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 | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 213 | 1054 | 233 | 0 | 221 | 0 | 0 | 107 | 0 |
N.S. |
1 | 1.05 | 5.19 | 1.15 | 0.00 | 1.09 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 1.078 | 6.936 | 12.896 | 0.000 | 0.119 | 0.000 | 0.000 | 0.255 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 262 | 311 | 354 | 0 | 341 | 0 | 0 | 125 | 0 |
N.S. |
1 | 1.07 | 1.26 | 1.44 | 0.00 | 1.39 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 1.553 | 3.724 | 17.308 | 0.000 | 7.347 | 0.000 | 0.000 | 0.257 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 205 | 252 | 291 | 0 | 306 | 0 | 0 | 123 | 0 |
N.S. |
1 | 1.06 | 1.30 | 1.50 | 0.00 | 1.58 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 1.153 | 2.057 | 8.600 | 0.000 | 5.514 | 0.000 | 0.000 | 0.273 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 160 | 491 | 236 | 0 | 215 | 0 | 0 | 115 | 0 |
N.S. |
1 | 1.04 | 3.19 | 1.53 | 0.00 | 1.40 | 0.00 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 0.731 | 6.425 | 8.885 | 0.000 | 0.113 | 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 | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 162 | 150 | 238 | 0 | 217 | 0 | 0 | 116 | 0 |
N.S. |
1 | 1.04 | 0.96 | 1.53 | 0.00 | 1.39 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.739 | 2.928 | 12.794 | 0.000 | 0.113 | 0.000 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 213 | 728 | 255 | 0 | 248 | 0 | 0 | 125 | 0 |
N.S. |
1 | 1.05 | 3.59 | 1.26 | 0.00 | 1.22 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 1.082 | 8.412 | 12.724 | 0.000 | 0.119 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-1) | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 268 | 239 | 293 | 0 | 270 | 0 | 0 | 127 | 0 |
N.S. |
1 | 1.07 | 0.96 | 1.17 | 0.00 | 1.08 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 1.442 | 9.375 | 12.727 | 0.000 | 0.118 | 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(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 293 | 317 | 378 | 422 | 0 | 407 | 0 | 0 | 145 | 0 |
N.S. |
1 | 1.08 | 1.29 | 1.44 | 0.00 | 1.39 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 1.988 | 5.133 | 17.027 | 0.000 | 12.627 | 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 | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 241 | 260 | 319 | 350 | 0 | 366 | 0 | 0 | 145 | 0 |
N.S. |
1 | 1.08 | 1.32 | 1.45 | 0.00 | 1.52 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 1.540 | 3.567 | 8.667 | 0.000 | 7.209 | 0.000 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 215 | 613 | 288 | 0 | 266 | 0 | 0 | 143 | 0 |
N.S. |
1 | 1.07 | 3.05 | 1.43 | 0.00 | 1.32 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 1.096 | 6.613 | 7.923 | 0.000 | 0.117 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 215 | 167 | 288 | 0 | 264 | 0 | 0 | 135 | 0 |
N.S. |
1 | 1.07 | 0.83 | 1.43 | 0.00 | 1.31 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 1.097 | 3.160 | 8.328 | 0.000 | 0.120 | 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 | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 217 | 168 | 288 | 0 | 266 | 0 | 0 | 136 | 0 |
N.S. |
1 | 1.07 | 0.83 | 1.42 | 0.00 | 1.31 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 1.085 | 3.027 | 13.003 | 0.000 | 0.119 | 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(-1) | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 268 | 798 | 305 | 0 | 298 | 0 | 0 | 145 | 0 |
N.S. |
1 | 1.07 | 3.19 | 1.22 | 0.00 | 1.19 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 1.435 | 9.686 | 11.830 | 0.000 | 0.119 | 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(-1) | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 297 | 323 | 262 | 343 | 0 | 319 | 0 | 0 | 147 | 0 |
N.S. |
1 | 1.09 | 0.88 | 1.15 | 0.00 | 1.07 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 1.848 | 11.210 | 12.434 | 0.000 | 0.125 | 0.000 | 0.000 | 0.198 | 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 | 105 | 97 | 91 | 86 | 101 | 81 | 252 | 89 | 95 | 117 |
N.S. |
1 | 0.92 | 0.87 | 0.82 | 0.96 | 0.77 | 2.40 | 0.85 | 0.90 | 1.11 |
time (sec) |
N/A | 0.575 | 0.316 | 9.017 | 0.185 | 0.080 | 0.196 | 0.175 | 0.164 | 41.567 |
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 | 84 | 86 | 75 | 65 | 79 | 60 | 168 | 68 | 63 | 84 |
N.S. |
1 | 1.02 | 0.89 | 0.77 | 0.94 | 0.71 | 2.00 | 0.81 | 0.75 | 1.00 |
time (sec) |
N/A | 0.415 | 0.265 | 5.365 | 0.102 | 0.079 | 0.135 | 0.153 | 0.163 | 41.273 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 51 | 51 | 55 | 42 | 94 | 45 | 45 | 50 |
N.S. |
1 | 1.00 | 0.98 | 0.98 | 1.06 | 0.81 | 1.81 | 0.87 | 0.87 | 0.96 |
time (sec) |
N/A | 0.214 | 0.174 | 2.454 | 0.215 | 0.080 | 0.094 | 0.173 | 0.170 | 41.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 46 | 48 | 47 | 54 | 0 | 79 | 54 | 100 |
N.S. |
1 | 1.00 | 1.31 | 1.37 | 1.34 | 1.54 | 0.00 | 2.26 | 1.54 | 2.86 |
time (sec) |
N/A | 0.445 | 0.052 | 2.128 | 0.179 | 0.091 | 0.000 | 0.150 | 0.166 | 41.151 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 43 | 50 | 73 | 85 | 0 | 84 | 79 | 114 |
N.S. |
1 | 1.00 | 1.23 | 1.43 | 2.09 | 2.43 | 0.00 | 2.40 | 2.26 | 3.26 |
time (sec) |
N/A | 0.437 | 0.016 | 3.543 | 0.081 | 0.091 | 0.000 | 0.191 | 0.172 | 41.255 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 64 | 75 | 75 | 95 | 96 | 0 | 151 | 279 | 104 |
N.S. |
1 | 1.05 | 1.23 | 1.23 | 1.56 | 1.57 | 0.00 | 2.48 | 4.57 | 1.70 |
time (sec) |
N/A | 0.557 | 0.023 | 5.037 | 0.040 | 0.091 | 0.000 | 0.191 | 0.172 | 41.658 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 91 | 67 | 81 | 127 | 115 | 0 | 210 | 194 | 145 |
N.S. |
1 | 0.98 | 0.72 | 0.87 | 1.37 | 1.24 | 0.00 | 2.26 | 2.09 | 1.56 |
time (sec) |
N/A | 0.655 | 0.334 | 6.838 | 0.049 | 0.090 | 0.000 | 0.204 | 0.170 | 42.430 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 106 | 85 | 119 | 163 | 136 | 0 | 304 | 482 | 194 |
N.S. |
1 | 0.93 | 0.75 | 1.04 | 1.43 | 1.19 | 0.00 | 2.67 | 4.23 | 1.70 |
time (sec) |
N/A | 0.714 | 0.785 | 7.230 | 0.044 | 0.087 | 0.000 | 0.160 | 0.191 | 43.990 |
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 | 189 | 164 | 146 | 147 | 176 | 142 | 459 | 156 | 139 | 307 |
N.S. |
1 | 0.87 | 0.77 | 0.78 | 0.93 | 0.75 | 2.43 | 0.83 | 0.74 | 1.62 |
time (sec) |
N/A | 0.815 | 1.923 | 31.687 | 0.041 | 0.096 | 0.312 | 0.167 | 0.164 | 38.081 |
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 | 170 | 177 | 118 | 118 | 142 | 114 | 338 | 124 | 112 | 169 |
N.S. |
1 | 1.04 | 0.69 | 0.69 | 0.84 | 0.67 | 1.99 | 0.73 | 0.66 | 0.99 |
time (sec) |
N/A | 0.639 | 2.840 | 12.233 | 0.036 | 0.086 | 0.195 | 0.185 | 0.163 | 40.900 |
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 | 107 | 110 | 90 | 114 | 108 | 85 | 199 | 93 | 75 | 115 |
N.S. |
1 | 1.03 | 0.84 | 1.07 | 1.01 | 0.79 | 1.86 | 0.87 | 0.70 | 1.07 |
time (sec) |
N/A | 0.357 | 1.044 | 1.680 | 0.043 | 0.079 | 0.159 | 0.200 | 0.173 | 40.951 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 120 | 94 | 92 | 87 | 0 | 178 | 82 | 169 |
N.S. |
1 | 1.00 | 1.40 | 1.09 | 1.07 | 1.01 | 0.00 | 2.07 | 0.95 | 1.97 |
time (sec) |
N/A | 0.603 | 1.700 | 2.529 | 0.049 | 0.093 | 0.000 | 0.189 | 0.167 | 41.369 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 109 | 79 | 103 | 117 | 0 | 152 | 101 | 169 |
N.S. |
1 | 1.00 | 1.82 | 1.32 | 1.72 | 1.95 | 0.00 | 2.53 | 1.68 | 2.82 |
time (sec) |
N/A | 0.573 | 2.144 | 4.465 | 0.036 | 0.093 | 0.000 | 0.174 | 0.178 | 42.430 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 84 | 87 | 104 | 140 | 136 | 0 | 190 | 321 | 176 |
N.S. |
1 | 1.05 | 1.09 | 1.30 | 1.75 | 1.70 | 0.00 | 2.38 | 4.01 | 2.20 |
time (sec) |
N/A | 0.640 | 0.287 | 6.123 | 0.050 | 0.093 | 0.000 | 0.185 | 0.173 | 42.404 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 122 | 97 | 118 | 172 | 150 | 0 | 294 | 314 | 227 |
N.S. |
1 | 1.05 | 0.84 | 1.02 | 1.48 | 1.29 | 0.00 | 2.53 | 2.71 | 1.96 |
time (sec) |
N/A | 0.810 | 0.758 | 7.829 | 0.046 | 0.091 | 0.000 | 0.168 | 0.264 | 45.012 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 149 | 120 | 148 | 228 | 180 | 0 | 478 | 533 | 314 |
N.S. |
1 | 0.96 | 0.77 | 0.95 | 1.46 | 1.15 | 0.00 | 3.06 | 3.42 | 2.01 |
time (sec) |
N/A | 0.941 | 0.852 | 8.529 | 0.044 | 0.109 | 0.000 | 0.178 | 0.245 | 45.425 |
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 | 269 | 231 | 289 | 213 | 266 | 211 | 721 | 230 | 210 | 352 |
N.S. |
1 | 0.86 | 1.07 | 0.79 | 0.99 | 0.78 | 2.68 | 0.86 | 0.78 | 1.31 |
time (sec) |
N/A | 1.226 | 2.164 | 147.715 | 0.044 | 0.093 | 0.449 | 0.197 | 0.276 | 42.936 |
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 | 243 | 252 | 176 | 176 | 217 | 174 | 551 | 188 | 156 | 277 |
N.S. |
1 | 1.04 | 0.72 | 0.72 | 0.89 | 0.72 | 2.27 | 0.77 | 0.64 | 1.14 |
time (sec) |
N/A | 0.887 | 3.255 | 42.582 | 0.045 | 0.087 | 0.305 | 0.212 | 0.167 | 42.565 |
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 | 171 | 179 | 140 | 180 | 171 | 136 | 386 | 148 | 124 | 202 |
N.S. |
1 | 1.05 | 0.82 | 1.05 | 1.00 | 0.80 | 2.26 | 0.87 | 0.73 | 1.18 |
time (sec) |
N/A | 0.567 | 1.600 | 1.577 | 0.037 | 0.084 | 0.210 | 0.222 | 0.163 | 42.202 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 146 | 159 | 135 | 145 | 131 | 0 | 314 | 112 | 1924 |
N.S. |
1 | 1.07 | 1.16 | 0.99 | 1.06 | 0.96 | 0.00 | 2.29 | 0.82 | 14.04 |
time (sec) |
N/A | 0.963 | 2.194 | 4.769 | 0.044 | 0.097 | 0.000 | 0.189 | 0.199 | 42.979 |
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 | 131 | 134 | 217 | 124 | 144 | 152 | 0 | 234 | 137 | 236 |
N.S. |
1 | 1.02 | 1.66 | 0.95 | 1.10 | 1.16 | 0.00 | 1.79 | 1.05 | 1.80 |
time (sec) |
N/A | 0.942 | 2.632 | 5.933 | 0.054 | 0.104 | 0.000 | 0.173 | 0.168 | 42.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 126 | 277 | 133 | 169 | 167 | 0 | 239 | 367 | 249 |
N.S. |
1 | 1.02 | 2.23 | 1.07 | 1.36 | 1.35 | 0.00 | 1.93 | 2.96 | 2.01 |
time (sec) |
N/A | 0.982 | 4.919 | 7.540 | 0.048 | 0.101 | 0.000 | 0.166 | 0.179 | 42.011 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 154 | 120 | 146 | 216 | 189 | 0 | 336 | 356 | 526 |
N.S. |
1 | 1.06 | 0.83 | 1.01 | 1.49 | 1.30 | 0.00 | 2.32 | 2.46 | 3.63 |
time (sec) |
N/A | 1.036 | 0.910 | 9.013 | 0.042 | 0.107 | 0.000 | 0.201 | 0.179 | 36.734 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 199 | 144 | 185 | 273 | 211 | 0 | 586 | 722 | 395 |
N.S. |
1 | 1.06 | 0.77 | 0.98 | 1.45 | 1.12 | 0.00 | 3.12 | 3.84 | 2.10 |
time (sec) |
N/A | 1.220 | 1.311 | 9.249 | 0.050 | 0.098 | 0.000 | 0.170 | 0.201 | 45.662 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 236 | 225 | 181 | 200 | 341 | 249 | 0 | 722 | 584 | 470 |
N.S. |
1 | 0.95 | 0.77 | 0.85 | 1.44 | 1.06 | 0.00 | 3.06 | 2.47 | 1.99 |
time (sec) |
N/A | 1.392 | 3.734 | 12.789 | 0.053 | 0.103 | 0.000 | 0.190 | 0.187 | 45.589 |
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 | 366 | 315 | 408 | 368 | 366 | 289 | 1017 | 313 | 270 | 436 |
N.S. |
1 | 0.86 | 1.11 | 1.01 | 1.00 | 0.79 | 2.78 | 0.86 | 0.74 | 1.19 |
time (sec) |
N/A | 1.803 | 2.528 | 5.770 | 0.043 | 0.100 | 0.617 | 0.166 | 0.184 | 45.595 |
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 | 325 | 336 | 333 | 242 | 307 | 243 | 811 | 263 | 227 | 403 |
N.S. |
1 | 1.03 | 1.02 | 0.74 | 0.94 | 0.75 | 2.50 | 0.81 | 0.70 | 1.24 |
time (sec) |
N/A | 1.192 | 4.210 | 212.169 | 0.042 | 0.102 | 0.459 | 0.198 | 0.175 | 42.896 |
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 | 241 | 254 | 263 | 258 | 246 | 197 | 580 | 212 | 168 | 307 |
N.S. |
1 | 1.05 | 1.09 | 1.07 | 1.02 | 0.82 | 2.41 | 0.88 | 0.70 | 1.27 |
time (sec) |
N/A | 0.818 | 1.875 | 3.617 | 0.050 | 0.092 | 0.323 | 0.178 | 0.169 | 42.403 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 214 | 210 | 191 | 208 | 183 | 0 | 603 | 161 | 369 |
N.S. |
1 | 1.07 | 1.05 | 0.96 | 1.04 | 0.92 | 0.00 | 3.02 | 0.80 | 1.84 |
time (sec) |
N/A | 1.389 | 2.764 | 15.218 | 0.038 | 0.095 | 0.000 | 0.208 | 0.175 | 43.198 |
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 | 195 | 204 | 257 | 164 | 197 | 196 | 0 | 371 | 179 | 2522 |
N.S. |
1 | 1.05 | 1.32 | 0.84 | 1.01 | 1.01 | 0.00 | 1.90 | 0.92 | 12.93 |
time (sec) |
N/A | 1.398 | 3.783 | 16.238 | 0.048 | 0.103 | 0.000 | 0.198 | 0.183 | 44.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 209 | 201 | 310 | 178 | 209 | 202 | 0 | 526 | 445 | 330 |
N.S. |
1 | 0.96 | 1.48 | 0.85 | 1.00 | 0.97 | 0.00 | 2.52 | 2.13 | 1.58 |
time (sec) |
N/A | 1.450 | 5.296 | 17.939 | 0.052 | 0.105 | 0.000 | 0.188 | 0.174 | 43.798 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 205 | 831 | 175 | 245 | 219 | 0 | 387 | 402 | 636 |
N.S. |
1 | 1.04 | 4.20 | 0.88 | 1.24 | 1.11 | 0.00 | 1.95 | 2.03 | 3.21 |
time (sec) |
N/A | 1.474 | 10.288 | 19.662 | 0.043 | 0.103 | 0.000 | 0.252 | 0.181 | 44.895 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 230 | 186 | 213 | 317 | 250 | 0 | 635 | 789 | 1969 |
N.S. |
1 | 1.06 | 0.86 | 0.99 | 1.47 | 1.16 | 0.00 | 2.94 | 3.65 | 9.12 |
time (sec) |
N/A | 1.512 | 1.582 | 19.530 | 0.047 | 0.104 | 0.000 | 0.210 | 0.179 | 44.199 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 267 | 283 | 254 | 237 | 386 | 281 | 0 | 850 | 773 | 555 |
N.S. |
1 | 1.06 | 0.95 | 0.89 | 1.45 | 1.05 | 0.00 | 3.18 | 2.90 | 2.08 |
time (sec) |
N/A | 1.753 | 6.184 | 21.598 | 0.052 | 0.104 | 0.000 | 0.204 | 0.178 | 45.211 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 324 | 302 | 244 | 277 | 474 | 327 | 0 | 1186 | 1117 | 706 |
N.S. |
1 | 0.93 | 0.75 | 0.85 | 1.46 | 1.01 | 0.00 | 3.66 | 3.45 | 2.18 |
time (sec) |
N/A | 2.011 | 3.534 | 23.469 | 0.046 | 0.108 | 0.000 | 0.245 | 0.188 | 44.832 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 195 | 152 | 240 | 0 | 541 | 0 | 360 | 23 | 4568 |
N.S. |
1 | 1.10 | 0.85 | 1.35 | 0.00 | 3.04 | 0.00 | 2.02 | 0.13 | 25.66 |
time (sec) |
N/A | 1.072 | 1.689 | 1.755 | 0.000 | 0.120 | 0.000 | 0.180 | 0.159 | 45.844 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 146 | 121 | 169 | 0 | 426 | 10409 | 227 | 22 | 3761 |
N.S. |
1 | 1.09 | 0.90 | 1.26 | 0.00 | 3.18 | 77.68 | 1.69 | 0.16 | 28.07 |
time (sec) |
N/A | 0.696 | 1.195 | 1.490 | 0.000 | 0.111 | 171.834 | 0.150 | 0.168 | 45.349 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 86 | 85 | 110 | 0 | 322 | 3225 | 142 | 10 | 541 |
N.S. |
1 | 0.97 | 0.96 | 1.24 | 0.00 | 3.62 | 36.24 | 1.60 | 0.11 | 6.08 |
time (sec) |
N/A | 0.499 | 0.873 | 1.383 | 0.000 | 0.107 | 56.425 | 0.136 | 0.161 | 42.302 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 68 | 73 | 0 | 242 | 524 | 296 | 1 | 344 |
N.S. |
1 | 1.00 | 1.01 | 1.09 | 0.00 | 3.61 | 7.82 | 4.42 | 0.01 | 5.13 |
time (sec) |
N/A | 0.299 | 0.251 | 1.228 | 0.000 | 0.105 | 11.326 | 0.202 | 0.161 | 42.833 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 112 | 92 | 0 | 304 | 0 | 127 | 31 | 342 |
N.S. |
1 | 1.00 | 1.47 | 1.21 | 0.00 | 4.00 | 0.00 | 1.67 | 0.41 | 4.50 |
time (sec) |
N/A | 0.390 | 0.634 | 1.717 | 0.000 | 0.418 | 0.000 | 0.178 | 0.172 | 42.943 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 96 | 129 | 144 | 0 | 460 | 0 | 175 | 18 | 675 |
N.S. |
1 | 0.97 | 1.30 | 1.45 | 0.00 | 4.65 | 0.00 | 1.77 | 0.18 | 6.82 |
time (sec) |
N/A | 0.521 | 1.364 | 1.922 | 0.000 | 0.183 | 0.000 | 0.243 | 0.166 | 43.584 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 154 | 300 | 229 | 0 | 589 | 0 | 269 | 95 | 4051 |
N.S. |
1 | 1.08 | 2.10 | 1.60 | 0.00 | 4.12 | 0.00 | 1.88 | 0.66 | 28.33 |
time (sec) |
N/A | 0.979 | 2.999 | 2.040 | 0.000 | 2.267 | 0.000 | 0.201 | 0.164 | 45.913 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 204 | 422 | 335 | 0 | 729 | 0 | 412 | 43 | 4696 |
N.S. |
1 | 1.09 | 2.26 | 1.79 | 0.00 | 3.90 | 0.00 | 2.20 | 0.23 | 25.11 |
time (sec) |
N/A | 1.395 | 3.696 | 2.188 | 0.000 | 0.506 | 0.000 | 0.209 | 0.169 | 47.153 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 263 | 277 | 184 | 267 | 0 | 964 | 0 | 338 | 214 | 6744 |
N.S. |
1 | 1.05 | 0.70 | 1.02 | 0.00 | 3.67 | 0.00 | 1.29 | 0.81 | 25.64 |
time (sec) |
N/A | 1.318 | 2.734 | 1.977 | 0.000 | 0.151 | 0.000 | 0.172 | 0.171 | 38.012 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 185 | 147 | 205 | 0 | 789 | 0 | 1116 | 108 | 3276 |
N.S. |
1 | 1.19 | 0.95 | 1.32 | 0.00 | 5.09 | 0.00 | 7.20 | 0.70 | 21.14 |
time (sec) |
N/A | 0.868 | 1.993 | 1.707 | 0.000 | 0.134 | 0.000 | 0.252 | 0.169 | 28.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 149 | 119 | 161 | 0 | 551 | 0 | 199 | 83 | 3775 |
N.S. |
1 | 1.22 | 0.98 | 1.32 | 0.00 | 4.52 | 0.00 | 1.63 | 0.68 | 30.94 |
time (sec) |
N/A | 0.644 | 1.360 | 1.394 | 0.000 | 0.117 | 0.000 | 0.146 | 0.164 | 30.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 111 | 97 | 128 | 0 | 379 | 4974 | 159 | 64 | 113 |
N.S. |
1 | 1.11 | 0.97 | 1.28 | 0.00 | 3.79 | 49.74 | 1.59 | 0.64 | 1.13 |
time (sec) |
N/A | 0.361 | 0.658 | 1.297 | 0.000 | 0.105 | 165.708 | 0.151 | 0.158 | 25.342 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 158 | 191 | 182 | 0 | 684 | 0 | 223 | 136 | 3763 |
N.S. |
1 | 1.19 | 1.44 | 1.37 | 0.00 | 5.14 | 0.00 | 1.68 | 1.02 | 28.29 |
time (sec) |
N/A | 0.735 | 1.424 | 2.052 | 0.000 | 2.458 | 0.000 | 0.202 | 0.177 | 30.394 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 208 | 240 | 241 | 0 | 1088 | 0 | 404 | 200 | 5464 |
N.S. |
1 | 1.10 | 1.27 | 1.28 | 0.00 | 5.76 | 0.00 | 2.14 | 1.06 | 28.91 |
time (sec) |
N/A | 1.212 | 3.049 | 2.359 | 0.000 | 6.320 | 0.000 | 0.198 | 0.169 | 30.655 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 284 | 438 | 326 | 0 | 1329 | 0 | 378 | 479 | 6692 |
N.S. |
1 | 1.05 | 1.62 | 1.21 | 0.00 | 4.92 | 0.00 | 1.40 | 1.77 | 24.79 |
time (sec) |
N/A | 1.732 | 7.568 | 2.651 | 0.000 | 11.108 | 0.000 | 0.219 | 0.168 | 31.242 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 398 | 424 | 734 | 402 | 0 | 1812 | 0 | 2712 | 623 | 10598 |
N.S. |
1 | 1.07 | 1.84 | 1.01 | 0.00 | 4.55 | 0.00 | 6.81 | 1.57 | 26.63 |
time (sec) |
N/A | 2.147 | 6.613 | 2.716 | 0.000 | 0.230 | 0.000 | 0.454 | 0.182 | 34.682 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 280 | 317 | 232 | 341 | 0 | 1561 | 0 | 543 | 521 | 5542 |
N.S. |
1 | 1.13 | 0.83 | 1.22 | 0.00 | 5.58 | 0.00 | 1.94 | 1.86 | 19.79 |
time (sec) |
N/A | 1.444 | 4.055 | 2.224 | 0.000 | 0.192 | 0.000 | 0.195 | 0.160 | 30.560 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 247 | 204 | 282 | 0 | 1152 | 0 | 455 | 380 | 6923 |
N.S. |
1 | 1.17 | 0.97 | 1.34 | 0.00 | 5.46 | 0.00 | 2.16 | 1.80 | 32.81 |
time (sec) |
N/A | 0.982 | 2.780 | 1.715 | 0.000 | 0.163 | 0.000 | 0.204 | 0.163 | 31.617 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 206 | 172 | 234 | 0 | 740 | 0 | 391 | 192 | 248 |
N.S. |
1 | 1.14 | 0.96 | 1.30 | 0.00 | 4.11 | 0.00 | 2.17 | 1.07 | 1.38 |
time (sec) |
N/A | 0.706 | 1.767 | 1.534 | 0.000 | 0.127 | 0.000 | 0.228 | 0.164 | 26.825 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 190 | 157 | 232 | 0 | 742 | 0 | 390 | 192 | 248 |
N.S. |
1 | 1.16 | 0.96 | 1.41 | 0.00 | 4.52 | 0.00 | 2.38 | 1.17 | 1.51 |
time (sec) |
N/A | 0.583 | 1.100 | 1.420 | 0.000 | 0.125 | 0.000 | 0.177 | 0.166 | 26.745 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 258 | 269 | 302 | 0 | 1400 | 0 | 481 | 568 | 6913 |
N.S. |
1 | 1.21 | 1.26 | 1.41 | 0.00 | 6.54 | 0.00 | 2.25 | 2.65 | 32.30 |
time (sec) |
N/A | 1.197 | 2.371 | 2.470 | 0.000 | 11.388 | 0.000 | 0.249 | 0.175 | 31.365 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 299 | 335 | 418 | 376 | 0 | 2100 | 0 | 574 | 977 | 9312 |
N.S. |
1 | 1.12 | 1.40 | 1.26 | 0.00 | 7.02 | 0.00 | 1.92 | 3.27 | 31.14 |
time (sec) |
N/A | 2.018 | 7.767 | 3.093 | 0.000 | 24.389 | 0.000 | 0.244 | 0.188 | 34.517 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 402 | 426 | 507 | 460 | 0 | 2416 | 0 | 1395 | 1637 | 10547 |
N.S. |
1 | 1.06 | 1.26 | 1.14 | 0.00 | 6.01 | 0.00 | 3.47 | 4.07 | 26.24 |
time (sec) |
N/A | 2.774 | 5.136 | 3.547 | 0.000 | 37.318 | 0.000 | 0.227 | 0.183 | 33.350 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 409 | 466 | 1278 | 552 | 0 | 2567 | 0 | 966 | 1271 | 7823 |
N.S. |
1 | 1.14 | 3.12 | 1.35 | 0.00 | 6.28 | 0.00 | 2.36 | 3.11 | 19.13 |
time (sec) |
N/A | 2.266 | 9.358 | 3.049 | 0.000 | 0.301 | 0.000 | 0.273 | 0.177 | 37.540 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 301 | 356 | 717 | 459 | 0 | 1857 | 0 | 813 | 1004 | 9733 |
N.S. |
1 | 1.18 | 2.38 | 1.52 | 0.00 | 6.17 | 0.00 | 2.70 | 3.34 | 32.34 |
time (sec) |
N/A | 1.499 | 6.405 | 2.141 | 0.000 | 0.229 | 0.000 | 0.223 | 0.268 | 32.601 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 274 | 319 | 251 | 371 | 0 | 1220 | 0 | 689 | 632 | 440 |
N.S. |
1 | 1.16 | 0.92 | 1.35 | 0.00 | 4.45 | 0.00 | 2.51 | 2.31 | 1.61 |
time (sec) |
N/A | 1.079 | 2.832 | 1.928 | 0.000 | 0.162 | 0.000 | 0.233 | 0.252 | 26.476 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 263 | 302 | 252 | 384 | 0 | 1232 | 0 | 722 | 467 | 451 |
N.S. |
1 | 1.15 | 0.96 | 1.46 | 0.00 | 4.68 | 0.00 | 2.75 | 1.78 | 1.71 |
time (sec) |
N/A | 1.055 | 2.208 | 1.774 | 0.000 | 0.166 | 0.000 | 0.197 | 0.254 | 27.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 237 | 279 | 227 | 372 | 0 | 1228 | 0 | 691 | 627 | 440 |
N.S. |
1 | 1.18 | 0.96 | 1.57 | 0.00 | 5.18 | 0.00 | 2.92 | 2.65 | 1.86 |
time (sec) |
N/A | 0.868 | 2.935 | 1.701 | 0.000 | 0.161 | 0.000 | 0.213 | 0.164 | 26.878 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 301 | 365 | 368 | 479 | 0 | 2269 | 0 | 837 | 1406 | 9727 |
N.S. |
1 | 1.21 | 1.22 | 1.59 | 0.00 | 7.54 | 0.00 | 2.78 | 4.67 | 32.32 |
time (sec) |
N/A | 1.839 | 2.972 | 3.128 | 0.000 | 32.689 | 0.000 | 0.283 | 0.177 | 32.360 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 420 | 476 | 549 | 587 | 0 | 3393 | 0 | 996 | 2086 | 13119 |
N.S. |
1 | 1.13 | 1.31 | 1.40 | 0.00 | 8.08 | 0.00 | 2.37 | 4.97 | 31.24 |
time (sec) |
N/A | 3.112 | 4.936 | 3.994 | 0.000 | 66.779 | 0.000 | 0.320 | 0.191 | 41.461 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 547 | 591 | 781 | 672 | 0 | 3819 | 0 | 1090 | 3080 | 14398 |
N.S. |
1 | 1.08 | 1.43 | 1.23 | 0.00 | 6.98 | 0.00 | 1.99 | 5.63 | 26.32 |
time (sec) |
N/A | 4.050 | 5.602 | 5.954 | 0.000 | 94.704 | 0.000 | 0.294 | 0.196 | 34.422 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 27 | 28 | 23 | 0 | 25 | 56 | 25 | 24 | 24 |
N.S. |
1 | 0.96 | 1.00 | 0.82 | 0.00 | 0.89 | 2.00 | 0.89 | 0.86 | 0.86 |
time (sec) |
N/A | 0.215 | 0.012 | 2.358 | 0.000 | 0.075 | 0.416 | 0.172 | 0.169 | 24.379 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 24 | 21 | 0 | 24 | 68 | 33 | 23 | 50 |
N.S. |
1 | 1.00 | 0.89 | 0.78 | 0.00 | 0.89 | 2.52 | 1.22 | 0.85 | 1.85 |
time (sec) |
N/A | 0.213 | 0.014 | 1.848 | 0.000 | 0.076 | 0.356 | 0.214 | 0.188 | 24.449 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 23 | 12 | 0 | 11 | 31 | 11 | 11 | 11 |
N.S. |
1 | 1.00 | 2.09 | 1.09 | 0.00 | 1.00 | 2.82 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.185 | 0.004 | 1.487 | 0.000 | 0.076 | 0.320 | 0.178 | 0.171 | 24.214 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | C | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 3 | 3 | 3 | 4 | 0 | 3 | 2 | 10 | 3 | 3 |
N.S. |
1 | 1.00 | 1.00 | 1.33 | 0.00 | 1.00 | 0.67 | 3.33 | 1.00 | 1.00 |
time (sec) |
N/A | 0.140 | 0.000 | 0.737 | 0.000 | 0.060 | 0.062 | 0.180 | 0.167 | 24.537 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 20 | 0 | 31 | 39 | 47 | 32 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.67 | 0.00 | 2.58 | 3.25 | 3.92 | 2.67 | 1.33 |
time (sec) |
N/A | 0.191 | 0.005 | 1.928 | 0.000 | 0.085 | 1.802 | 0.148 | 0.164 | 24.712 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 12 | 0 | 19 | 32 | 11 | 19 | 30 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 0.00 | 1.73 | 2.91 | 1.00 | 1.73 | 2.73 |
time (sec) |
N/A | 0.205 | 0.006 | 4.000 | 0.000 | 0.072 | 1.452 | 0.149 | 0.165 | 24.805 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 36 | 37 | 0 | 64 | 0 | 52 | 96 | 73 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 0.00 | 1.78 | 0.00 | 1.44 | 2.67 | 2.03 |
time (sec) |
N/A | 0.267 | 0.011 | 4.599 | 0.000 | 0.083 | 0.000 | 0.191 | 0.168 | 24.566 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 27 | 24 | 25 | 0 | 32 | 42 | 25 | 44 | 39 |
N.S. |
1 | 0.96 | 0.86 | 0.89 | 0.00 | 1.14 | 1.50 | 0.89 | 1.57 | 1.39 |
time (sec) |
N/A | 0.221 | 0.038 | 4.291 | 0.000 | 0.070 | 8.196 | 0.152 | 0.164 | 24.661 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 122 | 98 | 139 | 0 | 350 | 0 | 185 | 214 | 173 |
N.S. |
1 | 1.07 | 0.86 | 1.22 | 0.00 | 3.07 | 0.00 | 1.62 | 1.88 | 1.52 |
time (sec) |
N/A | 0.611 | 0.641 | 2.837 | 0.000 | 0.110 | 0.000 | 0.179 | 0.168 | 25.535 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 81 | 73 | 98 | 0 | 281 | 0 | 128 | 108 | 193 |
N.S. |
1 | 1.03 | 0.92 | 1.24 | 0.00 | 3.56 | 0.00 | 1.62 | 1.37 | 2.44 |
time (sec) |
N/A | 0.424 | 0.330 | 2.229 | 0.000 | 0.104 | 0.000 | 0.140 | 0.163 | 24.808 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 59 | 66 | 0 | 231 | 0 | 245 | 80 | 101 |
N.S. |
1 | 1.00 | 0.97 | 1.08 | 0.00 | 3.79 | 0.00 | 4.02 | 1.31 | 1.66 |
time (sec) |
N/A | 0.304 | 0.152 | 2.050 | 0.000 | 0.095 | 0.000 | 0.167 | 0.170 | 25.392 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 49 | 45 | 0 | 177 | 190 | 78 | 65 | 44 |
N.S. |
1 | 1.00 | 0.98 | 0.90 | 0.00 | 3.54 | 3.80 | 1.56 | 1.30 | 0.88 |
time (sec) |
N/A | 0.221 | 0.058 | 1.525 | 0.000 | 0.100 | 155.939 | 0.162 | 0.176 | 24.667 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 103 | 86 | 0 | 292 | 0 | 122 | 137 | 101 |
N.S. |
1 | 1.00 | 1.47 | 1.23 | 0.00 | 4.17 | 0.00 | 1.74 | 1.96 | 1.44 |
time (sec) |
N/A | 0.364 | 0.296 | 2.634 | 0.000 | 0.126 | 0.000 | 0.201 | 0.168 | 24.736 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 90 | 116 | 125 | 0 | 398 | 0 | 155 | 201 | 326 |
N.S. |
1 | 1.02 | 1.32 | 1.42 | 0.00 | 4.52 | 0.00 | 1.76 | 2.28 | 3.70 |
time (sec) |
N/A | 0.496 | 0.716 | 2.860 | 0.000 | 0.131 | 0.000 | 0.191 | 0.170 | 25.180 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 132 | 239 | 194 | 0 | 487 | 0 | 221 | 480 | 1099 |
N.S. |
1 | 1.07 | 1.94 | 1.58 | 0.00 | 3.96 | 0.00 | 1.80 | 3.90 | 8.93 |
time (sec) |
N/A | 0.839 | 1.684 | 3.144 | 0.000 | 0.203 | 0.000 | 0.197 | 0.180 | 25.218 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 386 | 408 | 292 | 1635 | 0 | 639 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.06 | 0.76 | 4.24 | 0.00 | 1.66 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 2.206 | 2.331 | 29.649 | 0.000 | 0.131 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 303 | 317 | 232 | 1305 | 0 | 561 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.05 | 0.77 | 4.31 | 0.00 | 1.85 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 1.610 | 1.652 | 16.412 | 0.000 | 0.114 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 237 | 179 | 993 | 0 | 492 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.03 | 0.77 | 4.30 | 0.00 | 2.13 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 1.235 | 3.555 | 15.572 | 0.000 | 0.106 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 172 | 146 | 600 | 0 | 437 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.01 | 0.85 | 3.51 | 0.00 | 2.56 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.860 | 0.915 | 10.843 | 0.000 | 0.101 | 0.000 | 0.000 | 0.173 | 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 | 179 | 107 | 247 | 0 | 0 | 0 | 0 | 51 | 0 |
N.S. |
1 | 1.01 | 0.60 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 1.257 | 12.802 | 7.994 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |