Detailed conclusion table per each integral is given by 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 just an F.
In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 28 | 28 | 27 | 24 | 27 | 22 | 31 | 24 |
N.S. | 1 | 0.93 | 0.93 | 0.90 | 0.80 | 0.90 | 0.73 | 1.03 | 0.80 |
time (sec) |
N/A | 0.330 | 0.074 | 0.619 | 0.268 | 0.504 | 0.067 | 0.415 | 7.380 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | C | B | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 21 | 15 | 30 | 36 | 47 | 22 | 21 | 21 |
N.S. | 1 | 1.24 | 0.88 | 1.76 | 2.12 | 2.76 | 1.29 | 1.24 | 1.24 |
time (sec) |
N/A | 0.087 | 0.016 | 1.809 | 0.478 | 0.373 | 0.045 | 0.407 | 9.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 26 | 26 | 38 | 38 | 22 | 38 | 25 |
N.S. | 1 | 0.00 | 0.93 | 0.93 | 1.36 | 1.36 | 0.79 | 1.36 | 0.89 |
time (sec) |
N/A | 13.842 | 0.208 | 0.304 | 0.355 | 0.380 | 0.204 | 0.456 | 7.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 13 | 13 | 12 | 9 | 11 | 10 | 11 | 11 |
N.S. | 1 | 0.52 | 0.52 | 0.48 | 0.36 | 0.44 | 0.40 | 0.44 | 0.44 |
time (sec) |
N/A | 0.139 | 0.036 | 7.779 | 0.287 | 0.383 | 0.037 | 0.399 | 8.779 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 14 | 14 | 13 | 12 | 12 | 8 | 14 | 12 |
N.S. | 1 | 0.88 | 0.88 | 0.81 | 0.75 | 0.75 | 0.50 | 0.88 | 0.75 |
time (sec) |
N/A | 0.020 | 0.004 | 1.390 | 0.250 | 0.350 | 0.028 | 0.416 | 7.795 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 48 | 32 | 33 | 37 | 28 | 29 | 28 | 32 |
N.S. | 1 | 1.66 | 1.10 | 1.14 | 1.28 | 0.97 | 1.00 | 0.97 | 1.10 |
time (sec) |
N/A | 0.093 | 0.087 | 1.727 | 0.270 | 0.374 | 0.246 | 0.416 | 0.178 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 25 | 26 | 27 | 24 | 24 | 24 | 24 | 24 |
N.S. | 1 | 0.89 | 0.93 | 0.96 | 0.86 | 0.86 | 0.86 | 0.86 | 0.86 |
time (sec) |
N/A | 0.066 | 0.053 | 0.096 | 0.286 | 0.500 | 0.084 | 0.413 | 7.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 32 | 18 | 19 | 0 | 21 | 14 | 18 | 20 |
N.S. | 1 | 1.78 | 1.00 | 1.06 | 0.00 | 1.17 | 0.78 | 1.00 | 1.11 |
time (sec) |
N/A | 0.067 | 0.241 | 1.065 | 0.000 | 0.409 | 0.035 | 0.400 | 0.154 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | C | B | B | B | B | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 40 | 385 | 42 | 47 | 51 | 51 | 51 |
N.S. | 1 | 0.00 | 1.90 | 18.33 | 2.00 | 2.24 | 2.43 | 2.43 | 2.43 |
time (sec) |
N/A | 17.566 | 0.202 | 0.663 | 6.494 | 0.372 | 4.081 | 0.525 | 8.244 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | C | A | A | F(-2) | B | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 33 | 95 | 44 | 45 | 0 | 67 | 55 |
N.S. |
1 | 0.00 | 1.14 | 3.28 | 1.52 | 1.55 | 0.00 | 2.31 | 1.90 |
time (sec) |
N/A | 6.272 | 0.150 | 83.617 | 0.331 | 0.396 | 0.000 | 0.627 | 9.716 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | B | B | A | B | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 40 | 32 | 59 | 65 | 31 | 59 | -1 |
N.S. | 1 | 0.00 | 1.29 | 1.03 | 1.90 | 2.10 | 1.00 | 1.90 | -0.03 |
time (sec) |
N/A | 3.707 | 8.747 | 0.513 | 0.328 | 0.376 | 0.109 | 0.433 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 0 | 11 | 11 | 10 | 10 | 8 | 10 | 10 |
N.S. | 1 | 0.00 | 1.10 | 1.10 | 1.00 | 1.00 | 0.80 | 1.00 | 1.00 |
time (sec) |
N/A | 0.269 | 0.123 | 0.448 | 0.295 | 0.369 | 0.036 | 0.408 | 0.132 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 19 | 19 | 20 | 19 | 19 | 17 | 20 | 19 |
N.S. | 1 | 0.90 | 0.90 | 0.95 | 0.90 | 0.90 | 0.81 | 0.95 | 0.90 |
time (sec) |
N/A | 0.160 | 0.012 | 0.453 | 0.251 | 0.459 | 0.052 | 0.418 | 7.571 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | B | B | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 30 | 30 | 935 | 0 | 115 | 114 | 0 | 90 |
N.S. | 1 | 1.11 | 1.11 | 34.63 | 0.00 | 4.26 | 4.22 | 0.00 | 3.33 |
time (sec) |
N/A | 0.291 | 0.166 | 7.023 | 0.000 | 0.376 | 0.477 | 0.000 | 9.806 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | C | F | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 31 | 223 | 0 | 39 | 32 | 33 | 145 |
N.S. | 1 | 0.00 | 0.97 | 6.97 | 0.00 | 1.22 | 1.00 | 1.03 | 4.53 |
time (sec) |
N/A | 11.639 | 0.247 | 0.946 | 0.000 | 0.377 | 0.693 | 1.573 | 9.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 21 | 27 | 80 | 20 | 20 | 22 | 20 | 22 |
N.S. | 1 | 1.05 | 1.35 | 4.00 | 1.00 | 1.00 | 1.10 | 1.00 | 1.10 |
time (sec) |
N/A | 1.353 | 0.164 | 0.325 | 0.316 | 0.361 | 0.657 | 0.454 | 7.233 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 37 | 119 | 107 | 93 | 94 | 107 | 123 |
N.S. | 1 | 0.00 | 1.37 | 4.41 | 3.96 | 3.44 | 3.48 | 3.96 | 4.56 |
time (sec) |
N/A | 24.633 | 0.189 | 0.872 | 0.726 | 0.362 | 0.503 | 0.739 | 9.175 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 11 | 10 | 11 | 10 | 10 | 12 | 10 | 10 |
N.S. | 1 | 0.69 | 0.62 | 0.69 | 0.62 | 0.62 | 0.75 | 0.62 | 0.62 |
time (sec) |
N/A | 0.005 | 0.006 | 0.234 | 0.265 | 0.362 | 0.045 | 0.396 | 7.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | B | B | B | B | F(-1) | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 54 | 71 | 89 | 86 | 99 | 0 | -1 |
N.S. |
1 | 0.00 | 1.54 | 2.03 | 2.54 | 2.46 | 2.83 | 0.00 | -0.03 |
time (sec) |
N/A | 50.892 | 0.256 | 11.374 | 0.357 | 0.373 | 0.247 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | A | B | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 26 | 24 | 997 | 26 | 55 | 37 | 36 | 74 |
N.S. | 1 | 1.18 | 1.09 | 45.32 | 1.18 | 2.50 | 1.68 | 1.64 | 3.36 |
time (sec) |
N/A | 0.864 | 0.048 | 11.146 | 0.259 | 0.384 | 0.106 | 0.464 | 7.265 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | F | A | A | A | A | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 28 | 0 | 43 | 35 | 27 | 33 | -1 |
N.S. | 1 | 0.00 | 0.90 | 0.00 | 1.39 | 1.13 | 0.87 | 1.06 | -0.03 |
time (sec) |
N/A | 77.042 | 0.171 | 180.000 | 0.551 | 0.372 | 1.233 | 0.719 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 2 | 2 | 2 | 3 | 2 | 2 | 2 | 3 | 2 |
N.S. | 1 | 1.00 | 1.00 | 1.50 | 1.00 | 1.00 | 1.00 | 1.50 | 1.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.221 | 0.272 | 0.338 | 0.024 | 0.395 | 0.006 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | B | B | B | B | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 32 | 30 | 66 | 62 | 53 | 71 | 44 |
N.S. | 1 | 0.00 | 1.07 | 1.00 | 2.20 | 2.07 | 1.77 | 2.37 | 1.47 |
time (sec) |
N/A | 7.390 | 0.179 | 0.735 | 0.406 | 0.389 | 0.168 | 0.431 | 8.922 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 11 | 11 | 9 | 8 | 8 | 8 | 8 | 8 |
N.S. | 1 | 0.92 | 0.92 | 0.75 | 0.67 | 0.67 | 0.67 | 0.67 | 0.67 |
time (sec) |
N/A | 0.006 | 0.003 | 0.427 | 0.266 | 0.383 | 0.019 | 0.395 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 13 | 12 | 12 | 14 | 12 | 12 |
N.S. | 1 | 1.00 | 1.00 | 0.87 | 0.80 | 0.80 | 0.93 | 0.80 | 0.80 |
time (sec) |
N/A | 0.015 | 0.023 | 0.240 | 0.258 | 0.347 | 0.029 | 0.407 | 0.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 77 | 23 | 71 | 62 | 62 | 63 | 62 | 21 |
N.S. | 1 | 3.50 | 1.05 | 3.23 | 2.82 | 2.82 | 2.86 | 2.82 | 0.95 |
time (sec) |
N/A | 0.502 | 2.814 | 0.444 | 0.263 | 0.361 | 0.072 | 0.391 | 7.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | F | F(-1) | B | B | B | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 31 | 0 | 0 | 147 | 143 | 175 | 1157 |
N.S. |
1 | 0.00 | 1.03 | 0.00 | 0.00 | 4.90 | 4.77 | 5.83 | 38.57 |
time (sec) |
N/A | 104.378 | 0.443 | 3.223 | 0.000 | 0.375 | 5.091 | 21.675 | 9.001 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 51 | 52 | 36 | 35 | 54 | 41 | 35 | 35 |
N.S. | 1 | 1.31 | 1.33 | 0.92 | 0.90 | 1.38 | 1.05 | 0.90 | 0.90 |
time (sec) |
N/A | 0.053 | 0.054 | 0.577 | 0.255 | 0.362 | 0.149 | 0.417 | 0.189 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | C | B | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 29 | 59 | 50 | 29 | 29 | 40 | 29 |
N.S. | 1 | 0.00 | 1.16 | 2.36 | 2.00 | 1.16 | 1.16 | 1.60 | 1.16 |
time (sec) |
N/A | 0.588 | 0.117 | 22.042 | 0.506 | 0.365 | 0.208 | 0.434 | 7.541 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | C | B | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 107 | 45 | 160 | 54 | 33 | 0 | 0 | 39 |
N.S. |
1 | 4.28 | 1.80 | 6.40 | 2.16 | 1.32 | 0.00 | 0.00 | 1.56 |
time (sec) |
N/A | 1.001 | 0.099 | 1.076 | 0.687 | 0.409 | 0.000 | 0.000 | 8.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | F | C | A | B | B | B | B |
verified |
N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 0 | 1028 | 38 | 97 | 90 | 125 | 78 |
N.S. | 1 | 0.00 | 0.00 | 35.45 | 1.31 | 3.34 | 3.10 | 4.31 | 2.69 |
time (sec) |
N/A | 4.078 | 0.585 | 65.041 | 0.535 | 0.380 | 0.622 | 4.182 | 8.282 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 22 | 33 | 0 | 32 | 0 | 20 | 21 |
N.S. |
1 | 0.00 | 0.88 | 1.32 | 0.00 | 1.28 | 0.00 | 0.80 | 0.84 |
time (sec) |
N/A | 5.678 | 0.054 | 0.261 | 0.000 | 0.356 | 0.000 | 0.450 | 8.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 27 | 33 | 27 | 40 | 19 | 25 | 25 |
N.S. | 1 | 1.00 | 0.87 | 1.06 | 0.87 | 1.29 | 0.61 | 0.81 | 0.81 |
time (sec) |
N/A | 0.142 | 0.019 | 0.243 | 0.269 | 0.351 | 0.048 | 0.409 | 0.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 12 | 12 | 12 | 11 | 11 | 12 | 11 | 11 |
N.S. | 1 | 0.75 | 0.75 | 0.75 | 0.69 | 0.69 | 0.75 | 0.69 | 0.69 |
time (sec) |
N/A | 0.140 | 0.057 | 0.127 | 0.303 | 0.480 | 0.315 | 0.423 | 7.573 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 24 | 26 | 28 | 22 | 33 | 22 | 22 | 21 |
N.S. | 1 | 1.04 | 1.13 | 1.22 | 0.96 | 1.43 | 0.96 | 0.96 | 0.91 |
time (sec) |
N/A | 0.066 | 0.023 | 3.273 | 0.260 | 0.347 | 0.105 | 0.406 | 0.190 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | B | F | B | B | F | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 25 | 113 | 0 | 93 | 654 | 0 | 155 |
N.S. | 1 | 0.00 | 0.86 | 3.90 | 0.00 | 3.21 | 22.55 | 0.00 | 5.34 |
time (sec) |
N/A | 18.679 | 0.341 | 1.026 | 0.000 | 0.365 | 0.455 | 0.000 | 9.708 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 24 | 24 | 23 | 79 | 26 | 20 | 30 | 24 |
N.S. | 1 | 1.09 | 1.09 | 1.05 | 3.59 | 1.18 | 0.91 | 1.36 | 1.09 |
time (sec) |
N/A | 0.037 | 0.045 | 0.395 | 0.285 | 0.437 | 0.075 | 0.422 | 8.382 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | C | A | A | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 43 | 26 | 27 | 37 | 26 | 31 | 35 | -1 |
N.S. | 1 | 1.59 | 0.96 | 1.00 | 1.37 | 0.96 | 1.15 | 1.30 | -0.04 |
time (sec) |
N/A | 1.005 | 0.195 | 0.074 | 0.314 | 0.376 | 0.203 | 0.437 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 22 | 22 | 52 | 30 | 22 | 32 | 22 | 22 |
N.S. | 1 | 1.16 | 1.16 | 2.74 | 1.58 | 1.16 | 1.68 | 1.16 | 1.16 |
time (sec) |
N/A | 0.378 | 0.055 | 1.178 | 0.281 | 0.373 | 0.225 | 0.416 | 7.699 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | F | F | A | F(-1) | F | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 0 | 0 | 39 | 0 | 0 | 20 |
N.S. |
1 | 0.00 | 1.00 | 0.00 | 0.00 | 1.70 | 0.00 | 0.00 | 0.87 |
time (sec) |
N/A | 1.925 | 0.138 | 0.227 | 0.000 | 0.369 | 0.000 | 0.000 | 7.780 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 28 | 27 | 28 | 28 | 41 | 28 | 26 |
N.S. | 1 | 0.00 | 1.12 | 1.08 | 1.12 | 1.12 | 1.64 | 1.12 | 1.04 |
time (sec) |
N/A | 1.997 | 0.145 | 47.129 | 0.282 | 0.370 | 0.136 | 0.430 | 7.485 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F(-1) | A | F | F | B | B | F | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 22 | 0 | 0 | 119 | 117 | 0 | 122 |
N.S. |
1 | 0.00 | 1.00 | 0.00 | 0.00 | 5.41 | 5.32 | 0.00 | 5.55 |
time (sec) |
N/A | 180.036 | 0.287 | 0.107 | 0.000 | 0.403 | 0.515 | 0.000 | 7.373 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | B | A | A | B | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 0 | 19 | 20 | 36 | 19 | 14 | 72 | 19 |
N.S. | 1 | 0.00 | 1.12 | 1.18 | 2.12 | 1.12 | 0.82 | 4.24 | 1.12 |
time (sec) |
N/A | 0.321 | 0.064 | 55.152 | 0.311 | 0.341 | 0.052 | 0.416 | 0.316 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 30 | 22 | 26 | 62 | 25 | 24 | 25 | 38 |
N.S. | 1 | 1.11 | 0.81 | 0.96 | 2.30 | 0.93 | 0.89 | 0.93 | 1.41 |
time (sec) |
N/A | 8.451 | 0.181 | 2.617 | 0.555 | 0.363 | 0.232 | 0.645 | 8.263 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | B | F(-2) | A | B | B | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 36 | 60 | 0 | 50 | 46 | 122 | -1 |
N.S. |
1 | 0.00 | 1.03 | 1.71 | 0.00 | 1.43 | 1.31 | 3.49 | -0.03 |
time (sec) |
N/A | 8.097 | 0.209 | 1.151 | 0.000 | 0.408 | 0.536 | 0.463 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 34 | 32 | 27 | 27 | 27 | 32 | 27 | 13 |
N.S. | 1 | 1.89 | 1.78 | 1.50 | 1.50 | 1.50 | 1.78 | 1.50 | 0.72 |
time (sec) |
N/A | 0.014 | 0.004 | 0.310 | 0.261 | 0.364 | 0.011 | 0.410 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | B | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 30 | 29 | 36 | 64 | 29 | 52 | 50 |
N.S. | 1 | 0.00 | 0.97 | 0.94 | 1.16 | 2.06 | 0.94 | 1.68 | 1.61 |
time (sec) |
N/A | 1.447 | 3.148 | 0.843 | 0.327 | 0.377 | 0.143 | 0.629 | 0.351 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 24 | 24 | 26 | 20 | 40 | 26 | 22 | 22 |
N.S. | 1 | 1.04 | 1.04 | 1.13 | 0.87 | 1.74 | 1.13 | 0.96 | 0.96 |
time (sec) |
N/A | 0.123 | 0.051 | 0.484 | 0.262 | 0.382 | 0.101 | 0.412 | 7.439 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 49 | 45 | 40 | 39 | 39 | 42 | 39 | 41 |
N.S. | 1 | 1.69 | 1.55 | 1.38 | 1.34 | 1.34 | 1.45 | 1.34 | 1.41 |
time (sec) |
N/A | 0.049 | 0.187 | 0.686 | 0.254 | 0.387 | 0.050 | 0.398 | 0.215 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | C | B | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 29 | 1016 | 139 | 34 | 31 | 34 | 24 |
N.S. | 1 | 0.00 | 1.26 | 44.17 | 6.04 | 1.48 | 1.35 | 1.48 | 1.04 |
time (sec) |
N/A | 23.230 | 0.270 | 2.646 | 0.257 | 0.383 | 0.069 | 0.419 | 1.286 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 23 | 20 | 19 | 19 | 19 | 19 | 19 |
N.S. | 1 | 1.00 | 1.15 | 1.00 | 0.95 | 0.95 | 0.95 | 0.95 | 0.95 |
time (sec) |
N/A | 0.023 | 0.019 | 0.625 | 0.261 | 0.387 | 0.029 | 0.426 | 7.190 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | C | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 30 | 19 | 23 | 23 | 14 | 27 | 18 |
N.S. | 1 | 0.00 | 1.30 | 0.83 | 1.00 | 1.00 | 0.61 | 1.17 | 0.78 |
time (sec) |
N/A | 0.728 | 0.101 | 3.637 | 0.305 | 0.365 | 0.164 | 0.411 | 7.487 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | B | A | B | F(-1) | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 60 | 57 | 55 | 53 | 71 | 0 | -1 |
N.S. |
1 | 0.00 | 1.82 | 1.73 | 1.67 | 1.61 | 2.15 | 0.00 | -0.03 |
time (sec) |
N/A | 2.725 | 8.181 | 1.877 | 0.323 | 0.374 | 0.108 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | B | A | F(-1) | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 29 | 34 | 68 | 33 | 0 | 41 | 22 |
N.S. |
1 | 0.00 | 0.97 | 1.13 | 2.27 | 1.10 | 0.00 | 1.37 | 0.73 |
time (sec) |
N/A | 1.296 | 0.144 | 1.283 | 0.523 | 0.479 | 0.000 | 0.435 | 7.746 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 21 | 21 | 20 | 26 | 20 | 19 | 26 | 26 |
N.S. | 1 | 1.05 | 1.05 | 1.00 | 1.30 | 1.00 | 0.95 | 1.30 | 1.30 |
time (sec) |
N/A | 0.297 | 0.122 | 2.283 | 0.522 | 0.374 | 0.160 | 0.492 | 8.246 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 27 | 27 | 24 | 32 | 21 | 24 | 21 | 13 |
N.S. | 1 | 1.93 | 1.93 | 1.71 | 2.29 | 1.50 | 1.71 | 1.50 | 0.93 |
time (sec) |
N/A | 0.050 | 0.012 | 0.230 | 0.268 | 0.346 | 0.050 | 0.413 | 7.301 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | C | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 370 | 19 | 412 | 259 | 257 | 296 | 271 | 231 |
N.S. | 1 | 19.47 | 1.00 | 21.68 | 13.63 | 13.53 | 15.58 | 14.26 | 12.16 |
time (sec) |
N/A | 0.472 | 0.055 | 0.602 | 0.498 | 0.418 | 0.245 | 0.419 | 0.412 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | B | A | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 63 | 20 | 64 | 37 | 37 | 32 | 37 | 32 |
N.S. | 1 | 3.50 | 1.11 | 3.56 | 2.06 | 2.06 | 1.78 | 2.06 | 1.78 |
time (sec) |
N/A | 1.028 | 0.074 | 3.363 | 0.290 | 0.355 | 0.053 | 0.401 | 8.369 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | C | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 277 | 65 | 93 | 59 | 80 | 141 | 39 |
N.S. | 1 | 0.00 | 8.66 | 2.03 | 2.91 | 1.84 | 2.50 | 4.41 | 1.22 |
time (sec) |
N/A | 36.086 | 0.613 | 3.690 | 0.535 | 0.362 | 0.298 | 0.492 | 0.462 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 34 | 25 | 35 | 29 | 27 | 29 | 31 | 684 |
N.S. | 1 | 1.62 | 1.19 | 1.67 | 1.38 | 1.29 | 1.38 | 1.48 | 32.57 |
time (sec) |
N/A | 0.166 | 0.024 | 0.465 | 0.260 | 0.439 | 0.408 | 0.432 | 10.305 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 11 | 22 | 33 | 11 | 10 | 11 | 11 |
N.S. | 1 | 1.00 | 0.85 | 1.69 | 2.54 | 0.85 | 0.77 | 0.85 | 0.85 |
time (sec) |
N/A | 0.081 | 0.052 | 0.636 | 0.301 | 0.366 | 0.050 | 0.401 | 7.688 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 16 | 17 | 16 | 11 | 11 | 14 | 12 | 11 |
N.S. | 1 | 0.89 | 0.94 | 0.89 | 0.61 | 0.61 | 0.78 | 0.67 | 0.61 |
time (sec) |
N/A | 0.013 | 0.004 | 0.651 | 0.275 | 0.364 | 0.038 | 0.394 | 7.969 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | B | A | B | B | B | F |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 54 | 72 | 43 | 105 | 60 | 55 | -1 |
N.S. | 1 | 0.00 | 1.93 | 2.57 | 1.54 | 3.75 | 2.14 | 1.96 | -0.04 |
time (sec) |
N/A | 24.116 | 0.181 | 0.204 | 0.307 | 0.427 | 3.359 | 0.453 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 20 | 19 | 30 | 30 | 14 | 21 | 18 |
N.S. | 1 | 0.00 | 0.91 | 0.86 | 1.36 | 1.36 | 0.64 | 0.95 | 0.82 |
time (sec) |
N/A | 0.263 | 2.303 | 46.833 | 0.294 | 0.371 | 0.048 | 0.401 | 7.598 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 23 | 23 | 35 | 29 | 15 | 37 | 45 |
N.S. | 1 | 0.00 | 0.96 | 0.96 | 1.46 | 1.21 | 0.62 | 1.54 | 1.88 |
time (sec) |
N/A | 1.225 | 1.762 | 26.246 | 0.290 | 0.379 | 0.100 | 0.417 | 6.338 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | B | B | F(-2) | B | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 35 | 33 | 52 | 62 | 0 | 66 | 30 |
N.S. |
1 | 0.00 | 1.52 | 1.43 | 2.26 | 2.70 | 0.00 | 2.87 | 1.30 |
time (sec) |
N/A | 1.421 | 1.720 | 0.555 | 0.299 | 0.377 | 0.000 | 0.425 | 0.270 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 12 | 12 | 9 | 8 | 8 | 12 | 9 | 8 |
N.S. | 1 | 0.60 | 0.60 | 0.45 | 0.40 | 0.40 | 0.60 | 0.45 | 0.40 |
time (sec) |
N/A | 0.004 | 0.002 | 0.234 | 0.251 | 0.355 | 0.018 | 0.421 | 5.432 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 11 | 8 | 8 | 7 | 8 | 8 |
N.S. | 1 | 1.00 | 1.00 | 1.22 | 0.89 | 0.89 | 0.78 | 0.89 | 0.89 |
time (sec) |
N/A | 0.016 | 0.004 | 0.490 | 0.271 | 0.368 | 0.031 | 0.408 | 5.429 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | C | A | B | F | A | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 167 | 36 | 119 | 0 | 66 | 66 | 177 | 39 |
N.S. | 1 | 4.91 | 1.06 | 3.50 | 0.00 | 1.94 | 1.94 | 5.21 | 1.15 |
time (sec) |
N/A | 4.189 | 0.094 | 1.879 | 0.000 | 0.385 | 0.316 | 0.410 | 7.785 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F(-1) | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 22 | 19 | 16 | 16 | 24 | 16 | 16 |
N.S. |
1 | 0.00 | 1.10 | 0.95 | 0.80 | 0.80 | 1.20 | 0.80 | 0.80 |
time (sec) |
N/A | 0.000 | 0.066 | 1.177 | 0.300 | 0.378 | 0.100 | 0.702 | 7.460 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | B | F | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 50 | 54 | 50 | 53 | 51 | 0 | 47 |
N.S. | 1 | 0.00 | 1.72 | 1.86 | 1.72 | 1.83 | 1.76 | 0.00 | 1.62 |
time (sec) |
N/A | 1.628 | 0.726 | 0.469 | 0.338 | 0.398 | 0.162 | 0.000 | 9.272 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 46 | 35 | 27 | 50 | 39 | 29 | 34 | 22 |
N.S. | 1 | 1.64 | 1.25 | 0.96 | 1.79 | 1.39 | 1.04 | 1.21 | 0.79 |
time (sec) |
N/A | 0.116 | 0.258 | 1.136 | 0.292 | 0.398 | 0.224 | 0.405 | 0.490 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 22 | 23 | 29 | 29 | 19 | 22 | 22 |
N.S. | 1 | 0.00 | 0.96 | 1.00 | 1.26 | 1.26 | 0.83 | 0.96 | 0.96 |
time (sec) |
N/A | 1.292 | 0.162 | 2.004 | 0.295 | 0.361 | 0.122 | 0.407 | 7.537 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 24 | 24 | 21 | 20 | 20 | 22 | 20 | 22 |
N.S. | 1 | 1.09 | 1.09 | 0.95 | 0.91 | 0.91 | 1.00 | 0.91 | 1.00 |
time (sec) |
N/A | 0.043 | 0.011 | 0.666 | 0.252 | 0.380 | 0.186 | 0.409 | 0.159 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | C | A | A | A | B | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 27 | 157 | 32 | 32 | 31 | 50 | 32 |
N.S. | 1 | 0.00 | 0.96 | 5.61 | 1.14 | 1.14 | 1.11 | 1.79 | 1.14 |
time (sec) |
N/A | 65.322 | 0.136 | 0.720 | 0.272 | 0.369 | 0.116 | 0.419 | 9.210 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | B | A | C | A | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 42 | 42 | 37 | 48 | 29 | 31 | 28 | 17 |
N.S. | 1 | 2.10 | 2.10 | 1.85 | 2.40 | 1.45 | 1.55 | 1.40 | 0.85 |
time (sec) |
N/A | 0.313 | 0.040 | 0.448 | 0.288 | 0.376 | 0.087 | 0.406 | 8.856 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 67 | 43 | 66 | 59 | 59 | 82 | 63 | 55 |
N.S. | 1 | 2.39 | 1.54 | 2.36 | 2.11 | 2.11 | 2.93 | 2.25 | 1.96 |
time (sec) |
N/A | 0.054 | 0.037 | 0.719 | 0.257 | 0.431 | 0.100 | 0.404 | 5.475 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 26 | 25 | 30 | 24 | 20 | 0 | 22 |
N.S. | 1 | 0.00 | 1.04 | 1.00 | 1.20 | 0.96 | 0.80 | 0.00 | 0.88 |
time (sec) |
N/A | 4.024 | 0.582 | 0.284 | 0.333 | 0.369 | 0.285 | 0.000 | 6.290 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 15 | 18 | 18 | 11 | 11 | 17 | 11 | 12 |
N.S. | 1 | 0.71 | 0.86 | 0.86 | 0.52 | 0.52 | 0.81 | 0.52 | 0.57 |
time (sec) |
N/A | 0.016 | 0.007 | 0.447 | 0.251 | 0.349 | 0.143 | 0.399 | 0.097 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 18 | 16 | 20 | 16 | 16 | 19 | 16 | 15 |
N.S. | 1 | 1.38 | 1.23 | 1.54 | 1.23 | 1.23 | 1.46 | 1.23 | 1.15 |
time (sec) |
N/A | 0.003 | 0.003 | 0.423 | 0.269 | 0.358 | 0.009 | 0.403 | 0.174 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 34 | 34 | 47 | 40 | 40 | 32 | 40 | 30 |
N.S. | 1 | 1.55 | 1.55 | 2.14 | 1.82 | 1.82 | 1.45 | 1.82 | 1.36 |
time (sec) |
N/A | 0.019 | 0.008 | 0.612 | 0.267 | 0.371 | 0.015 | 0.418 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 70 | 31 | 43 | 36 | 42 | 34 | 36 | 28 |
N.S. | 1 | 2.80 | 1.24 | 1.72 | 1.44 | 1.68 | 1.36 | 1.44 | 1.12 |
time (sec) |
N/A | 0.127 | 1.084 | 1.174 | 0.314 | 0.382 | 0.108 | 0.422 | 0.194 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 38 | 28 | 48 | 48 | 49 | 42 | 66 | 42 |
N.S. | 1 | 1.36 | 1.00 | 1.71 | 1.71 | 1.75 | 1.50 | 2.36 | 1.50 |
time (sec) |
N/A | 0.303 | 0.037 | 0.522 | 0.268 | 0.379 | 0.088 | 0.421 | 6.340 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 29 | 29 | 29 | 30 | 22 | 22 | 22 | 21 |
N.S. | 1 | 0.91 | 0.91 | 0.91 | 0.94 | 0.69 | 0.69 | 0.69 | 0.66 |
time (sec) |
N/A | 0.058 | 0.015 | 0.953 | 0.270 | 0.368 | 0.079 | 0.420 | 7.960 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 83 | 25 | 24 | 23 | 23 | 22 | 57 | 24 |
N.S. | 1 | 3.07 | 0.93 | 0.89 | 0.85 | 0.85 | 0.81 | 2.11 | 0.89 |
time (sec) |
N/A | 1.213 | 0.642 | 0.171 | 0.311 | 0.370 | 0.608 | 0.435 | 7.539 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 32 | 30 | 64 | 67 | 59 | 58 | 72 | 31 |
N.S. | 1 | 1.39 | 1.30 | 2.78 | 2.91 | 2.57 | 2.52 | 3.13 | 1.35 |
time (sec) |
N/A | 0.373 | 0.064 | 2.094 | 0.466 | 0.371 | 0.142 | 0.532 | 10.412 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 44 | 33 | 51 | 43 | 27 | 34 | 27 | 37 |
N.S. | 1 | 1.63 | 1.22 | 1.89 | 1.59 | 1.00 | 1.26 | 1.00 | 1.37 |
time (sec) |
N/A | 0.051 | 0.025 | 0.459 | 0.258 | 0.375 | 0.110 | 0.406 | 8.112 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F(-2) | F(-2) | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 26 | 24 | 24 | 0 | 26 | 0 | 0 | -1 |
N.S. |
1 | 1.08 | 1.00 | 1.00 | 0.00 | 1.08 | 0.00 | 0.00 | -0.04 |
time (sec) |
N/A | 0.211 | 0.136 | 0.629 | 0.000 | 0.366 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 24 | 22 | 20 | 19 | 19 | 17 | 19 | 19 |
N.S. | 1 | 1.14 | 1.05 | 0.95 | 0.90 | 0.90 | 0.81 | 0.90 | 0.90 |
time (sec) |
N/A | 0.024 | 0.007 | 3.031 | 0.259 | 0.354 | 0.078 | 0.397 | 7.582 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | C | A | B | B | B | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 44 | 371 | 49 | 53 | 49 | 61 | 50 |
N.S. | 1 | 0.00 | 1.76 | 14.84 | 1.96 | 2.12 | 1.96 | 2.44 | 2.00 |
time (sec) |
N/A | 12.712 | 0.131 | 12.034 | 0.569 | 0.379 | 1.460 | 0.831 | 9.882 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | A | B | B | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 56 | 24 | 46 | 142 | 32 | 31 | 32 | 21 |
N.S. | 1 | 2.67 | 1.14 | 2.19 | 6.76 | 1.52 | 1.48 | 1.52 | 1.00 |
time (sec) |
N/A | 0.368 | 0.205 | 0.143 | 0.268 | 0.371 | 0.040 | 0.420 | 8.741 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 21 | 21 | 35 | 20 | 17 | 20 | 20 |
N.S. | 1 | 0.00 | 1.00 | 1.00 | 1.67 | 0.95 | 0.81 | 0.95 | 0.95 |
time (sec) |
N/A | 10.066 | 0.339 | 0.286 | 0.297 | 0.420 | 0.112 | 0.478 | 6.743 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | C | A | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 32 | 149 | 32 | 31 | 29 | 33 | 31 |
N.S. | 1 | 0.00 | 1.07 | 4.97 | 1.07 | 1.03 | 0.97 | 1.10 | 1.03 |
time (sec) |
N/A | 7.304 | 0.079 | 0.808 | 0.740 | 0.357 | 3.992 | 0.570 | 8.803 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 11 | 12 | 13 | 12 | 12 | 12 | 13 | 12 |
N.S. | 1 | 0.85 | 0.92 | 1.00 | 0.92 | 0.92 | 0.92 | 1.00 | 0.92 |
time (sec) |
N/A | 0.011 | 0.004 | 1.794 | 0.262 | 0.366 | 0.082 | 0.404 | 0.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F | A | A | F | A | A | A | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 20 | 0 | 20 | 17 | 20 | 20 |
N.S. | 1 | 0.00 | 1.00 | 0.87 | 0.00 | 0.87 | 0.74 | 0.87 | 0.87 |
time (sec) |
N/A | 4.502 | 0.401 | 0.505 | 0.000 | 0.394 | 13.437 | 0.412 | 8.156 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 14 | 14 | 15 | 14 | 14 | 14 | 14 | 12 |
N.S. | 1 | 0.88 | 0.88 | 0.94 | 0.88 | 0.88 | 0.88 | 0.88 | 0.75 |
time (sec) |
N/A | 0.005 | 0.000 | 0.612 | 0.259 | 0.343 | 0.008 | 0.407 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | B | B | B | F | B | B | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 87 | 87 | 81 | 0 | 83 | 75 | 119 | -1 |
N.S. | 1 | 3.95 | 3.95 | 3.68 | 0.00 | 3.77 | 3.41 | 5.41 | -0.05 |
time (sec) |
N/A | 1.769 | 0.391 | 0.416 | 0.000 | 0.361 | 3.149 | 0.413 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 15 | 14 | 18 | 14 | 13 | 14 | 14 | 13 |
N.S. | 1 | 0.83 | 0.78 | 1.00 | 0.78 | 0.72 | 0.78 | 0.78 | 0.72 |
time (sec) |
N/A | 0.004 | 0.000 | 0.017 | 0.259 | 0.355 | 0.006 | 0.424 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | B | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 25 | 31 | 57 | 49 | 49 | 20 | 23 | 27 |
N.S. | 1 | 0.96 | 1.19 | 2.19 | 1.88 | 1.88 | 0.77 | 0.88 | 1.04 |
time (sec) |
N/A | 0.573 | 0.143 | 2.397 | 0.287 | 0.380 | 0.044 | 0.425 | 7.503 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | F(-1) | A | A | B | B | A | F(-1) | B |
verified |
N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 0 | 67 | 44 | 474 | 86 | 41 | 0 | 83 |
N.S. |
1 | 0.00 | 1.81 | 1.19 | 12.81 | 2.32 | 1.11 | 0.00 | 2.24 |
time (sec) |
N/A | 180.001 | 0.991 | 0.851 | 2.350 | 0.390 | 1.258 | 0.000 | 9.524 |