Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 84 | 81 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.45 | 1.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.174 | 0.031 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 7.398 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 84 | 73 | 0 | 0 | 0 | 0 | 0 | 144 | 0 |
N.S. |
1 | 1.45 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.48 | 0.00 |
time (sec) |
N/A | 0.177 | 0.065 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.545 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 82 | 73 | 0 | 0 | 0 | 0 | 0 | 86 | 0 |
N.S. |
1 | 1.41 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.48 | 0.00 |
time (sec) |
N/A | 0.173 | 0.044 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 74 | 73 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.28 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.166 | 0.025 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.620 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 74 | 73 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.28 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.165 | 0.024 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.717 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 81 | 73 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.40 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.168 | 0.038 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.722 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 82 | 81 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.41 | 1.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.170 | 0.028 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 8.090 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 343 | 437 | 317 | 0 | 0 | 2585 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.27 | 0.92 | 0.00 | 0.00 | 7.54 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.488 | 0.981 | 0.000 | 0.000 | 0.167 | 0.000 | 0.000 | 0.591 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 324 | 426 | 318 | 0 | 0 | 1562 | 0 | 0 | 335 | 0 |
N.S. |
1 | 1.31 | 0.98 | 0.00 | 0.00 | 4.82 | 0.00 | 0.00 | 1.03 | 0.00 |
time (sec) |
N/A | 0.456 | 0.970 | 0.000 | 0.000 | 0.126 | 0.000 | 0.000 | 12.142 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | B | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 284 | 417 | 286 | 0 | 0 | 711 | 0 | 0 | 444 | 0 |
N.S. |
1 | 1.47 | 1.01 | 0.00 | 0.00 | 2.50 | 0.00 | 0.00 | 1.56 | 0.00 |
time (sec) |
N/A | 0.451 | 0.714 | 0.000 | 0.000 | 0.129 | 0.000 | 0.000 | 13.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 32 | 27 | 0 | 104 | 0 | 0 | 830 | 199 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.00 | 3.25 | 0.00 | 0.00 | 25.94 | 6.22 |
time (sec) |
N/A | 0.136 | 0.026 | 0.174 | 0.000 | 0.111 | 0.000 | 0.000 | 13.930 | 0.401 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 46 | 54 | 0 | 235 | 0 | 0 | 1312 | 189 |
N.S. |
1 | 1.00 | 0.70 | 0.82 | 0.00 | 3.56 | 0.00 | 0.00 | 19.88 | 2.86 |
time (sec) |
N/A | 0.161 | 0.242 | 0.176 | 0.000 | 0.115 | 0.000 | 0.000 | 14.405 | 0.519 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 114 | 77 | 105 | 0 | 427 | 0 | 0 | 1854 | 278 |
N.S. |
1 | 1.13 | 0.76 | 1.04 | 0.00 | 4.23 | 0.00 | 0.00 | 18.36 | 2.75 |
time (sec) |
N/A | 0.183 | 0.392 | 0.175 | 0.000 | 0.104 | 0.000 | 0.000 | 15.591 | 0.641 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 162 | 118 | 171 | 0 | 649 | 0 | 0 | 2504 | 385 |
N.S. |
1 | 1.19 | 0.87 | 1.26 | 0.00 | 4.77 | 0.00 | 0.00 | 18.41 | 2.83 |
time (sec) |
N/A | 0.204 | 1.027 | 0.190 | 0.000 | 0.108 | 0.000 | 0.000 | 17.031 | 0.807 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 343 | 443 | 317 | 0 | 0 | 2585 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.29 | 0.92 | 0.00 | 0.00 | 7.54 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.482 | 0.732 | 0.000 | 0.000 | 0.141 | 0.000 | 0.000 | 0.604 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 299 | 402 | 293 | 0 | 0 | 1443 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.34 | 0.98 | 0.00 | 0.00 | 4.83 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.458 | 0.784 | 0.000 | 0.000 | 0.122 | 0.000 | 0.000 | 0.306 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 369 | 222 | 0 | 0 | 402 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.57 | 0.94 | 0.00 | 0.00 | 1.71 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.416 | 0.457 | 0.000 | 0.000 | 0.103 | 0.000 | 0.000 | 200.025 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 32 | 27 | 0 | 42 | 0 | 0 | 161 | 27 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.00 | 1.31 | 0.00 | 0.00 | 5.03 | 0.84 |
time (sec) |
N/A | 0.142 | 0.025 | 0.178 | 0.000 | 0.108 | 0.000 | 0.000 | 0.481 | 0.428 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 46 | 54 | 0 | 118 | 0 | 0 | 541 | 127 |
N.S. |
1 | 1.00 | 0.70 | 0.82 | 0.00 | 1.79 | 0.00 | 0.00 | 8.20 | 1.92 |
time (sec) |
N/A | 0.161 | 0.197 | 0.178 | 0.000 | 0.091 | 0.000 | 0.000 | 1.038 | 0.512 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 114 | 77 | 105 | 0 | 252 | 0 | 0 | 894 | 203 |
N.S. |
1 | 1.13 | 0.76 | 1.04 | 0.00 | 2.50 | 0.00 | 0.00 | 8.85 | 2.01 |
time (sec) |
N/A | 0.185 | 0.282 | 0.180 | 0.000 | 0.107 | 0.000 | 0.000 | 1.463 | 0.605 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 162 | 118 | 171 | 0 | 420 | 0 | 0 | 1330 | 292 |
N.S. |
1 | 1.19 | 0.87 | 1.26 | 0.00 | 3.09 | 0.00 | 0.00 | 9.78 | 2.15 |
time (sec) |
N/A | 0.201 | 0.935 | 0.190 | 0.000 | 0.114 | 0.000 | 0.000 | 2.004 | 0.714 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 82 | 73 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.41 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.174 | 0.037 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.828 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 74 | 73 | 0 | 0 | 0 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.28 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.165 | 0.022 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.358 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 74 | 73 | 0 | 0 | 0 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.28 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.165 | 0.019 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.257 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 81 | 73 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.40 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.173 | 0.031 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.365 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 82 | 73 | 0 | 0 | 0 | 0 | 0 | 176 | 0 |
N.S. |
1 | 1.41 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.03 | 0.00 |
time (sec) |
N/A | 0.172 | 0.038 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.896 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 84 | 81 | 0 | 0 | 0 | 0 | 0 | 375 | 0 |
N.S. |
1 | 1.45 | 1.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 6.47 | 0.00 |
time (sec) |
N/A | 0.170 | 0.027 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 82 | 71 | 0 | 0 | 0 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.46 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.21 | 0.00 |
time (sec) |
N/A | 0.194 | 0.047 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.088 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 80 | 71 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.43 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.173 | 0.031 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.656 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 72 | 71 | 0 | 0 | 0 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.29 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.166 | 0.020 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.327 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 72 | 71 | 0 | 0 | 0 | 0 | 0 | 87 | 0 |
N.S. |
1 | 1.29 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.55 | 0.00 |
time (sec) |
N/A | 0.170 | 0.020 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 79 | 71 | 0 | 0 | 0 | 0 | 0 | 133 | 0 |
N.S. |
1 | 1.41 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.38 | 0.00 |
time (sec) |
N/A | 0.167 | 0.027 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.360 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 80 | 79 | 0 | 0 | 0 | 0 | 0 | 181 | 0 |
N.S. |
1 | 1.43 | 1.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.23 | 0.00 |
time (sec) |
N/A | 0.169 | 0.021 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.895 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 343 | 434 | 317 | 0 | 0 | 2575 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.27 | 0.92 | 0.00 | 0.00 | 7.51 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.479 | 0.739 | 0.000 | 0.000 | 0.131 | 0.000 | 0.000 | 30.607 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 299 | 393 | 295 | 0 | 0 | 1455 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.31 | 0.99 | 0.00 | 0.00 | 4.87 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.433 | 0.750 | 0.000 | 0.000 | 0.118 | 0.000 | 0.000 | 14.301 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 362 | 223 | 0 | 0 | 402 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.54 | 0.95 | 0.00 | 0.00 | 1.71 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.406 | 0.443 | 0.000 | 0.000 | 0.087 | 0.000 | 0.000 | 200.023 | 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 | 30 | 30 | 30 | 27 | 0 | 42 | 0 | 0 | 87 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.00 | 1.40 | 0.00 | 0.00 | 2.90 | 0.00 |
time (sec) |
N/A | 0.140 | 0.020 | 0.177 | 0.000 | 0.074 | 0.000 | 0.000 | 0.385 | 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 | 66 | 66 | 46 | 53 | 0 | 118 | 0 | 0 | 340 | 0 |
N.S. |
1 | 1.00 | 0.70 | 0.80 | 0.00 | 1.79 | 0.00 | 0.00 | 5.15 | 0.00 |
time (sec) |
N/A | 0.158 | 0.163 | 0.182 | 0.000 | 0.077 | 0.000 | 0.000 | 0.681 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 114 | 77 | 105 | 0 | 252 | 0 | 0 | 638 | 0 |
N.S. |
1 | 1.13 | 0.76 | 1.04 | 0.00 | 2.50 | 0.00 | 0.00 | 6.32 | 0.00 |
time (sec) |
N/A | 0.179 | 0.292 | 0.187 | 0.000 | 0.095 | 0.000 | 0.000 | 0.968 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 162 | 118 | 171 | 0 | 420 | 0 | 0 | 985 | 0 |
N.S. |
1 | 1.19 | 0.87 | 1.26 | 0.00 | 3.09 | 0.00 | 0.00 | 7.24 | 0.00 |
time (sec) |
N/A | 0.206 | 0.881 | 0.191 | 0.000 | 0.087 | 0.000 | 0.000 | 1.372 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 368 | 473 | 357 | 0 | 0 | 2686 | 0 | 0 | 825 | 0 |
N.S. |
1 | 1.29 | 0.97 | 0.00 | 0.00 | 7.30 | 0.00 | 0.00 | 2.24 | 0.00 |
time (sec) |
N/A | 0.514 | 1.032 | 0.000 | 0.000 | 0.142 | 0.000 | 0.000 | 1.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 324 | 432 | 318 | 0 | 0 | 1562 | 0 | 0 | 531 | 0 |
N.S. |
1 | 1.33 | 0.98 | 0.00 | 0.00 | 4.82 | 0.00 | 0.00 | 1.64 | 0.00 |
time (sec) |
N/A | 0.469 | 0.914 | 0.000 | 0.000 | 0.137 | 0.000 | 0.000 | 0.886 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | B | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 397 | 268 | 0 | 0 | 504 | 0 | 0 | 255 | 0 |
N.S. |
1 | 1.54 | 1.04 | 0.00 | 0.00 | 1.95 | 0.00 | 0.00 | 0.99 | 0.00 |
time (sec) |
N/A | 0.435 | 0.520 | 0.000 | 0.000 | 0.115 | 0.000 | 0.000 | 0.433 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 27 | 0 | 42 | 0 | 0 | 87 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.00 | 1.40 | 0.00 | 0.00 | 2.90 | 0.87 |
time (sec) |
N/A | 0.137 | 0.022 | 0.181 | 0.000 | 0.087 | 0.000 | 0.000 | 0.462 | 0.434 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 45 | 53 | 0 | 126 | 0 | 0 | 133 | 72 |
N.S. |
1 | 1.00 | 0.70 | 0.83 | 0.00 | 1.97 | 0.00 | 0.00 | 2.08 | 1.12 |
time (sec) |
N/A | 0.157 | 0.265 | 0.176 | 0.000 | 0.096 | 0.000 | 0.000 | 0.844 | 0.519 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 110 | 77 | 105 | 0 | 273 | 0 | 0 | 181 | 132 |
N.S. |
1 | 1.12 | 0.79 | 1.07 | 0.00 | 2.79 | 0.00 | 0.00 | 1.85 | 1.35 |
time (sec) |
N/A | 0.186 | 0.346 | 0.177 | 0.000 | 0.104 | 0.000 | 0.000 | 1.285 | 0.595 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 158 | 118 | 171 | 0 | 457 | 0 | 0 | 229 | 209 |
N.S. |
1 | 1.18 | 0.88 | 1.28 | 0.00 | 3.41 | 0.00 | 0.00 | 1.71 | 1.56 |
time (sec) |
N/A | 0.212 | 0.929 | 0.181 | 0.000 | 0.127 | 0.000 | 0.000 | 1.788 | 0.704 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 80 | 71 | 0 | 0 | 0 | 0 | 0 | 318 | 0 |
N.S. |
1 | 1.43 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 5.68 | 0.00 |
time (sec) |
N/A | 0.178 | 0.038 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.657 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 72 | 71 | 0 | 0 | 0 | 0 | 0 | 270 | 0 |
N.S. |
1 | 1.29 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 4.82 | 0.00 |
time (sec) |
N/A | 0.167 | 0.019 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 3.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 72 | 71 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.29 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.176 | 0.019 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.341 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 79 | 71 | 0 | 0 | 0 | 0 | 0 | 87 | 0 |
N.S. |
1 | 1.41 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.55 | 0.00 |
time (sec) |
N/A | 0.171 | 0.029 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.534 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 80 | 71 | 0 | 0 | 0 | 0 | 0 | 216 | 0 |
N.S. |
1 | 1.43 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.86 | 0.00 |
time (sec) |
N/A | 0.176 | 0.037 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.899 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 82 | 79 | 0 | 0 | 0 | 0 | 0 | 420 | 0 |
N.S. |
1 | 1.46 | 1.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 7.50 | 0.00 |
time (sec) |
N/A | 0.191 | 0.028 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 110 | 94 | 389 | 246 | 497 | 4058 | 833 | 546 | 478 |
N.S. |
1 | 1.00 | 0.85 | 3.54 | 2.24 | 4.52 | 36.89 | 7.57 | 4.96 | 4.35 |
time (sec) |
N/A | 0.242 | 0.086 | 0.189 | 0.042 | 0.107 | 1.104 | 0.127 | 0.160 | 0.504 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 67 | 159 | 138 | 235 | 1506 | 385 | 241 | 226 |
N.S. |
1 | 1.00 | 0.86 | 2.04 | 1.77 | 3.01 | 19.31 | 4.94 | 3.09 | 2.90 |
time (sec) |
N/A | 0.208 | 0.081 | 0.157 | 0.048 | 0.103 | 0.622 | 0.126 | 0.153 | 0.358 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 41 | 49 | 63 | 83 | 377 | 132 | 75 | 88 |
N.S. |
1 | 1.00 | 0.89 | 1.07 | 1.37 | 1.80 | 8.20 | 2.87 | 1.63 | 1.91 |
time (sec) |
N/A | 0.173 | 0.045 | 0.132 | 0.039 | 0.130 | 0.345 | 0.122 | 0.153 | 0.281 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 51 | 0 | 0 | 0 | 0 | 0 | 94 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.84 | 0.00 |
time (sec) |
N/A | 0.155 | 0.043 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 52 | 0 | 0 | 0 | 0 | 0 | 1219 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 23.44 | 0.00 |
time (sec) |
N/A | 0.156 | 0.042 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 54 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.158 | 0.044 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 95 | 386 | 246 | 496 | 4058 | 833 | 546 | 478 |
N.S. |
1 | 1.00 | 0.86 | 3.48 | 2.22 | 4.47 | 36.56 | 7.50 | 4.92 | 4.31 |
time (sec) |
N/A | 0.249 | 0.085 | 0.189 | 0.064 | 0.082 | 1.052 | 0.134 | 0.147 | 0.516 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 67 | 159 | 138 | 237 | 1506 | 385 | 241 | 226 |
N.S. |
1 | 1.00 | 0.86 | 2.04 | 1.77 | 3.04 | 19.31 | 4.94 | 3.09 | 2.90 |
time (sec) |
N/A | 0.205 | 0.077 | 0.161 | 0.055 | 0.092 | 0.767 | 0.125 | 0.148 | 0.355 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 41 | 46 | 63 | 83 | 377 | 132 | 75 | 88 |
N.S. |
1 | 1.00 | 0.87 | 0.98 | 1.34 | 1.77 | 8.02 | 2.81 | 1.60 | 1.87 |
time (sec) |
N/A | 0.185 | 0.044 | 0.137 | 0.041 | 0.084 | 0.366 | 0.120 | 0.158 | 0.276 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 19 | 18 | 20 | 20 | 18 | 21 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.11 | 1.11 | 1.00 | 1.17 | 1.00 |
time (sec) |
N/A | 0.135 | 0.002 | 0.118 | 0.037 | 0.085 | 0.019 | 0.117 | 0.156 | 0.232 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 51 | 0 | 0 | 0 | 0 | 0 | 94 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.84 | 0.00 |
time (sec) |
N/A | 0.158 | 0.041 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 52 | 0 | 0 | 0 | 0 | 0 | 1218 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 23.88 | 0.00 |
time (sec) |
N/A | 0.157 | 0.044 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 54 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.161 | 0.044 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 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 | 30 | 30 | 30 | 0 | 0 | 0 | 29 | 0 | 97 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.97 | 0.00 | 3.23 | 0.00 |
time (sec) |
N/A | 0.138 | 0.061 | 0.000 | 0.000 | 0.000 | 1.175 | 0.000 | 0.157 | 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 | 35 | 35 | 35 | 0 | 0 | 0 | 31 | 0 | 96 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.89 | 0.00 | 2.74 | 0.00 |
time (sec) |
N/A | 0.138 | 0.062 | 0.000 | 0.000 | 0.000 | 1.534 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 0 | 0 | 0 | 37 | 0 | 693 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 1.12 | 0.00 | 21.00 | 0.00 |
time (sec) |
N/A | 0.139 | 0.075 | 0.000 | 0.000 | 0.000 | 44.983 | 0.000 | 0.244 | 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 | 37 | 37 | 37 | 0 | 0 | 0 | 42 | 0 | 693 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 1.14 | 0.00 | 18.73 | 0.00 |
time (sec) |
N/A | 0.135 | 0.078 | 0.000 | 0.000 | 0.000 | 42.575 | 0.000 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 12 | 106 | 17 | 20 | 23 | 14 | 11 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 9.64 | 1.55 | 1.82 | 2.09 | 1.27 | 1.00 |
time (sec) |
N/A | 0.126 | 0.043 | 0.140 | 0.047 | 0.086 | 0.106 | 0.127 | 0.157 | 0.270 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 74 | 73 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.21 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.173 | 0.041 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-2) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 146 | 112 | 322 | 0 | 512 | 0 | 0 | 86 | 528 |
N.S. |
1 | 1.02 | 0.78 | 2.25 | 0.00 | 3.58 | 0.00 | 0.00 | 0.60 | 3.69 |
time (sec) |
N/A | 0.228 | 0.079 | 0.345 | 0.000 | 0.092 | 0.000 | 0.000 | 0.167 | 0.597 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-2) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 59 | 127 | 0 | 206 | 0 | 0 | 68 | 220 |
N.S. |
1 | 1.00 | 0.69 | 1.48 | 0.00 | 2.40 | 0.00 | 0.00 | 0.79 | 2.56 |
time (sec) |
N/A | 0.183 | 0.056 | 0.293 | 0.000 | 0.086 | 0.000 | 0.000 | 0.161 | 0.422 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-2) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 36 | 45 | 0 | 60 | 0 | 0 | 50 | 102 |
N.S. |
1 | 1.00 | 0.92 | 1.15 | 0.00 | 1.54 | 0.00 | 0.00 | 1.28 | 2.62 |
time (sec) |
N/A | 0.147 | 0.041 | 0.293 | 0.000 | 0.081 | 0.000 | 0.000 | 0.153 | 0.305 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 66 | 65 | 0 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.18 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.179 | 0.047 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 72 | 71 | 0 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.20 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.181 | 0.040 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 72 | 89 | 0 | 0 | 0 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.20 | 1.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.178 | 0.062 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 72 | 92 | 0 | 0 | 0 | 0 | 0 | 74 | 0 |
N.S. |
1 | 1.20 | 1.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.23 | 0.00 |
time (sec) |
N/A | 0.184 | 0.061 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 72 | 71 | 0 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.12 | 1.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.188 | 0.041 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 75 | 74 | 0 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.27 | 1.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.188 | 0.049 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-2) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 38 | 41 | 0 | 59 | 0 | 0 | 50 | 97 |
N.S. |
1 | 1.00 | 1.03 | 1.11 | 0.00 | 1.59 | 0.00 | 0.00 | 1.35 | 2.62 |
time (sec) |
N/A | 0.148 | 0.040 | 0.323 | 0.000 | 0.086 | 0.000 | 0.000 | 0.153 | 0.297 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-2) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 60 | 123 | 0 | 207 | 0 | 0 | 68 | 214 |
N.S. |
1 | 1.00 | 0.75 | 1.54 | 0.00 | 2.59 | 0.00 | 0.00 | 0.85 | 2.68 |
time (sec) |
N/A | 0.183 | 0.053 | 0.335 | 0.000 | 0.088 | 0.000 | 0.000 | 0.153 | 0.416 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-2) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 136 | 113 | 318 | 0 | 509 | 0 | 0 | 86 | 525 |
N.S. |
1 | 1.04 | 0.86 | 2.43 | 0.00 | 3.89 | 0.00 | 0.00 | 0.66 | 4.01 |
time (sec) |
N/A | 0.225 | 0.069 | 0.394 | 0.000 | 0.103 | 0.000 | 0.000 | 0.153 | 0.577 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-2) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 192 | 195 | 661 | 0 | 959 | 0 | 0 | 104 | 944 |
N.S. |
1 | 1.03 | 1.05 | 3.55 | 0.00 | 5.16 | 0.00 | 0.00 | 0.56 | 5.08 |
time (sec) |
N/A | 0.265 | 0.092 | 0.385 | 0.000 | 0.119 | 0.000 | 0.000 | 0.152 | 0.938 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 72 | 71 | 0 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.20 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.194 | 0.012 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 75 | 74 | 0 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.32 | 1.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.183 | 0.048 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-2) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 36 | 42 | 0 | 58 | 0 | 0 | 50 | 98 |
N.S. |
1 | 1.00 | 1.00 | 1.17 | 0.00 | 1.61 | 0.00 | 0.00 | 1.39 | 2.72 |
time (sec) |
N/A | 0.145 | 0.037 | 0.312 | 0.000 | 0.086 | 0.000 | 0.000 | 0.155 | 0.332 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-2) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 59 | 124 | 0 | 205 | 0 | 0 | 68 | 214 |
N.S. |
1 | 1.00 | 0.75 | 1.57 | 0.00 | 2.59 | 0.00 | 0.00 | 0.86 | 2.71 |
time (sec) |
N/A | 0.175 | 0.053 | 0.316 | 0.000 | 0.105 | 0.000 | 0.000 | 0.158 | 0.414 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-2) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 134 | 112 | 319 | 0 | 507 | 0 | 0 | 86 | 528 |
N.S. |
1 | 1.03 | 0.86 | 2.45 | 0.00 | 3.90 | 0.00 | 0.00 | 0.66 | 4.06 |
time (sec) |
N/A | 0.208 | 0.070 | 0.381 | 0.000 | 0.096 | 0.000 | 0.000 | 0.172 | 0.587 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-2) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 189 | 195 | 662 | 0 | 954 | 0 | 0 | 104 | 945 |
N.S. |
1 | 1.02 | 1.05 | 3.58 | 0.00 | 5.16 | 0.00 | 0.00 | 0.56 | 5.11 |
time (sec) |
N/A | 0.243 | 0.093 | 0.382 | 0.000 | 0.178 | 0.000 | 0.000 | 0.151 | 0.927 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 83 | 75 | 0 | 0 | 0 | 0 | 0 | 106 | 0 |
N.S. |
1 | 1.36 | 1.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.74 | 0.00 |
time (sec) |
N/A | 0.183 | 0.073 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 84 | 83 | 0 | 0 | 0 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.47 | 1.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.23 | 0.00 |
time (sec) |
N/A | 0.195 | 0.062 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 51 | 0 | 0 | 0 | 0 | 0 | 94 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.84 | 0.00 |
time (sec) |
N/A | 0.157 | 0.006 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 53 | 57 | 92 | 93 | 233 | 78 | 115 | 46 |
N.S. |
1 | 1.00 | 0.93 | 1.00 | 1.61 | 1.63 | 4.09 | 1.37 | 2.02 | 0.81 |
time (sec) |
N/A | 0.198 | 0.017 | 0.158 | 0.033 | 0.103 | 0.367 | 0.128 | 0.154 | 0.251 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 95 | 54 | 56 | 0 | 85 | 0 | 0 | 478 | 81 |
N.S. |
1 | 1.00 | 0.57 | 0.59 | 0.00 | 0.89 | 0.00 | 0.00 | 5.03 | 0.85 |
time (sec) |
N/A | 0.198 | 0.181 | 0.646 | 0.000 | 0.082 | 0.000 | 0.000 | 0.158 | 0.578 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 46 | 62 | 0 | 84 | 0 | 0 | 180 | 119 |
N.S. |
1 | 1.00 | 0.47 | 0.64 | 0.00 | 0.87 | 0.00 | 0.00 | 1.86 | 1.23 |
time (sec) |
N/A | 0.188 | 0.259 | 0.560 | 0.000 | 0.088 | 0.000 | 0.000 | 0.153 | 1.205 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 46 | 66 | 0 | 84 | 0 | 0 | 180 | 142 |
N.S. |
1 | 1.00 | 0.47 | 0.68 | 0.00 | 0.87 | 0.00 | 0.00 | 1.86 | 1.46 |
time (sec) |
N/A | 0.187 | 0.127 | 0.448 | 0.000 | 0.097 | 0.000 | 0.000 | 0.151 | 0.485 |
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 | 47 | 47 | 47 | 0 | 0 | 0 | 39 | 0 | 19 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.83 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.155 | 0.029 | 0.000 | 0.000 | 0.000 | 17.337 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 88 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.163 | 0.025 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 0.000 |