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 | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 30 | 21 | 31 | 78 | 28 | 27 | 28 | 32 | 18 |
N.S. |
1 | 1.15 | 0.81 | 1.19 | 3.00 | 1.08 | 1.04 | 1.08 | 1.23 | 0.69 |
time (sec) |
N/A | 0.469 | 1.056 | 0.319 | 0.044 | 0.074 | 0.049 | 0.117 | 0.187 | 0.550 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | B | B | B | F(-2) | B | B | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 0 | 85 | 123 | 118 | 0 | 84 | 92 | 0 |
N.S. |
1 | 0.00 | 0.00 | 2.43 | 3.51 | 3.37 | 0.00 | 2.40 | 2.63 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 1.749 | 0.322 | 0.099 | 0.000 | 1.709 | 0.241 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | B | B | B | B | B | F | B | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 6740 | 329 | 628 | 4571 | 592 | 508 | 0 | 1046 | 0 |
N.S. |
1 | 224.67 | 10.97 | 20.93 | 152.37 | 19.73 | 16.93 | 0.00 | 34.87 | 0.00 |
time (sec) |
N/A | 31.486 | 0.227 | 0.332 | 0.389 | 0.090 | 12.127 | 0.000 | 0.219 | 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 | 17 | 16 | 14 | 14 | 13 | 18 | 8 | 13 | 15 | 13 |
N.S. |
1 | 0.94 | 0.82 | 0.82 | 0.76 | 1.06 | 0.47 | 0.76 | 0.88 | 0.76 |
time (sec) |
N/A | 0.183 | 0.004 | 0.330 | 0.056 | 0.060 | 0.044 | 0.110 | 0.210 | 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 | 21 | 21 | 21 | 17 | 29 | 16 | 19 | 24 | 17 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 1.38 | 0.76 | 0.90 | 1.14 | 0.81 | 0.76 |
time (sec) |
N/A | 0.418 | 0.155 | 1.379 | 0.176 | 0.067 | 0.165 | 0.118 | 0.203 | 0.946 |
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 | 13 | 13 | 15 | 14 | 14 | 14 | 14 | 14 | 14 |
N.S. |
1 | 1.30 | 1.30 | 1.50 | 1.40 | 1.40 | 1.40 | 1.40 | 1.40 | 1.40 |
time (sec) |
N/A | 0.144 | 0.000 | 0.061 | 0.037 | 0.055 | 0.022 | 0.110 | 0.227 | 0.017 |
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 | 24 | 0 | 21 | 18 | 34 | 17 | 15 | 28 | 37 | 18 |
N.S. |
1 | 0.00 | 0.88 | 0.75 | 1.42 | 0.71 | 0.62 | 1.17 | 1.54 | 0.75 |
time (sec) |
N/A | 0.000 | 2.239 | 0.568 | 0.190 | 0.075 | 0.190 | 0.121 | 0.245 | 0.700 |
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 | 26 | 80 | 29 | 29 | 28 | 37 | 27 | 28 | 39 | 28 |
N.S. |
1 | 3.08 | 1.12 | 1.12 | 1.08 | 1.42 | 1.04 | 1.08 | 1.50 | 1.08 |
time (sec) |
N/A | 0.861 | 5.030 | 0.463 | 0.173 | 0.075 | 0.219 | 0.115 | 0.195 | 0.835 |
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 | 35 | 0 | 33 | 28 | 27 | 43 | 29 | 63 | 70 | 52 |
N.S. |
1 | 0.00 | 0.94 | 0.80 | 0.77 | 1.23 | 0.83 | 1.80 | 2.00 | 1.49 |
time (sec) |
N/A | 0.000 | 3.105 | 0.670 | 0.106 | 0.077 | 0.105 | 0.125 | 0.194 | 0.234 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 76 | 44 | 464 | 38 | 46 | 64 | 69 | 71 |
N.S. |
1 | 0.00 | 2.45 | 1.42 | 14.97 | 1.23 | 1.48 | 2.06 | 2.23 | 2.29 |
time (sec) |
N/A | 0.000 | 0.992 | 12.370 | 0.160 | 0.071 | 0.314 | 0.135 | 0.245 | 1.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 34 | 34 | 33 | 32 | 38 | 34 | 32 | 833 | 0 |
N.S. |
1 | 1.21 | 1.21 | 1.18 | 1.14 | 1.36 | 1.21 | 1.14 | 29.75 | 0.00 |
time (sec) |
N/A | 1.070 | 0.120 | 0.353 | 0.166 | 0.071 | 0.112 | 0.443 | 0.223 | 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 | 15 | 31 | 19 | 21 | 30 | 26 | 20 | 30 | 20 | 14 |
N.S. |
1 | 2.07 | 1.27 | 1.40 | 2.00 | 1.73 | 1.33 | 2.00 | 1.33 | 0.93 |
time (sec) |
N/A | 0.225 | 0.008 | 0.126 | 0.038 | 0.067 | 0.053 | 0.114 | 0.194 | 0.511 |
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 | 18 | 18 | 17 | 13 | 16 | 17 | 13 | 18 | 14 |
N.S. |
1 | 0.78 | 0.78 | 0.74 | 0.57 | 0.70 | 0.74 | 0.57 | 0.78 | 0.61 |
time (sec) |
N/A | 0.757 | 0.059 | 0.348 | 0.092 | 0.068 | 0.110 | 0.110 | 0.207 | 0.548 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 28 | 25 | 43 | 83 | 20 | 112 | 31 | 24 |
N.S. |
1 | 0.00 | 1.12 | 1.00 | 1.72 | 3.32 | 0.80 | 4.48 | 1.24 | 0.96 |
time (sec) |
N/A | 0.000 | 0.165 | 3.106 | 0.093 | 0.076 | 0.497 | 0.870 | 0.229 | 0.883 |
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 | 20 | 0 | 20 | 20 | 19 | 19 | 19 | 23 | 20 | 19 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 0.95 | 0.95 | 0.95 | 1.15 | 1.00 | 0.95 |
time (sec) |
N/A | 0.000 | 1.015 | 28.438 | 0.119 | 0.064 | 0.334 | 0.321 | 0.212 | 0.913 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F(-2) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 36 | 30 | 37 | 30 | 29 | 0 | 82 | 63 |
N.S. |
1 | 0.00 | 1.12 | 0.94 | 1.16 | 0.94 | 0.91 | 0.00 | 2.56 | 1.97 |
time (sec) |
N/A | 0.000 | 1.040 | 1.383 | 0.281 | 0.084 | 0.194 | 0.000 | 200.011 | 0.861 |
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 | 28 | 27 | 33 | 32 | 31 | 36 | 27 | 50 |
N.S. |
1 | 0.00 | 0.93 | 0.90 | 1.10 | 1.07 | 1.03 | 1.20 | 0.90 | 1.67 |
time (sec) |
N/A | 0.000 | 0.576 | 2.367 | 0.199 | 0.072 | 0.149 | 0.126 | 0.222 | 0.750 |
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 | 29 | 29 | 25 | 24 | 24 | 22 | 24 | 31 | 27 |
N.S. |
1 | 1.04 | 1.04 | 0.89 | 0.86 | 0.86 | 0.79 | 0.86 | 1.11 | 0.96 |
time (sec) |
N/A | 0.289 | 0.065 | 0.214 | 0.035 | 0.067 | 0.048 | 0.113 | 0.198 | 0.529 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 105 | 22 | 18 | 18 | 17 | 14 | 0 | 22 | 19 |
N.S. |
1 | 5.53 | 1.16 | 0.95 | 0.95 | 0.89 | 0.74 | 0.00 | 1.16 | 1.00 |
time (sec) |
N/A | 0.456 | 0.104 | 0.939 | 0.098 | 0.074 | 2.406 | 0.000 | 0.209 | 0.102 |
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 | 21 | 21 | 20 | 20 | 20 | 22 | 22 | 20 | 33 |
N.S. |
1 | 0.91 | 0.91 | 0.87 | 0.87 | 0.87 | 0.96 | 0.96 | 0.87 | 1.43 |
time (sec) |
N/A | 0.281 | 0.012 | 0.592 | 0.033 | 0.065 | 0.291 | 0.109 | 0.236 | 0.113 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 26 | 26 | 25 | 28 | 24 | 0 | 28 | 98 | 27 |
N.S. |
1 | 1.18 | 1.18 | 1.14 | 1.27 | 1.09 | 0.00 | 1.27 | 4.45 | 1.23 |
time (sec) |
N/A | 1.175 | 0.173 | 3.400 | 0.157 | 0.073 | 0.000 | 0.132 | 0.264 | 0.747 |
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 | 27 | 0 | 33 | 27 | 37 | 36 | 31 | 36 | 48 | 112 |
N.S. |
1 | 0.00 | 1.22 | 1.00 | 1.37 | 1.33 | 1.15 | 1.33 | 1.78 | 4.15 |
time (sec) |
N/A | 0.000 | 0.048 | 30.000 | 0.074 | 0.071 | 0.190 | 0.194 | 0.205 | 0.769 |
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 | 22 | 0 | 22 | 20 | 25 | 23 | 29 | 22 | 22 | 35 |
N.S. |
1 | 0.00 | 1.00 | 0.91 | 1.14 | 1.05 | 1.32 | 1.00 | 1.00 | 1.59 |
time (sec) |
N/A | 0.000 | 0.234 | 0.560 | 0.072 | 0.072 | 0.070 | 0.115 | 0.196 | 0.725 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 30 | 16 | 16 | 15 | 15 | 12 | 15 | 17 | 16 |
N.S. |
1 | 1.88 | 1.00 | 1.00 | 0.94 | 0.94 | 0.75 | 0.94 | 1.06 | 1.00 |
time (sec) |
N/A | 0.239 | 0.294 | 0.085 | 0.094 | 0.063 | 0.045 | 0.114 | 0.218 | 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 | 14 | 10 | 10 | 9 | 10 | 10 | 12 | 11 | 10 | 8 |
N.S. |
1 | 0.71 | 0.71 | 0.64 | 0.71 | 0.71 | 0.86 | 0.79 | 0.71 | 0.57 |
time (sec) |
N/A | 0.136 | 0.001 | 0.126 | 0.026 | 0.060 | 0.024 | 0.109 | 0.200 | 0.555 |
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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 18 | 16 | 22 | 41 | 24 | 22 | 24 | 56 | 27 |
N.S. |
1 | 0.90 | 0.80 | 1.10 | 2.05 | 1.20 | 1.10 | 1.20 | 2.80 | 1.35 |
time (sec) |
N/A | 0.615 | 0.033 | 0.331 | 0.150 | 0.071 | 0.087 | 0.125 | 0.198 | 0.671 |
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 | 24 | 24 | 23 | 20 | 22 | 20 | 22 | 22 | 22 |
N.S. |
1 | 1.04 | 1.04 | 1.00 | 0.87 | 0.96 | 0.87 | 0.96 | 0.96 | 0.96 |
time (sec) |
N/A | 1.183 | 0.154 | 1.841 | 0.095 | 0.073 | 0.129 | 0.152 | 0.200 | 0.598 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 14 | 20 | 12 | 34 | 12 | 12 | 0 | 15 | 12 |
N.S. |
1 | 0.88 | 1.25 | 0.75 | 2.12 | 0.75 | 0.75 | 0.00 | 0.94 | 0.75 |
time (sec) |
N/A | 0.313 | 0.019 | 0.446 | 0.214 | 0.060 | 0.100 | 0.000 | 0.202 | 0.589 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 553 | 33 | 357 | 1988 | 253 | 0 | 375 | 365 | 163 |
N.S. |
1 | 17.84 | 1.06 | 11.52 | 64.13 | 8.16 | 0.00 | 12.10 | 11.77 | 5.26 |
time (sec) |
N/A | 4.562 | 0.083 | 28.827 | 0.253 | 0.079 | 0.000 | 0.137 | 0.201 | 0.868 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 30 | 105 | 38 | 31 | 31 | 37 | 39 | 0 |
N.S. |
1 | 0.00 | 1.11 | 3.89 | 1.41 | 1.15 | 1.15 | 1.37 | 1.44 | 0.00 |
time (sec) |
N/A | 0.000 | 0.698 | 3.921 | 0.282 | 0.075 | 0.188 | 0.198 | 0.200 | 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 | 30 | 28 | 28 | 27 | 26 | 26 | 24 | 27 | 26 | 26 |
N.S. |
1 | 0.93 | 0.93 | 0.90 | 0.87 | 0.87 | 0.80 | 0.90 | 0.87 | 0.87 |
time (sec) |
N/A | 0.334 | 0.013 | 0.046 | 0.025 | 0.059 | 0.062 | 0.117 | 0.221 | 0.587 |
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 | 23 | 21 | 24 | 24 | 26 | 22 | 21 | 30 |
N.S. |
1 | 1.00 | 0.68 | 0.62 | 0.71 | 0.71 | 0.76 | 0.65 | 0.62 | 0.88 |
time (sec) |
N/A | 0.249 | 0.007 | 0.081 | 0.036 | 0.063 | 0.106 | 0.120 | 0.206 | 0.564 |
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 | 21 | 11 | 11 | 11 | 10 | 13 | 8 | 11 | 14 | 10 |
N.S. |
1 | 0.52 | 0.52 | 0.52 | 0.48 | 0.62 | 0.38 | 0.52 | 0.67 | 0.48 |
time (sec) |
N/A | 0.151 | 0.002 | 0.069 | 0.040 | 0.057 | 0.042 | 0.112 | 0.191 | 0.017 |
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 | 33 | 0 | 27 | 27 | 36 | 36 | 26 | 36 | 46 | 35 |
N.S. |
1 | 0.00 | 0.82 | 0.82 | 1.09 | 1.09 | 0.79 | 1.09 | 1.39 | 1.06 |
time (sec) |
N/A | 0.000 | 2.247 | 0.325 | 0.088 | 0.069 | 0.078 | 0.115 | 0.202 | 0.684 |
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 | 24 | 0 | 24 | 18 | 16 | 16 | 19 | 16 | 19 | 17 |
N.S. |
1 | 0.00 | 1.00 | 0.75 | 0.67 | 0.67 | 0.79 | 0.67 | 0.79 | 0.71 |
time (sec) |
N/A | 0.000 | 0.130 | 0.162 | 0.081 | 0.072 | 0.103 | 0.126 | 0.220 | 0.638 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 0 | 29 | 25 | 44 | 0 | 0 | 75 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.07 | 0.93 | 1.63 | 0.00 | 0.00 | 2.78 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.491 | 0.298 | 0.075 | 0.000 | 0.000 | 184.177 | 0.000 |
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 | 35 | 0 | 33 | 31 | 32 | 34 | 27 | 32 | 33 | 32 |
N.S. |
1 | 0.00 | 0.94 | 0.89 | 0.91 | 0.97 | 0.77 | 0.91 | 0.94 | 0.91 |
time (sec) |
N/A | 0.000 | 0.636 | 0.444 | 0.082 | 0.073 | 0.105 | 0.115 | 0.283 | 0.602 |
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 | 25 | 0 | 25 | 22 | 27 | 21 | 17 | 27 | 24 | 106 |
N.S. |
1 | 0.00 | 1.00 | 0.88 | 1.08 | 0.84 | 0.68 | 1.08 | 0.96 | 4.24 |
time (sec) |
N/A | 0.000 | 0.616 | 3.542 | 0.209 | 0.068 | 0.119 | 0.153 | 0.236 | 0.827 |
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 | 17 | 0 | 17 | 17 | 18 | 16 | 12 | 16 | 17 | 16 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 1.06 | 0.94 | 0.71 | 0.94 | 1.00 | 0.94 |
time (sec) |
N/A | 0.000 | 1.756 | 0.533 | 0.177 | 0.070 | 0.216 | 0.202 | 0.258 | 0.762 |
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 | 5 | 5 | 6 | 5 | 5 | 5 | 5 | 5 | 5 |
N.S. |
1 | 0.29 | 0.29 | 0.35 | 0.29 | 0.29 | 0.29 | 0.29 | 0.29 | 0.29 |
time (sec) |
N/A | 0.133 | 0.000 | 0.041 | 0.034 | 0.055 | 0.013 | 0.105 | 0.221 | 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 | 25 | 25 | 24 | 23 | 23 | 22 | 23 | 46 | 24 |
N.S. |
1 | 1.04 | 1.04 | 1.00 | 0.96 | 0.96 | 0.92 | 0.96 | 1.92 | 1.00 |
time (sec) |
N/A | 0.179 | 0.044 | 0.121 | 0.034 | 0.072 | 0.073 | 0.112 | 0.232 | 0.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 36 | 20 | 17 | 209 | 18 | 51 | 39 | 18 | 135 |
N.S. |
1 | 1.44 | 0.80 | 0.68 | 8.36 | 0.72 | 2.04 | 1.56 | 0.72 | 5.40 |
time (sec) |
N/A | 0.660 | 0.064 | 0.893 | 0.188 | 0.073 | 0.166 | 0.107 | 0.242 | 1.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | F(-2) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 59 | 18 | 20 | 18 | 17 | 0 | 74 | 22 | 19 |
N.S. |
1 | 3.28 | 1.00 | 1.11 | 1.00 | 0.94 | 0.00 | 4.11 | 1.22 | 1.06 |
time (sec) |
N/A | 0.305 | 0.136 | 0.904 | 0.221 | 0.071 | 0.000 | 0.229 | 0.209 | 0.594 |
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 | 9 | 11 | 12 | 7 | 11 | 12 | 11 | 9 | 9 |
N.S. |
1 | 0.35 | 0.42 | 0.46 | 0.27 | 0.42 | 0.46 | 0.42 | 0.35 | 0.35 |
time (sec) |
N/A | 0.197 | 0.018 | 0.091 | 0.027 | 0.072 | 0.080 | 0.105 | 0.217 | 0.574 |
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 | 18 | 18 | 20 | 18 | 19 | 19 | 20 | 20 | 19 |
N.S. |
1 | 0.78 | 0.78 | 0.87 | 0.78 | 0.83 | 0.83 | 0.87 | 0.87 | 0.83 |
time (sec) |
N/A | 0.531 | 0.110 | 0.572 | 0.089 | 0.070 | 0.085 | 0.117 | 0.233 | 0.819 |
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 | 25 | 0 | 25 | 23 | 20 | 22 | 20 | 22 | 23 | 22 |
N.S. |
1 | 0.00 | 1.00 | 0.92 | 0.80 | 0.88 | 0.80 | 0.88 | 0.92 | 0.88 |
time (sec) |
N/A | 0.000 | 0.186 | 2.258 | 0.095 | 0.072 | 0.096 | 0.155 | 0.268 | 0.706 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 33 | 58 | 81 | 52 | 53 | 0 | 321 | 69 |
N.S. |
1 | 0.00 | 0.97 | 1.71 | 2.38 | 1.53 | 1.56 | 0.00 | 9.44 | 2.03 |
time (sec) |
N/A | 0.000 | 0.188 | 28.957 | 0.544 | 0.078 | 1.052 | 0.000 | 200.036 | 0.965 |
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 | 25 | 0 | 38 | 20 | 26 | 25 | 20 | 0 | 28 | 26 |
N.S. |
1 | 0.00 | 1.52 | 0.80 | 1.04 | 1.00 | 0.80 | 0.00 | 1.12 | 1.04 |
time (sec) |
N/A | 0.000 | 0.072 | 3.995 | 0.105 | 0.066 | 0.409 | 0.000 | 0.278 | 0.170 |
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 | 17 | 17 | 16 | 15 | 19 | 15 | 15 | 19 | 14 |
N.S. |
1 | 0.71 | 0.71 | 0.67 | 0.62 | 0.79 | 0.62 | 0.62 | 0.79 | 0.58 |
time (sec) |
N/A | 0.251 | 0.001 | 0.092 | 0.038 | 0.069 | 0.054 | 0.104 | 0.238 | 0.556 |
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 | 24 | 0 | 19 | 15 | 12 | 18 | 17 | 12 | 12 | 12 |
N.S. |
1 | 0.00 | 0.79 | 0.62 | 0.50 | 0.75 | 0.71 | 0.50 | 0.50 | 0.50 |
time (sec) |
N/A | 0.000 | 0.053 | 0.249 | 0.066 | 0.070 | 0.088 | 0.115 | 0.235 | 0.599 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | C | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 69 | 50 | 59 | 74 | 64 | 63 | 73 | 79 | 50 |
N.S. |
1 | 2.38 | 1.72 | 2.03 | 2.55 | 2.21 | 2.17 | 2.52 | 2.72 | 1.72 |
time (sec) |
N/A | 0.354 | 2.189 | 1.024 | 0.074 | 0.068 | 0.143 | 0.114 | 0.243 | 0.087 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 45 | 23 | 45 | 52 | 52 | 44 | 52 | 58 | 39 |
N.S. |
1 | 1.55 | 0.79 | 1.55 | 1.79 | 1.79 | 1.52 | 1.79 | 2.00 | 1.34 |
time (sec) |
N/A | 0.224 | 0.006 | 0.133 | 0.056 | 0.067 | 0.024 | 0.109 | 0.250 | 0.537 |
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 | 31 | 0 | 115 | 124 | 204 | 173 | 88 | 242 | 282 | 0 |
N.S. |
1 | 0.00 | 3.71 | 4.00 | 6.58 | 5.58 | 2.84 | 7.81 | 9.10 | 0.00 |
time (sec) |
N/A | 0.000 | 10.184 | 10.180 | 1.025 | 0.085 | 0.469 | 2.775 | 0.744 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 41 | 46 | 50 | 50 | 66 | 59 | 36 | 0 |
N.S. |
1 | 0.00 | 1.24 | 1.39 | 1.52 | 1.52 | 2.00 | 1.79 | 1.09 | 0.00 |
time (sec) |
N/A | 0.000 | 0.067 | 5.935 | 0.103 | 0.070 | 0.332 | 0.162 | 0.252 | 0.000 |
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 | 25 | 0 | 30 | 36 | 32 | 32 | 31 | 30 | 30 | 31 |
N.S. |
1 | 0.00 | 1.20 | 1.44 | 1.28 | 1.28 | 1.24 | 1.20 | 1.20 | 1.24 |
time (sec) |
N/A | 0.000 | 0.111 | 0.543 | 0.062 | 0.067 | 0.079 | 0.119 | 0.246 | 0.739 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 32 | 32 | 27 | 31 | 26 | 24 | 0 | 83 | 26 |
N.S. |
1 | 1.28 | 1.28 | 1.08 | 1.24 | 1.04 | 0.96 | 0.00 | 3.32 | 1.04 |
time (sec) |
N/A | 0.647 | 0.054 | 0.837 | 0.223 | 0.071 | 0.195 | 0.000 | 200.037 | 0.889 |
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 | 21 | 16 | 15 | 15 | 15 | 17 | 15 | 14 | 13 |
N.S. |
1 | 0.68 | 0.52 | 0.48 | 0.48 | 0.48 | 0.55 | 0.48 | 0.45 | 0.42 |
time (sec) |
N/A | 0.150 | 0.002 | 0.080 | 0.028 | 0.054 | 0.023 | 0.113 | 0.203 | 0.552 |
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 | 31 | 0 | 39 | 47 | 67 | 46 | 32 | 61 | 55 | 53 |
N.S. |
1 | 0.00 | 1.26 | 1.52 | 2.16 | 1.48 | 1.03 | 1.97 | 1.77 | 1.71 |
time (sec) |
N/A | 0.000 | 0.037 | 2.304 | 0.093 | 0.063 | 0.129 | 0.126 | 0.252 | 0.990 |
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 | 20 | 20 | 19 | 18 | 18 | 19 | 20 | 18 | 18 |
N.S. |
1 | 1.05 | 1.05 | 1.00 | 0.95 | 0.95 | 1.00 | 1.05 | 0.95 | 0.95 |
time (sec) |
N/A | 0.664 | 0.286 | 0.301 | 0.100 | 0.070 | 0.120 | 0.119 | 0.225 | 0.706 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F(-1) | A | A | A | A | A | F | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 0 | 28 | 44 | 30 | 20 | 30 | 139 | 31 |
N.S. |
1 | 0.00 | 0.00 | 0.93 | 1.47 | 1.00 | 0.67 | 1.00 | 4.63 | 1.03 |
time (sec) |
N/A | 0.000 | 0.000 | 21.296 | 0.242 | 0.071 | 0.257 | 0.431 | 200.026 | 0.857 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 14 | 35 | 13 | 14 | 0 | 15 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 2.33 | 0.87 | 0.93 | 0.00 | 1.00 | 0.87 |
time (sec) |
N/A | 0.195 | 0.007 | 0.433 | 0.159 | 0.068 | 0.078 | 0.000 | 0.231 | 0.545 |
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 | 29 | 0 | 45 | 38 | 39 | 46 | 31 | 38 | 33 | 31 |
N.S. |
1 | 0.00 | 1.55 | 1.31 | 1.34 | 1.59 | 1.07 | 1.31 | 1.14 | 1.07 |
time (sec) |
N/A | 0.000 | 0.057 | 6.920 | 0.227 | 0.075 | 0.468 | 0.133 | 0.245 | 1.040 |
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 | 24 | 0 | 23 | 23 | 28 | 22 | 22 | 22 | 39 | 226 |
N.S. |
1 | 0.00 | 0.96 | 0.96 | 1.17 | 0.92 | 0.92 | 0.92 | 1.62 | 9.42 |
time (sec) |
N/A | 0.000 | 0.559 | 7.220 | 0.349 | 0.067 | 0.170 | 0.229 | 0.244 | 0.867 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 90 | 79 | 52 | 79 | 86 | 82 | 80 | 108 | 80 |
N.S. |
1 | 2.73 | 2.39 | 1.58 | 2.39 | 2.61 | 2.48 | 2.42 | 3.27 | 2.42 |
time (sec) |
N/A | 0.837 | 0.108 | 0.667 | 0.053 | 0.065 | 2.302 | 0.126 | 0.234 | 0.246 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 53 | 60 | 76 | 56 | 56 | 3434 | 0 | 295 |
N.S. |
1 | 0.00 | 1.96 | 2.22 | 2.81 | 2.07 | 2.07 | 127.19 | 0.00 | 10.93 |
time (sec) |
N/A | 0.000 | 0.102 | 6.858 | 0.218 | 0.072 | 0.361 | 1.003 | 0.500 | 0.958 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 15 | 36 | 15 | 42 | 45 | 42 | 43 | 14 | 103 |
N.S. |
1 | 0.88 | 2.12 | 0.88 | 2.47 | 2.65 | 2.47 | 2.53 | 0.82 | 6.06 |
time (sec) |
N/A | 0.416 | 0.019 | 0.387 | 0.039 | 0.060 | 0.167 | 0.113 | 0.262 | 0.606 |
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 | 26 | 0 | 29 | 28 | 30 | 30 | 27 | 32 | 31 | 106 |
N.S. |
1 | 0.00 | 1.12 | 1.08 | 1.15 | 1.15 | 1.04 | 1.23 | 1.19 | 4.08 |
time (sec) |
N/A | 0.000 | 0.141 | 0.466 | 0.086 | 0.060 | 0.082 | 0.119 | 0.276 | 0.696 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | A | A | A | F(-1) | A | F | B |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 39 | 0 | 26 | 36 | 27 | 0 | 31 | 88 | 28 |
N.S. |
1 | 1.26 | 0.00 | 0.84 | 1.16 | 0.87 | 0.00 | 1.00 | 2.84 | 0.90 |
time (sec) |
N/A | 1.223 | 0.000 | 1.189 | 0.261 | 0.108 | 0.000 | 0.309 | 54.077 | 0.734 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 27 | 27 | 24 | 42 | 28 | 22 | 72 | 30 | 26 |
N.S. |
1 | 1.04 | 1.04 | 0.92 | 1.62 | 1.08 | 0.85 | 2.77 | 1.15 | 1.00 |
time (sec) |
N/A | 0.416 | 0.074 | 0.434 | 0.054 | 0.075 | 0.055 | 0.116 | 0.210 | 0.057 |
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 | 26 | 25 | 22 | 32 | 19 | 22 | 26 | 22 |
N.S. |
1 | 0.00 | 1.13 | 1.09 | 0.96 | 1.39 | 0.83 | 0.96 | 1.13 | 0.96 |
time (sec) |
N/A | 0.000 | 0.408 | 0.912 | 0.123 | 0.068 | 0.152 | 0.152 | 0.227 | 0.788 |
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 | 25 | 0 | 27 | 26 | 22 | 35 | 27 | 25 | 26 | 25 |
N.S. |
1 | 0.00 | 1.08 | 1.04 | 0.88 | 1.40 | 1.08 | 1.00 | 1.04 | 1.00 |
time (sec) |
N/A | 0.000 | 0.703 | 0.704 | 0.091 | 0.075 | 0.154 | 0.120 | 0.224 | 0.761 |
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 | 17 | 18 | 13 | 15 | 15 | 22 | 15 | 13 | 12 |
N.S. |
1 | 1.31 | 1.38 | 1.00 | 1.15 | 1.15 | 1.69 | 1.15 | 1.00 | 0.92 |
time (sec) |
N/A | 0.161 | 0.002 | 0.072 | 0.051 | 0.062 | 0.016 | 0.112 | 0.213 | 0.527 |
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 | 27 | 36 | 36 | 30 | 27 | 27 | 24 | 27 | 27 | 26 |
N.S. |
1 | 1.33 | 1.33 | 1.11 | 1.00 | 1.00 | 0.89 | 1.00 | 1.00 | 0.96 |
time (sec) |
N/A | 0.177 | 0.004 | 0.116 | 0.029 | 0.060 | 0.028 | 0.109 | 0.212 | 0.563 |
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 | 21 | 30 | 23 | 31 | 32 | 32 | 29 | 32 | 24 | 28 |
N.S. |
1 | 1.43 | 1.10 | 1.48 | 1.52 | 1.52 | 1.38 | 1.52 | 1.14 | 1.33 |
time (sec) |
N/A | 0.246 | 0.037 | 0.216 | 0.056 | 0.063 | 0.065 | 0.113 | 0.225 | 0.585 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | F | F | B | B | F(-1) | B | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 58 | 0 | 0 | 61 | 61 | 0 | 67 | 0 |
N.S. |
1 | 0.00 | 2.23 | 0.00 | 0.00 | 2.35 | 2.35 | 0.00 | 2.58 | 0.00 |
time (sec) |
N/A | 0.000 | 0.115 | 0.000 | 0.000 | 0.074 | 0.513 | 0.000 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 40 | 29 | 50 | 44 | 39 | 50 | 123 | 54 |
N.S. |
1 | 0.00 | 1.43 | 1.04 | 1.79 | 1.57 | 1.39 | 1.79 | 4.39 | 1.93 |
time (sec) |
N/A | 0.000 | 0.118 | 1.194 | 0.500 | 0.073 | 0.535 | 0.168 | 200.026 | 0.737 |
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 | 14 | 16 | 13 | 14 | 12 | 14 | 14 | 12 | 12 |
N.S. |
1 | 0.93 | 1.07 | 0.87 | 0.93 | 0.80 | 0.93 | 0.93 | 0.80 | 0.80 |
time (sec) |
N/A | 0.160 | 0.002 | 0.088 | 0.037 | 0.063 | 0.038 | 0.107 | 0.216 | 0.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | C | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 22 | 22 | 17 | 22 | 0 | 27 | 46 | 22 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 0.77 | 1.00 | 0.00 | 1.23 | 2.09 | 1.00 |
time (sec) |
N/A | 0.000 | 0.097 | 1.239 | 0.065 | 0.067 | 0.000 | 0.123 | 0.243 | 0.858 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | C | B | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 19 | 22 | 61 | 48 | 27 | 33 | 18 | 15 |
N.S. |
1 | 0.00 | 1.00 | 1.16 | 3.21 | 2.53 | 1.42 | 1.74 | 0.95 | 0.79 |
time (sec) |
N/A | 0.000 | 0.047 | 0.283 | 0.107 | 0.072 | 0.675 | 0.128 | 0.188 | 0.773 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 26 | 19 | 21 | 30 | 0 | 0 | 25 | 18 |
N.S. |
1 | 0.00 | 0.87 | 0.63 | 0.70 | 1.00 | 0.00 | 0.00 | 0.83 | 0.60 |
time (sec) |
N/A | 0.000 | 0.334 | 0.473 | 0.216 | 0.068 | 0.000 | 0.000 | 0.219 | 0.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 62 | 78 | 91 | 71 | 71 | 0 | 105 | 103 |
N.S. |
1 | 0.00 | 2.00 | 2.52 | 2.94 | 2.29 | 2.29 | 0.00 | 3.39 | 3.32 |
time (sec) |
N/A | 0.000 | 0.101 | 0.704 | 0.343 | 0.076 | 0.255 | 0.000 | 68.782 | 0.773 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | A | B | A | B | F | B | B |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 1504 | 1186 | 51 | 513 | 48 | 53 | 0 | 70 | 50 |
N.S. |
1 | 57.85 | 45.62 | 1.96 | 19.73 | 1.85 | 2.04 | 0.00 | 2.69 | 1.92 |
time (sec) |
N/A | 5.204 | 0.745 | 1.232 | 2.964 | 0.084 | 1.217 | 0.000 | 0.210 | 1.124 |
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 | 41 | 56 | 42 | 34 | 34 | 19 | 28 | 43 | 34 |
N.S. |
1 | 1.24 | 1.70 | 1.27 | 1.03 | 1.03 | 0.58 | 0.85 | 1.30 | 1.03 |
time (sec) |
N/A | 1.139 | 0.091 | 0.627 | 0.170 | 0.066 | 0.197 | 0.113 | 0.200 | 0.611 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | A | A | F | F | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 0 | 21 | 42 | 19 | 20 | 0 | 310 | 21 |
N.S. |
1 | 0.00 | 0.00 | 0.81 | 1.62 | 0.73 | 0.77 | 0.00 | 11.92 | 0.81 |
time (sec) |
N/A | 0.000 | 0.000 | 1.660 | 0.185 | 0.069 | 0.224 | 0.000 | 0.262 | 0.733 |
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 | 17 | 15 | 14 | 13 | 13 | 12 | 14 | 13 | 13 |
N.S. |
1 | 0.85 | 0.75 | 0.70 | 0.65 | 0.65 | 0.60 | 0.70 | 0.65 | 0.65 |
time (sec) |
N/A | 0.163 | 0.001 | 0.051 | 0.026 | 0.057 | 0.032 | 0.107 | 0.212 | 0.014 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 30 | 32 | 490 | 169 | 209 | 277 | 287 | 0 |
N.S. |
1 | 0.00 | 1.11 | 1.19 | 18.15 | 6.26 | 7.74 | 10.26 | 10.63 | 0.00 |
time (sec) |
N/A | 0.000 | 1.678 | 63.443 | 0.695 | 0.076 | 0.800 | 0.194 | 0.475 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 28 | 42 | 0 | 41 | 0 | 26 | 32 | 27 |
N.S. |
1 | 1.00 | 0.93 | 1.40 | 0.00 | 1.37 | 0.00 | 0.87 | 1.07 | 0.90 |
time (sec) |
N/A | 2.269 | 0.115 | 0.044 | 0.000 | 0.079 | 0.000 | 0.362 | 0.282 | 0.766 |
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 | 20 | 0 | 19 | 16 | 15 | 27 | 14 | 30 | 25 | 15 |
N.S. |
1 | 0.00 | 0.95 | 0.80 | 0.75 | 1.35 | 0.70 | 1.50 | 1.25 | 0.75 |
time (sec) |
N/A | 0.000 | 0.020 | 0.241 | 0.106 | 0.069 | 0.064 | 0.121 | 0.221 | 0.569 |
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 | 15 | 17 | 9 | 11 | 11 | 8 | 11 | 10 | 8 |
N.S. |
1 | 0.65 | 0.74 | 0.39 | 0.48 | 0.48 | 0.35 | 0.48 | 0.43 | 0.35 |
time (sec) |
N/A | 0.149 | 0.002 | 0.048 | 0.024 | 0.055 | 0.017 | 0.107 | 0.229 | 0.011 |
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 | 22 | 0 | 23 | 28 | 29 | 29 | 26 | 29 | 28 | 21 |
N.S. |
1 | 0.00 | 1.05 | 1.27 | 1.32 | 1.32 | 1.18 | 1.32 | 1.27 | 0.95 |
time (sec) |
N/A | 0.000 | 0.650 | 0.868 | 0.061 | 0.072 | 0.063 | 0.114 | 0.228 | 0.610 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 55 | 35 | 124 | 98 | 61 | 136 | 190 | 0 |
N.S. |
1 | 0.00 | 2.29 | 1.46 | 5.17 | 4.08 | 2.54 | 5.67 | 7.92 | 0.00 |
time (sec) |
N/A | 0.000 | 0.120 | 103.601 | 0.172 | 0.079 | 0.155 | 0.157 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 31 | 47 | 70 | 64 | 69 | 0 | 0 | 176 | 75 |
N.S. |
1 | 1.03 | 1.57 | 2.33 | 2.13 | 2.30 | 0.00 | 0.00 | 5.87 | 2.50 |
time (sec) |
N/A | 15.901 | 0.363 | 272.935 | 0.147 | 0.077 | 0.000 | 0.000 | 0.611 | 1.156 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 28 | 29 | 51 | 51 | 20 | 55 | 61 | 28 |
N.S. |
1 | 0.00 | 1.17 | 1.21 | 2.12 | 2.12 | 0.83 | 2.29 | 2.54 | 1.17 |
time (sec) |
N/A | 0.000 | 2.270 | 0.283 | 0.068 | 0.071 | 0.052 | 0.119 | 0.217 | 0.614 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 26 | 29 | 22 | 20 | 20 | 27 | 21 | 17 | 10 |
N.S. |
1 | 1.86 | 2.07 | 1.57 | 1.43 | 1.43 | 1.93 | 1.50 | 1.21 | 0.71 |
time (sec) |
N/A | 0.171 | 0.005 | 0.113 | 0.033 | 0.062 | 0.051 | 0.110 | 0.221 | 0.638 |
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 | 24 | 0 | 21 | 22 | 21 | 21 | 15 | 21 | 33 | 21 |
N.S. |
1 | 0.00 | 0.88 | 0.92 | 0.88 | 0.88 | 0.62 | 0.88 | 1.38 | 0.88 |
time (sec) |
N/A | 0.000 | 0.309 | 0.637 | 0.066 | 0.059 | 0.092 | 0.179 | 0.237 | 0.751 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 29 | 30 | 52 | 44 | 36 | 29 | 29 | 29 |
N.S. |
1 | 0.00 | 1.26 | 1.30 | 2.26 | 1.91 | 1.57 | 1.26 | 1.26 | 1.26 |
time (sec) |
N/A | 0.000 | 0.148 | 0.526 | 0.144 | 0.069 | 0.231 | 0.120 | 0.218 | 0.726 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 32 | 32 | 44 | 0 | 51 | 46 | 0 | 322 | 49 |
N.S. |
1 | 0.97 | 0.97 | 1.33 | 0.00 | 1.55 | 1.39 | 0.00 | 9.76 | 1.48 |
time (sec) |
N/A | 25.433 | 0.346 | 1.307 | 0.000 | 0.081 | 3.179 | 0.000 | 200.015 | 1.209 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 55 | 51 | 27 | 33 | 35 | 27 | 74 | 37 | 25 |
N.S. |
1 | 1.53 | 1.42 | 0.75 | 0.92 | 0.97 | 0.75 | 2.06 | 1.03 | 0.69 |
time (sec) |
N/A | 0.698 | 0.065 | 0.545 | 0.143 | 0.068 | 0.072 | 0.117 | 0.226 | 0.638 |
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 | 31 | 29 | 29 | 28 | 24 | 3523 | 33 | 30 |
N.S. |
1 | 0.00 | 1.29 | 1.21 | 1.21 | 1.17 | 1.00 | 146.79 | 1.38 | 1.25 |
time (sec) |
N/A | 0.000 | 0.191 | 252.498 | 7.840 | 0.073 | 2.705 | 161.151 | 0.320 | 1.770 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 55 | 42 | 46 | 53 | 38 | 44 | 45 | 48 | 45 |
N.S. |
1 | 2.39 | 1.83 | 2.00 | 2.30 | 1.65 | 1.91 | 1.96 | 2.09 | 1.96 |
time (sec) |
N/A | 0.298 | 0.055 | 0.636 | 0.034 | 0.073 | 0.116 | 0.119 | 0.229 | 0.606 |