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 | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 166 | 159 | 0 | 0 | 0 | 0 | 0 | 153 | 0 |
N.S. |
1 | 0.86 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.535 | 0.249 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 159 | 133 | 0 | 0 | 0 | 0 | 0 | 157 | 0 |
N.S. |
1 | 0.85 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.548 | 0.231 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 162 | 154 | 0 | 0 | 0 | 0 | 0 | 1039 | 0 |
N.S. |
1 | 0.84 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 5.36 | 0.00 |
time (sec) |
N/A | 0.577 | 0.294 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.179 | 0.000 |
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 | 66 | 58 | 39 | 75 | 101 | 101 | 109 | 101 | 76 | 101 |
N.S. |
1 | 0.88 | 0.59 | 1.14 | 1.53 | 1.53 | 1.65 | 1.53 | 1.15 | 1.53 |
time (sec) |
N/A | 0.307 | 0.012 | 0.328 | 0.030 | 0.066 | 0.048 | 0.114 | 0.146 | 29.170 |
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 | 52 | 47 | 31 | 69 | 92 | 92 | 100 | 92 | 68 | 92 |
N.S. |
1 | 0.90 | 0.60 | 1.33 | 1.77 | 1.77 | 1.92 | 1.77 | 1.31 | 1.77 |
time (sec) |
N/A | 0.281 | 0.008 | 0.325 | 0.028 | 0.066 | 0.046 | 0.117 | 0.148 | 0.048 |
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 | 35 | 33 | 23 | 45 | 59 | 59 | 63 | 59 | 44 | 59 |
N.S. |
1 | 0.94 | 0.66 | 1.29 | 1.69 | 1.69 | 1.80 | 1.69 | 1.26 | 1.69 |
time (sec) |
N/A | 0.257 | 0.008 | 0.298 | 0.032 | 0.086 | 0.040 | 0.121 | 0.141 | 0.033 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 37 | 16 | 47 | 47 | 48 | 47 | 35 | 47 |
N.S. |
1 | 1.00 | 2.18 | 0.94 | 2.76 | 2.76 | 2.82 | 2.76 | 2.06 | 2.76 |
time (sec) |
N/A | 0.222 | 0.009 | 0.289 | 0.032 | 0.065 | 0.037 | 0.125 | 0.143 | 0.029 |
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 | 36 | 44 | 38 | 32 | 33 | 37 | 36 | 44 | 35 | 33 |
N.S. |
1 | 1.22 | 1.06 | 0.89 | 0.92 | 1.03 | 1.00 | 1.22 | 0.97 | 0.92 |
time (sec) |
N/A | 0.244 | 0.007 | 0.257 | 0.031 | 0.095 | 0.066 | 0.111 | 0.145 | 0.063 |
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 | 13 | 13 | 25 | 13 | 19 | 19 | 17 | 12 | 32 | 12 |
N.S. |
1 | 1.00 | 1.92 | 1.00 | 1.46 | 1.46 | 1.31 | 0.92 | 2.46 | 0.92 |
time (sec) |
N/A | 0.228 | 0.007 | 0.286 | 0.031 | 0.066 | 0.089 | 0.120 | 0.143 | 28.410 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 16 | 41 | 41 | 42 | 15 | 31 | 40 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 2.28 | 2.28 | 2.33 | 0.83 | 1.72 | 2.22 |
time (sec) |
N/A | 0.211 | 0.008 | 0.280 | 0.031 | 0.082 | 0.109 | 0.119 | 0.145 | 27.572 |
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 | 87 | 76 | 52 | 65 | 102 | 147 | 99 | 68 | 181 | 83 |
N.S. |
1 | 0.87 | 0.60 | 0.75 | 1.17 | 1.69 | 1.14 | 0.78 | 2.08 | 0.95 |
time (sec) |
N/A | 0.293 | 0.015 | 0.301 | 0.029 | 0.098 | 0.239 | 0.121 | 0.151 | 0.111 |
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 | 122 | 105 | 80 | 92 | 130 | 191 | 129 | 91 | 233 | 111 |
N.S. |
1 | 0.86 | 0.66 | 0.75 | 1.07 | 1.57 | 1.06 | 0.75 | 1.91 | 0.91 |
time (sec) |
N/A | 0.329 | 0.018 | 0.312 | 0.034 | 0.071 | 0.297 | 0.129 | 0.143 | 28.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 72 | 0 | 0 | 0 | 0 | 0 | 720 | 0 |
N.S. |
1 | 1.00 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 11.43 | 0.00 |
time (sec) |
N/A | 0.283 | 0.017 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.149 | 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 | 127 | 128 | 107 | 123 | 182 | 137 | 547 | 124 | 177 | 220 |
N.S. |
1 | 1.01 | 0.84 | 0.97 | 1.43 | 1.08 | 4.31 | 0.98 | 1.39 | 1.73 |
time (sec) |
N/A | 0.301 | 0.148 | 0.547 | 0.113 | 0.083 | 1.180 | 0.124 | 0.145 | 0.128 |
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 | 105 | 104 | 91 | 107 | 136 | 114 | 374 | 101 | 139 | 174 |
N.S. |
1 | 0.99 | 0.87 | 1.02 | 1.30 | 1.09 | 3.56 | 0.96 | 1.32 | 1.66 |
time (sec) |
N/A | 0.281 | 0.132 | 0.454 | 0.116 | 0.078 | 0.995 | 0.129 | 0.152 | 0.049 |
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 | 83 | 80 | 75 | 91 | 90 | 93 | 224 | 78 | 101 | 128 |
N.S. |
1 | 0.96 | 0.90 | 1.10 | 1.08 | 1.12 | 2.70 | 0.94 | 1.22 | 1.54 |
time (sec) |
N/A | 0.263 | 0.108 | 0.391 | 0.109 | 0.081 | 0.839 | 0.118 | 0.147 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 54 | 57 | 64 | 45 | 62 | 94 | 46 | 61 | 80 |
N.S. |
1 | 0.98 | 1.04 | 1.16 | 0.82 | 1.13 | 1.71 | 0.84 | 1.11 | 1.45 |
time (sec) |
N/A | 0.242 | 0.097 | 0.332 | 0.104 | 0.081 | 1.320 | 0.130 | 0.153 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 27 | 28 | 0 | 31 | 0 | 37 | 26 | 46 |
N.S. |
1 | 1.00 | 1.69 | 1.75 | 0.00 | 1.94 | 0.00 | 2.31 | 1.62 | 2.88 |
time (sec) |
N/A | 0.217 | 0.010 | 0.502 | 0.000 | 0.073 | 0.000 | 0.126 | 0.144 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 51 | 43 | 42 | 0 | 87 | 0 | 0 | 70 | 48 |
N.S. |
1 | 0.94 | 0.80 | 0.78 | 0.00 | 1.61 | 0.00 | 0.00 | 1.30 | 0.89 |
time (sec) |
N/A | 0.242 | 0.015 | 0.529 | 0.000 | 0.085 | 0.000 | 0.000 | 0.148 | 26.915 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 75 | 59 | 58 | 0 | 141 | 0 | 0 | 139 | 64 |
N.S. |
1 | 0.99 | 0.78 | 0.76 | 0.00 | 1.86 | 0.00 | 0.00 | 1.83 | 0.84 |
time (sec) |
N/A | 0.266 | 0.025 | 0.612 | 0.000 | 0.081 | 0.000 | 0.000 | 0.146 | 27.151 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 99 | 75 | 74 | 0 | 197 | 0 | 0 | 208 | 145 |
N.S. |
1 | 1.01 | 0.77 | 0.76 | 0.00 | 2.01 | 0.00 | 0.00 | 2.12 | 1.48 |
time (sec) |
N/A | 0.275 | 0.029 | 0.720 | 0.000 | 0.092 | 0.000 | 0.000 | 0.150 | 27.398 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 123 | 91 | 90 | 0 | 249 | 0 | 0 | 279 | 177 |
N.S. |
1 | 1.02 | 0.76 | 0.75 | 0.00 | 2.08 | 0.00 | 0.00 | 2.32 | 1.48 |
time (sec) |
N/A | 0.286 | 0.034 | 0.881 | 0.000 | 0.115 | 0.000 | 0.000 | 0.151 | 27.293 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 55 | 50 | 67 | 63 | 80 | 0 | 0 | 29 | 52 |
N.S. |
1 | 0.66 | 0.60 | 0.81 | 0.76 | 0.96 | 0.00 | 0.00 | 0.35 | 0.63 |
time (sec) |
N/A | 0.446 | 0.037 | 0.332 | 0.048 | 0.093 | 0.000 | 0.000 | 0.149 | 27.416 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 46 | 42 | 38 | 41 | 50 | 0 | 17 | 13 | 0 |
N.S. |
1 | 0.62 | 0.57 | 0.51 | 0.55 | 0.68 | 0.00 | 0.23 | 0.18 | 0.00 |
time (sec) |
N/A | 0.453 | 0.017 | 0.322 | 0.037 | 0.086 | 0.000 | 0.118 | 0.140 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 46 | 42 | 38 | 41 | 50 | 0 | 17 | 13 | 0 |
N.S. |
1 | 0.62 | 0.57 | 0.51 | 0.55 | 0.68 | 0.00 | 0.23 | 0.18 | 0.00 |
time (sec) |
N/A | 0.405 | 0.016 | 0.325 | 0.041 | 0.079 | 0.000 | 0.116 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 40 | 35 | 48 | 47 | 0 | 14 | 11 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.80 | 1.09 | 1.07 | 0.00 | 0.32 | 0.25 | 0.00 |
time (sec) |
N/A | 0.322 | 0.012 | 0.318 | 0.041 | 0.080 | 0.000 | 0.113 | 0.142 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 37 | 37 | 35 | 0 | 262 | 0 | 14 | 10 | 0 |
N.S. |
1 | 0.56 | 0.56 | 0.53 | 0.00 | 3.97 | 0.00 | 0.21 | 0.15 | 0.00 |
time (sec) |
N/A | 0.429 | 0.014 | 0.324 | 0.000 | 0.108 | 0.000 | 0.129 | 0.143 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 41 | 41 | 39 | 0 | 264 | 0 | 14 | 14 | 0 |
N.S. |
1 | 0.59 | 0.59 | 0.57 | 0.00 | 3.83 | 0.00 | 0.20 | 0.20 | 0.00 |
time (sec) |
N/A | 0.449 | 0.013 | 0.325 | 0.000 | 0.101 | 0.000 | 0.117 | 0.141 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 62 | 57 | 53 | 0 | 68 | 0 | 35 | 28 | 0 |
N.S. |
1 | 0.68 | 0.63 | 0.58 | 0.00 | 0.75 | 0.00 | 0.38 | 0.31 | 0.00 |
time (sec) |
N/A | 0.363 | 0.020 | 0.335 | 0.000 | 0.075 | 0.000 | 0.107 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 77 | 60 | 71 | 0 | 98 | 0 | 65 | 46 | 0 |
N.S. |
1 | 0.55 | 0.43 | 0.51 | 0.00 | 0.70 | 0.00 | 0.46 | 0.33 | 0.00 |
time (sec) |
N/A | 0.386 | 0.030 | 0.333 | 0.000 | 0.076 | 0.000 | 0.126 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 92 | 68 | 87 | 0 | 120 | 0 | 87 | 62 | 0 |
N.S. |
1 | 0.49 | 0.36 | 0.47 | 0.00 | 0.64 | 0.00 | 0.47 | 0.33 | 0.00 |
time (sec) |
N/A | 0.396 | 0.033 | 0.355 | 0.000 | 0.081 | 0.000 | 0.109 | 0.141 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 234 | 107 | 76 | 103 | 0 | 142 | 0 | 109 | 78 | 0 |
N.S. |
1 | 0.46 | 0.32 | 0.44 | 0.00 | 0.61 | 0.00 | 0.47 | 0.33 | 0.00 |
time (sec) |
N/A | 0.407 | 0.039 | 0.355 | 0.000 | 0.103 | 0.000 | 0.179 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 39 | 40 | 13 | 227 | 0 | 0 | 15 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 0.33 | 5.82 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.336 | 0.016 | 0.329 | 0.037 | 0.106 | 0.000 | 0.000 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 59 | 59 | 77 | 50 | 343 | 0 | 47 | 55 | 0 |
N.S. |
1 | 0.66 | 0.66 | 0.86 | 0.56 | 3.81 | 0.00 | 0.52 | 0.61 | 0.00 |
time (sec) |
N/A | 0.375 | 0.030 | 0.333 | 0.040 | 0.098 | 0.000 | 0.142 | 0.141 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 88 | 83 | 155 | 83 | 451 | 0 | 0 | 138 | 0 |
N.S. |
1 | 0.48 | 0.45 | 0.85 | 0.45 | 2.46 | 0.00 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 0.412 | 0.046 | 0.343 | 0.044 | 0.110 | 0.000 | 0.000 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 276 | 117 | 101 | 227 | 135 | 565 | 0 | 0 | 225 | 0 |
N.S. |
1 | 0.42 | 0.37 | 0.82 | 0.49 | 2.05 | 0.00 | 0.00 | 0.82 | 0.00 |
time (sec) |
N/A | 0.431 | 0.051 | 0.345 | 0.046 | 0.109 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 111 | 115 | 0 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 0.81 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.456 | 0.043 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 91 | 77 | 0 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.07 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.348 | 0.061 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 91 | 75 | 0 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.08 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.350 | 0.052 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 60 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.280 | 0.023 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 59 | 56 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.05 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.240 | 0.023 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 75 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.314 | 0.025 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 74 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.313 | 0.023 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 119 | 105 | 0 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 0.89 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.495 | 0.101 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 119 | 103 | 0 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 0.89 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.496 | 0.099 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 86 | 88 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 0.90 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.403 | 0.042 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 86 | 83 | 0 | 0 | 0 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.04 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.353 | 0.034 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 101 | 103 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 0.91 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.455 | 0.047 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 102 | 102 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 0.91 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.456 | 0.048 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.149 | 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 | 73 | 65 | 39 | 61 | 81 | 81 | 87 | 78 | 60 | 81 |
N.S. |
1 | 0.89 | 0.53 | 0.84 | 1.11 | 1.11 | 1.19 | 1.07 | 0.82 | 1.11 |
time (sec) |
N/A | 0.281 | 0.010 | 0.265 | 0.032 | 0.069 | 0.037 | 0.118 | 0.146 | 0.046 |
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 | 55 | 50 | 31 | 52 | 69 | 69 | 70 | 66 | 52 | 69 |
N.S. |
1 | 0.91 | 0.56 | 0.95 | 1.25 | 1.25 | 1.27 | 1.20 | 0.95 | 1.25 |
time (sec) |
N/A | 0.265 | 0.009 | 0.252 | 0.033 | 0.069 | 0.033 | 0.126 | 0.143 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 35 | 32 | 29 | 37 | 37 | 36 | 54 | 28 | 37 |
N.S. |
1 | 0.95 | 0.86 | 0.78 | 1.00 | 1.00 | 0.97 | 1.46 | 0.76 | 1.00 |
time (sec) |
N/A | 0.254 | 0.008 | 0.249 | 0.024 | 0.104 | 0.030 | 0.149 | 0.140 | 0.050 |
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 | 16 | 16 | 20 | 14 | 20 | 20 | 19 | 34 | 17 | 17 |
N.S. |
1 | 1.00 | 1.25 | 0.88 | 1.25 | 1.25 | 1.19 | 2.12 | 1.06 | 1.06 |
time (sec) |
N/A | 0.206 | 0.005 | 0.211 | 0.025 | 0.063 | 0.028 | 0.110 | 0.148 | 0.036 |
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 | 15 | 15 | 18 | 13 | 14 | 14 | 12 | 15 | 12 | 13 |
N.S. |
1 | 1.00 | 1.20 | 0.87 | 0.93 | 0.93 | 0.80 | 1.00 | 0.80 | 0.87 |
time (sec) |
N/A | 0.228 | 0.010 | 0.256 | 0.031 | 0.067 | 0.054 | 0.132 | 0.151 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 44 | 33 | 51 | 63 | 76 | 56 | 55 | 93 | 47 |
N.S. |
1 | 0.90 | 0.67 | 1.04 | 1.29 | 1.55 | 1.14 | 1.12 | 1.90 | 0.96 |
time (sec) |
N/A | 0.270 | 0.012 | 0.273 | 0.031 | 0.077 | 0.143 | 0.121 | 0.142 | 27.529 |
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 | 84 | 73 | 61 | 76 | 91 | 121 | 83 | 97 | 145 | 72 |
N.S. |
1 | 0.87 | 0.73 | 0.90 | 1.08 | 1.44 | 0.99 | 1.15 | 1.73 | 0.86 |
time (sec) |
N/A | 0.293 | 0.022 | 0.279 | 0.030 | 0.076 | 0.207 | 0.116 | 0.147 | 27.564 |
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 | 119 | 102 | 80 | 92 | 140 | 217 | 143 | 122 | 269 | 120 |
N.S. |
1 | 0.86 | 0.67 | 0.77 | 1.18 | 1.82 | 1.20 | 1.03 | 2.26 | 1.01 |
time (sec) |
N/A | 0.329 | 0.022 | 0.290 | 0.034 | 0.094 | 0.300 | 0.150 | 0.144 | 27.279 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 192 | 96 | 97 | 117 | 184 | 0 | 0 | 100 | 0 |
N.S. |
1 | 1.36 | 0.68 | 0.69 | 0.83 | 1.30 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.519 | 0.098 | 0.400 | 0.114 | 0.112 | 0.000 | 0.000 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 160 | 88 | 89 | 93 | 168 | 0 | 221 | 81 | 0 |
N.S. |
1 | 1.24 | 0.68 | 0.69 | 0.72 | 1.30 | 0.00 | 1.71 | 0.63 | 0.00 |
time (sec) |
N/A | 0.473 | 0.073 | 0.375 | 0.112 | 0.089 | 0.000 | 0.154 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 120 | 80 | 80 | 70 | 150 | 0 | 174 | 62 | 0 |
N.S. |
1 | 1.21 | 0.81 | 0.81 | 0.71 | 1.52 | 0.00 | 1.76 | 0.63 | 0.00 |
time (sec) |
N/A | 0.378 | 0.060 | 0.366 | 0.109 | 0.086 | 0.000 | 0.184 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 94 | 99 | 69 | 47 | 134 | 0 | 126 | 43 | 0 |
N.S. |
1 | 1.22 | 1.29 | 0.90 | 0.61 | 1.74 | 0.00 | 1.64 | 0.56 | 0.00 |
time (sec) |
N/A | 0.307 | 0.051 | 0.342 | 0.113 | 0.090 | 0.000 | 0.148 | 0.143 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 83 | 99 | 120 | 0 | 184 | 0 | 124 | 32 | 0 |
N.S. |
1 | 1.06 | 1.27 | 1.54 | 0.00 | 2.36 | 0.00 | 1.59 | 0.41 | 0.00 |
time (sec) |
N/A | 0.423 | 0.061 | 0.336 | 0.000 | 0.101 | 0.000 | 0.147 | 0.143 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 90 | 106 | 100 | 0 | 201 | 0 | 168 | 39 | 0 |
N.S. |
1 | 1.10 | 1.29 | 1.22 | 0.00 | 2.45 | 0.00 | 2.05 | 0.48 | 0.00 |
time (sec) |
N/A | 0.427 | 0.065 | 0.366 | 0.000 | 0.099 | 0.000 | 0.140 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 87 | 76 | 79 | 0 | 137 | 0 | 152 | 52 | 0 |
N.S. |
1 | 1.12 | 0.97 | 1.01 | 0.00 | 1.76 | 0.00 | 1.95 | 0.67 | 0.00 |
time (sec) |
N/A | 0.403 | 0.093 | 0.382 | 0.000 | 0.083 | 0.000 | 0.136 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 114 | 82 | 86 | 0 | 153 | 0 | 210 | 71 | 0 |
N.S. |
1 | 1.15 | 0.83 | 0.87 | 0.00 | 1.55 | 0.00 | 2.12 | 0.72 | 0.00 |
time (sec) |
N/A | 0.429 | 0.106 | 0.381 | 0.000 | 0.097 | 0.000 | 0.141 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 149 | 95 | 95 | 0 | 169 | 0 | 258 | 90 | 0 |
N.S. |
1 | 1.15 | 0.73 | 0.73 | 0.00 | 1.30 | 0.00 | 1.98 | 0.69 | 0.00 |
time (sec) |
N/A | 0.472 | 0.112 | 0.398 | 0.000 | 0.090 | 0.000 | 0.141 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 120 | 117 | 90 | 130 | 180 | 255 | 224 | 82 | 0 |
N.S. |
1 | 1.20 | 1.17 | 0.90 | 1.30 | 1.80 | 2.55 | 2.24 | 0.82 | 0.00 |
time (sec) |
N/A | 0.325 | 0.097 | 0.332 | 0.109 | 0.090 | 1.732 | 0.153 | 0.143 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 146 | 135 | 106 | 154 | 241 | 325 | 320 | 122 | 0 |
N.S. |
1 | 1.19 | 1.10 | 0.86 | 1.25 | 1.96 | 2.64 | 2.60 | 0.99 | 0.00 |
time (sec) |
N/A | 0.336 | 0.148 | 0.352 | 0.110 | 0.103 | 2.636 | 0.194 | 0.143 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 172 | 151 | 122 | 173 | 286 | 648 | 416 | 160 | 0 |
N.S. |
1 | 1.18 | 1.03 | 0.84 | 1.18 | 1.96 | 4.44 | 2.85 | 1.10 | 0.00 |
time (sec) |
N/A | 0.367 | 0.135 | 0.344 | 0.132 | 0.092 | 3.334 | 0.194 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 66 | 100 | 74 | 40 | 150 | 0 | 107 | 49 | 0 |
N.S. |
1 | 1.02 | 1.54 | 1.14 | 0.62 | 2.31 | 0.00 | 1.65 | 0.75 | 0.00 |
time (sec) |
N/A | 0.276 | 0.068 | 0.303 | 0.113 | 0.085 | 0.000 | 0.145 | 0.143 | 0.000 |
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 | 57 | 63 | 31 | 60 | 47 | 0 | 82 | 54 | 33 |
N.S. |
1 | 0.88 | 0.97 | 0.48 | 0.92 | 0.72 | 0.00 | 1.26 | 0.83 | 0.51 |
time (sec) |
N/A | 0.251 | 0.036 | 0.329 | 0.035 | 0.083 | 0.000 | 0.134 | 0.147 | 26.892 |
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 | 88 | 79 | 47 | 79 | 75 | 0 | 220 | 104 | 56 |
N.S. |
1 | 1.00 | 0.90 | 0.53 | 0.90 | 0.85 | 0.00 | 2.50 | 1.18 | 0.64 |
time (sec) |
N/A | 0.282 | 0.049 | 0.322 | 0.033 | 0.103 | 0.000 | 0.148 | 0.148 | 27.338 |
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 | 111 | 119 | 96 | 64 | 98 | 124 | 0 | 300 | 150 | 133 |
N.S. |
1 | 1.07 | 0.86 | 0.58 | 0.88 | 1.12 | 0.00 | 2.70 | 1.35 | 1.20 |
time (sec) |
N/A | 0.301 | 0.056 | 0.323 | 0.036 | 0.217 | 0.000 | 0.193 | 0.147 | 27.104 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F(-2) | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 172 | 111 | 0 | 0 | 0 | 0 | 0 | 56 | 0 |
N.S. |
1 | 1.00 | 0.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.464 | 0.129 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 54 | 74 | 0 | 0 | 0 | 648 | 0 | 195 | 0 |
N.S. |
1 | 0.82 | 1.12 | 0.00 | 0.00 | 0.00 | 9.82 | 0.00 | 2.95 | 0.00 |
time (sec) |
N/A | 0.276 | 0.023 | 0.000 | 0.000 | 0.000 | 7.670 | 0.000 | 0.150 | 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 | 152 | 170 | 107 | 123 | 154 | 136 | 547 | 126 | 177 | 220 |
N.S. |
1 | 1.12 | 0.70 | 0.81 | 1.01 | 0.89 | 3.60 | 0.83 | 1.16 | 1.45 |
time (sec) |
N/A | 0.356 | 0.157 | 0.625 | 0.114 | 0.076 | 2.440 | 0.153 | 0.149 | 0.132 |
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 | 130 | 146 | 91 | 107 | 108 | 115 | 377 | 102 | 139 | 174 |
N.S. |
1 | 1.12 | 0.70 | 0.82 | 0.83 | 0.88 | 2.90 | 0.78 | 1.07 | 1.34 |
time (sec) |
N/A | 0.329 | 0.127 | 0.490 | 0.108 | 0.084 | 1.862 | 0.135 | 0.143 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 122 | 75 | 91 | 147 | 92 | 228 | 78 | 101 | 128 |
N.S. |
1 | 1.13 | 0.69 | 0.84 | 1.36 | 0.85 | 2.11 | 0.72 | 0.94 | 1.19 |
time (sec) |
N/A | 0.320 | 0.113 | 0.431 | 0.108 | 0.083 | 1.481 | 0.133 | 0.151 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 95 | 70 | 71 | 122 | 63 | 0 | 46 | 61 | 74 |
N.S. |
1 | 1.16 | 0.85 | 0.87 | 1.49 | 0.77 | 0.00 | 0.56 | 0.74 | 0.90 |
time (sec) |
N/A | 0.285 | 0.111 | 0.359 | 0.110 | 0.087 | 0.000 | 0.137 | 0.143 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 29 | 28 | 0 | 55 | 0 | 66 | 90 | 32 |
N.S. |
1 | 1.00 | 1.61 | 1.56 | 0.00 | 3.06 | 0.00 | 3.67 | 5.00 | 1.78 |
time (sec) |
N/A | 0.223 | 0.011 | 0.575 | 0.000 | 0.078 | 0.000 | 0.133 | 0.144 | 26.323 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 43 | 42 | 0 | 89 | 0 | 145 | 96 | 125 |
N.S. |
1 | 1.00 | 0.46 | 0.45 | 0.00 | 0.95 | 0.00 | 1.54 | 1.02 | 1.33 |
time (sec) |
N/A | 0.298 | 0.016 | 0.672 | 0.000 | 0.075 | 0.000 | 0.142 | 0.150 | 26.853 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 118 | 59 | 58 | 0 | 144 | 0 | 0 | 140 | 125 |
N.S. |
1 | 1.02 | 0.51 | 0.50 | 0.00 | 1.24 | 0.00 | 0.00 | 1.21 | 1.08 |
time (sec) |
N/A | 0.324 | 0.021 | 0.808 | 0.000 | 0.083 | 0.000 | 0.000 | 0.150 | 28.737 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 142 | 75 | 74 | 0 | 195 | 0 | 0 | 210 | 156 |
N.S. |
1 | 1.03 | 0.54 | 0.54 | 0.00 | 1.41 | 0.00 | 0.00 | 1.52 | 1.13 |
time (sec) |
N/A | 0.332 | 0.029 | 1.045 | 0.000 | 0.092 | 0.000 | 0.000 | 0.145 | 27.907 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 225 | 81 | 81 | 77 | 0 | 399 | 0 | 62 | 52 | 0 |
N.S. |
1 | 0.36 | 0.36 | 0.34 | 0.00 | 1.77 | 0.00 | 0.28 | 0.23 | 0.00 |
time (sec) |
N/A | 0.531 | 0.031 | 0.348 | 0.000 | 0.111 | 0.000 | 0.118 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 69 | 69 | 68 | 0 | 383 | 0 | 52 | 43 | 0 |
N.S. |
1 | 0.38 | 0.38 | 0.37 | 0.00 | 2.08 | 0.00 | 0.28 | 0.23 | 0.00 |
time (sec) |
N/A | 0.499 | 0.027 | 0.349 | 0.000 | 0.114 | 0.000 | 0.133 | 0.143 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 63 | 63 | 61 | 0 | 367 | 0 | 46 | 36 | 0 |
N.S. |
1 | 0.42 | 0.42 | 0.41 | 0.00 | 2.46 | 0.00 | 0.31 | 0.24 | 0.00 |
time (sec) |
N/A | 0.434 | 0.032 | 0.407 | 0.000 | 0.109 | 0.000 | 0.119 | 0.140 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 53 | 53 | 52 | 0 | 347 | 0 | 36 | 27 | 0 |
N.S. |
1 | 0.48 | 0.48 | 0.47 | 0.00 | 3.15 | 0.00 | 0.33 | 0.25 | 0.00 |
time (sec) |
N/A | 0.367 | 0.021 | 0.343 | 0.000 | 0.107 | 0.000 | 0.123 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 44 | 44 | 42 | 0 | 0 | 0 | 20 | 17 | 0 |
N.S. |
1 | 0.43 | 0.43 | 0.41 | 0.00 | 0.00 | 0.00 | 0.20 | 0.17 | 0.00 |
time (sec) |
N/A | 0.469 | 0.013 | 0.342 | 0.000 | 0.000 | 0.000 | 0.112 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 50 | 50 | 49 | 0 | 0 | 0 | 26 | 24 | 0 |
N.S. |
1 | 0.47 | 0.47 | 0.46 | 0.00 | 0.00 | 0.00 | 0.24 | 0.22 | 0.00 |
time (sec) |
N/A | 0.476 | 0.019 | 0.349 | 0.000 | 0.000 | 0.000 | 0.126 | 0.141 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 62 | 62 | 62 | 0 | 447 | 0 | 37 | 37 | 0 |
N.S. |
1 | 0.42 | 0.42 | 0.42 | 0.00 | 3.02 | 0.00 | 0.25 | 0.25 | 0.00 |
time (sec) |
N/A | 0.476 | 0.024 | 0.345 | 0.000 | 0.146 | 0.000 | 0.127 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 72 | 72 | 70 | 0 | 477 | 0 | 45 | 45 | 0 |
N.S. |
1 | 0.39 | 0.39 | 0.37 | 0.00 | 2.55 | 0.00 | 0.24 | 0.24 | 0.00 |
time (sec) |
N/A | 0.487 | 0.026 | 0.352 | 0.000 | 0.111 | 0.000 | 0.116 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 77 | 77 | 78 | 0 | 503 | 0 | 53 | 53 | 0 |
N.S. |
1 | 0.35 | 0.35 | 0.35 | 0.00 | 2.28 | 0.00 | 0.24 | 0.24 | 0.00 |
time (sec) |
N/A | 0.497 | 0.030 | 0.348 | 0.000 | 0.154 | 0.000 | 0.133 | 0.140 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 94 | 68 | 87 | 0 | 120 | 0 | 87 | 62 | 0 |
N.S. |
1 | 0.50 | 0.36 | 0.46 | 0.00 | 0.63 | 0.00 | 0.46 | 0.33 | 0.00 |
time (sec) |
N/A | 0.418 | 0.033 | 0.360 | 0.000 | 0.092 | 0.000 | 0.131 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 79 | 60 | 87 | 0 | 120 | 0 | 87 | 62 | 0 |
N.S. |
1 | 0.56 | 0.42 | 0.61 | 0.00 | 0.85 | 0.00 | 0.61 | 0.44 | 0.00 |
time (sec) |
N/A | 0.405 | 0.030 | 0.342 | 0.000 | 0.083 | 0.000 | 0.126 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 64 | 52 | 71 | 0 | 98 | 0 | 65 | 46 | 0 |
N.S. |
1 | 0.67 | 0.55 | 0.75 | 0.00 | 1.03 | 0.00 | 0.68 | 0.48 | 0.00 |
time (sec) |
N/A | 0.384 | 0.028 | 0.344 | 0.000 | 0.077 | 0.000 | 0.115 | 0.142 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 58 | 47 | 70 | 67 | 0 | 34 | 28 | 0 |
N.S. |
1 | 1.00 | 1.29 | 1.04 | 1.56 | 1.49 | 0.00 | 0.76 | 0.62 | 0.00 |
time (sec) |
N/A | 0.345 | 0.022 | 0.335 | 0.048 | 0.084 | 0.000 | 0.108 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 54 | 54 | 61 | 33 | 381 | 0 | 0 | 39 | 0 |
N.S. |
1 | 0.66 | 0.66 | 0.74 | 0.40 | 4.65 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.367 | 0.026 | 0.342 | 0.041 | 0.110 | 0.000 | 0.000 | 0.150 | 0.000 |
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 | 46 | 46 | 53 | 38 | 29 | 72 | 0 | 15 | 25 | 58 |
N.S. |
1 | 1.00 | 1.15 | 0.83 | 0.63 | 1.57 | 0.00 | 0.33 | 0.54 | 1.26 |
time (sec) |
N/A | 0.346 | 0.042 | 0.336 | 0.041 | 0.084 | 0.000 | 0.109 | 0.143 | 26.764 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 87 | 73 | 148 | 93 | 461 | 0 | 0 | 139 | 0 |
N.S. |
1 | 0.48 | 0.40 | 0.81 | 0.51 | 2.53 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.410 | 0.045 | 0.345 | 0.043 | 0.122 | 0.000 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 275 | 116 | 101 | 227 | 122 | 559 | 0 | 0 | 223 | 0 |
N.S. |
1 | 0.42 | 0.37 | 0.83 | 0.44 | 2.03 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.439 | 0.056 | 0.349 | 0.046 | 0.117 | 0.000 | 0.000 | 0.144 | 0.000 |