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 | 45 | 45 | 44 | 34 | 34 | 34 | 41 | 34 | 33 | 34 |
N.S. |
1 | 1.00 | 0.98 | 0.76 | 0.76 | 0.76 | 0.91 | 0.76 | 0.73 | 0.76 |
time (sec) |
N/A | 0.295 | 0.002 | 0.695 | 0.027 | 0.062 | 0.017 | 0.316 | 0.243 | 0.033 |
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 | 35 | 35 | 29 | 29 | 29 | 32 | 29 | 28 | 29 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.83 | 0.83 | 0.91 | 0.83 | 0.80 | 0.83 |
time (sec) |
N/A | 0.279 | 0.001 | 0.668 | 0.037 | 0.064 | 0.016 | 0.823 | 0.155 | 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 | 30 | 30 | 30 | 24 | 24 | 24 | 27 | 24 | 23 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.80 | 0.80 | 0.90 | 0.80 | 0.77 | 0.80 |
time (sec) |
N/A | 0.285 | 0.002 | 0.201 | 0.045 | 0.061 | 0.014 | 0.321 | 0.153 | 0.020 |
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 | 25 | 25 | 25 | 19 | 19 | 19 | 19 | 19 | 18 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.76 | 0.76 | 0.76 | 0.76 | 0.76 | 0.72 | 0.76 |
time (sec) |
N/A | 0.261 | 0.002 | 0.195 | 0.038 | 0.063 | 0.019 | 0.329 | 0.174 | 0.033 |
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 | 30 | 30 | 34 | 21 | 22 | 22 | 27 | 23 | 22 | 20 |
N.S. |
1 | 1.00 | 1.13 | 0.70 | 0.73 | 0.73 | 0.90 | 0.77 | 0.73 | 0.67 |
time (sec) |
N/A | 0.276 | 0.013 | 0.734 | 0.036 | 0.067 | 0.029 | 0.323 | 0.150 | 0.035 |
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 | 34 | 34 | 39 | 25 | 26 | 37 | 24 | 48 | 39 | 24 |
N.S. |
1 | 1.00 | 1.15 | 0.74 | 0.76 | 1.09 | 0.71 | 1.41 | 1.15 | 0.71 |
time (sec) |
N/A | 0.279 | 0.016 | 0.720 | 0.026 | 0.071 | 0.035 | 0.310 | 0.159 | 0.033 |
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 | 38 | 38 | 35 | 27 | 31 | 47 | 29 | 27 | 53 | 27 |
N.S. |
1 | 1.00 | 0.92 | 0.71 | 0.82 | 1.24 | 0.76 | 0.71 | 1.39 | 0.71 |
time (sec) |
N/A | 0.298 | 0.036 | 0.721 | 0.026 | 0.073 | 0.046 | 0.358 | 0.150 | 0.039 |
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 | 44 | 44 | 36 | 28 | 38 | 52 | 36 | 29 | 67 | 34 |
N.S. |
1 | 1.00 | 0.82 | 0.64 | 0.86 | 1.18 | 0.82 | 0.66 | 1.52 | 0.77 |
time (sec) |
N/A | 0.298 | 0.017 | 0.697 | 0.030 | 0.073 | 0.051 | 0.316 | 0.167 | 12.205 |
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 | 49 | 49 | 49 | 39 | 39 | 39 | 46 | 39 | 38 | 39 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.80 | 0.80 | 0.94 | 0.80 | 0.78 | 0.80 |
time (sec) |
N/A | 0.330 | 0.002 | 0.875 | 0.030 | 0.066 | 0.018 | 0.308 | 0.154 | 0.035 |
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 | 40 | 40 | 40 | 34 | 34 | 34 | 37 | 34 | 33 | 34 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.85 | 0.85 | 0.92 | 0.85 | 0.82 | 0.85 |
time (sec) |
N/A | 0.313 | 0.001 | 0.887 | 0.027 | 0.065 | 0.017 | 0.313 | 0.147 | 0.027 |
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 | 29 | 29 | 29 | 29 | 29 | 28 | 29 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.88 | 0.88 | 0.88 | 0.88 | 0.85 | 0.88 |
time (sec) |
N/A | 0.302 | 0.001 | 0.750 | 0.024 | 0.065 | 0.016 | 0.298 | 0.154 | 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 | 28 | 28 | 28 | 24 | 24 | 24 | 26 | 24 | 23 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.86 | 0.86 | 0.93 | 0.86 | 0.82 | 0.86 |
time (sec) |
N/A | 0.288 | 0.001 | 0.760 | 0.032 | 0.067 | 0.019 | 0.349 | 0.159 | 0.020 |
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 | 37 | 37 | 32 | 26 | 27 | 27 | 32 | 28 | 27 | 25 |
N.S. |
1 | 1.00 | 0.86 | 0.70 | 0.73 | 0.73 | 0.86 | 0.76 | 0.73 | 0.68 |
time (sec) |
N/A | 0.297 | 0.014 | 0.924 | 0.030 | 0.069 | 0.036 | 0.340 | 0.161 | 0.025 |
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 | 41 | 41 | 44 | 30 | 31 | 42 | 34 | 57 | 44 | 29 |
N.S. |
1 | 1.00 | 1.07 | 0.73 | 0.76 | 1.02 | 0.83 | 1.39 | 1.07 | 0.71 |
time (sec) |
N/A | 0.291 | 0.021 | 0.928 | 0.031 | 0.072 | 0.041 | 1.063 | 0.167 | 0.027 |
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 | 45 | 45 | 42 | 32 | 36 | 52 | 37 | 32 | 58 | 32 |
N.S. |
1 | 1.00 | 0.93 | 0.71 | 0.80 | 1.16 | 0.82 | 0.71 | 1.29 | 0.71 |
time (sec) |
N/A | 0.306 | 0.031 | 0.922 | 0.026 | 0.066 | 0.050 | 0.332 | 0.163 | 0.037 |
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 | 49 | 49 | 46 | 32 | 41 | 62 | 41 | 32 | 72 | 37 |
N.S. |
1 | 1.00 | 0.94 | 0.65 | 0.84 | 1.27 | 0.84 | 0.65 | 1.47 | 0.76 |
time (sec) |
N/A | 0.303 | 0.034 | 0.927 | 0.026 | 0.097 | 0.055 | 0.352 | 0.158 | 12.292 |
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 | 44 | 44 | 37 | 31 | 32 | 32 | 42 | 33 | 32 | 30 |
N.S. |
1 | 1.00 | 0.84 | 0.70 | 0.73 | 0.73 | 0.95 | 0.75 | 0.73 | 0.68 |
time (sec) |
N/A | 0.299 | 0.015 | 0.896 | 0.032 | 0.066 | 0.039 | 0.318 | 0.162 | 0.030 |
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 | 37 | 37 | 32 | 26 | 27 | 27 | 36 | 28 | 27 | 25 |
N.S. |
1 | 1.00 | 0.86 | 0.70 | 0.73 | 0.73 | 0.97 | 0.76 | 0.73 | 0.68 |
time (sec) |
N/A | 0.286 | 0.014 | 0.865 | 0.030 | 0.063 | 0.037 | 0.342 | 0.155 | 0.027 |
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 | 30 | 30 | 27 | 21 | 22 | 22 | 27 | 23 | 22 | 20 |
N.S. |
1 | 1.00 | 0.90 | 0.70 | 0.73 | 0.73 | 0.90 | 0.77 | 0.73 | 0.67 |
time (sec) |
N/A | 0.276 | 0.010 | 0.724 | 0.032 | 0.068 | 0.033 | 0.351 | 0.166 | 0.031 |
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 | 23 | 23 | 22 | 16 | 17 | 17 | 20 | 18 | 17 | 15 |
N.S. |
1 | 1.00 | 0.96 | 0.70 | 0.74 | 0.74 | 0.87 | 0.78 | 0.74 | 0.65 |
time (sec) |
N/A | 0.270 | 0.008 | 0.718 | 0.034 | 0.068 | 0.030 | 0.301 | 0.162 | 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 | 26 | 26 | 26 | 17 | 20 | 20 | 24 | 22 | 20 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.65 | 0.77 | 0.77 | 0.92 | 0.85 | 0.77 | 0.62 |
time (sec) |
N/A | 0.291 | 0.008 | 0.911 | 0.030 | 0.072 | 0.052 | 0.351 | 0.162 | 0.096 |
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 | 32 | 32 | 30 | 25 | 26 | 37 | 26 | 43 | 46 | 22 |
N.S. |
1 | 1.00 | 0.94 | 0.78 | 0.81 | 1.16 | 0.81 | 1.34 | 1.44 | 0.69 |
time (sec) |
N/A | 0.296 | 0.026 | 0.893 | 0.035 | 0.069 | 0.060 | 0.324 | 0.157 | 12.337 |
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 | 43 | 43 | 35 | 31 | 36 | 55 | 34 | 33 | 76 | 26 |
N.S. |
1 | 1.00 | 0.81 | 0.72 | 0.84 | 1.28 | 0.79 | 0.77 | 1.77 | 0.60 |
time (sec) |
N/A | 0.306 | 0.030 | 0.897 | 0.029 | 0.068 | 0.064 | 0.345 | 0.160 | 12.299 |
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 | 54 | 54 | 40 | 36 | 46 | 75 | 44 | 38 | 106 | 36 |
N.S. |
1 | 1.00 | 0.74 | 0.67 | 0.85 | 1.39 | 0.81 | 0.70 | 1.96 | 0.67 |
time (sec) |
N/A | 0.330 | 0.043 | 0.894 | 0.027 | 0.072 | 0.070 | 0.351 | 0.155 | 12.277 |
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 | 46 | 46 | 49 | 35 | 36 | 47 | 39 | 66 | 49 | 34 |
N.S. |
1 | 1.00 | 1.07 | 0.76 | 0.78 | 1.02 | 0.85 | 1.43 | 1.07 | 0.74 |
time (sec) |
N/A | 0.316 | 0.020 | 0.889 | 0.031 | 0.071 | 0.044 | 0.322 | 0.169 | 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 | 39 | 39 | 44 | 30 | 31 | 42 | 32 | 57 | 44 | 29 |
N.S. |
1 | 1.00 | 1.13 | 0.77 | 0.79 | 1.08 | 0.82 | 1.46 | 1.13 | 0.74 |
time (sec) |
N/A | 0.304 | 0.017 | 0.863 | 0.039 | 0.063 | 0.041 | 0.299 | 0.155 | 0.026 |
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 | 32 | 32 | 39 | 25 | 26 | 37 | 26 | 48 | 39 | 24 |
N.S. |
1 | 1.00 | 1.22 | 0.78 | 0.81 | 1.16 | 0.81 | 1.50 | 1.22 | 0.75 |
time (sec) |
N/A | 0.291 | 0.015 | 0.767 | 0.028 | 0.070 | 0.041 | 0.294 | 0.160 | 0.032 |
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 | 25 | 25 | 26 | 20 | 21 | 32 | 17 | 32 | 34 | 19 |
N.S. |
1 | 1.00 | 1.04 | 0.80 | 0.84 | 1.28 | 0.68 | 1.28 | 1.36 | 0.76 |
time (sec) |
N/A | 0.267 | 0.017 | 0.720 | 0.034 | 0.064 | 0.035 | 0.321 | 0.166 | 0.035 |
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 | 32 | 32 | 30 | 25 | 26 | 37 | 26 | 43 | 46 | 22 |
N.S. |
1 | 1.00 | 0.94 | 0.78 | 0.81 | 1.16 | 0.81 | 1.34 | 1.44 | 0.69 |
time (sec) |
N/A | 0.296 | 0.028 | 0.895 | 0.026 | 0.073 | 0.056 | 0.315 | 0.153 | 0.096 |
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 | 43 | 43 | 62 | 36 | 36 | 55 | 36 | 40 | 76 | 27 |
N.S. |
1 | 1.00 | 1.44 | 0.84 | 0.84 | 1.28 | 0.84 | 0.93 | 1.77 | 0.63 |
time (sec) |
N/A | 0.313 | 0.029 | 0.889 | 0.027 | 0.069 | 0.062 | 0.366 | 0.166 | 12.680 |
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 | 54 | 54 | 47 | 43 | 46 | 75 | 46 | 51 | 106 | 37 |
N.S. |
1 | 1.00 | 0.87 | 0.80 | 0.85 | 1.39 | 0.85 | 0.94 | 1.96 | 0.69 |
time (sec) |
N/A | 0.330 | 0.039 | 0.888 | 0.035 | 0.070 | 0.067 | 0.312 | 0.161 | 0.044 |
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 | 65 | 65 | 52 | 48 | 56 | 95 | 54 | 60 | 138 | 48 |
N.S. |
1 | 1.00 | 0.80 | 0.74 | 0.86 | 1.46 | 0.83 | 0.92 | 2.12 | 0.74 |
time (sec) |
N/A | 0.338 | 0.042 | 0.889 | 0.030 | 0.069 | 0.073 | 0.361 | 0.160 | 0.047 |
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 | 50 | 50 | 51 | 37 | 41 | 57 | 42 | 37 | 63 | 36 |
N.S. |
1 | 1.00 | 1.02 | 0.74 | 0.82 | 1.14 | 0.84 | 0.74 | 1.26 | 0.72 |
time (sec) |
N/A | 0.325 | 0.022 | 0.874 | 0.027 | 0.069 | 0.057 | 0.321 | 0.155 | 12.315 |
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 | 45 | 45 | 46 | 32 | 36 | 52 | 37 | 32 | 58 | 31 |
N.S. |
1 | 1.00 | 1.02 | 0.71 | 0.80 | 1.16 | 0.82 | 0.71 | 1.29 | 0.69 |
time (sec) |
N/A | 0.312 | 0.019 | 0.862 | 0.027 | 0.067 | 0.054 | 0.349 | 0.167 | 0.033 |
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 | 38 | 38 | 35 | 27 | 31 | 47 | 31 | 27 | 53 | 26 |
N.S. |
1 | 1.00 | 0.92 | 0.71 | 0.82 | 1.24 | 0.82 | 0.71 | 1.39 | 0.68 |
time (sec) |
N/A | 0.296 | 0.020 | 0.731 | 0.033 | 0.065 | 0.055 | 0.300 | 0.160 | 0.037 |
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 | 31 | 31 | 26 | 22 | 28 | 37 | 24 | 24 | 48 | 21 |
N.S. |
1 | 1.00 | 0.84 | 0.71 | 0.90 | 1.19 | 0.77 | 0.77 | 1.55 | 0.68 |
time (sec) |
N/A | 0.286 | 0.016 | 0.693 | 0.030 | 0.071 | 0.052 | 0.333 | 0.157 | 0.030 |
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 | 43 | 43 | 35 | 31 | 36 | 55 | 34 | 33 | 76 | 25 |
N.S. |
1 | 1.00 | 0.81 | 0.72 | 0.84 | 1.28 | 0.79 | 0.77 | 1.77 | 0.58 |
time (sec) |
N/A | 0.318 | 0.030 | 0.914 | 0.028 | 0.071 | 0.067 | 0.340 | 0.163 | 0.044 |
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 | 54 | 54 | 47 | 44 | 46 | 75 | 44 | 51 | 106 | 38 |
N.S. |
1 | 1.00 | 0.87 | 0.81 | 0.85 | 1.39 | 0.81 | 0.94 | 1.96 | 0.70 |
time (sec) |
N/A | 0.324 | 0.035 | 0.896 | 0.028 | 0.075 | 0.073 | 0.355 | 0.160 | 12.665 |
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 | 65 | 65 | 77 | 48 | 56 | 95 | 54 | 48 | 138 | 45 |
N.S. |
1 | 1.00 | 1.18 | 0.74 | 0.86 | 1.46 | 0.83 | 0.74 | 2.12 | 0.69 |
time (sec) |
N/A | 0.343 | 0.033 | 0.895 | 0.033 | 0.066 | 0.084 | 0.294 | 0.161 | 12.376 |
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 | 76 | 76 | 57 | 53 | 66 | 115 | 65 | 55 | 170 | 55 |
N.S. |
1 | 1.00 | 0.75 | 0.70 | 0.87 | 1.51 | 0.86 | 0.72 | 2.24 | 0.72 |
time (sec) |
N/A | 0.363 | 0.041 | 0.903 | 0.036 | 0.070 | 0.082 | 0.300 | 0.156 | 12.682 |
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 | 32 | 32 | 32 | 25 | 26 | 37 | 26 | 43 | 46 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 0.81 | 1.16 | 0.81 | 1.34 | 1.44 | 0.69 |
time (sec) |
N/A | 0.291 | 0.019 | 0.905 | 0.035 | 0.070 | 0.056 | 0.305 | 0.167 | 12.619 |
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 | 79 | 79 | 38 | 35 | 55 | 39 | 70 | 55 | 38 | 55 |
N.S. |
1 | 1.00 | 0.48 | 0.44 | 0.70 | 0.49 | 0.89 | 0.70 | 0.48 | 0.70 |
time (sec) |
N/A | 0.324 | 0.037 | 0.934 | 0.032 | 0.071 | 0.705 | 0.278 | 0.158 | 0.040 |
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 | 66 | 66 | 33 | 30 | 46 | 34 | 58 | 46 | 33 | 46 |
N.S. |
1 | 1.00 | 0.50 | 0.45 | 0.70 | 0.52 | 0.88 | 0.70 | 0.50 | 0.70 |
time (sec) |
N/A | 0.309 | 0.032 | 0.843 | 0.034 | 0.066 | 0.673 | 0.243 | 0.159 | 0.032 |
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 | 53 | 53 | 28 | 25 | 37 | 29 | 46 | 37 | 28 | 37 |
N.S. |
1 | 1.00 | 0.53 | 0.47 | 0.70 | 0.55 | 0.87 | 0.70 | 0.53 | 0.70 |
time (sec) |
N/A | 0.296 | 0.027 | 0.743 | 0.026 | 0.095 | 0.628 | 0.319 | 0.152 | 0.043 |
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 | 40 | 40 | 23 | 20 | 28 | 24 | 34 | 28 | 23 | 23 |
N.S. |
1 | 1.00 | 0.58 | 0.50 | 0.70 | 0.60 | 0.85 | 0.70 | 0.58 | 0.58 |
time (sec) |
N/A | 0.273 | 0.024 | 0.746 | 0.035 | 0.067 | 0.505 | 0.272 | 0.161 | 13.050 |
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 | 69 | 73 | 53 | 39 | 64 | 51 | 76 | 67 | 63 | 48 |
N.S. |
1 | 1.06 | 0.77 | 0.57 | 0.93 | 0.74 | 1.10 | 0.97 | 0.91 | 0.70 |
time (sec) |
N/A | 0.364 | 0.099 | 0.998 | 0.107 | 0.081 | 2.046 | 0.305 | 0.161 | 12.415 |
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 | 72 | 83 | 58 | 51 | 71 | 66 | 182 | 74 | 107 | 55 |
N.S. |
1 | 1.15 | 0.81 | 0.71 | 0.99 | 0.92 | 2.53 | 1.03 | 1.49 | 0.76 |
time (sec) |
N/A | 0.398 | 0.161 | 1.006 | 0.112 | 0.074 | 29.430 | 0.300 | 0.166 | 0.081 |
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 | 81 | 97 | 58 | 51 | 83 | 75 | 342 | 77 | 152 | 63 |
N.S. |
1 | 1.20 | 0.72 | 0.63 | 1.02 | 0.93 | 4.22 | 0.95 | 1.88 | 0.78 |
time (sec) |
N/A | 0.380 | 0.239 | 1.023 | 0.117 | 0.071 | 114.268 | 0.343 | 0.155 | 12.508 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 112 | 60 | 51 | 92 | 86 | 0 | 77 | 197 | 72 |
N.S. |
1 | 1.27 | 0.68 | 0.58 | 1.05 | 0.98 | 0.00 | 0.88 | 2.24 | 0.82 |
time (sec) |
N/A | 0.394 | 0.300 | 1.032 | 0.148 | 0.078 | 0.000 | 0.308 | 0.165 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 141 | 65 | 56 | 110 | 101 | 0 | 86 | 253 | 92 |
N.S. |
1 | 1.31 | 0.60 | 0.52 | 1.02 | 0.94 | 0.00 | 0.80 | 2.34 | 0.85 |
time (sec) |
N/A | 0.417 | 0.370 | 1.021 | 0.147 | 0.074 | 0.000 | 0.322 | 0.159 | 12.104 |
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 | 79 | 79 | 38 | 35 | 55 | 44 | 70 | 55 | 43 | 55 |
N.S. |
1 | 1.00 | 0.48 | 0.44 | 0.70 | 0.56 | 0.89 | 0.70 | 0.54 | 0.70 |
time (sec) |
N/A | 0.340 | 0.038 | 1.252 | 0.044 | 0.066 | 0.810 | 0.336 | 0.173 | 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 | 66 | 66 | 33 | 30 | 46 | 39 | 58 | 46 | 38 | 46 |
N.S. |
1 | 1.00 | 0.50 | 0.45 | 0.70 | 0.59 | 0.88 | 0.70 | 0.58 | 0.70 |
time (sec) |
N/A | 0.313 | 0.036 | 1.648 | 0.043 | 0.116 | 0.744 | 0.298 | 0.162 | 0.026 |
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 | 53 | 53 | 28 | 25 | 37 | 34 | 46 | 37 | 33 | 37 |
N.S. |
1 | 1.00 | 0.53 | 0.47 | 0.70 | 0.64 | 0.87 | 0.70 | 0.62 | 0.70 |
time (sec) |
N/A | 0.300 | 0.028 | 1.018 | 0.027 | 0.068 | 0.730 | 0.300 | 0.166 | 0.043 |
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 | 40 | 40 | 23 | 20 | 28 | 29 | 34 | 28 | 28 | 23 |
N.S. |
1 | 1.00 | 0.58 | 0.50 | 0.70 | 0.72 | 0.85 | 0.70 | 0.70 | 0.58 |
time (sec) |
N/A | 0.276 | 0.025 | 1.200 | 0.034 | 0.072 | 0.566 | 0.277 | 0.161 | 0.035 |
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 | 82 | 86 | 58 | 44 | 73 | 56 | 88 | 76 | 74 | 57 |
N.S. |
1 | 1.05 | 0.71 | 0.54 | 0.89 | 0.68 | 1.07 | 0.93 | 0.90 | 0.70 |
time (sec) |
N/A | 0.348 | 0.104 | 1.030 | 0.119 | 0.074 | 2.220 | 0.352 | 0.175 | 12.605 |
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 | 89 | 96 | 63 | 56 | 80 | 71 | 196 | 83 | 118 | 64 |
N.S. |
1 | 1.08 | 0.71 | 0.63 | 0.90 | 0.80 | 2.20 | 0.93 | 1.33 | 0.72 |
time (sec) |
N/A | 0.452 | 0.158 | 1.026 | 0.128 | 0.079 | 30.059 | 0.921 | 0.173 | 12.270 |
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 | 94 | 110 | 63 | 56 | 92 | 80 | 354 | 86 | 163 | 74 |
N.S. |
1 | 1.17 | 0.67 | 0.60 | 0.98 | 0.85 | 3.77 | 0.91 | 1.73 | 0.79 |
time (sec) |
N/A | 0.491 | 0.246 | 1.073 | 0.108 | 0.088 | 113.630 | 0.335 | 0.163 | 0.070 |
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 | 79 | 79 | 38 | 34 | 55 | 34 | 70 | 55 | 33 | 55 |
N.S. |
1 | 1.00 | 0.48 | 0.43 | 0.70 | 0.43 | 0.89 | 0.70 | 0.42 | 0.70 |
time (sec) |
N/A | 0.322 | 0.038 | 1.376 | 0.028 | 0.072 | 0.703 | 0.305 | 0.167 | 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 | 66 | 66 | 33 | 29 | 46 | 29 | 58 | 46 | 28 | 46 |
N.S. |
1 | 1.00 | 0.50 | 0.44 | 0.70 | 0.44 | 0.88 | 0.70 | 0.42 | 0.70 |
time (sec) |
N/A | 0.312 | 0.033 | 1.411 | 0.027 | 0.067 | 0.670 | 0.342 | 0.160 | 0.026 |
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 | 53 | 53 | 28 | 24 | 37 | 24 | 46 | 37 | 23 | 37 |
N.S. |
1 | 1.00 | 0.53 | 0.45 | 0.70 | 0.45 | 0.87 | 0.70 | 0.43 | 0.70 |
time (sec) |
N/A | 0.282 | 0.028 | 0.773 | 0.028 | 0.093 | 0.630 | 0.623 | 0.161 | 0.037 |
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 | 40 | 40 | 23 | 19 | 28 | 19 | 34 | 28 | 18 | 23 |
N.S. |
1 | 1.00 | 0.58 | 0.48 | 0.70 | 0.48 | 0.85 | 0.70 | 0.45 | 0.58 |
time (sec) |
N/A | 0.277 | 0.023 | 0.757 | 0.027 | 0.070 | 0.453 | 0.272 | 0.162 | 0.031 |
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 | 54 | 58 | 46 | 34 | 55 | 46 | 65 | 58 | 52 | 37 |
N.S. |
1 | 1.07 | 0.85 | 0.63 | 1.02 | 0.85 | 1.20 | 1.07 | 0.96 | 0.69 |
time (sec) |
N/A | 0.326 | 0.093 | 1.042 | 0.105 | 0.074 | 1.404 | 0.277 | 0.157 | 0.058 |
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 | 61 | 70 | 53 | 45 | 62 | 61 | 172 | 65 | 96 | 44 |
N.S. |
1 | 1.15 | 0.87 | 0.74 | 1.02 | 1.00 | 2.82 | 1.07 | 1.57 | 0.72 |
time (sec) |
N/A | 0.316 | 0.161 | 1.055 | 0.112 | 0.073 | 28.836 | 0.308 | 0.167 | 12.407 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 83 | 53 | 46 | 74 | 70 | 0 | 68 | 141 | 54 |
N.S. |
1 | 1.22 | 0.78 | 0.68 | 1.09 | 1.03 | 0.00 | 1.00 | 2.07 | 0.79 |
time (sec) |
N/A | 0.327 | 0.218 | 1.072 | 0.132 | 0.077 | 0.000 | 0.363 | 0.164 | 12.188 |
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 | 79 | 79 | 38 | 35 | 55 | 34 | 70 | 55 | 35 | 55 |
N.S. |
1 | 1.00 | 0.48 | 0.44 | 0.70 | 0.43 | 0.89 | 0.70 | 0.44 | 0.70 |
time (sec) |
N/A | 0.325 | 0.048 | 1.036 | 0.032 | 0.089 | 0.940 | 0.280 | 0.169 | 0.031 |
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 | 66 | 66 | 33 | 30 | 46 | 29 | 58 | 46 | 30 | 46 |
N.S. |
1 | 1.00 | 0.50 | 0.45 | 0.70 | 0.44 | 0.88 | 0.70 | 0.45 | 0.70 |
time (sec) |
N/A | 0.314 | 0.039 | 1.003 | 0.026 | 0.071 | 0.864 | 0.278 | 0.163 | 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 | 53 | 53 | 28 | 25 | 37 | 24 | 46 | 37 | 25 | 37 |
N.S. |
1 | 1.00 | 0.53 | 0.47 | 0.70 | 0.45 | 0.87 | 0.70 | 0.47 | 0.70 |
time (sec) |
N/A | 0.291 | 0.031 | 0.774 | 0.033 | 0.080 | 0.785 | 0.687 | 0.166 | 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 | 40 | 40 | 23 | 20 | 28 | 19 | 34 | 28 | 20 | 23 |
N.S. |
1 | 1.00 | 0.58 | 0.50 | 0.70 | 0.48 | 0.85 | 0.70 | 0.50 | 0.58 |
time (sec) |
N/A | 0.271 | 0.026 | 0.757 | 0.037 | 0.075 | 0.580 | 1.152 | 0.168 | 0.031 |
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 | 54 | 58 | 46 | 34 | 55 | 60 | 63 | 58 | 61 | 37 |
N.S. |
1 | 1.07 | 0.85 | 0.63 | 1.02 | 1.11 | 1.17 | 1.07 | 1.13 | 0.69 |
time (sec) |
N/A | 0.335 | 0.119 | 1.016 | 0.106 | 0.076 | 2.020 | 0.321 | 0.166 | 0.069 |
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 | 61 | 70 | 53 | 41 | 65 | 71 | 173 | 68 | 116 | 46 |
N.S. |
1 | 1.15 | 0.87 | 0.67 | 1.07 | 1.16 | 2.84 | 1.11 | 1.90 | 0.75 |
time (sec) |
N/A | 0.330 | 0.177 | 1.029 | 0.112 | 0.086 | 43.841 | 0.285 | 0.161 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 97 | 58 | 46 | 83 | 86 | 0 | 77 | 178 | 62 |
N.S. |
1 | 1.20 | 0.72 | 0.57 | 1.02 | 1.06 | 0.00 | 0.95 | 2.20 | 0.77 |
time (sec) |
N/A | 0.353 | 0.256 | 1.035 | 0.104 | 0.076 | 0.000 | 0.331 | 0.165 | 12.303 |
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 | 79 | 79 | 38 | 35 | 51 | 46 | 70 | 51 | 42 | 51 |
N.S. |
1 | 1.00 | 0.48 | 0.44 | 0.65 | 0.58 | 0.89 | 0.65 | 0.53 | 0.65 |
time (sec) |
N/A | 0.320 | 0.052 | 1.023 | 0.031 | 0.079 | 0.931 | 0.297 | 0.163 | 0.031 |
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 | 66 | 66 | 33 | 30 | 42 | 41 | 58 | 42 | 37 | 42 |
N.S. |
1 | 1.00 | 0.50 | 0.45 | 0.64 | 0.62 | 0.88 | 0.64 | 0.56 | 0.64 |
time (sec) |
N/A | 0.302 | 0.039 | 0.996 | 0.027 | 0.078 | 0.896 | 0.277 | 0.172 | 0.043 |
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 | 53 | 53 | 28 | 25 | 33 | 36 | 102 | 33 | 32 | 39 |
N.S. |
1 | 1.00 | 0.53 | 0.47 | 0.62 | 0.68 | 1.92 | 0.62 | 0.60 | 0.74 |
time (sec) |
N/A | 0.277 | 0.035 | 0.773 | 0.031 | 0.076 | 0.208 | 0.364 | 0.159 | 13.012 |
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 | 40 | 40 | 23 | 20 | 24 | 31 | 75 | 24 | 27 | 19 |
N.S. |
1 | 1.00 | 0.58 | 0.50 | 0.60 | 0.78 | 1.88 | 0.60 | 0.68 | 0.48 |
time (sec) |
N/A | 0.259 | 0.030 | 0.757 | 0.038 | 0.074 | 0.197 | 0.534 | 0.166 | 12.928 |
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 | 56 | 58 | 48 | 38 | 51 | 70 | 65 | 54 | 116 | 33 |
N.S. |
1 | 1.04 | 0.86 | 0.68 | 0.91 | 1.25 | 1.16 | 0.96 | 2.07 | 0.59 |
time (sec) |
N/A | 0.322 | 0.126 | 1.019 | 0.118 | 0.082 | 2.376 | 0.645 | 0.160 | 12.993 |
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 | 74 | 83 | 58 | 46 | 74 | 85 | 185 | 70 | 178 | 56 |
N.S. |
1 | 1.12 | 0.78 | 0.62 | 1.00 | 1.15 | 2.50 | 0.95 | 2.41 | 0.76 |
time (sec) |
N/A | 0.378 | 0.216 | 1.074 | 0.118 | 0.073 | 44.602 | 0.320 | 0.168 | 0.079 |
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 | 94 | 110 | 63 | 51 | 92 | 100 | 354 | 82 | 240 | 72 |
N.S. |
1 | 1.17 | 0.67 | 0.54 | 0.98 | 1.06 | 3.77 | 0.87 | 2.55 | 0.77 |
time (sec) |
N/A | 0.456 | 0.274 | 1.059 | 0.116 | 0.076 | 122.688 | 0.329 | 0.168 | 12.937 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 185 | 84 | 113 | 104 | 84 | 0 | 356 | 116 | 0 |
N.S. |
1 | 1.16 | 0.52 | 0.71 | 0.65 | 0.52 | 0.00 | 2.22 | 0.72 | 0.00 |
time (sec) |
N/A | 0.421 | 0.382 | 1.077 | 0.109 | 0.078 | 0.000 | 0.394 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 158 | 79 | 108 | 87 | 79 | 0 | 275 | 99 | 0 |
N.S. |
1 | 1.14 | 0.57 | 0.78 | 0.63 | 0.57 | 0.00 | 1.99 | 0.72 | 0.00 |
time (sec) |
N/A | 0.372 | 0.322 | 1.003 | 0.108 | 0.089 | 0.000 | 0.336 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 131 | 74 | 103 | 70 | 74 | 0 | 203 | 82 | 1197 |
N.S. |
1 | 1.13 | 0.64 | 0.89 | 0.60 | 0.64 | 0.00 | 1.75 | 0.71 | 10.32 |
time (sec) |
N/A | 0.332 | 0.254 | 1.000 | 0.112 | 0.082 | 0.000 | 0.348 | 0.162 | 27.662 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 104 | 77 | 87 | 58 | 69 | 0 | 54 | 65 | 944 |
N.S. |
1 | 1.11 | 0.82 | 0.93 | 0.62 | 0.73 | 0.00 | 0.57 | 0.69 | 10.04 |
time (sec) |
N/A | 0.308 | 0.485 | 0.984 | 0.113 | 0.091 | 0.000 | 0.506 | 0.174 | 24.594 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 104 | 64 | 99 | 65 | 83 | 0 | 71 | 63 | 0 |
N.S. |
1 | 1.11 | 0.68 | 1.05 | 0.69 | 0.88 | 0.00 | 0.76 | 0.67 | 0.00 |
time (sec) |
N/A | 0.318 | 0.215 | 0.980 | 0.112 | 0.078 | 0.000 | 0.319 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 104 | 64 | 113 | 0 | 93 | 0 | 71 | 95 | 0 |
N.S. |
1 | 1.13 | 0.70 | 1.23 | 0.00 | 1.01 | 0.00 | 0.77 | 1.03 | 0.00 |
time (sec) |
N/A | 0.314 | 0.206 | 0.970 | 0.000 | 0.077 | 0.000 | 0.333 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 99 | 66 | 127 | 79 | 103 | 0 | 71 | 127 | 0 |
N.S. |
1 | 1.03 | 0.69 | 1.32 | 0.82 | 1.07 | 0.00 | 0.74 | 1.32 | 0.00 |
time (sec) |
N/A | 0.323 | 0.161 | 0.977 | 0.126 | 0.085 | 0.000 | 0.319 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 72 | 32 | 27 | 115 | 53 | 0 | 51 | 48 | 72 |
N.S. |
1 | 1.07 | 0.48 | 0.40 | 1.72 | 0.79 | 0.00 | 0.76 | 0.72 | 1.07 |
time (sec) |
N/A | 0.281 | 0.129 | 0.981 | 0.117 | 0.090 | 0.000 | 0.311 | 0.169 | 0.239 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 99 | 37 | 32 | 156 | 63 | 0 | 64 | 58 | 90 |
N.S. |
1 | 1.11 | 0.42 | 0.36 | 1.75 | 0.71 | 0.00 | 0.72 | 0.65 | 1.01 |
time (sec) |
N/A | 0.297 | 0.150 | 0.980 | 0.125 | 0.081 | 0.000 | 0.344 | 0.161 | 0.210 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 126 | 42 | 37 | 202 | 73 | 0 | 77 | 68 | 106 |
N.S. |
1 | 1.14 | 0.38 | 0.33 | 1.82 | 0.66 | 0.00 | 0.69 | 0.61 | 0.95 |
time (sec) |
N/A | 0.321 | 0.170 | 0.975 | 0.156 | 0.088 | 0.000 | 0.400 | 0.181 | 0.232 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 212 | 89 | 118 | 116 | 89 | 0 | 446 | 133 | 0 |
N.S. |
1 | 1.16 | 0.49 | 0.65 | 0.64 | 0.49 | 0.00 | 2.45 | 0.73 | 0.00 |
time (sec) |
N/A | 0.412 | 0.452 | 1.001 | 0.120 | 0.083 | 0.000 | 0.689 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 185 | 84 | 113 | 99 | 84 | 0 | 356 | 116 | 0 |
N.S. |
1 | 1.16 | 0.52 | 0.71 | 0.62 | 0.52 | 0.00 | 2.22 | 0.72 | 0.00 |
time (sec) |
N/A | 0.379 | 0.386 | 1.005 | 0.122 | 0.118 | 0.000 | 0.367 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 158 | 79 | 108 | 87 | 79 | 0 | 275 | 99 | 0 |
N.S. |
1 | 1.14 | 0.57 | 0.78 | 0.63 | 0.57 | 0.00 | 1.99 | 0.72 | 0.00 |
time (sec) |
N/A | 0.358 | 0.299 | 0.980 | 0.116 | 0.088 | 0.000 | 0.323 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 131 | 74 | 103 | 75 | 74 | 0 | 63 | 82 | 0 |
N.S. |
1 | 1.13 | 0.64 | 0.89 | 0.65 | 0.64 | 0.00 | 0.54 | 0.71 | 0.00 |
time (sec) |
N/A | 0.338 | 0.260 | 0.958 | 0.119 | 0.077 | 0.000 | 0.329 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 131 | 77 | 116 | 154 | 88 | 0 | 84 | 74 | 0 |
N.S. |
1 | 1.13 | 0.66 | 1.00 | 1.33 | 0.76 | 0.00 | 0.72 | 0.64 | 0.00 |
time (sec) |
N/A | 0.324 | 0.646 | 0.940 | 0.121 | 0.091 | 0.000 | 0.333 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 131 | 69 | 130 | 154 | 98 | 0 | 83 | 106 | 0 |
N.S. |
1 | 1.11 | 0.58 | 1.10 | 1.31 | 0.83 | 0.00 | 0.70 | 0.90 | 0.00 |
time (sec) |
N/A | 0.326 | 0.265 | 0.951 | 0.116 | 0.086 | 0.000 | 0.344 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 128 | 71 | 144 | 186 | 108 | 0 | 84 | 138 | 0 |
N.S. |
1 | 1.08 | 0.60 | 1.22 | 1.58 | 0.92 | 0.00 | 0.71 | 1.17 | 0.00 |
time (sec) |
N/A | 0.322 | 0.235 | 0.954 | 0.123 | 0.111 | 0.000 | 0.333 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 126 | 71 | 158 | 237 | 118 | 0 | 84 | 170 | 0 |
N.S. |
1 | 1.07 | 0.60 | 1.34 | 2.01 | 1.00 | 0.00 | 0.71 | 1.44 | 0.00 |
time (sec) |
N/A | 0.330 | 0.184 | 0.968 | 0.131 | 0.079 | 0.000 | 0.342 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 72 | 32 | 27 | 278 | 63 | 0 | 51 | 58 | 90 |
N.S. |
1 | 1.07 | 0.48 | 0.40 | 4.15 | 0.94 | 0.00 | 0.76 | 0.87 | 1.34 |
time (sec) |
N/A | 0.274 | 0.152 | 1.025 | 0.113 | 0.084 | 0.000 | 0.333 | 0.164 | 0.231 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 99 | 37 | 32 | 340 | 73 | 0 | 64 | 68 | 106 |
N.S. |
1 | 1.11 | 0.42 | 0.36 | 3.82 | 0.82 | 0.00 | 0.72 | 0.76 | 1.19 |
time (sec) |
N/A | 0.298 | 0.172 | 1.022 | 0.148 | 0.081 | 0.000 | 0.368 | 0.161 | 12.563 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 126 | 42 | 37 | 406 | 83 | 0 | 77 | 78 | 124 |
N.S. |
1 | 1.14 | 0.38 | 0.33 | 3.66 | 0.75 | 0.00 | 0.69 | 0.70 | 1.12 |
time (sec) |
N/A | 0.324 | 0.211 | 0.988 | 0.126 | 0.091 | 0.000 | 0.370 | 0.166 | 12.606 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 239 | 94 | 123 | 128 | 94 | 0 | 545 | 150 | 0 |
N.S. |
1 | 1.17 | 0.46 | 0.60 | 0.63 | 0.46 | 0.00 | 2.67 | 0.74 | 0.00 |
time (sec) |
N/A | 0.435 | 0.482 | 1.041 | 0.115 | 0.089 | 0.000 | 0.389 | 0.171 | 0.000 |