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 | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 224 | 286 | 190 | 258 | 0 | 228 | 0 | 0 | 1012 | 0 |
N.S. |
1 | 1.28 | 0.85 | 1.15 | 0.00 | 1.02 | 0.00 | 0.00 | 4.52 | 0.00 |
time (sec) |
N/A | 0.755 | 10.933 | 4.102 | 0.000 | 0.078 | 0.000 | 0.000 | 0.245 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 320 | 151 | 293 | 0 | 281 | 0 | 0 | 871 | 0 |
N.S. |
1 | 1.24 | 0.59 | 1.14 | 0.00 | 1.09 | 0.00 | 0.00 | 3.38 | 0.00 |
time (sec) |
N/A | 0.845 | 11.047 | 5.108 | 0.000 | 0.079 | 0.000 | 0.000 | 0.247 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 359 | 161 | 328 | 0 | 338 | 0 | 0 | 1299 | 0 |
N.S. |
1 | 1.23 | 0.55 | 1.12 | 0.00 | 1.16 | 0.00 | 0.00 | 4.45 | 0.00 |
time (sec) |
N/A | 0.948 | 11.064 | 6.680 | 0.000 | 0.082 | 0.000 | 0.000 | 0.252 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 243 | 141 | 172 | 0 | 124 | 172 | 0 | 111 | 0 |
N.S. |
1 | 1.44 | 0.83 | 1.02 | 0.00 | 0.73 | 1.02 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.677 | 10.104 | 7.925 | 0.000 | 0.078 | 1.944 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 209 | 121 | 160 | 0 | 112 | 122 | 0 | 59 | 0 |
N.S. |
1 | 1.45 | 0.84 | 1.11 | 0.00 | 0.78 | 0.85 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.590 | 10.079 | 5.694 | 0.000 | 0.077 | 1.480 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 90 | 88 | 137 | 0 | 91 | 78 | 0 | 25 | 0 |
N.S. |
1 | 0.74 | 0.73 | 1.13 | 0.00 | 0.75 | 0.64 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.439 | 0.016 | 2.171 | 0.000 | 0.073 | 0.920 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 66 | 60 | 0 | 23 | 37 | 0 | 30 | 46 |
N.S. |
1 | 1.00 | 1.12 | 1.02 | 0.00 | 0.39 | 0.63 | 0.00 | 0.51 | 0.78 |
time (sec) |
N/A | 0.283 | 0.027 | 0.688 | 0.000 | 0.068 | 0.422 | 0.000 | 0.194 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 214 | 135 | 191 | 0 | 113 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.37 | 0.87 | 1.22 | 0.00 | 0.72 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.587 | 0.109 | 1.232 | 0.000 | 0.079 | 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 | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 248 | 174 | 226 | 0 | 171 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.28 | 0.90 | 1.17 | 0.00 | 0.89 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.683 | 10.513 | 1.633 | 0.000 | 0.078 | 0.000 | 0.000 | 0.191 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 292 | 190 | 261 | 0 | 228 | 0 | 0 | 69 | 0 |
N.S. |
1 | 1.29 | 0.84 | 1.15 | 0.00 | 1.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.753 | 10.711 | 2.250 | 0.000 | 0.080 | 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 | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 235 | 129 | 203 | 0 | 164 | 0 | 0 | 274 | 0 |
N.S. |
1 | 1.37 | 0.75 | 1.18 | 0.00 | 0.95 | 0.00 | 0.00 | 1.59 | 0.00 |
time (sec) |
N/A | 0.656 | 10.120 | 17.716 | 0.000 | 0.083 | 0.000 | 0.000 | 0.225 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 201 | 111 | 181 | 0 | 145 | 0 | 0 | 140 | 0 |
N.S. |
1 | 1.36 | 0.75 | 1.22 | 0.00 | 0.98 | 0.00 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 0.586 | 10.089 | 6.016 | 0.000 | 0.081 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 233 | 71 | 121 | 0 | 85 | 0 | 0 | 36 | 0 |
N.S. |
1 | 3.28 | 1.00 | 1.70 | 0.00 | 1.20 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.732 | 0.019 | 3.829 | 0.000 | 0.078 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | A | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 0 | 112 | 188 | 0 | 110 | 83 | 0 | 47 | 0 |
N.S. |
1 | 0.00 | 1.18 | 1.98 | 0.00 | 1.16 | 0.87 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.000 | 0.025 | 2.138 | 0.000 | 0.077 | 2.715 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 87 | 64 | 90 | 0 | 73 | 39 | 0 | 40 | 46 |
N.S. |
1 | 1.00 | 0.74 | 1.03 | 0.00 | 0.84 | 0.45 | 0.00 | 0.46 | 0.53 |
time (sec) |
N/A | 0.329 | 0.012 | 0.716 | 0.000 | 0.077 | 0.483 | 0.000 | 0.178 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 287 | 175 | 271 | 0 | 226 | 0 | 0 | 69 | 0 |
N.S. |
1 | 1.49 | 0.91 | 1.40 | 0.00 | 1.17 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.816 | 10.422 | 1.236 | 0.000 | 0.077 | 0.000 | 0.000 | 0.200 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 327 | 190 | 306 | 0 | 239 | 0 | 0 | 80 | 0 |
N.S. |
1 | 1.44 | 0.84 | 1.35 | 0.00 | 1.05 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.835 | 10.656 | 1.737 | 0.000 | 0.088 | 0.000 | 0.000 | 0.199 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 261 | 361 | 155 | 341 | 0 | 336 | 0 | 0 | 91 | 0 |
N.S. |
1 | 1.38 | 0.59 | 1.31 | 0.00 | 1.29 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.932 | 10.726 | 2.326 | 0.000 | 0.085 | 0.000 | 0.000 | 0.202 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 253 | 155 | 222 | 0 | 166 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.36 | 0.83 | 1.19 | 0.00 | 0.89 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.698 | 10.155 | 6.142 | 0.000 | 0.076 | 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 | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 248 | 172 | 222 | 0 | 170 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.30 | 0.90 | 1.16 | 0.00 | 0.89 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.693 | 0.280 | 3.976 | 0.000 | 0.077 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 0 | 147 | 270 | 0 | 224 | 83 | 0 | 67 | 0 |
N.S. |
1 | 0.00 | 0.77 | 1.41 | 0.00 | 1.17 | 0.43 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.000 | 10.091 | 2.189 | 0.000 | 0.082 | 4.616 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 119 | 90 | 127 | 0 | 107 | 39 | 0 | 52 | 46 |
N.S. |
1 | 1.07 | 0.81 | 1.14 | 0.00 | 0.96 | 0.35 | 0.00 | 0.47 | 0.41 |
time (sec) |
N/A | 0.368 | 0.027 | 0.726 | 0.000 | 0.077 | 0.506 | 0.000 | 0.174 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 366 | 163 | 340 | 0 | 335 | 0 | 0 | 91 | 0 |
N.S. |
1 | 1.61 | 0.72 | 1.50 | 0.00 | 1.48 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.950 | 10.663 | 1.302 | 0.000 | 0.091 | 0.000 | 0.000 | 0.213 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 261 | 400 | 235 | 375 | 0 | 391 | 0 | 0 | 92 | 0 |
N.S. |
1 | 1.53 | 0.90 | 1.44 | 0.00 | 1.50 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 1.023 | 10.669 | 1.769 | 0.000 | 0.093 | 0.000 | 0.000 | 0.206 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 295 | 439 | 185 | 410 | 0 | 445 | 0 | 0 | 91 | 0 |
N.S. |
1 | 1.49 | 0.63 | 1.39 | 0.00 | 1.51 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 1.095 | 10.967 | 2.358 | 0.000 | 0.091 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 36 | 27 | 0 | 23 | 61 | 0 | 18 | 0 |
N.S. |
1 | 1.00 | 2.77 | 2.08 | 0.00 | 1.77 | 4.69 | 0.00 | 1.38 | 0.00 |
time (sec) |
N/A | 0.272 | 0.003 | 0.889 | 0.000 | 0.074 | 0.707 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 43 | 45 | 88 | 0 | 42 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.13 | 1.18 | 2.32 | 0.00 | 1.11 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.316 | 10.204 | 1.556 | 0.000 | 0.090 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 72 | 58 | 63 | 0 | 21 | 51 | 0 | 18 | 0 |
N.S. |
1 | 1.36 | 1.09 | 1.19 | 0.00 | 0.40 | 0.96 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.276 | 10.047 | 1.076 | 0.000 | 0.066 | 0.670 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 56 | 52 | 93 | 0 | 44 | 0 | 0 | 28 | 0 |
N.S. |
1 | 0.73 | 0.68 | 1.21 | 0.00 | 0.57 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.273 | 10.150 | 1.855 | 0.000 | 0.076 | 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 | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 173 | 119 | 138 | 0 | 298 | 0 | 83 | 93 | 0 |
N.S. |
1 | 0.88 | 0.61 | 0.70 | 0.00 | 1.52 | 0.00 | 0.42 | 0.47 | 0.00 |
time (sec) |
N/A | 0.476 | 3.327 | 0.208 | 0.000 | 0.086 | 0.000 | 0.116 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 141 | 108 | 117 | 0 | 276 | 0 | 69 | 73 | 0 |
N.S. |
1 | 0.90 | 0.69 | 0.75 | 0.00 | 1.77 | 0.00 | 0.44 | 0.47 | 0.00 |
time (sec) |
N/A | 0.413 | 2.891 | 0.197 | 0.000 | 0.086 | 0.000 | 0.130 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 111 | 97 | 96 | 0 | 254 | 0 | 55 | 53 | 0 |
N.S. |
1 | 0.96 | 0.84 | 0.83 | 0.00 | 2.19 | 0.00 | 0.47 | 0.46 | 0.00 |
time (sec) |
N/A | 0.357 | 1.665 | 0.192 | 0.000 | 0.079 | 0.000 | 0.159 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 88 | 86 | 73 | 0 | 225 | 0 | 43 | 33 | 0 |
N.S. |
1 | 1.13 | 1.10 | 0.94 | 0.00 | 2.88 | 0.00 | 0.55 | 0.42 | 0.00 |
time (sec) |
N/A | 0.330 | 1.345 | 0.187 | 0.000 | 0.085 | 0.000 | 0.112 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 104 | 122 | 180 | 0 | 279 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.11 | 1.30 | 1.91 | 0.00 | 2.97 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.397 | 2.505 | 0.426 | 0.000 | 0.087 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 112 | 110 | 308 | 0 | 294 | 0 | 0 | 242 | 0 |
N.S. |
1 | 1.20 | 1.18 | 3.31 | 0.00 | 3.16 | 0.00 | 0.00 | 2.60 | 0.00 |
time (sec) |
N/A | 0.369 | 2.837 | 0.459 | 0.000 | 0.088 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 149 | 123 | 452 | 0 | 366 | 0 | 0 | 452 | 0 |
N.S. |
1 | 1.16 | 0.96 | 3.53 | 0.00 | 2.86 | 0.00 | 0.00 | 3.53 | 0.00 |
time (sec) |
N/A | 0.415 | 3.098 | 0.458 | 0.000 | 0.088 | 0.000 | 0.000 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 276 | 228 | 141 | 180 | 0 | 341 | 0 | 111 | 133 | 0 |
N.S. |
1 | 0.83 | 0.51 | 0.65 | 0.00 | 1.24 | 0.00 | 0.40 | 0.48 | 0.00 |
time (sec) |
N/A | 0.570 | 5.081 | 0.246 | 0.000 | 0.087 | 0.000 | 0.148 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 236 | 196 | 130 | 159 | 0 | 319 | 0 | 97 | 113 | 0 |
N.S. |
1 | 0.83 | 0.55 | 0.67 | 0.00 | 1.35 | 0.00 | 0.41 | 0.48 | 0.00 |
time (sec) |
N/A | 0.503 | 4.599 | 0.200 | 0.000 | 0.142 | 0.000 | 0.156 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 164 | 119 | 138 | 0 | 297 | 0 | 83 | 93 | 0 |
N.S. |
1 | 0.84 | 0.61 | 0.70 | 0.00 | 1.52 | 0.00 | 0.42 | 0.47 | 0.00 |
time (sec) |
N/A | 0.433 | 3.015 | 0.198 | 0.000 | 0.083 | 0.000 | 0.107 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 134 | 108 | 117 | 0 | 275 | 0 | 69 | 143 | 0 |
N.S. |
1 | 0.86 | 0.69 | 0.75 | 0.00 | 1.76 | 0.00 | 0.44 | 0.92 | 0.00 |
time (sec) |
N/A | 0.417 | 2.688 | 0.197 | 0.000 | 0.084 | 0.000 | 0.137 | 0.261 | 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 | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 111 | 97 | 96 | 0 | 253 | 0 | 0 | 113 | 0 |
N.S. |
1 | 0.98 | 0.86 | 0.85 | 0.00 | 2.24 | 0.00 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.356 | 4.119 | 0.198 | 0.000 | 0.084 | 0.000 | 0.000 | 0.243 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 128 | 163 | 204 | 0 | 401 | 0 | 165 | 289 | 0 |
N.S. |
1 | 0.98 | 1.24 | 1.56 | 0.00 | 3.06 | 0.00 | 1.26 | 2.21 | 0.00 |
time (sec) |
N/A | 0.450 | 4.770 | 0.481 | 0.000 | 0.090 | 0.000 | 0.224 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 130 | 156 | 373 | 0 | 442 | 0 | 0 | 442 | 0 |
N.S. |
1 | 1.06 | 1.27 | 3.03 | 0.00 | 3.59 | 0.00 | 0.00 | 3.59 | 0.00 |
time (sec) |
N/A | 0.464 | 4.864 | 0.464 | 0.000 | 0.107 | 0.000 | 0.000 | 0.333 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 146 | 122 | 452 | 0 | 360 | 0 | 0 | 451 | 0 |
N.S. |
1 | 1.17 | 0.98 | 3.62 | 0.00 | 2.88 | 0.00 | 0.00 | 3.61 | 0.00 |
time (sec) |
N/A | 0.414 | 5.013 | 0.471 | 0.000 | 0.092 | 0.000 | 0.000 | 0.274 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 183 | 134 | 596 | 0 | 432 | 0 | 0 | 587 | 0 |
N.S. |
1 | 1.14 | 0.84 | 3.72 | 0.00 | 2.70 | 0.00 | 0.00 | 3.67 | 0.00 |
time (sec) |
N/A | 0.454 | 4.918 | 0.498 | 0.000 | 0.094 | 0.000 | 0.000 | 0.295 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 217 | 145 | 740 | 0 | 498 | 0 | 0 | 854 | 0 |
N.S. |
1 | 1.11 | 0.74 | 3.79 | 0.00 | 2.55 | 0.00 | 0.00 | 4.38 | 0.00 |
time (sec) |
N/A | 0.586 | 4.991 | 0.515 | 0.000 | 0.102 | 0.000 | 0.000 | 0.326 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 230 | 254 | 139 | 884 | 0 | 564 | 0 | 0 | 1011 | 0 |
N.S. |
1 | 1.10 | 0.60 | 3.84 | 0.00 | 2.45 | 0.00 | 0.00 | 4.40 | 0.00 |
time (sec) |
N/A | 0.659 | 5.394 | 0.549 | 0.000 | 0.106 | 0.000 | 0.000 | 0.324 | 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 | 21 | 21 | 33 | 16 | 15 | 25 | 15 | 25 | 21 | 15 |
N.S. |
1 | 1.00 | 1.57 | 0.76 | 0.71 | 1.19 | 0.71 | 1.19 | 1.00 | 0.71 |
time (sec) |
N/A | 0.230 | 0.033 | 0.225 | 0.104 | 0.067 | 0.070 | 0.133 | 0.172 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 70 | 40 | 0 | 120 | 0 | 25 | 21 | 0 |
N.S. |
1 | 1.00 | 3.33 | 1.90 | 0.00 | 5.71 | 0.00 | 1.19 | 1.00 | 0.00 |
time (sec) |
N/A | 0.256 | 0.913 | 0.168 | 0.000 | 0.075 | 0.000 | 0.162 | 200.018 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 150 | 109 | 117 | 0 | 275 | 0 | 0 | 73 | 0 |
N.S. |
1 | 0.96 | 0.70 | 0.75 | 0.00 | 1.76 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.449 | 3.391 | 0.221 | 0.000 | 0.085 | 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 | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 118 | 98 | 96 | 0 | 253 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.02 | 0.84 | 0.83 | 0.00 | 2.18 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.380 | 3.018 | 0.204 | 0.000 | 0.082 | 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 | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 88 | 86 | 75 | 0 | 225 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.13 | 1.10 | 0.96 | 0.00 | 2.88 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.332 | 2.549 | 0.200 | 0.000 | 0.086 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 65 | 50 | 54 | 0 | 123 | 0 | 0 | 15 | 0 |
N.S. |
1 | 1.59 | 1.22 | 1.32 | 0.00 | 3.00 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.294 | 1.328 | 0.184 | 0.000 | 0.081 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 78 | 78 | 249 | 0 | 153 | 0 | 0 | 81 | 0 |
N.S. |
1 | 1.44 | 1.44 | 4.61 | 0.00 | 2.83 | 0.00 | 0.00 | 1.50 | 0.00 |
time (sec) |
N/A | 0.318 | 1.632 | 0.814 | 0.000 | 0.076 | 0.000 | 0.000 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 112 | 111 | 488 | 0 | 298 | 0 | 0 | 208 | 0 |
N.S. |
1 | 1.20 | 1.19 | 5.25 | 0.00 | 3.20 | 0.00 | 0.00 | 2.24 | 0.00 |
time (sec) |
N/A | 0.361 | 2.669 | 0.820 | 0.000 | 0.079 | 0.000 | 0.000 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 149 | 123 | 711 | 0 | 366 | 0 | 0 | 345 | 0 |
N.S. |
1 | 1.16 | 0.96 | 5.55 | 0.00 | 2.86 | 0.00 | 0.00 | 2.70 | 0.00 |
time (sec) |
N/A | 0.447 | 3.051 | 0.835 | 0.000 | 0.087 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 140 | 143 | 96 | 0 | 296 | 0 | 62 | 137 | 0 |
N.S. |
1 | 0.92 | 0.93 | 0.63 | 0.00 | 1.93 | 0.00 | 0.41 | 0.90 | 0.00 |
time (sec) |
N/A | 0.445 | 5.380 | 0.249 | 0.000 | 0.083 | 0.000 | 0.119 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 108 | 127 | 83 | 0 | 267 | 0 | 46 | 114 | 0 |
N.S. |
1 | 0.96 | 1.13 | 0.74 | 0.00 | 2.38 | 0.00 | 0.41 | 1.02 | 0.00 |
time (sec) |
N/A | 0.396 | 5.053 | 0.236 | 0.000 | 0.084 | 0.000 | 0.137 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 81 | 112 | 72 | 0 | 243 | 0 | 35 | 90 | 0 |
N.S. |
1 | 1.08 | 1.49 | 0.96 | 0.00 | 3.24 | 0.00 | 0.47 | 1.20 | 0.00 |
time (sec) |
N/A | 0.327 | 4.887 | 0.217 | 0.000 | 0.086 | 0.000 | 0.128 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 42 | 37 | 0 | 43 | 0 | 14 | 39 | 29 |
N.S. |
1 | 1.00 | 1.27 | 1.12 | 0.00 | 1.30 | 0.00 | 0.42 | 1.18 | 0.88 |
time (sec) |
N/A | 0.278 | 4.275 | 0.203 | 0.000 | 0.071 | 0.000 | 0.116 | 0.207 | 17.969 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 101 | 108 | 343 | 0 | 272 | 0 | 0 | 327 | 0 |
N.S. |
1 | 1.06 | 1.14 | 3.61 | 0.00 | 2.86 | 0.00 | 0.00 | 3.44 | 0.00 |
time (sec) |
N/A | 0.360 | 3.055 | 0.800 | 0.000 | 0.084 | 0.000 | 0.000 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 138 | 123 | 1068 | 0 | 368 | 0 | 0 | 373 | 0 |
N.S. |
1 | 1.05 | 0.94 | 8.15 | 0.00 | 2.81 | 0.00 | 0.00 | 2.85 | 0.00 |
time (sec) |
N/A | 0.435 | 2.964 | 0.858 | 0.000 | 0.086 | 0.000 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 175 | 140 | 981 | 0 | 398 | 0 | 0 | 755 | 0 |
N.S. |
1 | 1.05 | 0.84 | 5.87 | 0.00 | 2.38 | 0.00 | 0.00 | 4.52 | 0.00 |
time (sec) |
N/A | 0.518 | 4.811 | 0.881 | 0.000 | 0.089 | 0.000 | 0.000 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 173 | 155 | 141 | 0 | 394 | 0 | 76 | 212 | 0 |
N.S. |
1 | 0.91 | 0.81 | 0.74 | 0.00 | 2.06 | 0.00 | 0.40 | 1.11 | 0.00 |
time (sec) |
N/A | 0.511 | 5.763 | 0.289 | 0.000 | 0.094 | 0.000 | 0.209 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 139 | 140 | 128 | 0 | 367 | 0 | 62 | 189 | 0 |
N.S. |
1 | 0.93 | 0.93 | 0.85 | 0.00 | 2.45 | 0.00 | 0.41 | 1.26 | 0.00 |
time (sec) |
N/A | 0.437 | 5.634 | 0.274 | 0.000 | 0.090 | 0.000 | 0.194 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 110 | 117 | 107 | 0 | 324 | 0 | 39 | 151 | 0 |
N.S. |
1 | 1.00 | 1.06 | 0.97 | 0.00 | 2.95 | 0.00 | 0.35 | 1.37 | 0.00 |
time (sec) |
N/A | 0.379 | 5.394 | 0.226 | 0.000 | 0.084 | 0.000 | 0.164 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 87 | 54 | 47 | 0 | 71 | 0 | 0 | 83 | 86 |
N.S. |
1 | 1.24 | 0.77 | 0.67 | 0.00 | 1.01 | 0.00 | 0.00 | 1.19 | 1.23 |
time (sec) |
N/A | 0.329 | 5.162 | 0.222 | 0.000 | 0.069 | 0.000 | 0.000 | 0.196 | 17.330 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 79 | 55 | 48 | 0 | 74 | 0 | 0 | 84 | 89 |
N.S. |
1 | 1.08 | 0.75 | 0.66 | 0.00 | 1.01 | 0.00 | 0.00 | 1.15 | 1.22 |
time (sec) |
N/A | 0.306 | 5.027 | 0.205 | 0.000 | 0.069 | 0.000 | 0.000 | 0.208 | 17.373 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 128 | 121 | 606 | 0 | 372 | 0 | 0 | 542 | 0 |
N.S. |
1 | 0.98 | 0.92 | 4.63 | 0.00 | 2.84 | 0.00 | 0.00 | 4.14 | 0.00 |
time (sec) |
N/A | 0.428 | 5.170 | 0.569 | 0.000 | 0.087 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 165 | 140 | 745 | 0 | 356 | 0 | 0 | 755 | 0 |
N.S. |
1 | 0.99 | 0.84 | 4.46 | 0.00 | 2.13 | 0.00 | 0.00 | 4.52 | 0.00 |
time (sec) |
N/A | 0.482 | 3.647 | 0.842 | 0.000 | 0.092 | 0.000 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 202 | 148 | 1660 | 0 | 504 | 0 | 0 | 604 | 0 |
N.S. |
1 | 1.00 | 0.73 | 8.18 | 0.00 | 2.48 | 0.00 | 0.00 | 2.98 | 0.00 |
time (sec) |
N/A | 0.562 | 3.650 | 0.891 | 0.000 | 0.092 | 0.000 | 0.000 | 0.235 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 239 | 164 | 1325 | 0 | 568 | 0 | 0 | 1181 | 0 |
N.S. |
1 | 1.00 | 0.69 | 5.54 | 0.00 | 2.38 | 0.00 | 0.00 | 4.94 | 0.00 |
time (sec) |
N/A | 0.637 | 5.429 | 0.524 | 0.000 | 0.100 | 0.000 | 0.000 | 0.274 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | B | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 2 | 2 | 32 | 29 | 0 | 28 | 0 | 0 | 2 | 0 |
N.S. |
1 | 1.00 | 16.00 | 14.50 | 0.00 | 14.00 | 0.00 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.231 | 0.781 | 0.103 | 0.000 | 0.070 | 0.000 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | B | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 2 | 2 | 42 | 29 | 0 | 81 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.00 | 21.00 | 14.50 | 0.00 | 40.50 | 0.00 | 0.00 | 4.50 | 0.00 |
time (sec) |
N/A | 0.233 | 0.771 | 0.102 | 0.000 | 0.072 | 0.000 | 0.000 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 46 | 32 | 39 | 0 | 28 | 0 | 0 | 5 | 0 |
N.S. |
1 | 2.00 | 1.39 | 1.70 | 0.00 | 1.22 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.275 | 0.757 | 0.116 | 0.000 | 0.067 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 44 | 38 | 37 | 0 | 73 | 0 | 0 | 4 | 0 |
N.S. |
1 | 1.76 | 1.52 | 1.48 | 0.00 | 2.92 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.281 | 0.760 | 0.105 | 0.000 | 0.065 | 0.000 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 40 | 34 | 33 | 0 | 65 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.90 | 1.62 | 1.57 | 0.00 | 3.10 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.268 | 0.696 | 0.109 | 0.000 | 0.069 | 0.000 | 0.000 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 46 | 23 | 39 | 0 | 19 | 0 | 0 | 5 | 0 |
N.S. |
1 | 2.00 | 1.00 | 1.70 | 0.00 | 0.83 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.279 | 0.723 | 0.112 | 0.000 | 0.066 | 0.000 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 30 | 38 | 25 | 0 | 73 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.43 | 1.81 | 1.19 | 0.00 | 3.48 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.265 | 0.686 | 0.107 | 0.000 | 0.066 | 0.000 | 0.000 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 34 | 23 | 29 | 0 | 75 | 0 | 0 | 11 | 0 |
N.S. |
1 | 1.48 | 1.00 | 1.26 | 0.00 | 3.26 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.283 | 0.730 | 0.441 | 0.000 | 0.069 | 0.000 | 0.000 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 72 | 71 | 59 | 0 | 137 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.60 | 1.58 | 1.31 | 0.00 | 3.04 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.522 | 4.671 | 0.185 | 0.000 | 0.069 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 24 | 0 | 0 | 26 | 0 | 93 | 34 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 0.00 | 0.00 | 1.18 | 0.00 | 4.23 | 1.55 |
time (sec) |
N/A | 0.229 | 0.081 | 0.146 | 0.000 | 0.000 | 2.629 | 0.000 | 0.187 | 17.102 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 0 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.05 | 0.00 |
time (sec) |
N/A | 0.264 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 177 | 0 | 0 | 0 | 0 | 0 | 551 | 0 |
N.S. |
1 | 1.00 | 4.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 13.12 | 0.00 |
time (sec) |
N/A | 0.265 | 0.238 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 0 | 0 | 0 | 0 | 0 | 0 | 551 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 13.12 | 0.00 |
time (sec) |
N/A | 0.278 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 40 | 31 | 0 | 46 | 58 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 0.67 | 0.52 | 0.00 | 0.77 | 0.97 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.281 | 10.035 | 0.431 | 0.000 | 0.074 | 0.640 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 49 | 40 | 0 | 77 | 68 | 0 | 57 | 0 |
N.S. |
1 | 1.00 | 0.55 | 0.45 | 0.00 | 0.87 | 0.76 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.318 | 10.030 | 0.903 | 0.000 | 0.079 | 0.811 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 88 | 153 | 0 | 95 | 75 | 0 | 65 | 0 |
N.S. |
1 | 1.00 | 0.84 | 1.46 | 0.00 | 0.90 | 0.71 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.334 | 10.052 | 1.009 | 0.000 | 0.074 | 0.885 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 40 | 31 | 0 | 46 | 58 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 0.67 | 0.52 | 0.00 | 0.77 | 0.97 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.282 | 0.001 | 0.370 | 0.000 | 0.078 | 0.654 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 24 | 51 | 0 | 56 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.00 | 0.34 | 0.73 | 0.00 | 0.80 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.423 | 10.147 | 0.866 | 0.000 | 0.111 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 62 | 34 | 0 | 48 | 61 | 0 | 40 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.54 | 0.00 | 0.76 | 0.97 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.285 | 10.044 | 0.568 | 0.000 | 0.073 | 0.686 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 44 | 52 | 0 | 77 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.00 | 0.59 | 0.70 | 0.00 | 1.04 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.443 | 10.145 | 1.046 | 0.000 | 0.108 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 40 | 31 | 0 | 28 | 58 | 0 | 36 | 0 |
N.S. |
1 | 1.00 | 0.40 | 0.31 | 0.00 | 0.28 | 0.58 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.353 | 10.032 | 0.296 | 0.000 | 0.080 | 0.635 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 150 | 49 | 40 | 0 | 77 | 68 | 0 | 56 | 0 |
N.S. |
1 | 1.00 | 0.33 | 0.27 | 0.00 | 0.51 | 0.45 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.411 | 10.027 | 0.688 | 0.000 | 0.074 | 0.797 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 182 | 87 | 153 | 0 | 96 | 75 | 0 | 64 | 0 |
N.S. |
1 | 1.00 | 0.48 | 0.84 | 0.00 | 0.53 | 0.41 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.450 | 10.059 | 0.997 | 0.000 | 0.081 | 0.869 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 40 | 31 | 0 | 28 | 58 | 0 | 36 | 0 |
N.S. |
1 | 1.00 | 0.40 | 0.31 | 0.00 | 0.28 | 0.58 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.342 | 0.001 | 0.275 | 0.000 | 0.079 | 0.640 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 24 | 51 | 0 | 32 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.00 | 0.34 | 0.73 | 0.00 | 0.46 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.410 | 10.098 | 0.362 | 0.000 | 0.106 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 62 | 34 | 0 | 31 | 63 | 0 | 39 | 0 |
N.S. |
1 | 1.00 | 0.58 | 0.32 | 0.00 | 0.29 | 0.59 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.367 | 10.039 | 0.402 | 0.000 | 0.063 | 0.693 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 44 | 107 | 0 | 75 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 0.59 | 1.45 | 0.00 | 1.01 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.426 | 10.098 | 0.440 | 0.000 | 0.097 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 152 | 90 | 0 | 0 | 0 | 56 | 0 | 69 | 0 |
N.S. |
1 | 1.35 | 0.80 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.451 | 10.181 | 0.000 | 0.000 | 0.000 | 1.910 | 0.000 | 0.203 | 0.000 |