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 | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 89 | 85 | 155 | 0 | 461 | 0 | 0 | 139 | 0 |
N.S. |
1 | 0.48 | 0.46 | 0.84 | 0.00 | 2.51 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.504 | 0.034 | 0.903 | 0.000 | 0.128 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 89 | 84 | 150 | 0 | 457 | 0 | 0 | 134 | 0 |
N.S. |
1 | 0.48 | 0.46 | 0.82 | 0.00 | 2.48 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.509 | 0.041 | 0.955 | 0.000 | 0.106 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 74 | 60 | 150 | 0 | 459 | 0 | 0 | 134 | 0 |
N.S. |
1 | 0.54 | 0.44 | 1.09 | 0.00 | 3.35 | 0.00 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 0.435 | 0.043 | 0.223 | 0.000 | 0.103 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 89 | 85 | 155 | 0 | 455 | 0 | 0 | 139 | 0 |
N.S. |
1 | 0.48 | 0.46 | 0.84 | 0.00 | 2.47 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.394 | 0.031 | 0.223 | 0.000 | 0.111 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 92 | 86 | 182 | 0 | 0 | 0 | 0 | 166 | 0 |
N.S. |
1 | 0.37 | 0.34 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.527 | 0.041 | 0.214 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 295 | 104 | 97 | 211 | 0 | 0 | 0 | 0 | 195 | 0 |
N.S. |
1 | 0.35 | 0.33 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.520 | 0.055 | 0.212 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 345 | 122 | 115 | 231 | 0 | 0 | 0 | 0 | 215 | 0 |
N.S. |
1 | 0.35 | 0.33 | 0.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.540 | 0.086 | 0.212 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 277 | 118 | 103 | 227 | 0 | 567 | 0 | 0 | 226 | 0 |
N.S. |
1 | 0.43 | 0.37 | 0.82 | 0.00 | 2.05 | 0.00 | 0.00 | 0.82 | 0.00 |
time (sec) |
N/A | 0.443 | 0.052 | 0.218 | 0.000 | 0.109 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 78 | 82 | 227 | 0 | 0 | 316 | 0 | 152 | 0 |
N.S. |
1 | 0.98 | 1.02 | 2.84 | 0.00 | 0.00 | 3.95 | 0.00 | 1.90 | 0.00 |
time (sec) |
N/A | 0.317 | 0.035 | 0.216 | 0.000 | 0.000 | 5.793 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 72 | 143 | 0 | 0 | 204 | 0 | 98 | 0 |
N.S. |
1 | 1.00 | 0.95 | 1.88 | 0.00 | 0.00 | 2.68 | 0.00 | 1.29 | 0.00 |
time (sec) |
N/A | 0.288 | 0.031 | 0.193 | 0.000 | 0.000 | 3.368 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 78 | 82 | 0 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 0.98 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.316 | 0.026 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 78 | 82 | 0 | 0 | 0 | 0 | 0 | 76 | 0 |
N.S. |
1 | 0.98 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 0.311 | 0.026 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 78 | 82 | 0 | 0 | 0 | 0 | 0 | 116 | 0 |
N.S. |
1 | 0.98 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.45 | 0.00 |
time (sec) |
N/A | 0.315 | 0.029 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 70 | 99 | 82 | 285 | 1760 | 460 | 336 | 374 |
N.S. |
1 | 1.00 | 0.85 | 1.21 | 1.00 | 3.48 | 21.46 | 5.61 | 4.10 | 4.56 |
time (sec) |
N/A | 0.352 | 0.031 | 0.202 | 0.030 | 0.075 | 0.440 | 0.126 | 0.166 | 15.486 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 54 | 65 | 54 | 128 | 585 | 197 | 138 | 160 |
N.S. |
1 | 1.00 | 1.00 | 1.20 | 1.00 | 2.37 | 10.83 | 3.65 | 2.56 | 2.96 |
time (sec) |
N/A | 0.310 | 0.108 | 0.049 | 0.026 | 0.073 | 0.289 | 0.118 | 0.181 | 15.348 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 20 | 26 | 24 | 29 | 82 | 41 | 25 | 26 |
N.S. |
1 | 1.00 | 0.83 | 1.08 | 1.00 | 1.21 | 3.42 | 1.71 | 1.04 | 1.08 |
time (sec) |
N/A | 0.271 | 0.010 | 0.031 | 0.025 | 0.083 | 0.182 | 0.118 | 0.141 | 15.297 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | B | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 100 | 0 | 0 | 44 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 1.00 | 4.55 | 0.00 | 0.00 | 2.00 | 0.00 | 1.50 | 0.00 |
time (sec) |
N/A | 0.266 | 0.006 | 0.172 | 0.000 | 0.000 | 1.311 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 67 | 177 | 0 | 0 | 673 | 0 | 29 | 0 |
N.S. |
1 | 1.00 | 0.96 | 2.53 | 0.00 | 0.00 | 9.61 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.311 | 0.031 | 0.217 | 0.000 | 0.000 | 3.317 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 67 | 224 | 0 | 0 | 2173 | 0 | 46 | 0 |
N.S. |
1 | 1.00 | 0.96 | 3.20 | 0.00 | 0.00 | 31.04 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.317 | 0.031 | 0.325 | 0.000 | 0.000 | 5.349 | 0.000 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 274 | 115 | 102 | 376 | 144 | 476 | 0 | 0 | 341 | 468 |
N.S. |
1 | 0.42 | 0.37 | 1.37 | 0.53 | 1.74 | 0.00 | 0.00 | 1.24 | 1.71 |
time (sec) |
N/A | 0.510 | 0.071 | 0.218 | 0.043 | 0.092 | 0.000 | 0.000 | 0.149 | 15.427 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 85 | 84 | 179 | 80 | 211 | 0 | 0 | 141 | 228 |
N.S. |
1 | 0.49 | 0.48 | 1.03 | 0.46 | 1.21 | 0.00 | 0.00 | 0.81 | 1.31 |
time (sec) |
N/A | 0.472 | 0.071 | 0.213 | 0.051 | 0.084 | 0.000 | 0.000 | 0.149 | 15.229 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 54 | 49 | 51 | 30 | 80 | 0 | 0 | 27 | 51 |
N.S. |
1 | 0.66 | 0.60 | 0.62 | 0.37 | 0.98 | 0.00 | 0.00 | 0.33 | 0.62 |
time (sec) |
N/A | 0.439 | 0.022 | 0.214 | 0.043 | 0.083 | 0.000 | 0.000 | 0.140 | 15.137 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 51 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.425 | 0.020 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 103 | 107 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 0.77 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.490 | 0.033 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 103 | 107 | 0 | 0 | 0 | 0 | 0 | 51 | 0 |
N.S. |
1 | 0.77 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.498 | 0.035 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 110 | 114 | 0 | 0 | 0 | 391 | 0 | 68 | 0 |
N.S. |
1 | 0.81 | 0.84 | 0.00 | 0.00 | 0.00 | 2.88 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.450 | 0.038 | 0.000 | 0.000 | 0.000 | 41.733 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 91 | 77 | 47 | 0 | 0 | 258 | 0 | 190 | 0 |
N.S. |
1 | 1.07 | 0.91 | 0.55 | 0.00 | 0.00 | 3.04 | 0.00 | 2.24 | 0.00 |
time (sec) |
N/A | 0.358 | 0.063 | 0.224 | 0.000 | 0.000 | 9.305 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 91 | 76 | 47 | 0 | 0 | 257 | 0 | 190 | 0 |
N.S. |
1 | 1.08 | 0.90 | 0.56 | 0.00 | 0.00 | 3.06 | 0.00 | 2.26 | 0.00 |
time (sec) |
N/A | 0.349 | 0.047 | 0.214 | 0.000 | 0.000 | 7.056 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 60 | 47 | 0 | 0 | 243 | 0 | 100 | 0 |
N.S. |
1 | 1.00 | 1.03 | 0.81 | 0.00 | 0.00 | 4.19 | 0.00 | 1.72 | 0.00 |
time (sec) |
N/A | 0.274 | 0.023 | 0.214 | 0.000 | 0.000 | 6.154 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | B | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 59 | 59 | 44 | 0 | 0 | 236 | 0 | 90 | 0 |
N.S. |
1 | 1.13 | 1.13 | 0.85 | 0.00 | 0.00 | 4.54 | 0.00 | 1.73 | 0.00 |
time (sec) |
N/A | 0.244 | 0.015 | 0.211 | 0.000 | 0.000 | 5.335 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 74 | 90 | 0 | 0 | 286 | 0 | 62 | 0 |
N.S. |
1 | 1.00 | 1.03 | 1.25 | 0.00 | 0.00 | 3.97 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.314 | 0.025 | 0.227 | 0.000 | 0.000 | 9.519 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 77 | 93 | 0 | 0 | 284 | 0 | 65 | 0 |
N.S. |
1 | 1.00 | 1.03 | 1.24 | 0.00 | 0.00 | 3.79 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.326 | 0.022 | 0.225 | 0.000 | 0.000 | 7.523 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 80 | 112 | 0 | 0 | 292 | 0 | 65 | 0 |
N.S. |
1 | 1.00 | 1.03 | 1.44 | 0.00 | 0.00 | 3.74 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.314 | 0.017 | 0.237 | 0.000 | 0.000 | 11.352 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 119 | 105 | 0 | 0 | 0 | 272 | 0 | 202 | 0 |
N.S. |
1 | 0.89 | 0.78 | 0.00 | 0.00 | 0.00 | 2.03 | 0.00 | 1.51 | 0.00 |
time (sec) |
N/A | 0.485 | 0.089 | 0.000 | 0.000 | 0.000 | 9.517 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 119 | 104 | 0 | 0 | 0 | 270 | 0 | 202 | 0 |
N.S. |
1 | 0.89 | 0.78 | 0.00 | 0.00 | 0.00 | 2.03 | 0.00 | 1.52 | 0.00 |
time (sec) |
N/A | 0.481 | 0.101 | 0.000 | 0.000 | 0.000 | 7.896 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 86 | 88 | 0 | 0 | 0 | 311 | 0 | 105 | 0 |
N.S. |
1 | 0.90 | 0.92 | 0.00 | 0.00 | 0.00 | 3.24 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.388 | 0.039 | 0.000 | 0.000 | 0.000 | 6.597 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 86 | 86 | 0 | 0 | 0 | 306 | 0 | 95 | 0 |
N.S. |
1 | 0.96 | 0.96 | 0.00 | 0.00 | 0.00 | 3.40 | 0.00 | 1.06 | 0.00 |
time (sec) |
N/A | 0.342 | 0.020 | 0.000 | 0.000 | 0.000 | 6.371 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 100 | 102 | 0 | 0 | 0 | 299 | 0 | 64 | 0 |
N.S. |
1 | 0.91 | 0.93 | 0.00 | 0.00 | 0.00 | 2.72 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.446 | 0.043 | 0.000 | 0.000 | 0.000 | 9.531 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 103 | 105 | 0 | 0 | 0 | 298 | 0 | 67 | 0 |
N.S. |
1 | 0.91 | 0.93 | 0.00 | 0.00 | 0.00 | 2.64 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.440 | 0.049 | 0.000 | 0.000 | 0.000 | 7.700 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 106 | 108 | 0 | 0 | 0 | 306 | 0 | 67 | 0 |
N.S. |
1 | 0.91 | 0.93 | 0.00 | 0.00 | 0.00 | 2.64 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.450 | 0.030 | 0.000 | 0.000 | 0.000 | 11.322 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 28 | 22 | 21 | 23 | 23 | 24 | 23 | 20 | 20 |
N.S. |
1 | 0.97 | 0.76 | 0.72 | 0.79 | 0.79 | 0.83 | 0.79 | 0.69 | 0.69 |
time (sec) |
N/A | 0.259 | 0.006 | 0.228 | 0.034 | 0.080 | 0.031 | 0.114 | 0.150 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 28 | 22 | 21 | 23 | 23 | 26 | 23 | 20 | 20 |
N.S. |
1 | 0.97 | 0.76 | 0.72 | 0.79 | 0.79 | 0.90 | 0.79 | 0.69 | 0.69 |
time (sec) |
N/A | 0.264 | 0.006 | 0.189 | 0.030 | 0.068 | 0.025 | 0.118 | 0.154 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 28 | 22 | 21 | 23 | 23 | 24 | 23 | 20 | 20 |
N.S. |
1 | 0.97 | 0.76 | 0.72 | 0.79 | 0.79 | 0.83 | 0.79 | 0.69 | 0.69 |
time (sec) |
N/A | 0.254 | 0.005 | 0.187 | 0.031 | 0.059 | 0.030 | 0.112 | 0.154 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 28 | 22 | 21 | 23 | 23 | 26 | 23 | 20 | 20 |
N.S. |
1 | 0.97 | 0.76 | 0.72 | 0.79 | 0.79 | 0.90 | 0.79 | 0.69 | 0.69 |
time (sec) |
N/A | 0.247 | 0.005 | 0.191 | 0.027 | 0.063 | 0.024 | 0.123 | 0.154 | 0.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 19 | 14 | 19 | 19 | 19 | 19 | 17 | 17 |
N.S. |
1 | 1.00 | 1.27 | 0.93 | 1.27 | 1.27 | 1.27 | 1.27 | 1.13 | 1.13 |
time (sec) |
N/A | 0.211 | 0.005 | 0.184 | 0.030 | 0.064 | 0.028 | 0.116 | 0.148 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 19 | 19 | 18 | 19 | 19 | 20 | 20 | 19 | 19 |
N.S. |
1 | 0.90 | 0.90 | 0.86 | 0.90 | 0.90 | 0.95 | 0.95 | 0.90 | 0.90 |
time (sec) |
N/A | 0.251 | 0.008 | 0.191 | 0.027 | 0.109 | 0.047 | 0.112 | 0.156 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 18 | 18 | 19 | 19 | 23 | 17 | 20 | 20 | 20 |
N.S. |
1 | 0.95 | 0.95 | 1.00 | 1.00 | 1.21 | 0.89 | 1.05 | 1.05 | 1.05 |
time (sec) |
N/A | 0.254 | 0.006 | 0.197 | 0.028 | 0.086 | 0.065 | 0.128 | 0.152 | 0.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 22 | 22 | 21 | 20 | 25 | 22 | 21 | 22 | 22 |
N.S. |
1 | 0.96 | 0.96 | 0.91 | 0.87 | 1.09 | 0.96 | 0.91 | 0.96 | 0.96 |
time (sec) |
N/A | 0.253 | 0.009 | 0.204 | 0.030 | 0.066 | 0.071 | 0.116 | 0.153 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 21 | 21 | 21 | 24 | 21 | 20 | 21 |
N.S. |
1 | 1.00 | 1.00 | 1.40 | 1.40 | 1.40 | 1.60 | 1.40 | 1.33 | 1.40 |
time (sec) |
N/A | 0.242 | 0.005 | 0.208 | 0.030 | 0.063 | 0.077 | 0.119 | 0.150 | 0.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 40 | 32 | 31 | 40 | 40 | 41 | 40 | 30 | 40 |
N.S. |
1 | 0.83 | 0.67 | 0.65 | 0.83 | 0.83 | 0.85 | 0.83 | 0.62 | 0.83 |
time (sec) |
N/A | 0.304 | 0.007 | 0.213 | 0.030 | 0.062 | 0.029 | 0.119 | 0.157 | 15.305 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 40 | 40 | 31 | 40 | 40 | 44 | 40 | 30 | 40 |
N.S. |
1 | 0.83 | 0.83 | 0.65 | 0.83 | 0.83 | 0.92 | 0.83 | 0.62 | 0.83 |
time (sec) |
N/A | 0.291 | 0.008 | 0.211 | 0.030 | 0.058 | 0.028 | 0.117 | 0.147 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 40 | 32 | 31 | 40 | 40 | 41 | 40 | 30 | 40 |
N.S. |
1 | 0.83 | 0.67 | 0.65 | 0.83 | 0.83 | 0.85 | 0.83 | 0.62 | 0.83 |
time (sec) |
N/A | 0.291 | 0.006 | 0.218 | 0.025 | 0.096 | 0.028 | 0.118 | 0.154 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 40 | 32 | 31 | 40 | 40 | 44 | 40 | 30 | 40 |
N.S. |
1 | 0.83 | 0.67 | 0.65 | 0.83 | 0.83 | 0.92 | 0.83 | 0.62 | 0.83 |
time (sec) |
N/A | 0.276 | 0.006 | 0.213 | 0.031 | 0.068 | 0.027 | 0.120 | 0.149 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 33 | 23 | 28 | 36 | 36 | 36 | 36 | 28 | 36 |
N.S. |
1 | 0.94 | 0.66 | 0.80 | 1.03 | 1.03 | 1.03 | 1.03 | 0.80 | 1.03 |
time (sec) |
N/A | 0.250 | 0.006 | 0.210 | 0.025 | 0.073 | 0.031 | 0.117 | 0.153 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 31 | 34 | 28 | 36 | 36 | 39 | 37 | 30 | 36 |
N.S. |
1 | 0.78 | 0.85 | 0.70 | 0.90 | 0.90 | 0.98 | 0.92 | 0.75 | 0.90 |
time (sec) |
N/A | 0.277 | 0.011 | 0.218 | 0.026 | 0.064 | 0.053 | 0.125 | 0.156 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 33 | 36 | 32 | 39 | 41 | 36 | 40 | 32 | 39 |
N.S. |
1 | 0.80 | 0.88 | 0.78 | 0.95 | 1.00 | 0.88 | 0.98 | 0.78 | 0.95 |
time (sec) |
N/A | 0.285 | 0.007 | 0.215 | 0.029 | 0.074 | 0.094 | 0.123 | 0.150 | 0.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 30 | 37 | 37 | 39 | 37 | 30 | 29 |
N.S. |
1 | 1.00 | 1.00 | 1.76 | 2.18 | 2.18 | 2.29 | 2.18 | 1.76 | 1.71 |
time (sec) |
N/A | 0.259 | 0.005 | 0.232 | 0.026 | 0.066 | 0.078 | 0.127 | 0.154 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 31 | 38 | 30 | 36 | 40 | 37 | 37 | 32 | 32 |
N.S. |
1 | 0.79 | 0.97 | 0.77 | 0.92 | 1.03 | 0.95 | 0.95 | 0.82 | 0.82 |
time (sec) |
N/A | 0.284 | 0.006 | 0.230 | 0.033 | 0.068 | 0.095 | 0.118 | 0.162 | 0.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 35 | 35 | 32 | 40 | 42 | 41 | 41 | 32 | 32 |
N.S. |
1 | 0.81 | 0.81 | 0.74 | 0.93 | 0.98 | 0.95 | 0.95 | 0.74 | 0.74 |
time (sec) |
N/A | 0.283 | 0.007 | 0.243 | 0.035 | 0.082 | 0.119 | 0.116 | 0.149 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 34 | 23 | 31 | 40 | 40 | 42 | 40 | 30 | 40 |
N.S. |
1 | 0.81 | 0.55 | 0.74 | 0.95 | 0.95 | 1.00 | 0.95 | 0.71 | 0.95 |
time (sec) |
N/A | 0.283 | 0.006 | 0.243 | 0.027 | 0.070 | 0.171 | 0.121 | 0.154 | 0.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 70 | 70 | 55 | 73 | 73 | 76 | 73 | 54 | 73 |
N.S. |
1 | 0.80 | 0.80 | 0.63 | 0.84 | 0.84 | 0.87 | 0.84 | 0.62 | 0.84 |
time (sec) |
N/A | 0.321 | 0.012 | 0.217 | 0.033 | 0.058 | 0.043 | 0.119 | 0.154 | 14.967 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 70 | 70 | 55 | 73 | 73 | 82 | 73 | 54 | 73 |
N.S. |
1 | 0.80 | 0.80 | 0.63 | 0.84 | 0.84 | 0.94 | 0.84 | 0.62 | 0.84 |
time (sec) |
N/A | 0.332 | 0.011 | 0.217 | 0.026 | 0.060 | 0.041 | 0.139 | 0.151 | 0.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 73 | 70 | 55 | 73 | 73 | 78 | 73 | 54 | 73 |
N.S. |
1 | 0.87 | 0.83 | 0.65 | 0.87 | 0.87 | 0.93 | 0.87 | 0.64 | 0.87 |
time (sec) |
N/A | 0.340 | 0.012 | 0.215 | 0.027 | 0.083 | 0.043 | 0.121 | 0.160 | 0.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 61 | 70 | 55 | 73 | 73 | 82 | 73 | 54 | 73 |
N.S. |
1 | 0.88 | 1.01 | 0.80 | 1.06 | 1.06 | 1.19 | 1.06 | 0.78 | 1.06 |
time (sec) |
N/A | 0.306 | 0.011 | 0.219 | 0.026 | 0.061 | 0.041 | 0.119 | 0.150 | 0.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 47 | 31 | 52 | 69 | 69 | 70 | 69 | 52 | 69 |
N.S. |
1 | 0.90 | 0.60 | 1.00 | 1.33 | 1.33 | 1.35 | 1.33 | 1.00 | 1.33 |
time (sec) |
N/A | 0.262 | 0.008 | 0.212 | 0.026 | 0.063 | 0.050 | 0.128 | 0.154 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 61 | 51 | 52 | 69 | 69 | 76 | 70 | 54 | 69 |
N.S. |
1 | 0.77 | 0.65 | 0.66 | 0.87 | 0.87 | 0.96 | 0.89 | 0.68 | 0.87 |
time (sec) |
N/A | 0.305 | 0.019 | 0.221 | 0.034 | 0.073 | 0.078 | 0.116 | 0.155 | 0.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 59 | 59 | 54 | 70 | 75 | 70 | 71 | 56 | 70 |
N.S. |
1 | 0.78 | 0.78 | 0.71 | 0.92 | 0.99 | 0.92 | 0.93 | 0.74 | 0.92 |
time (sec) |
N/A | 0.316 | 0.012 | 0.221 | 0.026 | 0.064 | 0.114 | 0.118 | 0.156 | 0.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 61 | 58 | 54 | 69 | 75 | 75 | 70 | 56 | 71 |
N.S. |
1 | 0.78 | 0.74 | 0.69 | 0.88 | 0.96 | 0.96 | 0.90 | 0.72 | 0.91 |
time (sec) |
N/A | 0.322 | 0.009 | 0.237 | 0.031 | 0.071 | 0.117 | 0.121 | 0.155 | 0.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 55 | 55 | 52 | 70 | 74 | 70 | 71 | 55 | 69 |
N.S. |
1 | 0.76 | 0.76 | 0.72 | 0.97 | 1.03 | 0.97 | 0.99 | 0.76 | 0.96 |
time (sec) |
N/A | 0.324 | 0.015 | 0.231 | 0.025 | 0.061 | 0.127 | 0.118 | 0.157 | 0.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 61 | 39 | 59 | 79 | 79 | 87 | 79 | 60 | 79 |
N.S. |
1 | 0.88 | 0.57 | 0.86 | 1.14 | 1.14 | 1.26 | 1.14 | 0.87 | 1.14 |
time (sec) |
N/A | 0.288 | 0.010 | 0.220 | 0.034 | 0.058 | 0.056 | 0.118 | 0.154 | 0.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 52 | 49 | 50 | 57 | 59 | 53 | 70 | 61 | 64 |
N.S. |
1 | 0.83 | 0.78 | 0.79 | 0.90 | 0.94 | 0.84 | 1.11 | 0.97 | 1.02 |
time (sec) |
N/A | 0.332 | 0.018 | 0.207 | 0.034 | 0.062 | 0.117 | 0.117 | 0.156 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 45 | 41 | 43 | 49 | 51 | 44 | 53 | 53 | 54 |
N.S. |
1 | 0.85 | 0.77 | 0.81 | 0.92 | 0.96 | 0.83 | 1.00 | 1.00 | 1.02 |
time (sec) |
N/A | 0.303 | 0.013 | 0.208 | 0.025 | 0.073 | 0.167 | 0.115 | 0.157 | 14.733 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 34 | 28 | 34 | 40 | 42 | 32 | 39 | 44 | 38 |
N.S. |
1 | 0.87 | 0.72 | 0.87 | 1.03 | 1.08 | 0.82 | 1.00 | 1.13 | 0.97 |
time (sec) |
N/A | 0.299 | 0.011 | 0.229 | 0.031 | 0.071 | 0.098 | 0.129 | 0.156 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 28 | 23 | 28 | 31 | 30 | 24 | 30 | 36 | 27 |
N.S. |
1 | 0.93 | 0.77 | 0.93 | 1.03 | 1.00 | 0.80 | 1.00 | 1.20 | 0.90 |
time (sec) |
N/A | 0.279 | 0.008 | 0.243 | 0.027 | 0.069 | 0.071 | 0.117 | 0.158 | 0.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 18 | 14 | 15 | 15 | 12 | 15 | 13 | 13 |
N.S. |
1 | 1.00 | 1.20 | 0.93 | 1.00 | 1.00 | 0.80 | 1.00 | 0.87 | 0.87 |
time (sec) |
N/A | 0.228 | 0.007 | 0.256 | 0.026 | 0.062 | 0.075 | 0.113 | 0.164 | 14.349 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 24 | 24 | 25 | 30 | 35 | 19 | 32 | 41 | 22 |
N.S. |
1 | 0.77 | 0.77 | 0.81 | 0.97 | 1.13 | 0.61 | 1.03 | 1.32 | 0.71 |
time (sec) |
N/A | 0.287 | 0.011 | 0.246 | 0.030 | 0.073 | 0.113 | 0.117 | 0.158 | 14.828 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 35 | 35 | 35 | 42 | 57 | 31 | 45 | 64 | 34 |
N.S. |
1 | 0.81 | 0.81 | 0.81 | 0.98 | 1.33 | 0.72 | 1.05 | 1.49 | 0.79 |
time (sec) |
N/A | 0.304 | 0.019 | 0.251 | 0.030 | 0.068 | 0.147 | 0.132 | 0.159 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 49 | 52 | 47 | 56 | 75 | 46 | 56 | 77 | 47 |
N.S. |
1 | 0.82 | 0.87 | 0.78 | 0.93 | 1.25 | 0.77 | 0.93 | 1.28 | 0.78 |
time (sec) |
N/A | 0.311 | 0.032 | 0.251 | 0.027 | 0.070 | 0.140 | 0.132 | 0.157 | 0.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 57 | 71 | 55 | 64 | 83 | 54 | 64 | 85 | 55 |
N.S. |
1 | 0.80 | 1.00 | 0.77 | 0.90 | 1.17 | 0.76 | 0.90 | 1.20 | 0.77 |
time (sec) |
N/A | 0.323 | 0.016 | 0.227 | 0.025 | 0.089 | 0.207 | 0.123 | 0.157 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 68 | 68 | 58 | 75 | 95 | 71 | 61 | 102 | 77 |
N.S. |
1 | 0.86 | 0.86 | 0.73 | 0.95 | 1.20 | 0.90 | 0.77 | 1.29 | 0.97 |
time (sec) |
N/A | 0.348 | 0.016 | 0.257 | 0.029 | 0.077 | 0.225 | 0.125 | 0.160 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 62 | 53 | 52 | 66 | 79 | 63 | 52 | 97 | 65 |
N.S. |
1 | 0.89 | 0.76 | 0.74 | 0.94 | 1.13 | 0.90 | 0.74 | 1.39 | 0.93 |
time (sec) |
N/A | 0.349 | 0.015 | 0.237 | 0.028 | 0.073 | 0.226 | 0.121 | 0.163 | 15.568 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 46 | 35 | 52 | 66 | 78 | 61 | 52 | 94 | 49 |
N.S. |
1 | 0.90 | 0.69 | 1.02 | 1.29 | 1.53 | 1.20 | 1.02 | 1.84 | 0.96 |
time (sec) |
N/A | 0.327 | 0.009 | 0.241 | 0.033 | 0.076 | 0.167 | 0.138 | 0.158 | 0.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 46 | 34 | 47 | 59 | 77 | 53 | 47 | 93 | 42 |
N.S. |
1 | 0.90 | 0.67 | 0.92 | 1.16 | 1.51 | 1.04 | 0.92 | 1.82 | 0.82 |
time (sec) |
N/A | 0.298 | 0.009 | 0.229 | 0.030 | 0.065 | 0.164 | 0.125 | 0.160 | 24.943 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 46 | 35 | 51 | 63 | 76 | 56 | 51 | 94 | 47 |
N.S. |
1 | 0.90 | 0.69 | 1.00 | 1.24 | 1.49 | 1.10 | 1.00 | 1.84 | 0.92 |
time (sec) |
N/A | 0.264 | 0.007 | 0.235 | 0.025 | 0.086 | 0.227 | 0.119 | 0.159 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 52 | 48 | 42 | 60 | 89 | 58 | 50 | 114 | 60 |
N.S. |
1 | 0.81 | 0.75 | 0.66 | 0.94 | 1.39 | 0.91 | 0.78 | 1.78 | 0.94 |
time (sec) |
N/A | 0.314 | 0.020 | 0.227 | 0.027 | 0.082 | 0.318 | 0.119 | 0.155 | 25.163 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 64 | 57 | 54 | 76 | 120 | 76 | 65 | 137 | 76 |
N.S. |
1 | 0.82 | 0.73 | 0.69 | 0.97 | 1.54 | 0.97 | 0.83 | 1.76 | 0.97 |
time (sec) |
N/A | 0.339 | 0.026 | 0.232 | 0.028 | 0.071 | 0.504 | 0.152 | 0.161 | 25.708 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 82 | 72 | 70 | 92 | 141 | 92 | 79 | 159 | 91 |
N.S. |
1 | 0.83 | 0.73 | 0.71 | 0.93 | 1.42 | 0.93 | 0.80 | 1.61 | 0.92 |
time (sec) |
N/A | 0.351 | 0.069 | 0.251 | 0.032 | 0.075 | 0.457 | 0.118 | 0.158 | 0.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 90 | 87 | 78 | 100 | 150 | 100 | 87 | 167 | 100 |
N.S. |
1 | 0.82 | 0.79 | 0.71 | 0.91 | 1.36 | 0.91 | 0.79 | 1.52 | 0.91 |
time (sec) |
N/A | 0.374 | 0.050 | 0.228 | 0.033 | 0.106 | 0.448 | 0.123 | 0.162 | 25.195 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 91 | 87 | 76 | 94 | 123 | 92 | 75 | 145 | 94 |
N.S. |
1 | 0.87 | 0.83 | 0.72 | 0.90 | 1.17 | 0.88 | 0.71 | 1.38 | 0.90 |
time (sec) |
N/A | 0.363 | 0.023 | 0.230 | 0.028 | 0.095 | 0.358 | 0.148 | 0.159 | 0.310 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 75 | 64 | 76 | 94 | 123 | 88 | 75 | 145 | 78 |
N.S. |
1 | 0.87 | 0.74 | 0.88 | 1.09 | 1.43 | 1.02 | 0.87 | 1.69 | 0.91 |
time (sec) |
N/A | 0.341 | 0.014 | 0.230 | 0.039 | 0.089 | 0.283 | 0.122 | 0.157 | 0.076 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 75 | 64 | 76 | 94 | 123 | 88 | 75 | 145 | 77 |
N.S. |
1 | 0.87 | 0.74 | 0.88 | 1.09 | 1.43 | 1.02 | 0.87 | 1.69 | 0.90 |
time (sec) |
N/A | 0.351 | 0.012 | 0.316 | 0.034 | 0.066 | 0.230 | 0.123 | 0.159 | 25.231 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 30 | 33 | 49 | 49 | 48 | 45 | 37 | 28 |
N.S. |
1 | 1.00 | 0.97 | 1.06 | 1.58 | 1.58 | 1.55 | 1.45 | 1.19 | 0.90 |
time (sec) |
N/A | 0.275 | 0.008 | 0.277 | 0.034 | 0.068 | 0.183 | 0.120 | 0.161 | 25.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 60 | 60 | 64 | 93 | 123 | 87 | 74 | 145 | 73 |
N.S. |
1 | 0.88 | 0.88 | 0.94 | 1.37 | 1.81 | 1.28 | 1.09 | 2.13 | 1.07 |
time (sec) |
N/A | 0.305 | 0.010 | 0.232 | 0.027 | 0.068 | 0.213 | 0.130 | 0.157 | 24.892 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 75 | 63 | 76 | 91 | 121 | 83 | 74 | 145 | 72 |
N.S. |
1 | 0.87 | 0.73 | 0.88 | 1.06 | 1.41 | 0.97 | 0.86 | 1.69 | 0.84 |
time (sec) |
N/A | 0.291 | 0.011 | 0.231 | 0.027 | 0.065 | 0.221 | 0.108 | 0.162 | 25.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 75 | 66 | 60 | 89 | 143 | 87 | 73 | 172 | 88 |
N.S. |
1 | 0.81 | 0.71 | 0.65 | 0.96 | 1.54 | 0.94 | 0.78 | 1.85 | 0.95 |
time (sec) |
N/A | 0.338 | 0.035 | 0.228 | 0.032 | 0.079 | 0.360 | 0.135 | 0.163 | 24.910 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 89 | 78 | 74 | 104 | 175 | 104 | 88 | 201 | 104 |
N.S. |
1 | 0.82 | 0.72 | 0.68 | 0.95 | 1.61 | 0.95 | 0.81 | 1.84 | 0.95 |
time (sec) |
N/A | 0.369 | 0.048 | 0.241 | 0.045 | 0.076 | 0.413 | 0.134 | 0.155 | 0.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 111 | 98 | 94 | 120 | 197 | 121 | 102 | 221 | 119 |
N.S. |
1 | 0.83 | 0.73 | 0.70 | 0.90 | 1.47 | 0.90 | 0.76 | 1.65 | 0.89 |
time (sec) |
N/A | 0.415 | 0.060 | 0.234 | 0.034 | 0.113 | 0.551 | 0.118 | 0.163 | 25.342 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 104 | 82 | 92 | 140 | 217 | 143 | 91 | 269 | 122 |
N.S. |
1 | 0.86 | 0.68 | 0.76 | 1.16 | 1.79 | 1.18 | 0.75 | 2.22 | 1.01 |
time (sec) |
N/A | 0.345 | 0.020 | 0.234 | 0.035 | 0.086 | 0.365 | 0.172 | 0.157 | 0.129 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 191 | 96 | 97 | 120 | 184 | 0 | 0 | 100 | 0 |
N.S. |
1 | 1.24 | 0.62 | 0.63 | 0.78 | 1.19 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.519 | 0.118 | 0.299 | 0.228 | 0.088 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 160 | 88 | 89 | 96 | 168 | 0 | 84 | 81 | 0 |
N.S. |
1 | 1.24 | 0.68 | 0.69 | 0.74 | 1.30 | 0.00 | 0.65 | 0.63 | 0.00 |
time (sec) |
N/A | 0.465 | 0.088 | 0.287 | 0.210 | 0.084 | 0.000 | 0.882 | 0.160 | 0.000 |