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 | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 87 | 61 | 57 | 72 | 88 | 0 | 128 | 23 | 0 |
N.S. |
1 | 0.90 | 0.63 | 0.59 | 0.74 | 0.91 | 0.00 | 1.32 | 0.24 | 0.00 |
time (sec) |
N/A | 0.273 | 0.519 | 0.849 | 0.028 | 0.078 | 0.000 | 0.156 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 135 | 69 | 75 | 0 | 172 | 0 | 201 | 23 | 0 |
N.S. |
1 | 1.06 | 0.54 | 0.59 | 0.00 | 1.35 | 0.00 | 1.58 | 0.18 | 0.00 |
time (sec) |
N/A | 0.639 | 0.541 | 0.527 | 0.000 | 0.121 | 0.000 | 0.162 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 66 | 51 | 41 | 55 | 68 | 0 | 99 | 23 | 0 |
N.S. |
1 | 0.90 | 0.70 | 0.56 | 0.75 | 0.93 | 0.00 | 1.36 | 0.32 | 0.00 |
time (sec) |
N/A | 0.259 | 0.293 | 0.353 | 0.028 | 0.081 | 0.000 | 0.149 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 99 | 59 | 65 | 0 | 132 | 0 | 147 | 23 | 0 |
N.S. |
1 | 1.04 | 0.62 | 0.68 | 0.00 | 1.39 | 0.00 | 1.55 | 0.24 | 0.00 |
time (sec) |
N/A | 0.482 | 0.262 | 0.278 | 0.000 | 0.098 | 0.000 | 0.160 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 45 | 41 | 31 | 38 | 46 | 0 | 70 | 23 | 0 |
N.S. |
1 | 0.92 | 0.84 | 0.63 | 0.78 | 0.94 | 0.00 | 1.43 | 0.47 | 0.00 |
time (sec) |
N/A | 0.249 | 0.213 | 0.218 | 0.032 | 0.073 | 0.000 | 0.141 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 49 | 55 | 0 | 92 | 0 | 93 | 23 | 0 |
N.S. |
1 | 1.00 | 0.78 | 0.87 | 0.00 | 1.46 | 0.00 | 1.48 | 0.37 | 0.00 |
time (sec) |
N/A | 0.344 | 0.204 | 0.172 | 0.000 | 0.082 | 0.000 | 0.156 | 0.162 | 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 | 24 | 24 | 24 | 21 | 20 | 25 | 58 | 38 | 24 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.83 | 1.04 | 2.42 | 1.58 | 1.00 | 0.83 |
time (sec) |
N/A | 0.203 | 0.107 | 0.087 | 0.031 | 0.086 | 0.150 | 0.148 | 0.244 | 25.674 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 32 | 40 | 32 | 58 | 96 | 0 | 59 | 21 | 0 |
N.S. |
1 | 0.80 | 1.00 | 0.80 | 1.45 | 2.40 | 0.00 | 1.48 | 0.52 | 0.00 |
time (sec) |
N/A | 0.235 | 0.174 | 0.136 | 0.113 | 0.104 | 0.000 | 0.134 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 46 | 83 | 0 | 159 | 0 | 102 | 23 | 0 |
N.S. |
1 | 1.00 | 0.64 | 1.15 | 0.00 | 2.21 | 0.00 | 1.42 | 0.32 | 0.00 |
time (sec) |
N/A | 0.328 | 0.339 | 0.182 | 0.000 | 0.104 | 0.000 | 0.157 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 89 | 42 | 90 | 117 | 99 | 0 | 112 | 23 | 0 |
N.S. |
1 | 0.94 | 0.44 | 0.95 | 1.23 | 1.04 | 0.00 | 1.18 | 0.24 | 0.00 |
time (sec) |
N/A | 0.363 | 0.257 | 0.185 | 0.106 | 0.096 | 0.000 | 0.140 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 142 | 54 | 157 | 0 | 182 | 0 | 178 | 23 | 0 |
N.S. |
1 | 1.04 | 0.39 | 1.15 | 0.00 | 1.33 | 0.00 | 1.30 | 0.17 | 0.00 |
time (sec) |
N/A | 0.560 | 0.325 | 0.199 | 0.000 | 0.090 | 0.000 | 0.160 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 153 | 44 | 118 | 168 | 121 | 0 | 146 | 23 | 0 |
N.S. |
1 | 1.03 | 0.30 | 0.79 | 1.13 | 0.81 | 0.00 | 0.98 | 0.15 | 0.00 |
time (sec) |
N/A | 0.529 | 0.257 | 0.203 | 0.122 | 0.087 | 0.000 | 0.137 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 212 | 61 | 254 | 0 | 204 | 0 | 239 | 23 | 0 |
N.S. |
1 | 1.08 | 0.31 | 1.29 | 0.00 | 1.04 | 0.00 | 1.21 | 0.12 | 0.00 |
time (sec) |
N/A | 0.902 | 0.376 | 0.200 | 0.000 | 0.105 | 0.000 | 0.163 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 87 | 61 | 57 | 72 | 110 | 0 | 132 | 51 | 0 |
N.S. |
1 | 0.90 | 0.63 | 0.59 | 0.74 | 1.13 | 0.00 | 1.36 | 0.53 | 0.00 |
time (sec) |
N/A | 0.272 | 0.410 | 0.856 | 0.029 | 0.094 | 0.000 | 0.153 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 171 | 79 | 87 | 0 | 210 | 0 | 162 | 51 | 0 |
N.S. |
1 | 1.08 | 0.50 | 0.55 | 0.00 | 1.32 | 0.00 | 1.02 | 0.32 | 0.00 |
time (sec) |
N/A | 0.796 | 0.642 | 0.538 | 0.000 | 0.099 | 0.000 | 0.143 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 66 | 51 | 41 | 55 | 88 | 0 | 102 | 51 | 0 |
N.S. |
1 | 0.90 | 0.70 | 0.56 | 0.75 | 1.21 | 0.00 | 1.40 | 0.70 | 0.00 |
time (sec) |
N/A | 0.267 | 0.191 | 0.384 | 0.035 | 0.117 | 0.000 | 0.140 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 135 | 69 | 77 | 0 | 166 | 0 | 132 | 51 | 0 |
N.S. |
1 | 1.06 | 0.54 | 0.61 | 0.00 | 1.31 | 0.00 | 1.04 | 0.40 | 0.00 |
time (sec) |
N/A | 0.635 | 0.178 | 0.297 | 0.000 | 0.102 | 0.000 | 0.137 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 45 | 41 | 31 | 38 | 66 | 252 | 72 | 51 | 0 |
N.S. |
1 | 0.92 | 0.84 | 0.63 | 0.78 | 1.35 | 5.14 | 1.47 | 1.04 | 0.00 |
time (sec) |
N/A | 0.249 | 0.103 | 0.241 | 0.032 | 0.086 | 4.972 | 0.137 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 99 | 59 | 67 | 0 | 122 | 0 | 102 | 51 | 0 |
N.S. |
1 | 1.04 | 0.62 | 0.71 | 0.00 | 1.28 | 0.00 | 1.07 | 0.54 | 0.00 |
time (sec) |
N/A | 0.484 | 0.166 | 0.203 | 0.000 | 0.089 | 0.000 | 0.134 | 0.182 | 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 | 24 | 24 | 24 | 21 | 20 | 40 | 90 | 38 | 35 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.83 | 1.67 | 3.75 | 1.58 | 1.46 | 0.83 |
time (sec) |
N/A | 0.209 | 0.053 | 0.087 | 0.030 | 0.088 | 1.379 | 0.127 | 0.203 | 25.520 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 52 | 62 | 49 | 80 | 72 | 0 | 73 | 47 | 0 |
N.S. |
1 | 0.84 | 1.00 | 0.79 | 1.29 | 1.16 | 0.00 | 1.18 | 0.76 | 0.00 |
time (sec) |
N/A | 0.244 | 0.131 | 0.157 | 0.113 | 0.105 | 0.000 | 0.132 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 37 | 98 | 26 | 0 | 38 | 51 | 37 |
N.S. |
1 | 1.00 | 1.00 | 1.42 | 3.77 | 1.00 | 0.00 | 1.46 | 1.96 | 1.42 |
time (sec) |
N/A | 0.238 | 0.225 | 0.186 | 0.163 | 0.091 | 0.000 | 0.131 | 0.194 | 25.769 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 65 | 72 | 70 | 94 | 96 | 0 | 91 | 51 | 0 |
N.S. |
1 | 0.89 | 0.99 | 0.96 | 1.29 | 1.32 | 0.00 | 1.25 | 0.70 | 0.00 |
time (sec) |
N/A | 0.368 | 0.210 | 0.192 | 0.107 | 0.080 | 0.000 | 0.138 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | B | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 51 | 107 | 0 | 206 | 0 | 95 | 51 | 0 |
N.S. |
1 | 1.00 | 0.48 | 1.00 | 0.00 | 1.93 | 0.00 | 0.89 | 0.48 | 0.00 |
time (sec) |
N/A | 0.465 | 0.204 | 0.213 | 0.000 | 0.128 | 0.000 | 0.132 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 124 | 44 | 101 | 151 | 152 | 0 | 128 | 51 | 0 |
N.S. |
1 | 0.98 | 0.35 | 0.80 | 1.19 | 1.20 | 0.00 | 1.01 | 0.40 | 0.00 |
time (sec) |
N/A | 0.504 | 0.085 | 0.209 | 0.105 | 0.087 | 0.000 | 0.136 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 177 | 54 | 176 | 0 | 239 | 0 | 143 | 51 | 0 |
N.S. |
1 | 1.05 | 0.32 | 1.04 | 0.00 | 1.41 | 0.00 | 0.85 | 0.30 | 0.00 |
time (sec) |
N/A | 0.773 | 0.233 | 0.214 | 0.000 | 0.138 | 0.000 | 0.132 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 66 | 51 | 41 | 55 | 114 | 0 | 108 | 83 | 0 |
N.S. |
1 | 0.90 | 0.70 | 0.56 | 0.75 | 1.56 | 0.00 | 1.48 | 1.14 | 0.00 |
time (sec) |
N/A | 0.273 | 0.220 | 69.231 | 0.035 | 0.086 | 0.000 | 0.144 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 171 | 79 | 87 | 0 | 219 | 0 | 172 | 83 | 0 |
N.S. |
1 | 1.08 | 0.50 | 0.55 | 0.00 | 1.38 | 0.00 | 1.08 | 0.52 | 0.00 |
time (sec) |
N/A | 0.838 | 0.345 | 24.240 | 0.000 | 0.095 | 0.000 | 0.145 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 45 | 41 | 31 | 38 | 88 | 335 | 76 | 83 | 0 |
N.S. |
1 | 0.92 | 0.84 | 0.63 | 0.78 | 1.80 | 6.84 | 1.55 | 1.69 | 0.00 |
time (sec) |
N/A | 0.264 | 0.144 | 6.657 | 0.035 | 0.080 | 45.103 | 0.138 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 135 | 69 | 77 | 0 | 167 | 0 | 140 | 83 | 0 |
N.S. |
1 | 1.06 | 0.54 | 0.61 | 0.00 | 1.31 | 0.00 | 1.10 | 0.65 | 0.00 |
time (sec) |
N/A | 0.662 | 0.297 | 1.737 | 0.000 | 0.079 | 0.000 | 0.142 | 0.216 | 0.000 |
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 | 24 | 24 | 24 | 21 | 20 | 61 | 126 | 38 | 47 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.83 | 2.54 | 5.25 | 1.58 | 1.96 | 0.83 |
time (sec) |
N/A | 0.212 | 0.067 | 0.394 | 0.028 | 0.073 | 15.217 | 0.134 | 0.164 | 25.612 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 74 | 73 | 66 | 97 | 89 | 0 | 91 | 77 | 0 |
N.S. |
1 | 0.86 | 0.85 | 0.77 | 1.13 | 1.03 | 0.00 | 1.06 | 0.90 | 0.00 |
time (sec) |
N/A | 0.260 | 0.198 | 0.865 | 0.117 | 0.099 | 0.000 | 0.133 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 36 | 45 | 191 | 41 | 0 | 72 | 83 | 88 |
N.S. |
1 | 1.00 | 0.65 | 0.82 | 3.47 | 0.75 | 0.00 | 1.31 | 1.51 | 1.60 |
time (sec) |
N/A | 0.392 | 0.239 | 5.026 | 0.168 | 0.080 | 0.000 | 0.130 | 0.213 | 26.502 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 61 | 75 | 66 | 94 | 102 | 0 | 91 | 83 | 0 |
N.S. |
1 | 0.88 | 1.09 | 0.96 | 1.36 | 1.48 | 0.00 | 1.32 | 1.20 | 0.00 |
time (sec) |
N/A | 0.381 | 0.396 | 36.740 | 0.113 | 0.091 | 0.000 | 0.133 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 47 | 184 | 43 | 0 | 38 | 83 | 225 |
N.S. |
1 | 1.00 | 1.00 | 1.57 | 6.13 | 1.43 | 0.00 | 1.27 | 2.77 | 7.50 |
time (sec) |
N/A | 0.255 | 0.180 | 117.549 | 0.169 | 0.078 | 0.000 | 0.138 | 0.214 | 30.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 100 | 110 | 107 | 134 | 141 | 0 | 112 | 83 | 0 |
N.S. |
1 | 0.97 | 1.07 | 1.04 | 1.30 | 1.37 | 0.00 | 1.09 | 0.81 | 0.00 |
time (sec) |
N/A | 0.539 | 0.306 | 0.169 | 0.115 | 0.085 | 0.000 | 0.137 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | B | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 142 | 51 | 120 | 0 | 251 | 0 | 111 | 83 | 0 |
N.S. |
1 | 1.02 | 0.37 | 0.86 | 0.00 | 1.81 | 0.00 | 0.80 | 0.60 | 0.00 |
time (sec) |
N/A | 0.644 | 0.278 | 0.160 | 0.000 | 0.108 | 0.000 | 0.128 | 0.264 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 159 | 44 | 113 | 185 | 202 | 0 | 144 | 83 | 0 |
N.S. |
1 | 1.00 | 0.28 | 0.71 | 1.16 | 1.27 | 0.00 | 0.91 | 0.52 | 0.00 |
time (sec) |
N/A | 0.661 | 0.108 | 0.159 | 0.111 | 0.118 | 0.000 | 0.138 | 0.317 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 87 | 64 | 57 | 72 | 154 | 0 | 140 | 113 | 0 |
N.S. |
1 | 0.90 | 0.66 | 0.59 | 0.74 | 1.59 | 0.00 | 1.44 | 1.16 | 0.00 |
time (sec) |
N/A | 0.292 | 0.653 | 0.142 | 0.036 | 0.100 | 0.000 | 0.146 | 0.302 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 243 | 102 | 107 | 0 | 296 | 0 | 236 | 113 | 0 |
N.S. |
1 | 1.09 | 0.46 | 0.48 | 0.00 | 1.33 | 0.00 | 1.06 | 0.51 | 0.00 |
time (sec) |
N/A | 1.225 | 0.592 | 178.403 | 0.000 | 0.109 | 0.000 | 0.149 | 0.302 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 66 | 54 | 41 | 55 | 128 | 0 | 108 | 113 | 0 |
N.S. |
1 | 0.90 | 0.74 | 0.56 | 0.75 | 1.75 | 0.00 | 1.48 | 1.55 | 0.00 |
time (sec) |
N/A | 0.270 | 0.293 | 69.319 | 0.032 | 0.105 | 0.000 | 0.145 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 207 | 92 | 97 | 0 | 244 | 0 | 204 | 113 | 0 |
N.S. |
1 | 1.08 | 0.48 | 0.51 | 0.00 | 1.28 | 0.00 | 1.07 | 0.59 | 0.00 |
time (sec) |
N/A | 1.000 | 0.266 | 24.119 | 0.000 | 0.093 | 0.000 | 0.147 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 45 | 44 | 31 | 38 | 102 | 0 | 76 | 113 | 0 |
N.S. |
1 | 0.92 | 0.90 | 0.63 | 0.78 | 2.08 | 0.00 | 1.55 | 2.31 | 0.00 |
time (sec) |
N/A | 0.268 | 0.158 | 6.693 | 0.028 | 0.094 | 0.000 | 0.138 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 171 | 82 | 87 | 0 | 192 | 0 | 172 | 113 | 0 |
N.S. |
1 | 1.08 | 0.52 | 0.55 | 0.00 | 1.21 | 0.00 | 1.08 | 0.71 | 0.00 |
time (sec) |
N/A | 0.814 | 0.240 | 1.729 | 0.000 | 0.084 | 0.000 | 0.141 | 0.219 | 0.000 |
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 | 24 | 24 | 24 | 21 | 20 | 74 | 156 | 38 | 57 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.83 | 3.08 | 6.50 | 1.58 | 2.38 | 0.83 |
time (sec) |
N/A | 0.214 | 0.114 | 0.390 | 0.028 | 0.079 | 162.568 | 0.134 | 0.180 | 25.605 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 96 | 85 | 83 | 115 | 102 | 0 | 107 | 105 | 0 |
N.S. |
1 | 0.87 | 0.77 | 0.75 | 1.05 | 0.93 | 0.00 | 0.97 | 0.95 | 0.00 |
time (sec) |
N/A | 0.270 | 0.377 | 0.869 | 0.110 | 0.093 | 0.000 | 0.136 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 48 | 55 | 237 | 54 | 0 | 105 | 113 | 0 |
N.S. |
1 | 1.00 | 0.54 | 0.62 | 2.66 | 0.61 | 0.00 | 1.18 | 1.27 | 0.00 |
time (sec) |
N/A | 0.520 | 0.368 | 4.945 | 0.164 | 0.076 | 0.000 | 0.143 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 85 | 42 | 83 | 112 | 116 | 0 | 107 | 113 | 0 |
N.S. |
1 | 0.93 | 0.46 | 0.91 | 1.23 | 1.27 | 0.00 | 1.18 | 1.24 | 0.00 |
time (sec) |
N/A | 0.383 | 0.095 | 37.424 | 0.113 | 0.088 | 0.000 | 0.132 | 0.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 42 | 57 | 320 | 57 | 0 | 76 | 113 | 118 |
N.S. |
1 | 1.00 | 0.69 | 0.93 | 5.25 | 0.93 | 0.00 | 1.25 | 1.85 | 1.93 |
time (sec) |
N/A | 0.376 | 0.252 | 121.166 | 0.169 | 0.099 | 0.000 | 0.138 | 0.291 | 37.219 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 103 | 108 | 75 | 132 | 139 | 0 | 149 | 113 | 0 |
N.S. |
1 | 0.97 | 1.02 | 0.71 | 1.25 | 1.31 | 0.00 | 1.41 | 1.07 | 0.00 |
time (sec) |
N/A | 0.525 | 0.318 | 0.151 | 0.116 | 0.092 | 0.000 | 0.143 | 0.341 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 47 | 270 | 54 | 0 | 38 | 113 | 86 |
N.S. |
1 | 1.00 | 1.00 | 1.57 | 9.00 | 1.80 | 0.00 | 1.27 | 3.77 | 2.87 |
time (sec) |
N/A | 0.245 | 0.427 | 0.149 | 0.172 | 0.071 | 0.000 | 0.139 | 0.246 | 30.365 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 135 | 120 | 144 | 168 | 184 | 0 | 128 | 113 | 0 |
N.S. |
1 | 1.00 | 0.89 | 1.07 | 1.24 | 1.36 | 0.00 | 0.95 | 0.84 | 0.00 |
time (sec) |
N/A | 0.679 | 0.613 | 0.159 | 0.109 | 0.090 | 0.000 | 0.139 | 0.278 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | B | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 177 | 64 | 139 | 0 | 297 | 0 | 127 | 113 | 0 |
N.S. |
1 | 1.04 | 0.37 | 0.81 | 0.00 | 1.74 | 0.00 | 0.74 | 0.66 | 0.00 |
time (sec) |
N/A | 0.805 | 0.764 | 0.163 | 0.000 | 0.129 | 0.000 | 0.135 | 0.252 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 194 | 44 | 129 | 219 | 245 | 0 | 160 | 113 | 0 |
N.S. |
1 | 1.02 | 0.23 | 0.68 | 1.15 | 1.28 | 0.00 | 0.84 | 0.59 | 0.00 |
time (sec) |
N/A | 0.829 | 0.121 | 0.168 | 0.114 | 0.109 | 0.000 | 0.143 | 0.260 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 247 | 64 | 208 | 0 | 331 | 0 | 175 | 113 | 0 |
N.S. |
1 | 1.06 | 0.27 | 0.89 | 0.00 | 1.42 | 0.00 | 0.75 | 0.48 | 0.00 |
time (sec) |
N/A | 1.150 | 1.328 | 0.169 | 0.000 | 0.110 | 0.000 | 0.143 | 0.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 87 | 61 | 57 | 281 | 82 | 0 | 112 | 36 | 0 |
N.S. |
1 | 0.90 | 0.63 | 0.59 | 2.90 | 0.85 | 0.00 | 1.15 | 0.37 | 0.00 |
time (sec) |
N/A | 0.278 | 0.320 | 0.812 | 0.039 | 0.081 | 0.000 | 0.144 | 0.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 99 | 59 | 64 | 0 | 155 | 0 | 84 | 36 | 0 |
N.S. |
1 | 1.04 | 0.62 | 0.67 | 0.00 | 1.63 | 0.00 | 0.88 | 0.38 | 0.00 |
time (sec) |
N/A | 0.524 | 0.279 | 0.479 | 0.000 | 0.080 | 0.000 | 0.158 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 66 | 51 | 41 | 160 | 62 | 0 | 90 | 36 | 0 |
N.S. |
1 | 0.90 | 0.70 | 0.56 | 2.19 | 0.85 | 0.00 | 1.23 | 0.49 | 0.00 |
time (sec) |
N/A | 0.260 | 0.165 | 0.327 | 0.035 | 0.105 | 0.000 | 0.150 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 49 | 54 | 0 | 115 | 0 | 65 | 36 | 0 |
N.S. |
1 | 1.00 | 0.78 | 0.86 | 0.00 | 1.83 | 0.00 | 1.03 | 0.57 | 0.00 |
time (sec) |
N/A | 0.361 | 0.089 | 0.236 | 0.000 | 0.080 | 0.000 | 0.155 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 45 | 34 | 31 | 75 | 40 | 0 | 68 | 36 | 0 |
N.S. |
1 | 0.92 | 0.69 | 0.63 | 1.53 | 0.82 | 0.00 | 1.39 | 0.73 | 0.00 |
time (sec) |
N/A | 0.252 | 0.081 | 0.184 | 0.030 | 0.076 | 0.000 | 0.150 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 44 | 0 | 71 | 0 | 40 | 36 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.47 | 0.00 | 2.37 | 0.00 | 1.33 | 1.20 | 0.00 |
time (sec) |
N/A | 0.228 | 0.085 | 0.149 | 0.000 | 0.086 | 0.000 | 0.156 | 0.161 | 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 | 22 | 22 | 22 | 21 | 20 | 20 | 32 | 38 | 19 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.91 | 0.91 | 1.45 | 1.73 | 0.86 | 0.91 |
time (sec) |
N/A | 0.208 | 0.034 | 0.077 | 0.026 | 0.075 | 0.297 | 0.159 | 0.165 | 25.970 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | B | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 54 | 39 | 54 | 78 | 90 | 0 | 123 | 34 | 0 |
N.S. |
1 | 0.90 | 0.65 | 0.90 | 1.30 | 1.50 | 0.00 | 2.05 | 0.57 | 0.00 |
time (sec) |
N/A | 0.243 | 0.057 | 0.125 | 0.112 | 0.110 | 0.000 | 0.148 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 107 | 52 | 134 | 0 | 200 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.05 | 0.51 | 1.31 | 0.00 | 1.96 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.427 | 0.215 | 0.155 | 0.000 | 0.099 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | B | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 118 | 42 | 107 | 132 | 145 | 0 | 195 | 36 | 0 |
N.S. |
1 | 1.02 | 0.36 | 0.92 | 1.14 | 1.25 | 0.00 | 1.68 | 0.31 | 0.00 |
time (sec) |
N/A | 0.398 | 0.078 | 0.158 | 0.106 | 0.096 | 0.000 | 0.150 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 177 | 61 | 241 | 0 | 230 | 0 | 144 | 36 | 0 |
N.S. |
1 | 1.09 | 0.38 | 1.49 | 0.00 | 1.42 | 0.00 | 0.89 | 0.22 | 0.00 |
time (sec) |
N/A | 0.746 | 0.163 | 0.169 | 0.000 | 0.140 | 0.000 | 0.170 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 190 | 44 | 135 | 183 | 167 | 0 | 233 | 36 | 0 |
N.S. |
1 | 1.09 | 0.25 | 0.77 | 1.05 | 0.95 | 0.00 | 1.33 | 0.21 | 0.00 |
time (sec) |
N/A | 0.682 | 0.090 | 0.173 | 0.112 | 0.096 | 0.000 | 0.156 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 249 | 61 | 330 | 0 | 250 | 0 | 262 | 36 | 0 |
N.S. |
1 | 1.13 | 0.28 | 1.49 | 0.00 | 1.13 | 0.00 | 1.19 | 0.16 | 0.00 |
time (sec) |
N/A | 1.136 | 0.225 | 0.180 | 0.000 | 0.102 | 0.000 | 0.173 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 87 | 54 | 57 | 72 | 72 | 0 | 112 | 46 | 0 |
N.S. |
1 | 0.90 | 0.56 | 0.59 | 0.74 | 0.74 | 0.00 | 1.15 | 0.47 | 0.00 |
time (sec) |
N/A | 0.287 | 0.255 | 0.809 | 0.032 | 0.092 | 0.000 | 0.139 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 52 | 57 | 0 | 142 | 0 | 68 | 46 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.90 | 0.00 | 2.25 | 0.00 | 1.08 | 0.73 | 0.00 |
time (sec) |
N/A | 0.375 | 0.199 | 0.534 | 0.000 | 0.085 | 0.000 | 0.131 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 66 | 44 | 41 | 55 | 52 | 0 | 90 | 46 | 0 |
N.S. |
1 | 0.90 | 0.60 | 0.56 | 0.75 | 0.71 | 0.00 | 1.23 | 0.63 | 0.00 |
time (sec) |
N/A | 0.273 | 0.125 | 0.353 | 0.028 | 0.084 | 0.000 | 0.139 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 42 | 47 | 0 | 98 | 0 | 40 | 46 | 0 |
N.S. |
1 | 1.00 | 1.40 | 1.57 | 0.00 | 3.27 | 0.00 | 1.33 | 1.53 | 0.00 |
time (sec) |
N/A | 0.242 | 0.078 | 0.268 | 0.000 | 0.082 | 0.000 | 0.139 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 43 | 32 | 29 | 36 | 28 | 0 | 65 | 59 | 0 |
N.S. |
1 | 0.91 | 0.68 | 0.62 | 0.77 | 0.60 | 0.00 | 1.38 | 1.26 | 0.00 |
time (sec) |
N/A | 0.267 | 0.064 | 0.210 | 0.028 | 0.091 | 0.000 | 0.136 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 84 | 95 | 0 | 196 | 0 | 114 | 46 | 0 |
N.S. |
1 | 1.00 | 1.11 | 1.25 | 0.00 | 2.58 | 0.00 | 1.50 | 0.61 | 0.00 |
time (sec) |
N/A | 0.337 | 0.174 | 0.242 | 0.000 | 0.085 | 0.000 | 0.136 | 0.165 | 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 | 22 | 22 | 22 | 21 | 20 | 33 | 34 | 40 | 29 | 50 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.91 | 1.50 | 1.55 | 1.82 | 1.32 | 2.27 |
time (sec) |
N/A | 0.217 | 0.040 | 0.082 | 0.033 | 0.082 | 0.571 | 0.134 | 0.189 | 25.979 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | B | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 83 | 41 | 71 | 91 | 132 | 0 | 142 | 44 | 0 |
N.S. |
1 | 0.93 | 0.46 | 0.80 | 1.02 | 1.48 | 0.00 | 1.60 | 0.49 | 0.00 |
time (sec) |
N/A | 0.273 | 0.090 | 0.145 | 0.104 | 0.106 | 0.000 | 0.142 | 0.264 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 142 | 60 | 212 | 0 | 240 | 0 | 199 | 46 | 0 |
N.S. |
1 | 1.06 | 0.45 | 1.58 | 0.00 | 1.79 | 0.00 | 1.49 | 0.34 | 0.00 |
time (sec) |
N/A | 0.601 | 0.256 | 0.180 | 0.000 | 0.146 | 0.000 | 0.150 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 155 | 42 | 124 | 146 | 187 | 0 | 211 | 46 | 0 |
N.S. |
1 | 1.03 | 0.28 | 0.83 | 0.97 | 1.25 | 0.00 | 1.41 | 0.31 | 0.00 |
time (sec) |
N/A | 0.550 | 0.090 | 0.187 | 0.105 | 0.094 | 0.000 | 0.148 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 214 | 58 | 311 | 0 | 270 | 0 | 220 | 46 | 0 |
N.S. |
1 | 1.10 | 0.30 | 1.59 | 0.00 | 1.38 | 0.00 | 1.13 | 0.24 | 0.00 |
time (sec) |
N/A | 0.962 | 0.249 | 0.204 | 0.000 | 0.107 | 0.000 | 0.145 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 227 | 44 | 152 | 197 | 207 | 0 | 249 | 46 | 0 |
N.S. |
1 | 1.08 | 0.21 | 0.72 | 0.93 | 0.98 | 0.00 | 1.18 | 0.22 | 0.00 |
time (sec) |
N/A | 0.876 | 0.105 | 0.195 | 0.112 | 0.134 | 0.000 | 0.142 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 256 | 286 | 61 | 394 | 0 | 290 | 0 | 271 | 46 | 0 |
N.S. |
1 | 1.12 | 0.24 | 1.54 | 0.00 | 1.13 | 0.00 | 1.06 | 0.18 | 0.00 |
time (sec) |
N/A | 1.356 | 0.267 | 0.205 | 0.000 | 0.141 | 0.000 | 0.147 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 99 | 59 | 67 | 0 | 201 | 0 | 90 | 56 | 0 |
N.S. |
1 | 1.04 | 0.62 | 0.71 | 0.00 | 2.12 | 0.00 | 0.95 | 0.59 | 0.00 |
time (sec) |
N/A | 0.503 | 0.736 | 2.840 | 0.000 | 0.088 | 0.000 | 0.130 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 108 | 64 | 67 | 89 | 82 | 0 | 134 | 56 | 0 |
N.S. |
1 | 0.89 | 0.53 | 0.55 | 0.74 | 0.68 | 0.00 | 1.11 | 0.46 | 0.00 |
time (sec) |
N/A | 0.289 | 0.330 | 1.898 | 0.035 | 0.085 | 0.000 | 0.137 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 52 | 57 | 0 | 161 | 0 | 68 | 56 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.90 | 0.00 | 2.56 | 0.00 | 1.08 | 0.89 | 0.00 |
time (sec) |
N/A | 0.359 | 0.402 | 1.166 | 0.000 | 0.077 | 0.000 | 0.141 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 87 | 54 | 57 | 72 | 62 | 0 | 112 | 56 | 0 |
N.S. |
1 | 0.90 | 0.56 | 0.59 | 0.74 | 0.64 | 0.00 | 1.15 | 0.58 | 0.00 |
time (sec) |
N/A | 0.280 | 0.200 | 0.753 | 0.030 | 0.102 | 0.000 | 0.133 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 42 | 47 | 0 | 117 | 0 | 40 | 56 | 0 |
N.S. |
1 | 1.00 | 1.40 | 1.57 | 0.00 | 3.90 | 0.00 | 1.33 | 1.87 | 0.00 |
time (sec) |
N/A | 0.231 | 0.145 | 0.512 | 0.000 | 0.075 | 0.000 | 0.127 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 64 | 44 | 41 | 55 | 40 | 0 | 88 | 56 | 0 |
N.S. |
1 | 0.90 | 0.62 | 0.58 | 0.77 | 0.56 | 0.00 | 1.24 | 0.79 | 0.00 |
time (sec) |
N/A | 0.267 | 0.097 | 0.355 | 0.029 | 0.072 | 0.000 | 0.136 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 114 | 96 | 112 | 0 | 215 | 0 | 140 | 56 | 0 |
N.S. |
1 | 1.06 | 0.89 | 1.04 | 0.00 | 1.99 | 0.00 | 1.30 | 0.52 | 0.00 |
time (sec) |
N/A | 0.471 | 0.223 | 0.272 | 0.000 | 0.103 | 0.000 | 0.145 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 41 | 30 | 29 | 42 | 41 | 245 | 64 | 69 | 0 |
N.S. |
1 | 0.91 | 0.67 | 0.64 | 0.93 | 0.91 | 5.44 | 1.42 | 1.53 | 0.00 |
time (sec) |
N/A | 0.250 | 0.078 | 0.222 | 0.030 | 0.097 | 2.360 | 0.140 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 100 | 121 | 0 | 252 | 0 | 139 | 56 | 0 |
N.S. |
1 | 1.00 | 1.33 | 1.61 | 0.00 | 3.36 | 0.00 | 1.85 | 0.75 | 0.00 |
time (sec) |
N/A | 0.326 | 0.281 | 0.178 | 0.000 | 0.093 | 0.000 | 0.147 | 0.180 | 0.000 |
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 | 24 | 24 | 24 | 21 | 20 | 48 | 65 | 40 | 39 | 72 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.83 | 2.00 | 2.71 | 1.67 | 1.62 | 3.00 |
time (sec) |
N/A | 0.212 | 0.054 | 0.085 | 0.026 | 0.076 | 2.158 | 0.137 | 0.168 | 30.764 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 112 | 41 | 88 | 114 | 169 | 0 | 158 | 54 | 0 |
N.S. |
1 | 0.99 | 0.36 | 0.78 | 1.01 | 1.50 | 0.00 | 1.40 | 0.48 | 0.00 |
time (sec) |
N/A | 0.270 | 0.103 | 0.150 | 0.112 | 0.127 | 0.000 | 0.145 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 177 | 52 | 288 | 0 | 280 | 0 | 218 | 56 | 0 |
N.S. |
1 | 1.06 | 0.31 | 1.72 | 0.00 | 1.68 | 0.00 | 1.31 | 0.34 | 0.00 |
time (sec) |
N/A | 0.792 | 0.284 | 0.179 | 0.000 | 0.108 | 0.000 | 0.148 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 192 | 42 | 141 | 167 | 225 | 0 | 227 | 56 | 0 |
N.S. |
1 | 1.04 | 0.23 | 0.76 | 0.90 | 1.22 | 0.00 | 1.23 | 0.30 | 0.00 |
time (sec) |
N/A | 0.713 | 0.111 | 0.190 | 0.135 | 0.152 | 0.000 | 0.148 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 251 | 54 | 381 | 0 | 308 | 0 | 255 | 56 | 0 |
N.S. |
1 | 1.08 | 0.23 | 1.64 | 0.00 | 1.32 | 0.00 | 1.09 | 0.24 | 0.00 |
time (sec) |
N/A | 1.135 | 0.252 | 0.203 | 0.000 | 0.141 | 0.000 | 0.149 | 0.174 | 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 | 124 | 130 | 64 | 231 | 0 | 115 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.05 | 0.52 | 1.86 | 0.00 | 0.93 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.568 | 0.443 | 2.904 | 0.000 | 0.098 | 0.000 | 0.000 | 0.188 | 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 | 95 | 96 | 64 | 214 | 0 | 110 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.01 | 0.67 | 2.25 | 0.00 | 1.16 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.440 | 0.329 | 1.690 | 0.000 | 0.143 | 0.000 | 0.000 | 0.169 | 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 | 95 | 96 | 64 | 179 | 0 | 94 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.01 | 0.67 | 1.88 | 0.00 | 0.99 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.432 | 0.258 | 0.715 | 0.000 | 0.084 | 0.000 | 0.000 | 0.175 | 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 | 63 | 63 | 64 | 120 | 0 | 84 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.00 | 1.02 | 1.90 | 0.00 | 1.33 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.323 | 0.233 | 0.513 | 0.000 | 0.101 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 62 | 57 | 0 | 75 | 0 | 0 | 40 | 45 |
N.S. |
1 | 1.00 | 1.02 | 0.93 | 0.00 | 1.23 | 0.00 | 0.00 | 0.66 | 0.74 |
time (sec) |
N/A | 0.321 | 0.465 | 0.295 | 0.000 | 0.112 | 0.000 | 0.000 | 0.165 | 0.557 |