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 | B | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 70 | 165 | 0 | 0 | 0 | 0 | 0 | 85 | 0 |
N.S. |
1 | 1.06 | 2.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.29 | 0.00 |
time (sec) |
N/A | 0.549 | 8.560 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 70 | 165 | 0 | 0 | 0 | 0 | 0 | 59 | 0 |
N.S. |
1 | 1.06 | 2.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.527 | 7.886 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 67 | 150 | 0 | 0 | 0 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.06 | 2.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.352 | 1.491 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | B | F | F | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 40 | 1261 | 137 | 115 | 0 | 0 | 72 | 62 |
N.S. |
1 | 1.00 | 1.00 | 31.52 | 3.42 | 2.88 | 0.00 | 0.00 | 1.80 | 1.55 |
time (sec) |
N/A | 0.256 | 1.398 | 7.037 | 0.151 | 0.088 | 0.000 | 0.000 | 0.210 | 1.815 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | A | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 61 | 0 | 304 | 139 | 0 | 0 | 113 | 260 |
N.S. |
1 | 1.00 | 0.66 | 0.00 | 3.30 | 1.51 | 0.00 | 0.00 | 1.23 | 2.83 |
time (sec) |
N/A | 0.416 | 1.891 | 0.000 | 0.300 | 0.086 | 0.000 | 0.000 | 0.161 | 5.229 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 145 | 129 | 0 | 0 | 172 | 0 | 0 | 152 | 321 |
N.S. |
1 | 0.98 | 0.87 | 0.00 | 0.00 | 1.16 | 0.00 | 0.00 | 1.03 | 2.17 |
time (sec) |
N/A | 0.606 | 2.430 | 0.000 | 0.000 | 0.098 | 0.000 | 0.000 | 0.175 | 9.653 |
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 | 60 | 56 | 53 | 69 | 70 | 57 | 56 | 70 | 118 | 68 |
N.S. |
1 | 0.93 | 0.88 | 1.15 | 1.17 | 0.95 | 0.93 | 1.17 | 1.97 | 1.13 |
time (sec) |
N/A | 0.291 | 0.128 | 14.594 | 0.030 | 0.078 | 1.503 | 0.202 | 0.160 | 0.657 |
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 | 41 | 47 | 48 | 45 | 44 | 48 | 80 | 46 |
N.S. |
1 | 1.00 | 0.93 | 1.07 | 1.09 | 1.02 | 1.00 | 1.09 | 1.82 | 1.05 |
time (sec) |
N/A | 0.284 | 0.067 | 3.662 | 0.037 | 0.077 | 1.054 | 0.178 | 0.181 | 0.651 |
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 | 25 | 20 | 30 | 34 | 25 | 42 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.71 | 1.07 | 1.21 | 0.89 | 1.50 | 0.82 |
time (sec) |
N/A | 0.268 | 0.011 | 0.869 | 0.031 | 0.078 | 0.679 | 0.156 | 0.202 | 0.639 |
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 | 17 | 17 | 22 | 16 | 27 | 24 | 18 | 24 | 21 |
N.S. |
1 | 1.00 | 1.00 | 1.29 | 0.94 | 1.59 | 1.41 | 1.06 | 1.41 | 1.24 |
time (sec) |
N/A | 0.157 | 0.006 | 0.197 | 0.044 | 0.082 | 0.058 | 0.136 | 0.201 | 0.662 |
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 | 43 | 44 | 46 | 36 | 38 | 35 | 0 | 41 | 34 | 31 |
N.S. |
1 | 1.02 | 1.07 | 0.84 | 0.88 | 0.81 | 0.00 | 0.95 | 0.79 | 0.72 |
time (sec) |
N/A | 0.262 | 0.038 | 1.158 | 0.131 | 0.106 | 0.000 | 0.168 | 0.203 | 0.693 |
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 | 65 | 70 | 62 | 52 | 61 | 51 | 0 | 53 | 65 | 41 |
N.S. |
1 | 1.08 | 0.95 | 0.80 | 0.94 | 0.78 | 0.00 | 0.82 | 1.00 | 0.63 |
time (sec) |
N/A | 0.325 | 0.068 | 4.884 | 0.112 | 0.098 | 0.000 | 0.153 | 0.197 | 0.708 |
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 | 87 | 96 | 57 | 62 | 82 | 62 | 0 | 64 | 93 | 76 |
N.S. |
1 | 1.10 | 0.66 | 0.71 | 0.94 | 0.71 | 0.00 | 0.74 | 1.07 | 0.87 |
time (sec) |
N/A | 0.408 | 0.073 | 20.726 | 0.107 | 0.082 | 0.000 | 0.175 | 0.159 | 1.004 |
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 | 74 | 79 | 74 | 63 | 86 | 88 | 0 | 141 | 272 | 175 |
N.S. |
1 | 1.07 | 1.00 | 0.85 | 1.16 | 1.19 | 0.00 | 1.91 | 3.68 | 2.36 |
time (sec) |
N/A | 0.419 | 0.009 | 8.039 | 0.042 | 0.096 | 0.000 | 0.217 | 0.150 | 4.310 |
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 | 52 | 53 | 52 | 50 | 61 | 74 | 0 | 99 | 170 | 105 |
N.S. |
1 | 1.02 | 1.00 | 0.96 | 1.17 | 1.42 | 0.00 | 1.90 | 3.27 | 2.02 |
time (sec) |
N/A | 0.331 | 0.009 | 2.394 | 0.048 | 0.093 | 0.000 | 0.212 | 0.151 | 2.607 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 32 | 31 | 54 | 37 | 54 | 64 | 38 |
N.S. |
1 | 1.00 | 1.00 | 1.33 | 1.29 | 2.25 | 1.54 | 2.25 | 2.67 | 1.58 |
time (sec) |
N/A | 0.243 | 0.007 | 0.626 | 0.029 | 0.089 | 2.233 | 0.161 | 0.158 | 0.721 |
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 | 24 | 24 | 46 | 23 | 23 | 23 | 0 | 129 | 23 | 38 |
N.S. |
1 | 1.00 | 1.92 | 0.96 | 0.96 | 0.96 | 0.00 | 5.38 | 0.96 | 1.58 |
time (sec) |
N/A | 0.239 | 0.029 | 0.753 | 0.038 | 0.077 | 0.000 | 0.163 | 0.199 | 0.697 |
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 | 44 | 44 | 44 | 36 | 35 | 38 | 0 | 11886 | 52 | 47 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.80 | 0.86 | 0.00 | 270.14 | 1.18 | 1.07 |
time (sec) |
N/A | 0.274 | 0.005 | 2.666 | 0.031 | 0.086 | 0.000 | 2.126 | 0.187 | 0.759 |
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 | 60 | 56 | 60 | 46 | 49 | 51 | 0 | 27424 | 83 | 67 |
N.S. |
1 | 0.93 | 1.00 | 0.77 | 0.82 | 0.85 | 0.00 | 457.07 | 1.38 | 1.12 |
time (sec) |
N/A | 0.276 | 0.007 | 9.598 | 0.034 | 0.108 | 0.000 | 5.078 | 0.189 | 0.752 |
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 | 74 | 64 | 74 | 56 | 58 | 62 | 0 | 49370 | 111 | 87 |
N.S. |
1 | 0.86 | 1.00 | 0.76 | 0.78 | 0.84 | 0.00 | 667.16 | 1.50 | 1.18 |
time (sec) |
N/A | 0.281 | 0.024 | 36.894 | 0.029 | 0.083 | 0.000 | 10.875 | 0.209 | 0.795 |
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 | 119 | 129 | 133 | 138 | 133 | 122 | 0 | 156 | 241 | 132 |
N.S. |
1 | 1.08 | 1.12 | 1.16 | 1.12 | 1.03 | 0.00 | 1.31 | 2.03 | 1.11 |
time (sec) |
N/A | 0.321 | 0.384 | 115.438 | 0.045 | 0.088 | 0.000 | 0.230 | 0.212 | 0.729 |
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 | 97 | 107 | 104 | 110 | 104 | 100 | 0 | 118 | 187 | 102 |
N.S. |
1 | 1.10 | 1.07 | 1.13 | 1.07 | 1.03 | 0.00 | 1.22 | 1.93 | 1.05 |
time (sec) |
N/A | 0.295 | 0.481 | 30.104 | 0.039 | 0.079 | 0.000 | 0.214 | 0.209 | 0.688 |
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 | 75 | 64 | 54 | 82 | 71 | 79 | 0 | 80 | 133 | 71 |
N.S. |
1 | 0.85 | 0.72 | 1.09 | 0.95 | 1.05 | 0.00 | 1.07 | 1.77 | 0.95 |
time (sec) |
N/A | 0.274 | 0.139 | 8.134 | 0.031 | 0.108 | 0.000 | 0.198 | 0.184 | 0.663 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | A | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 46 | 48 | 20 | 55 | 0 | 41 | 79 | 39 |
N.S. |
1 | 1.00 | 2.09 | 2.18 | 0.91 | 2.50 | 0.00 | 1.86 | 3.59 | 1.77 |
time (sec) |
N/A | 0.221 | 0.029 | 2.544 | 0.033 | 0.081 | 0.000 | 0.184 | 0.208 | 0.691 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 69 | 43 | 41 | 44 | 48 | 49 | 42 | 136 |
N.S. |
1 | 1.00 | 1.77 | 1.10 | 1.05 | 1.13 | 1.23 | 1.26 | 1.08 | 3.49 |
time (sec) |
N/A | 0.258 | 0.095 | 0.251 | 0.115 | 0.081 | 0.082 | 0.141 | 0.179 | 0.786 |
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 | 49 | 78 | 52 | 64 | 55 | 52 | 0 | 61 | 63 | 50 |
N.S. |
1 | 1.59 | 1.06 | 1.31 | 1.12 | 1.06 | 0.00 | 1.24 | 1.29 | 1.02 |
time (sec) |
N/A | 0.254 | 0.272 | 2.112 | 0.113 | 0.084 | 0.000 | 0.189 | 0.153 | 0.723 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 139 | 197 | 97 | 85 | 75 | 0 | 89 | 115 | 83 |
N.S. |
1 | 1.46 | 2.07 | 1.02 | 0.89 | 0.79 | 0.00 | 0.94 | 1.21 | 0.87 |
time (sec) |
N/A | 0.301 | 2.141 | 9.248 | 0.145 | 0.119 | 0.000 | 0.210 | 0.154 | 0.798 |
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 | 129 | 130 | 168 | 149 | 180 | 142 | 0 | 343 | 530 | 328 |
N.S. |
1 | 1.01 | 1.30 | 1.16 | 1.40 | 1.10 | 0.00 | 2.66 | 4.11 | 2.54 |
time (sec) |
N/A | 0.415 | 0.052 | 15.413 | 0.038 | 0.096 | 0.000 | 0.292 | 0.163 | 3.560 |
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 | 97 | 101 | 120 | 118 | 129 | 120 | 0 | 249 | 382 | 216 |
N.S. |
1 | 1.04 | 1.24 | 1.22 | 1.33 | 1.24 | 0.00 | 2.57 | 3.94 | 2.23 |
time (sec) |
N/A | 0.400 | 0.036 | 4.398 | 0.043 | 0.098 | 0.000 | 0.252 | 0.174 | 3.385 |
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 | 61 | 68 | 67 | 83 | 82 | 96 | 0 | 122 | 221 | 106 |
N.S. |
1 | 1.11 | 1.10 | 1.36 | 1.34 | 1.57 | 0.00 | 2.00 | 3.62 | 1.74 |
time (sec) |
N/A | 0.357 | 0.027 | 1.112 | 0.060 | 0.100 | 0.000 | 0.238 | 0.196 | 1.177 |
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 | 47 | 46 | 84 | 53 | 60 | 62 | 0 | 1100 | 73 | 66 |
N.S. |
1 | 0.98 | 1.79 | 1.13 | 1.28 | 1.32 | 0.00 | 23.40 | 1.55 | 1.40 |
time (sec) |
N/A | 0.341 | 0.351 | 1.182 | 0.037 | 0.090 | 0.000 | 0.424 | 0.156 | 0.771 |
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 | 55 | 54 | 67 | 52 | 52 | 53 | 0 | 11162 | 74 | 77 |
N.S. |
1 | 0.98 | 1.22 | 0.95 | 0.95 | 0.96 | 0.00 | 202.95 | 1.35 | 1.40 |
time (sec) |
N/A | 0.392 | 0.036 | 4.784 | 0.034 | 0.080 | 0.000 | 14.483 | 0.198 | 0.797 |
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 | 81 | 77 | 69 | 88 | 77 | 74 | 0 | 28204 | 119 | 115 |
N.S. |
1 | 0.95 | 0.85 | 1.09 | 0.95 | 0.91 | 0.00 | 348.20 | 1.47 | 1.42 |
time (sec) |
N/A | 0.422 | 0.119 | 20.719 | 0.054 | 0.088 | 0.000 | 29.803 | 0.198 | 0.863 |
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 | 107 | 100 | 92 | 108 | 98 | 94 | 0 | 52002 | 163 | 176 |
N.S. |
1 | 0.93 | 0.86 | 1.01 | 0.92 | 0.88 | 0.00 | 486.00 | 1.52 | 1.64 |
time (sec) |
N/A | 0.451 | 0.195 | 67.698 | 0.048 | 0.089 | 0.000 | 54.047 | 0.217 | 0.956 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 123 | 113 | 128 | 117 | 113 | 0 | 80368 | 207 | 192 |
N.S. |
1 | 0.92 | 0.85 | 0.96 | 0.88 | 0.85 | 0.00 | 604.27 | 1.56 | 1.44 |
time (sec) |
N/A | 0.469 | 0.375 | 186.213 | 0.041 | 0.093 | 0.000 | 79.009 | 0.210 | 1.205 |
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 | 194 | 192 | 177 | 219 | 176 | 150 | 0 | 220 | 351 | 175 |
N.S. |
1 | 0.99 | 0.91 | 1.13 | 0.91 | 0.77 | 0.00 | 1.13 | 1.81 | 0.90 |
time (sec) |
N/A | 0.363 | 1.350 | 188.985 | 0.037 | 0.100 | 0.000 | 0.272 | 0.173 | 0.755 |
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 | 138 | 115 | 115 | 173 | 142 | 128 | 0 | 166 | 275 | 139 |
N.S. |
1 | 0.83 | 0.83 | 1.25 | 1.03 | 0.93 | 0.00 | 1.20 | 1.99 | 1.01 |
time (sec) |
N/A | 0.329 | 0.403 | 68.531 | 0.047 | 0.093 | 0.000 | 0.237 | 0.170 | 0.705 |
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 | 75 | 64 | 54 | 127 | 98 | 105 | 0 | 112 | 199 | 97 |
N.S. |
1 | 0.85 | 0.72 | 1.69 | 1.31 | 1.40 | 0.00 | 1.49 | 2.65 | 1.29 |
time (sec) |
N/A | 0.276 | 0.261 | 15.345 | 0.031 | 0.083 | 0.000 | 0.234 | 0.179 | 0.652 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | A | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 57 | 72 | 20 | 78 | 0 | 57 | 122 | 55 |
N.S. |
1 | 1.00 | 2.59 | 3.27 | 0.91 | 3.55 | 0.00 | 2.59 | 5.55 | 2.50 |
time (sec) |
N/A | 0.215 | 0.113 | 4.440 | 0.036 | 0.082 | 0.000 | 0.198 | 0.193 | 0.655 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 79 | 73 | 78 | 71 | 94 | 80 | 78 | 106 |
N.S. |
1 | 1.00 | 1.10 | 1.01 | 1.08 | 0.99 | 1.31 | 1.11 | 1.08 | 1.47 |
time (sec) |
N/A | 0.378 | 0.171 | 0.286 | 0.161 | 0.083 | 0.101 | 0.173 | 0.230 | 0.679 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 119 | 401 | 98 | 81 | 79 | 0 | 87 | 146 | 141 |
N.S. |
1 | 1.23 | 4.13 | 1.01 | 0.84 | 0.81 | 0.00 | 0.90 | 1.51 | 1.45 |
time (sec) |
N/A | 0.319 | 0.507 | 4.334 | 0.122 | 0.100 | 0.000 | 0.231 | 0.189 | 0.728 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 130 | 488 | 114 | 110 | 100 | 0 | 112 | 136 | 109 |
N.S. |
1 | 1.55 | 5.81 | 1.36 | 1.31 | 1.19 | 0.00 | 1.33 | 1.62 | 1.30 |
time (sec) |
N/A | 0.288 | 0.785 | 17.803 | 0.121 | 0.118 | 0.000 | 0.295 | 0.229 | 0.816 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 214 | 390 | 155 | 147 | 128 | 0 | 142 | 202 | 141 |
N.S. |
1 | 1.46 | 2.65 | 1.05 | 1.00 | 0.87 | 0.00 | 0.97 | 1.37 | 0.96 |
time (sec) |
N/A | 0.361 | 5.633 | 66.299 | 0.172 | 0.128 | 0.000 | 0.307 | 0.204 | 1.332 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 159 | 637 | 248 | 208 | 170 | 0 | 465 | 809 | 423 |
N.S. |
1 | 0.99 | 3.96 | 1.54 | 1.29 | 1.06 | 0.00 | 2.89 | 5.02 | 2.63 |
time (sec) |
N/A | 0.581 | 2.065 | 30.783 | 0.041 | 0.108 | 0.000 | 0.348 | 0.196 | 4.527 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 130 | 464 | 198 | 157 | 147 | 0 | 333 | 595 | 293 |
N.S. |
1 | 1.02 | 3.62 | 1.55 | 1.23 | 1.15 | 0.00 | 2.60 | 4.65 | 2.29 |
time (sec) |
N/A | 0.558 | 1.518 | 8.771 | 0.052 | 0.095 | 0.000 | 0.318 | 0.188 | 4.359 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 97 | 293 | 146 | 111 | 123 | 0 | 171 | 364 | 160 |
N.S. |
1 | 1.08 | 3.26 | 1.62 | 1.23 | 1.37 | 0.00 | 1.90 | 4.04 | 1.78 |
time (sec) |
N/A | 0.483 | 1.513 | 2.413 | 0.040 | 0.117 | 0.000 | 0.275 | 0.183 | 2.640 |
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 | 73 | 70 | 131 | 96 | 84 | 109 | 0 | 4309 | 156 | 116 |
N.S. |
1 | 0.96 | 1.79 | 1.32 | 1.15 | 1.49 | 0.00 | 59.03 | 2.14 | 1.59 |
time (sec) |
N/A | 0.455 | 1.126 | 2.679 | 0.057 | 0.119 | 0.000 | 2.045 | 0.150 | 1.312 |
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 | 88 | 82 | 81 | 75 | 77 | 77 | 0 | 24430 | 117 | 104 |
N.S. |
1 | 0.93 | 0.92 | 0.85 | 0.88 | 0.88 | 0.00 | 277.61 | 1.33 | 1.18 |
time (sec) |
N/A | 0.521 | 0.483 | 9.711 | 0.033 | 0.086 | 0.000 | 121.745 | 0.157 | 0.851 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 113 | 121 | 125 | 107 | 102 | 0 | 0 | 183 | 147 |
N.S. |
1 | 1.02 | 1.09 | 1.13 | 0.96 | 0.92 | 0.00 | 0.00 | 1.65 | 1.32 |
time (sec) |
N/A | 0.582 | 0.817 | 35.876 | 0.039 | 0.092 | 0.000 | 0.000 | 0.150 | 0.971 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 130 | 141 | 145 | 126 | 123 | 0 | 101962 | 249 | 214 |
N.S. |
1 | 0.98 | 1.07 | 1.10 | 0.95 | 0.93 | 0.00 | 772.44 | 1.89 | 1.62 |
time (sec) |
N/A | 0.581 | 1.905 | 113.409 | 0.039 | 0.091 | 0.000 | 77.226 | 0.160 | 1.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 159 | 167 | 165 | 147 | 147 | 0 | 0 | 315 | 259 |
N.S. |
1 | 0.96 | 1.01 | 1.00 | 0.89 | 0.89 | 0.00 | 0.00 | 1.91 | 1.57 |
time (sec) |
N/A | 0.614 | 4.373 | 292.115 | 0.048 | 0.102 | 0.000 | 0.000 | 0.169 | 1.143 |
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 | 116 | 103 | 99 | 106 | 108 | 183 | 0 | 139 | 954 | 119 |
N.S. |
1 | 0.89 | 0.85 | 0.91 | 0.93 | 1.58 | 0.00 | 1.20 | 8.22 | 1.03 |
time (sec) |
N/A | 0.306 | 0.818 | 29.983 | 0.029 | 0.107 | 0.000 | 0.147 | 0.224 | 0.918 |
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 | 59 | 52 | 52 | 53 | 53 | 117 | 0 | 57 | 378 | 57 |
N.S. |
1 | 0.88 | 0.88 | 0.90 | 0.90 | 1.98 | 0.00 | 0.97 | 6.41 | 0.97 |
time (sec) |
N/A | 0.267 | 0.096 | 7.482 | 0.050 | 0.103 | 0.000 | 0.142 | 0.222 | 0.713 |
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 | 18 | 18 | 18 | 19 | 18 | 59 | 0 | 19 | 66 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 3.28 | 0.00 | 1.06 | 3.67 | 1.00 |
time (sec) |
N/A | 0.220 | 0.012 | 1.561 | 0.032 | 0.097 | 0.000 | 0.148 | 0.207 | 0.723 |
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 | 93 | 158 | 143 | 120 | 141 | 119 | 0 | 168 | 174 | 156 |
N.S. |
1 | 1.70 | 1.54 | 1.29 | 1.52 | 1.28 | 0.00 | 1.81 | 1.87 | 1.68 |
time (sec) |
N/A | 0.384 | 0.384 | 2.063 | 0.116 | 0.101 | 0.000 | 0.144 | 0.180 | 0.948 |
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 | 152 | 245 | 225 | 197 | 271 | 208 | 0 | 277 | 353 | 318 |
N.S. |
1 | 1.61 | 1.48 | 1.30 | 1.78 | 1.37 | 0.00 | 1.82 | 2.32 | 2.09 |
time (sec) |
N/A | 0.477 | 0.819 | 8.100 | 0.132 | 0.111 | 0.000 | 0.153 | 0.164 | 1.254 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 150 | 321 | 269 | 361 | 259 | 0 | 278 | 549 | 724 |
N.S. |
1 | 1.07 | 2.29 | 1.92 | 2.58 | 1.85 | 0.00 | 1.99 | 3.92 | 5.17 |
time (sec) |
N/A | 1.007 | 1.583 | 15.611 | 0.130 | 0.173 | 0.000 | 0.270 | 0.160 | 2.543 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 80 | 109 | 129 | 163 | 191 | 0 | 136 | 113 | 310 |
N.S. |
1 | 1.01 | 1.38 | 1.63 | 2.06 | 2.42 | 0.00 | 1.72 | 1.43 | 3.92 |
time (sec) |
N/A | 0.503 | 0.332 | 3.850 | 0.124 | 0.118 | 0.000 | 0.215 | 0.165 | 0.943 |
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 | 46 | 46 | 45 | 43 | 80 | 131 | 0 | 74 | 52 | 39 |
N.S. |
1 | 1.00 | 0.98 | 0.93 | 1.74 | 2.85 | 0.00 | 1.61 | 1.13 | 0.85 |
time (sec) |
N/A | 0.227 | 0.087 | 1.074 | 0.124 | 0.096 | 0.000 | 0.199 | 0.196 | 0.771 |
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 | 90 | 83 | 79 | 90 | 142 | 187 | 0 | 118 | 118 | 110 |
N.S. |
1 | 0.92 | 0.88 | 1.00 | 1.58 | 2.08 | 0.00 | 1.31 | 1.31 | 1.22 |
time (sec) |
N/A | 0.504 | 0.352 | 1.349 | 0.109 | 0.103 | 0.000 | 0.204 | 0.159 | 0.863 |
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 | 165 | 151 | 137 | 221 | 379 | 262 | 0 | 286 | 265 | 342 |
N.S. |
1 | 0.92 | 0.83 | 1.34 | 2.30 | 1.59 | 0.00 | 1.73 | 1.61 | 2.07 |
time (sec) |
N/A | 0.949 | 1.071 | 4.009 | 0.140 | 0.104 | 0.000 | 0.227 | 0.163 | 3.696 |
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 | 178 | 156 | 229 | 201 | 186 | 386 | 0 | 242 | 7571 | 258 |
N.S. |
1 | 0.88 | 1.29 | 1.13 | 1.04 | 2.17 | 0.00 | 1.36 | 42.53 | 1.45 |
time (sec) |
N/A | 0.365 | 1.642 | 254.471 | 0.039 | 0.122 | 0.000 | 0.203 | 0.210 | 0.762 |
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 | 116 | 100 | 122 | 114 | 115 | 281 | 0 | 137 | 3952 | 130 |
N.S. |
1 | 0.86 | 1.05 | 0.98 | 0.99 | 2.42 | 0.00 | 1.18 | 34.07 | 1.12 |
time (sec) |
N/A | 0.311 | 1.992 | 58.227 | 0.047 | 0.107 | 0.000 | 0.188 | 0.214 | 0.717 |
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 | 61 | 51 | 51 | 57 | 60 | 178 | 0 | 62 | 1477 | 67 |
N.S. |
1 | 0.84 | 0.84 | 0.93 | 0.98 | 2.92 | 0.00 | 1.02 | 24.21 | 1.10 |
time (sec) |
N/A | 0.269 | 0.078 | 15.566 | 0.039 | 0.102 | 0.000 | 0.178 | 0.222 | 0.727 |
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 | 20 | 20 | 32 | 21 | 20 | 57 | 0 | 20 | 169 | 20 |
N.S. |
1 | 1.00 | 1.60 | 1.05 | 1.00 | 2.85 | 0.00 | 1.00 | 8.45 | 1.00 |
time (sec) |
N/A | 0.223 | 0.100 | 3.419 | 0.036 | 0.094 | 0.000 | 0.169 | 0.215 | 0.697 |
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 | 152 | 210 | 304 | 154 | 282 | 279 | 0 | 269 | 480 | 246 |
N.S. |
1 | 1.38 | 2.00 | 1.01 | 1.86 | 1.84 | 0.00 | 1.77 | 3.16 | 1.62 |
time (sec) |
N/A | 0.432 | 2.738 | 4.225 | 0.115 | 0.108 | 0.000 | 0.201 | 0.216 | 1.083 |
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 | 235 | 322 | 416 | 248 | 502 | 424 | 0 | 400 | 752 | 463 |
N.S. |
1 | 1.37 | 1.77 | 1.06 | 2.14 | 1.80 | 0.00 | 1.70 | 3.20 | 1.97 |
time (sec) |
N/A | 0.548 | 2.205 | 16.877 | 0.128 | 0.124 | 0.000 | 0.193 | 0.240 | 1.933 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | A | F | B | B | B |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 222 | 747 | 454 | 827 | 472 | 0 | 530 | 6643 | 2654 |
N.S. |
1 | 0.87 | 2.93 | 1.78 | 3.24 | 1.85 | 0.00 | 2.08 | 26.05 | 10.41 |
time (sec) |
N/A | 0.521 | 6.210 | 150.115 | 0.139 | 0.235 | 0.000 | 0.302 | 0.247 | 3.697 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | B | F | A | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 161 | 709 | 259 | 471 | 355 | 0 | 280 | 2966 | 585 |
N.S. |
1 | 0.88 | 3.85 | 1.41 | 2.56 | 1.93 | 0.00 | 1.52 | 16.12 | 3.18 |
time (sec) |
N/A | 0.406 | 6.410 | 30.712 | 0.143 | 0.138 | 0.000 | 0.278 | 0.187 | 2.205 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 104 | 120 | 135 | 212 | 293 | 0 | 166 | 1912 | 383 |
N.S. |
1 | 1.14 | 1.32 | 1.48 | 2.33 | 3.22 | 0.00 | 1.82 | 21.01 | 4.21 |
time (sec) |
N/A | 0.342 | 0.807 | 7.899 | 0.116 | 0.127 | 0.000 | 0.274 | 0.194 | 1.326 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 103 | 78 | 118 | 182 | 215 | 0 | 138 | 186 | 136 |
N.S. |
1 | 1.26 | 0.95 | 1.44 | 2.22 | 2.62 | 0.00 | 1.68 | 2.27 | 1.66 |
time (sec) |
N/A | 0.310 | 0.372 | 1.922 | 0.123 | 0.090 | 0.000 | 0.245 | 0.177 | 1.053 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 173 | 153 | 172 | 348 | 302 | 0 | 286 | 403 | 286 |
N.S. |
1 | 1.10 | 0.97 | 1.10 | 2.22 | 1.92 | 0.00 | 1.82 | 2.57 | 1.82 |
time (sec) |
N/A | 0.383 | 0.574 | 2.324 | 0.130 | 0.103 | 0.000 | 0.268 | 0.153 | 3.090 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 241 | 273 | 249 | 320 | 772 | 418 | 0 | 438 | 654 | 674 |
N.S. |
1 | 1.13 | 1.03 | 1.33 | 3.20 | 1.73 | 0.00 | 1.82 | 2.71 | 2.80 |
time (sec) |
N/A | 0.536 | 1.096 | 8.433 | 0.166 | 0.124 | 0.000 | 0.286 | 0.176 | 4.413 |
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 | 185 | 160 | 272 | 195 | 200 | 476 | 0 | 220 | 13621 | 234 |
N.S. |
1 | 0.86 | 1.47 | 1.05 | 1.08 | 2.57 | 0.00 | 1.19 | 73.63 | 1.26 |
time (sec) |
N/A | 0.409 | 0.935 | 0.820 | 0.033 | 0.140 | 0.000 | 0.229 | 0.210 | 0.762 |
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 | 121 | 102 | 140 | 115 | 128 | 354 | 0 | 123 | 7160 | 143 |
N.S. |
1 | 0.84 | 1.16 | 0.95 | 1.06 | 2.93 | 0.00 | 1.02 | 59.17 | 1.18 |
time (sec) |
N/A | 0.318 | 2.422 | 164.796 | 0.060 | 0.122 | 0.000 | 0.219 | 0.218 | 0.719 |
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 | 69 | 57 | 57 | 63 | 78 | 284 | 0 | 65 | 3133 | 80 |
N.S. |
1 | 0.83 | 0.83 | 0.91 | 1.13 | 4.12 | 0.00 | 0.94 | 45.41 | 1.16 |
time (sec) |
N/A | 0.280 | 0.176 | 36.720 | 0.045 | 0.109 | 0.000 | 0.209 | 0.189 | 0.720 |
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 | 22 | 22 | 22 | 21 | 20 | 142 | 0 | 20 | 65 | 39 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.91 | 6.45 | 0.00 | 0.91 | 2.95 | 1.77 |
time (sec) |
N/A | 0.225 | 0.116 | 7.442 | 0.037 | 0.095 | 0.000 | 0.194 | 0.187 | 0.678 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | F(-2) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 263 | 458 | 219 | 458 | 503 | 0 | 369 | 1303 | 419 |
N.S. |
1 | 1.30 | 2.27 | 1.08 | 2.27 | 2.49 | 0.00 | 1.83 | 6.45 | 2.07 |
time (sec) |
N/A | 0.505 | 6.196 | 10.330 | 0.159 | 0.120 | 0.000 | 0.228 | 0.185 | 1.701 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | F(-2) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 295 | 386 | 596 | 312 | 738 | 671 | 0 | 613 | 1475 | 715 |
N.S. |
1 | 1.31 | 2.02 | 1.06 | 2.50 | 2.27 | 0.00 | 2.08 | 5.00 | 2.42 |
time (sec) |
N/A | 0.623 | 6.165 | 41.042 | 0.150 | 0.175 | 0.000 | 0.244 | 0.341 | 2.587 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | B | F | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 223 | 688 | 444 | 902 | 564 | 0 | 510 | 10737 | 1203 |
N.S. |
1 | 0.87 | 2.68 | 1.73 | 3.51 | 2.19 | 0.00 | 1.98 | 41.78 | 4.68 |
time (sec) |
N/A | 0.482 | 2.083 | 291.074 | 0.144 | 0.180 | 0.000 | 0.397 | 0.230 | 4.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | F | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 164 | 396 | 269 | 518 | 513 | 0 | 314 | 7694 | 1311 |
N.S. |
1 | 1.11 | 2.68 | 1.82 | 3.50 | 3.47 | 0.00 | 2.12 | 51.99 | 8.86 |
time (sec) |
N/A | 0.399 | 2.219 | 93.885 | 0.140 | 0.144 | 0.000 | 0.383 | 0.228 | 2.870 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | B | B | F | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 117 | 132 | 191 | 326 | 294 | 0 | 221 | 2842 | 260 |
N.S. |
1 | 1.23 | 1.39 | 2.01 | 3.43 | 3.09 | 0.00 | 2.33 | 29.92 | 2.74 |
time (sec) |
N/A | 0.325 | 0.280 | 16.752 | 0.132 | 0.099 | 0.000 | 0.347 | 0.179 | 3.030 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 170 | 110 | 280 | 412 | 352 | 0 | 293 | 5579 | 443 |
N.S. |
1 | 1.10 | 0.71 | 1.81 | 2.66 | 2.27 | 0.00 | 1.89 | 35.99 | 2.86 |
time (sec) |
N/A | 0.362 | 0.959 | 3.502 | 0.129 | 0.105 | 0.000 | 0.320 | 0.174 | 1.895 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 250 | 183 | 283 | 658 | 480 | 0 | 399 | 1025 | 610 |
N.S. |
1 | 1.13 | 0.83 | 1.28 | 2.98 | 2.17 | 0.00 | 1.81 | 4.64 | 2.76 |
time (sec) |
N/A | 0.491 | 1.550 | 4.958 | 0.141 | 0.119 | 0.000 | 0.380 | 0.175 | 4.513 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 310 | 359 | 371 | 457 | 1229 | 619 | 0 | 640 | 1324 | 1128 |
N.S. |
1 | 1.16 | 1.20 | 1.47 | 3.96 | 2.00 | 0.00 | 2.06 | 4.27 | 3.64 |
time (sec) |
N/A | 0.636 | 1.736 | 24.188 | 0.199 | 0.142 | 0.000 | 0.407 | 0.218 | 6.238 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 123 | 69 | 225 | 0 | 145 | 0 | 0 | 51 | 0 |
N.S. |
1 | 1.02 | 0.57 | 1.86 | 0.00 | 1.20 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.625 | 0.725 | 45.288 | 0.000 | 0.102 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 93 | 58 | 103 | 0 | 123 | 0 | 0 | 51 | 0 |
N.S. |
1 | 1.01 | 0.63 | 1.12 | 0.00 | 1.34 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.473 | 0.494 | 37.912 | 0.000 | 0.118 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 89 | 58 | 199 | 0 | 120 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.01 | 0.66 | 2.26 | 0.00 | 1.36 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.464 | 0.407 | 12.400 | 0.000 | 0.105 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 42 | 83 | 0 | 74 | 0 | 0 | 29 | 39 |
N.S. |
1 | 1.00 | 0.72 | 1.43 | 0.00 | 1.28 | 0.00 | 0.00 | 0.50 | 0.67 |
time (sec) |
N/A | 0.345 | 0.334 | 9.277 | 0.000 | 0.092 | 0.000 | 0.000 | 0.168 | 0.387 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 54 | 193 | 0 | 89 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.00 | 0.93 | 3.33 | 0.00 | 1.53 | 0.00 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 0.351 | 0.363 | 8.906 | 0.000 | 0.088 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 95 | 69 | 103 | 0 | 103 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.01 | 0.73 | 1.10 | 0.00 | 1.10 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.463 | 0.336 | 10.365 | 0.000 | 0.095 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 95 | 74 | 209 | 0 | 111 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.01 | 0.79 | 2.22 | 0.00 | 1.18 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.450 | 0.666 | 19.632 | 0.000 | 0.102 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 131 | 94 | 117 | 0 | 118 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.07 | 0.76 | 0.95 | 0.00 | 0.96 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.574 | 0.531 | 21.794 | 0.000 | 0.110 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 139 | 127 | 204 | 0 | 172 | 0 | 0 | 86 | 0 |
N.S. |
1 | 0.97 | 0.89 | 1.43 | 0.00 | 1.20 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.708 | 1.186 | 165.453 | 0.000 | 0.092 | 0.000 | 0.000 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 135 | 126 | 392 | 0 | 171 | 0 | 0 | 78 | 0 |
N.S. |
1 | 0.94 | 0.88 | 2.74 | 0.00 | 1.20 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.723 | 0.946 | 23.286 | 0.000 | 0.097 | 0.000 | 0.000 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 104 | 87 | 163 | 0 | 133 | 0 | 0 | 55 | 0 |
N.S. |
1 | 1.01 | 0.84 | 1.58 | 0.00 | 1.29 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.545 | 0.888 | 15.451 | 0.000 | 0.095 | 0.000 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 95 | 64 | 377 | 0 | 122 | 0 | 0 | 87 | 0 |
N.S. |
1 | 1.00 | 0.67 | 3.97 | 0.00 | 1.28 | 0.00 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 0.554 | 1.480 | 14.792 | 0.000 | 0.087 | 0.000 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 132 | 101 | 187 | 0 | 131 | 0 | 0 | 87 | 0 |
N.S. |
1 | 0.95 | 0.73 | 1.35 | 0.00 | 0.94 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.698 | 1.390 | 15.512 | 0.000 | 0.098 | 0.000 | 0.000 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 141 | 92 | 398 | 0 | 139 | 0 | 0 | 87 | 0 |
N.S. |
1 | 0.97 | 0.63 | 2.74 | 0.00 | 0.96 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.734 | 1.692 | 25.415 | 0.000 | 0.127 | 0.000 | 0.000 | 0.235 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 177 | 127 | 212 | 0 | 154 | 0 | 0 | 87 | 0 |
N.S. |
1 | 0.96 | 0.69 | 1.15 | 0.00 | 0.84 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.899 | 2.846 | 26.705 | 0.000 | 0.117 | 0.000 | 0.000 | 0.218 | 0.000 |