 | 17 | 14 | 8 |
N.S. |
1 | 1.50 | 1.50 | 0.90 | 1.40 | 1.40 | 1.70 | 1.40 | 0.80 |
time (sec) |
N/A | 0.132 | 0.002 | 0.059 | 0.188 | 0.239 | 0.019 | 0.278 | 0.051 |
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 | 26 | 0 | 25 | 23 | 102 | 21 | 24 | 80 | 149 |
N.S. |
1 | 0.00 | 0.96 | 0.88 | 3.92 | 0.81 | 0.92 | 3.08 | 5.73 |
time (sec) |
N/A | 0.000 | 0.310 | 1.369 | 0.335 | 0.256 | 0.134 | 0.392 | 14.203 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F(-1) | A | A | A | A | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 28 | 31 | 27 | 0 | 23 | 26 | 24 | 23 | 30 |
N.S. |
1 | 1.11 | 0.96 | 0.00 | 0.82 | 0.93 | 0.86 | 0.82 | 1.07 |
time (sec) |
N/A | 0.587 | 0.047 | 0.000 | 0.327 | 0.245 | 0.384 | 0.298 | 14.105 |
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 | 26 | 0 | 21 | 22 | 63 | 21 | 22 | 24 | 21 |
N.S. |
1 | 0.00 | 0.81 | 0.85 | 2.42 | 0.81 | 0.85 | 0.92 | 0.81 |
time (sec) |
N/A | 0.000 | 0.148 | 9.570 | 0.354 | 0.244 | 0.228 | 0.383 | 14.246 |
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 | 30 | 0 | 35 | 30 | 65 | 31 | 24 | 31 | 29 |
N.S. |
1 | 0.00 | 1.17 | 1.00 | 2.17 | 1.03 | 0.80 | 1.03 | 0.97 |
time (sec) |
N/A | 0.000 | 5.076 | 0.328 | 0.309 | 0.261 | 0.099 | 0.274 | 13.754 |
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 | 34 | 27 | 27 | 31 | 31 | 24 | 31 | 26 |
N.S. |
1 | 1.36 | 1.08 | 1.08 | 1.24 | 1.24 | 0.96 | 1.24 | 1.04 |
time (sec) |
N/A | 0.169 | 0.238 | 0.549 | 0.178 | 0.258 | 0.090 | 0.279 | 13.183 |
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 | 10 | 19 | 7 | 8 | 8 | 7 | 13 | 6 |
N.S. |
1 | 0.77 | 1.46 | 0.54 | 0.62 | 0.62 | 0.54 | 1.00 | 0.46 |
time (sec) |
N/A | 0.130 | 0.007 | 0.518 | 0.176 | 0.247 | 0.038 | 0.297 | 0.065 |
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 | 49 | 46 | 44 | 44 | 42 | 46 | 0 |
N.S. |
1 | 0.00 | 1.53 | 1.44 | 1.38 | 1.38 | 1.31 | 1.44 | 0.00 |
time (sec) |
N/A | 0.000 | 0.226 | 107.277 | 0.399 | 0.262 | 5.194 | 1.377 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 16 | 15 | 17 | 17 | 17 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.76 | 0.71 | 0.81 | 0.81 | 0.81 | 0.71 |
time (sec) |
N/A | 0.203 | 0.010 | 1.106 | 0.182 | 0.259 | 0.040 | 0.269 | 13.191 |
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 | 31 | 30 | 50 | 66 | 34 | 54 | 48 |
N.S. |
1 | 0.00 | 0.97 | 0.94 | 1.56 | 2.06 | 1.06 | 1.69 | 1.50 |
time (sec) |
N/A | 0.000 | 0.106 | 9.383 | 0.230 | 0.251 | 0.098 | 0.302 | 13.574 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 174 | 32 | 92 | 368 | 86 | 105 | 103 | 31 |
N.S. |
1 | 6.69 | 1.23 | 3.54 | 14.15 | 3.31 | 4.04 | 3.96 | 1.19 |
time (sec) |
N/A | 0.743 | 1.567 | 0.432 | 0.191 | 0.251 | 0.097 | 0.270 | 13.534 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 66 | 23 | 106 | 113 | 60 | 130 | 0 |
N.S. |
1 | 0.00 | 2.36 | 0.82 | 3.79 | 4.04 | 2.14 | 4.64 | 0.00 |
time (sec) |
N/A | 0.000 | 3.873 | 1.000 | 0.249 | 0.268 | 0.176 | 0.510 | 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 | 30 | 26 | 29 | 22 | 19 | 19 | 44 | 19 | 17 |
N.S. |
1 | 0.87 | 0.97 | 0.73 | 0.63 | 0.63 | 1.47 | 0.63 | 0.57 |
time (sec) |
N/A | 0.157 | 0.005 | 0.149 | 0.174 | 0.265 | 0.089 | 0.291 | 12.916 |
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 | 35 | 0 | 34 | 28 | 27 | 29 | 29 | 0 | 27 |
N.S. |
1 | 0.00 | 0.97 | 0.80 | 0.77 | 0.83 | 0.83 | 0.00 | 0.77 |
time (sec) |
N/A | 0.000 | 0.266 | 0.178 | 0.594 | 0.272 | 22.089 | 0.000 | 14.176 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 299 | 158 | 47 | 606 | 45 | 51 | 45 | 400 |
N.S. |
1 | 11.50 | 6.08 | 1.81 | 23.31 | 1.73 | 1.96 | 1.73 | 15.38 |
time (sec) |
N/A | 0.759 | 0.429 | 0.475 | 0.278 | 0.247 | 0.105 | 0.269 | 1.342 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | B | B | C | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 217 | 111 | 128 | 219 | 131 | 122 | 230 | 207 |
N.S. |
1 | 7.48 | 3.83 | 4.41 | 7.55 | 4.52 | 4.21 | 7.93 | 7.14 |
time (sec) |
N/A | 1.480 | 0.087 | 0.699 | 0.244 | 0.265 | 0.132 | 0.270 | 14.113 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 66 | 60 | 80 | 67 | 151 | 76 | 16 | 84 |
N.S. |
1 | 3.00 | 2.73 | 3.64 | 3.05 | 6.86 | 3.45 | 0.73 | 3.82 |
time (sec) |
N/A | 0.429 | 0.057 | 0.497 | 0.175 | 0.262 | 0.596 | 0.266 | 12.490 |
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 | 21 | 39 | 39 | 39 | 36 | 36 | 36 | 38 | 36 |
N.S. |
1 | 1.86 | 1.86 | 1.86 | 1.71 | 1.71 | 1.71 | 1.81 | 1.71 |
time (sec) |
N/A | 0.445 | 0.059 | 0.454 | 0.188 | 0.269 | 5.443 | 0.302 | 13.352 |
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 | 11 | 9 | 10 | 9 | 9 | 7 | 9 | 7 |
N.S. |
1 | 0.55 | 0.45 | 0.50 | 0.45 | 0.45 | 0.35 | 0.45 | 0.35 |
time (sec) |
N/A | 0.123 | 0.000 | 0.033 | 0.180 | 0.233 | 0.017 | 0.283 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | B | A | B | A | A | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 3127 | 49 | 29 | 60 | 28 | 24 | 60 | 25 |
N.S. |
1 | 130.29 | 2.04 | 1.21 | 2.50 | 1.17 | 1.00 | 2.50 | 1.04 |
time (sec) |
N/A | 6.437 | 1.932 | 0.529 | 0.789 | 0.247 | 0.101 | 0.489 | 13.767 |