Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 122 | 87 | 120 | 184 | 113 | 151 | 0 | 121 | 0 |
N.S. |
1 | 0.98 | 0.70 | 0.97 | 1.48 | 0.91 | 1.22 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 0.316 | 0.065 | 0.407 | 0.037 | 0.091 | 0.689 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 132 | 88 | 109 | 166 | 109 | 138 | 0 | 122 | 0 |
N.S. |
1 | 1.10 | 0.73 | 0.91 | 1.38 | 0.91 | 1.15 | 0.00 | 1.02 | 0.00 |
time (sec) |
N/A | 0.333 | 0.040 | 0.685 | 0.037 | 0.092 | 0.494 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 102 | 78 | 101 | 145 | 103 | 126 | 0 | 102 | 0 |
N.S. |
1 | 1.00 | 0.76 | 0.99 | 1.42 | 1.01 | 1.24 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.314 | 0.055 | 0.364 | 0.034 | 0.100 | 0.366 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 90 | 77 | 85 | 127 | 98 | 117 | 0 | 103 | 0 |
N.S. |
1 | 1.03 | 0.89 | 0.98 | 1.46 | 1.13 | 1.34 | 0.00 | 1.18 | 0.00 |
time (sec) |
N/A | 0.254 | 0.036 | 0.681 | 0.026 | 0.110 | 0.282 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 77 | 86 | 73 | 97 | 83 | 90 | 0 | 75 | 0 |
N.S. |
1 | 1.03 | 1.15 | 0.97 | 1.29 | 1.11 | 1.20 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.265 | 0.021 | 0.195 | 0.032 | 0.093 | 0.149 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 153 | 113 | 159 | 0 | 0 | 0 | 0 | 76 | 0 |
N.S. |
1 | 1.38 | 1.02 | 1.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.686 | 0.039 | 0.931 | 0.000 | 0.000 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 68 | 74 | 67 | 64 | 156 | 0 | 0 | 92 | 0 |
N.S. |
1 | 1.03 | 1.12 | 1.02 | 0.97 | 2.36 | 0.00 | 0.00 | 1.39 | 0.00 |
time (sec) |
N/A | 0.314 | 0.021 | 0.237 | 0.032 | 0.127 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 154 | 111 | 151 | 0 | 0 | 0 | 0 | 71 | 0 |
N.S. |
1 | 1.20 | 0.87 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 1.143 | 0.036 | 0.738 | 0.000 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 79 | 93 | 83 | 91 | 169 | 0 | 0 | 104 | 0 |
N.S. |
1 | 0.99 | 1.16 | 1.04 | 1.14 | 2.11 | 0.00 | 0.00 | 1.30 | 0.00 |
time (sec) |
N/A | 0.331 | 0.025 | 0.238 | 0.027 | 0.126 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 169 | 119 | 163 | 319 | 165 | 230 | 0 | 164 | 0 |
N.S. |
1 | 0.93 | 0.66 | 0.90 | 1.76 | 0.91 | 1.27 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 0.480 | 0.068 | 0.456 | 0.038 | 0.101 | 1.286 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 187 | 115 | 146 | 292 | 161 | 218 | 0 | 165 | 0 |
N.S. |
1 | 1.04 | 0.64 | 0.81 | 1.62 | 0.89 | 1.21 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 0.427 | 0.059 | 0.771 | 0.034 | 0.111 | 0.941 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 149 | 111 | 144 | 261 | 153 | 202 | 0 | 145 | 0 |
N.S. |
1 | 0.95 | 0.71 | 0.92 | 1.66 | 0.97 | 1.29 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 0.481 | 0.060 | 0.432 | 0.034 | 0.107 | 0.668 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 117 | 104 | 116 | 234 | 149 | 190 | 0 | 146 | 0 |
N.S. |
1 | 0.98 | 0.87 | 0.97 | 1.95 | 1.24 | 1.58 | 0.00 | 1.22 | 0.00 |
time (sec) |
N/A | 0.292 | 0.083 | 0.736 | 0.035 | 0.090 | 0.576 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 124 | 95 | 116 | 194 | 133 | 165 | 0 | 118 | 0 |
N.S. |
1 | 0.97 | 0.74 | 0.91 | 1.52 | 1.04 | 1.29 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 0.379 | 0.047 | 0.256 | 0.034 | 0.095 | 0.322 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 243 | 173 | 222 | 0 | 0 | 0 | 0 | 120 | 0 |
N.S. |
1 | 1.41 | 1.01 | 1.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 0.993 | 0.126 | 1.026 | 0.000 | 0.000 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | F(-2) | B | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 114 | 124 | 112 | 143 | 228 | 0 | 0 | 139 | 0 |
N.S. |
1 | 0.95 | 1.03 | 0.93 | 1.19 | 1.90 | 0.00 | 0.00 | 1.16 | 0.00 |
time (sec) |
N/A | 0.690 | 0.081 | 0.296 | 0.028 | 0.118 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 251 | 151 | 240 | 0 | 0 | 0 | 0 | 137 | 0 |
N.S. |
1 | 1.34 | 0.81 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 1.102 | 0.160 | 1.077 | 0.000 | 0.000 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | F(-2) | B | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 134 | 133 | 112 | 137 | 243 | 0 | 0 | 147 | 0 |
N.S. |
1 | 1.06 | 1.06 | 0.89 | 1.09 | 1.93 | 0.00 | 0.00 | 1.17 | 0.00 |
time (sec) |
N/A | 0.710 | 0.083 | 0.286 | 0.036 | 0.124 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 226 | 210 | 143 | 202 | 465 | 201 | 289 | 0 | 205 | 0 |
N.S. |
1 | 0.93 | 0.63 | 0.89 | 2.06 | 0.89 | 1.28 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 0.693 | 0.088 | 0.451 | 0.037 | 0.101 | 2.248 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 199 | 192 | 139 | 173 | 429 | 197 | 280 | 0 | 206 | 0 |
N.S. |
1 | 0.96 | 0.70 | 0.87 | 2.16 | 0.99 | 1.41 | 0.00 | 1.04 | 0.00 |
time (sec) |
N/A | 0.402 | 0.080 | 0.763 | 0.040 | 0.122 | 1.650 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 190 | 135 | 183 | 388 | 189 | 265 | 0 | 186 | 0 |
N.S. |
1 | 0.94 | 0.67 | 0.91 | 1.92 | 0.94 | 1.31 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 0.572 | 0.075 | 0.429 | 0.036 | 0.093 | 1.176 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 140 | 128 | 143 | 352 | 185 | 253 | 0 | 187 | 0 |
N.S. |
1 | 0.97 | 0.88 | 0.99 | 2.43 | 1.28 | 1.74 | 0.00 | 1.29 | 0.00 |
time (sec) |
N/A | 0.302 | 0.106 | 0.738 | 0.037 | 0.092 | 0.934 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 162 | 119 | 153 | 301 | 169 | 221 | 0 | 159 | 0 |
N.S. |
1 | 0.95 | 0.70 | 0.90 | 1.77 | 0.99 | 1.30 | 0.00 | 0.94 | 0.00 |
time (sec) |
N/A | 0.755 | 0.058 | 0.268 | 0.035 | 0.093 | 0.573 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 348 | 216 | 271 | 0 | 0 | 0 | 0 | 161 | 0 |
N.S. |
1 | 1.57 | 0.98 | 1.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 2.254 | 0.159 | 1.017 | 0.000 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |
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 | 160 | 146 | 163 | 149 | 231 | 276 | 0 | 0 | 180 | 0 |
N.S. |
1 | 0.91 | 1.02 | 0.93 | 1.44 | 1.72 | 0.00 | 0.00 | 1.12 | 0.00 |
time (sec) |
N/A | 0.901 | 0.101 | 0.289 | 0.035 | 0.112 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 249 | 356 | 244 | 289 | 0 | 0 | 0 | 0 | 179 | 0 |
N.S. |
1 | 1.43 | 0.98 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 1.758 | 0.141 | 1.115 | 0.000 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 156 | 171 | 153 | 208 | 289 | 0 | 0 | 188 | 0 |
N.S. |
1 | 0.90 | 0.98 | 0.88 | 1.20 | 1.66 | 0.00 | 0.00 | 1.08 | 0.00 |
time (sec) |
N/A | 0.620 | 0.104 | 0.290 | 0.033 | 0.113 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 170 | 170 | 208 | 0 | 0 | 0 | 0 | 56 | 0 |
N.S. |
1 | 1.09 | 1.09 | 1.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.882 | 0.162 | 0.731 | 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 | C | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 141 | 181 | 146 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.04 | 1.34 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.670 | 0.142 | 1.069 | 0.000 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 99 | 121 | 170 | 0 | 0 | 0 | 0 | 45 | 0 |
N.S. |
1 | 0.92 | 1.12 | 1.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.738 | 0.161 | 1.250 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | B | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 75 | 167 | 84 | 0 | 0 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.03 | 2.29 | 1.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.657 | 0.048 | 0.655 | 0.000 | 0.000 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 59 | 135 | 143 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 0.84 | 1.93 | 2.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.600 | 0.023 | 0.632 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | B | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 65 | 207 | 161 | 0 | 0 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.07 | 3.39 | 2.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.636 | 0.063 | 0.917 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 96 | 182 | 176 | 0 | 0 | 0 | 0 | 43 | 0 |
N.S. |
1 | 0.95 | 1.80 | 1.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.638 | 0.109 | 0.698 | 0.000 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | B | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 112 | 240 | 217 | 0 | 0 | 0 | 0 | 67 | 0 |
N.S. |
1 | 0.99 | 2.12 | 1.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.639 | 0.176 | 1.135 | 0.000 | 0.000 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 160 | 247 | 215 | 0 | 0 | 0 | 0 | 60 | 0 |
N.S. |
1 | 1.03 | 1.58 | 1.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.885 | 0.137 | 0.682 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 181 | 268 | 224 | 0 | 0 | 0 | 0 | 127 | 0 |
N.S. |
1 | 1.06 | 1.57 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.884 | 0.196 | 1.154 | 0.000 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 147 | 241 | 140 | 0 | 0 | 0 | 0 | 132 | 0 |
N.S. |
1 | 1.01 | 1.66 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 0.687 | 0.154 | 0.878 | 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 | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 117 | 221 | 195 | 0 | 0 | 0 | 0 | 116 | 0 |
N.S. |
1 | 0.92 | 1.74 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 0.722 | 0.164 | 0.675 | 0.000 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 74 | 61 | 0 | 65 | 0 | 0 | 88 | 0 |
N.S. |
1 | 1.00 | 1.35 | 1.11 | 0.00 | 1.18 | 0.00 | 0.00 | 1.60 | 0.00 |
time (sec) |
N/A | 0.394 | 0.097 | 0.345 | 0.000 | 0.093 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 114 | 216 | 195 | 0 | 0 | 0 | 0 | 107 | 0 |
N.S. |
1 | 0.92 | 1.74 | 1.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.870 | 0.065 | 0.599 | 0.000 | 0.000 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | B | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 115 | 234 | 217 | 0 | 0 | 0 | 0 | 138 | 0 |
N.S. |
1 | 1.05 | 2.13 | 1.97 | 0.00 | 0.00 | 0.00 | 0.00 | 1.25 | 0.00 |
time (sec) |
N/A | 0.891 | 0.311 | 1.095 | 0.000 | 0.000 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 182 | 253 | 227 | 0 | 0 | 0 | 0 | 123 | 0 |
N.S. |
1 | 1.16 | 1.61 | 1.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.860 | 0.386 | 0.676 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | B | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 191 | 326 | 242 | 0 | 0 | 0 | 0 | 163 | 0 |
N.S. |
1 | 1.39 | 2.38 | 1.77 | 0.00 | 0.00 | 0.00 | 0.00 | 1.19 | 0.00 |
time (sec) |
N/A | 0.974 | 0.311 | 1.158 | 0.000 | 0.000 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 215 | 280 | 311 | 268 | 0 | 0 | 0 | 0 | 138 | 0 |
N.S. |
1 | 1.30 | 1.45 | 1.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 1.282 | 0.415 | 1.282 | 0.000 | 0.000 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 201 | 341 | 247 | 0 | 0 | 0 | 0 | 210 | 0 |
N.S. |
1 | 1.08 | 1.83 | 1.33 | 0.00 | 0.00 | 0.00 | 0.00 | 1.13 | 0.00 |
time (sec) |
N/A | 1.124 | 0.397 | 0.665 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 95 | 79 | 108 | 0 | 99 | 0 | 0 | 162 | 0 |
N.S. |
1 | 0.98 | 0.81 | 1.11 | 0.00 | 1.02 | 0.00 | 0.00 | 1.67 | 0.00 |
time (sec) |
N/A | 0.483 | 0.134 | 0.358 | 0.000 | 0.085 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 170 | 340 | 247 | 0 | 0 | 0 | 0 | 207 | 0 |
N.S. |
1 | 0.92 | 1.85 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 | 1.12 | 0.00 |
time (sec) |
N/A | 1.193 | 0.196 | 0.655 | 0.000 | 0.000 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 78 | 56 | 76 | 0 | 98 | 0 | 0 | 160 | 0 |
N.S. |
1 | 0.98 | 0.70 | 0.95 | 0.00 | 1.22 | 0.00 | 0.00 | 2.00 | 0.00 |
time (sec) |
N/A | 0.254 | 0.107 | 0.414 | 0.000 | 0.086 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 164 | 341 | 248 | 0 | 0 | 0 | 0 | 199 | 0 |
N.S. |
1 | 0.92 | 1.92 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 1.12 | 0.00 |
time (sec) |
N/A | 0.716 | 0.092 | 0.567 | 0.000 | 0.000 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 183 | 289 | 280 | 0 | 0 | 0 | 0 | 238 | 0 |
N.S. |
1 | 1.15 | 1.82 | 1.76 | 0.00 | 0.00 | 0.00 | 0.00 | 1.50 | 0.00 |
time (sec) |
N/A | 1.012 | 0.419 | 1.158 | 0.000 | 0.000 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 249 | 298 | 291 | 0 | 0 | 0 | 0 | 214 | 0 |
N.S. |
1 | 1.18 | 1.41 | 1.38 | 0.00 | 0.00 | 0.00 | 0.00 | 1.01 | 0.00 |
time (sec) |
N/A | 1.267 | 0.704 | 1.239 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 280 | 353 | 344 | 0 | 0 | 0 | 0 | 271 | 0 |
N.S. |
1 | 1.30 | 1.63 | 1.59 | 0.00 | 0.00 | 0.00 | 0.00 | 1.25 | 0.00 |
time (sec) |
N/A | 1.747 | 0.559 | 1.203 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 271 | 364 | 374 | 333 | 0 | 0 | 0 | 0 | 229 | 0 |
N.S. |
1 | 1.34 | 1.38 | 1.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 2.357 | 0.954 | 1.232 | 0.000 | 0.000 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 144 | 132 | 189 | 191 | 185 | 301 | 0 | 104 | 0 |
N.S. |
1 | 0.92 | 0.84 | 1.20 | 1.22 | 1.18 | 1.92 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.439 | 0.202 | 1.109 | 0.040 | 0.092 | 3.066 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 102 | 106 | 164 | 134 | 158 | 221 | 0 | 84 | 0 |
N.S. |
1 | 0.94 | 0.97 | 1.50 | 1.23 | 1.45 | 2.03 | 0.00 | 0.77 | 0.00 |
time (sec) |
N/A | 0.381 | 0.172 | 1.124 | 0.042 | 0.096 | 1.002 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 58 | 63 | 108 | 73 | 127 | 141 | 0 | 62 | 0 |
N.S. |
1 | 0.95 | 1.03 | 1.77 | 1.20 | 2.08 | 2.31 | 0.00 | 1.02 | 0.00 |
time (sec) |
N/A | 0.276 | 0.126 | 1.098 | 0.041 | 0.103 | 0.357 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 91 | 131 | 171 | 0 | 0 | 0 | 0 | 75 | 0 |
N.S. |
1 | 1.02 | 1.47 | 1.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.588 | 0.185 | 0.959 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 106 | 185 | 231 | 0 | 0 | 0 | 0 | 96 | 0 |
N.S. |
1 | 0.94 | 1.64 | 2.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.598 | 2.259 | 0.986 | 0.000 | 0.000 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 114 | 79 | 156 | 0 | 0 | 0 | 0 | 85 | 0 |
N.S. |
1 | 0.99 | 0.69 | 1.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.534 | 0.179 | 0.635 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 69 | 100 | 0 | 0 | 0 | 0 | 60 | 0 |
N.S. |
1 | 1.00 | 1.03 | 1.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.318 | 0.094 | 0.660 | 0.000 | 0.000 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | B | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 75 | 155 | 0 | 0 | 110 | 0 | 67 | 0 |
N.S. |
1 | 1.00 | 1.23 | 2.54 | 0.00 | 0.00 | 1.80 | 0.00 | 1.10 | 0.00 |
time (sec) |
N/A | 0.375 | 0.210 | 0.877 | 0.000 | 0.000 | 1.610 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 58 | 96 | 501 | 133 | 217 | 0 | 0 | 75 | 0 |
N.S. |
1 | 0.94 | 1.55 | 8.08 | 2.15 | 3.50 | 0.00 | 0.00 | 1.21 | 0.00 |
time (sec) |
N/A | 0.495 | 0.161 | 1.050 | 0.039 | 0.143 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 104 | 145 | 957 | 135 | 257 | 0 | 0 | 94 | 0 |
N.S. |
1 | 0.92 | 1.28 | 8.47 | 1.19 | 2.27 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.614 | 0.179 | 1.066 | 0.039 | 0.124 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 154 | 124 | 217 | 202 | 229 | 381 | 0 | 150 | 0 |
N.S. |
1 | 0.89 | 0.72 | 1.25 | 1.17 | 1.32 | 2.20 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.792 | 0.230 | 1.115 | 0.042 | 0.107 | 29.399 | 0.000 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 112 | 100 | 195 | 145 | 199 | 301 | 0 | 130 | 0 |
N.S. |
1 | 0.90 | 0.80 | 1.56 | 1.16 | 1.59 | 2.41 | 0.00 | 1.04 | 0.00 |
time (sec) |
N/A | 0.678 | 0.188 | 1.167 | 0.041 | 0.102 | 9.324 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 68 | 72 | 139 | 85 | 167 | 221 | 0 | 108 | 0 |
N.S. |
1 | 0.88 | 0.94 | 1.81 | 1.10 | 2.17 | 2.87 | 0.00 | 1.40 | 0.00 |
time (sec) |
N/A | 0.304 | 0.131 | 1.142 | 0.038 | 0.112 | 3.059 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 143 | 180 | 228 | 0 | 0 | 0 | 0 | 122 | 0 |
N.S. |
1 | 1.07 | 1.34 | 1.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 0.855 | 0.342 | 0.951 | 0.000 | 0.000 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 151 | 292 | 291 | 0 | 0 | 0 | 0 | 146 | 0 |
N.S. |
1 | 0.97 | 1.88 | 1.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.94 | 0.00 |
time (sec) |
N/A | 0.893 | 1.232 | 0.928 | 0.000 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 178 | 154 | 214 | 0 | 0 | 262 | 0 | 132 | 0 |
N.S. |
1 | 1.10 | 0.95 | 1.32 | 0.00 | 0.00 | 1.62 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.822 | 0.368 | 1.026 | 0.000 | 0.000 | 5.416 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 129 | 111 | 152 | 0 | 0 | 185 | 0 | 108 | 0 |
N.S. |
1 | 1.08 | 0.93 | 1.28 | 0.00 | 0.00 | 1.55 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 0.479 | 0.169 | 1.048 | 0.000 | 0.000 | 1.656 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 122 | 122 | 208 | 0 | 0 | 0 | 0 | 114 | 0 |
N.S. |
1 | 1.13 | 1.13 | 1.93 | 0.00 | 0.00 | 0.00 | 0.00 | 1.06 | 0.00 |
time (sec) |
N/A | 0.712 | 0.352 | 0.999 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 121 | 125 | 622 | 0 | 0 | 0 | 0 | 120 | 0 |
N.S. |
1 | 1.05 | 1.09 | 5.41 | 0.00 | 0.00 | 0.00 | 0.00 | 1.04 | 0.00 |
time (sec) |
N/A | 0.974 | 0.285 | 0.995 | 0.000 | 0.000 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 68 | 127 | 1189 | 168 | 265 | 0 | 0 | 124 | 0 |
N.S. |
1 | 0.87 | 1.63 | 15.24 | 2.15 | 3.40 | 0.00 | 0.00 | 1.59 | 0.00 |
time (sec) |
N/A | 0.413 | 0.241 | 1.194 | 0.047 | 0.135 | 0.000 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 112 | 168 | 1828 | 146 | 306 | 0 | 0 | 143 | 0 |
N.S. |
1 | 0.87 | 1.30 | 14.17 | 1.13 | 2.37 | 0.00 | 0.00 | 1.11 | 0.00 |
time (sec) |
N/A | 0.563 | 0.268 | 1.185 | 0.044 | 0.166 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 159 | 207 | 2580 | 203 | 342 | 0 | 0 | 162 | 0 |
N.S. |
1 | 0.88 | 1.15 | 14.33 | 1.13 | 1.90 | 0.00 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.582 | 0.289 | 1.219 | 0.047 | 0.167 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 164 | 132 | 233 | 213 | 299 | 0 | 0 | 197 | 0 |
N.S. |
1 | 0.87 | 0.70 | 1.23 | 1.13 | 1.58 | 0.00 | 0.00 | 1.04 | 0.00 |
time (sec) |
N/A | 0.511 | 0.280 | 1.136 | 0.044 | 0.116 | 0.000 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 120 | 108 | 217 | 156 | 263 | 379 | 0 | 177 | 0 |
N.S. |
1 | 0.85 | 0.77 | 1.54 | 1.11 | 1.87 | 2.69 | 0.00 | 1.26 | 0.00 |
time (sec) |
N/A | 0.435 | 0.243 | 1.132 | 0.043 | 0.122 | 92.056 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 75 | 80 | 170 | 96 | 225 | 299 | 0 | 155 | 0 |
N.S. |
1 | 0.81 | 0.86 | 1.83 | 1.03 | 2.42 | 3.22 | 0.00 | 1.67 | 0.00 |
time (sec) |
N/A | 0.308 | 0.145 | 1.098 | 0.039 | 0.103 | 28.471 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 205 | 257 | 284 | 0 | 0 | 0 | 0 | 170 | 0 |
N.S. |
1 | 1.15 | 1.44 | 1.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 1.214 | 0.431 | 0.960 | 0.000 | 0.000 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 214 | 349 | 348 | 0 | 0 | 0 | 0 | 194 | 0 |
N.S. |
1 | 1.04 | 1.70 | 1.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 1.287 | 1.402 | 0.993 | 0.000 | 0.000 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 212 | 252 | 196 | 267 | 0 | 0 | 350 | 0 | 179 | 0 |
N.S. |
1 | 1.19 | 0.92 | 1.26 | 0.00 | 0.00 | 1.65 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 1.967 | 0.605 | 1.063 | 0.000 | 0.000 | 48.105 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 186 | 153 | 202 | 0 | 0 | 265 | 0 | 155 | 0 |
N.S. |
1 | 1.08 | 0.88 | 1.17 | 0.00 | 0.00 | 1.53 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.738 | 0.299 | 1.085 | 0.000 | 0.000 | 16.183 | 0.000 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 197 | 168 | 261 | 0 | 0 | 0 | 0 | 162 | 0 |
N.S. |
1 | 1.10 | 0.94 | 1.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 0.782 | 0.484 | 1.042 | 0.000 | 0.000 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 193 | 179 | 692 | 0 | 0 | 0 | 0 | 176 | 0 |
N.S. |
1 | 1.16 | 1.08 | 4.17 | 0.00 | 0.00 | 0.00 | 0.00 | 1.06 | 0.00 |
time (sec) |
N/A | 0.857 | 0.450 | 1.010 | 0.000 | 0.000 | 0.000 | 0.000 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 191 | 165 | 1356 | 0 | 0 | 0 | 0 | 179 | 0 |
N.S. |
1 | 1.15 | 0.99 | 8.17 | 0.00 | 0.00 | 0.00 | 0.00 | 1.08 | 0.00 |
time (sec) |
N/A | 0.953 | 0.387 | 1.018 | 0.000 | 0.000 | 0.000 | 0.000 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 78 | 158 | 2165 | 201 | 335 | 0 | 0 | 174 | 0 |
N.S. |
1 | 0.83 | 1.68 | 23.03 | 2.14 | 3.56 | 0.00 | 0.00 | 1.85 | 0.00 |
time (sec) |
N/A | 0.338 | 0.314 | 1.237 | 0.057 | 0.164 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 137 | 199 | 2989 | 157 | 380 | 0 | 0 | 193 | 0 |
N.S. |
1 | 0.88 | 1.28 | 19.16 | 1.01 | 2.44 | 0.00 | 0.00 | 1.24 | 0.00 |
time (sec) |
N/A | 0.452 | 0.334 | 1.405 | 0.053 | 0.142 | 0.000 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 169 | 238 | 3924 | 214 | 422 | 0 | 0 | 212 | 0 |
N.S. |
1 | 0.86 | 1.21 | 20.02 | 1.09 | 2.15 | 0.00 | 0.00 | 1.08 | 0.00 |
time (sec) |
N/A | 0.630 | 0.361 | 1.295 | 0.057 | 0.159 | 0.000 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 160 | 108 | 172 | 174 | 161 | 184 | 0 | 89 | 0 |
N.S. |
1 | 1.07 | 0.72 | 1.15 | 1.17 | 1.08 | 1.23 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.833 | 0.223 | 1.326 | 0.041 | 0.112 | 10.683 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 134 | 111 | 165 | 0 | 0 | 185 | 0 | 90 | 0 |
N.S. |
1 | 1.06 | 0.88 | 1.31 | 0.00 | 0.00 | 1.47 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.911 | 0.330 | 1.193 | 0.000 | 0.000 | 5.988 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 101 | 82 | 133 | 117 | 132 | 124 | 0 | 69 | 0 |
N.S. |
1 | 1.03 | 0.84 | 1.36 | 1.19 | 1.35 | 1.27 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 0.458 | 0.186 | 1.290 | 0.041 | 0.096 | 3.703 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 69 | 107 | 0 | 0 | 122 | 0 | 70 | 0 |
N.S. |
1 | 1.00 | 0.92 | 1.43 | 0.00 | 0.00 | 1.63 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.385 | 0.238 | 0.977 | 0.000 | 0.000 | 2.875 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 49 | 72 | 55 | 96 | 60 | 0 | 43 | 0 |
N.S. |
1 | 1.00 | 1.17 | 1.71 | 1.31 | 2.29 | 1.43 | 0.00 | 1.02 | 0.00 |
time (sec) |
N/A | 0.242 | 0.135 | 0.722 | 0.036 | 0.104 | 2.026 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 53 | 28 | 0 | 87 | 0 | 37 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.12 | 1.12 | 0.00 | 3.48 | 0.00 | 1.48 | 0.00 |
time (sec) |
N/A | 0.210 | 0.005 | 0.641 | 0.035 | 0.000 | 2.029 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 57 | 96 | 118 | 0 | 0 | 0 | 0 | 67 | 0 |
N.S. |
1 | 1.02 | 1.71 | 2.11 | 0.00 | 0.00 | 0.00 | 0.00 | 1.20 | 0.00 |
time (sec) |
N/A | 0.401 | 0.195 | 0.827 | 0.000 | 0.000 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 52 | 84 | 101 | 132 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.00 | 1.27 | 2.05 | 2.46 | 3.22 | 0.00 | 0.00 | 1.27 | 0.00 |
time (sec) |
N/A | 0.277 | 0.136 | 0.951 | 0.038 | 0.127 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 109 | 185 | 216 | 0 | 0 | 0 | 0 | 100 | 0 |
N.S. |
1 | 0.95 | 1.61 | 1.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.618 | 1.872 | 1.011 | 0.000 | 0.000 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 95 | 106 | 373 | 121 | 222 | 0 | 0 | 79 | 0 |
N.S. |
1 | 0.98 | 1.09 | 3.85 | 1.25 | 2.29 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.435 | 0.164 | 1.195 | 0.038 | 0.124 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 129 | 131 | 279 | 0 | 196 | 0 | 0 | 169 | 0 |
N.S. |
1 | 0.94 | 0.96 | 2.04 | 0.00 | 1.43 | 0.00 | 0.00 | 1.23 | 0.00 |
time (sec) |
N/A | 0.445 | 0.275 | 1.335 | 0.000 | 0.137 | 0.000 | 0.000 | 0.190 | 0.000 |