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 | N/A | N/A | N/A | F(-2) | F(-2) | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 0 | 0 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 0.00 | 0.12 | 0.92 |
time (sec) |
N/A | 0.580 | 33.776 | 0.224 | 0.000 | 0.000 | 0.000 | 218.806 | 0.346 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 62 | 0 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 2.38 | 0.00 | 0.12 | 0.92 |
time (sec) |
N/A | 0.081 | 1.789 | 0.536 | 0.000 | 0.265 | 0.000 | 241.727 | 0.371 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | F(-2) | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 190 | 190 | 255 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.553 | 0.783 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | F(-2) | F(-1) | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 224 | 224 | 311 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.793 | 0.656 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | F(-2) | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 222 | 222 | 261 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.717 | 0.769 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | F(-2) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 183 | 183 | 300 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.433 | 0.437 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | F(-1) | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 0 | 0 | 0 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.92 |
time (sec) |
N/A | 0.507 | 9.927 | 0.183 | 0.000 | 0.000 | 0.000 | 0.000 | 0.363 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 0 | 0 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 0.00 | 0.12 | 0.92 |
time (sec) |
N/A | 0.588 | 9.373 | 0.197 | 0.000 | 0.000 | 0.000 | 254.935 | 0.358 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | F(-1) | F(-2) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 0 | 0 | 0 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.92 |
time (sec) |
N/A | 0.543 | 16.584 | 0.222 | 0.000 | 0.000 | 0.000 | 0.000 | 0.358 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 22 | 0 | 0 | 0 | 3 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.85 | 0.00 | 0.00 | 0.00 | 0.12 | 0.92 |
time (sec) |
N/A | 0.562 | 40.005 | 0.230 | 0.000 | 0.000 | 0.000 | 257.280 | 0.358 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 0 | 22 | 19 | 3 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 0.00 | 1.10 | 0.95 | 0.15 | 1.10 |
time (sec) |
N/A | 0.045 | 0.878 | 0.095 | 0.000 | 0.250 | 0.604 | 54.735 | 0.448 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 21 | 0 | 21 | 0 | 20 | 20 |
N.S. |
1 | 1.00 | 1.00 | 1.05 | 0.00 | 1.05 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.023 | 0.005 | 0.338 | 0.000 | 0.249 | 0.000 | 0.270 | 0.443 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 28 | 30 | 30 | 0 | 3 | 30 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.07 | 1.07 | 0.00 | 0.11 | 1.07 |
time (sec) |
N/A | 0.060 | 0.653 | 1.216 | 0.645 | 0.258 | 0.000 | 80.871 | 0.695 |
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 | 107 | 107 | 127 | 108 | 108 | 110 | 138 | 0 | 105 |
N.S. |
1 | 1.00 | 1.19 | 1.01 | 1.01 | 1.03 | 1.29 | 0.00 | 0.98 |
time (sec) |
N/A | 0.065 | 0.008 | 0.183 | 0.289 | 0.246 | 0.420 | 0.000 | 0.716 |
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 | 94 | 94 | 119 | 104 | 105 | 107 | 128 | 0 | 101 |
N.S. |
1 | 1.00 | 1.27 | 1.11 | 1.12 | 1.14 | 1.36 | 0.00 | 1.07 |
time (sec) |
N/A | 0.080 | 0.021 | 0.175 | 0.198 | 0.257 | 0.370 | 0.000 | 0.701 |
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 | 82 | 82 | 103 | 87 | 88 | 89 | 114 | 0 | 85 |
N.S. |
1 | 1.00 | 1.26 | 1.06 | 1.07 | 1.09 | 1.39 | 0.00 | 1.04 |
time (sec) |
N/A | 0.044 | 0.007 | 0.164 | 0.267 | 0.253 | 0.360 | 0.000 | 0.337 |
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 | 68 | 68 | 85 | 76 | 80 | 82 | 94 | 0 | 75 |
N.S. |
1 | 1.00 | 1.25 | 1.12 | 1.18 | 1.21 | 1.38 | 0.00 | 1.10 |
time (sec) |
N/A | 0.048 | 0.008 | 0.065 | 0.212 | 0.240 | 0.315 | 0.000 | 0.609 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 83 | 120 | 104 | 0 | 0 | 0 | 88 |
N.S. |
1 | 1.00 | 1.08 | 1.56 | 1.35 | 0.00 | 0.00 | 0.00 | 1.14 |
time (sec) |
N/A | 0.065 | 0.001 | 0.142 | 0.412 | 0.000 | 0.000 | 0.000 | 0.819 |
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 | 57 | 57 | 73 | 74 | 73 | 74 | 80 | 0 | 69 |
N.S. |
1 | 1.00 | 1.28 | 1.30 | 1.28 | 1.30 | 1.40 | 0.00 | 1.21 |
time (sec) |
N/A | 0.053 | 0.007 | 0.090 | 0.183 | 0.246 | 0.328 | 0.000 | 0.261 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 86 | 129 | 0 | 0 | 0 | 0 | 91 |
N.S. |
1 | 1.00 | 1.12 | 1.68 | 0.00 | 0.00 | 0.00 | 0.00 | 1.18 |
time (sec) |
N/A | 0.069 | 0.008 | 0.177 | 0.000 | 0.000 | 0.000 | 0.000 | 0.849 |
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 | 83 | 83 | 98 | 97 | 93 | 85 | 116 | 0 | 92 |
N.S. |
1 | 1.00 | 1.18 | 1.17 | 1.12 | 1.02 | 1.40 | 0.00 | 1.11 |
time (sec) |
N/A | 0.069 | 0.027 | 0.106 | 0.209 | 0.243 | 0.365 | 0.000 | 0.653 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 97 | 96 | 80 | 75 | 99 | 0 | 162 |
N.S. |
1 | 1.00 | 1.18 | 1.17 | 0.98 | 0.91 | 1.21 | 0.00 | 1.98 |
time (sec) |
N/A | 0.058 | 0.008 | 0.138 | 0.299 | 0.239 | 0.306 | 0.000 | 0.735 |
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 | 110 | 110 | 131 | 119 | 116 | 111 | 153 | 0 | 111 |
N.S. |
1 | 1.00 | 1.19 | 1.08 | 1.05 | 1.01 | 1.39 | 0.00 | 1.01 |
time (sec) |
N/A | 0.087 | 0.033 | 0.113 | 0.214 | 0.248 | 0.502 | 0.000 | 0.263 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 97 | 109 | 103 | 98 | 122 | 0 | 130 |
N.S. |
1 | 1.00 | 0.92 | 1.04 | 0.98 | 0.93 | 1.16 | 0.00 | 1.24 |
time (sec) |
N/A | 0.070 | 0.007 | 0.128 | 0.285 | 0.272 | 0.371 | 0.000 | 0.706 |
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 | 185 | 185 | 173 | 197 | 184 | 201 | 260 | 0 | 374 |
N.S. |
1 | 1.00 | 0.94 | 1.06 | 0.99 | 1.09 | 1.41 | 0.00 | 2.02 |
time (sec) |
N/A | 0.117 | 0.077 | 0.413 | 0.289 | 0.255 | 0.534 | 0.000 | 0.618 |
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 | 161 | 161 | 162 | 181 | 181 | 186 | 245 | 0 | 191 |
N.S. |
1 | 1.00 | 1.01 | 1.12 | 1.12 | 1.16 | 1.52 | 0.00 | 1.19 |
time (sec) |
N/A | 0.154 | 0.089 | 0.332 | 0.213 | 0.276 | 0.475 | 0.000 | 0.907 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 115 | 140 | 186 | 156 | 166 | 219 | 0 | 167 |
N.S. |
1 | 1.00 | 1.22 | 1.62 | 1.36 | 1.44 | 1.90 | 0.00 | 1.45 |
time (sec) |
N/A | 0.069 | 0.059 | 0.309 | 0.277 | 0.249 | 0.412 | 0.000 | 0.507 |
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 | 124 | 124 | 130 | 137 | 147 | 150 | 194 | 0 | 150 |
N.S. |
1 | 1.00 | 1.05 | 1.10 | 1.19 | 1.21 | 1.56 | 0.00 | 1.21 |
time (sec) |
N/A | 0.097 | 0.050 | 0.197 | 0.215 | 0.252 | 0.393 | 0.000 | 0.754 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 137 | 123 | 175 | 172 | 0 | 0 | 0 | 157 |
N.S. |
1 | 1.00 | 0.90 | 1.28 | 1.26 | 0.00 | 0.00 | 0.00 | 1.15 |
time (sec) |
N/A | 0.108 | 0.078 | 0.271 | 0.435 | 0.000 | 0.000 | 0.000 | 0.818 |
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 | 109 | 109 | 114 | 134 | 130 | 140 | 165 | 0 | 135 |
N.S. |
1 | 1.00 | 1.05 | 1.23 | 1.19 | 1.28 | 1.51 | 0.00 | 1.24 |
time (sec) |
N/A | 0.098 | 0.080 | 0.220 | 0.189 | 0.245 | 0.451 | 0.000 | 0.818 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 128 | 128 | 118 | 178 | 153 | 0 | 0 | 0 | 157 |
N.S. |
1 | 1.00 | 0.92 | 1.39 | 1.20 | 0.00 | 0.00 | 0.00 | 1.23 |
time (sec) |
N/A | 0.101 | 0.085 | 0.378 | 0.450 | 0.000 | 0.000 | 0.000 | 0.783 |
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 | 115 | 115 | 119 | 139 | 135 | 139 | 180 | 0 | 142 |
N.S. |
1 | 1.00 | 1.03 | 1.21 | 1.17 | 1.21 | 1.57 | 0.00 | 1.23 |
time (sec) |
N/A | 0.110 | 0.085 | 0.221 | 0.194 | 0.249 | 0.439 | 0.000 | 0.777 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 139 | 139 | 130 | 194 | 0 | 0 | 0 | 0 | 177 |
N.S. |
1 | 1.00 | 0.94 | 1.40 | 0.00 | 0.00 | 0.00 | 0.00 | 1.27 |
time (sec) |
N/A | 0.112 | 0.073 | 0.372 | 0.000 | 0.000 | 0.000 | 0.000 | 0.899 |
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 | 150 | 150 | 149 | 167 | 166 | 160 | 235 | 0 | 179 |
N.S. |
1 | 1.00 | 0.99 | 1.11 | 1.11 | 1.07 | 1.57 | 0.00 | 1.19 |
time (sec) |
N/A | 0.124 | 0.096 | 0.278 | 0.196 | 0.250 | 0.546 | 0.000 | 0.523 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 112 | 167 | 145 | 145 | 192 | 0 | 256 |
N.S. |
1 | 1.00 | 1.01 | 1.50 | 1.31 | 1.31 | 1.73 | 0.00 | 2.31 |
time (sec) |
N/A | 0.099 | 0.067 | 0.264 | 0.266 | 0.267 | 0.420 | 0.000 | 0.911 |
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 | 186 | 186 | 177 | 202 | 197 | 194 | 289 | 0 | 232 |
N.S. |
1 | 1.00 | 0.95 | 1.09 | 1.06 | 1.04 | 1.55 | 0.00 | 1.25 |
time (sec) |
N/A | 0.154 | 0.145 | 0.262 | 0.206 | 0.273 | 0.722 | 0.000 | 0.708 |
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 | 240 | 285 | 244 | 301 | 268 | 304 | 411 | 0 | 599 |
N.S. |
1 | 1.19 | 1.02 | 1.25 | 1.12 | 1.27 | 1.71 | 0.00 | 2.50 |
time (sec) |
N/A | 0.305 | 0.152 | 0.316 | 0.279 | 0.268 | 0.758 | 0.000 | 0.727 |
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 | 239 | 239 | 252 | 272 | 265 | 277 | 389 | 0 | 296 |
N.S. |
1 | 1.00 | 1.05 | 1.14 | 1.11 | 1.16 | 1.63 | 0.00 | 1.24 |
time (sec) |
N/A | 0.241 | 0.161 | 0.323 | 0.185 | 0.271 | 0.721 | 0.000 | 1.102 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 158 | 158 | 217 | 264 | 232 | 258 | 350 | 0 | 442 |
N.S. |
1 | 1.00 | 1.37 | 1.67 | 1.47 | 1.63 | 2.22 | 0.00 | 2.80 |
time (sec) |
N/A | 0.092 | 0.082 | 0.515 | 0.272 | 0.259 | 0.609 | 0.000 | 0.630 |
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 | 188 | 188 | 192 | 210 | 222 | 229 | 306 | 0 | 238 |
N.S. |
1 | 1.00 | 1.02 | 1.12 | 1.18 | 1.22 | 1.63 | 0.00 | 1.27 |
time (sec) |
N/A | 0.094 | 0.067 | 0.265 | 0.218 | 0.263 | 0.495 | 0.000 | 0.455 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 228 | 228 | 190 | 257 | 251 | 0 | 0 | 0 | 232 |
N.S. |
1 | 1.00 | 0.83 | 1.13 | 1.10 | 0.00 | 0.00 | 0.00 | 1.02 |
time (sec) |
N/A | 0.142 | 0.108 | 0.337 | 0.461 | 0.000 | 0.000 | 0.000 | 0.905 |
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 | 160 | 160 | 169 | 193 | 197 | 206 | 258 | 0 | 236 |
N.S. |
1 | 1.00 | 1.06 | 1.21 | 1.23 | 1.29 | 1.61 | 0.00 | 1.48 |
time (sec) |
N/A | 0.164 | 0.088 | 0.267 | 0.191 | 0.285 | 0.623 | 0.000 | 0.710 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 200 | 200 | 170 | 240 | 223 | 0 | 0 | 0 | 224 |
N.S. |
1 | 1.00 | 0.85 | 1.20 | 1.12 | 0.00 | 0.00 | 0.00 | 1.12 |
time (sec) |
N/A | 0.132 | 0.111 | 0.498 | 0.437 | 0.000 | 0.000 | 0.000 | 0.841 |
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 | 158 | 158 | 166 | 195 | 193 | 205 | 272 | 0 | 203 |
N.S. |
1 | 1.00 | 1.05 | 1.23 | 1.22 | 1.30 | 1.72 | 0.00 | 1.28 |
time (sec) |
N/A | 0.168 | 0.106 | 0.294 | 0.207 | 0.274 | 0.615 | 0.000 | 0.721 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 200 | 200 | 169 | 241 | 218 | 0 | 0 | 0 | 234 |
N.S. |
1 | 1.00 | 0.84 | 1.20 | 1.09 | 0.00 | 0.00 | 0.00 | 1.17 |
time (sec) |
N/A | 0.134 | 0.176 | 0.530 | 0.461 | 0.000 | 0.000 | 0.000 | 0.834 |
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 | 177 | 177 | 184 | 208 | 208 | 214 | 289 | 0 | 194 |
N.S. |
1 | 1.00 | 1.04 | 1.18 | 1.18 | 1.21 | 1.63 | 0.00 | 1.10 |
time (sec) |
N/A | 0.177 | 0.118 | 0.269 | 0.224 | 0.272 | 0.589 | 0.000 | 0.733 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 228 | 228 | 175 | 258 | 0 | 0 | 0 | 0 | 261 |
N.S. |
1 | 1.00 | 0.77 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 1.14 |
time (sec) |
N/A | 0.151 | 0.107 | 0.517 | 0.000 | 0.000 | 0.000 | 0.000 | 1.005 |
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 | 224 | 224 | 230 | 247 | 247 | 243 | 362 | 0 | 236 |
N.S. |
1 | 1.00 | 1.03 | 1.10 | 1.10 | 1.08 | 1.62 | 0.00 | 1.05 |
time (sec) |
N/A | 0.209 | 0.122 | 0.272 | 0.193 | 0.281 | 0.751 | 0.000 | 0.835 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 152 | 152 | 154 | 249 | 218 | 228 | 309 | 0 | 301 |
N.S. |
1 | 1.00 | 1.01 | 1.64 | 1.43 | 1.50 | 2.03 | 0.00 | 1.98 |
time (sec) |
N/A | 0.130 | 0.125 | 0.349 | 0.288 | 0.263 | 0.564 | 0.000 | 0.733 |
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 | 244 | 244 | 212 | 245 | 226 | 237 | 314 | 0 | 233 |
N.S. |
1 | 1.00 | 0.87 | 1.00 | 0.93 | 0.97 | 1.29 | 0.00 | 0.95 |
time (sec) |
N/A | 0.123 | 0.071 | 0.352 | 0.199 | 0.257 | 0.658 | 0.000 | 0.227 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 361 | 361 | 475 | 503 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.32 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.281 | 0.275 | 0.411 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 311 | 311 | 441 | 394 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.42 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.178 | 0.098 | 0.269 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 353 | 353 | 484 | 435 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.37 | 1.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.281 | 0.149 | 0.298 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 409 | 409 | 514 | 571 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.26 | 1.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.345 | 0.228 | 0.408 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 555 | 555 | 766 | 526 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.38 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.480 | 2.549 | 0.944 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 517 | 517 | 461 | 400 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.297 | 0.171 | 0.516 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 561 | 561 | 467 | 537 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.375 | 0.543 | 0.891 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 403 | 403 | 522 | 716 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.30 | 1.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.326 | 7.195 | 0.441 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 98 | 99 | 0 | 234 | 0 | 0 | 696 |
N.S. |
1 | 1.00 | 1.08 | 1.09 | 0.00 | 2.57 | 0.00 | 0.00 | 7.65 |
time (sec) |
N/A | 0.043 | 0.126 | 0.507 | 0.000 | 0.277 | 0.000 | 0.000 | 0.957 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 443 | 443 | 590 | 808 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.33 | 1.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.350 | 5.088 | 0.484 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 489 | 489 | 643 | 851 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.31 | 1.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.374 | 9.889 | 0.611 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 1335 | 1335 | 877 | 2305 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.66 | 1.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.373 | 9.209 | 1.858 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 819 | 819 | 861 | 2173 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.05 | 2.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.571 | 9.118 | 1.164 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 1382 | 1382 | 992 | 2568 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.72 | 1.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.055 | 12.748 | 1.484 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 532 | 532 | 589 | 817 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.11 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.447 | 9.840 | 0.657 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 130 | 130 | 158 | 211 | 0 | 697 | 0 | 0 | 273 |
N.S. |
1 | 1.00 | 1.22 | 1.62 | 0.00 | 5.36 | 0.00 | 0.00 | 2.10 |
time (sec) |
N/A | 0.122 | 2.462 | 1.122 | 0.000 | 0.374 | 0.000 | 0.000 | 3.713 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 131 | 131 | 131 | 157 | 0 | 637 | 0 | 0 | 201 |
N.S. |
1 | 1.00 | 1.00 | 1.20 | 0.00 | 4.86 | 0.00 | 0.00 | 1.53 |
time (sec) |
N/A | 0.073 | 0.799 | 0.704 | 0.000 | 0.351 | 0.000 | 0.000 | 2.881 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 574 | 574 | 645 | 903 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.12 | 1.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.428 | 10.059 | 0.596 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 629 | 629 | 723 | 951 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.15 | 1.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.473 | 12.586 | 1.003 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 966 | 966 | 1744 | 3774 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.81 | 3.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.491 | 12.537 | 2.095 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 893 | 893 | 1745 | 4007 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.95 | 4.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.602 | 10.773 | 1.992 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 1518 | 1518 | 2005 | 5730 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.32 | 3.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.741 | 13.082 | 2.391 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 223 | 223 | 391 | 0 | 0 | 1200 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.75 | 0.00 | 0.00 | 5.38 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.252 | 0.410 | 0.000 | 0.000 | 2.310 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 27 | 22 | 3 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.17 | 0.96 | 0.13 | 1.00 |
time (sec) |
N/A | 0.112 | 14.025 | 0.192 | 0.000 | 0.265 | 23.805 | 95.511 | 0.698 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 140 | 140 | 279 | 0 | 0 | 879 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.99 | 0.00 | 0.00 | 6.28 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.098 | 0.424 | 0.000 | 0.000 | 0.630 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 18 | 0 | 20 | 19 | 3 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 0.00 | 1.00 | 0.95 | 0.15 | 1.00 |
time (sec) |
N/A | 0.016 | 5.945 | 0.186 | 0.000 | 0.263 | 7.153 | 91.783 | 0.646 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 23 | 20 | 3 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.00 | 0.87 | 0.13 | 1.00 |
time (sec) |
N/A | 0.106 | 10.410 | 0.189 | 0.000 | 0.247 | 5.549 | 283.976 | 0.852 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 23 | 22 | 3 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.00 | 0.96 | 0.13 | 1.00 |
time (sec) |
N/A | 0.096 | 10.446 | 0.182 | 0.000 | 0.278 | 2.818 | 281.837 | 1.088 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 23 | 22 | 3 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.00 | 0.96 | 0.13 | 1.00 |
time (sec) |
N/A | 0.110 | 11.962 | 0.212 | 0.000 | 0.251 | 3.777 | 288.606 | 1.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 137 | 137 | 288 | 0 | 0 | 858 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.10 | 0.00 | 0.00 | 6.26 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.188 | 0.486 | 0.000 | 0.000 | 0.390 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | F(-1) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 23 | 22 | 0 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.00 | 0.96 | 0.00 | 1.00 |
time (sec) |
N/A | 0.117 | 14.134 | 0.243 | 0.000 | 0.267 | 8.932 | 0.000 | 1.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | A | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 224 | 224 | 413 | 0 | 0 | 1156 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.84 | 0.00 | 0.00 | 5.16 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.241 | 0.465 | 0.000 | 0.000 | 0.632 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 279 | 279 | 418 | 0 | 0 | 1566 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.50 | 0.00 | 0.00 | 5.61 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.310 | 0.535 | 0.000 | 0.000 | 8.758 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 43 | 22 | 3 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.87 | 0.96 | 0.13 | 1.00 |
time (sec) |
N/A | 0.128 | 13.877 | 0.338 | 0.000 | 0.275 | 63.745 | 95.980 | 0.810 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 181 | 181 | 313 | 0 | 0 | 1192 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.73 | 0.00 | 0.00 | 6.59 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.152 | 0.358 | 0.000 | 0.000 | 2.135 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 18 | 0 | 37 | 19 | 3 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 0.00 | 1.85 | 0.95 | 0.15 | 1.00 |
time (sec) |
N/A | 0.019 | 6.383 | 0.506 | 0.000 | 0.254 | 30.621 | 93.244 | 0.676 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | F(-1) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 40 | 20 | 0 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.74 | 0.87 | 0.00 | 1.00 |
time (sec) |
N/A | 0.124 | 10.596 | 0.520 | 0.000 | 0.264 | 22.240 | 0.000 | 0.955 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | F(-1) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 40 | 22 | 0 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.74 | 0.96 | 0.00 | 1.00 |
time (sec) |
N/A | 0.114 | 11.621 | 0.320 | 0.000 | 0.256 | 13.825 | 0.000 | 1.366 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | F(-1) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 40 | 22 | 0 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.74 | 0.96 | 0.00 | 1.00 |
time (sec) |
N/A | 0.125 | 12.436 | 0.421 | 0.000 | 0.264 | 10.203 | 0.000 | 1.143 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | F(-1) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 40 | 22 | 0 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.74 | 0.96 | 0.00 | 1.00 |
time (sec) |
N/A | 0.121 | 35.170 | 0.395 | 0.000 | 0.268 | 9.477 | 0.000 | 1.092 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | F(-1) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 40 | 22 | 0 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 1.74 | 0.96 | 0.00 | 1.00 |
time (sec) |
N/A | 0.130 | 13.742 | 0.398 | 0.000 | 0.273 | 15.590 | 0.000 | 1.255 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | A | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 178 | 178 | 334 | 0 | 0 | 1145 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.88 | 0.00 | 0.00 | 6.43 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.216 | 0.443 | 0.000 | 0.000 | 0.602 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 345 | 345 | 470 | 0 | 0 | 1978 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.36 | 0.00 | 0.00 | 5.73 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.397 | 0.683 | 0.000 | 0.000 | 29.096 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 67 | 22 | 3 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 2.91 | 0.96 | 0.13 | 1.00 |
time (sec) |
N/A | 0.140 | 14.765 | 0.470 | 0.000 | 0.257 | 176.222 | 98.120 | 0.786 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F(-2) | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 233 | 233 | 353 | 0 | 0 | 1562 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.52 | 0.00 | 0.00 | 6.70 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.219 | 0.431 | 0.000 | 0.000 | 8.400 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 18 | 0 | 61 | 19 | 3 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 0.00 | 3.05 | 0.95 | 0.15 | 1.00 |
time (sec) |
N/A | 0.022 | 6.895 | 0.617 | 0.000 | 0.251 | 77.099 | 94.142 | 0.711 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | F(-1) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 64 | 20 | 0 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 2.78 | 0.87 | 0.00 | 1.00 |
time (sec) |
N/A | 0.139 | 10.803 | 0.621 | 0.000 | 0.283 | 40.393 | 0.000 | 0.990 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | F(-1) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 64 | 22 | 0 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 2.78 | 0.96 | 0.00 | 1.00 |
time (sec) |
N/A | 0.123 | 12.129 | 0.589 | 0.000 | 0.294 | 59.851 | 0.000 | 1.589 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | F(-1) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 64 | 22 | 0 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 2.78 | 0.96 | 0.00 | 1.00 |
time (sec) |
N/A | 0.145 | 12.449 | 0.504 | 0.000 | 0.262 | 40.467 | 0.000 | 1.266 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | F(-1) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 0 | 64 | 22 | 0 | 23 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 0.00 | 2.78 | 0.96 | 0.00 | 1.00 |
time (sec) |
N/A | 0.126 | 11.685 | 0.524 | 0.000 | 0.280 | 42.003 | 0.000 | 1.349 |