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 | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 18 | 17 | 17 | 15 | 17 | 18 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.85 | 0.85 | 0.75 | 0.85 | 0.90 | 0.85 |
time (sec) |
N/A | 0.169 | 0.014 | 0.118 | 0.030 | 0.068 | 0.039 | 0.113 | 0.364 | 0.459 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | C | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 90 | 18 | 23 | 48 | 22 | 19 | 77 | 20 | 18 |
N.S. |
1 | 5.00 | 1.00 | 1.28 | 2.67 | 1.22 | 1.06 | 4.28 | 1.11 | 1.00 |
time (sec) |
N/A | 0.679 | 0.015 | 0.341 | 0.079 | 0.065 | 0.085 | 0.117 | 0.239 | 0.499 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 15 | 15 | 14 | 13 | 29 | 10 | 13 | 17 | 13 |
N.S. |
1 | 0.88 | 0.88 | 0.82 | 0.76 | 1.71 | 0.59 | 0.76 | 1.00 | 0.76 |
time (sec) |
N/A | 0.177 | 0.037 | 0.092 | 0.025 | 0.064 | 0.055 | 0.110 | 0.298 | 0.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 99 | 72 | 84 | 87 | 87 | 92 | 87 | 95 | 84 |
N.S. |
1 | 3.67 | 2.67 | 3.11 | 3.22 | 3.22 | 3.41 | 3.22 | 3.52 | 3.11 |
time (sec) |
N/A | 0.286 | 0.017 | 0.154 | 0.025 | 0.056 | 0.037 | 0.112 | 0.267 | 0.501 |
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 | 17 | 12 | 14 | 13 | 14 | 12 | 10 | 14 | 12 | 12 |
N.S. |
1 | 0.71 | 0.82 | 0.76 | 0.82 | 0.71 | 0.59 | 0.82 | 0.71 | 0.71 |
time (sec) |
N/A | 0.171 | 0.006 | 0.064 | 0.030 | 0.057 | 0.040 | 0.112 | 0.247 | 0.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 0 | 30 | 41 | 36 | 31 | 28 | 35 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.25 | 1.71 | 1.50 | 1.29 | 1.17 | 1.46 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 1.642 | 0.154 | 0.073 | 0.290 | 0.133 | 0.267 | 0.000 |
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 | 14 | 13 | 13 | 14 | 13 | 13 | 8 | 13 | 14 | 12 |
N.S. |
1 | 0.93 | 0.93 | 1.00 | 0.93 | 0.93 | 0.57 | 0.93 | 1.00 | 0.86 |
time (sec) |
N/A | 0.372 | 0.035 | 0.075 | 0.061 | 0.065 | 0.064 | 0.114 | 0.250 | 0.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 16 | 16 | 15 | 14 | 14 | 14 | 14 | 16 | 0 |
N.S. |
1 | 0.89 | 0.89 | 0.83 | 0.78 | 0.78 | 0.78 | 0.78 | 0.89 | 0.00 |
time (sec) |
N/A | 0.472 | 0.019 | 0.587 | 0.075 | 0.073 | 0.084 | 0.140 | 0.252 | 0.000 |
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 | 16 | 24 | 11 | 11 | 11 | 10 | 8 | 10 | 12 | 10 |
N.S. |
1 | 1.50 | 0.69 | 0.69 | 0.69 | 0.62 | 0.50 | 0.62 | 0.75 | 0.62 |
time (sec) |
N/A | 0.188 | 0.018 | 0.241 | 0.042 | 0.061 | 0.042 | 0.116 | 0.268 | 0.034 |
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 | 35 | 37 | 36 | 30 | 28 | 53 | 24 | 30 | 63 | 27 |
N.S. |
1 | 1.06 | 1.03 | 0.86 | 0.80 | 1.51 | 0.69 | 0.86 | 1.80 | 0.77 |
time (sec) |
N/A | 0.448 | 0.023 | 0.177 | 0.042 | 0.061 | 0.595 | 0.123 | 0.289 | 0.479 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | B | A | A | B | B | F(-1) |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 34 | 221 | 72 | 54 | 24 | 77 | 74 | 0 |
N.S. |
1 | 0.00 | 1.06 | 6.91 | 2.25 | 1.69 | 0.75 | 2.41 | 2.31 | 0.00 |
time (sec) |
N/A | 0.000 | 0.120 | 2.703 | 0.147 | 0.076 | 0.264 | 0.813 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | F(-1) | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 31 | 31 | 79 | 30 | 0 | 79 | 60 | 78 |
N.S. |
1 | 0.00 | 1.07 | 1.07 | 2.72 | 1.03 | 0.00 | 2.72 | 2.07 | 2.69 |
time (sec) |
N/A | 0.000 | 0.264 | 0.062 | 0.469 | 0.072 | 0.000 | 1.281 | 0.259 | 1.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | F(-2) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 27 | 32 | 0 | 46 | 31 | 0 | 35 | 28 |
N.S. |
1 | 0.00 | 0.96 | 1.14 | 0.00 | 1.64 | 1.11 | 0.00 | 1.25 | 1.00 |
time (sec) |
N/A | 0.000 | 0.202 | 7.525 | 0.000 | 0.077 | 0.836 | 0.000 | 0.243 | 0.608 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F(-1) | A | A | A | A | B | B | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 0 | 33 | 50 | 51 | 34 | 56 | 58 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.10 | 1.67 | 1.70 | 1.13 | 1.87 | 1.93 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.744 | 0.171 | 0.072 | 0.091 | 0.139 | 0.259 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 74 | 35 | 19 | 168 | 18 | 29 | 41 | 19 | 26 |
N.S. |
1 | 3.08 | 1.46 | 0.79 | 7.00 | 0.75 | 1.21 | 1.71 | 0.79 | 1.08 |
time (sec) |
N/A | 0.836 | 0.062 | 0.492 | 0.170 | 0.073 | 0.114 | 0.121 | 0.237 | 0.869 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 52 | 52 | 66 | 82 | 73 | 58 | 442 | 64 | 90 |
N.S. |
1 | 2.36 | 2.36 | 3.00 | 3.73 | 3.32 | 2.64 | 20.09 | 2.91 | 4.09 |
time (sec) |
N/A | 0.238 | 0.008 | 0.288 | 0.026 | 0.064 | 0.061 | 0.111 | 0.250 | 0.462 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 147 | 23 | 72 | 133 | 95 | 80 | 125 | 85 | 76 |
N.S. |
1 | 6.39 | 1.00 | 3.13 | 5.78 | 4.13 | 3.48 | 5.43 | 3.70 | 3.30 |
time (sec) |
N/A | 0.368 | 0.146 | 0.534 | 0.038 | 0.073 | 0.162 | 0.108 | 0.257 | 0.514 |
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 | 7 | 7 | 7 | 7 | 6 | 6 | 5 | 6 | 9 | 6 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.86 | 0.86 | 0.71 | 0.86 | 1.29 | 0.86 |
time (sec) |
N/A | 0.151 | 0.012 | 0.074 | 0.034 | 0.056 | 0.034 | 0.105 | 0.217 | 0.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 37 | 58 | 45 | 38 | 36 | 38 | 37 | 35 |
N.S. |
1 | 0.00 | 1.32 | 2.07 | 1.61 | 1.36 | 1.29 | 1.36 | 1.32 | 1.25 |
time (sec) |
N/A | 0.000 | 0.099 | 0.038 | 0.091 | 0.075 | 0.110 | 0.146 | 0.237 | 0.609 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 381 | 51 | 74 | 207 | 138 | 87 | 174 | 170 | 126 |
N.S. |
1 | 11.91 | 1.59 | 2.31 | 6.47 | 4.31 | 2.72 | 5.44 | 5.31 | 3.94 |
time (sec) |
N/A | 3.254 | 0.180 | 15.425 | 0.175 | 0.076 | 0.112 | 0.124 | 0.290 | 0.577 |
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 | 24 | 21 | 30 | 22 | 21 | 26 | 19 | 22 | 36 | 19 |
N.S. |
1 | 0.88 | 1.25 | 0.92 | 0.88 | 1.08 | 0.79 | 0.92 | 1.50 | 0.79 |
time (sec) |
N/A | 0.180 | 0.009 | 0.216 | 0.024 | 0.067 | 0.087 | 0.109 | 0.235 | 0.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 31 | 27 | 27 | 27 | 22 | 566 | 45 | 168 |
N.S. |
1 | 0.00 | 1.00 | 0.87 | 0.87 | 0.87 | 0.71 | 18.26 | 1.45 | 5.42 |
time (sec) |
N/A | 0.000 | 0.317 | 67.196 | 0.195 | 0.071 | 0.249 | 0.397 | 0.263 | 0.652 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 71 | 39 | 46 | 46 | 46 | 42 | 51 | 77 | 48 |
N.S. |
1 | 2.73 | 1.50 | 1.77 | 1.77 | 1.77 | 1.62 | 1.96 | 2.96 | 1.85 |
time (sec) |
N/A | 0.463 | 0.484 | 0.458 | 0.035 | 0.077 | 0.069 | 0.121 | 0.281 | 0.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | C | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 87 | 31 | 59 | 86 | 55 | 70 | 63 | 69 | 28 |
N.S. |
1 | 2.64 | 0.94 | 1.79 | 2.61 | 1.67 | 2.12 | 1.91 | 2.09 | 0.85 |
time (sec) |
N/A | 0.479 | 0.202 | 1.006 | 0.075 | 0.068 | 0.125 | 0.121 | 0.234 | 0.465 |
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 | 22 | 29 | 22 | 23 | 25 | 28 | 19 | 29 | 30 | 23 |
N.S. |
1 | 1.32 | 1.00 | 1.05 | 1.14 | 1.27 | 0.86 | 1.32 | 1.36 | 1.05 |
time (sec) |
N/A | 0.216 | 0.053 | 0.190 | 0.030 | 0.066 | 0.054 | 0.113 | 0.212 | 0.438 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | F(-2) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 31 | 36 | 47 | 108 | 31 | 0 | 40 | 49 |
N.S. |
1 | 0.00 | 1.03 | 1.20 | 1.57 | 3.60 | 1.03 | 0.00 | 1.33 | 1.63 |
time (sec) |
N/A | 0.000 | 0.502 | 17.421 | 0.220 | 0.081 | 5.568 | 0.000 | 0.351 | 0.826 |
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 | 28 | 24 | 24 | 21 | 20 | 20 | 20 | 20 | 23 | 22 |
N.S. |
1 | 0.86 | 0.86 | 0.75 | 0.71 | 0.71 | 0.71 | 0.71 | 0.82 | 0.79 |
time (sec) |
N/A | 0.260 | 0.071 | 0.269 | 0.032 | 0.065 | 0.058 | 0.110 | 0.234 | 0.086 |
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 | 33 | 33 | 33 | 30 | 28 | 30 | 31 | 28 | 30 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.85 | 0.91 | 0.94 | 0.85 | 0.91 | 0.85 |
time (sec) |
N/A | 0.209 | 0.003 | 0.046 | 0.026 | 0.061 | 0.036 | 0.114 | 0.235 | 0.023 |
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 | 26 | 52 | 48 | 39 | 36 | 57 | 34 | 47 | 68 | 45 |
N.S. |
1 | 2.00 | 1.85 | 1.50 | 1.38 | 2.19 | 1.31 | 1.81 | 2.62 | 1.73 |
time (sec) |
N/A | 0.462 | 0.266 | 0.408 | 0.038 | 0.075 | 0.071 | 0.126 | 0.235 | 0.518 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 56 | 56 | 57 | 63 | 53 | 53 | 56 | 47 | 19 |
N.S. |
1 | 3.11 | 3.11 | 3.17 | 3.50 | 2.94 | 2.94 | 3.11 | 2.61 | 1.06 |
time (sec) |
N/A | 0.240 | 0.013 | 0.662 | 0.031 | 0.069 | 0.065 | 0.115 | 0.207 | 0.532 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | F | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 17 | 25 | 49 | 74 | 22 | 0 | 402 | 40 |
N.S. |
1 | 0.00 | 0.81 | 1.19 | 2.33 | 3.52 | 1.05 | 0.00 | 19.14 | 1.90 |
time (sec) |
N/A | 0.000 | 5.230 | 1.747 | 0.689 | 0.076 | 0.640 | 0.000 | 0.265 | 0.620 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 48 | 51 | 80 | 49 | 44 | 67 | 133 | 110 |
N.S. |
1 | 0.00 | 1.50 | 1.59 | 2.50 | 1.53 | 1.38 | 2.09 | 4.16 | 3.44 |
time (sec) |
N/A | 0.000 | 0.174 | 1.806 | 0.367 | 0.072 | 0.245 | 0.644 | 21.046 | 0.758 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 180 | 34 | 41 | 36 | 32 | 37 | 0 | 135 | 40 |
N.S. |
1 | 5.14 | 0.97 | 1.17 | 1.03 | 0.91 | 1.06 | 0.00 | 3.86 | 1.14 |
time (sec) |
N/A | 17.819 | 0.191 | 10.593 | 0.135 | 0.073 | 0.194 | 0.000 | 200.028 | 0.734 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 73 | 31 | 45 | 27 | 41 | 19 | 54 | 69 | 0 |
N.S. |
1 | 2.61 | 1.11 | 1.61 | 0.96 | 1.46 | 0.68 | 1.93 | 2.46 | 0.00 |
time (sec) |
N/A | 1.449 | 1.237 | 3.959 | 0.118 | 0.077 | 109.441 | 0.130 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 62 | 21 | 27 | 29 | 29 | 24 | 30 | 285 | 21 |
N.S. |
1 | 2.70 | 0.91 | 1.17 | 1.26 | 1.26 | 1.04 | 1.30 | 12.39 | 0.91 |
time (sec) |
N/A | 3.580 | 0.261 | 5.244 | 0.080 | 0.071 | 0.286 | 0.127 | 0.267 | 0.576 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 26 | 30 | 26 | 27 | 31 | 0 | 32 | 47 |
N.S. |
1 | 0.00 | 0.96 | 1.11 | 0.96 | 1.00 | 1.15 | 0.00 | 1.19 | 1.74 |
time (sec) |
N/A | 0.000 | 0.082 | 19.927 | 0.209 | 0.078 | 2.384 | 0.000 | 0.242 | 0.994 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 43 | 53 | 173 | 53 | 41 | 53 | 65 | 48 |
N.S. |
1 | 0.00 | 1.72 | 2.12 | 6.92 | 2.12 | 1.64 | 2.12 | 2.60 | 1.92 |
time (sec) |
N/A | 0.000 | 0.051 | 6.183 | 0.154 | 0.076 | 0.064 | 0.280 | 0.228 | 0.623 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 30 | 21 | 59 | 56 | 49 | 0 | 72 | 65 |
N.S. |
1 | 0.00 | 1.11 | 0.78 | 2.19 | 2.07 | 1.81 | 0.00 | 2.67 | 2.41 |
time (sec) |
N/A | 0.000 | 5.072 | 0.514 | 0.389 | 0.085 | 0.282 | 0.000 | 0.228 | 0.783 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | C | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 39 | 32 | 77 | 23 | 49 | 46 | 31 | 43 |
N.S. |
1 | 0.00 | 1.39 | 1.14 | 2.75 | 0.82 | 1.75 | 1.64 | 1.11 | 1.54 |
time (sec) |
N/A | 0.000 | 0.154 | 0.230 | 0.077 | 0.066 | 0.057 | 0.118 | 0.219 | 0.474 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 21 | 21 | 21 | 21 | 19 | 0 | 23 | 20 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 1.00 | 1.00 | 0.90 | 0.00 | 1.10 | 0.95 |
time (sec) |
N/A | 0.000 | 1.980 | 0.970 | 0.090 | 0.066 | 0.108 | 0.000 | 0.225 | 0.541 |
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 | 15 | 12 | 10 | 11 | 10 | 10 | 7 | 10 | 13 | 10 |
N.S. |
1 | 0.80 | 0.67 | 0.73 | 0.67 | 0.67 | 0.47 | 0.67 | 0.87 | 0.67 |
time (sec) |
N/A | 0.171 | 0.006 | 0.077 | 0.027 | 0.057 | 0.034 | 0.117 | 0.226 | 0.530 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 27 | 28 | 44 | 56 | 24 | 56 | 58 | 34 |
N.S. |
1 | 0.00 | 0.90 | 0.93 | 1.47 | 1.87 | 0.80 | 1.87 | 1.93 | 1.13 |
time (sec) |
N/A | 0.000 | 1.618 | 0.188 | 0.081 | 0.071 | 0.068 | 0.123 | 0.224 | 0.545 |
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 | 14 | 13 | 11 | 12 | 11 | 11 | 10 | 11 | 12 | 9 |
N.S. |
1 | 0.93 | 0.79 | 0.86 | 0.79 | 0.79 | 0.71 | 0.79 | 0.86 | 0.64 |
time (sec) |
N/A | 0.149 | 0.002 | 0.092 | 0.030 | 0.062 | 0.034 | 0.116 | 0.220 | 0.028 |
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 | 9 | 15 | 13 | 11 | 15 | 9 | 8 | 13 | 9 | 9 |
N.S. |
1 | 1.67 | 1.44 | 1.22 | 1.67 | 1.00 | 0.89 | 1.44 | 1.00 | 1.00 |
time (sec) |
N/A | 0.163 | 0.003 | 0.036 | 0.033 | 0.066 | 0.042 | 0.112 | 0.247 | 0.449 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | B | F(-2) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 33 | 52 | 0 | 51 | 42 | 0 | 200 | 141 |
N.S. |
1 | 0.00 | 1.03 | 1.62 | 0.00 | 1.59 | 1.31 | 0.00 | 6.25 | 4.41 |
time (sec) |
N/A | 0.000 | 0.344 | 189.573 | 0.000 | 0.076 | 8.220 | 0.000 | 200.023 | 1.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | A | B | F | B | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 0 | 32 | 61 | 29 | 36 | 0 | 29 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.60 | 3.05 | 1.45 | 1.80 | 0.00 | 1.45 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 1.110 | 0.174 | 0.070 | 0.227 | 0.000 | 0.872 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 50 | 19 | 15 | 41 | 44 | 17 | 14 | 17 | 14 |
N.S. |
1 | 2.17 | 0.83 | 0.65 | 1.78 | 1.91 | 0.74 | 0.61 | 0.74 | 0.61 |
time (sec) |
N/A | 0.400 | 0.031 | 0.862 | 0.166 | 0.071 | 0.179 | 0.118 | 0.208 | 0.112 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | B | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 2439 | 69 | 32 | 243 | 55 | 26 | 32 | 73 | 239 |
N.S. |
1 | 78.68 | 2.23 | 1.03 | 7.84 | 1.77 | 0.84 | 1.03 | 2.35 | 7.71 |
time (sec) |
N/A | 6.840 | 5.072 | 1.346 | 0.372 | 0.066 | 0.219 | 0.122 | 0.209 | 0.755 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | C | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 241 | 35 | 73 | 259 | 75 | 90 | 82 | 83 | 31 |
N.S. |
1 | 10.48 | 1.52 | 3.17 | 11.26 | 3.26 | 3.91 | 3.57 | 3.61 | 1.35 |
time (sec) |
N/A | 0.585 | 0.029 | 0.233 | 0.042 | 0.071 | 0.118 | 0.117 | 0.207 | 0.539 |
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 | 19 | 16 | 21 | 20 | 18 | 20 | 17 | 18 | 20 | 19 |
N.S. |
1 | 0.84 | 1.11 | 1.05 | 0.95 | 1.05 | 0.89 | 0.95 | 1.05 | 1.00 |
time (sec) |
N/A | 0.151 | 0.000 | 0.088 | 0.031 | 0.061 | 0.020 | 0.112 | 0.217 | 0.001 |
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 | 24 | 16 | 16 | 16 | 15 | 15 | 12 | 15 | 16 | 15 |
N.S. |
1 | 0.67 | 0.67 | 0.67 | 0.62 | 0.62 | 0.50 | 0.62 | 0.67 | 0.62 |
time (sec) |
N/A | 0.183 | 0.016 | 0.096 | 0.028 | 0.072 | 0.039 | 0.112 | 0.252 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 24 | 41 | 42 | 19 | 42 | 33 | 139 |
N.S. |
1 | 0.00 | 1.00 | 1.04 | 1.78 | 1.83 | 0.83 | 1.83 | 1.43 | 6.04 |
time (sec) |
N/A | 0.000 | 0.084 | 0.791 | 0.186 | 0.070 | 0.134 | 0.197 | 0.307 | 0.795 |
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 | 13 | 13 | 16 | 14 | 13 | 13 | 14 | 13 | 18 | 13 |
N.S. |
1 | 1.00 | 1.23 | 1.08 | 1.00 | 1.00 | 1.08 | 1.00 | 1.38 | 1.00 |
time (sec) |
N/A | 0.203 | 0.000 | 0.062 | 0.029 | 0.061 | 0.013 | 0.110 | 0.355 | 0.001 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 79 | 21 | 16 | 0 | 15 | 0 | 0 | 17 | 15 |
N.S. |
1 | 3.95 | 1.05 | 0.80 | 0.00 | 0.75 | 0.00 | 0.00 | 0.85 | 0.75 |
time (sec) |
N/A | 0.276 | 1.720 | 0.324 | 0.000 | 0.069 | 0.000 | 0.000 | 0.398 | 0.561 |
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 | 28 | 44 | 30 | 27 | 26 | 20 | 32 | 26 | 26 | 24 |
N.S. |
1 | 1.57 | 1.07 | 0.96 | 0.93 | 0.71 | 1.14 | 0.93 | 0.93 | 0.86 |
time (sec) |
N/A | 0.543 | 0.039 | 0.396 | 0.069 | 0.064 | 0.140 | 0.110 | 0.372 | 0.593 |
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 | 13 | 11 | 11 | 12 | 11 | 11 | 10 | 11 | 11 | 11 |
N.S. |
1 | 0.85 | 0.85 | 0.92 | 0.85 | 0.85 | 0.77 | 0.85 | 0.85 | 0.85 |
time (sec) |
N/A | 0.147 | 0.002 | 1.660 | 0.027 | 0.066 | 0.039 | 0.110 | 0.211 | 0.471 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 22 | 19 | 23 | 65 | 22 | 19 | 0 | 22 | 19 |
N.S. |
1 | 1.05 | 0.90 | 1.10 | 3.10 | 1.05 | 0.90 | 0.00 | 1.05 | 0.90 |
time (sec) |
N/A | 0.608 | 0.019 | 1.355 | 0.073 | 0.075 | 0.126 | 0.000 | 0.216 | 1.091 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | F(-1) | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 40 | 19 | 47 | 0 | 0 | 29 | 24 |
N.S. |
1 | 0.00 | 1.00 | 1.74 | 0.83 | 2.04 | 0.00 | 0.00 | 1.26 | 1.04 |
time (sec) |
N/A | 0.000 | 0.188 | 0.584 | 0.087 | 0.072 | 0.000 | 0.000 | 0.245 | 0.595 |
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 | 29 | 27 | 27 | 26 | 19 | 27 | 19 | 21 | 25 | 17 |
N.S. |
1 | 0.93 | 0.93 | 0.90 | 0.66 | 0.93 | 0.66 | 0.72 | 0.86 | 0.59 |
time (sec) |
N/A | 0.500 | 0.124 | 36.468 | 0.164 | 0.069 | 0.265 | 0.168 | 0.207 | 1.290 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 21 | 21 | 20 | 33 | 19 | 19 | 19 | 19 | 12 |
N.S. |
1 | 1.24 | 1.24 | 1.18 | 1.94 | 1.12 | 1.12 | 1.12 | 1.12 | 0.71 |
time (sec) |
N/A | 0.323 | 0.008 | 0.449 | 0.027 | 0.080 | 0.046 | 0.111 | 0.224 | 0.470 |
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 | 10 | 10 | 10 | 8 | 7 | 16 | 7 | 16 | 8 | 7 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.70 | 1.60 | 0.70 | 1.60 | 0.80 | 0.70 |
time (sec) |
N/A | 0.217 | 0.001 | 0.094 | 0.034 | 0.059 | 0.030 | 0.114 | 0.254 | 0.464 |
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 | 14 | 13 | 21 | 15 | 14 | 14 | 14 | 14 | 13 | 14 |
N.S. |
1 | 0.93 | 1.50 | 1.07 | 1.00 | 1.00 | 1.00 | 1.00 | 0.93 | 1.00 |
time (sec) |
N/A | 0.280 | 0.006 | 0.205 | 0.029 | 0.061 | 0.045 | 0.107 | 0.239 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 32 | 28 | 23 | 31 | 24 | 26 | 24 | 26 | 17 |
N.S. |
1 | 1.78 | 1.56 | 1.28 | 1.72 | 1.33 | 1.44 | 1.33 | 1.44 | 0.94 |
time (sec) |
N/A | 0.415 | 0.048 | 0.421 | 0.069 | 0.069 | 0.067 | 0.107 | 0.237 | 0.541 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 97 | 88 | 99 | 116 | 71 | 89 | 97 | 0 |
N.S. |
1 | 0.00 | 3.23 | 2.93 | 3.30 | 3.87 | 2.37 | 2.97 | 3.23 | 0.00 |
time (sec) |
N/A | 0.000 | 0.146 | 61.577 | 0.121 | 0.079 | 2.585 | 0.200 | 0.247 | 0.000 |
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 | 16 | 21 | 10 | 8 | 16 | 8 | 10 | 7 | 9 | 7 |
N.S. |
1 | 1.31 | 0.62 | 0.50 | 1.00 | 0.50 | 0.62 | 0.44 | 0.56 | 0.44 |
time (sec) |
N/A | 0.185 | 0.019 | 0.058 | 0.032 | 0.069 | 0.037 | 0.107 | 0.267 | 0.438 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 49 | 27 | 22 | 22 | 21 | 26 | 31 | 23 | 22 |
N.S. |
1 | 2.13 | 1.17 | 0.96 | 0.96 | 0.91 | 1.13 | 1.35 | 1.00 | 0.96 |
time (sec) |
N/A | 0.367 | 0.024 | 0.389 | 0.040 | 0.070 | 0.423 | 0.120 | 0.259 | 0.117 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 31 | 28 | 89 | 30 | 26 | 65 | 51 | 68 |
N.S. |
1 | 0.00 | 0.97 | 0.88 | 2.78 | 0.94 | 0.81 | 2.03 | 1.59 | 2.12 |
time (sec) |
N/A | 0.000 | 1.250 | 0.496 | 0.338 | 0.071 | 0.565 | 0.119 | 0.261 | 1.543 |
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 | 17 | 11 | 11 | 12 | 11 | 11 | 12 | 12 | 11 | 11 |
N.S. |
1 | 0.65 | 0.65 | 0.71 | 0.65 | 0.65 | 0.71 | 0.71 | 0.65 | 0.65 |
time (sec) |
N/A | 0.327 | 0.078 | 0.318 | 0.036 | 0.075 | 0.148 | 0.112 | 0.234 | 0.792 |
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 | 8 | 8 | 8 | 6 | 5 | 5 | 5 | 5 | 6 | 5 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 0.62 | 0.62 | 0.62 | 0.62 | 0.75 | 0.62 |
time (sec) |
N/A | 0.134 | 0.000 | 0.086 | 0.041 | 0.057 | 0.021 | 0.108 | 0.212 | 0.013 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | C | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 23 | 16 | 19 | 23 | 12 | 18 | 21 | 15 |
N.S. |
1 | 0.00 | 1.05 | 0.73 | 0.86 | 1.05 | 0.55 | 0.82 | 0.95 | 0.68 |
time (sec) |
N/A | 0.000 | 0.103 | 0.138 | 0.088 | 0.069 | 0.112 | 0.114 | 0.242 | 0.493 |
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 | 24 | 38 | 26 | 23 | 32 | 30 | 22 | 33 | 38 | 23 |
N.S. |
1 | 1.58 | 1.08 | 0.96 | 1.33 | 1.25 | 0.92 | 1.38 | 1.58 | 0.96 |
time (sec) |
N/A | 0.372 | 0.007 | 0.330 | 0.032 | 0.070 | 0.074 | 0.119 | 0.268 | 0.516 |
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 | 22 | 19 | 19 | 16 | 18 | 18 | 14 | 18 | 17 | 15 |
N.S. |
1 | 0.86 | 0.86 | 0.73 | 0.82 | 0.82 | 0.64 | 0.82 | 0.77 | 0.68 |
time (sec) |
N/A | 0.276 | 0.000 | 0.093 | 0.034 | 0.056 | 0.017 | 0.112 | 0.249 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | F(-2) | B | F(-2) | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 62 | 64 | 0 | 58 | 0 | 0 | 91 | 75 |
N.S. |
1 | 0.00 | 1.94 | 2.00 | 0.00 | 1.81 | 0.00 | 0.00 | 2.84 | 2.34 |
time (sec) |
N/A | 0.000 | 0.292 | 33.742 | 0.000 | 0.076 | 0.000 | 0.000 | 0.233 | 0.874 |
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 | 29 | 37 | 16 | 17 | 16 | 16 | 12 | 16 | 16 | 16 |
N.S. |
1 | 1.28 | 0.55 | 0.59 | 0.55 | 0.55 | 0.41 | 0.55 | 0.55 | 0.55 |
time (sec) |
N/A | 0.351 | 0.007 | 0.055 | 0.038 | 0.063 | 0.053 | 0.114 | 0.262 | 0.034 |
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 | 19 | 13 | 13 | 10 | 13 | 17 | 7 | 13 | 14 | 9 |
N.S. |
1 | 0.68 | 0.68 | 0.53 | 0.68 | 0.89 | 0.37 | 0.68 | 0.74 | 0.47 |
time (sec) |
N/A | 0.184 | 0.006 | 0.255 | 0.025 | 0.061 | 0.032 | 0.113 | 0.230 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 30 | 28 | 27 | 27 | 24 | 27 | 34 | 28 |
N.S. |
1 | 0.00 | 0.97 | 0.90 | 0.87 | 0.87 | 0.77 | 0.87 | 1.10 | 0.90 |
time (sec) |
N/A | 0.000 | 1.234 | 0.140 | 0.064 | 0.071 | 0.083 | 0.123 | 0.267 | 0.529 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 65 | 49 | 45 | 0 | 70 | 68 | 165 | 59 | 41 |
N.S. |
1 | 2.32 | 1.75 | 1.61 | 0.00 | 2.50 | 2.43 | 5.89 | 2.11 | 1.46 |
time (sec) |
N/A | 0.747 | 0.449 | 1.033 | 0.000 | 0.101 | 0.100 | 0.136 | 0.252 | 0.633 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | B | B | F | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 107 | 58 | 120 | 62 | 65 | 0 | 254 | 138 |
N.S. |
1 | 0.00 | 3.34 | 1.81 | 3.75 | 1.94 | 2.03 | 0.00 | 7.94 | 4.31 |
time (sec) |
N/A | 0.000 | 1.036 | 0.070 | 0.417 | 0.077 | 18.802 | 0.000 | 200.032 | 0.855 |
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 | 22 | 26 | 22 | 20 | 22 | 20 | 20 | 22 | 22 | 23 |
N.S. |
1 | 1.18 | 1.00 | 0.91 | 1.00 | 0.91 | 0.91 | 1.00 | 1.00 | 1.05 |
time (sec) |
N/A | 0.169 | 0.006 | 0.102 | 0.025 | 0.060 | 0.070 | 0.109 | 0.258 | 0.448 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 24 | 25 | 23 | 53 | 35 | 64 | 20 |
N.S. |
1 | 0.00 | 1.00 | 1.04 | 1.09 | 1.00 | 2.30 | 1.52 | 2.78 | 0.87 |
time (sec) |
N/A | 0.000 | 1.335 | 7.313 | 0.158 | 0.074 | 10.695 | 0.178 | 0.243 | 0.622 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 21 | 16 | 21 | 61 | 22 | 0 | 27 | 22 |
N.S. |
1 | 0.00 | 1.00 | 0.76 | 1.00 | 2.90 | 1.05 | 0.00 | 1.29 | 1.05 |
time (sec) |
N/A | 0.000 | 2.444 | 1.604 | 0.251 | 0.075 | 1.594 | 0.000 | 0.227 | 0.558 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 0 | 15 | 16 | 15 | 15 | 10 | 15 | 15 | 15 |
N.S. |
1 | 0.00 | 1.00 | 1.07 | 1.00 | 1.00 | 0.67 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.000 | 0.313 | 3.138 | 0.069 | 0.061 | 0.055 | 0.123 | 0.251 | 0.122 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 47 | 17 | 18 | 29 | 17 | 17 | 32 | 17 | 17 |
N.S. |
1 | 2.35 | 0.85 | 0.90 | 1.45 | 0.85 | 0.85 | 1.60 | 0.85 | 0.85 |
time (sec) |
N/A | 0.665 | 0.085 | 0.773 | 0.072 | 0.074 | 0.135 | 0.123 | 0.281 | 0.618 |
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 | 16 | 16 | 16 | 16 | 15 | 13 | 14 | 15 | 16 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.94 | 0.81 | 0.88 | 0.94 | 1.00 | 0.94 |
time (sec) |
N/A | 0.213 | 0.015 | 0.348 | 0.069 | 0.066 | 0.100 | 0.114 | 0.217 | 0.546 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 65 | 22 | 37 | 55 | 39 | 51 | 74 | 21 | 25 |
N.S. |
1 | 2.95 | 1.00 | 1.68 | 2.50 | 1.77 | 2.32 | 3.36 | 0.95 | 1.14 |
time (sec) |
N/A | 0.241 | 0.016 | 1.471 | 0.024 | 0.067 | 0.098 | 0.108 | 0.226 | 0.541 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | A | A | A | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 0 | 27 | 50 | 25 | 22 | 29 | 29 | 25 |
N.S. |
1 | 0.00 | 0.00 | 0.96 | 1.79 | 0.89 | 0.79 | 1.04 | 1.04 | 0.89 |
time (sec) |
N/A | 0.000 | 0.000 | 0.409 | 0.155 | 0.069 | 0.177 | 0.498 | 0.244 | 0.652 |
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 | 22 | 18 | 18 | 17 | 18 | 18 | 15 | 20 | 18 | 18 |
N.S. |
1 | 0.82 | 0.82 | 0.77 | 0.82 | 0.82 | 0.68 | 0.91 | 0.82 | 0.82 |
time (sec) |
N/A | 0.591 | 0.093 | 0.467 | 0.141 | 0.080 | 0.074 | 0.112 | 0.214 | 0.568 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 23 | 20 | 21 | 19 | 17 | 139 | 21 | 19 |
N.S. |
1 | 0.00 | 0.92 | 0.80 | 0.84 | 0.76 | 0.68 | 5.56 | 0.84 | 0.76 |
time (sec) |
N/A | 0.000 | 0.182 | 0.342 | 0.163 | 0.071 | 0.138 | 0.140 | 0.241 | 0.572 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 27 | 22 | 25 | 25 | 22 | 67 | 52 | 31 |
N.S. |
1 | 0.00 | 1.12 | 0.92 | 1.04 | 1.04 | 0.92 | 2.79 | 2.17 | 1.29 |
time (sec) |
N/A | 0.000 | 0.486 | 1.102 | 0.162 | 0.070 | 0.142 | 0.154 | 0.249 | 0.737 |
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 | 21 | 36 | 21 | 22 | 35 | 30 | 46 | 44 | 40 | 20 |
N.S. |
1 | 1.71 | 1.00 | 1.05 | 1.67 | 1.43 | 2.19 | 2.10 | 1.90 | 0.95 |
time (sec) |
N/A | 0.211 | 0.005 | 0.148 | 0.032 | 0.068 | 0.070 | 0.137 | 0.281 | 0.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 17 | 17 | 16 | 15 | 41 | 15 | 41 | 40 | 15 |
N.S. |
1 | 0.94 | 0.94 | 0.89 | 0.83 | 2.28 | 0.83 | 2.28 | 2.22 | 0.83 |
time (sec) |
N/A | 0.204 | 0.021 | 0.091 | 0.041 | 0.073 | 0.073 | 0.115 | 0.232 | 0.516 |
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 | 14 | 14 | 14 | 13 | 15 | 15 | 14 | 23 | 12 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 1.07 | 1.07 | 1.00 | 1.64 | 0.86 | 1.21 |
time (sec) |
N/A | 0.186 | 0.005 | 0.072 | 0.036 | 0.062 | 0.116 | 0.111 | 0.212 | 0.041 |
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 | 15 | 13 | 8 | 13 | 8 | 11 | 8 | 8 | 10 | 8 |
N.S. |
1 | 0.87 | 0.53 | 0.87 | 0.53 | 0.73 | 0.53 | 0.53 | 0.67 | 0.53 |
time (sec) |
N/A | 0.143 | 0.000 | 0.047 | 0.023 | 0.049 | 0.015 | 0.111 | 0.234 | 0.001 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | C | F | A | A | F | B | B |
verified |
N/A | N/A | N/A | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 0 | 192 | 0 | 40 | 31 | 0 | 33 | 30 |
N.S. |
1 | 0.00 | 0.00 | 6.19 | 0.00 | 1.29 | 1.00 | 0.00 | 1.06 | 0.97 |
time (sec) |
N/A | 0.000 | 0.000 | 0.163 | 0.000 | 0.070 | 57.550 | 0.000 | 0.284 | 0.982 |
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 | 16 | 22 | 18 | 22 | 20 | 21 | 20 | 23 | 22 | 16 |
N.S. |
1 | 1.38 | 1.12 | 1.38 | 1.25 | 1.31 | 1.25 | 1.44 | 1.38 | 1.00 |
time (sec) |
N/A | 0.179 | 0.011 | 0.153 | 0.026 | 0.064 | 0.112 | 0.108 | 0.218 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 39 | 14 | 14 | 13 | 13 | 10 | 13 | 14 | 13 |
N.S. |
1 | 2.79 | 1.00 | 1.00 | 0.93 | 0.93 | 0.71 | 0.93 | 1.00 | 0.93 |
time (sec) |
N/A | 0.507 | 0.014 | 0.165 | 0.080 | 0.062 | 0.082 | 0.115 | 0.245 | 0.738 |
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 | 14 | 17 | 17 | 18 | 17 | 15 | 14 | 17 | 17 | 17 |
N.S. |
1 | 1.21 | 1.21 | 1.29 | 1.21 | 1.07 | 1.00 | 1.21 | 1.21 | 1.21 |
time (sec) |
N/A | 0.218 | 0.002 | 0.112 | 0.036 | 0.065 | 0.048 | 0.121 | 0.239 | 0.457 |
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 | 28 | 23 | 37 | 23 | 38 | 45 | 36 | 38 | 44 | 44 |
N.S. |
1 | 0.82 | 1.32 | 0.82 | 1.36 | 1.61 | 1.29 | 1.36 | 1.57 | 1.57 |
time (sec) |
N/A | 0.303 | 0.021 | 0.164 | 0.027 | 0.058 | 0.436 | 0.109 | 0.215 | 0.499 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 20 | 46 | 55 | 49 | 42 | 57 | 41 | 0 |
N.S. |
1 | 0.00 | 0.87 | 2.00 | 2.39 | 2.13 | 1.83 | 2.48 | 1.78 | 0.00 |
time (sec) |
N/A | 0.000 | 5.022 | 6.032 | 0.078 | 0.071 | 0.171 | 0.135 | 0.212 | 0.000 |
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 | 22 | 16 | 16 | 22 | 21 | 21 | 24 | 22 | 21 | 16 |
N.S. |
1 | 0.73 | 0.73 | 1.00 | 0.95 | 0.95 | 1.09 | 1.00 | 0.95 | 0.73 |
time (sec) |
N/A | 0.179 | 0.002 | 0.088 | 0.037 | 0.068 | 0.045 | 0.116 | 0.248 | 0.037 |