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 | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 171 | 57 | 125 | 0 | 53 | 49 | 0 | 73 | 0 |
N.S. |
1 | 1.12 | 0.37 | 0.82 | 0.00 | 0.35 | 0.32 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.238 | 10.013 | 0.855 | 0.000 | 0.077 | 1.835 | 0.000 | 0.248 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 173 | 57 | 135 | 0 | 53 | 53 | 0 | 75 | 0 |
N.S. |
1 | 1.13 | 0.37 | 0.88 | 0.00 | 0.35 | 0.35 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.243 | 10.011 | 1.332 | 0.000 | 0.073 | 15.784 | 0.000 | 0.293 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 210 | 57 | 151 | 0 | 70 | 53 | 0 | 76 | 0 |
N.S. |
1 | 1.14 | 0.31 | 0.82 | 0.00 | 0.38 | 0.29 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.268 | 10.011 | 1.888 | 0.000 | 0.071 | 150.908 | 0.000 | 0.387 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 215 | 250 | 57 | 162 | 0 | 81 | 0 | 0 | 76 | 0 |
N.S. |
1 | 1.16 | 0.27 | 0.75 | 0.00 | 0.38 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.293 | 10.028 | 2.747 | 0.000 | 0.073 | 0.000 | 0.000 | 0.518 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 329 | 371 | 89 | 232 | 0 | 85 | 46 | 0 | 89 | 0 |
N.S. |
1 | 1.13 | 0.27 | 0.71 | 0.00 | 0.26 | 0.14 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.392 | 10.042 | 1.051 | 0.000 | 0.076 | 8.410 | 0.000 | 0.292 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 297 | 338 | 57 | 218 | 0 | 63 | 46 | 0 | 62 | 0 |
N.S. |
1 | 1.14 | 0.19 | 0.73 | 0.00 | 0.21 | 0.15 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.372 | 10.010 | 0.470 | 0.000 | 0.081 | 1.349 | 0.000 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 297 | 337 | 55 | 208 | 0 | 60 | 49 | 0 | 69 | 0 |
N.S. |
1 | 1.13 | 0.19 | 0.70 | 0.00 | 0.20 | 0.16 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.360 | 10.011 | 0.458 | 0.000 | 0.076 | 1.109 | 0.000 | 0.315 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 298 | 337 | 57 | 216 | 0 | 60 | 53 | 0 | 75 | 0 |
N.S. |
1 | 1.13 | 0.19 | 0.72 | 0.00 | 0.20 | 0.18 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.359 | 10.012 | 0.659 | 0.000 | 0.080 | 5.096 | 0.000 | 0.296 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 332 | 377 | 57 | 234 | 0 | 78 | 53 | 0 | 76 | 0 |
N.S. |
1 | 1.14 | 0.17 | 0.70 | 0.00 | 0.23 | 0.16 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.395 | 10.012 | 1.015 | 0.000 | 0.071 | 46.269 | 0.000 | 0.345 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 123 | 74 | 133 | 0 | 45 | 53 | 0 | 61 | 0 |
N.S. |
1 | 1.04 | 0.63 | 1.13 | 0.00 | 0.38 | 0.45 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.235 | 7.740 | 0.367 | 0.000 | 0.065 | 1.687 | 0.000 | 0.293 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 95 | 51 | 124 | 0 | 40 | 53 | 0 | 47 | 0 |
N.S. |
1 | 1.00 | 0.54 | 1.31 | 0.00 | 0.42 | 0.56 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.201 | 6.442 | 0.447 | 0.000 | 0.068 | 0.707 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 51 | 129 | 0 | 46 | 49 | 0 | 58 | 0 |
N.S. |
1 | 1.00 | 0.53 | 1.33 | 0.00 | 0.47 | 0.51 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.201 | 10.013 | 0.450 | 0.000 | 0.066 | 1.490 | 0.000 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 136 | 53 | 137 | 0 | 52 | 60 | 0 | 60 | 0 |
N.S. |
1 | 1.09 | 0.42 | 1.10 | 0.00 | 0.42 | 0.48 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.232 | 10.012 | 0.443 | 0.000 | 0.067 | 16.137 | 0.000 | 0.270 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 141 | 74 | 194 | 0 | 56 | 53 | 0 | 62 | 0 |
N.S. |
1 | 0.78 | 0.41 | 1.07 | 0.00 | 0.31 | 0.29 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.235 | 9.109 | 0.484 | 0.000 | 0.070 | 4.442 | 0.000 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 99 | 51 | 183 | 0 | 39 | 53 | 0 | 43 | 0 |
N.S. |
1 | 0.64 | 0.33 | 1.18 | 0.00 | 0.25 | 0.34 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.200 | 6.573 | 0.460 | 0.000 | 0.069 | 0.592 | 0.000 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 98 | 51 | 184 | 0 | 46 | 56 | 0 | 52 | 0 |
N.S. |
1 | 0.66 | 0.34 | 1.23 | 0.00 | 0.31 | 0.38 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.204 | 10.011 | 0.459 | 0.000 | 0.066 | 0.762 | 0.000 | 0.281 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 144 | 53 | 192 | 0 | 55 | 49 | 0 | 60 | 0 |
N.S. |
1 | 0.75 | 0.27 | 0.99 | 0.00 | 0.28 | 0.25 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.237 | 10.011 | 0.575 | 0.000 | 0.069 | 4.815 | 0.000 | 0.242 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 178 | 87 | 141 | 0 | 62 | 44 | 0 | 69 | 0 |
N.S. |
1 | 1.14 | 0.56 | 0.90 | 0.00 | 0.40 | 0.28 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.250 | 10.025 | 0.825 | 0.000 | 0.076 | 10.155 | 0.000 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 140 | 69 | 125 | 0 | 41 | 44 | 0 | 48 | 0 |
N.S. |
1 | 1.10 | 0.54 | 0.98 | 0.00 | 0.32 | 0.35 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.220 | 10.026 | 0.433 | 0.000 | 0.076 | 1.034 | 0.000 | 0.327 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 110 | 54 | 104 | 0 | 22 | 44 | 0 | 30 | 0 |
N.S. |
1 | 1.13 | 0.56 | 1.07 | 0.00 | 0.23 | 0.45 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.194 | 10.015 | 0.711 | 0.000 | 0.073 | 0.639 | 0.000 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 142 | 56 | 123 | 0 | 45 | 48 | 0 | 32 | 0 |
N.S. |
1 | 1.10 | 0.43 | 0.95 | 0.00 | 0.35 | 0.37 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.223 | 10.014 | 1.197 | 0.000 | 0.068 | 2.005 | 0.000 | 0.243 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 182 | 56 | 138 | 0 | 57 | 51 | 0 | 32 | 0 |
N.S. |
1 | 1.15 | 0.35 | 0.87 | 0.00 | 0.36 | 0.32 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.247 | 10.016 | 1.869 | 0.000 | 0.073 | 21.186 | 0.000 | 0.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 304 | 347 | 87 | 221 | 0 | 72 | 44 | 0 | 68 | 0 |
N.S. |
1 | 1.14 | 0.29 | 0.73 | 0.00 | 0.24 | 0.14 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.403 | 10.039 | 1.040 | 0.000 | 0.079 | 30.424 | 0.000 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 273 | 309 | 69 | 210 | 0 | 54 | 44 | 0 | 49 | 0 |
N.S. |
1 | 1.13 | 0.25 | 0.77 | 0.00 | 0.20 | 0.16 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.338 | 10.026 | 0.735 | 0.000 | 0.072 | 3.148 | 0.000 | 0.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 236 | 278 | 56 | 132 | 0 | 27 | 44 | 0 | 25 | 0 |
N.S. |
1 | 1.18 | 0.24 | 0.56 | 0.00 | 0.11 | 0.19 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.320 | 10.019 | 0.341 | 0.000 | 0.070 | 0.525 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 268 | 309 | 54 | 196 | 0 | 51 | 48 | 0 | 32 | 0 |
N.S. |
1 | 1.15 | 0.20 | 0.73 | 0.00 | 0.19 | 0.18 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.353 | 10.013 | 0.951 | 0.000 | 0.066 | 0.826 | 0.000 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 306 | 349 | 56 | 219 | 0 | 65 | 51 | 0 | 32 | 0 |
N.S. |
1 | 1.14 | 0.18 | 0.72 | 0.00 | 0.21 | 0.17 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.378 | 10.012 | 1.599 | 0.000 | 0.069 | 6.722 | 0.000 | 0.284 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 175 | 74 | 128 | 0 | 86 | 44 | 0 | 133 | 0 |
N.S. |
1 | 1.14 | 0.48 | 0.84 | 0.00 | 0.56 | 0.29 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.247 | 10.022 | 1.727 | 0.000 | 0.084 | 12.711 | 0.000 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 138 | 59 | 115 | 0 | 61 | 44 | 0 | 109 | 0 |
N.S. |
1 | 1.10 | 0.47 | 0.92 | 0.00 | 0.49 | 0.35 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.216 | 10.019 | 0.439 | 0.000 | 0.074 | 1.101 | 0.000 | 0.241 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 139 | 59 | 114 | 0 | 58 | 44 | 0 | 41 | 0 |
N.S. |
1 | 1.10 | 0.47 | 0.90 | 0.00 | 0.46 | 0.35 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.220 | 9.867 | 1.257 | 0.000 | 0.071 | 0.943 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 175 | 59 | 124 | 0 | 79 | 48 | 0 | 43 | 0 |
N.S. |
1 | 1.14 | 0.38 | 0.81 | 0.00 | 0.51 | 0.31 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.252 | 10.012 | 2.365 | 0.000 | 0.077 | 3.932 | 0.000 | 0.268 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 299 | 344 | 73 | 210 | 0 | 94 | 44 | 0 | 130 | 0 |
N.S. |
1 | 1.15 | 0.24 | 0.70 | 0.00 | 0.31 | 0.15 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.386 | 10.029 | 1.940 | 0.000 | 0.081 | 37.622 | 0.000 | 0.293 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 266 | 304 | 60 | 197 | 0 | 76 | 44 | 0 | 110 | 0 |
N.S. |
1 | 1.14 | 0.23 | 0.74 | 0.00 | 0.29 | 0.17 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.360 | 10.020 | 0.993 | 0.000 | 0.075 | 3.629 | 0.000 | 0.277 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 266 | 307 | 59 | 197 | 0 | 65 | 44 | 0 | 36 | 0 |
N.S. |
1 | 1.15 | 0.22 | 0.74 | 0.00 | 0.24 | 0.17 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.344 | 10.013 | 0.414 | 0.000 | 0.072 | 0.656 | 0.000 | 0.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 296 | 342 | 57 | 197 | 0 | 83 | 48 | 0 | 43 | 0 |
N.S. |
1 | 1.16 | 0.19 | 0.67 | 0.00 | 0.28 | 0.16 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.390 | 10.013 | 2.046 | 0.000 | 0.076 | 1.538 | 0.000 | 0.252 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 331 | 382 | 59 | 219 | 0 | 101 | 51 | 0 | 43 | 0 |
N.S. |
1 | 1.15 | 0.18 | 0.66 | 0.00 | 0.31 | 0.15 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.412 | 10.014 | 2.810 | 0.000 | 0.074 | 14.480 | 0.000 | 0.308 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 212 | 92 | 230 | 0 | 125 | 44 | 0 | 244 | 0 |
N.S. |
1 | 1.16 | 0.50 | 1.26 | 0.00 | 0.68 | 0.24 | 0.00 | 1.33 | 0.00 |
time (sec) |
N/A | 0.261 | 10.057 | 3.367 | 0.000 | 0.089 | 102.882 | 0.000 | 0.344 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 175 | 80 | 205 | 0 | 108 | 44 | 0 | 135 | 0 |
N.S. |
1 | 1.13 | 0.52 | 1.32 | 0.00 | 0.70 | 0.28 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.246 | 10.036 | 1.753 | 0.000 | 0.077 | 12.396 | 0.000 | 0.352 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 176 | 79 | 208 | 0 | 98 | 44 | 0 | 200 | 0 |
N.S. |
1 | 1.13 | 0.51 | 1.33 | 0.00 | 0.63 | 0.28 | 0.00 | 1.28 | 0.00 |
time (sec) |
N/A | 0.228 | 10.035 | 0.621 | 0.000 | 0.075 | 1.897 | 0.000 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 175 | 79 | 198 | 0 | 97 | 44 | 0 | 52 | 0 |
N.S. |
1 | 1.11 | 0.50 | 1.26 | 0.00 | 0.62 | 0.28 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.249 | 10.028 | 2.108 | 0.000 | 0.077 | 2.359 | 0.000 | 0.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 211 | 59 | 226 | 0 | 115 | 48 | 0 | 54 | 0 |
N.S. |
1 | 1.14 | 0.32 | 1.22 | 0.00 | 0.62 | 0.26 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.271 | 10.013 | 4.118 | 0.000 | 0.076 | 7.677 | 0.000 | 0.354 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 300 | 341 | 80 | 258 | 0 | 116 | 44 | 0 | 218 | 0 |
N.S. |
1 | 1.14 | 0.27 | 0.86 | 0.00 | 0.39 | 0.15 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.391 | 10.044 | 1.984 | 0.000 | 0.081 | 39.180 | 0.000 | 0.353 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 304 | 344 | 74 | 263 | 0 | 118 | 44 | 0 | 199 | 0 |
N.S. |
1 | 1.13 | 0.24 | 0.87 | 0.00 | 0.39 | 0.14 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.377 | 10.028 | 1.641 | 0.000 | 0.077 | 3.647 | 0.000 | 0.308 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 302 | 343 | 59 | 256 | 0 | 103 | 44 | 0 | 47 | 0 |
N.S. |
1 | 1.14 | 0.20 | 0.85 | 0.00 | 0.34 | 0.15 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.383 | 10.012 | 0.622 | 0.000 | 0.073 | 1.411 | 0.000 | 0.235 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 333 | 378 | 57 | 287 | 0 | 119 | 48 | 0 | 54 | 0 |
N.S. |
1 | 1.14 | 0.17 | 0.86 | 0.00 | 0.36 | 0.14 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.402 | 10.013 | 3.790 | 0.000 | 0.072 | 3.779 | 0.000 | 0.449 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 362 | 418 | 59 | 312 | 0 | 137 | 51 | 0 | 54 | 0 |
N.S. |
1 | 1.15 | 0.16 | 0.86 | 0.00 | 0.38 | 0.14 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.425 | 10.021 | 4.681 | 0.000 | 0.095 | 24.103 | 0.000 | 0.406 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 61 | 131 | 0 | 42 | 51 | 0 | 49 | 0 |
N.S. |
1 | 1.00 | 0.69 | 1.47 | 0.00 | 0.47 | 0.57 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.198 | 10.024 | 0.477 | 0.000 | 0.064 | 0.929 | 0.000 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 56 | 114 | 0 | 21 | 51 | 0 | 36 | 0 |
N.S. |
1 | 1.00 | 0.88 | 1.78 | 0.00 | 0.33 | 0.80 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.177 | 10.029 | 0.477 | 0.000 | 0.085 | 0.580 | 0.000 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 99 | 53 | 132 | 0 | 47 | 54 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 0.54 | 1.33 | 0.00 | 0.47 | 0.55 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.204 | 10.015 | 0.678 | 0.000 | 0.069 | 1.893 | 0.000 | 0.243 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 107 | 61 | 184 | 0 | 50 | 51 | 0 | 50 | 0 |
N.S. |
1 | 0.65 | 0.37 | 1.12 | 0.00 | 0.30 | 0.31 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.206 | 10.028 | 0.520 | 0.000 | 0.068 | 3.206 | 0.000 | 0.268 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 67 | 53 | 152 | 0 | 20 | 51 | 0 | 31 | 0 |
N.S. |
1 | 0.56 | 0.44 | 1.27 | 0.00 | 0.17 | 0.42 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.185 | 10.021 | 0.389 | 0.000 | 0.070 | 0.506 | 0.000 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 107 | 51 | 182 | 0 | 48 | 54 | 0 | 38 | 0 |
N.S. |
1 | 0.66 | 0.31 | 1.12 | 0.00 | 0.30 | 0.33 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.212 | 10.020 | 0.621 | 0.000 | 0.067 | 0.817 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 129 | 67 | 134 | 0 | 81 | 51 | 0 | 114 | 0 |
N.S. |
1 | 1.02 | 0.53 | 1.06 | 0.00 | 0.64 | 0.40 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.236 | 10.023 | 0.677 | 0.000 | 0.071 | 12.112 | 0.000 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 95 | 59 | 126 | 0 | 63 | 51 | 0 | 58 | 0 |
N.S. |
1 | 1.00 | 0.62 | 1.33 | 0.00 | 0.66 | 0.54 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.201 | 9.848 | 0.463 | 0.000 | 0.067 | 1.057 | 0.000 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 59 | 122 | 0 | 61 | 51 | 0 | 40 | 0 |
N.S. |
1 | 1.00 | 0.61 | 1.26 | 0.00 | 0.63 | 0.53 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.207 | 8.883 | 0.664 | 0.000 | 0.066 | 0.936 | 0.000 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 138 | 58 | 133 | 0 | 80 | 54 | 0 | 42 | 0 |
N.S. |
1 | 1.04 | 0.44 | 1.00 | 0.00 | 0.60 | 0.41 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.234 | 10.017 | 0.806 | 0.000 | 0.071 | 3.886 | 0.000 | 0.327 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 147 | 67 | 210 | 0 | 85 | 51 | 0 | 111 | 0 |
N.S. |
1 | 0.73 | 0.33 | 1.04 | 0.00 | 0.42 | 0.25 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.227 | 10.027 | 0.675 | 0.000 | 0.070 | 36.105 | 0.000 | 0.274 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 110 | 59 | 186 | 0 | 74 | 51 | 0 | 96 | 0 |
N.S. |
1 | 0.65 | 0.35 | 1.09 | 0.00 | 0.44 | 0.30 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.210 | 10.017 | 0.535 | 0.000 | 0.071 | 3.446 | 0.000 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 101 | 58 | 182 | 0 | 63 | 51 | 0 | 35 | 0 |
N.S. |
1 | 0.64 | 0.37 | 1.16 | 0.00 | 0.40 | 0.32 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.206 | 7.676 | 0.418 | 0.000 | 0.067 | 0.653 | 0.000 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 146 | 58 | 216 | 0 | 76 | 54 | 0 | 42 | 0 |
N.S. |
1 | 0.74 | 0.29 | 1.09 | 0.00 | 0.38 | 0.27 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.235 | 10.020 | 0.721 | 0.000 | 0.072 | 1.564 | 0.000 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 15 | 0 | 9 | 32 | 0 | 22 | 16 |
N.S. |
1 | 1.00 | 1.10 | 0.75 | 0.00 | 0.45 | 1.60 | 0.00 | 1.10 | 0.80 |
time (sec) |
N/A | 0.152 | 10.028 | 0.403 | 0.000 | 0.065 | 0.463 | 0.000 | 0.200 | 0.162 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 43 | 77 | 0 | 9 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 0.84 | 1.51 | 0.00 | 0.18 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.210 | 10.022 | 0.335 | 0.000 | 0.064 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 24 | 19 | 0 | 20 | 36 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 1.14 | 0.90 | 0.00 | 0.95 | 1.71 | 0.00 | 1.48 | 0.00 |
time (sec) |
N/A | 0.147 | 10.018 | 0.991 | 0.000 | 0.062 | 0.448 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 23 | 18 | 0 | 13 | 32 | 0 | 22 | 0 |
N.S. |
1 | 1.00 | 0.34 | 0.27 | 0.00 | 0.19 | 0.48 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.172 | 10.016 | 0.605 | 0.000 | 0.066 | 0.434 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 537 | 570 | 85 | 0 | 0 | 0 | 46 | 0 | 66 | 0 |
N.S. |
1 | 1.06 | 0.16 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.558 | 10.044 | 0.000 | 0.000 | 0.000 | 7.936 | 0.000 | 0.439 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1045 | 85 | 56 | 0 | 0 | 0 | 46 | 0 | 43 | 0 |
N.S. |
1 | 0.08 | 0.05 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.225 | 10.012 | 0.000 | 0.000 | 0.000 | 2.395 | 0.000 | 0.592 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 998 | 85 | 56 | 0 | 0 | 0 | 46 | 0 | 43 | 0 |
N.S. |
1 | 0.09 | 0.06 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.212 | 10.011 | 0.000 | 0.000 | 0.000 | 0.793 | 0.000 | 0.421 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 512 | 547 | 56 | 0 | 0 | 0 | 46 | 0 | 44 | 0 |
N.S. |
1 | 1.07 | 0.11 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.505 | 10.013 | 0.000 | 0.000 | 0.000 | 0.795 | 0.000 | 0.466 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 510 | 537 | 54 | 0 | 0 | 0 | 46 | 0 | 44 | 0 |
N.S. |
1 | 1.05 | 0.11 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.491 | 10.009 | 0.000 | 0.000 | 0.000 | 0.721 | 0.000 | 0.517 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1018 | 83 | 54 | 0 | 0 | 0 | 49 | 0 | 46 | 0 |
N.S. |
1 | 0.08 | 0.05 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.218 | 10.012 | 0.000 | 0.000 | 0.000 | 1.031 | 0.000 | 0.594 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 565 | 601 | 89 | 0 | 0 | 0 | 46 | 0 | 85 | 0 |
N.S. |
1 | 1.06 | 0.16 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.532 | 10.053 | 0.000 | 0.000 | 0.000 | 13.738 | 0.000 | 0.480 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1073 | 116 | 57 | 0 | 0 | 0 | 46 | 0 | 62 | 0 |
N.S. |
1 | 0.11 | 0.05 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.238 | 10.027 | 0.000 | 0.000 | 0.000 | 4.720 | 0.000 | 0.635 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1024 | 116 | 57 | 0 | 0 | 0 | 46 | 0 | 62 | 0 |
N.S. |
1 | 0.11 | 0.06 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.236 | 10.011 | 0.000 | 0.000 | 0.000 | 1.352 | 0.000 | 0.453 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 538 | 578 | 57 | 0 | 0 | 0 | 46 | 0 | 63 | 0 |
N.S. |
1 | 1.07 | 0.11 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.525 | 10.010 | 0.000 | 0.000 | 0.000 | 1.036 | 0.000 | 0.483 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 540 | 568 | 55 | 0 | 0 | 0 | 46 | 0 | 63 | 0 |
N.S. |
1 | 1.05 | 0.10 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.515 | 10.010 | 0.000 | 0.000 | 0.000 | 1.040 | 0.000 | 0.529 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1045 | 115 | 55 | 0 | 0 | 0 | 49 | 0 | 65 | 0 |
N.S. |
1 | 0.11 | 0.05 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.246 | 10.014 | 0.000 | 0.000 | 0.000 | 1.896 | 0.000 | 0.643 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 507 | 539 | 69 | 0 | 0 | 0 | 44 | 0 | 49 | 0 |
N.S. |
1 | 1.06 | 0.14 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.493 | 10.034 | 0.000 | 0.000 | 0.000 | 5.631 | 0.000 | 0.467 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 483 | 518 | 56 | 0 | 0 | 0 | 44 | 0 | 33 | 0 |
N.S. |
1 | 1.07 | 0.12 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.476 | 10.014 | 0.000 | 0.000 | 0.000 | 0.695 | 0.000 | 0.468 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 479 | 508 | 54 | 0 | 0 | 0 | 44 | 0 | 35 | 0 |
N.S. |
1 | 1.06 | 0.11 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.472 | 10.010 | 0.000 | 0.000 | 0.000 | 0.827 | 0.000 | 0.561 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 517 | 553 | 56 | 0 | 0 | 0 | 48 | 0 | 35 | 0 |
N.S. |
1 | 1.07 | 0.11 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.505 | 10.013 | 0.000 | 0.000 | 0.000 | 11.902 | 0.000 | 0.876 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1011 | 87 | 69 | 0 | 0 | 0 | 44 | 0 | 48 | 0 |
N.S. |
1 | 0.09 | 0.07 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.218 | 10.032 | 0.000 | 0.000 | 0.000 | 49.754 | 0.000 | 0.475 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1019 | 58 | 56 | 0 | 0 | 0 | 44 | 0 | 27 | 0 |
N.S. |
1 | 0.06 | 0.05 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 0.191 | 10.017 | 0.000 | 0.000 | 0.000 | 1.658 | 0.000 | 0.366 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 965 | 58 | 56 | 0 | 0 | 0 | 44 | 0 | 27 | 0 |
N.S. |
1 | 0.06 | 0.06 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 0.186 | 10.009 | 0.000 | 0.000 | 0.000 | 0.660 | 0.000 | 0.316 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 985 | 89 | 54 | 0 | 0 | 0 | 48 | 0 | 35 | 0 |
N.S. |
1 | 0.09 | 0.05 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.217 | 10.010 | 0.000 | 0.000 | 0.000 | 1.370 | 0.000 | 0.524 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1013 | 91 | 56 | 0 | 0 | 0 | 48 | 0 | 35 | 0 |
N.S. |
1 | 0.09 | 0.06 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 0.213 | 10.010 | 0.000 | 0.000 | 0.000 | 3.375 | 0.000 | 0.667 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1021 | 129 | 56 | 0 | 0 | 0 | 51 | 0 | 35 | 0 |
N.S. |
1 | 0.13 | 0.05 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 0.242 | 10.020 | 0.000 | 0.000 | 0.000 | 98.794 | 0.000 | 1.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 503 | 533 | 59 | 0 | 0 | 0 | 44 | 0 | 111 | 0 |
N.S. |
1 | 1.06 | 0.12 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.481 | 10.031 | 0.000 | 0.000 | 0.000 | 6.989 | 0.000 | 1.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1045 | 87 | 59 | 0 | 0 | 0 | 44 | 0 | 38 | 0 |
N.S. |
1 | 0.08 | 0.06 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.219 | 10.013 | 0.000 | 0.000 | 0.000 | 2.248 | 0.000 | 0.501 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 998 | 87 | 59 | 0 | 0 | 0 | 44 | 0 | 38 | 0 |
N.S. |
1 | 0.09 | 0.06 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.213 | 10.013 | 0.000 | 0.000 | 0.000 | 1.058 | 0.000 | 0.425 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 512 | 546 | 59 | 0 | 0 | 0 | 44 | 0 | 44 | 0 |
N.S. |
1 | 1.07 | 0.12 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.493 | 10.016 | 0.000 | 0.000 | 0.000 | 1.187 | 0.000 | 1.039 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 514 | 537 | 60 | 0 | 0 | 0 | 44 | 0 | 46 | 0 |
N.S. |
1 | 1.04 | 0.12 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.513 | 10.036 | 0.000 | 0.000 | 0.000 | 1.534 | 0.000 | 1.304 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1018 | 122 | 57 | 0 | 0 | 0 | 48 | 0 | 46 | 0 |
N.S. |
1 | 0.12 | 0.06 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.245 | 10.024 | 0.000 | 0.000 | 0.000 | 2.795 | 0.000 | 1.559 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 540 | 574 | 80 | 0 | 0 | 0 | 44 | 0 | 201 | 0 |
N.S. |
1 | 1.06 | 0.15 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.515 | 10.048 | 0.000 | 0.000 | 0.000 | 6.857 | 0.000 | 3.408 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1078 | 123 | 59 | 0 | 0 | 0 | 44 | 0 | 49 | 0 |
N.S. |
1 | 0.11 | 0.05 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.249 | 10.034 | 0.000 | 0.000 | 0.000 | 3.560 | 0.000 | 0.938 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1029 | 123 | 59 | 0 | 0 | 0 | 44 | 0 | 49 | 0 |
N.S. |
1 | 0.12 | 0.06 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.249 | 10.023 | 0.000 | 0.000 | 0.000 | 1.877 | 0.000 | 0.868 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 543 | 582 | 59 | 0 | 0 | 0 | 44 | 0 | 55 | 0 |
N.S. |
1 | 1.07 | 0.11 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.524 | 10.023 | 0.000 | 0.000 | 0.000 | 2.106 | 0.000 | 2.910 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 545 | 573 | 79 | 0 | 0 | 0 | 44 | 0 | 57 | 0 |
N.S. |
1 | 1.05 | 0.14 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.525 | 10.044 | 0.000 | 0.000 | 0.000 | 3.870 | 0.000 | 3.335 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1049 | 158 | 57 | 0 | 0 | 0 | 48 | 0 | 57 | 0 |
N.S. |
1 | 0.15 | 0.05 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.273 | 10.023 | 0.000 | 0.000 | 0.000 | 7.884 | 0.000 | 4.029 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 245 | 24 | 17 | 0 | 0 | 31 | 0 | 23 | 0 |
N.S. |
1 | 1.03 | 0.10 | 0.07 | 0.00 | 0.00 | 0.13 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.297 | 10.010 | 0.415 | 0.000 | 0.000 | 0.594 | 0.000 | 0.247 | 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 | 69 | 69 | 67 | 0 | 0 | 0 | 58 | 0 | 40 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.84 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.176 | 0.210 | 0.000 | 0.000 | 0.000 | 1.419 | 0.000 | 0.283 | 0.000 |