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 | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 236 | 124 | 141 | 0 | 308 | 0 | 125 | 119 | 0 |
N.S. |
1 | 1.07 | 0.56 | 0.64 | 0.00 | 1.39 | 0.00 | 0.57 | 0.54 | 0.00 |
time (sec) |
N/A | 0.784 | 0.686 | 0.266 | 0.000 | 0.110 | 0.000 | 0.122 | 0.230 | 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 | 153 | 194 | 113 | 122 | 0 | 287 | 0 | 83 | 101 | 0 |
N.S. |
1 | 1.27 | 0.74 | 0.80 | 0.00 | 1.88 | 0.00 | 0.54 | 0.66 | 0.00 |
time (sec) |
N/A | 0.549 | 0.568 | 0.237 | 0.000 | 0.103 | 0.000 | 0.133 | 0.226 | 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 | 151 | 158 | 102 | 103 | 0 | 264 | 0 | 81 | 83 | 0 |
N.S. |
1 | 1.05 | 0.68 | 0.68 | 0.00 | 1.75 | 0.00 | 0.54 | 0.55 | 0.00 |
time (sec) |
N/A | 0.439 | 0.562 | 0.282 | 0.000 | 0.131 | 0.000 | 0.129 | 0.226 | 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 | 116 | 119 | 91 | 83 | 0 | 233 | 0 | 57 | 61 | 0 |
N.S. |
1 | 1.03 | 0.78 | 0.72 | 0.00 | 2.01 | 0.00 | 0.49 | 0.53 | 0.00 |
time (sec) |
N/A | 0.366 | 0.417 | 0.231 | 0.000 | 0.128 | 0.000 | 0.124 | 0.236 | 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 | 116 | 110 | 116 | 86 | 0 | 320 | 0 | 71 | 156 | 0 |
N.S. |
1 | 0.95 | 1.00 | 0.74 | 0.00 | 2.76 | 0.00 | 0.61 | 1.34 | 0.00 |
time (sec) |
N/A | 0.383 | 0.477 | 0.280 | 0.000 | 0.152 | 0.000 | 0.134 | 0.233 | 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 | 121 | 116 | 121 | 92 | 0 | 381 | 0 | 76 | 239 | 0 |
N.S. |
1 | 0.96 | 1.00 | 0.76 | 0.00 | 3.15 | 0.00 | 0.63 | 1.98 | 0.00 |
time (sec) |
N/A | 0.408 | 0.558 | 0.255 | 0.000 | 0.122 | 0.000 | 0.129 | 0.425 | 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 | 165 | 145 | 136 | 116 | 0 | 425 | 0 | 107 | 27 | 0 |
N.S. |
1 | 0.88 | 0.82 | 0.70 | 0.00 | 2.58 | 0.00 | 0.65 | 0.16 | 0.00 |
time (sec) |
N/A | 0.459 | 0.763 | 0.307 | 0.000 | 0.123 | 0.000 | 0.131 | 200.049 | 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 | 203 | 174 | 147 | 135 | 0 | 447 | 0 | 133 | 235 | 0 |
N.S. |
1 | 0.86 | 0.72 | 0.67 | 0.00 | 2.20 | 0.00 | 0.66 | 1.16 | 0.00 |
time (sec) |
N/A | 0.515 | 0.756 | 0.247 | 0.000 | 0.235 | 0.000 | 0.127 | 0.277 | 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 | 132 | 105 | 136 | 116 | 0 | 424 | 0 | 94 | 243 | 0 |
N.S. |
1 | 0.80 | 1.03 | 0.88 | 0.00 | 3.21 | 0.00 | 0.71 | 1.84 | 0.00 |
time (sec) |
N/A | 0.422 | 10.100 | 0.315 | 0.000 | 0.143 | 0.000 | 0.131 | 0.423 | 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 | 160 | 167 | 67 | 62 | 56 | 71 | 0 | 122 | 47 | 103 |
N.S. |
1 | 1.04 | 0.42 | 0.39 | 0.35 | 0.44 | 0.00 | 0.76 | 0.29 | 0.64 |
time (sec) |
N/A | 0.733 | 0.183 | 0.266 | 0.038 | 0.107 | 0.000 | 0.126 | 0.213 | 6.762 |
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 | 125 | 56 | 51 | 57 | 60 | 0 | 85 | 36 | 82 |
N.S. |
1 | 1.05 | 0.47 | 0.43 | 0.48 | 0.50 | 0.00 | 0.71 | 0.30 | 0.69 |
time (sec) |
N/A | 0.414 | 0.136 | 0.237 | 0.038 | 0.087 | 0.000 | 0.119 | 0.196 | 6.477 |
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 | 78 | 78 | 44 | 39 | 33 | 48 | 0 | 47 | 25 | 61 |
N.S. |
1 | 1.00 | 0.56 | 0.50 | 0.42 | 0.62 | 0.00 | 0.60 | 0.32 | 0.78 |
time (sec) |
N/A | 0.316 | 0.124 | 0.260 | 0.037 | 0.102 | 0.000 | 0.125 | 0.216 | 6.364 |
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 | 36 | 36 | 35 | 32 | 29 | 39 | 0 | 23 | 17 | 32 |
N.S. |
1 | 1.00 | 0.97 | 0.89 | 0.81 | 1.08 | 0.00 | 0.64 | 0.47 | 0.89 |
time (sec) |
N/A | 0.243 | 0.102 | 0.235 | 0.035 | 0.112 | 0.000 | 0.123 | 0.207 | 6.384 |
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 | 52 | 52 | 73 | 58 | 0 | 138 | 0 | 31 | 38 | 0 |
N.S. |
1 | 1.00 | 1.40 | 1.12 | 0.00 | 2.65 | 0.00 | 0.60 | 0.73 | 0.00 |
time (sec) |
N/A | 0.297 | 0.116 | 0.270 | 0.000 | 0.179 | 0.000 | 0.116 | 0.206 | 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 | 93 | 93 | 116 | 89 | 0 | 244 | 0 | 70 | 59 | 0 |
N.S. |
1 | 1.00 | 1.25 | 0.96 | 0.00 | 2.62 | 0.00 | 0.75 | 0.63 | 0.00 |
time (sec) |
N/A | 0.377 | 0.212 | 0.234 | 0.000 | 0.107 | 0.000 | 0.137 | 0.203 | 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 | 141 | 143 | 141 | 114 | 0 | 279 | 0 | 96 | 82 | 0 |
N.S. |
1 | 1.01 | 1.00 | 0.81 | 0.00 | 1.98 | 0.00 | 0.68 | 0.58 | 0.00 |
time (sec) |
N/A | 0.456 | 0.253 | 0.270 | 0.000 | 0.129 | 0.000 | 0.115 | 0.216 | 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 | 201 | 211 | 78 | 73 | 86 | 82 | 0 | 159 | 58 | 124 |
N.S. |
1 | 1.05 | 0.39 | 0.36 | 0.43 | 0.41 | 0.00 | 0.79 | 0.29 | 0.62 |
time (sec) |
N/A | 0.791 | 0.172 | 0.228 | 0.036 | 0.102 | 0.000 | 0.124 | 0.225 | 6.811 |
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 | 160 | 169 | 67 | 62 | 57 | 71 | 0 | 122 | 47 | 103 |
N.S. |
1 | 1.06 | 0.42 | 0.39 | 0.36 | 0.44 | 0.00 | 0.76 | 0.29 | 0.64 |
time (sec) |
N/A | 0.468 | 0.189 | 0.255 | 0.038 | 0.096 | 0.000 | 0.121 | 0.211 | 6.725 |
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 | 125 | 55 | 50 | 57 | 59 | 0 | 85 | 36 | 82 |
N.S. |
1 | 1.05 | 0.46 | 0.42 | 0.48 | 0.50 | 0.00 | 0.71 | 0.30 | 0.69 |
time (sec) |
N/A | 0.359 | 0.130 | 0.226 | 0.041 | 0.097 | 0.000 | 0.118 | 0.201 | 6.697 |
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 | 78 | 78 | 44 | 39 | 34 | 46 | 0 | 47 | 25 | 61 |
N.S. |
1 | 1.00 | 0.56 | 0.50 | 0.44 | 0.59 | 0.00 | 0.60 | 0.32 | 0.78 |
time (sec) |
N/A | 0.287 | 0.108 | 0.267 | 0.043 | 0.111 | 0.000 | 0.121 | 0.198 | 6.639 |
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 | 86 | 86 | 104 | 81 | 0 | 220 | 0 | 55 | 47 | 0 |
N.S. |
1 | 1.00 | 1.21 | 0.94 | 0.00 | 2.56 | 0.00 | 0.64 | 0.55 | 0.00 |
time (sec) |
N/A | 0.364 | 0.187 | 0.233 | 0.000 | 0.103 | 0.000 | 0.128 | 0.197 | 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 | 90 | 90 | 117 | 86 | 0 | 242 | 0 | 70 | 60 | 0 |
N.S. |
1 | 1.00 | 1.30 | 0.96 | 0.00 | 2.69 | 0.00 | 0.78 | 0.67 | 0.00 |
time (sec) |
N/A | 0.382 | 0.216 | 0.243 | 0.000 | 0.125 | 0.000 | 0.137 | 0.202 | 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 | 138 | 137 | 141 | 114 | 0 | 279 | 0 | 103 | 82 | 0 |
N.S. |
1 | 0.99 | 1.02 | 0.83 | 0.00 | 2.02 | 0.00 | 0.75 | 0.59 | 0.00 |
time (sec) |
N/A | 0.450 | 0.263 | 0.266 | 0.000 | 0.141 | 0.000 | 0.129 | 0.223 | 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 | 182 | 187 | 152 | 140 | 0 | 301 | 0 | 140 | 100 | 0 |
N.S. |
1 | 1.03 | 0.84 | 0.77 | 0.00 | 1.65 | 0.00 | 0.77 | 0.55 | 0.00 |
time (sec) |
N/A | 0.546 | 0.306 | 0.234 | 0.000 | 0.105 | 0.000 | 0.129 | 0.212 | 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 | 39 | 39 | 47 | 58 | 0 | 106 | 0 | 57 | 24 | 0 |
N.S. |
1 | 1.00 | 1.21 | 1.49 | 0.00 | 2.72 | 0.00 | 1.46 | 0.62 | 0.00 |
time (sec) |
N/A | 0.284 | 0.293 | 0.227 | 0.000 | 0.087 | 0.000 | 0.127 | 0.208 | 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 | 262 | 348 | 171 | 215 | 0 | 367 | 0 | 204 | 151 | 0 |
N.S. |
1 | 1.33 | 0.65 | 0.82 | 0.00 | 1.40 | 0.00 | 0.78 | 0.58 | 0.00 |
time (sec) |
N/A | 2.566 | 0.311 | 0.244 | 0.000 | 0.109 | 0.000 | 0.122 | 0.198 | 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 | 263 | 300 | 171 | 193 | 0 | 345 | 0 | 193 | 133 | 0 |
N.S. |
1 | 1.14 | 0.65 | 0.73 | 0.00 | 1.31 | 0.00 | 0.73 | 0.51 | 0.00 |
time (sec) |
N/A | 1.860 | 0.255 | 0.274 | 0.000 | 0.121 | 0.000 | 0.130 | 0.195 | 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 | 248 | 149 | 167 | 0 | 323 | 0 | 138 | 115 | 0 |
N.S. |
1 | 1.35 | 0.81 | 0.91 | 0.00 | 1.76 | 0.00 | 0.75 | 0.62 | 0.00 |
time (sec) |
N/A | 1.376 | 0.266 | 0.262 | 0.000 | 0.119 | 0.000 | 0.124 | 0.191 | 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 | 183 | 195 | 149 | 141 | 0 | 301 | 0 | 127 | 97 | 0 |
N.S. |
1 | 1.07 | 0.81 | 0.77 | 0.00 | 1.64 | 0.00 | 0.69 | 0.53 | 0.00 |
time (sec) |
N/A | 0.840 | 0.223 | 0.270 | 0.000 | 0.100 | 0.000 | 0.130 | 0.219 | 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 | 104 | 149 | 124 | 115 | 0 | 273 | 0 | 65 | 75 | 0 |
N.S. |
1 | 1.43 | 1.19 | 1.11 | 0.00 | 2.62 | 0.00 | 0.62 | 0.72 | 0.00 |
time (sec) |
N/A | 0.498 | 0.235 | 0.234 | 0.000 | 0.113 | 0.000 | 0.120 | 0.233 | 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 | 101 | 101 | 118 | 91 | 0 | 251 | 0 | 64 | 60 | 0 |
N.S. |
1 | 1.00 | 1.17 | 0.90 | 0.00 | 2.49 | 0.00 | 0.63 | 0.59 | 0.00 |
time (sec) |
N/A | 0.361 | 0.179 | 0.262 | 0.000 | 0.113 | 0.000 | 0.129 | 0.245 | 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 | 65 | 65 | 86 | 68 | 0 | 169 | 0 | 40 | 49 | 0 |
N.S. |
1 | 1.00 | 1.32 | 1.05 | 0.00 | 2.60 | 0.00 | 0.62 | 0.75 | 0.00 |
time (sec) |
N/A | 0.293 | 0.137 | 0.221 | 0.000 | 0.106 | 0.000 | 0.125 | 0.194 | 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 | 114 | 126 | 118 | 88 | 0 | 308 | 0 | 76 | 77 | 0 |
N.S. |
1 | 1.11 | 1.04 | 0.77 | 0.00 | 2.70 | 0.00 | 0.67 | 0.68 | 0.00 |
time (sec) |
N/A | 0.437 | 0.243 | 0.239 | 0.000 | 0.147 | 0.000 | 0.122 | 0.208 | 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 | 155 | 163 | 187 | 117 | 0 | 438 | 0 | 111 | 103 | 0 |
N.S. |
1 | 1.05 | 1.21 | 0.75 | 0.00 | 2.83 | 0.00 | 0.72 | 0.66 | 0.00 |
time (sec) |
N/A | 0.479 | 0.285 | 0.245 | 0.000 | 0.130 | 0.000 | 0.131 | 0.191 | 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 | 205 | 195 | 215 | 146 | 0 | 480 | 0 | 133 | 135 | 0 |
N.S. |
1 | 0.95 | 1.05 | 0.71 | 0.00 | 2.34 | 0.00 | 0.65 | 0.66 | 0.00 |
time (sec) |
N/A | 0.546 | 0.362 | 0.286 | 0.000 | 0.146 | 0.000 | 0.122 | 0.193 | 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 | 266 | 352 | 171 | 232 | 0 | 413 | 0 | 213 | 209 | 0 |
N.S. |
1 | 1.32 | 0.64 | 0.87 | 0.00 | 1.55 | 0.00 | 0.80 | 0.79 | 0.00 |
time (sec) |
N/A | 2.474 | 0.380 | 0.246 | 0.000 | 0.101 | 0.000 | 0.132 | 0.242 | 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 | 266 | 300 | 160 | 221 | 0 | 392 | 0 | 199 | 191 | 0 |
N.S. |
1 | 1.13 | 0.60 | 0.83 | 0.00 | 1.47 | 0.00 | 0.75 | 0.72 | 0.00 |
time (sec) |
N/A | 1.729 | 0.365 | 0.293 | 0.000 | 0.101 | 0.000 | 0.135 | 0.193 | 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 | 186 | 244 | 149 | 199 | 0 | 369 | 0 | 140 | 173 | 0 |
N.S. |
1 | 1.31 | 0.80 | 1.07 | 0.00 | 1.98 | 0.00 | 0.75 | 0.93 | 0.00 |
time (sec) |
N/A | 1.193 | 0.296 | 0.294 | 0.000 | 0.134 | 0.000 | 0.129 | 0.205 | 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 | 195 | 138 | 173 | 0 | 344 | 0 | 124 | 151 | 0 |
N.S. |
1 | 1.06 | 0.75 | 0.94 | 0.00 | 1.87 | 0.00 | 0.67 | 0.82 | 0.00 |
time (sec) |
N/A | 0.763 | 0.337 | 0.247 | 0.000 | 0.096 | 0.000 | 0.135 | 0.186 | 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 | 143 | 149 | 127 | 145 | 0 | 315 | 0 | 91 | 127 | 0 |
N.S. |
1 | 1.04 | 0.89 | 1.01 | 0.00 | 2.20 | 0.00 | 0.64 | 0.89 | 0.00 |
time (sec) |
N/A | 0.466 | 0.330 | 0.286 | 0.000 | 0.124 | 0.000 | 0.126 | 0.210 | 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 | 106 | 106 | 122 | 122 | 0 | 299 | 0 | 72 | 119 | 0 |
N.S. |
1 | 1.00 | 1.15 | 1.15 | 0.00 | 2.82 | 0.00 | 0.68 | 1.12 | 0.00 |
time (sec) |
N/A | 0.352 | 0.254 | 0.244 | 0.000 | 0.126 | 0.000 | 0.127 | 0.205 | 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 | 109 | 109 | 122 | 123 | 0 | 297 | 0 | 77 | 117 | 0 |
N.S. |
1 | 1.00 | 1.12 | 1.13 | 0.00 | 2.72 | 0.00 | 0.71 | 1.07 | 0.00 |
time (sec) |
N/A | 0.348 | 0.247 | 0.267 | 0.000 | 0.105 | 0.000 | 0.123 | 0.195 | 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 | 155 | 165 | 178 | 165 | 0 | 451 | 0 | 106 | 186 | 0 |
N.S. |
1 | 1.06 | 1.15 | 1.06 | 0.00 | 2.91 | 0.00 | 0.68 | 1.20 | 0.00 |
time (sec) |
N/A | 0.465 | 0.339 | 0.253 | 0.000 | 0.102 | 0.000 | 0.126 | 0.212 | 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 | 197 | 203 | 197 | 200 | 0 | 505 | 0 | 162 | 227 | 0 |
N.S. |
1 | 1.03 | 1.00 | 1.02 | 0.00 | 2.56 | 0.00 | 0.82 | 1.15 | 0.00 |
time (sec) |
N/A | 0.520 | 0.451 | 0.296 | 0.000 | 0.118 | 0.000 | 0.128 | 0.192 | 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 | 249 | 242 | 216 | 227 | 0 | 547 | 0 | 167 | 261 | 0 |
N.S. |
1 | 0.97 | 0.87 | 0.91 | 0.00 | 2.20 | 0.00 | 0.67 | 1.05 | 0.00 |
time (sec) |
N/A | 0.596 | 0.466 | 0.300 | 0.000 | 0.119 | 0.000 | 0.126 | 0.190 | 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 | 266 | 385 | 171 | 238 | 0 | 462 | 0 | 194 | 279 | 0 |
N.S. |
1 | 1.45 | 0.64 | 0.89 | 0.00 | 1.74 | 0.00 | 0.73 | 1.05 | 0.00 |
time (sec) |
N/A | 2.460 | 0.480 | 0.297 | 0.000 | 0.111 | 0.000 | 0.135 | 0.185 | 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 | 266 | 341 | 160 | 227 | 0 | 439 | 0 | 192 | 261 | 0 |
N.S. |
1 | 1.28 | 0.60 | 0.85 | 0.00 | 1.65 | 0.00 | 0.72 | 0.98 | 0.00 |
time (sec) |
N/A | 1.810 | 0.419 | 0.300 | 0.000 | 0.117 | 0.000 | 0.130 | 0.196 | 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 | 225 | 289 | 149 | 216 | 0 | 414 | 0 | 154 | 239 | 0 |
N.S. |
1 | 1.28 | 0.66 | 0.96 | 0.00 | 1.84 | 0.00 | 0.68 | 1.06 | 0.00 |
time (sec) |
N/A | 1.272 | 0.369 | 0.296 | 0.000 | 0.121 | 0.000 | 0.135 | 0.215 | 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 | 236 | 138 | 206 | 0 | 385 | 0 | 121 | 215 | 0 |
N.S. |
1 | 1.28 | 0.75 | 1.12 | 0.00 | 2.09 | 0.00 | 0.66 | 1.17 | 0.00 |
time (sec) |
N/A | 0.842 | 0.357 | 0.256 | 0.000 | 0.127 | 0.000 | 0.125 | 0.239 | 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 | 145 | 194 | 135 | 178 | 0 | 365 | 0 | 100 | 203 | 0 |
N.S. |
1 | 1.34 | 0.93 | 1.23 | 0.00 | 2.52 | 0.00 | 0.69 | 1.40 | 0.00 |
time (sec) |
N/A | 0.529 | 0.307 | 0.270 | 0.000 | 0.156 | 0.000 | 0.129 | 0.223 | 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 | 147 | 155 | 133 | 181 | 0 | 365 | 0 | 106 | 203 | 0 |
N.S. |
1 | 1.05 | 0.90 | 1.23 | 0.00 | 2.48 | 0.00 | 0.72 | 1.38 | 0.00 |
time (sec) |
N/A | 0.409 | 0.298 | 0.239 | 0.000 | 0.282 | 0.000 | 0.133 | 0.200 | 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 | 150 | 158 | 135 | 181 | 0 | 365 | 0 | 106 | 203 | 0 |
N.S. |
1 | 1.05 | 0.90 | 1.21 | 0.00 | 2.43 | 0.00 | 0.71 | 1.35 | 0.00 |
time (sec) |
N/A | 0.396 | 0.275 | 0.283 | 0.000 | 0.112 | 0.000 | 0.141 | 0.194 | 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 | 193 | 203 | 191 | 250 | 0 | 539 | 0 | 128 | 320 | 0 |
N.S. |
1 | 1.05 | 0.99 | 1.30 | 0.00 | 2.79 | 0.00 | 0.66 | 1.66 | 0.00 |
time (sec) |
N/A | 0.527 | 0.406 | 0.238 | 0.000 | 0.115 | 0.000 | 0.126 | 0.193 | 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 | 236 | 244 | 209 | 235 | 0 | 595 | 0 | 165 | 365 | 0 |
N.S. |
1 | 1.03 | 0.89 | 1.00 | 0.00 | 2.52 | 0.00 | 0.70 | 1.55 | 0.00 |
time (sec) |
N/A | 0.600 | 0.481 | 0.292 | 0.000 | 0.117 | 0.000 | 0.133 | 0.193 | 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 | 288 | 281 | 228 | 245 | 0 | 637 | 0 | 238 | 399 | 0 |
N.S. |
1 | 0.98 | 0.79 | 0.85 | 0.00 | 2.21 | 0.00 | 0.83 | 1.39 | 0.00 |
time (sec) |
N/A | 0.653 | 0.589 | 0.293 | 0.000 | 0.122 | 0.000 | 0.131 | 0.196 | 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 | 222 | 247 | 155 | 134 | 0 | 349 | 0 | 175 | 110 | 0 |
N.S. |
1 | 1.11 | 0.70 | 0.60 | 0.00 | 1.57 | 0.00 | 0.79 | 0.50 | 0.00 |
time (sec) |
N/A | 1.167 | 0.699 | 0.298 | 0.000 | 0.101 | 0.000 | 0.138 | 0.199 | 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 | 180 | 196 | 141 | 118 | 0 | 324 | 0 | 135 | 95 | 0 |
N.S. |
1 | 1.09 | 0.78 | 0.66 | 0.00 | 1.80 | 0.00 | 0.75 | 0.53 | 0.00 |
time (sec) |
N/A | 0.817 | 0.593 | 0.254 | 0.000 | 0.106 | 0.000 | 0.136 | 0.195 | 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 | 138 | 144 | 129 | 99 | 0 | 296 | 0 | 97 | 81 | 0 |
N.S. |
1 | 1.04 | 0.93 | 0.72 | 0.00 | 2.14 | 0.00 | 0.70 | 0.59 | 0.00 |
time (sec) |
N/A | 0.471 | 0.559 | 0.282 | 0.000 | 0.123 | 0.000 | 0.130 | 0.199 | 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 | 100 | 147 | 123 | 88 | 0 | 281 | 0 | 72 | 80 | 0 |
N.S. |
1 | 1.47 | 1.23 | 0.88 | 0.00 | 2.81 | 0.00 | 0.72 | 0.80 | 0.00 |
time (sec) |
N/A | 0.423 | 0.502 | 0.232 | 0.000 | 0.114 | 0.000 | 0.128 | 0.194 | 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 | 104 | 104 | 124 | 91 | 0 | 281 | 0 | 72 | 80 | 0 |
N.S. |
1 | 1.00 | 1.19 | 0.88 | 0.00 | 2.70 | 0.00 | 0.69 | 0.77 | 0.00 |
time (sec) |
N/A | 0.351 | 0.478 | 0.237 | 0.000 | 0.092 | 0.000 | 0.123 | 0.195 | 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 | 157 | 179 | 117 | 0 | 431 | 0 | 104 | 123 | 0 |
N.S. |
1 | 1.05 | 1.20 | 0.79 | 0.00 | 2.89 | 0.00 | 0.70 | 0.83 | 0.00 |
time (sec) |
N/A | 0.453 | 0.609 | 0.231 | 0.000 | 0.116 | 0.000 | 0.125 | 0.203 | 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 | 193 | 189 | 200 | 134 | 0 | 461 | 0 | 143 | 141 | 0 |
N.S. |
1 | 0.98 | 1.04 | 0.69 | 0.00 | 2.39 | 0.00 | 0.74 | 0.73 | 0.00 |
time (sec) |
N/A | 0.533 | 0.773 | 0.254 | 0.000 | 0.109 | 0.000 | 0.132 | 0.220 | 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 | 246 | 224 | 219 | 159 | 0 | 504 | 0 | 168 | 169 | 0 |
N.S. |
1 | 0.91 | 0.89 | 0.65 | 0.00 | 2.05 | 0.00 | 0.68 | 0.69 | 0.00 |
time (sec) |
N/A | 0.591 | 0.833 | 0.305 | 0.000 | 0.118 | 0.000 | 0.128 | 0.230 | 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 | 157 | 173 | 66 | 66 | 45 | 79 | 0 | 126 | 49 | 107 |
N.S. |
1 | 1.10 | 0.42 | 0.42 | 0.29 | 0.50 | 0.00 | 0.80 | 0.31 | 0.68 |
time (sec) |
N/A | 0.530 | 0.534 | 0.247 | 0.040 | 0.094 | 0.000 | 0.130 | 0.225 | 7.907 |
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 | 114 | 126 | 55 | 55 | 43 | 68 | 0 | 87 | 38 | 86 |
N.S. |
1 | 1.11 | 0.48 | 0.48 | 0.38 | 0.60 | 0.00 | 0.76 | 0.33 | 0.75 |
time (sec) |
N/A | 0.401 | 0.497 | 0.276 | 0.037 | 0.098 | 0.000 | 0.131 | 0.206 | 7.523 |
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 | 74 | 74 | 43 | 44 | 23 | 57 | 0 | 51 | 27 | 66 |
N.S. |
1 | 1.00 | 0.58 | 0.59 | 0.31 | 0.77 | 0.00 | 0.69 | 0.36 | 0.89 |
time (sec) |
N/A | 0.312 | 0.453 | 0.234 | 0.038 | 0.085 | 0.000 | 0.123 | 0.205 | 7.702 |
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 | 36 | 36 | 35 | 36 | 16 | 48 | 0 | 23 | 19 | 50 |
N.S. |
1 | 1.00 | 0.97 | 1.00 | 0.44 | 1.33 | 0.00 | 0.64 | 0.53 | 1.39 |
time (sec) |
N/A | 0.252 | 0.386 | 0.269 | 0.038 | 0.077 | 0.000 | 0.125 | 0.227 | 7.947 |
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 | 89 | 89 | 108 | 81 | 0 | 258 | 0 | 61 | 67 | 0 |
N.S. |
1 | 1.00 | 1.21 | 0.91 | 0.00 | 2.90 | 0.00 | 0.69 | 0.75 | 0.00 |
time (sec) |
N/A | 0.392 | 0.492 | 0.250 | 0.000 | 0.105 | 0.000 | 0.122 | 0.199 | 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 | 130 | 141 | 126 | 96 | 0 | 286 | 0 | 98 | 83 | 0 |
N.S. |
1 | 1.08 | 0.97 | 0.74 | 0.00 | 2.20 | 0.00 | 0.75 | 0.64 | 0.00 |
time (sec) |
N/A | 0.492 | 0.629 | 0.300 | 0.000 | 0.099 | 0.000 | 0.130 | 0.224 | 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 | 182 | 191 | 144 | 117 | 0 | 321 | 0 | 125 | 102 | 0 |
N.S. |
1 | 1.05 | 0.79 | 0.64 | 0.00 | 1.76 | 0.00 | 0.69 | 0.56 | 0.00 |
time (sec) |
N/A | 0.566 | 0.716 | 0.296 | 0.000 | 0.129 | 0.000 | 0.127 | 0.220 | 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 | 198 | 217 | 77 | 77 | 71 | 90 | 0 | 166 | 60 | 128 |
N.S. |
1 | 1.10 | 0.39 | 0.39 | 0.36 | 0.45 | 0.00 | 0.84 | 0.30 | 0.65 |
time (sec) |
N/A | 0.609 | 0.563 | 0.280 | 0.046 | 0.161 | 0.000 | 0.139 | 0.201 | 7.556 |
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 | 155 | 170 | 67 | 66 | 46 | 80 | 0 | 127 | 49 | 107 |
N.S. |
1 | 1.10 | 0.43 | 0.43 | 0.30 | 0.52 | 0.00 | 0.82 | 0.32 | 0.69 |
time (sec) |
N/A | 0.499 | 0.499 | 0.247 | 0.039 | 0.086 | 0.000 | 0.128 | 0.200 | 6.665 |
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 | 121 | 55 | 55 | 43 | 68 | 0 | 87 | 38 | 86 |
N.S. |
1 | 1.02 | 0.46 | 0.46 | 0.36 | 0.57 | 0.00 | 0.73 | 0.32 | 0.72 |
time (sec) |
N/A | 0.382 | 0.436 | 0.282 | 0.043 | 0.113 | 0.000 | 0.128 | 0.195 | 6.863 |
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 | 74 | 74 | 43 | 44 | 23 | 55 | 0 | 46 | 27 | 66 |
N.S. |
1 | 1.00 | 0.58 | 0.59 | 0.31 | 0.74 | 0.00 | 0.62 | 0.36 | 0.89 |
time (sec) |
N/A | 0.296 | 0.382 | 0.241 | 0.037 | 0.095 | 0.000 | 0.124 | 0.217 | 6.698 |
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 | 86 | 125 | 108 | 78 | 0 | 254 | 0 | 53 | 67 | 0 |
N.S. |
1 | 1.45 | 1.26 | 0.91 | 0.00 | 2.95 | 0.00 | 0.62 | 0.78 | 0.00 |
time (sec) |
N/A | 0.455 | 0.441 | 0.243 | 0.000 | 0.127 | 0.000 | 0.129 | 0.216 | 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 | 130 | 131 | 126 | 96 | 0 | 286 | 0 | 95 | 83 | 0 |
N.S. |
1 | 1.01 | 0.97 | 0.74 | 0.00 | 2.20 | 0.00 | 0.73 | 0.64 | 0.00 |
time (sec) |
N/A | 0.461 | 0.615 | 0.283 | 0.000 | 0.147 | 0.000 | 0.136 | 0.225 | 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 | 180 | 185 | 144 | 117 | 0 | 321 | 0 | 119 | 102 | 0 |
N.S. |
1 | 1.03 | 0.80 | 0.65 | 0.00 | 1.78 | 0.00 | 0.66 | 0.57 | 0.00 |
time (sec) |
N/A | 0.554 | 0.673 | 0.253 | 0.000 | 0.105 | 0.000 | 0.134 | 0.200 | 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 | 268 | 337 | 152 | 191 | 0 | 455 | 0 | 219 | 193 | 0 |
N.S. |
1 | 1.26 | 0.57 | 0.71 | 0.00 | 1.70 | 0.00 | 0.82 | 0.72 | 0.00 |
time (sec) |
N/A | 1.840 | 0.884 | 0.302 | 0.000 | 0.204 | 0.000 | 0.133 | 0.215 | 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 | 188 | 285 | 144 | 175 | 0 | 430 | 0 | 147 | 178 | 0 |
N.S. |
1 | 1.52 | 0.77 | 0.93 | 0.00 | 2.29 | 0.00 | 0.78 | 0.95 | 0.00 |
time (sec) |
N/A | 1.381 | 0.724 | 0.250 | 0.000 | 0.112 | 0.000 | 0.135 | 0.207 | 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 | 182 | 230 | 130 | 157 | 0 | 401 | 0 | 142 | 161 | 0 |
N.S. |
1 | 1.26 | 0.71 | 0.86 | 0.00 | 2.20 | 0.00 | 0.78 | 0.88 | 0.00 |
time (sec) |
N/A | 0.855 | 0.682 | 0.306 | 0.000 | 0.122 | 0.000 | 0.143 | 0.203 | 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 | 144 | 190 | 125 | 138 | 0 | 379 | 0 | 110 | 156 | 0 |
N.S. |
1 | 1.32 | 0.87 | 0.96 | 0.00 | 2.63 | 0.00 | 0.76 | 1.08 | 0.00 |
time (sec) |
N/A | 0.548 | 0.642 | 0.269 | 0.000 | 0.104 | 0.000 | 0.130 | 0.229 | 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 | 150 | 150 | 126 | 139 | 0 | 383 | 0 | 114 | 154 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.93 | 0.00 | 2.55 | 0.00 | 0.76 | 1.03 | 0.00 |
time (sec) |
N/A | 0.426 | 0.626 | 0.286 | 0.000 | 0.125 | 0.000 | 0.122 | 0.223 | 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 | 115 | 153 | 125 | 141 | 0 | 379 | 0 | 110 | 156 | 0 |
N.S. |
1 | 1.33 | 1.09 | 1.23 | 0.00 | 3.30 | 0.00 | 0.96 | 1.36 | 0.00 |
time (sec) |
N/A | 0.438 | 0.602 | 0.242 | 0.000 | 0.110 | 0.000 | 0.124 | 0.218 | 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 | 193 | 196 | 182 | 199 | 0 | 557 | 0 | 141 | 251 | 0 |
N.S. |
1 | 1.02 | 0.94 | 1.03 | 0.00 | 2.89 | 0.00 | 0.73 | 1.30 | 0.00 |
time (sec) |
N/A | 0.550 | 0.742 | 0.280 | 0.000 | 0.110 | 0.000 | 0.128 | 0.195 | 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 | 235 | 235 | 199 | 230 | 0 | 609 | 0 | 209 | 289 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.98 | 0.00 | 2.59 | 0.00 | 0.89 | 1.23 | 0.00 |
time (sec) |
N/A | 0.617 | 1.046 | 0.374 | 0.000 | 0.132 | 0.000 | 0.124 | 0.210 | 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 | 249 | 245 | 208 | 241 | 0 | 633 | 0 | 202 | 307 | 0 |
N.S. |
1 | 0.98 | 0.84 | 0.97 | 0.00 | 2.54 | 0.00 | 0.81 | 1.23 | 0.00 |
time (sec) |
N/A | 0.642 | 1.033 | 0.282 | 0.000 | 0.148 | 0.000 | 0.133 | 0.210 | 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 | 268 | 429 | 166 | 246 | 0 | 481 | 0 | 207 | 288 | 0 |
N.S. |
1 | 1.60 | 0.62 | 0.92 | 0.00 | 1.79 | 0.00 | 0.77 | 1.07 | 0.00 |
time (sec) |
N/A | 2.610 | 1.123 | 0.262 | 0.000 | 0.115 | 0.000 | 0.146 | 0.225 | 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 | 266 | 386 | 152 | 236 | 0 | 456 | 0 | 191 | 273 | 0 |
N.S. |
1 | 1.45 | 0.57 | 0.89 | 0.00 | 1.71 | 0.00 | 0.72 | 1.03 | 0.00 |
time (sec) |
N/A | 1.951 | 1.031 | 0.296 | 0.000 | 0.132 | 0.000 | 0.143 | 0.219 | 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 | 223 | 281 | 144 | 218 | 0 | 427 | 0 | 153 | 256 | 0 |
N.S. |
1 | 1.26 | 0.65 | 0.98 | 0.00 | 1.91 | 0.00 | 0.69 | 1.15 | 0.00 |
time (sec) |
N/A | 0.945 | 0.852 | 0.260 | 0.000 | 0.130 | 0.000 | 0.137 | 0.223 | 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 | 183 | 280 | 138 | 199 | 0 | 409 | 0 | 125 | 251 | 0 |
N.S. |
1 | 1.53 | 0.75 | 1.09 | 0.00 | 2.23 | 0.00 | 0.68 | 1.37 | 0.00 |
time (sec) |
N/A | 0.924 | 0.795 | 0.288 | 0.000 | 0.110 | 0.000 | 0.141 | 0.216 | 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 | 188 | 243 | 137 | 200 | 0 | 409 | 0 | 133 | 249 | 0 |
N.S. |
1 | 1.29 | 0.73 | 1.06 | 0.00 | 2.18 | 0.00 | 0.71 | 1.32 | 0.00 |
time (sec) |
N/A | 0.593 | 0.740 | 0.243 | 0.000 | 0.123 | 0.000 | 0.138 | 0.213 | 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 | 153 | 199 | 138 | 202 | 0 | 413 | 0 | 132 | 251 | 0 |
N.S. |
1 | 1.30 | 0.90 | 1.32 | 0.00 | 2.70 | 0.00 | 0.86 | 1.64 | 0.00 |
time (sec) |
N/A | 0.505 | 0.754 | 0.243 | 0.000 | 0.106 | 0.000 | 0.134 | 0.193 | 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 | 156 | 202 | 138 | 202 | 0 | 409 | 0 | 125 | 251 | 0 |
N.S. |
1 | 1.29 | 0.88 | 1.29 | 0.00 | 2.62 | 0.00 | 0.80 | 1.61 | 0.00 |
time (sec) |
N/A | 0.475 | 0.736 | 0.270 | 0.000 | 0.122 | 0.000 | 0.132 | 0.204 | 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 | 231 | 235 | 194 | 298 | 0 | 587 | 0 | 157 | 410 | 0 |
N.S. |
1 | 1.02 | 0.84 | 1.29 | 0.00 | 2.54 | 0.00 | 0.68 | 1.77 | 0.00 |
time (sec) |
N/A | 0.594 | 0.890 | 0.263 | 0.000 | 0.145 | 0.000 | 0.132 | 0.229 | 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 | 275 | 275 | 212 | 254 | 0 | 639 | 0 | 196 | 448 | 0 |
N.S. |
1 | 1.00 | 0.77 | 0.92 | 0.00 | 2.32 | 0.00 | 0.71 | 1.63 | 0.00 |
time (sec) |
N/A | 0.669 | 1.176 | 0.303 | 0.000 | 0.145 | 0.000 | 0.130 | 0.222 | 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 | 331 | 312 | 231 | 264 | 0 | 681 | 0 | 270 | 475 | 0 |
N.S. |
1 | 0.94 | 0.70 | 0.80 | 0.00 | 2.06 | 0.00 | 0.82 | 1.44 | 0.00 |
time (sec) |
N/A | 0.741 | 1.317 | 0.328 | 0.000 | 0.133 | 0.000 | 0.135 | 0.248 | 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 | 307 | 482 | 163 | 255 | 0 | 582 | 0 | 228 | 368 | 0 |
N.S. |
1 | 1.57 | 0.53 | 0.83 | 0.00 | 1.90 | 0.00 | 0.74 | 1.20 | 0.00 |
time (sec) |
N/A | 2.676 | 1.209 | 0.312 | 0.000 | 0.121 | 0.000 | 0.151 | 0.199 | 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 | 264 | 428 | 152 | 245 | 0 | 553 | 0 | 190 | 351 | 0 |
N.S. |
1 | 1.62 | 0.58 | 0.93 | 0.00 | 2.09 | 0.00 | 0.72 | 1.33 | 0.00 |
time (sec) |
N/A | 2.033 | 1.056 | 0.299 | 0.000 | 0.120 | 0.000 | 0.140 | 0.218 | 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 | 224 | 387 | 149 | 260 | 0 | 531 | 0 | 162 | 346 | 0 |
N.S. |
1 | 1.73 | 0.67 | 1.16 | 0.00 | 2.37 | 0.00 | 0.72 | 1.54 | 0.00 |
time (sec) |
N/A | 1.475 | 0.988 | 0.273 | 0.000 | 0.131 | 0.000 | 0.139 | 0.197 | 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 | 227 | 334 | 149 | 263 | 0 | 535 | 0 | 171 | 346 | 0 |
N.S. |
1 | 1.47 | 0.66 | 1.16 | 0.00 | 2.36 | 0.00 | 0.75 | 1.52 | 0.00 |
time (sec) |
N/A | 1.031 | 0.901 | 0.251 | 0.000 | 0.106 | 0.000 | 0.141 | 0.221 | 0.000 |