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 | F | C | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 243 | 0 | 203 | 473 | 0 | 0 | 0 | 0 | 237 | 0 |
N.S. |
1 | 0.00 | 0.84 | 1.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 0.000 | 21.885 | 1.283 | 0.000 | 0.000 | 0.000 | 0.000 | 37.602 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 0 | 193 | 463 | 0 | 0 | 0 | 0 | 199 | 0 |
N.S. |
1 | 0.00 | 0.90 | 2.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.000 | 21.869 | 0.458 | 0.000 | 0.000 | 0.000 | 0.000 | 30.661 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F | F | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 307 | 326 | 430 | 0 | 0 | 0 | 0 | 161 | 0 |
N.S. |
1 | 1.66 | 1.76 | 2.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 1.288 | 23.162 | 0.346 | 0.000 | 0.000 | 0.000 | 0.000 | 24.687 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F | F | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 165 | 301 | 346 | 0 | 0 | 0 | 0 | 128 | 0 |
N.S. |
1 | 1.06 | 1.93 | 2.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.82 | 0.00 |
time (sec) |
N/A | 0.957 | 22.606 | 0.355 | 0.000 | 0.000 | 0.000 | 0.000 | 20.916 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 0 | 183 | 416 | 0 | 0 | 0 | 0 | 158 | 0 |
N.S. |
1 | 0.00 | 0.99 | 2.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.000 | 21.951 | 0.472 | 0.000 | 0.000 | 0.000 | 0.000 | 25.749 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 0 | 193 | 446 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 0.00 | 0.90 | 2.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.000 | 22.055 | 0.730 | 0.000 | 0.000 | 0.000 | 0.000 | 200.031 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 243 | 0 | 203 | 476 | 0 | 0 | 0 | 0 | 420 | 0 |
N.S. |
1 | 0.00 | 0.84 | 1.96 | 0.00 | 0.00 | 0.00 | 0.00 | 1.73 | 0.00 |
time (sec) |
N/A | 0.000 | 22.038 | 0.893 | 0.000 | 0.000 | 0.000 | 0.000 | 22.664 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 360 | 0 | 632 | 510 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 0.00 | 1.76 | 1.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.000 | 24.866 | 1.292 | 0.000 | 0.000 | 0.000 | 0.000 | 200.037 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 331 | 0 | 625 | 500 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 0.00 | 1.89 | 1.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.000 | 24.735 | 0.400 | 0.000 | 0.000 | 0.000 | 0.000 | 200.031 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 302 | 683 | 654 | 490 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 2.26 | 2.17 | 1.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 1.093 | 24.003 | 0.326 | 0.000 | 0.000 | 0.000 | 0.000 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 271 | 440 | 632 | 346 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.62 | 2.33 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.752 | 23.868 | 0.294 | 0.000 | 0.000 | 0.000 | 0.000 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 302 | 0 | 659 | 490 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 0.00 | 2.18 | 1.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.000 | 24.211 | 0.446 | 0.000 | 0.000 | 0.000 | 0.000 | 200.030 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 331 | 0 | 623 | 520 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 0.00 | 1.88 | 1.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.000 | 26.104 | 0.625 | 0.000 | 0.000 | 0.000 | 0.000 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 360 | 0 | 643 | 550 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 0.00 | 1.79 | 1.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.000 | 25.004 | 0.865 | 0.000 | 0.000 | 0.000 | 0.000 | 200.029 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 170 | 117 | 251 | 129 | 116 | 0 | 149 | 187 | 0 |
N.S. |
1 | 1.24 | 0.85 | 1.83 | 0.94 | 0.85 | 0.00 | 1.09 | 1.36 | 0.00 |
time (sec) |
N/A | 0.618 | 0.254 | 0.274 | 0.124 | 0.082 | 0.000 | 0.232 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 179 | 117 | 251 | 129 | 116 | 0 | 149 | 187 | 0 |
N.S. |
1 | 1.31 | 0.85 | 1.83 | 0.94 | 0.85 | 0.00 | 1.09 | 1.36 | 0.00 |
time (sec) |
N/A | 0.679 | 0.005 | 0.106 | 0.111 | 0.082 | 0.000 | 0.200 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 119 | 82 | 109 | 0 | 69 | 0 | 0 | 92 | 0 |
N.S. |
1 | 0.82 | 0.57 | 0.75 | 0.00 | 0.48 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 1.230 | 10.144 | 1.893 | 0.000 | 0.065 | 0.000 | 0.000 | 0.823 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 109 | 77 | 104 | 0 | 64 | 0 | 0 | 70 | 0 |
N.S. |
1 | 0.96 | 0.68 | 0.91 | 0.00 | 0.56 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.889 | 10.083 | 0.754 | 0.000 | 0.067 | 0.000 | 0.000 | 0.805 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 119 | 137 | 120 | 0 | 97 | 0 | 0 | 81 | 0 |
N.S. |
1 | 0.82 | 0.94 | 0.82 | 0.00 | 0.66 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 1.171 | 10.132 | 0.783 | 0.000 | 0.071 | 0.000 | 0.000 | 0.864 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 116 | 130 | 123 | 0 | 114 | 0 | 0 | 93 | 0 |
N.S. |
1 | 0.77 | 0.86 | 0.81 | 0.00 | 0.75 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 1.190 | 10.146 | 0.869 | 0.000 | 0.077 | 0.000 | 0.000 | 1.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 121 | 87 | 106 | 0 | 85 | 0 | 0 | 87 | 0 |
N.S. |
1 | 0.90 | 0.65 | 0.79 | 0.00 | 0.63 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 1.267 | 10.070 | 0.868 | 0.000 | 0.069 | 0.000 | 0.000 | 1.322 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 148 | 92 | 111 | 0 | 90 | 0 | 0 | 110 | 0 |
N.S. |
1 | 0.88 | 0.55 | 0.66 | 0.00 | 0.54 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 1.328 | 10.071 | 0.869 | 0.000 | 0.071 | 0.000 | 0.000 | 1.611 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 161 | 295 | 123 | 0 | 63 | 0 | 0 | 122 | 0 |
N.S. |
1 | 1.01 | 1.86 | 0.77 | 0.00 | 0.40 | 0.00 | 0.00 | 0.77 | 0.00 |
time (sec) |
N/A | 1.241 | 33.578 | 6.121 | 0.000 | 0.068 | 0.000 | 0.000 | 1.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 134 | 287 | 118 | 0 | 58 | 0 | 0 | 99 | 0 |
N.S. |
1 | 1.07 | 2.30 | 0.94 | 0.00 | 0.46 | 0.00 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.922 | 32.345 | 4.153 | 0.000 | 0.069 | 0.000 | 0.000 | 0.879 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 169 | 290 | 121 | 0 | 0 | 0 | 0 | 106 | 0 |
N.S. |
1 | 1.33 | 2.28 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 1.217 | 21.683 | 4.880 | 0.000 | 0.000 | 0.000 | 0.000 | 1.543 | 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 | 175 | 248 | 211 | 215 | 0 | 1006 | 0 | 133 | 327 | 0 |
N.S. |
1 | 1.42 | 1.21 | 1.23 | 0.00 | 5.75 | 0.00 | 0.76 | 1.87 | 0.00 |
time (sec) |
N/A | 1.207 | 0.546 | 0.322 | 0.000 | 0.199 | 0.000 | 0.120 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 232 | 306 | 246 | 266 | 0 | 1836 | 0 | 182 | 541 | 0 |
N.S. |
1 | 1.32 | 1.06 | 1.15 | 0.00 | 7.91 | 0.00 | 0.78 | 2.33 | 0.00 |
time (sec) |
N/A | 1.332 | 0.656 | 0.225 | 0.000 | 1.887 | 0.000 | 0.163 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 318 | 518 | 322 | 1550 | 0 | 4145 | 0 | 367 | 2073 | 0 |
N.S. |
1 | 1.63 | 1.01 | 4.87 | 0.00 | 13.03 | 0.00 | 1.15 | 6.52 | 0.00 |
time (sec) |
N/A | 2.528 | 1.381 | 0.214 | 0.000 | 26.840 | 0.000 | 0.129 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 510 | 800 | 500 | 3918 | 0 | 8113 | 0 | 908 | 4913 | 0 |
N.S. |
1 | 1.57 | 0.98 | 7.68 | 0.00 | 15.91 | 0.00 | 1.78 | 9.63 | 0.00 |
time (sec) |
N/A | 3.154 | 2.494 | 0.263 | 0.000 | 133.717 | 0.000 | 0.170 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 310 | 413 | 289 | 669 | 0 | 2365 | 0 | 271 | 558 | 0 |
N.S. |
1 | 1.33 | 0.93 | 2.16 | 0.00 | 7.63 | 0.00 | 0.87 | 1.80 | 0.00 |
time (sec) |
N/A | 1.915 | 1.038 | 0.197 | 0.000 | 18.249 | 0.000 | 0.155 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-1) | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 402 | 595 | 400 | 2349 | 0 | 0 | 0 | 477 | 1928 | 0 |
N.S. |
1 | 1.48 | 1.00 | 5.84 | 0.00 | 0.00 | 0.00 | 1.19 | 4.80 | 0.00 |
time (sec) |
N/A | 2.798 | 2.057 | 0.210 | 0.000 | 0.000 | 0.000 | 0.142 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 229 | 156 | 280 | 337 | 366 | 0 | 0 | 550 | 0 |
N.S. |
1 | 1.48 | 1.01 | 1.81 | 2.17 | 2.36 | 0.00 | 0.00 | 3.55 | 0.00 |
time (sec) |
N/A | 0.775 | 0.777 | 0.306 | 0.134 | 0.090 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | C | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 161 | 156 | 289 | 286 | 366 | 1550 | 0 | 550 | 0 |
N.S. |
1 | 1.05 | 1.01 | 1.88 | 1.86 | 2.38 | 10.06 | 0.00 | 3.57 | 0.00 |
time (sec) |
N/A | 0.737 | 0.636 | 0.272 | 0.113 | 0.095 | 9.257 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 260 | 156 | 297 | 0 | 366 | 0 | 0 | 550 | 0 |
N.S. |
1 | 1.45 | 0.87 | 1.66 | 0.00 | 2.04 | 0.00 | 0.00 | 3.07 | 0.00 |
time (sec) |
N/A | 0.966 | 0.717 | 0.270 | 0.000 | 0.090 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 188 | 156 | 289 | 286 | 366 | 1261 | 0 | 550 | 0 |
N.S. |
1 | 1.05 | 0.87 | 1.61 | 1.60 | 2.04 | 7.04 | 0.00 | 3.07 | 0.00 |
time (sec) |
N/A | 0.813 | 0.009 | 0.253 | 0.120 | 0.093 | 9.287 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 229 | 156 | 280 | 0 | 366 | 0 | 0 | 550 | 0 |
N.S. |
1 | 1.28 | 0.87 | 1.56 | 0.00 | 2.04 | 0.00 | 0.00 | 3.07 | 0.00 |
time (sec) |
N/A | 0.919 | 0.005 | 0.315 | 0.000 | 0.092 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 260 | 156 | 297 | 0 | 366 | 0 | 0 | 550 | 0 |
N.S. |
1 | 1.45 | 0.87 | 1.66 | 0.00 | 2.04 | 0.00 | 0.00 | 3.07 | 0.00 |
time (sec) |
N/A | 1.037 | 0.005 | 0.321 | 0.000 | 0.100 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 318 | 348 | 310 | 502 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.09 | 0.97 | 1.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 1.373 | 22.861 | 4.938 | 0.000 | 0.000 | 0.000 | 0.000 | 200.021 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 481 | 503 | 1214 | 819 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.05 | 2.52 | 1.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.762 | 24.518 | 4.867 | 0.000 | 0.000 | 0.000 | 0.000 | 200.028 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 581 | 614 | 1922 | 903 | 0 | 0 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.06 | 3.31 | 1.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 2.255 | 28.715 | 4.970 | 0.000 | 0.000 | 0.000 | 0.000 | 200.032 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 438 | 1103 | 336 | 515 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 2.52 | 0.77 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 3.799 | 22.869 | 5.242 | 0.000 | 0.000 | 0.000 | 0.000 | 200.036 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 685 | 1496 | 1315 | 844 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 2.18 | 1.92 | 1.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 4.157 | 25.194 | 4.849 | 0.000 | 0.000 | 0.000 | 0.000 | 200.030 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 783 | 1619 | 2091 | 926 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 2.07 | 2.67 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 5.852 | 28.192 | 4.950 | 0.000 | 0.000 | 0.000 | 0.000 | 200.029 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 659 | 0 | 519 | 2133 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 0.00 | 0.79 | 3.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.000 | 30.279 | 11.763 | 0.000 | 0.000 | 0.000 | 0.000 | 200.036 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 659 | 0 | 718 | 2136 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 0.00 | 1.09 | 3.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.000 | 27.725 | 7.368 | 0.000 | 0.000 | 0.000 | 0.000 | 200.033 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1042 | 0 | 1503 | 2158 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 0.00 | 1.44 | 2.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 0.000 | 30.206 | 6.129 | 0.000 | 0.000 | 0.000 | 0.000 | 200.030 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 677 | 0 | 734 | 2187 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 0.00 | 1.08 | 3.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.000 | 26.044 | 7.491 | 0.000 | 0.000 | 0.000 | 0.000 | 200.031 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1064 | 0 | 2191 | 2217 | 0 | 0 | 0 | 0 | 34 | 0 |
N.S. |
1 | 0.00 | 2.06 | 2.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 0.000 | 33.620 | 7.506 | 0.000 | 0.000 | 0.000 | 0.000 | 200.032 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1060 | 0 | 3448 | 2208 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 0.00 | 3.25 | 2.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 0.000 | 34.059 | 7.527 | 0.000 | 0.000 | 0.000 | 0.000 | 200.029 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | N/A | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1075 | 0 | 4178 | 2257 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 0.00 | 3.89 | 2.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 |
time (sec) |
N/A | 0.000 | 34.305 | 7.579 | 0.000 | 0.000 | 0.000 | 0.000 | 200.028 | 0.000 |