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 | 46 | 42 | 37 | 37 | 36 | 36 | 68 | 36 | 79 | 36 |
N.S. |
1 | 0.91 | 0.80 | 0.80 | 0.78 | 0.78 | 1.48 | 0.78 | 1.72 | 0.78 |
time (sec) |
N/A | 0.366 | 0.144 | 12.685 | 0.050 | 0.084 | 0.908 | 0.122 | 0.168 | 25.805 |
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 | 29 | 48 | 26 | 26 | 36 | 42 | 36 | 25 | 26 |
N.S. |
1 | 0.94 | 1.55 | 0.84 | 0.84 | 1.16 | 1.35 | 1.16 | 0.81 | 0.84 |
time (sec) |
N/A | 0.346 | 0.118 | 8.481 | 0.050 | 0.088 | 0.628 | 0.128 | 0.164 | 0.062 |
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 | 42 | 37 | 37 | 36 | 36 | 68 | 36 | 63 | 36 |
N.S. |
1 | 0.91 | 0.80 | 0.80 | 0.78 | 0.78 | 1.48 | 0.78 | 1.37 | 0.78 |
time (sec) |
N/A | 0.363 | 0.090 | 7.484 | 0.035 | 0.080 | 0.446 | 0.117 | 0.164 | 0.043 |
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 | 15 | 15 | 15 | 14 | 13 | 34 | 20 | 13 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 2.27 | 1.33 | 0.87 | 0.87 | 0.87 |
time (sec) |
N/A | 0.305 | 0.005 | 4.908 | 0.035 | 0.075 | 0.290 | 0.116 | 0.159 | 25.856 |
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 | 40 | 39 | 35 | 35 | 37 | 35 | 0 | 45 | 70 | 53 |
N.S. |
1 | 0.98 | 0.88 | 0.88 | 0.92 | 0.88 | 0.00 | 1.12 | 1.75 | 1.32 |
time (sec) |
N/A | 0.355 | 0.040 | 2.492 | 0.030 | 0.096 | 0.000 | 0.127 | 0.220 | 25.777 |
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 | 37 | 34 | 39 | 50 | 32 | 33 | 0 | 42 | 43 | 31 |
N.S. |
1 | 0.92 | 1.05 | 1.35 | 0.86 | 0.89 | 0.00 | 1.14 | 1.16 | 0.84 |
time (sec) |
N/A | 0.385 | 0.150 | 3.003 | 0.039 | 0.095 | 0.000 | 0.158 | 0.254 | 25.864 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 35 | 33 | 51 | 41 | 54 | 0 | 47 | 148 | 37 |
N.S. |
1 | 0.81 | 0.77 | 1.19 | 0.95 | 1.26 | 0.00 | 1.09 | 3.44 | 0.86 |
time (sec) |
N/A | 0.398 | 0.051 | 1.688 | 0.039 | 0.099 | 0.000 | 0.141 | 0.178 | 25.707 |
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 | 38 | 32 | 38 | 70 | 35 | 35 | 0 | 37 | 185 | 38 |
N.S. |
1 | 0.84 | 1.00 | 1.84 | 0.92 | 0.92 | 0.00 | 0.97 | 4.87 | 1.00 |
time (sec) |
N/A | 0.346 | 0.131 | 2.773 | 0.042 | 0.097 | 0.000 | 0.164 | 0.163 | 25.867 |
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 | 41 | 38 | 54 | 39 | 44 | 44 | 37 | 38 |
N.S. |
1 | 1.00 | 0.95 | 0.88 | 1.26 | 0.91 | 1.02 | 1.02 | 0.86 | 0.88 |
time (sec) |
N/A | 0.487 | 0.028 | 0.549 | 0.045 | 0.089 | 0.106 | 0.141 | 0.173 | 25.545 |
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 | 41 | 35 | 41 | 32 | 35 | 35 | 60 | 35 | 33 | 39 |
N.S. |
1 | 0.85 | 1.00 | 0.78 | 0.85 | 0.85 | 1.46 | 0.85 | 0.80 | 0.95 |
time (sec) |
N/A | 0.337 | 0.159 | 1.047 | 0.036 | 0.085 | 0.403 | 0.146 | 0.172 | 25.440 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 14 | 13 | 35 | 63 | 35 | 33 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 2.33 | 4.20 | 2.33 | 2.20 | 0.87 |
time (sec) |
N/A | 0.317 | 0.011 | 1.952 | 0.040 | 0.090 | 0.549 | 0.155 | 0.165 | 25.277 |
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 | 41 | 46 | 36 | 35 | 35 | 66 | 35 | 35 | 40 |
N.S. |
1 | 0.89 | 1.00 | 0.78 | 0.76 | 0.76 | 1.43 | 0.76 | 0.76 | 0.87 |
time (sec) |
N/A | 0.367 | 0.145 | 3.539 | 0.043 | 0.124 | 0.824 | 0.152 | 0.177 | 25.445 |
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 | 31 | 29 | 46 | 26 | 69 | 35 | 63 | 35 | 35 | 25 |
N.S. |
1 | 0.94 | 1.48 | 0.84 | 2.23 | 1.13 | 2.03 | 1.13 | 1.13 | 0.81 |
time (sec) |
N/A | 0.350 | 0.035 | 6.543 | 0.033 | 0.083 | 1.153 | 0.161 | 0.169 | 25.452 |
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 | 41 | 46 | 36 | 35 | 35 | 66 | 35 | 35 | 40 |
N.S. |
1 | 0.89 | 1.00 | 0.78 | 0.76 | 0.76 | 1.43 | 0.76 | 0.76 | 0.87 |
time (sec) |
N/A | 0.359 | 0.195 | 12.164 | 0.049 | 0.114 | 1.618 | 0.161 | 0.163 | 25.876 |
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 | 44 | 46 | 36 | 79 | 35 | 63 | 35 | 35 | 35 |
N.S. |
1 | 0.96 | 1.00 | 0.78 | 1.72 | 0.76 | 1.37 | 0.76 | 0.76 | 0.76 |
time (sec) |
N/A | 0.378 | 0.032 | 25.137 | 0.030 | 0.117 | 2.338 | 0.151 | 0.172 | 25.434 |
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 | 41 | 46 | 36 | 35 | 35 | 66 | 35 | 35 | 40 |
N.S. |
1 | 0.89 | 1.00 | 0.78 | 0.76 | 0.76 | 1.43 | 0.76 | 0.76 | 0.87 |
time (sec) |
N/A | 0.360 | 0.144 | 40.694 | 0.044 | 0.125 | 3.240 | 0.151 | 0.165 | 19.177 |
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 | 46 | 44 | 46 | 46 | 89 | 35 | 63 | 35 | 35 | 45 |
N.S. |
1 | 0.96 | 1.00 | 1.00 | 1.93 | 0.76 | 1.37 | 0.76 | 0.76 | 0.98 |
time (sec) |
N/A | 0.375 | 0.032 | 88.975 | 0.050 | 0.106 | 4.335 | 0.156 | 0.170 | 25.458 |
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 | 60 | 63 | 78 | 68 | 66 | 84 | 0 | 83 | 118 | 147 |
N.S. |
1 | 1.05 | 1.30 | 1.13 | 1.10 | 1.40 | 0.00 | 1.38 | 1.97 | 2.45 |
time (sec) |
N/A | 0.388 | 0.028 | 1.746 | 0.037 | 0.103 | 0.000 | 0.149 | 0.173 | 28.915 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 42 | 50 | 92 | 45 | 45 | 0 | 46 | 272 | 50 |
N.S. |
1 | 0.84 | 1.00 | 1.84 | 0.90 | 0.90 | 0.00 | 0.92 | 5.44 | 1.00 |
time (sec) |
N/A | 0.353 | 0.160 | 3.209 | 0.037 | 0.100 | 0.000 | 0.191 | 0.235 | 25.549 |
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 | 53 | 45 | 75 | 48 | 56 | 60 | 0 | 74 | 59 | 88 |
N.S. |
1 | 0.85 | 1.42 | 0.91 | 1.06 | 1.13 | 0.00 | 1.40 | 1.11 | 1.66 |
time (sec) |
N/A | 0.363 | 0.132 | 5.013 | 0.026 | 0.106 | 0.000 | 0.120 | 0.234 | 30.600 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 37 | 40 | 33 | 35 | 35 | 0 | 45 | 52 | 66 |
N.S. |
1 | 0.92 | 1.00 | 0.82 | 0.88 | 0.88 | 0.00 | 1.12 | 1.30 | 1.65 |
time (sec) |
N/A | 0.363 | 0.020 | 3.024 | 0.051 | 0.098 | 0.000 | 0.135 | 0.153 | 25.515 |
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 | 38 | 33 | 60 | 38 | 46 | 50 | 0 | 60 | 43 | 62 |
N.S. |
1 | 0.87 | 1.58 | 1.00 | 1.21 | 1.32 | 0.00 | 1.58 | 1.13 | 1.63 |
time (sec) |
N/A | 0.370 | 0.107 | 2.034 | 0.043 | 0.106 | 0.000 | 0.120 | 0.169 | 26.748 |
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 | 27 | 26 | 27 | 23 | 25 | 25 | 0 | 31 | 44 | 35 |
N.S. |
1 | 0.96 | 1.00 | 0.85 | 0.93 | 0.93 | 0.00 | 1.15 | 1.63 | 1.30 |
time (sec) |
N/A | 0.353 | 0.019 | 1.741 | 0.036 | 0.097 | 0.000 | 0.128 | 0.163 | 25.422 |
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 | 23 | 21 | 42 | 28 | 34 | 38 | 0 | 41 | 22 | 35 |
N.S. |
1 | 0.91 | 1.83 | 1.22 | 1.48 | 1.65 | 0.00 | 1.78 | 0.96 | 1.52 |
time (sec) |
N/A | 0.319 | 0.045 | 1.497 | 0.036 | 0.089 | 0.000 | 0.119 | 0.163 | 25.511 |
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 | 11 | 13 | 11 | 17 | 11 | 19 | 29 | 12 | 31 | 24 |
N.S. |
1 | 1.18 | 1.00 | 1.55 | 1.00 | 1.73 | 2.64 | 1.09 | 2.82 | 2.18 |
time (sec) |
N/A | 0.287 | 0.007 | 0.777 | 0.052 | 0.088 | 0.081 | 0.126 | 0.191 | 0.432 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 15 | 12 | 28 | 30 | 0 | 30 | 43 | 11 |
N.S. |
1 | 1.00 | 1.36 | 1.09 | 2.55 | 2.73 | 0.00 | 2.73 | 3.91 | 1.00 |
time (sec) |
N/A | 0.297 | 0.008 | 1.825 | 0.029 | 0.099 | 0.000 | 0.121 | 0.165 | 25.323 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 20 | 42 | 30 | 36 | 52 | 0 | 43 | 39 | 23 |
N.S. |
1 | 0.87 | 1.83 | 1.30 | 1.57 | 2.26 | 0.00 | 1.87 | 1.70 | 1.00 |
time (sec) |
N/A | 0.326 | 0.136 | 1.651 | 0.038 | 0.105 | 0.000 | 0.123 | 0.165 | 25.290 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 24 | 39 | 23 | 40 | 56 | 0 | 47 | 132 | 35 |
N.S. |
1 | 0.89 | 1.44 | 0.85 | 1.48 | 2.07 | 0.00 | 1.74 | 4.89 | 1.30 |
time (sec) |
N/A | 0.338 | 0.024 | 2.266 | 0.045 | 0.127 | 0.000 | 0.123 | 0.157 | 0.087 |
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 | 38 | 32 | 57 | 40 | 50 | 67 | 0 | 56 | 105 | 33 |
N.S. |
1 | 0.84 | 1.50 | 1.05 | 1.32 | 1.76 | 0.00 | 1.47 | 2.76 | 0.87 |
time (sec) |
N/A | 0.354 | 0.090 | 2.000 | 0.030 | 0.123 | 0.000 | 0.123 | 0.161 | 25.317 |
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 | 39 | 39 | 54 | 33 | 65 | 67 | 0 | 56 | 216 | 46 |
N.S. |
1 | 1.00 | 1.38 | 0.85 | 1.67 | 1.72 | 0.00 | 1.44 | 5.54 | 1.18 |
time (sec) |
N/A | 0.343 | 0.026 | 2.427 | 0.035 | 0.092 | 0.000 | 0.119 | 0.166 | 0.062 |
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 | 53 | 44 | 72 | 50 | 60 | 77 | 0 | 66 | 167 | 45 |
N.S. |
1 | 0.83 | 1.36 | 0.94 | 1.13 | 1.45 | 0.00 | 1.25 | 3.15 | 0.85 |
time (sec) |
N/A | 0.355 | 0.109 | 2.234 | 0.029 | 0.096 | 0.000 | 0.125 | 0.201 | 25.293 |
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 | 57 | 51 | 69 | 43 | 85 | 77 | 0 | 66 | 300 | 56 |
N.S. |
1 | 0.89 | 1.21 | 0.75 | 1.49 | 1.35 | 0.00 | 1.16 | 5.26 | 0.98 |
time (sec) |
N/A | 0.359 | 0.042 | 3.148 | 0.043 | 0.112 | 0.000 | 0.126 | 0.273 | 25.303 |
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 | 50 | 42 | 50 | 62 | 42 | 43 | 0 | 42 | 45 | 43 |
N.S. |
1 | 0.84 | 1.00 | 1.24 | 0.84 | 0.86 | 0.00 | 0.84 | 0.90 | 0.86 |
time (sec) |
N/A | 0.372 | 0.029 | 7.746 | 0.048 | 0.085 | 0.000 | 0.131 | 0.174 | 25.842 |
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 | 57 | 79 | 41 | 66 | 63 | 52 | 0 | 55 | 64 | 47 |
N.S. |
1 | 1.39 | 0.72 | 1.16 | 1.11 | 0.91 | 0.00 | 0.96 | 1.12 | 0.82 |
time (sec) |
N/A | 0.385 | 0.318 | 4.621 | 0.130 | 0.090 | 0.000 | 0.139 | 0.160 | 25.895 |
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 | 38 | 32 | 38 | 52 | 32 | 33 | 0 | 32 | 33 | 35 |
N.S. |
1 | 0.84 | 1.00 | 1.37 | 0.84 | 0.87 | 0.00 | 0.84 | 0.87 | 0.92 |
time (sec) |
N/A | 0.366 | 0.022 | 3.421 | 0.036 | 0.117 | 0.000 | 0.134 | 0.188 | 25.753 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 50 | 31 | 54 | 43 | 40 | 0 | 43 | 48 | 43 |
N.S. |
1 | 1.39 | 0.86 | 1.50 | 1.19 | 1.11 | 0.00 | 1.19 | 1.33 | 1.19 |
time (sec) |
N/A | 0.364 | 0.290 | 2.674 | 0.107 | 0.100 | 0.000 | 0.141 | 0.160 | 25.994 |
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 | 23 | 18 | 23 | 42 | 20 | 22 | 0 | 20 | 24 | 23 |
N.S. |
1 | 0.78 | 1.00 | 1.83 | 0.87 | 0.96 | 0.00 | 0.87 | 1.04 | 1.00 |
time (sec) |
N/A | 0.349 | 0.016 | 2.567 | 0.029 | 0.113 | 0.000 | 0.129 | 0.162 | 25.752 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 29 | 18 | 18 | 39 | 17 | 35 | 17 | 15 |
N.S. |
1 | 1.00 | 1.93 | 1.20 | 1.20 | 2.60 | 1.13 | 2.33 | 1.13 | 1.00 |
time (sec) |
N/A | 0.290 | 0.019 | 0.497 | 0.122 | 0.099 | 0.062 | 0.129 | 0.159 | 0.062 |
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 | 11 | 11 | 11 | 12 | 13 | 13 | 17 | 13 | 11 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 1.18 | 1.18 | 1.55 | 1.18 | 1.00 | 1.18 |
time (sec) |
N/A | 0.302 | 0.012 | 0.655 | 0.045 | 0.087 | 0.080 | 0.122 | 0.162 | 25.810 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 21 | 27 | 30 | 36 | 50 | 0 | 44 | 53 | 22 |
N.S. |
1 | 0.91 | 1.17 | 1.30 | 1.57 | 2.17 | 0.00 | 1.91 | 2.30 | 0.96 |
time (sec) |
N/A | 0.315 | 0.023 | 1.733 | 0.036 | 0.100 | 0.000 | 0.121 | 0.171 | 0.022 |
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 | 22 | 19 | 13 | 31 | 22 | 33 | 0 | 16 | 32 | 14 |
N.S. |
1 | 0.86 | 0.59 | 1.41 | 1.00 | 1.50 | 0.00 | 0.73 | 1.45 | 0.64 |
time (sec) |
N/A | 0.351 | 0.061 | 2.950 | 0.037 | 0.083 | 0.000 | 0.136 | 0.172 | 25.788 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 52 | 27 | 50 | 61 | 85 | 0 | 67 | 121 | 48 |
N.S. |
1 | 1.16 | 0.60 | 1.11 | 1.36 | 1.89 | 0.00 | 1.49 | 2.69 | 1.07 |
time (sec) |
N/A | 0.360 | 0.018 | 1.997 | 0.031 | 0.099 | 0.000 | 0.122 | 0.208 | 25.775 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 33 | 46 | 46 | 32 | 43 | 0 | 32 | 55 | 33 |
N.S. |
1 | 0.87 | 1.21 | 1.21 | 0.84 | 1.13 | 0.00 | 0.84 | 1.45 | 0.87 |
time (sec) |
N/A | 0.359 | 0.178 | 3.114 | 0.046 | 0.098 | 0.000 | 0.140 | 0.251 | 25.741 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 83 | 27 | 68 | 79 | 95 | 0 | 80 | 185 | 67 |
N.S. |
1 | 1.26 | 0.41 | 1.03 | 1.20 | 1.44 | 0.00 | 1.21 | 2.80 | 1.02 |
time (sec) |
N/A | 0.393 | 0.019 | 2.061 | 0.045 | 0.117 | 0.000 | 0.127 | 0.165 | 25.842 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 45 | 58 | 63 | 45 | 71 | 0 | 62 | 89 | 85 |
N.S. |
1 | 0.78 | 1.00 | 1.09 | 0.78 | 1.22 | 0.00 | 1.07 | 1.53 | 1.47 |
time (sec) |
N/A | 0.394 | 0.028 | 4.990 | 0.043 | 0.099 | 0.000 | 0.137 | 0.177 | 25.953 |
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 | 60 | 64 | 103 | 70 | 66 | 93 | 0 | 83 | 84 | 129 |
N.S. |
1 | 1.07 | 1.72 | 1.17 | 1.10 | 1.55 | 0.00 | 1.38 | 1.40 | 2.15 |
time (sec) |
N/A | 0.420 | 0.193 | 2.891 | 0.031 | 0.106 | 0.000 | 0.138 | 0.185 | 26.639 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 33 | 35 | 53 | 35 | 61 | 0 | 48 | 75 | 62 |
N.S. |
1 | 0.77 | 0.81 | 1.23 | 0.81 | 1.42 | 0.00 | 1.12 | 1.74 | 1.44 |
time (sec) |
N/A | 0.386 | 0.074 | 2.048 | 0.043 | 0.118 | 0.000 | 0.130 | 0.168 | 25.661 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 52 | 86 | 60 | 56 | 83 | 0 | 65 | 68 | 77 |
N.S. |
1 | 1.16 | 1.91 | 1.33 | 1.24 | 1.84 | 0.00 | 1.44 | 1.51 | 1.71 |
time (sec) |
N/A | 0.354 | 0.106 | 1.592 | 0.040 | 0.098 | 0.000 | 0.128 | 0.160 | 25.618 |
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 | 28 | 30 | 28 | 29 | 23 | 47 | 53 | 27 | 67 | 78 |
N.S. |
1 | 1.07 | 1.00 | 1.04 | 0.82 | 1.68 | 1.89 | 0.96 | 2.39 | 2.79 |
time (sec) |
N/A | 0.404 | 0.012 | 0.766 | 0.045 | 0.096 | 0.205 | 0.121 | 0.170 | 28.842 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 75 | 50 | 46 | 72 | 0 | 54 | 42 | 48 |
N.S. |
1 | 1.00 | 2.21 | 1.47 | 1.35 | 2.12 | 0.00 | 1.59 | 1.24 | 1.41 |
time (sec) |
N/A | 0.406 | 0.091 | 1.136 | 0.037 | 0.107 | 0.000 | 0.127 | 0.169 | 25.546 |
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 | 15 | 15 | 14 | 13 | 18 | 22 | 13 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 1.20 | 1.47 | 0.87 | 0.87 | 0.87 |
time (sec) |
N/A | 0.323 | 0.017 | 0.597 | 0.038 | 0.085 | 0.109 | 0.118 | 0.163 | 25.356 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 24 | 39 | 23 | 36 | 65 | 0 | 43 | 87 | 34 |
N.S. |
1 | 0.89 | 1.44 | 0.85 | 1.33 | 2.41 | 0.00 | 1.59 | 3.22 | 1.26 |
time (sec) |
N/A | 0.332 | 0.025 | 1.890 | 0.045 | 0.084 | 0.000 | 0.126 | 0.169 | 25.363 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 51 | 143 | 52 | 61 | 96 | 0 | 67 | 75 | 49 |
N.S. |
1 | 1.16 | 3.25 | 1.18 | 1.39 | 2.18 | 0.00 | 1.52 | 1.70 | 1.11 |
time (sec) |
N/A | 0.359 | 0.440 | 1.829 | 0.045 | 0.104 | 0.000 | 0.125 | 0.254 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 35 | 61 | 43 | 64 | 102 | 0 | 69 | 175 | 39 |
N.S. |
1 | 0.81 | 1.42 | 1.00 | 1.49 | 2.37 | 0.00 | 1.60 | 4.07 | 0.91 |
time (sec) |
N/A | 0.381 | 0.067 | 2.144 | 0.033 | 0.093 | 0.000 | 0.122 | 0.225 | 25.368 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 63 | 205 | 70 | 73 | 112 | 0 | 79 | 139 | 60 |
N.S. |
1 | 1.05 | 3.42 | 1.17 | 1.22 | 1.87 | 0.00 | 1.32 | 2.32 | 1.00 |
time (sec) |
N/A | 0.395 | 0.605 | 2.233 | 0.032 | 0.085 | 0.000 | 0.132 | 0.213 | 0.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 49 | 67 | 61 | 82 | 112 | 0 | 78 | 259 | 74 |
N.S. |
1 | 0.84 | 1.16 | 1.05 | 1.41 | 1.93 | 0.00 | 1.34 | 4.47 | 1.28 |
time (sec) |
N/A | 0.381 | 0.031 | 2.233 | 0.028 | 0.101 | 0.000 | 0.122 | 0.185 | 0.110 |
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 | 58 | 68 | 90 | 56 | 68 | 0 | 56 | 55 | 55 |
N.S. |
1 | 0.85 | 1.00 | 1.32 | 0.82 | 1.00 | 0.00 | 0.82 | 0.81 | 0.81 |
time (sec) |
N/A | 0.389 | 0.037 | 13.319 | 0.034 | 0.100 | 0.000 | 0.139 | 0.171 | 25.594 |
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 | 72 | 91 | 53 | 94 | 75 | 89 | 0 | 68 | 82 | 56 |
N.S. |
1 | 1.26 | 0.74 | 1.31 | 1.04 | 1.24 | 0.00 | 0.94 | 1.14 | 0.78 |
time (sec) |
N/A | 0.428 | 0.462 | 7.714 | 0.113 | 0.090 | 0.000 | 0.150 | 0.173 | 26.772 |
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 | 53 | 46 | 53 | 80 | 44 | 56 | 0 | 44 | 45 | 45 |
N.S. |
1 | 0.87 | 1.00 | 1.51 | 0.83 | 1.06 | 0.00 | 0.83 | 0.85 | 0.85 |
time (sec) |
N/A | 0.374 | 0.035 | 4.922 | 0.028 | 0.084 | 0.000 | 0.132 | 0.180 | 25.802 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 62 | 43 | 78 | 55 | 79 | 0 | 55 | 66 | 46 |
N.S. |
1 | 1.22 | 0.84 | 1.53 | 1.08 | 1.55 | 0.00 | 1.08 | 1.29 | 0.90 |
time (sec) |
N/A | 0.399 | 0.339 | 3.382 | 0.123 | 0.078 | 0.000 | 0.146 | 0.176 | 26.156 |
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 | 37 | 34 | 37 | 68 | 35 | 48 | 0 | 35 | 35 | 32 |
N.S. |
1 | 0.92 | 1.00 | 1.84 | 0.95 | 1.30 | 0.00 | 0.95 | 0.95 | 0.86 |
time (sec) |
N/A | 0.351 | 0.026 | 2.881 | 0.029 | 0.077 | 0.000 | 0.128 | 0.163 | 25.755 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 33 | 29 | 34 | 84 | 27 | 62 | 28 | 23 |
N.S. |
1 | 1.00 | 1.22 | 1.07 | 1.26 | 3.11 | 1.00 | 2.30 | 1.04 | 0.85 |
time (sec) |
N/A | 0.401 | 0.016 | 0.631 | 0.112 | 0.105 | 0.076 | 0.133 | 0.178 | 25.580 |
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 | 26 | 26 | 26 | 22 | 25 | 38 | 39 | 25 | 23 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.96 | 1.46 | 1.50 | 0.96 | 0.88 | 0.85 |
time (sec) |
N/A | 0.346 | 0.019 | 0.857 | 0.032 | 0.072 | 0.151 | 0.127 | 0.235 | 25.592 |
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 | 15 | 15 | 15 | 14 | 13 | 34 | 24 | 13 | 29 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 2.27 | 1.60 | 0.87 | 1.93 | 0.87 |
time (sec) |
N/A | 0.321 | 0.013 | 0.766 | 0.025 | 0.071 | 0.637 | 0.142 | 0.225 | 25.610 |
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 | 15 | 15 | 14 | 13 | 26 | 22 | 13 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 1.73 | 1.47 | 0.87 | 0.87 | 0.87 |
time (sec) |
N/A | 0.326 | 0.013 | 0.681 | 0.027 | 0.070 | 0.151 | 0.121 | 0.159 | 25.381 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 33 | 31 | 40 | 50 | 94 | 0 | 56 | 69 | 32 |
N.S. |
1 | 0.87 | 0.82 | 1.05 | 1.32 | 2.47 | 0.00 | 1.47 | 1.82 | 0.84 |
time (sec) |
N/A | 0.350 | 0.018 | 1.888 | 0.032 | 0.084 | 0.000 | 0.118 | 0.169 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 31 | 45 | 46 | 35 | 54 | 0 | 35 | 43 | 36 |
N.S. |
1 | 0.84 | 1.22 | 1.24 | 0.95 | 1.46 | 0.00 | 0.95 | 1.16 | 0.97 |
time (sec) |
N/A | 0.364 | 0.323 | 3.010 | 0.032 | 0.076 | 0.000 | 0.134 | 0.170 | 25.545 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 64 | 31 | 68 | 73 | 130 | 0 | 79 | 135 | 61 |
N.S. |
1 | 1.07 | 0.52 | 1.13 | 1.22 | 2.17 | 0.00 | 1.32 | 2.25 | 1.02 |
time (sec) |
N/A | 0.401 | 0.020 | 2.170 | 0.033 | 0.110 | 0.000 | 0.124 | 0.174 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 45 | 43 | 46 | 44 | 66 | 0 | 31 | 65 | 45 |
N.S. |
1 | 0.85 | 0.81 | 0.87 | 0.83 | 1.25 | 0.00 | 0.58 | 1.23 | 0.85 |
time (sec) |
N/A | 0.369 | 0.066 | 3.180 | 0.030 | 0.073 | 0.000 | 0.135 | 0.187 | 25.428 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 95 | 31 | 86 | 91 | 140 | 0 | 92 | 199 | 79 |
N.S. |
1 | 1.17 | 0.38 | 1.06 | 1.12 | 1.73 | 0.00 | 1.14 | 2.46 | 0.98 |
time (sec) |
N/A | 0.416 | 0.019 | 2.493 | 0.030 | 0.097 | 0.000 | 0.129 | 0.165 | 25.505 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 59 | 69 | 89 | 56 | 100 | 0 | 74 | 99 | 92 |
N.S. |
1 | 0.86 | 1.00 | 1.29 | 0.81 | 1.45 | 0.00 | 1.07 | 1.43 | 1.33 |
time (sec) |
N/A | 0.418 | 0.045 | 9.210 | 0.033 | 0.101 | 0.000 | 0.142 | 0.162 | 26.683 |
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 | 95 | 141 | 98 | 89 | 132 | 0 | 96 | 100 | 157 |
N.S. |
1 | 1.17 | 1.74 | 1.21 | 1.10 | 1.63 | 0.00 | 1.19 | 1.23 | 1.94 |
time (sec) |
N/A | 0.443 | 0.204 | 5.198 | 0.048 | 0.135 | 0.000 | 0.127 | 0.176 | 25.453 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 45 | 58 | 81 | 49 | 90 | 0 | 60 | 89 | 74 |
N.S. |
1 | 0.78 | 1.00 | 1.40 | 0.84 | 1.55 | 0.00 | 1.03 | 1.53 | 1.28 |
time (sec) |
N/A | 0.392 | 0.032 | 3.019 | 0.028 | 0.120 | 0.000 | 0.137 | 0.237 | 25.560 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 83 | 123 | 88 | 79 | 122 | 0 | 77 | 84 | 105 |
N.S. |
1 | 1.28 | 1.89 | 1.35 | 1.22 | 1.88 | 0.00 | 1.18 | 1.29 | 1.62 |
time (sec) |
N/A | 0.397 | 0.128 | 1.967 | 0.027 | 0.098 | 0.000 | 0.137 | 0.187 | 25.604 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 44 | 39 | 39 | 38 | 83 | 66 | 38 | 79 | 182 |
N.S. |
1 | 1.05 | 0.93 | 0.93 | 0.90 | 1.98 | 1.57 | 0.90 | 1.88 | 4.33 |
time (sec) |
N/A | 0.530 | 0.015 | 0.884 | 0.027 | 0.104 | 0.304 | 0.129 | 0.156 | 31.008 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 60 | 113 | 78 | 71 | 112 | 0 | 67 | 58 | 78 |
N.S. |
1 | 1.09 | 2.05 | 1.42 | 1.29 | 2.04 | 0.00 | 1.22 | 1.05 | 1.42 |
time (sec) |
N/A | 0.580 | 0.121 | 1.230 | 0.029 | 0.094 | 0.000 | 0.132 | 0.176 | 25.456 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 14 | 13 | 39 | 42 | 25 | 25 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 2.60 | 2.80 | 1.67 | 1.67 | 1.67 |
time (sec) |
N/A | 0.369 | 0.009 | 0.872 | 0.025 | 0.078 | 0.221 | 0.129 | 0.165 | 25.391 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 60 | 113 | 68 | 65 | 111 | 0 | 88 | 52 | 48 |
N.S. |
1 | 1.09 | 2.05 | 1.24 | 1.18 | 2.02 | 0.00 | 1.60 | 0.95 | 0.87 |
time (sec) |
N/A | 0.580 | 0.136 | 1.348 | 0.033 | 0.085 | 0.000 | 0.133 | 0.155 | 25.628 |
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 | 15 | 15 | 15 | 14 | 13 | 27 | 22 | 13 | 13 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 1.80 | 1.47 | 0.87 | 0.87 | 1.53 |
time (sec) |
N/A | 0.324 | 0.013 | 0.705 | 0.030 | 0.080 | 0.213 | 0.128 | 0.175 | 25.454 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 37 | 54 | 33 | 51 | 105 | 0 | 55 | 99 | 79 |
N.S. |
1 | 0.92 | 1.35 | 0.82 | 1.28 | 2.62 | 0.00 | 1.38 | 2.48 | 1.98 |
time (sec) |
N/A | 0.366 | 0.025 | 2.018 | 0.054 | 0.105 | 0.000 | 0.125 | 0.163 | 0.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 82 | 129 | 70 | 79 | 132 | 0 | 79 | 85 | 66 |
N.S. |
1 | 1.26 | 1.98 | 1.08 | 1.22 | 2.03 | 0.00 | 1.22 | 1.31 | 1.02 |
time (sec) |
N/A | 0.404 | 4.781 | 2.220 | 0.038 | 0.121 | 0.000 | 0.130 | 0.167 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 47 | 54 | 61 | 74 | 138 | 0 | 78 | 185 | 82 |
N.S. |
1 | 0.81 | 0.93 | 1.05 | 1.28 | 2.38 | 0.00 | 1.34 | 3.19 | 1.41 |
time (sec) |
N/A | 0.389 | 0.357 | 2.418 | 0.045 | 0.097 | 0.000 | 0.127 | 0.164 | 0.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 94 | 268 | 88 | 91 | 148 | 0 | 92 | 149 | 78 |
N.S. |
1 | 1.16 | 3.31 | 1.09 | 1.12 | 1.83 | 0.00 | 1.14 | 1.84 | 0.96 |
time (sec) |
N/A | 0.441 | 0.732 | 2.345 | 0.036 | 0.089 | 0.000 | 0.127 | 0.159 | 0.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 61 | 91 | 79 | 92 | 148 | 0 | 89 | 269 | 64 |
N.S. |
1 | 0.88 | 1.32 | 1.14 | 1.33 | 2.14 | 0.00 | 1.29 | 3.90 | 0.93 |
time (sec) |
N/A | 0.397 | 0.113 | 2.550 | 0.029 | 0.102 | 0.000 | 0.132 | 0.176 | 25.440 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 27 | 14 | 14 | 33 | 29 | 14 | 20 | 14 |
N.S. |
1 | 1.00 | 1.59 | 0.82 | 0.82 | 1.94 | 1.71 | 0.82 | 1.18 | 0.82 |
time (sec) |
N/A | 0.335 | 0.044 | 0.927 | 0.026 | 0.073 | 0.026 | 0.122 | 0.235 | 25.611 |
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 | 17 | 17 | 22 | 14 | 30 | 15 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.29 | 0.82 | 1.76 | 0.88 | 0.82 | 0.82 | 0.82 |
time (sec) |
N/A | 0.354 | 0.012 | 0.933 | 0.032 | 0.089 | 0.045 | 0.116 | 0.159 | 25.483 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 19 | 18 | 24 | 37 | 0 | 23 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.82 | 1.09 | 1.68 | 0.00 | 1.05 | 0.82 |
time (sec) |
N/A | 0.325 | 0.041 | 1.594 | 0.026 | 0.090 | 2.933 | 0.000 | 0.153 | 0.129 |
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 | 22 | 22 | 19 | 18 | 21 | 37 | 21 | 20 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.82 | 0.95 | 1.68 | 0.95 | 0.91 | 0.82 |
time (sec) |
N/A | 0.327 | 0.020 | 1.651 | 0.031 | 0.099 | 0.260 | 0.126 | 0.158 | 0.067 |
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 | 20 | 20 | 20 | 19 | 18 | 18 | 36 | 18 | 17 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.90 | 0.90 | 1.80 | 0.90 | 0.85 | 0.90 |
time (sec) |
N/A | 0.318 | 0.016 | 1.659 | 0.027 | 0.076 | 0.426 | 0.124 | 0.175 | 25.564 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 19 | 18 | 26 | 34 | 0 | 25 | 37 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.90 | 1.30 | 1.70 | 0.00 | 1.25 | 1.85 |
time (sec) |
N/A | 0.321 | 0.028 | 1.674 | 0.036 | 0.087 | 0.810 | 0.000 | 0.156 | 0.203 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 19 | 18 | 26 | 36 | 0 | 25 | 53 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.82 | 1.18 | 1.64 | 0.00 | 1.14 | 2.41 |
time (sec) |
N/A | 0.333 | 0.033 | 1.794 | 0.025 | 0.111 | 3.549 | 0.000 | 0.175 | 25.784 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 19 | 18 | 26 | 36 | 0 | 25 | 65 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.82 | 1.18 | 1.64 | 0.00 | 1.14 | 2.95 |
time (sec) |
N/A | 0.331 | 0.150 | 1.766 | 0.030 | 0.083 | 30.009 | 0.000 | 0.166 | 52.967 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 19 | 18 | 26 | 0 | 0 | 25 | 65 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.82 | 1.18 | 0.00 | 0.00 | 1.14 | 2.95 |
time (sec) |
N/A | 0.329 | 0.073 | 1.730 | 0.033 | 0.099 | 0.000 | 0.000 | 0.157 | 30.652 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 137 | 60 | 249 | 0 | 119 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.09 | 0.48 | 1.98 | 0.00 | 0.94 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.969 | 0.168 | 11.273 | 0.000 | 0.097 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 137 | 60 | 236 | 0 | 107 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.09 | 0.48 | 1.87 | 0.00 | 0.85 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.952 | 0.148 | 9.647 | 0.000 | 0.094 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 103 | 57 | 223 | 0 | 106 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.05 | 0.58 | 2.28 | 0.00 | 1.08 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.771 | 0.058 | 7.096 | 0.000 | 0.096 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 103 | 57 | 208 | 0 | 90 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.05 | 0.58 | 2.12 | 0.00 | 0.92 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.739 | 0.074 | 5.292 | 0.000 | 0.085 | 0.000 | 0.000 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 58 | 194 | 0 | 87 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 0.84 | 2.81 | 0.00 | 1.26 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.570 | 0.097 | 4.569 | 0.000 | 0.089 | 0.000 | 0.000 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 58 | 188 | 0 | 78 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 0.84 | 2.72 | 0.00 | 1.13 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.563 | 0.110 | 3.521 | 0.000 | 0.083 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 60 | 198 | 0 | 105 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 0.88 | 2.91 | 0.00 | 1.54 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.598 | 0.100 | 4.235 | 0.000 | 0.077 | 0.000 | 0.000 | 0.169 | 0.000 |