Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 159 | 126 | 122 | 0 | 762 | 0 | 234 | 437 | 205 |
N.S. |
1 | 1.14 | 0.90 | 0.87 | 0.00 | 5.44 | 0.00 | 1.67 | 3.12 | 1.46 |
time (sec) |
N/A | 0.470 | 0.854 | 1.556 | 0.000 | 0.108 | 0.000 | 0.122 | 0.212 | 11.999 |
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 | 167 | 195 | 168 | 143 | 0 | 1206 | 0 | 298 | 804 | 243 |
N.S. |
1 | 1.17 | 1.01 | 0.86 | 0.00 | 7.22 | 0.00 | 1.78 | 4.81 | 1.46 |
time (sec) |
N/A | 0.517 | 1.043 | 1.543 | 0.000 | 0.183 | 0.000 | 0.153 | 0.264 | 11.535 |
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 | 196 | 231 | 220 | 165 | 0 | 1838 | 0 | 386 | 1299 | 284 |
N.S. |
1 | 1.18 | 1.12 | 0.84 | 0.00 | 9.38 | 0.00 | 1.97 | 6.63 | 1.45 |
time (sec) |
N/A | 0.558 | 1.385 | 1.494 | 0.000 | 0.204 | 0.000 | 0.166 | 0.219 | 11.232 |
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 | 198 | 217 | 277 | 228 | 0 | 968 | 0 | 474 | 907 | 535 |
N.S. |
1 | 1.10 | 1.40 | 1.15 | 0.00 | 4.89 | 0.00 | 2.39 | 4.58 | 2.70 |
time (sec) |
N/A | 0.575 | 2.240 | 2.208 | 0.000 | 0.115 | 0.000 | 0.152 | 0.208 | 0.249 |
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 | 171 | 188 | 212 | 201 | 0 | 680 | 0 | 340 | 543 | 436 |
N.S. |
1 | 1.10 | 1.24 | 1.18 | 0.00 | 3.98 | 0.00 | 1.99 | 3.18 | 2.55 |
time (sec) |
N/A | 0.515 | 1.679 | 2.167 | 0.000 | 0.104 | 0.000 | 0.135 | 0.221 | 11.276 |
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 | 152 | 166 | 162 | 161 | 0 | 765 | 0 | 235 | 583 | 337 |
N.S. |
1 | 1.09 | 1.07 | 1.06 | 0.00 | 5.03 | 0.00 | 1.55 | 3.84 | 2.22 |
time (sec) |
N/A | 0.459 | 1.479 | 2.091 | 0.000 | 0.100 | 0.000 | 0.120 | 0.276 | 11.182 |
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 | 162 | 172 | 172 | 159 | 0 | 894 | 0 | 259 | 661 | 309 |
N.S. |
1 | 1.06 | 1.06 | 0.98 | 0.00 | 5.52 | 0.00 | 1.60 | 4.08 | 1.91 |
time (sec) |
N/A | 0.465 | 1.570 | 2.148 | 0.000 | 0.103 | 0.000 | 0.636 | 0.210 | 11.029 |
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 | 172 | 186 | 171 | 145 | 0 | 1043 | 0 | 285 | 742 | 296 |
N.S. |
1 | 1.08 | 0.99 | 0.84 | 0.00 | 6.06 | 0.00 | 1.66 | 4.31 | 1.72 |
time (sec) |
N/A | 0.515 | 1.479 | 1.568 | 0.000 | 0.107 | 0.000 | 0.207 | 0.207 | 0.148 |
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 | 182 | 200 | 170 | 170 | 0 | 1176 | 0 | 311 | 821 | 297 |
N.S. |
1 | 1.10 | 0.93 | 0.93 | 0.00 | 6.46 | 0.00 | 1.71 | 4.51 | 1.63 |
time (sec) |
N/A | 0.527 | 1.668 | 1.488 | 0.000 | 0.112 | 0.000 | 0.218 | 0.280 | 11.003 |
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 | 214 | 166 | 169 | 0 | 1325 | 0 | 331 | 903 | 307 |
N.S. |
1 | 1.19 | 0.92 | 0.94 | 0.00 | 7.36 | 0.00 | 1.84 | 5.02 | 1.71 |
time (sec) |
N/A | 0.540 | 0.976 | 1.453 | 0.000 | 0.111 | 0.000 | 0.238 | 0.209 | 11.093 |
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 | 206 | 251 | 218 | 206 | 0 | 1714 | 0 | 445 | 1014 | 398 |
N.S. |
1 | 1.22 | 1.06 | 1.00 | 0.00 | 8.32 | 0.00 | 2.16 | 4.92 | 1.93 |
time (sec) |
N/A | 0.585 | 2.287 | 1.599 | 0.000 | 0.195 | 0.000 | 0.172 | 0.198 | 11.455 |
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 | 233 | 287 | 280 | 227 | 0 | 2474 | 0 | 509 | 1661 | 436 |
N.S. |
1 | 1.23 | 1.20 | 0.97 | 0.00 | 10.62 | 0.00 | 2.18 | 7.13 | 1.87 |
time (sec) |
N/A | 0.620 | 2.570 | 1.567 | 0.000 | 0.331 | 0.000 | 0.235 | 0.208 | 11.480 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 93 | 196 | 230 | 1323 | 197 | 2018 | 401 | 213 | 1541 |
N.S. |
1 | 0.64 | 1.34 | 1.58 | 9.06 | 1.35 | 13.82 | 2.75 | 1.46 | 10.55 |
time (sec) |
N/A | 0.549 | 1.085 | 1.033 | 0.046 | 0.072 | 7.538 | 0.180 | 0.270 | 13.817 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 93 | 163 | 189 | 996 | 156 | 1516 | 326 | 172 | 1095 |
N.S. |
1 | 0.64 | 1.12 | 1.29 | 6.82 | 1.07 | 10.38 | 2.23 | 1.18 | 7.50 |
time (sec) |
N/A | 0.555 | 1.070 | 0.959 | 0.041 | 0.070 | 4.545 | 0.157 | 0.212 | 12.414 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 93 | 130 | 121 | 693 | 124 | 1080 | 255 | 131 | 734 |
N.S. |
1 | 0.64 | 0.89 | 0.83 | 4.75 | 0.85 | 7.40 | 1.75 | 0.90 | 5.03 |
time (sec) |
N/A | 0.478 | 1.061 | 0.838 | 0.040 | 0.071 | 4.165 | 0.169 | 0.202 | 12.013 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 93 | 97 | 68 | 452 | 81 | 704 | 181 | 90 | 438 |
N.S. |
1 | 0.74 | 0.78 | 0.54 | 3.62 | 0.65 | 5.63 | 1.45 | 0.72 | 3.50 |
time (sec) |
N/A | 0.465 | 1.047 | 0.708 | 0.037 | 0.078 | 2.690 | 0.208 | 0.287 | 11.613 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 66 | 64 | 32 | 251 | 48 | 393 | 110 | 49 | 219 |
N.S. |
1 | 1.61 | 1.56 | 0.78 | 6.12 | 1.17 | 9.59 | 2.68 | 1.20 | 5.34 |
time (sec) |
N/A | 0.373 | 1.042 | 0.553 | 0.035 | 0.086 | 1.809 | 1.135 | 0.213 | 11.469 |
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 | 27 | 27 | 18 | 15 | 14 | 20 | 90 | 18 | 21 | 76 |
N.S. |
1 | 1.00 | 0.67 | 0.56 | 0.52 | 0.74 | 3.33 | 0.67 | 0.78 | 2.81 |
time (sec) |
N/A | 0.257 | 0.011 | 0.714 | 0.027 | 0.070 | 0.328 | 0.138 | 0.203 | 11.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 78 | 61 | 88 | 0 | 62 | 0 | 96 | 72 | 0 |
N.S. |
1 | 0.60 | 0.47 | 0.68 | 0.00 | 0.48 | 0.00 | 0.74 | 0.55 | 0.00 |
time (sec) |
N/A | 0.403 | 1.041 | 0.868 | 0.000 | 0.076 | 0.000 | 0.198 | 0.281 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 79 | 87 | 111 | 0 | 92 | 0 | 101 | 112 | 0 |
N.S. |
1 | 0.60 | 0.66 | 0.84 | 0.00 | 0.70 | 0.00 | 0.77 | 0.85 | 0.00 |
time (sec) |
N/A | 0.424 | 1.065 | 0.868 | 0.000 | 0.084 | 0.000 | 0.145 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 87 | 73 | 98 | 0 | 100 | 0 | 105 | 113 | 0 |
N.S. |
1 | 0.62 | 0.52 | 0.70 | 0.00 | 0.71 | 0.00 | 0.75 | 0.81 | 0.00 |
time (sec) |
N/A | 0.435 | 1.056 | 1.027 | 0.000 | 0.077 | 0.000 | 0.200 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 71 | 66 | 0 | 84 | 0 | 122 | 69 | 75 |
N.S. |
1 | 1.00 | 1.73 | 1.61 | 0.00 | 2.05 | 0.00 | 2.98 | 1.68 | 1.83 |
time (sec) |
N/A | 0.292 | 1.043 | 1.151 | 0.000 | 0.071 | 0.000 | 0.180 | 0.263 | 11.193 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 93 | 73 | 68 | 0 | 98 | 0 | 137 | 95 | 77 |
N.S. |
1 | 1.11 | 0.87 | 0.81 | 0.00 | 1.17 | 0.00 | 1.63 | 1.13 | 0.92 |
time (sec) |
N/A | 0.442 | 1.042 | 1.209 | 0.000 | 0.078 | 0.000 | 0.255 | 0.196 | 11.129 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 93 | 73 | 68 | 0 | 109 | 0 | 152 | 106 | 77 |
N.S. |
1 | 0.73 | 0.57 | 0.53 | 0.00 | 0.85 | 0.00 | 1.19 | 0.83 | 0.60 |
time (sec) |
N/A | 0.434 | 1.051 | 1.325 | 0.000 | 0.073 | 0.000 | 0.171 | 0.207 | 11.201 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 93 | 73 | 68 | 0 | 120 | 0 | 165 | 117 | 77 |
N.S. |
1 | 0.64 | 0.50 | 0.47 | 0.00 | 0.82 | 0.00 | 1.13 | 0.80 | 0.53 |
time (sec) |
N/A | 0.431 | 1.043 | 1.588 | 0.000 | 0.068 | 0.000 | 0.200 | 0.236 | 11.212 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 93 | 73 | 68 | 0 | 131 | 0 | 180 | 128 | 77 |
N.S. |
1 | 0.64 | 0.50 | 0.47 | 0.00 | 0.90 | 0.00 | 1.23 | 0.88 | 0.53 |
time (sec) |
N/A | 0.435 | 1.043 | 1.954 | 0.000 | 0.073 | 0.000 | 0.180 | 0.208 | 11.185 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 254 | 147 | 432 | 564 | 2152 | 489 | 48164 | 895 | 547 | 0 |
N.S. |
1 | 0.58 | 1.70 | 2.22 | 8.47 | 1.93 | 189.62 | 3.52 | 2.15 | 0.00 |
time (sec) |
N/A | 0.835 | 1.162 | 1.953 | 0.059 | 0.073 | 2.104 | 0.214 | 0.270 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 254 | 147 | 377 | 489 | 1736 | 418 | 29211 | 774 | 472 | 0 |
N.S. |
1 | 0.58 | 1.48 | 1.93 | 6.83 | 1.65 | 115.00 | 3.05 | 1.86 | 0.00 |
time (sec) |
N/A | 0.757 | 1.142 | 1.763 | 0.048 | 0.071 | 1.898 | 0.234 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 254 | 147 | 322 | 414 | 1323 | 360 | 17473 | 657 | 397 | 0 |
N.S. |
1 | 0.58 | 1.27 | 1.63 | 5.21 | 1.42 | 68.79 | 2.59 | 1.56 | 0.00 |
time (sec) |
N/A | 0.720 | 1.119 | 1.552 | 0.044 | 0.073 | 1.831 | 0.802 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 147 | 267 | 339 | 998 | 285 | 10220 | 537 | 322 | 0 |
N.S. |
1 | 0.67 | 1.22 | 1.55 | 4.56 | 1.30 | 46.67 | 2.45 | 1.47 | 0.00 |
time (sec) |
N/A | 0.674 | 1.103 | 1.493 | 0.045 | 0.071 | 1.666 | 0.195 | 0.264 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 120 | 212 | 264 | 693 | 225 | 5727 | 418 | 247 | 0 |
N.S. |
1 | 0.70 | 1.23 | 1.53 | 4.03 | 1.31 | 33.30 | 2.43 | 1.44 | 0.00 |
time (sec) |
N/A | 0.587 | 1.090 | 1.408 | 0.040 | 0.069 | 1.543 | 0.176 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 93 | 157 | 189 | 452 | 156 | 2968 | 298 | 172 | 0 |
N.S. |
1 | 0.74 | 1.26 | 1.51 | 3.62 | 1.25 | 23.74 | 2.38 | 1.38 | 0.00 |
time (sec) |
N/A | 0.496 | 1.075 | 1.286 | 0.038 | 0.068 | 1.416 | 0.211 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 66 | 102 | 114 | 251 | 96 | 1312 | 182 | 97 | 0 |
N.S. |
1 | 1.61 | 2.49 | 2.78 | 6.12 | 2.34 | 32.00 | 4.44 | 2.37 | 0.00 |
time (sec) |
N/A | 0.381 | 1.043 | 1.121 | 0.034 | 0.067 | 1.630 | 0.196 | 0.278 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 25 | 19 | 23 | 42 | 158 | 86 | 43 | 30 |
N.S. |
1 | 1.00 | 0.93 | 0.70 | 0.85 | 1.56 | 5.85 | 3.19 | 1.59 | 1.11 |
time (sec) |
N/A | 0.263 | 0.010 | 1.053 | 0.028 | 0.067 | 0.171 | 0.172 | 0.205 | 11.287 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 126 | 133 | 221 | 0 | 179 | 0 | 274 | 208 | 0 |
N.S. |
1 | 0.60 | 0.63 | 1.05 | 0.00 | 0.85 | 0.00 | 1.30 | 0.99 | 0.00 |
time (sec) |
N/A | 0.488 | 1.082 | 1.382 | 0.000 | 0.083 | 0.000 | 0.224 | 0.266 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 132 | 183 | 223 | 0 | 267 | 0 | 278 | 297 | 0 |
N.S. |
1 | 0.55 | 0.77 | 0.93 | 0.00 | 1.12 | 0.00 | 1.16 | 1.24 | 0.00 |
time (sec) |
N/A | 0.555 | 1.144 | 1.454 | 0.000 | 0.074 | 0.000 | 0.195 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 238 | 131 | 185 | 219 | 0 | 291 | 0 | 273 | 330 | 0 |
N.S. |
1 | 0.55 | 0.78 | 0.92 | 0.00 | 1.22 | 0.00 | 1.15 | 1.39 | 0.00 |
time (sec) |
N/A | 0.552 | 1.140 | 1.411 | 0.000 | 0.075 | 0.000 | 0.168 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 238 | 131 | 181 | 222 | 0 | 292 | 0 | 267 | 309 | 0 |
N.S. |
1 | 0.55 | 0.76 | 0.93 | 0.00 | 1.23 | 0.00 | 1.12 | 1.30 | 0.00 |
time (sec) |
N/A | 0.544 | 1.115 | 1.607 | 0.000 | 0.079 | 0.000 | 0.170 | 0.275 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 139 | 144 | 208 | 0 | 268 | 0 | 275 | 269 | 0 |
N.S. |
1 | 0.57 | 0.59 | 0.85 | 0.00 | 1.09 | 0.00 | 1.12 | 1.09 | 0.00 |
time (sec) |
N/A | 0.546 | 1.111 | 1.720 | 0.000 | 0.073 | 0.000 | 0.187 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 158 | 177 | 0 | 215 | 0 | 297 | 192 | 449 |
N.S. |
1 | 1.00 | 3.85 | 4.32 | 0.00 | 5.24 | 0.00 | 7.24 | 4.68 | 10.95 |
time (sec) |
N/A | 0.292 | 1.079 | 1.770 | 0.000 | 0.075 | 0.000 | 0.160 | 0.202 | 11.336 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 86 | 162 | 187 | 0 | 236 | 0 | 314 | 240 | 449 |
N.S. |
1 | 1.02 | 1.93 | 2.23 | 0.00 | 2.81 | 0.00 | 3.74 | 2.86 | 5.35 |
time (sec) |
N/A | 0.362 | 1.069 | 2.040 | 0.000 | 0.072 | 0.000 | 0.182 | 0.256 | 11.205 |
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 | 128 | 130 | 162 | 187 | 0 | 247 | 0 | 329 | 251 | 449 |
N.S. |
1 | 1.02 | 1.27 | 1.46 | 0.00 | 1.93 | 0.00 | 2.57 | 1.96 | 3.51 |
time (sec) |
N/A | 0.411 | 1.074 | 2.163 | 0.000 | 0.073 | 0.000 | 0.167 | 0.211 | 11.358 |
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 | 172 | 145 | 162 | 187 | 0 | 258 | 0 | 342 | 262 | 449 |
N.S. |
1 | 0.84 | 0.94 | 1.09 | 0.00 | 1.50 | 0.00 | 1.99 | 1.52 | 2.61 |
time (sec) |
N/A | 0.543 | 1.068 | 2.601 | 0.000 | 0.075 | 0.000 | 0.194 | 0.288 | 11.440 |
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 | 216 | 147 | 162 | 187 | 0 | 269 | 0 | 357 | 273 | 449 |
N.S. |
1 | 0.68 | 0.75 | 0.87 | 0.00 | 1.25 | 0.00 | 1.65 | 1.26 | 2.08 |
time (sec) |
N/A | 0.536 | 1.081 | 2.937 | 0.000 | 0.072 | 0.000 | 0.185 | 0.212 | 11.591 |
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 | 254 | 147 | 162 | 187 | 0 | 280 | 0 | 370 | 284 | 449 |
N.S. |
1 | 0.58 | 0.64 | 0.74 | 0.00 | 1.10 | 0.00 | 1.46 | 1.12 | 1.77 |
time (sec) |
N/A | 0.529 | 1.069 | 3.674 | 0.000 | 0.083 | 0.000 | 0.154 | 0.204 | 11.542 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-2) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 254 | 147 | 162 | 187 | 0 | 291 | 0 | 385 | 295 | 449 |
N.S. |
1 | 0.58 | 0.64 | 0.74 | 0.00 | 1.15 | 0.00 | 1.52 | 1.16 | 1.77 |
time (sec) |
N/A | 0.532 | 1.077 | 4.288 | 0.000 | 0.081 | 0.000 | 0.188 | 0.264 | 11.249 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 362 | 201 | 756 | 1034 | 3175 | 892 | 352553 | 1573 | 1017 | 0 |
N.S. |
1 | 0.56 | 2.09 | 2.86 | 8.77 | 2.46 | 973.90 | 4.35 | 2.81 | 0.00 |
time (sec) |
N/A | 1.264 | 1.309 | 3.273 | 0.069 | 0.088 | 3.081 | 0.219 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 362 | 201 | 679 | 925 | 2653 | 797 | 216311 | 1406 | 908 | 0 |
N.S. |
1 | 0.56 | 1.88 | 2.56 | 7.33 | 2.20 | 597.54 | 3.88 | 2.51 | 0.00 |
time (sec) |
N/A | 1.223 | 1.259 | 2.746 | 0.061 | 0.078 | 2.675 | 0.212 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 362 | 201 | 602 | 816 | 2153 | 706 | 132085 | 1243 | 799 | 0 |
N.S. |
1 | 0.56 | 1.66 | 2.25 | 5.95 | 1.95 | 364.88 | 3.43 | 2.21 | 0.00 |
time (sec) |
N/A | 1.067 | 1.229 | 2.096 | 0.054 | 0.075 | 2.255 | 0.192 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 311 | 199 | 525 | 707 | 1736 | 599 | 80036 | 1077 | 690 | 0 |
N.S. |
1 | 0.64 | 1.69 | 2.27 | 5.58 | 1.93 | 257.35 | 3.46 | 2.22 | 0.00 |
time (sec) |
N/A | 0.995 | 1.195 | 1.780 | 0.058 | 0.072 | 2.147 | 0.169 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 263 | 171 | 448 | 598 | 1323 | 517 | 47855 | 912 | 581 | 0 |
N.S. |
1 | 0.65 | 1.70 | 2.27 | 5.03 | 1.97 | 181.96 | 3.47 | 2.21 | 0.00 |
time (sec) |
N/A | 0.870 | 1.185 | 1.469 | 0.047 | 0.076 | 1.874 | 0.198 | 0.270 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 147 | 371 | 489 | 998 | 418 | 27980 | 746 | 472 | 0 |
N.S. |
1 | 0.67 | 1.69 | 2.23 | 4.56 | 1.91 | 127.76 | 3.41 | 2.16 | 0.00 |
time (sec) |
N/A | 0.798 | 1.152 | 1.356 | 0.052 | 0.069 | 1.733 | 0.173 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 120 | 294 | 380 | 693 | 327 | 15698 | 583 | 363 | 0 |
N.S. |
1 | 0.70 | 1.71 | 2.21 | 4.03 | 1.90 | 91.27 | 3.39 | 2.11 | 0.00 |
time (sec) |
N/A | 0.669 | 1.127 | 1.315 | 0.039 | 0.070 | 1.581 | 0.201 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 93 | 217 | 271 | 452 | 234 | 8136 | 417 | 254 | 0 |
N.S. |
1 | 0.74 | 1.74 | 2.17 | 3.62 | 1.87 | 65.09 | 3.34 | 2.03 | 0.00 |
time (sec) |
N/A | 0.564 | 1.095 | 1.116 | 0.036 | 0.070 | 1.398 | 0.203 | 0.259 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 66 | 140 | 162 | 251 | 142 | 3618 | 254 | 145 | 0 |
N.S. |
1 | 1.61 | 3.41 | 3.95 | 6.12 | 3.46 | 88.24 | 6.20 | 3.54 | 0.00 |
time (sec) |
N/A | 0.376 | 1.066 | 1.038 | 0.035 | 0.068 | 1.533 | 0.177 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 25 | 19 | 23 | 64 | 226 | 120 | 65 | 14 |
N.S. |
1 | 1.00 | 0.93 | 0.70 | 0.85 | 2.37 | 8.37 | 4.44 | 2.41 | 0.52 |
time (sec) |
N/A | 0.259 | 0.012 | 0.908 | 0.031 | 0.081 | 0.329 | 0.148 | 0.202 | 11.467 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 298 | 174 | 248 | 428 | 0 | 351 | 0 | 543 | 411 | 0 |
N.S. |
1 | 0.58 | 0.83 | 1.44 | 0.00 | 1.18 | 0.00 | 1.82 | 1.38 | 0.00 |
time (sec) |
N/A | 0.590 | 1.159 | 1.600 | 0.000 | 0.075 | 0.000 | 0.159 | 0.277 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 345 | 184 | 320 | 407 | 0 | 496 | 0 | 542 | 549 | 0 |
N.S. |
1 | 0.53 | 0.93 | 1.18 | 0.00 | 1.44 | 0.00 | 1.57 | 1.59 | 0.00 |
time (sec) |
N/A | 0.758 | 1.254 | 1.208 | 0.000 | 0.092 | 0.000 | 0.167 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 347 | 186 | 321 | 398 | 0 | 548 | 0 | 530 | 625 | 0 |
N.S. |
1 | 0.54 | 0.93 | 1.15 | 0.00 | 1.58 | 0.00 | 1.53 | 1.80 | 0.00 |
time (sec) |
N/A | 0.724 | 1.170 | 1.408 | 0.000 | 0.075 | 0.000 | 0.166 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 345 | 184 | 320 | 390 | 0 | 576 | 0 | 524 | 645 | 0 |
N.S. |
1 | 0.53 | 0.93 | 1.13 | 0.00 | 1.67 | 0.00 | 1.52 | 1.87 | 0.00 |
time (sec) |
N/A | 0.699 | 1.183 | 1.506 | 0.000 | 0.078 | 0.000 | 0.169 | 0.304 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 344 | 183 | 318 | 384 | 0 | 571 | 0 | 525 | 634 | 0 |
N.S. |
1 | 0.53 | 0.92 | 1.12 | 0.00 | 1.66 | 0.00 | 1.53 | 1.84 | 0.00 |
time (sec) |
N/A | 0.681 | 1.178 | 1.569 | 0.000 | 0.079 | 0.000 | 0.188 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 344 | 183 | 315 | 388 | 0 | 542 | 0 | 519 | 576 | 0 |
N.S. |
1 | 0.53 | 0.92 | 1.13 | 0.00 | 1.58 | 0.00 | 1.51 | 1.67 | 0.00 |
time (sec) |
N/A | 0.658 | 1.216 | 1.920 | 0.000 | 0.078 | 0.000 | 0.183 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-2) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 356 | 195 | 258 | 374 | 0 | 492 | 0 | 527 | 498 | 0 |
N.S. |
1 | 0.55 | 0.72 | 1.05 | 0.00 | 1.38 | 0.00 | 1.48 | 1.40 | 0.00 |
time (sec) |
N/A | 0.655 | 1.194 | 2.267 | 0.000 | 0.080 | 0.000 | 0.176 | 0.289 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 289 | 330 | 0 | 398 | 0 | 564 | 383 | 1010 |
N.S. |
1 | 1.00 | 7.05 | 8.05 | 0.00 | 9.71 | 0.00 | 13.76 | 9.34 | 24.63 |
time (sec) |
N/A | 0.288 | 1.131 | 2.964 | 0.000 | 0.079 | 0.000 | 0.160 | 0.228 | 11.715 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 86 | 295 | 351 | 0 | 430 | 0 | 583 | 453 | 1010 |
N.S. |
1 | 1.02 | 3.51 | 4.18 | 0.00 | 5.12 | 0.00 | 6.94 | 5.39 | 12.02 |
time (sec) |
N/A | 0.370 | 1.134 | 3.853 | 0.000 | 0.084 | 0.000 | 0.192 | 0.245 | 11.582 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 130 | 295 | 351 | 0 | 441 | 0 | 598 | 464 | 1010 |
N.S. |
1 | 1.02 | 2.30 | 2.74 | 0.00 | 3.45 | 0.00 | 4.67 | 3.62 | 7.89 |
time (sec) |
N/A | 0.408 | 1.132 | 5.102 | 0.000 | 0.080 | 0.000 | 0.185 | 0.232 | 11.628 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 174 | 295 | 351 | 0 | 452 | 0 | 611 | 475 | 1010 |
N.S. |
1 | 1.01 | 1.72 | 2.04 | 0.00 | 2.63 | 0.00 | 3.55 | 2.76 | 5.87 |
time (sec) |
N/A | 0.442 | 1.120 | 7.075 | 0.000 | 0.076 | 0.000 | 0.174 | 0.220 | 11.512 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-2) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 198 | 295 | 351 | 0 | 463 | 0 | 626 | 486 | 1010 |
N.S. |
1 | 0.92 | 1.37 | 1.62 | 0.00 | 2.14 | 0.00 | 2.90 | 2.25 | 4.68 |
time (sec) |
N/A | 0.678 | 1.129 | 9.833 | 0.000 | 0.078 | 0.000 | 0.191 | 0.293 | 11.539 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-2) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 260 | 201 | 295 | 351 | 0 | 474 | 0 | 639 | 497 | 1010 |
N.S. |
1 | 0.77 | 1.13 | 1.35 | 0.00 | 1.82 | 0.00 | 2.46 | 1.91 | 3.88 |
time (sec) |
N/A | 0.652 | 1.127 | 13.649 | 0.000 | 0.074 | 0.000 | 0.180 | 0.212 | 11.378 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-2) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 304 | 199 | 295 | 351 | 0 | 485 | 0 | 654 | 508 | 1010 |
N.S. |
1 | 0.65 | 0.97 | 1.15 | 0.00 | 1.60 | 0.00 | 2.15 | 1.67 | 3.32 |
time (sec) |
N/A | 0.673 | 1.132 | 20.983 | 0.000 | 0.086 | 0.000 | 0.198 | 0.196 | 11.698 |
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 | 362 | 201 | 295 | 351 | 0 | 496 | 0 | 667 | 519 | 1010 |
N.S. |
1 | 0.56 | 0.81 | 0.97 | 0.00 | 1.37 | 0.00 | 1.84 | 1.43 | 2.79 |
time (sec) |
N/A | 0.637 | 1.130 | 28.522 | 0.000 | 0.083 | 0.000 | 0.160 | 0.250 | 11.773 |
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 | 362 | 201 | 295 | 351 | 0 | 507 | 0 | 682 | 530 | 1010 |
N.S. |
1 | 0.56 | 0.81 | 0.97 | 0.00 | 1.40 | 0.00 | 1.88 | 1.46 | 2.79 |
time (sec) |
N/A | 0.637 | 1.132 | 44.131 | 0.000 | 0.079 | 0.000 | 0.207 | 0.212 | 11.645 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-2) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 362 | 201 | 295 | 351 | 0 | 518 | 0 | 695 | 541 | 1010 |
N.S. |
1 | 0.56 | 0.81 | 0.97 | 0.00 | 1.43 | 0.00 | 1.92 | 1.49 | 2.79 |
time (sec) |
N/A | 0.674 | 1.127 | 60.066 | 0.000 | 0.087 | 0.000 | 0.176 | 0.227 | 11.359 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 30 | 27 | 688 | 42 | 1632 | 97 | 43 | 0 |
N.S. |
1 | 1.00 | 0.77 | 0.69 | 17.64 | 1.08 | 41.85 | 2.49 | 1.10 | 0.00 |
time (sec) |
N/A | 0.292 | 0.027 | 1.167 | 0.041 | 0.074 | 3.675 | 0.167 | 0.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 30 | 27 | 432 | 31 | 1015 | 82 | 32 | 0 |
N.S. |
1 | 1.00 | 0.77 | 0.69 | 11.08 | 0.79 | 26.03 | 2.10 | 0.82 | 0.00 |
time (sec) |
N/A | 0.294 | 0.013 | 0.943 | 0.040 | 0.066 | 2.747 | 0.158 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 30 | 27 | 239 | 20 | 578 | 69 | 21 | 0 |
N.S. |
1 | 1.00 | 0.77 | 0.69 | 6.13 | 0.51 | 14.82 | 1.77 | 0.54 | 0.00 |
time (sec) |
N/A | 0.289 | 0.015 | 0.928 | 0.034 | 0.080 | 1.953 | 0.158 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 39 | 28 | 25 | 95 | 10 | 282 | 42 | 10 | 0 |
N.S. |
1 | 0.98 | 0.70 | 0.62 | 2.38 | 0.25 | 7.05 | 1.05 | 0.25 | 0.00 |
time (sec) |
N/A | 0.276 | 0.013 | 0.828 | 0.029 | 0.070 | 1.346 | 0.187 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 15 | 14 | 13 | 1 | 20 | 20 | 1 | 76 |
N.S. |
1 | 1.00 | 0.62 | 0.58 | 0.54 | 0.04 | 0.83 | 0.83 | 0.04 | 3.17 |
time (sec) |
N/A | 0.246 | 0.024 | 0.704 | 0.035 | 0.071 | 0.859 | 0.188 | 0.293 | 12.197 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 26 | 25 | 0 | 10 | 0 | 17 | 10 | 0 |
N.S. |
1 | 1.00 | 0.74 | 0.71 | 0.00 | 0.29 | 0.00 | 0.49 | 0.29 | 0.00 |
time (sec) |
N/A | 0.286 | 0.011 | 0.951 | 0.000 | 0.071 | 0.000 | 0.193 | 0.206 | 0.000 |
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 | 38 | 38 | 28 | 27 | 0 | 13 | 0 | 40 | 12 | 28 |
N.S. |
1 | 1.00 | 0.74 | 0.71 | 0.00 | 0.34 | 0.00 | 1.05 | 0.32 | 0.74 |
time (sec) |
N/A | 0.302 | 0.012 | 1.036 | 0.000 | 0.077 | 0.000 | 0.169 | 0.210 | 11.827 |
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 | 42 | 39 | 30 | 27 | 0 | 24 | 0 | 56 | 23 | 28 |
N.S. |
1 | 0.93 | 0.71 | 0.64 | 0.00 | 0.57 | 0.00 | 1.33 | 0.55 | 0.67 |
time (sec) |
N/A | 0.293 | 0.013 | 1.036 | 0.000 | 0.074 | 0.000 | 0.160 | 0.278 | 11.860 |
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 | 42 | 39 | 30 | 27 | 0 | 35 | 0 | 71 | 34 | 28 |
N.S. |
1 | 0.93 | 0.71 | 0.64 | 0.00 | 0.83 | 0.00 | 1.69 | 0.81 | 0.67 |
time (sec) |
N/A | 0.277 | 0.014 | 1.209 | 0.000 | 0.076 | 0.000 | 0.164 | 0.197 | 11.851 |
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 | 42 | 39 | 30 | 27 | 0 | 46 | 0 | 84 | 45 | 28 |
N.S. |
1 | 0.93 | 0.71 | 0.64 | 0.00 | 1.10 | 0.00 | 2.00 | 1.07 | 0.67 |
time (sec) |
N/A | 0.292 | 0.016 | 1.219 | 0.000 | 0.081 | 0.000 | 0.150 | 0.213 | 11.974 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 130 | 170 | 216 | 754 | 268 | 0 | 212 | 297 | 0 |
N.S. |
1 | 0.63 | 0.82 | 1.04 | 3.64 | 1.29 | 0.00 | 1.02 | 1.43 | 0.00 |
time (sec) |
N/A | 0.566 | 1.104 | 1.642 | 0.036 | 0.079 | 0.000 | 0.153 | 0.278 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 101 | 120 | 149 | 481 | 173 | 0 | 153 | 197 | 0 |
N.S. |
1 | 0.62 | 0.74 | 0.91 | 2.95 | 1.06 | 0.00 | 0.94 | 1.21 | 0.00 |
time (sec) |
N/A | 0.483 | 1.077 | 1.421 | 0.033 | 0.082 | 0.000 | 0.181 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 77 | 74 | 104 | 272 | 92 | 0 | 89 | 112 | 0 |
N.S. |
1 | 0.68 | 0.65 | 0.91 | 2.39 | 0.81 | 0.00 | 0.78 | 0.98 | 0.00 |
time (sec) |
N/A | 0.441 | 1.054 | 1.385 | 0.036 | 0.076 | 0.000 | 0.142 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 58 | 185 | 48 | 117 | 39 | 0 | 49 | 49 | 0 |
N.S. |
1 | 0.83 | 2.64 | 0.69 | 1.67 | 0.56 | 0.00 | 0.70 | 0.70 | 0.00 |
time (sec) |
N/A | 0.372 | 1.217 | 1.190 | 0.029 | 0.071 | 0.000 | 0.199 | 0.289 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 16 | 19 | 23 | 13 | 34 | 20 | 12 | 23 |
N.S. |
1 | 1.00 | 0.64 | 0.76 | 0.92 | 0.52 | 1.36 | 0.80 | 0.48 | 0.92 |
time (sec) |
N/A | 0.254 | 0.010 | 1.121 | 0.039 | 0.070 | 0.190 | 0.163 | 0.226 | 11.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 83 | 57 | 77 | 0 | 93 | 0 | 138 | 115 | 0 |
N.S. |
1 | 0.69 | 0.48 | 0.64 | 0.00 | 0.78 | 0.00 | 1.15 | 0.96 | 0.00 |
time (sec) |
N/A | 0.427 | 1.045 | 1.372 | 0.000 | 0.079 | 0.000 | 0.191 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 107 | 92 | 181 | 0 | 241 | 0 | 232 | 459 | 0 |
N.S. |
1 | 0.63 | 0.54 | 1.07 | 0.00 | 1.43 | 0.00 | 1.37 | 2.72 | 0.00 |
time (sec) |
N/A | 0.499 | 1.083 | 1.440 | 0.000 | 0.081 | 0.000 | 0.164 | 0.302 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 136 | 135 | 331 | 0 | 495 | 0 | 322 | 821 | 0 |
N.S. |
1 | 0.61 | 0.61 | 1.48 | 0.00 | 2.22 | 0.00 | 1.44 | 3.68 | 0.00 |
time (sec) |
N/A | 0.559 | 1.138 | 1.618 | 0.000 | 0.089 | 0.000 | 0.217 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 155 | 232 | 290 | 1010 | 426 | 0 | 296 | 469 | 0 |
N.S. |
1 | 0.60 | 0.90 | 1.13 | 3.93 | 1.66 | 0.00 | 1.15 | 1.82 | 0.00 |
time (sec) |
N/A | 0.637 | 1.140 | 1.782 | 0.147 | 0.077 | 0.000 | 0.180 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 129 | 170 | 215 | 755 | 292 | 0 | 201 | 309 | 0 |
N.S. |
1 | 0.63 | 0.83 | 1.04 | 3.67 | 1.42 | 0.00 | 0.98 | 1.50 | 0.00 |
time (sec) |
N/A | 0.545 | 1.112 | 1.685 | 0.081 | 0.079 | 0.000 | 0.211 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 112 | 91 | 140 | 533 | 176 | 0 | 134 | 180 | 0 |
N.S. |
1 | 0.68 | 0.55 | 0.85 | 3.25 | 1.07 | 0.00 | 0.82 | 1.10 | 0.00 |
time (sec) |
N/A | 0.484 | 1.073 | 1.468 | 0.059 | 0.078 | 0.000 | 0.159 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 60 | 69 | 274 | 84 | 0 | 67 | 69 | 77 |
N.S. |
1 | 1.00 | 1.46 | 1.68 | 6.68 | 2.05 | 0.00 | 1.63 | 1.68 | 1.88 |
time (sec) |
N/A | 0.302 | 1.053 | 1.323 | 0.038 | 0.071 | 0.000 | 0.187 | 0.223 | 11.244 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 64 | 246 | 35 | 118 | 50 | 0 | 33 | 48 | 43 |
N.S. |
1 | 1.60 | 6.15 | 0.88 | 2.95 | 1.25 | 0.00 | 0.82 | 1.20 | 1.08 |
time (sec) |
N/A | 0.373 | 1.208 | 1.181 | 0.027 | 0.068 | 0.000 | 0.215 | 0.272 | 11.476 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 18 | 19 | 23 | 35 | 97 | 20 | 34 | 30 |
N.S. |
1 | 1.00 | 0.67 | 0.70 | 0.85 | 1.30 | 3.59 | 0.74 | 1.26 | 1.11 |
time (sec) |
N/A | 0.261 | 0.018 | 1.095 | 0.034 | 0.067 | 0.392 | 0.150 | 0.219 | 11.502 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 133 | 116 | 251 | 0 | 425 | 0 | 311 | 499 | 0 |
N.S. |
1 | 0.63 | 0.55 | 1.20 | 0.00 | 2.02 | 0.00 | 1.48 | 2.38 | 0.00 |
time (sec) |
N/A | 0.538 | 1.106 | 1.395 | 0.000 | 0.081 | 0.000 | 0.201 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 260 | 158 | 144 | 483 | 0 | 751 | 0 | 428 | 1236 | 0 |
N.S. |
1 | 0.61 | 0.55 | 1.86 | 0.00 | 2.89 | 0.00 | 1.65 | 4.75 | 0.00 |
time (sec) |
N/A | 0.599 | 1.124 | 1.540 | 0.000 | 0.090 | 0.000 | 0.183 | 0.277 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 323 | 196 | 184 | 738 | 0 | 1151 | 0 | 550 | 1840 | 0 |
N.S. |
1 | 0.61 | 0.57 | 2.28 | 0.00 | 3.56 | 0.00 | 1.70 | 5.70 | 0.00 |
time (sec) |
N/A | 0.685 | 1.135 | 1.573 | 0.000 | 0.097 | 0.000 | 0.165 | 0.220 | 0.000 |