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 | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 61 | 52 | 51 | 56 | 80 | 53 | 57 | 51 |
N.S. |
1 | 1.00 | 0.97 | 0.83 | 0.81 | 0.89 | 1.27 | 0.84 | 0.90 | 0.81 |
time (sec) |
N/A | 0.319 | 0.042 | 0.361 | 0.029 | 0.079 | 1.649 | 0.175 | 0.236 | 0.062 |
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 | 63 | 61 | 52 | 51 | 56 | 80 | 53 | 57 | 51 |
N.S. |
1 | 1.00 | 0.97 | 0.83 | 0.81 | 0.89 | 1.27 | 0.84 | 0.90 | 0.81 |
time (sec) |
N/A | 0.311 | 0.041 | 0.356 | 0.029 | 0.071 | 1.191 | 0.223 | 0.267 | 0.052 |
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 | 63 | 61 | 52 | 51 | 56 | 80 | 53 | 57 | 51 |
N.S. |
1 | 1.00 | 0.97 | 0.83 | 0.81 | 0.89 | 1.27 | 0.84 | 0.90 | 0.81 |
time (sec) |
N/A | 0.309 | 0.035 | 0.352 | 0.031 | 0.074 | 0.863 | 0.201 | 0.330 | 0.052 |
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 | 63 | 61 | 52 | 51 | 56 | 66 | 53 | 57 | 51 |
N.S. |
1 | 1.00 | 0.97 | 0.83 | 0.81 | 0.89 | 1.05 | 0.84 | 0.90 | 0.81 |
time (sec) |
N/A | 0.307 | 0.034 | 0.355 | 0.034 | 0.072 | 0.928 | 0.199 | 0.380 | 0.051 |
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 | 63 | 61 | 52 | 51 | 56 | 80 | 53 | 57 | 51 |
N.S. |
1 | 1.00 | 0.97 | 0.83 | 0.81 | 0.89 | 1.27 | 0.84 | 0.90 | 0.81 |
time (sec) |
N/A | 0.313 | 0.034 | 0.359 | 0.033 | 0.074 | 0.579 | 0.208 | 0.260 | 0.052 |
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 | 63 | 61 | 52 | 51 | 56 | 80 | 53 | 57 | 51 |
N.S. |
1 | 1.00 | 0.97 | 0.83 | 0.81 | 0.89 | 1.27 | 0.84 | 0.90 | 0.81 |
time (sec) |
N/A | 0.316 | 0.036 | 0.359 | 0.030 | 0.078 | 0.603 | 0.212 | 0.240 | 0.051 |
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 | 63 | 61 | 52 | 51 | 56 | 80 | 53 | 57 | 51 |
N.S. |
1 | 1.00 | 0.97 | 0.83 | 0.81 | 0.89 | 1.27 | 0.84 | 0.90 | 0.81 |
time (sec) |
N/A | 0.310 | 0.036 | 0.335 | 0.041 | 0.075 | 0.684 | 0.200 | 0.262 | 0.052 |
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 | 63 | 60 | 52 | 51 | 54 | 80 | 53 | 55 | 51 |
N.S. |
1 | 1.00 | 0.95 | 0.83 | 0.81 | 0.86 | 1.27 | 0.84 | 0.87 | 0.81 |
time (sec) |
N/A | 0.314 | 0.036 | 0.339 | 0.028 | 0.085 | 0.839 | 0.228 | 0.212 | 0.054 |
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 | 85 | 85 | 85 | 76 | 73 | 78 | 114 | 77 | 80 | 69 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.86 | 0.92 | 1.34 | 0.91 | 0.94 | 0.81 |
time (sec) |
N/A | 0.367 | 0.086 | 0.400 | 0.039 | 0.083 | 2.925 | 0.192 | 0.237 | 0.042 |
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 | 85 | 85 | 85 | 76 | 73 | 78 | 114 | 77 | 80 | 69 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.86 | 0.92 | 1.34 | 0.91 | 0.94 | 0.81 |
time (sec) |
N/A | 0.368 | 0.116 | 0.391 | 0.029 | 0.076 | 2.221 | 0.180 | 0.233 | 0.037 |
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 | 85 | 85 | 97 | 76 | 73 | 78 | 114 | 77 | 80 | 69 |
N.S. |
1 | 1.00 | 1.14 | 0.89 | 0.86 | 0.92 | 1.34 | 0.91 | 0.94 | 0.81 |
time (sec) |
N/A | 0.355 | 0.053 | 0.388 | 0.052 | 0.086 | 1.614 | 0.231 | 0.189 | 0.036 |
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 | 85 | 85 | 83 | 76 | 73 | 78 | 95 | 77 | 80 | 69 |
N.S. |
1 | 1.00 | 0.98 | 0.89 | 0.86 | 0.92 | 1.12 | 0.91 | 0.94 | 0.81 |
time (sec) |
N/A | 0.348 | 0.056 | 0.393 | 0.046 | 0.077 | 1.526 | 0.211 | 0.218 | 0.035 |
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 | 85 | 85 | 83 | 76 | 73 | 78 | 114 | 77 | 80 | 69 |
N.S. |
1 | 1.00 | 0.98 | 0.89 | 0.86 | 0.92 | 1.34 | 0.91 | 0.94 | 0.81 |
time (sec) |
N/A | 0.352 | 0.053 | 0.386 | 0.032 | 0.080 | 1.290 | 0.175 | 0.262 | 0.035 |
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 | 85 | 85 | 83 | 76 | 73 | 78 | 114 | 77 | 80 | 69 |
N.S. |
1 | 1.00 | 0.98 | 0.89 | 0.86 | 0.92 | 1.34 | 0.91 | 0.94 | 0.81 |
time (sec) |
N/A | 0.348 | 0.049 | 0.391 | 0.030 | 0.082 | 1.305 | 0.217 | 0.209 | 0.036 |
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 | 85 | 85 | 83 | 76 | 73 | 78 | 114 | 77 | 80 | 69 |
N.S. |
1 | 1.00 | 0.98 | 0.89 | 0.86 | 0.92 | 1.34 | 0.91 | 0.94 | 0.81 |
time (sec) |
N/A | 0.347 | 0.045 | 0.390 | 0.037 | 0.078 | 1.413 | 0.212 | 0.191 | 0.036 |
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 | 85 | 85 | 83 | 76 | 73 | 78 | 114 | 77 | 80 | 69 |
N.S. |
1 | 1.00 | 0.98 | 0.89 | 0.86 | 0.92 | 1.34 | 0.91 | 0.94 | 0.81 |
time (sec) |
N/A | 0.346 | 0.043 | 0.389 | 0.038 | 0.078 | 1.727 | 0.221 | 0.275 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 277 | 172 | 164 | 237 | 770 | 0 | 298 | 334 | 115 |
N.S. |
1 | 1.29 | 0.80 | 0.77 | 1.11 | 3.60 | 0.00 | 1.39 | 1.56 | 0.54 |
time (sec) |
N/A | 0.830 | 0.246 | 0.456 | 0.113 | 0.101 | 0.000 | 0.236 | 0.202 | 0.175 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 213 | 275 | 173 | 162 | 259 | 647 | 0 | 298 | 332 | 788 |
N.S. |
1 | 1.29 | 0.81 | 0.76 | 1.22 | 3.04 | 0.00 | 1.40 | 1.56 | 3.70 |
time (sec) |
N/A | 0.834 | 0.252 | 0.449 | 0.116 | 0.101 | 0.000 | 0.250 | 0.214 | 9.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 258 | 152 | 140 | 214 | 749 | 348 | 264 | 309 | 92 |
N.S. |
1 | 1.33 | 0.78 | 0.72 | 1.10 | 3.86 | 1.79 | 1.36 | 1.59 | 0.47 |
time (sec) |
N/A | 0.771 | 0.195 | 0.447 | 0.119 | 0.092 | 94.011 | 0.227 | 0.189 | 9.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 256 | 150 | 138 | 235 | 597 | 275 | 263 | 307 | 789 |
N.S. |
1 | 1.34 | 0.79 | 0.72 | 1.23 | 3.13 | 1.44 | 1.38 | 1.61 | 4.13 |
time (sec) |
N/A | 0.746 | 0.176 | 0.445 | 0.132 | 0.091 | 46.439 | 0.186 | 0.223 | 9.161 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 239 | 135 | 124 | 194 | 691 | 303 | 251 | 292 | 71 |
N.S. |
1 | 1.38 | 0.78 | 0.72 | 1.12 | 3.99 | 1.75 | 1.45 | 1.69 | 0.41 |
time (sec) |
N/A | 0.701 | 0.176 | 0.446 | 0.121 | 0.105 | 18.677 | 0.224 | 0.209 | 9.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 237 | 134 | 127 | 218 | 570 | 238 | 251 | 289 | 739 |
N.S. |
1 | 1.38 | 0.78 | 0.74 | 1.27 | 3.31 | 1.38 | 1.46 | 1.68 | 4.30 |
time (sec) |
N/A | 0.704 | 0.172 | 0.448 | 0.114 | 0.100 | 8.087 | 0.228 | 0.242 | 0.239 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 237 | 135 | 127 | 194 | 705 | 309 | 251 | 306 | 71 |
N.S. |
1 | 1.38 | 0.78 | 0.74 | 1.13 | 4.10 | 1.80 | 1.46 | 1.78 | 0.41 |
time (sec) |
N/A | 0.718 | 0.215 | 0.438 | 0.125 | 0.111 | 5.242 | 0.204 | 0.234 | 8.988 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 239 | 136 | 124 | 218 | 590 | 257 | 251 | 319 | 811 |
N.S. |
1 | 1.38 | 0.79 | 0.72 | 1.26 | 3.41 | 1.49 | 1.45 | 1.84 | 4.69 |
time (sec) |
N/A | 0.727 | 0.231 | 0.448 | 0.117 | 0.091 | 6.744 | 0.250 | 0.215 | 9.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 255 | 152 | 140 | 213 | 738 | 258 | 268 | 349 | 90 |
N.S. |
1 | 1.34 | 0.80 | 0.73 | 1.12 | 3.86 | 1.35 | 1.40 | 1.83 | 0.47 |
time (sec) |
N/A | 0.762 | 0.230 | 0.452 | 0.121 | 0.107 | 36.028 | 0.214 | 0.197 | 8.985 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 257 | 154 | 141 | 247 | 643 | 303 | 257 | 349 | 555 |
N.S. |
1 | 1.32 | 0.79 | 0.73 | 1.27 | 3.31 | 1.56 | 1.32 | 1.80 | 2.86 |
time (sec) |
N/A | 0.766 | 0.243 | 0.454 | 0.118 | 0.094 | 27.259 | 0.228 | 0.193 | 8.994 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 213 | 274 | 174 | 158 | 237 | 784 | 304 | 291 | 370 | 107 |
N.S. |
1 | 1.29 | 0.82 | 0.74 | 1.11 | 3.68 | 1.43 | 1.37 | 1.74 | 0.50 |
time (sec) |
N/A | 0.790 | 0.280 | 0.452 | 0.130 | 0.108 | 105.566 | 0.232 | 0.210 | 0.178 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 276 | 176 | 160 | 276 | 672 | 340 | 291 | 370 | 563 |
N.S. |
1 | 1.29 | 0.82 | 0.75 | 1.29 | 3.14 | 1.59 | 1.36 | 1.73 | 2.63 |
time (sec) |
N/A | 0.791 | 0.283 | 0.449 | 0.140 | 0.137 | 131.680 | 0.262 | 0.196 | 9.295 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 319 | 206 | 193 | 298 | 748 | 0 | 335 | 666 | 857 |
N.S. |
1 | 1.24 | 0.80 | 0.75 | 1.16 | 2.91 | 0.00 | 1.30 | 2.59 | 3.33 |
time (sec) |
N/A | 0.881 | 0.650 | 0.474 | 0.134 | 0.104 | 0.000 | 0.219 | 0.197 | 9.243 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 302 | 184 | 170 | 247 | 848 | 0 | 299 | 641 | 127 |
N.S. |
1 | 1.29 | 0.78 | 0.72 | 1.05 | 3.61 | 0.00 | 1.27 | 2.73 | 0.54 |
time (sec) |
N/A | 0.863 | 0.620 | 0.474 | 0.116 | 0.101 | 0.000 | 0.253 | 0.211 | 9.210 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 300 | 183 | 169 | 271 | 696 | 0 | 298 | 639 | 823 |
N.S. |
1 | 1.29 | 0.79 | 0.73 | 1.16 | 2.99 | 0.00 | 1.28 | 2.74 | 3.53 |
time (sec) |
N/A | 0.865 | 0.524 | 0.470 | 0.116 | 0.110 | 0.000 | 0.201 | 0.208 | 0.216 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 213 | 283 | 162 | 153 | 223 | 793 | 0 | 283 | 622 | 106 |
N.S. |
1 | 1.33 | 0.76 | 0.72 | 1.05 | 3.72 | 0.00 | 1.33 | 2.92 | 0.50 |
time (sec) |
N/A | 0.840 | 0.530 | 0.467 | 0.115 | 0.099 | 0.000 | 0.243 | 0.209 | 9.266 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 281 | 161 | 152 | 250 | 669 | 0 | 283 | 618 | 744 |
N.S. |
1 | 1.33 | 0.76 | 0.72 | 1.18 | 3.17 | 0.00 | 1.34 | 2.93 | 3.53 |
time (sec) |
N/A | 0.834 | 0.521 | 0.454 | 0.126 | 0.101 | 0.000 | 0.250 | 0.188 | 9.302 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 263 | 152 | 146 | 217 | 776 | 0 | 273 | 607 | 91 |
N.S. |
1 | 1.32 | 0.76 | 0.73 | 1.08 | 3.88 | 0.00 | 1.36 | 3.04 | 0.46 |
time (sec) |
N/A | 0.795 | 0.478 | 0.428 | 0.127 | 0.107 | 0.000 | 0.215 | 0.209 | 0.171 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 263 | 151 | 146 | 241 | 658 | 0 | 273 | 605 | 750 |
N.S. |
1 | 1.32 | 0.76 | 0.73 | 1.20 | 3.29 | 0.00 | 1.36 | 3.02 | 3.75 |
time (sec) |
N/A | 0.779 | 0.514 | 0.432 | 0.127 | 0.105 | 0.000 | 0.252 | 0.197 | 8.988 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 280 | 162 | 153 | 222 | 789 | 0 | 278 | 650 | 104 |
N.S. |
1 | 1.35 | 0.78 | 0.74 | 1.07 | 3.79 | 0.00 | 1.34 | 3.12 | 0.50 |
time (sec) |
N/A | 0.841 | 0.557 | 0.428 | 0.119 | 0.118 | 0.000 | 0.213 | 0.209 | 8.748 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 213 | 283 | 165 | 153 | 251 | 691 | 0 | 283 | 663 | 859 |
N.S. |
1 | 1.33 | 0.77 | 0.72 | 1.18 | 3.24 | 0.00 | 1.33 | 3.11 | 4.03 |
time (sec) |
N/A | 0.829 | 0.569 | 0.429 | 0.122 | 0.112 | 0.000 | 0.222 | 0.216 | 9.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 232 | 300 | 187 | 170 | 250 | 838 | 0 | 303 | 693 | 121 |
N.S. |
1 | 1.29 | 0.81 | 0.73 | 1.08 | 3.61 | 0.00 | 1.31 | 2.99 | 0.52 |
time (sec) |
N/A | 0.919 | 0.553 | 0.430 | 0.125 | 0.124 | 0.000 | 0.260 | 0.193 | 0.183 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 234 | 302 | 187 | 170 | 286 | 742 | 0 | 292 | 693 | 595 |
N.S. |
1 | 1.29 | 0.80 | 0.73 | 1.22 | 3.17 | 0.00 | 1.25 | 2.96 | 2.54 |
time (sec) |
N/A | 0.874 | 0.645 | 0.430 | 0.118 | 0.104 | 0.000 | 0.253 | 0.188 | 9.450 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 256 | 319 | 209 | 190 | 276 | 886 | 0 | 328 | 716 | 142 |
N.S. |
1 | 1.25 | 0.82 | 0.74 | 1.08 | 3.46 | 0.00 | 1.28 | 2.80 | 0.55 |
time (sec) |
N/A | 0.911 | 0.793 | 0.428 | 0.113 | 0.114 | 0.000 | 0.252 | 0.231 | 9.616 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 266 | 329 | 204 | 189 | 306 | 776 | 0 | 321 | 975 | 865 |
N.S. |
1 | 1.24 | 0.77 | 0.71 | 1.15 | 2.92 | 0.00 | 1.21 | 3.67 | 3.25 |
time (sec) |
N/A | 0.879 | 0.604 | 0.477 | 0.117 | 0.115 | 0.000 | 0.252 | 0.182 | 0.248 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 244 | 312 | 184 | 173 | 256 | 872 | 0 | 304 | 958 | 138 |
N.S. |
1 | 1.28 | 0.75 | 0.71 | 1.05 | 3.57 | 0.00 | 1.25 | 3.93 | 0.57 |
time (sec) |
N/A | 0.896 | 0.685 | 0.472 | 0.123 | 0.117 | 0.000 | 0.275 | 0.189 | 9.511 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 242 | 310 | 184 | 172 | 283 | 748 | 0 | 304 | 956 | 760 |
N.S. |
1 | 1.28 | 0.76 | 0.71 | 1.17 | 3.09 | 0.00 | 1.26 | 3.95 | 3.14 |
time (sec) |
N/A | 0.872 | 0.637 | 0.476 | 0.131 | 0.119 | 0.000 | 0.239 | 0.212 | 9.629 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 230 | 292 | 171 | 166 | 251 | 871 | 0 | 293 | 945 | 122 |
N.S. |
1 | 1.27 | 0.74 | 0.72 | 1.09 | 3.79 | 0.00 | 1.27 | 4.11 | 0.53 |
time (sec) |
N/A | 0.812 | 0.699 | 0.448 | 0.115 | 0.106 | 0.000 | 0.228 | 0.206 | 9.398 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 293 | 173 | 167 | 280 | 763 | 0 | 298 | 943 | 799 |
N.S. |
1 | 1.26 | 0.74 | 0.72 | 1.20 | 3.27 | 0.00 | 1.28 | 4.05 | 3.43 |
time (sec) |
N/A | 0.829 | 0.664 | 0.406 | 0.127 | 0.111 | 0.000 | 0.221 | 0.196 | 9.139 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 236 | 293 | 175 | 168 | 253 | 878 | 0 | 298 | 945 | 124 |
N.S. |
1 | 1.24 | 0.74 | 0.71 | 1.07 | 3.72 | 0.00 | 1.26 | 4.00 | 0.53 |
time (sec) |
N/A | 0.836 | 0.643 | 0.400 | 0.123 | 0.105 | 0.000 | 0.219 | 0.194 | 8.953 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 232 | 292 | 172 | 166 | 276 | 749 | 0 | 293 | 943 | 780 |
N.S. |
1 | 1.26 | 0.74 | 0.72 | 1.19 | 3.23 | 0.00 | 1.26 | 4.06 | 3.36 |
time (sec) |
N/A | 0.802 | 0.648 | 0.402 | 0.131 | 0.107 | 0.000 | 0.185 | 0.220 | 0.336 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 238 | 309 | 187 | 173 | 255 | 870 | 0 | 300 | 1000 | 133 |
N.S. |
1 | 1.30 | 0.79 | 0.73 | 1.07 | 3.66 | 0.00 | 1.26 | 4.20 | 0.56 |
time (sec) |
N/A | 0.905 | 0.704 | 0.434 | 0.124 | 0.105 | 0.000 | 0.192 | 0.219 | 0.190 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 243 | 312 | 187 | 173 | 285 | 770 | 0 | 304 | 1011 | 888 |
N.S. |
1 | 1.28 | 0.77 | 0.71 | 1.17 | 3.17 | 0.00 | 1.25 | 4.16 | 3.65 |
time (sec) |
N/A | 0.873 | 0.632 | 0.431 | 0.126 | 0.103 | 0.000 | 0.224 | 0.203 | 9.548 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 263 | 329 | 209 | 190 | 285 | 918 | 0 | 326 | 1041 | 152 |
N.S. |
1 | 1.25 | 0.79 | 0.72 | 1.08 | 3.49 | 0.00 | 1.24 | 3.96 | 0.58 |
time (sec) |
N/A | 0.935 | 0.666 | 0.443 | 0.137 | 0.098 | 0.000 | 0.179 | 0.222 | 9.280 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 265 | 331 | 210 | 190 | 321 | 822 | 0 | 315 | 1041 | 626 |
N.S. |
1 | 1.25 | 0.79 | 0.72 | 1.21 | 3.10 | 0.00 | 1.19 | 3.93 | 2.36 |
time (sec) |
N/A | 0.907 | 0.729 | 0.433 | 0.130 | 0.105 | 0.000 | 0.220 | 0.228 | 9.278 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 288 | 348 | 231 | 210 | 311 | 966 | 0 | 351 | 1064 | 173 |
N.S. |
1 | 1.21 | 0.80 | 0.73 | 1.08 | 3.35 | 0.00 | 1.22 | 3.69 | 0.60 |
time (sec) |
N/A | 0.951 | 0.695 | 0.443 | 0.134 | 0.100 | 0.000 | 0.209 | 0.212 | 9.204 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 288 | 350 | 231 | 210 | 353 | 854 | 0 | 351 | 1064 | 639 |
N.S. |
1 | 1.22 | 0.80 | 0.73 | 1.23 | 2.97 | 0.00 | 1.22 | 3.69 | 2.22 |
time (sec) |
N/A | 0.957 | 0.688 | 0.437 | 0.140 | 0.097 | 0.000 | 0.223 | 0.258 | 9.603 |
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 | 218 | 214 | 189 | 178 | 321 | 368 | 345 | 245 | 261 | 289 |
N.S. |
1 | 0.98 | 0.87 | 0.82 | 1.47 | 1.69 | 1.58 | 1.12 | 1.20 | 1.33 |
time (sec) |
N/A | 0.683 | 0.910 | 0.524 | 0.043 | 0.179 | 0.732 | 0.224 | 0.296 | 10.100 |
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 | 181 | 180 | 170 | 159 | 273 | 321 | 318 | 211 | 222 | 233 |
N.S. |
1 | 0.99 | 0.94 | 0.88 | 1.51 | 1.77 | 1.76 | 1.17 | 1.23 | 1.29 |
time (sec) |
N/A | 0.640 | 0.664 | 0.477 | 0.046 | 0.133 | 0.670 | 0.189 | 0.319 | 9.817 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 128 | 147 | 140 | 225 | 272 | 287 | 177 | 183 | 177 |
N.S. |
1 | 1.02 | 1.18 | 1.12 | 1.80 | 2.18 | 2.30 | 1.42 | 1.46 | 1.42 |
time (sec) |
N/A | 0.474 | 0.573 | 0.483 | 0.041 | 0.105 | 0.655 | 0.202 | 0.230 | 9.955 |
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 | 107 | 111 | 126 | 116 | 177 | 223 | 255 | 140 | 144 | 140 |
N.S. |
1 | 1.04 | 1.18 | 1.08 | 1.65 | 2.08 | 2.38 | 1.31 | 1.35 | 1.31 |
time (sec) |
N/A | 0.433 | 0.394 | 0.456 | 0.040 | 0.103 | 0.623 | 0.216 | 0.200 | 10.159 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 94 | 97 | 91 | 128 | 172 | 0 | 103 | 104 | 117 |
N.S. |
1 | 0.94 | 0.97 | 0.91 | 1.28 | 1.72 | 0.00 | 1.03 | 1.04 | 1.17 |
time (sec) |
N/A | 0.451 | 0.123 | 0.445 | 0.042 | 0.106 | 0.000 | 0.206 | 0.187 | 9.971 |
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 | 97 | 89 | 87 | 83 | 105 | 161 | 0 | 87 | 104 | 0 |
N.S. |
1 | 0.92 | 0.90 | 0.86 | 1.08 | 1.66 | 0.00 | 0.90 | 1.07 | 0.00 |
time (sec) |
N/A | 0.452 | 0.173 | 0.460 | 0.040 | 0.103 | 0.000 | 0.239 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 86 | 99 | 86 | 96 | 160 | 0 | 163 | 99 | 0 |
N.S. |
1 | 1.08 | 1.24 | 1.08 | 1.20 | 2.00 | 0.00 | 2.04 | 1.24 | 0.00 |
time (sec) |
N/A | 0.456 | 0.108 | 0.453 | 0.037 | 0.101 | 0.000 | 0.344 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 65 | 44 | 47 | 111 | 59 | 0 | 250 | 111 | 113 |
N.S. |
1 | 1.07 | 0.72 | 0.77 | 1.82 | 0.97 | 0.00 | 4.10 | 1.82 | 1.85 |
time (sec) |
N/A | 0.398 | 0.103 | 0.422 | 0.044 | 0.097 | 0.000 | 0.622 | 0.186 | 9.741 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 99 | 66 | 66 | 161 | 85 | 0 | 310 | 152 | 160 |
N.S. |
1 | 1.03 | 0.69 | 0.69 | 1.68 | 0.89 | 0.00 | 3.23 | 1.58 | 1.67 |
time (sec) |
N/A | 0.453 | 0.146 | 0.431 | 0.041 | 0.099 | 0.000 | 0.761 | 0.195 | 9.797 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 133 | 88 | 84 | 209 | 109 | 0 | 370 | 191 | 210 |
N.S. |
1 | 1.00 | 0.66 | 0.63 | 1.57 | 0.82 | 0.00 | 2.78 | 1.44 | 1.58 |
time (sec) |
N/A | 0.517 | 0.164 | 0.442 | 0.041 | 0.110 | 0.000 | 1.150 | 0.213 | 10.006 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 167 | 110 | 104 | 257 | 133 | 0 | 430 | 230 | 260 |
N.S. |
1 | 0.98 | 0.65 | 0.61 | 1.51 | 0.78 | 0.00 | 2.53 | 1.35 | 1.53 |
time (sec) |
N/A | 0.596 | 0.196 | 0.438 | 0.041 | 0.160 | 0.000 | 1.847 | 0.213 | 10.937 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 127 | 82 | 91 | 106 | 106 | 0 | 140 | 97 | 103 |
N.S. |
1 | 0.97 | 0.63 | 0.69 | 0.81 | 0.81 | 0.00 | 1.07 | 0.74 | 0.79 |
time (sec) |
N/A | 0.478 | 0.071 | 0.865 | 0.042 | 0.098 | 0.000 | 0.204 | 0.210 | 9.765 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 93 | 64 | 67 | 83 | 82 | 0 | 105 | 74 | 83 |
N.S. |
1 | 0.99 | 0.68 | 0.71 | 0.88 | 0.87 | 0.00 | 1.12 | 0.79 | 0.88 |
time (sec) |
N/A | 0.417 | 0.048 | 0.747 | 0.054 | 0.087 | 0.000 | 0.182 | 0.182 | 9.618 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 41 | 45 | 51 | 57 | 0 | 72 | 50 | 60 |
N.S. |
1 | 1.00 | 0.67 | 0.74 | 0.84 | 0.93 | 0.00 | 1.18 | 0.82 | 0.98 |
time (sec) |
N/A | 0.325 | 0.041 | 0.668 | 0.041 | 0.087 | 0.000 | 0.161 | 0.233 | 9.650 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 79 | 84 | 84 | 0 | 154 | 0 | 116 | 100 | 99 |
N.S. |
1 | 1.01 | 1.08 | 1.08 | 0.00 | 1.97 | 0.00 | 1.49 | 1.28 | 1.27 |
time (sec) |
N/A | 0.390 | 0.094 | 0.675 | 0.000 | 0.096 | 0.000 | 0.186 | 0.193 | 9.639 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 92 | 94 | 95 | 0 | 164 | 0 | 78 | 162 | 0 |
N.S. |
1 | 0.92 | 0.94 | 0.95 | 0.00 | 1.64 | 0.00 | 0.78 | 1.62 | 0.00 |
time (sec) |
N/A | 0.422 | 0.121 | 0.763 | 0.000 | 0.111 | 0.000 | 0.210 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 99 | 106 | 103 | 0 | 193 | 0 | 132 | 186 | 0 |
N.S. |
1 | 0.96 | 1.03 | 1.00 | 0.00 | 1.87 | 0.00 | 1.28 | 1.81 | 0.00 |
time (sec) |
N/A | 0.427 | 0.133 | 0.866 | 0.000 | 0.111 | 0.000 | 0.219 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 221 | 248 | 197 | 363 | 418 | 726 | 280 | 300 | 0 |
N.S. |
1 | 0.99 | 1.11 | 0.88 | 1.63 | 1.87 | 3.26 | 1.26 | 1.35 | 0.00 |
time (sec) |
N/A | 0.694 | 1.222 | 0.486 | 0.042 | 0.253 | 1.289 | 0.185 | 0.309 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 169 | 226 | 178 | 315 | 369 | 672 | 246 | 261 | 0 |
N.S. |
1 | 1.01 | 1.35 | 1.07 | 1.89 | 2.21 | 4.02 | 1.47 | 1.56 | 0.00 |
time (sec) |
N/A | 0.571 | 0.989 | 0.476 | 0.049 | 0.183 | 1.094 | 0.183 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 152 | 199 | 159 | 267 | 316 | 614 | 207 | 222 | 236 |
N.S. |
1 | 1.03 | 1.34 | 1.07 | 1.80 | 2.14 | 4.15 | 1.40 | 1.50 | 1.59 |
time (sec) |
N/A | 0.491 | 0.756 | 0.468 | 0.042 | 0.130 | 0.962 | 0.219 | 0.210 | 9.848 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 140 | 157 | 140 | 216 | 275 | 551 | 178 | 183 | 0 |
N.S. |
1 | 0.97 | 1.09 | 0.97 | 1.50 | 1.91 | 3.83 | 1.24 | 1.27 | 0.00 |
time (sec) |
N/A | 0.533 | 0.595 | 0.471 | 0.041 | 0.104 | 4.304 | 0.198 | 0.206 | 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 | 137 | 134 | 124 | 116 | 168 | 224 | 0 | 142 | 144 | 0 |
N.S. |
1 | 0.98 | 0.91 | 0.85 | 1.23 | 1.64 | 0.00 | 1.04 | 1.05 | 0.00 |
time (sec) |
N/A | 0.543 | 0.200 | 0.472 | 0.042 | 0.097 | 0.000 | 0.216 | 0.211 | 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 | 128 | 117 | 116 | 101 | 148 | 209 | 0 | 121 | 143 | 0 |
N.S. |
1 | 0.91 | 0.91 | 0.79 | 1.16 | 1.63 | 0.00 | 0.95 | 1.12 | 0.00 |
time (sec) |
N/A | 0.522 | 0.322 | 0.469 | 0.040 | 0.090 | 0.000 | 0.298 | 0.203 | 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 | 133 | 120 | 120 | 101 | 167 | 189 | 0 | 225 | 131 | 0 |
N.S. |
1 | 0.90 | 0.90 | 0.76 | 1.26 | 1.42 | 0.00 | 1.69 | 0.98 | 0.00 |
time (sec) |
N/A | 0.558 | 0.231 | 0.463 | 0.044 | 0.091 | 0.000 | 0.363 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 111 | 110 | 107 | 177 | 207 | 0 | 254 | 141 | 0 |
N.S. |
1 | 1.07 | 1.06 | 1.03 | 1.70 | 1.99 | 0.00 | 2.44 | 1.36 | 0.00 |
time (sec) |
N/A | 0.490 | 0.177 | 0.470 | 0.049 | 0.090 | 0.000 | 0.695 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 65 | 44 | 48 | 193 | 82 | 0 | 370 | 152 | 156 |
N.S. |
1 | 1.07 | 0.72 | 0.79 | 3.16 | 1.34 | 0.00 | 6.07 | 2.49 | 2.56 |
time (sec) |
N/A | 0.401 | 0.168 | 0.432 | 0.042 | 0.087 | 0.000 | 1.158 | 0.227 | 10.294 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 99 | 66 | 68 | 241 | 109 | 0 | 430 | 191 | 206 |
N.S. |
1 | 1.03 | 0.69 | 0.71 | 2.51 | 1.14 | 0.00 | 4.48 | 1.99 | 2.15 |
time (sec) |
N/A | 0.457 | 0.209 | 0.473 | 0.050 | 0.102 | 0.000 | 1.455 | 0.194 | 10.580 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 133 | 89 | 87 | 289 | 134 | 0 | 490 | 230 | 256 |
N.S. |
1 | 1.00 | 0.67 | 0.65 | 2.17 | 1.01 | 0.00 | 3.68 | 1.73 | 1.92 |
time (sec) |
N/A | 0.543 | 0.252 | 0.445 | 0.047 | 0.135 | 0.000 | 1.650 | 0.201 | 11.103 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 167 | 110 | 106 | 337 | 157 | 0 | 550 | 269 | 306 |
N.S. |
1 | 0.98 | 0.65 | 0.62 | 1.98 | 0.92 | 0.00 | 3.24 | 1.58 | 1.80 |
time (sec) |
N/A | 0.607 | 0.285 | 0.461 | 0.050 | 0.184 | 0.000 | 2.056 | 0.250 | 11.829 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 201 | 132 | 124 | 385 | 181 | 0 | 582 | 308 | 356 |
N.S. |
1 | 0.97 | 0.64 | 0.60 | 1.86 | 0.87 | 0.00 | 2.81 | 1.49 | 1.72 |
time (sec) |
N/A | 0.677 | 0.339 | 0.488 | 0.052 | 0.299 | 0.000 | 2.113 | 0.210 | 12.425 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 161 | 113 | 115 | 150 | 154 | 0 | 175 | 143 | 143 |
N.S. |
1 | 0.96 | 0.67 | 0.68 | 0.89 | 0.92 | 0.00 | 1.04 | 0.85 | 0.85 |
time (sec) |
N/A | 0.582 | 0.092 | 0.857 | 0.043 | 0.103 | 0.000 | 0.209 | 0.188 | 9.296 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 127 | 94 | 91 | 128 | 131 | 0 | 140 | 120 | 124 |
N.S. |
1 | 0.97 | 0.72 | 0.69 | 0.98 | 1.00 | 0.00 | 1.07 | 0.92 | 0.95 |
time (sec) |
N/A | 0.501 | 0.086 | 0.739 | 0.049 | 0.098 | 0.000 | 0.218 | 0.188 | 9.432 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 95 | 70 | 67 | 105 | 106 | 0 | 105 | 97 | 103 |
N.S. |
1 | 0.99 | 0.73 | 0.70 | 1.09 | 1.10 | 0.00 | 1.09 | 1.01 | 1.07 |
time (sec) |
N/A | 0.406 | 0.056 | 0.665 | 0.046 | 0.089 | 0.000 | 0.163 | 0.203 | 8.911 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 41 | 45 | 80 | 80 | 0 | 72 | 73 | 83 |
N.S. |
1 | 1.00 | 0.67 | 0.74 | 1.31 | 1.31 | 0.00 | 1.18 | 1.20 | 1.36 |
time (sec) |
N/A | 0.353 | 0.036 | 0.669 | 0.045 | 0.083 | 0.000 | 0.224 | 0.195 | 9.154 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 104 | 108 | 99 | 0 | 201 | 0 | 140 | 141 | 0 |
N.S. |
1 | 1.02 | 1.06 | 0.97 | 0.00 | 1.97 | 0.00 | 1.37 | 1.38 | 0.00 |
time (sec) |
N/A | 0.461 | 0.126 | 0.751 | 0.000 | 0.097 | 0.000 | 0.182 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 118 | 109 | 149 | 0 | 190 | 0 | 124 | 190 | 0 |
N.S. |
1 | 0.89 | 0.82 | 1.12 | 0.00 | 1.43 | 0.00 | 0.93 | 1.43 | 0.00 |
time (sec) |
N/A | 0.532 | 0.145 | 0.886 | 0.000 | 0.111 | 0.000 | 0.279 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 120 | 114 | 117 | 0 | 212 | 0 | 145 | 204 | 0 |
N.S. |
1 | 0.89 | 0.84 | 0.87 | 0.00 | 1.57 | 0.00 | 1.07 | 1.51 | 0.00 |
time (sec) |
N/A | 0.486 | 0.169 | 1.026 | 0.000 | 0.107 | 0.000 | 0.262 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 127 | 132 | 128 | 0 | 245 | 0 | 158 | 228 | 0 |
N.S. |
1 | 0.91 | 0.94 | 0.91 | 0.00 | 1.75 | 0.00 | 1.13 | 1.63 | 0.00 |
time (sec) |
N/A | 0.490 | 0.216 | 1.207 | 0.000 | 0.122 | 0.000 | 0.293 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 158 | 154 | 153 | 0 | 294 | 0 | 214 | 267 | 0 |
N.S. |
1 | 0.89 | 0.87 | 0.86 | 0.00 | 1.66 | 0.00 | 1.21 | 1.51 | 0.00 |
time (sec) |
N/A | 0.592 | 0.280 | 1.451 | 0.000 | 0.122 | 0.000 | 0.269 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 192 | 172 | 176 | 0 | 340 | 0 | 210 | 306 | 0 |
N.S. |
1 | 0.90 | 0.80 | 0.82 | 0.00 | 1.59 | 0.00 | 0.98 | 1.43 | 0.00 |
time (sec) |
N/A | 0.656 | 0.372 | 1.731 | 0.000 | 0.152 | 0.000 | 0.271 | 0.270 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 226 | 198 | 201 | 0 | 388 | 0 | 294 | 345 | 0 |
N.S. |
1 | 0.90 | 0.79 | 0.80 | 0.00 | 1.55 | 0.00 | 1.17 | 1.37 | 0.00 |
time (sec) |
N/A | 0.777 | 0.386 | 2.122 | 0.000 | 0.198 | 0.000 | 0.261 | 0.358 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 168 | 155 | 140 | 231 | 275 | 224 | 184 | 183 | 0 |
N.S. |
1 | 0.95 | 0.88 | 0.80 | 1.31 | 1.56 | 1.27 | 1.05 | 1.04 | 0.00 |
time (sec) |
N/A | 0.602 | 0.513 | 0.471 | 0.040 | 0.123 | 0.839 | 0.204 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 134 | 133 | 121 | 183 | 226 | 201 | 150 | 144 | 0 |
N.S. |
1 | 0.96 | 0.96 | 0.87 | 1.32 | 1.63 | 1.45 | 1.08 | 1.04 | 0.00 |
time (sec) |
N/A | 0.544 | 0.418 | 0.461 | 0.040 | 0.111 | 0.798 | 0.240 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 87 | 108 | 100 | 134 | 177 | 170 | 112 | 105 | 0 |
N.S. |
1 | 1.05 | 1.30 | 1.20 | 1.61 | 2.13 | 2.05 | 1.35 | 1.27 | 0.00 |
time (sec) |
N/A | 0.413 | 0.290 | 0.451 | 0.037 | 0.098 | 0.795 | 0.223 | 0.236 | 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 | 66 | 65 | 91 | 84 | 88 | 131 | 139 | 77 | 69 | 89 |
N.S. |
1 | 0.98 | 1.38 | 1.27 | 1.33 | 1.98 | 2.11 | 1.17 | 1.05 | 1.35 |
time (sec) |
N/A | 0.364 | 0.170 | 0.445 | 0.041 | 0.102 | 0.798 | 0.224 | 0.189 | 9.537 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 62 | 77 | 67 | 56 | 136 | 0 | 66 | 56 | 57 |
N.S. |
1 | 1.09 | 1.35 | 1.18 | 0.98 | 2.39 | 0.00 | 1.16 | 0.98 | 1.00 |
time (sec) |
N/A | 0.386 | 0.078 | 0.450 | 0.037 | 0.097 | 0.000 | 0.247 | 0.183 | 9.191 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 65 | 43 | 40 | 70 | 38 | 0 | 124 | 70 | 39 |
N.S. |
1 | 1.07 | 0.70 | 0.66 | 1.15 | 0.62 | 0.00 | 2.03 | 1.15 | 0.64 |
time (sec) |
N/A | 0.394 | 0.086 | 0.425 | 0.043 | 0.096 | 0.000 | 0.316 | 0.224 | 8.920 |