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 | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 127 | 228 | 0 | 134 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.00 | 1.19 | 2.13 | 0.00 | 1.25 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.716 | 1.992 | 5.038 | 0.000 | 0.083 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 135 | 136 | 250 | 0 | 157 | 0 | 0 | 75 | 0 |
N.S. |
1 | 1.00 | 1.01 | 1.85 | 0.00 | 1.16 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.856 | 2.438 | 9.835 | 0.000 | 0.087 | 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 | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 163 | 149 | 272 | 0 | 170 | 0 | 0 | 75 | 0 |
N.S. |
1 | 1.01 | 0.93 | 1.69 | 0.00 | 1.06 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.988 | 2.826 | 13.165 | 0.000 | 0.091 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 187 | 279 | 439 | 0 | 215 | 0 | 0 | 103 | 0 |
N.S. |
1 | 1.00 | 1.49 | 2.35 | 0.00 | 1.15 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.541 | 3.563 | 64.059 | 0.000 | 0.091 | 0.000 | 0.000 | 0.311 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 157 | 259 | 386 | 0 | 200 | 0 | 0 | 103 | 0 |
N.S. |
1 | 1.00 | 1.65 | 2.46 | 0.00 | 1.27 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.502 | 2.532 | 64.521 | 0.000 | 0.091 | 0.000 | 0.000 | 0.319 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 131 | 157 | 371 | 0 | 179 | 0 | 0 | 103 | 0 |
N.S. |
1 | 1.00 | 1.20 | 2.83 | 0.00 | 1.37 | 0.00 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.468 | 2.294 | 63.625 | 0.000 | 0.091 | 0.000 | 0.000 | 0.332 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 131 | 135 | 172 | 0 | 148 | 0 | 0 | 95 | 0 |
N.S. |
1 | 1.00 | 1.03 | 1.31 | 0.00 | 1.13 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.460 | 2.343 | 6.598 | 0.000 | 0.097 | 0.000 | 0.000 | 0.268 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 131 | 137 | 250 | 0 | 156 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.00 | 1.05 | 1.91 | 0.00 | 1.19 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.459 | 2.249 | 8.141 | 0.000 | 0.088 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 161 | 146 | 272 | 0 | 170 | 0 | 0 | 103 | 0 |
N.S. |
1 | 1.00 | 0.91 | 1.69 | 0.00 | 1.06 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.497 | 3.021 | 14.605 | 0.000 | 0.089 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 187 | 156 | 260 | 0 | 183 | 0 | 0 | 103 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.39 | 0.00 | 0.98 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.577 | 3.701 | 20.535 | 0.000 | 0.105 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 187 | 271 | 439 | 0 | 215 | 0 | 0 | 131 | 0 |
N.S. |
1 | 1.00 | 1.45 | 2.35 | 0.00 | 1.15 | 0.00 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 0.560 | 4.616 | 193.434 | 0.000 | 0.165 | 0.000 | 0.000 | 0.366 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 161 | 278 | 386 | 0 | 202 | 0 | 0 | 131 | 0 |
N.S. |
1 | 1.00 | 1.73 | 2.40 | 0.00 | 1.25 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.518 | 5.504 | 197.470 | 0.000 | 0.092 | 0.000 | 0.000 | 0.374 | 0.000 |
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 | 118 | 118 | 70 | 292 | 0 | 121 | 0 | 0 | 131 | 0 |
N.S. |
1 | 1.00 | 0.59 | 2.47 | 0.00 | 1.03 | 0.00 | 0.00 | 1.11 | 0.00 |
time (sec) |
N/A | 0.474 | 3.009 | 203.730 | 0.000 | 0.094 | 0.000 | 0.000 | 0.382 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 159 | 150 | 194 | 0 | 162 | 0 | 0 | 121 | 0 |
N.S. |
1 | 1.00 | 0.94 | 1.22 | 0.00 | 1.02 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.498 | 4.447 | 19.520 | 0.000 | 0.091 | 0.000 | 0.000 | 0.317 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 161 | 146 | 272 | 0 | 170 | 0 | 0 | 90 | 0 |
N.S. |
1 | 1.00 | 0.91 | 1.69 | 0.00 | 1.06 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.569 | 4.509 | 19.970 | 0.000 | 0.098 | 0.000 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 187 | 156 | 260 | 0 | 183 | 0 | 0 | 131 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.39 | 0.00 | 0.98 | 0.00 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 0.554 | 5.010 | 22.804 | 0.000 | 0.097 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 168 | 285 | 413 | 0 | 248 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.02 | 1.74 | 2.52 | 0.00 | 1.51 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.840 | 4.094 | 4.582 | 0.000 | 0.095 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 140 | 256 | 253 | 0 | 196 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.03 | 1.88 | 1.86 | 0.00 | 1.44 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.751 | 2.634 | 2.320 | 0.000 | 0.085 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 116 | 180 | 200 | 0 | 184 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.05 | 1.64 | 1.82 | 0.00 | 1.67 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.632 | 1.548 | 1.317 | 0.000 | 0.111 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 115 | 181 | 198 | 0 | 184 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.05 | 1.65 | 1.80 | 0.00 | 1.67 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.655 | 1.516 | 2.142 | 0.000 | 0.105 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 116 | 311 | 199 | 0 | 186 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.04 | 2.78 | 1.78 | 0.00 | 1.66 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.640 | 2.373 | 2.965 | 0.000 | 0.090 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 144 | 312 | 215 | 0 | 207 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.03 | 2.23 | 1.54 | 0.00 | 1.48 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.761 | 5.106 | 4.390 | 0.000 | 0.098 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 172 | 341 | 229 | 0 | 217 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.02 | 2.03 | 1.36 | 0.00 | 1.29 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.799 | 3.639 | 5.648 | 0.000 | 0.098 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 211 | 287 | 413 | 0 | 328 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.04 | 1.42 | 2.04 | 0.00 | 1.62 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 1.143 | 3.344 | 9.409 | 0.000 | 0.094 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 182 | 252 | 405 | 0 | 278 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.03 | 1.43 | 2.30 | 0.00 | 1.58 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 1.050 | 1.956 | 3.211 | 0.000 | 0.097 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 159 | 242 | 257 | 0 | 277 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.07 | 1.62 | 1.72 | 0.00 | 1.86 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.885 | 1.816 | 1.480 | 0.000 | 0.099 | 0.000 | 0.000 | 0.157 | 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 | 77 | 77 | 98 | 188 | 0 | 150 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.00 | 1.27 | 2.44 | 0.00 | 1.95 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.451 | 0.905 | 3.174 | 0.000 | 0.089 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 159 | 239 | 257 | 0 | 277 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.07 | 1.60 | 1.72 | 0.00 | 1.86 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.929 | 2.141 | 3.510 | 0.000 | 0.123 | 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 | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 158 | 259 | 257 | 0 | 277 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.04 | 1.70 | 1.69 | 0.00 | 1.82 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.901 | 2.779 | 4.719 | 0.000 | 0.092 | 0.000 | 0.000 | 0.248 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 187 | 257 | 270 | 0 | 287 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.05 | 1.44 | 1.52 | 0.00 | 1.61 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 1.080 | 2.644 | 5.337 | 0.000 | 0.101 | 0.000 | 0.000 | 0.254 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 214 | 271 | 283 | 0 | 297 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.07 | 1.36 | 1.42 | 0.00 | 1.48 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 1.093 | 3.101 | 6.795 | 0.000 | 0.098 | 0.000 | 0.000 | 0.281 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 234 | 363 | 555 | 0 | 354 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.06 | 1.64 | 2.51 | 0.00 | 1.60 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 1.386 | 3.118 | 4.850 | 0.000 | 0.096 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 210 | 274 | 268 | 0 | 353 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.08 | 1.41 | 1.37 | 0.00 | 1.81 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 1.235 | 2.975 | 1.888 | 0.000 | 0.093 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 210 | 363 | 270 | 0 | 353 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.08 | 1.86 | 1.38 | 0.00 | 1.81 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 1.208 | 2.765 | 4.646 | 0.000 | 0.100 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 210 | 363 | 270 | 0 | 353 | 0 | 0 | 76 | 0 |
N.S. |
1 | 1.08 | 1.86 | 1.38 | 0.00 | 1.81 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 1.206 | 2.946 | 4.275 | 0.000 | 0.094 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 210 | 272 | 270 | 0 | 353 | 0 | 0 | 76 | 0 |
N.S. |
1 | 1.08 | 1.39 | 1.38 | 0.00 | 1.81 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 1.223 | 3.978 | 5.046 | 0.000 | 0.110 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 210 | 378 | 270 | 0 | 353 | 0 | 0 | 76 | 0 |
N.S. |
1 | 1.08 | 1.94 | 1.38 | 0.00 | 1.81 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 1.248 | 3.457 | 5.266 | 0.000 | 0.105 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 238 | 285 | 283 | 0 | 363 | 0 | 0 | 76 | 0 |
N.S. |
1 | 1.08 | 1.29 | 1.28 | 0.00 | 1.64 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 1.389 | 3.966 | 6.329 | 0.000 | 0.105 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 184 | 71 | 110 | 283 | 81 | 0 | 143 | 30 | 163 |
N.S. |
1 | 1.20 | 0.46 | 0.72 | 1.85 | 0.53 | 0.00 | 0.93 | 0.20 | 1.07 |
time (sec) |
N/A | 0.829 | 0.232 | 13.036 | 0.173 | 0.085 | 0.000 | 0.386 | 0.202 | 47.195 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 141 | 61 | 97 | 237 | 71 | 0 | 116 | 30 | 134 |
N.S. |
1 | 1.23 | 0.53 | 0.84 | 2.06 | 0.62 | 0.00 | 1.01 | 0.26 | 1.17 |
time (sec) |
N/A | 0.667 | 0.142 | 11.806 | 0.163 | 0.080 | 0.000 | 0.359 | 0.188 | 1.817 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 98 | 51 | 84 | 190 | 59 | 0 | 87 | 30 | 84 |
N.S. |
1 | 1.27 | 0.66 | 1.09 | 2.47 | 0.77 | 0.00 | 1.13 | 0.39 | 1.09 |
time (sec) |
N/A | 0.492 | 0.112 | 10.836 | 0.187 | 0.077 | 0.000 | 0.410 | 0.187 | 0.767 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 39 | 52 | 98 | 40 | 0 | 58 | 28 | 43 |
N.S. |
1 | 1.00 | 1.08 | 1.44 | 2.72 | 1.11 | 0.00 | 1.61 | 0.78 | 1.19 |
time (sec) |
N/A | 0.350 | 0.070 | 9.860 | 0.189 | 0.077 | 0.000 | 0.410 | 0.166 | 0.278 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 70 | 139 | 146 | 119 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.00 | 1.23 | 2.44 | 2.56 | 2.09 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.362 | 0.103 | 12.162 | 0.275 | 0.089 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 93 | 97 | 0 | 791 | 88 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.01 | 1.05 | 0.00 | 8.60 | 0.96 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.496 | 0.149 | 0.000 | 0.314 | 0.086 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 136 | 111 | 239 | 1059 | 108 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 0.82 | 1.76 | 7.79 | 0.79 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.650 | 0.296 | 13.055 | 0.314 | 0.096 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 187 | 72 | 85 | 263 | 86 | 0 | 0 | 65 | 221 |
N.S. |
1 | 1.16 | 0.45 | 0.53 | 1.63 | 0.53 | 0.00 | 0.00 | 0.40 | 1.37 |
time (sec) |
N/A | 0.834 | 0.295 | 6.993 | 0.174 | 0.106 | 0.000 | 0.000 | 0.238 | 46.219 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 144 | 62 | 75 | 217 | 73 | 0 | 0 | 65 | 135 |
N.S. |
1 | 1.19 | 0.51 | 0.62 | 1.79 | 0.60 | 0.00 | 0.00 | 0.54 | 1.12 |
time (sec) |
N/A | 0.674 | 0.200 | 6.690 | 0.224 | 0.087 | 0.000 | 0.000 | 0.236 | 1.634 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 102 | 52 | 65 | 125 | 60 | 0 | 0 | 65 | 91 |
N.S. |
1 | 1.26 | 0.64 | 0.80 | 1.54 | 0.74 | 0.00 | 0.00 | 0.80 | 1.12 |
time (sec) |
N/A | 0.524 | 0.147 | 6.840 | 0.178 | 0.079 | 0.000 | 0.000 | 0.234 | 0.768 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 97 | 85 | 105 | 997 | 91 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.01 | 0.89 | 1.09 | 10.39 | 0.95 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.529 | 0.218 | 6.905 | 0.296 | 0.092 | 0.000 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 96 | 99 | 117 | 803 | 90 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.01 | 1.04 | 1.23 | 8.45 | 0.95 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.544 | 0.166 | 12.549 | 0.267 | 0.096 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 139 | 112 | 124 | 1080 | 112 | 0 | 0 | 65 | 0 |
N.S. |
1 | 0.99 | 0.80 | 0.89 | 7.71 | 0.80 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.720 | 0.340 | 9.826 | 0.437 | 0.092 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 182 | 126 | 139 | 1942 | 123 | 0 | 0 | 65 | 0 |
N.S. |
1 | 1.01 | 0.70 | 0.77 | 10.79 | 0.68 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.873 | 0.575 | 9.822 | 0.511 | 0.088 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 233 | 84 | 91 | 289 | 107 | 0 | 0 | 104 | 306 |
N.S. |
1 | 1.16 | 0.42 | 0.45 | 1.44 | 0.53 | 0.00 | 0.00 | 0.52 | 1.52 |
time (sec) |
N/A | 1.102 | 5.995 | 2.559 | 0.177 | 0.121 | 0.000 | 0.000 | 0.299 | 50.195 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 186 | 74 | 87 | 243 | 94 | 0 | 0 | 104 | 227 |
N.S. |
1 | 1.16 | 0.46 | 0.54 | 1.51 | 0.58 | 0.00 | 0.00 | 0.65 | 1.41 |
time (sec) |
N/A | 0.893 | 5.821 | 4.933 | 0.196 | 0.090 | 0.000 | 0.000 | 0.277 | 46.734 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 148 | 64 | 77 | 151 | 81 | 0 | 0 | 104 | 137 |
N.S. |
1 | 1.22 | 0.53 | 0.64 | 1.25 | 0.67 | 0.00 | 0.00 | 0.86 | 1.13 |
time (sec) |
N/A | 0.742 | 0.324 | 4.583 | 0.159 | 0.083 | 0.000 | 0.000 | 0.284 | 1.658 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 143 | 404 | 131 | 1395 | 128 | 0 | 0 | 104 | 0 |
N.S. |
1 | 1.04 | 2.93 | 0.95 | 10.11 | 0.93 | 0.00 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 0.768 | 6.338 | 2.825 | 0.358 | 0.089 | 0.000 | 0.000 | 0.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 138 | 202 | 135 | 973 | 111 | 0 | 0 | 98 | 0 |
N.S. |
1 | 1.03 | 1.51 | 1.01 | 7.26 | 0.83 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.747 | 3.166 | 14.683 | 0.336 | 0.087 | 0.000 | 0.000 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 142 | 202 | 132 | 1106 | 120 | 0 | 0 | 80 | 0 |
N.S. |
1 | 1.01 | 1.44 | 0.94 | 7.90 | 0.86 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.747 | 3.206 | 14.853 | 0.317 | 0.086 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 186 | 202 | 140 | 1964 | 133 | 0 | 0 | 104 | 0 |
N.S. |
1 | 1.03 | 1.12 | 0.78 | 10.91 | 0.74 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.924 | 3.261 | 10.588 | 0.404 | 0.089 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 220 | 229 | 202 | 156 | 7450 | 146 | 0 | 0 | 104 | 0 |
N.S. |
1 | 1.04 | 0.92 | 0.71 | 33.86 | 0.66 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 1.090 | 3.269 | 11.786 | 0.577 | 0.109 | 0.000 | 0.000 | 0.270 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | C | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 163 | 1540 | 185 | 989 | 130 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.06 | 10.00 | 1.20 | 6.42 | 0.84 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.802 | 8.005 | 6.670 | 0.474 | 0.108 | 0.000 | 0.000 | 0.235 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | C | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 123 | 473 | 143 | 801 | 114 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.04 | 4.01 | 1.21 | 6.79 | 0.97 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.631 | 6.785 | 6.923 | 0.506 | 0.106 | 0.000 | 0.000 | 0.245 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 83 | 178 | 110 | 648 | 86 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.01 | 2.17 | 1.34 | 7.90 | 1.05 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.443 | 2.322 | 6.796 | 0.472 | 0.097 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 68 | 85 | 505 | 39 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.00 | 1.45 | 1.81 | 10.74 | 0.83 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.324 | 0.123 | 6.145 | 0.529 | 0.092 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 75 | 171 | 99 | 689 | 70 | 0 | 0 | 41 | 0 |
N.S. |
1 | 0.80 | 1.82 | 1.05 | 7.33 | 0.74 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.522 | 0.845 | 3.430 | 0.555 | 0.093 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 112 | 257 | 152 | 0 | 125 | 0 | 0 | 45 | 0 |
N.S. |
1 | 0.90 | 2.06 | 1.22 | 0.00 | 1.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.717 | 1.045 | 9.119 | 0.000 | 0.092 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 208 | 1542 | 136 | 1006 | 141 | 0 | 0 | 43 | 0 |
N.S. |
1 | 1.10 | 8.16 | 0.72 | 5.32 | 0.75 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 1.046 | 8.117 | 6.990 | 0.478 | 0.104 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 160 | 475 | 124 | 818 | 125 | 0 | 0 | 43 | 0 |
N.S. |
1 | 1.06 | 3.15 | 0.82 | 5.42 | 0.83 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.737 | 6.875 | 6.994 | 0.559 | 0.097 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 114 | 180 | 102 | 665 | 98 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.01 | 1.59 | 0.90 | 5.88 | 0.87 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.499 | 2.081 | 7.134 | 0.579 | 0.102 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 76 | 71 | 83 | 522 | 144 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.36 | 1.27 | 1.48 | 9.32 | 2.57 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.362 | 0.112 | 7.029 | 0.634 | 0.107 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 116 | 173 | 108 | 698 | 89 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.10 | 1.65 | 1.03 | 6.65 | 0.85 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.615 | 0.561 | 4.294 | 0.601 | 0.106 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 158 | 259 | 141 | 0 | 143 | 0 | 0 | 51 | 0 |
N.S. |
1 | 0.94 | 1.54 | 0.84 | 0.00 | 0.85 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.836 | 0.702 | 10.111 | 0.000 | 0.111 | 0.000 | 0.000 | 0.186 | 0.000 |
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 | 197 | 208 | 591 | 146 | 0 | 161 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.06 | 3.00 | 0.74 | 0.00 | 0.82 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 1.011 | 7.601 | 7.201 | 0.000 | 0.105 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 160 | 458 | 125 | 0 | 136 | 0 | 0 | 51 | 0 |
N.S. |
1 | 1.02 | 2.92 | 0.80 | 0.00 | 0.87 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.756 | 6.579 | 7.241 | 0.000 | 0.134 | 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 | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 118 | 99 | 132 | 0 | 126 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.01 | 0.85 | 1.13 | 0.00 | 1.08 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.522 | 0.618 | 7.115 | 0.000 | 0.111 | 0.000 | 0.000 | 0.163 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 118 | 140 | 118 | 0 | 125 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.01 | 1.20 | 1.01 | 0.00 | 1.07 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.541 | 0.483 | 4.344 | 0.000 | 0.103 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 161 | 316 | 198 | 0 | 182 | 0 | 0 | 69 | 0 |
N.S. |
1 | 0.93 | 1.82 | 1.14 | 0.00 | 1.05 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.887 | 7.040 | 4.301 | 0.000 | 0.162 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 203 | 316 | 182 | 0 | 201 | 0 | 0 | 69 | 0 |
N.S. |
1 | 0.95 | 1.48 | 0.85 | 0.00 | 0.94 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 1.123 | 7.017 | 10.231 | 0.000 | 0.153 | 0.000 | 0.000 | 0.172 | 0.000 |
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 | 237 | 256 | 641 | 186 | 0 | 195 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.08 | 2.70 | 0.78 | 0.00 | 0.82 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 1.306 | 8.392 | 7.224 | 0.000 | 0.108 | 0.000 | 0.000 | 0.167 | 0.000 |
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 | 197 | 208 | 508 | 165 | 0 | 170 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.06 | 2.58 | 0.84 | 0.00 | 0.86 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 1.067 | 6.890 | 7.165 | 0.000 | 0.109 | 0.000 | 0.000 | 0.175 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 164 | 131 | 164 | 0 | 169 | 0 | 0 | 55 | 0 |
N.S. |
1 | 1.04 | 0.83 | 1.04 | 0.00 | 1.08 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.795 | 1.075 | 7.170 | 0.000 | 0.136 | 0.000 | 0.000 | 0.163 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 164 | 122 | 156 | 0 | 167 | 0 | 0 | 79 | 0 |
N.S. |
1 | 1.04 | 0.78 | 0.99 | 0.00 | 1.06 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.779 | 0.752 | 4.403 | 0.000 | 0.105 | 0.000 | 0.000 | 0.176 | 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 | 157 | 164 | 164 | 157 | 0 | 169 | 0 | 0 | 87 | 0 |
N.S. |
1 | 1.04 | 1.04 | 1.00 | 0.00 | 1.08 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.799 | 0.798 | 4.279 | 0.000 | 0.105 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 207 | 373 | 216 | 0 | 235 | 0 | 0 | 87 | 0 |
N.S. |
1 | 0.97 | 1.74 | 1.01 | 0.00 | 1.10 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 1.162 | 3.097 | 4.446 | 0.000 | 0.233 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 254 | 251 | 412 | 220 | 0 | 245 | 0 | 0 | 87 | 0 |
N.S. |
1 | 0.99 | 1.62 | 0.87 | 0.00 | 0.96 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 1.511 | 4.224 | 9.951 | 0.000 | 0.240 | 0.000 | 0.000 | 0.183 | 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 | 277 | 300 | 696 | 216 | 0 | 229 | 0 | 0 | 73 | 0 |
N.S. |
1 | 1.08 | 2.51 | 0.78 | 0.00 | 0.83 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 1.630 | 9.144 | 7.407 | 0.000 | 0.116 | 0.000 | 0.000 | 0.169 | 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 | 237 | 256 | 561 | 195 | 0 | 204 | 0 | 0 | 71 | 0 |
N.S. |
1 | 1.08 | 2.37 | 0.82 | 0.00 | 0.86 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 1.325 | 7.026 | 7.710 | 0.000 | 0.146 | 0.000 | 0.000 | 0.171 | 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 | 197 | 212 | 153 | 194 | 0 | 203 | 0 | 0 | 65 | 0 |
N.S. |
1 | 1.08 | 0.78 | 0.98 | 0.00 | 1.03 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 1.073 | 4.097 | 7.559 | 0.000 | 0.135 | 0.000 | 0.000 | 0.174 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 212 | 125 | 188 | 0 | 203 | 0 | 0 | 95 | 0 |
N.S. |
1 | 1.08 | 0.63 | 0.95 | 0.00 | 1.03 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 1.046 | 1.295 | 4.614 | 0.000 | 0.107 | 0.000 | 0.000 | 0.167 | 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 | 197 | 212 | 153 | 186 | 0 | 203 | 0 | 0 | 105 | 0 |
N.S. |
1 | 1.08 | 0.78 | 0.94 | 0.00 | 1.03 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 1.036 | 3.929 | 4.586 | 0.000 | 0.112 | 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 | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 212 | 196 | 191 | 0 | 203 | 0 | 0 | 105 | 0 |
N.S. |
1 | 1.08 | 0.99 | 0.97 | 0.00 | 1.03 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 1.053 | 4.789 | 4.531 | 0.000 | 0.117 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 254 | 255 | 454 | 259 | 0 | 279 | 0 | 0 | 105 | 0 |
N.S. |
1 | 1.00 | 1.79 | 1.02 | 0.00 | 1.10 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 1.483 | 7.560 | 4.738 | 0.000 | 0.272 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 294 | 299 | 460 | 259 | 0 | 289 | 0 | 0 | 105 | 0 |
N.S. |
1 | 1.02 | 1.56 | 0.88 | 0.00 | 0.98 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 1.812 | 4.487 | 10.485 | 0.000 | 0.335 | 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 | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 237 | 260 | 163 | 222 | 0 | 237 | 0 | 0 | 123 | 0 |
N.S. |
1 | 1.10 | 0.69 | 0.94 | 0.00 | 1.00 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 1.350 | 4.767 | 4.547 | 0.000 | 0.142 | 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 | A | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 237 | 260 | 396 | 224 | 0 | 237 | 0 | 0 | 123 | 0 |
N.S. |
1 | 1.10 | 1.67 | 0.95 | 0.00 | 1.00 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 1.354 | 6.112 | 4.411 | 0.000 | 0.116 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | A | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 51 | 0 | 121 | 41 | 0 | 0 | 51 | 44 |
N.S. |
1 | 1.00 | 1.34 | 0.00 | 3.18 | 1.08 | 0.00 | 0.00 | 1.34 | 1.16 |
time (sec) |
N/A | 0.382 | 0.139 | 0.000 | 0.182 | 0.083 | 0.000 | 0.000 | 0.292 | 41.209 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 302 | 294 | 282 | 0 | 0 | 0 | 0 | 0 | 95 | 0 |
N.S. |
1 | 0.97 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 1.300 | 2.688 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 232 | 229 | 167 | 0 | 0 | 0 | 0 | 0 | 74 | 0 |
N.S. |
1 | 0.99 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.889 | 1.465 | 0.000 | 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 | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 170 | 138 | 0 | 0 | 0 | 0 | 0 | 53 | 0 |
N.S. |
1 | 0.98 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.482 | 0.549 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.245 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 131 | 111 | 0 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.311 | 0.277 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.240 | 0.000 |