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 | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 219 | 85 | 199 | 0 | 89 | 202 | 0 | 93 | 0 |
N.S. |
1 | 1.04 | 0.40 | 0.95 | 0.00 | 0.42 | 0.96 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.297 | 10.051 | 0.751 | 0.000 | 0.106 | 9.241 | 0.000 | 0.259 | 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 | 211 | 220 | 86 | 195 | 0 | 78 | 212 | 0 | 94 | 0 |
N.S. |
1 | 1.04 | 0.41 | 0.92 | 0.00 | 0.37 | 1.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.298 | 10.065 | 1.043 | 0.000 | 0.098 | 61.776 | 0.000 | 0.301 | 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 | 377 | 384 | 97 | 262 | 0 | 105 | 199 | 0 | 83 | 0 |
N.S. |
1 | 1.02 | 0.26 | 0.69 | 0.00 | 0.28 | 0.53 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.439 | 10.077 | 0.796 | 0.000 | 0.126 | 5.202 | 0.000 | 0.218 | 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 | 367 | 381 | 84 | 245 | 0 | 95 | 202 | 0 | 88 | 0 |
N.S. |
1 | 1.04 | 0.23 | 0.67 | 0.00 | 0.26 | 0.55 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.433 | 10.047 | 0.773 | 0.000 | 0.101 | 7.884 | 0.000 | 0.255 | 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 | 362 | 381 | 84 | 242 | 0 | 84 | 212 | 0 | 94 | 0 |
N.S. |
1 | 1.05 | 0.23 | 0.67 | 0.00 | 0.23 | 0.59 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.416 | 10.049 | 0.839 | 0.000 | 0.093 | 21.584 | 0.000 | 0.283 | 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 | 372 | 385 | 85 | 266 | 0 | 105 | 223 | 0 | 95 | 0 |
N.S. |
1 | 1.03 | 0.23 | 0.72 | 0.00 | 0.28 | 0.60 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.431 | 10.056 | 1.255 | 0.000 | 0.099 | 178.934 | 0.000 | 0.332 | 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 | 174 | 186 | 96 | 190 | 0 | 75 | 94 | 0 | 67 | 0 |
N.S. |
1 | 1.07 | 0.55 | 1.09 | 0.00 | 0.43 | 0.54 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.258 | 10.087 | 0.609 | 0.000 | 0.088 | 4.485 | 0.000 | 0.227 | 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 | 139 | 152 | 79 | 168 | 0 | 50 | 94 | 0 | 45 | 0 |
N.S. |
1 | 1.09 | 0.57 | 1.21 | 0.00 | 0.36 | 0.68 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.250 | 10.044 | 0.638 | 0.000 | 0.100 | 1.681 | 0.000 | 0.215 | 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 | 138 | 151 | 81 | 178 | 0 | 60 | 97 | 0 | 54 | 0 |
N.S. |
1 | 1.09 | 0.59 | 1.29 | 0.00 | 0.43 | 0.70 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.241 | 10.036 | 0.904 | 0.000 | 0.081 | 4.147 | 0.000 | 0.245 | 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 | 176 | 191 | 88 | 194 | 0 | 72 | 104 | 0 | 56 | 0 |
N.S. |
1 | 1.09 | 0.50 | 1.10 | 0.00 | 0.41 | 0.59 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.273 | 10.057 | 1.375 | 0.000 | 0.101 | 44.438 | 0.000 | 0.281 | 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 | 338 | 355 | 96 | 242 | 0 | 92 | 94 | 0 | 68 | 0 |
N.S. |
1 | 1.05 | 0.28 | 0.72 | 0.00 | 0.27 | 0.28 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.420 | 10.088 | 0.966 | 0.000 | 0.086 | 11.921 | 0.000 | 0.228 | 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 | 299 | 322 | 80 | 222 | 0 | 56 | 94 | 0 | 41 | 0 |
N.S. |
1 | 1.08 | 0.27 | 0.74 | 0.00 | 0.19 | 0.31 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.374 | 10.055 | 0.532 | 0.000 | 0.084 | 2.759 | 0.000 | 0.225 | 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 | 290 | 316 | 82 | 223 | 0 | 63 | 97 | 0 | 50 | 0 |
N.S. |
1 | 1.09 | 0.28 | 0.77 | 0.00 | 0.22 | 0.33 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.381 | 10.029 | 0.709 | 0.000 | 0.095 | 2.200 | 0.000 | 0.240 | 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 | 342 | 358 | 82 | 243 | 0 | 79 | 104 | 0 | 56 | 0 |
N.S. |
1 | 1.05 | 0.24 | 0.71 | 0.00 | 0.23 | 0.30 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.417 | 10.035 | 1.089 | 0.000 | 0.107 | 14.253 | 0.000 | 0.272 | 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 | 208 | 221 | 111 | 252 | 0 | 145 | 94 | 0 | 69 | 0 |
N.S. |
1 | 1.06 | 0.53 | 1.21 | 0.00 | 0.70 | 0.45 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.294 | 10.100 | 1.561 | 0.000 | 0.127 | 143.848 | 0.000 | 0.228 | 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 | 169 | 184 | 85 | 223 | 0 | 106 | 94 | 0 | 48 | 0 |
N.S. |
1 | 1.09 | 0.50 | 1.32 | 0.00 | 0.63 | 0.56 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.270 | 10.077 | 1.240 | 0.000 | 0.094 | 13.509 | 0.000 | 0.238 | 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 | 144 | 157 | 75 | 191 | 0 | 88 | 94 | 0 | 30 | 0 |
N.S. |
1 | 1.09 | 0.52 | 1.33 | 0.00 | 0.61 | 0.65 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.255 | 10.044 | 0.961 | 0.000 | 0.109 | 8.697 | 0.000 | 0.237 | 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 | 176 | 188 | 91 | 222 | 0 | 117 | 97 | 0 | 32 | 0 |
N.S. |
1 | 1.07 | 0.52 | 1.26 | 0.00 | 0.66 | 0.55 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.276 | 10.045 | 1.634 | 0.000 | 0.129 | 22.780 | 0.000 | 0.233 | 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 | 213 | 224 | 82 | 251 | 0 | 132 | 104 | 0 | 32 | 0 |
N.S. |
1 | 1.05 | 0.38 | 1.18 | 0.00 | 0.62 | 0.49 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.290 | 10.059 | 2.370 | 0.000 | 0.094 | 124.422 | 0.000 | 0.251 | 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 | 332 | 350 | 84 | 278 | 0 | 123 | 94 | 0 | 49 | 0 |
N.S. |
1 | 1.05 | 0.25 | 0.84 | 0.00 | 0.37 | 0.28 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.413 | 10.091 | 1.468 | 0.000 | 0.094 | 47.336 | 0.000 | 0.234 | 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 | 301 | 329 | 76 | 252 | 0 | 99 | 94 | 0 | 25 | 0 |
N.S. |
1 | 1.09 | 0.25 | 0.84 | 0.00 | 0.33 | 0.31 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.403 | 10.069 | 0.772 | 0.000 | 0.116 | 6.149 | 0.000 | 0.202 | 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 | 333 | 352 | 77 | 281 | 0 | 117 | 97 | 0 | 32 | 0 |
N.S. |
1 | 1.06 | 0.23 | 0.84 | 0.00 | 0.35 | 0.29 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.411 | 10.031 | 1.543 | 0.000 | 0.083 | 13.209 | 0.000 | 0.222 | 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 | 379 | 391 | 78 | 324 | 0 | 140 | 104 | 0 | 32 | 0 |
N.S. |
1 | 1.03 | 0.21 | 0.85 | 0.00 | 0.37 | 0.27 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.446 | 10.038 | 2.089 | 0.000 | 0.118 | 51.650 | 0.000 | 0.244 | 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 | 212 | 217 | 116 | 283 | 0 | 179 | 0 | 0 | 133 | 0 |
N.S. |
1 | 1.02 | 0.55 | 1.33 | 0.00 | 0.84 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.286 | 10.133 | 2.503 | 0.000 | 0.106 | 0.000 | 0.000 | 0.261 | 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 | 180 | 196 | 105 | 245 | 0 | 153 | 94 | 0 | 109 | 0 |
N.S. |
1 | 1.09 | 0.58 | 1.36 | 0.00 | 0.85 | 0.52 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.280 | 10.102 | 1.196 | 0.000 | 0.109 | 62.094 | 0.000 | 0.265 | 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 | 187 | 197 | 108 | 225 | 0 | 149 | 94 | 0 | 41 | 0 |
N.S. |
1 | 1.05 | 0.58 | 1.20 | 0.00 | 0.80 | 0.50 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.287 | 10.077 | 1.498 | 0.000 | 0.085 | 42.792 | 0.000 | 0.259 | 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 | 213 | 222 | 120 | 267 | 0 | 174 | 97 | 0 | 43 | 0 |
N.S. |
1 | 1.04 | 0.56 | 1.25 | 0.00 | 0.82 | 0.46 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.299 | 10.063 | 2.977 | 0.000 | 0.106 | 125.708 | 0.000 | 0.293 | 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 | 373 | 387 | 116 | 337 | 0 | 187 | 0 | 0 | 130 | 0 |
N.S. |
1 | 1.04 | 0.31 | 0.90 | 0.00 | 0.50 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.438 | 10.107 | 2.704 | 0.000 | 0.103 | 0.000 | 0.000 | 0.287 | 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 | 344 | 362 | 97 | 300 | 0 | 177 | 0 | 0 | 110 | 0 |
N.S. |
1 | 1.05 | 0.28 | 0.87 | 0.00 | 0.51 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.424 | 10.097 | 1.409 | 0.000 | 0.111 | 0.000 | 0.000 | 0.257 | 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 | 344 | 364 | 84 | 281 | 0 | 153 | 94 | 0 | 36 | 0 |
N.S. |
1 | 1.06 | 0.24 | 0.82 | 0.00 | 0.44 | 0.27 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.424 | 10.085 | 1.350 | 0.000 | 0.078 | 32.524 | 0.000 | 0.215 | 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 | 377 | 388 | 86 | 327 | 0 | 178 | 97 | 0 | 43 | 0 |
N.S. |
1 | 1.03 | 0.23 | 0.87 | 0.00 | 0.47 | 0.26 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.440 | 10.051 | 2.734 | 0.000 | 0.091 | 72.828 | 0.000 | 0.264 | 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 | 103 | 107 | 80 | 68 | 118 | 99 | 141 | 104 | 305 | 96 |
N.S. |
1 | 1.04 | 0.78 | 0.66 | 1.15 | 0.96 | 1.37 | 1.01 | 2.96 | 0.93 |
time (sec) |
N/A | 0.230 | 0.062 | 0.410 | 0.039 | 0.075 | 0.780 | 0.131 | 0.240 | 0.539 |
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 | 73 | 77 | 56 | 49 | 84 | 74 | 107 | 73 | 237 | 76 |
N.S. |
1 | 1.05 | 0.77 | 0.67 | 1.15 | 1.01 | 1.47 | 1.00 | 3.25 | 1.04 |
time (sec) |
N/A | 0.216 | 0.044 | 0.411 | 0.046 | 0.098 | 0.698 | 0.122 | 0.228 | 0.444 |
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 | 46 | 50 | 34 | 31 | 49 | 50 | 71 | 44 | 168 | 54 |
N.S. |
1 | 1.09 | 0.74 | 0.67 | 1.07 | 1.09 | 1.54 | 0.96 | 3.65 | 1.17 |
time (sec) |
N/A | 0.189 | 0.026 | 0.400 | 0.041 | 0.077 | 0.644 | 0.117 | 0.237 | 0.436 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 103 | 85 | 89 | 87 | 157 | 73 | 213 | 76 | 68 |
N.S. |
1 | 1.20 | 0.99 | 1.03 | 1.01 | 1.83 | 0.85 | 2.48 | 0.88 | 0.79 |
time (sec) |
N/A | 0.210 | 0.093 | 0.999 | 0.153 | 0.100 | 10.370 | 0.130 | 0.246 | 0.696 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | C | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 117 | 97 | 102 | 148 | 585 | 92 | 253 | 92 | 110 |
N.S. |
1 | 1.12 | 0.93 | 0.98 | 1.42 | 5.62 | 0.88 | 2.43 | 0.88 | 1.06 |
time (sec) |
N/A | 0.222 | 0.202 | 0.819 | 0.136 | 0.118 | 15.781 | 0.134 | 0.264 | 1.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | C | C | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 116 | 115 | 113 | 209 | 675 | 88 | 322 | 117 | 140 |
N.S. |
1 | 0.94 | 0.93 | 0.92 | 1.70 | 5.49 | 0.72 | 2.62 | 0.95 | 1.14 |
time (sec) |
N/A | 0.226 | 0.245 | 0.584 | 0.155 | 0.105 | 38.157 | 0.134 | 0.287 | 1.355 |
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 | 149 | 141 | 89 | 0 | 0 | 0 | 63 | 0 | 125 | 0 |
N.S. |
1 | 0.95 | 0.60 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.233 | 5.857 | 0.000 | 0.000 | 0.000 | 1.016 | 0.000 | 0.251 | 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 | 116 | 112 | 75 | 0 | 0 | 0 | 60 | 0 | 83 | 0 |
N.S. |
1 | 0.97 | 0.65 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 0.200 | 0.046 | 0.000 | 0.000 | 0.000 | 0.903 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 112 | 78 | 0 | 0 | 0 | 58 | 0 | 114 | 80 |
N.S. |
1 | 0.97 | 0.67 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.98 | 0.69 |
time (sec) |
N/A | 0.207 | 6.113 | 0.000 | 0.000 | 0.000 | 1.068 | 0.000 | 0.249 | 0.908 |
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 | 118 | 110 | 80 | 0 | 0 | 0 | 66 | 0 | 118 | 0 |
N.S. |
1 | 0.93 | 0.68 | 0.00 | 0.00 | 0.00 | 0.56 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.208 | 6.297 | 0.000 | 0.000 | 0.000 | 1.144 | 0.000 | 0.276 | 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 | 148 | 138 | 80 | 0 | 0 | 0 | 71 | 0 | 118 | 0 |
N.S. |
1 | 0.93 | 0.54 | 0.00 | 0.00 | 0.00 | 0.48 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.230 | 10.064 | 0.000 | 0.000 | 0.000 | 1.279 | 0.000 | 0.304 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 107 | 80 | 68 | 118 | 100 | 141 | 239 | 329 | 96 |
N.S. |
1 | 1.04 | 0.78 | 0.66 | 1.15 | 0.97 | 1.37 | 2.32 | 3.19 | 0.93 |
time (sec) |
N/A | 0.233 | 0.064 | 0.409 | 0.038 | 0.100 | 0.880 | 0.122 | 0.230 | 0.521 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 77 | 56 | 49 | 84 | 75 | 107 | 183 | 261 | 76 |
N.S. |
1 | 1.05 | 0.77 | 0.67 | 1.15 | 1.03 | 1.47 | 2.51 | 3.58 | 1.04 |
time (sec) |
N/A | 0.210 | 0.049 | 0.401 | 0.078 | 0.087 | 0.787 | 0.121 | 0.233 | 0.443 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 50 | 34 | 31 | 49 | 51 | 117 | 120 | 193 | 54 |
N.S. |
1 | 1.09 | 0.74 | 0.67 | 1.07 | 1.11 | 2.54 | 2.61 | 4.20 | 1.17 |
time (sec) |
N/A | 0.188 | 0.029 | 0.515 | 0.046 | 0.087 | 0.290 | 0.120 | 0.237 | 0.399 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 100 | 86 | 89 | 90 | 195 | 73 | 214 | 76 | 67 |
N.S. |
1 | 1.15 | 0.99 | 1.02 | 1.03 | 2.24 | 0.84 | 2.46 | 0.87 | 0.77 |
time (sec) |
N/A | 0.216 | 0.096 | 0.437 | 0.153 | 0.096 | 9.925 | 0.132 | 0.233 | 0.659 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | C | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 115 | 101 | 92 | 152 | 710 | 92 | 258 | 93 | 109 |
N.S. |
1 | 1.06 | 0.94 | 0.85 | 1.41 | 6.57 | 0.85 | 2.39 | 0.86 | 1.01 |
time (sec) |
N/A | 0.230 | 0.213 | 0.553 | 0.114 | 0.106 | 13.688 | 0.127 | 0.264 | 1.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | C | C | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 117 | 115 | 118 | 206 | 786 | 88 | 319 | 117 | 140 |
N.S. |
1 | 0.96 | 0.94 | 0.97 | 1.69 | 6.44 | 0.72 | 2.61 | 0.96 | 1.15 |
time (sec) |
N/A | 0.228 | 0.266 | 0.676 | 0.130 | 0.110 | 30.538 | 0.131 | 0.291 | 1.396 |
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 | 180 | 165 | 89 | 0 | 0 | 0 | 63 | 0 | 125 | 0 |
N.S. |
1 | 0.92 | 0.49 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.250 | 7.042 | 0.000 | 0.000 | 0.000 | 1.153 | 0.000 | 0.284 | 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 | 145 | 133 | 75 | 0 | 0 | 0 | 60 | 0 | 83 | 0 |
N.S. |
1 | 0.92 | 0.52 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.218 | 0.040 | 0.000 | 0.000 | 0.000 | 1.003 | 0.000 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 133 | 78 | 0 | 0 | 0 | 58 | 0 | 114 | 80 |
N.S. |
1 | 0.94 | 0.55 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 | 0.81 | 0.57 |
time (sec) |
N/A | 0.224 | 7.272 | 0.000 | 0.000 | 0.000 | 1.181 | 0.000 | 0.265 | 0.878 |
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 | 146 | 134 | 80 | 0 | 0 | 0 | 66 | 0 | 118 | 0 |
N.S. |
1 | 0.92 | 0.55 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.232 | 7.139 | 0.000 | 0.000 | 0.000 | 1.339 | 0.000 | 0.275 | 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 | 182 | 165 | 80 | 0 | 0 | 0 | 71 | 0 | 118 | 0 |
N.S. |
1 | 0.91 | 0.44 | 0.00 | 0.00 | 0.00 | 0.39 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.249 | 10.065 | 0.000 | 0.000 | 0.000 | 1.344 | 0.000 | 0.315 | 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 | 103 | 107 | 80 | 68 | 118 | 124 | 325 | 104 | 373 | 117 |
N.S. |
1 | 1.04 | 0.78 | 0.66 | 1.15 | 1.20 | 3.16 | 1.01 | 3.62 | 1.14 |
time (sec) |
N/A | 0.232 | 0.073 | 0.404 | 0.035 | 0.066 | 1.387 | 0.122 | 0.227 | 0.590 |
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 | 73 | 77 | 56 | 49 | 84 | 98 | 216 | 73 | 305 | 97 |
N.S. |
1 | 1.05 | 0.77 | 0.67 | 1.15 | 1.34 | 2.96 | 1.00 | 4.18 | 1.33 |
time (sec) |
N/A | 0.211 | 0.048 | 0.389 | 0.038 | 0.072 | 0.513 | 0.128 | 0.236 | 0.495 |
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 | 46 | 50 | 34 | 31 | 49 | 73 | 165 | 44 | 236 | 76 |
N.S. |
1 | 1.09 | 0.74 | 0.67 | 1.07 | 1.59 | 3.59 | 0.96 | 5.13 | 1.65 |
time (sec) |
N/A | 0.187 | 0.030 | 0.391 | 0.034 | 0.086 | 0.411 | 0.126 | 0.231 | 0.457 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 121 | 109 | 108 | 99 | 200 | 347 | 234 | 118 | 103 |
N.S. |
1 | 1.17 | 1.06 | 1.05 | 0.96 | 1.94 | 3.37 | 2.27 | 1.15 | 1.00 |
time (sec) |
N/A | 0.217 | 0.123 | 0.431 | 0.134 | 0.109 | 20.753 | 0.127 | 0.247 | 0.762 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 136 | 117 | 124 | 177 | 601 | 170 | 315 | 130 | 143 |
N.S. |
1 | 1.05 | 0.91 | 0.96 | 1.37 | 4.66 | 1.32 | 2.44 | 1.01 | 1.11 |
time (sec) |
N/A | 0.239 | 0.205 | 0.564 | 0.134 | 0.109 | 18.560 | 0.128 | 0.308 | 1.333 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | C | C | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 141 | 117 | 120 | 217 | 659 | 184 | 320 | 130 | 155 |
N.S. |
1 | 1.05 | 0.87 | 0.90 | 1.62 | 4.92 | 1.37 | 2.39 | 0.97 | 1.16 |
time (sec) |
N/A | 0.235 | 0.311 | 0.574 | 0.121 | 0.114 | 45.025 | 0.127 | 0.312 | 1.748 |
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 | 182 | 165 | 94 | 0 | 0 | 0 | 131 | 0 | 167 | 0 |
N.S. |
1 | 0.91 | 0.52 | 0.00 | 0.00 | 0.00 | 0.72 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 0.249 | 7.736 | 0.000 | 0.000 | 0.000 | 1.806 | 0.000 | 0.278 | 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 | 145 | 134 | 77 | 0 | 0 | 0 | 128 | 0 | 125 | 0 |
N.S. |
1 | 0.92 | 0.53 | 0.00 | 0.00 | 0.00 | 0.88 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.215 | 0.040 | 0.000 | 0.000 | 0.000 | 1.609 | 0.000 | 0.278 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 134 | 79 | 0 | 0 | 0 | 122 | 0 | 156 | 80 |
N.S. |
1 | 0.95 | 0.56 | 0.00 | 0.00 | 0.00 | 0.87 | 0.00 | 1.11 | 0.57 |
time (sec) |
N/A | 0.221 | 8.027 | 0.000 | 0.000 | 0.000 | 1.931 | 0.000 | 0.301 | 1.225 |
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 | 146 | 135 | 82 | 0 | 0 | 0 | 128 | 0 | 146 | 0 |
N.S. |
1 | 0.92 | 0.56 | 0.00 | 0.00 | 0.00 | 0.88 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.225 | 7.913 | 0.000 | 0.000 | 0.000 | 1.984 | 0.000 | 0.290 | 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 | 148 | 134 | 82 | 0 | 0 | 0 | 141 | 0 | 143 | 0 |
N.S. |
1 | 0.91 | 0.55 | 0.00 | 0.00 | 0.00 | 0.95 | 0.00 | 0.97 | 0.00 |
time (sec) |
N/A | 0.230 | 10.059 | 0.000 | 0.000 | 0.000 | 2.183 | 0.000 | 0.306 | 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 | 184 | 163 | 82 | 0 | 0 | 0 | 146 | 0 | 160 | 0 |
N.S. |
1 | 0.89 | 0.45 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.250 | 10.058 | 0.000 | 0.000 | 0.000 | 2.389 | 0.000 | 0.301 | 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 | 103 | 107 | 80 | 68 | 118 | 76 | 124 | 107 | 261 | 79 |
N.S. |
1 | 1.04 | 0.78 | 0.66 | 1.15 | 0.74 | 1.20 | 1.04 | 2.53 | 0.77 |
time (sec) |
N/A | 0.229 | 0.057 | 0.411 | 0.045 | 0.072 | 0.826 | 0.124 | 0.217 | 0.557 |
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 | 73 | 77 | 56 | 49 | 84 | 52 | 92 | 79 | 193 | 57 |
N.S. |
1 | 1.05 | 0.77 | 0.67 | 1.15 | 0.71 | 1.26 | 1.08 | 2.64 | 0.78 |
time (sec) |
N/A | 0.204 | 0.042 | 0.408 | 0.037 | 0.076 | 0.759 | 0.114 | 0.209 | 0.511 |
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 | 46 | 50 | 34 | 31 | 49 | 30 | 58 | 47 | 127 | 35 |
N.S. |
1 | 1.09 | 0.74 | 0.67 | 1.07 | 0.65 | 1.26 | 1.02 | 2.76 | 0.76 |
time (sec) |
N/A | 0.183 | 0.029 | 0.497 | 0.033 | 0.076 | 0.713 | 0.127 | 0.222 | 0.476 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 82 | 71 | 79 | 75 | 173 | 68 | 196 | 156 | 52 |
N.S. |
1 | 1.15 | 1.00 | 1.11 | 1.06 | 2.44 | 0.96 | 2.76 | 2.20 | 0.73 |
time (sec) |
N/A | 0.201 | 0.066 | 0.520 | 0.111 | 0.104 | 4.668 | 0.130 | 0.219 | 0.770 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | C | C | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 92 | 94 | 85 | 154 | 707 | 85 | 253 | 35 | 97 |
N.S. |
1 | 0.99 | 1.01 | 0.91 | 1.66 | 7.60 | 0.91 | 2.72 | 0.38 | 1.04 |
time (sec) |
N/A | 0.210 | 0.157 | 0.560 | 0.122 | 0.128 | 6.221 | 0.128 | 0.219 | 1.090 |
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 | 180 | 171 | 114 | 0 | 0 | 0 | 60 | 0 | 35 | 0 |
N.S. |
1 | 0.95 | 0.63 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.253 | 10.074 | 0.000 | 0.000 | 0.000 | 1.149 | 0.000 | 0.215 | 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 | 147 | 141 | 91 | 0 | 0 | 0 | 60 | 0 | 35 | 0 |
N.S. |
1 | 0.96 | 0.62 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.230 | 10.064 | 0.000 | 0.000 | 0.000 | 1.059 | 0.000 | 0.243 | 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 | 116 | 111 | 74 | 0 | 0 | 0 | 56 | 0 | 31 | 0 |
N.S. |
1 | 0.96 | 0.64 | 0.00 | 0.00 | 0.00 | 0.48 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.205 | 0.021 | 0.000 | 0.000 | 0.000 | 0.787 | 0.000 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 110 | 77 | 0 | 0 | 0 | 54 | 0 | 31 | 80 |
N.S. |
1 | 1.01 | 0.71 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 0.28 | 0.73 |
time (sec) |
N/A | 0.208 | 10.025 | 0.000 | 0.000 | 0.000 | 0.873 | 0.000 | 0.227 | 0.868 |
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 | 146 | 140 | 78 | 0 | 0 | 0 | 63 | 0 | 35 | 0 |
N.S. |
1 | 0.96 | 0.53 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.227 | 10.027 | 0.000 | 0.000 | 0.000 | 1.028 | 0.000 | 0.239 | 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 | 182 | 171 | 78 | 0 | 0 | 0 | 68 | 0 | 35 | 0 |
N.S. |
1 | 0.94 | 0.43 | 0.00 | 0.00 | 0.00 | 0.37 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.252 | 10.027 | 0.000 | 0.000 | 0.000 | 1.152 | 0.000 | 0.239 | 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 | 101 | 105 | 80 | 68 | 118 | 76 | 131 | 101 | 237 | 79 |
N.S. |
1 | 1.04 | 0.79 | 0.67 | 1.17 | 0.75 | 1.30 | 1.00 | 2.35 | 0.78 |
time (sec) |
N/A | 0.233 | 0.059 | 0.412 | 0.031 | 0.099 | 0.775 | 0.123 | 0.203 | 0.521 |
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 | 71 | 75 | 56 | 49 | 83 | 51 | 97 | 70 | 169 | 57 |
N.S. |
1 | 1.06 | 0.79 | 0.69 | 1.17 | 0.72 | 1.37 | 0.99 | 2.38 | 0.80 |
time (sec) |
N/A | 0.207 | 0.044 | 0.410 | 0.042 | 0.095 | 0.647 | 0.119 | 0.226 | 0.473 |
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 | 44 | 48 | 33 | 31 | 48 | 29 | 61 | 38 | 104 | 35 |
N.S. |
1 | 1.09 | 0.75 | 0.70 | 1.09 | 0.66 | 1.39 | 0.86 | 2.36 | 0.80 |
time (sec) |
N/A | 0.189 | 0.032 | 0.390 | 0.031 | 0.081 | 0.609 | 0.122 | 0.259 | 0.505 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 85 | 70 | 75 | 76 | 164 | 66 | 196 | 112 | 56 |
N.S. |
1 | 1.21 | 1.00 | 1.07 | 1.09 | 2.34 | 0.94 | 2.80 | 1.60 | 0.80 |
time (sec) |
N/A | 0.199 | 0.077 | 0.425 | 0.140 | 0.096 | 5.254 | 0.128 | 0.253 | 0.740 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | C | C | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 99 | 95 | 104 | 158 | 607 | 85 | 257 | 35 | 101 |
N.S. |
1 | 1.04 | 1.00 | 1.09 | 1.66 | 6.39 | 0.89 | 2.71 | 0.37 | 1.06 |
time (sec) |
N/A | 0.207 | 0.164 | 0.676 | 0.129 | 0.102 | 7.592 | 0.131 | 0.242 | 1.017 |
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 | 182 | 177 | 137 | 0 | 0 | 0 | 60 | 0 | 35 | 0 |
N.S. |
1 | 0.97 | 0.75 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.255 | 10.100 | 0.000 | 0.000 | 0.000 | 1.230 | 0.000 | 0.244 | 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 | 149 | 147 | 113 | 0 | 0 | 0 | 60 | 0 | 35 | 0 |
N.S. |
1 | 0.99 | 0.76 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.236 | 10.075 | 0.000 | 0.000 | 0.000 | 1.122 | 0.000 | 0.257 | 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 | 118 | 117 | 89 | 0 | 0 | 0 | 60 | 0 | 35 | 0 |
N.S. |
1 | 0.99 | 0.75 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.213 | 10.058 | 0.000 | 0.000 | 0.000 | 1.051 | 0.000 | 0.273 | 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 | 88 | 88 | 74 | 0 | 0 | 0 | 56 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.64 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.185 | 0.022 | 0.000 | 0.000 | 0.000 | 0.800 | 0.000 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 78 | 0 | 0 | 0 | 54 | 0 | 31 | 80 |
N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 0.64 | 0.00 | 0.36 | 0.94 |
time (sec) |
N/A | 0.192 | 10.026 | 0.000 | 0.000 | 0.000 | 0.930 | 0.000 | 0.231 | 0.871 |
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 | 120 | 115 | 78 | 0 | 0 | 0 | 63 | 0 | 35 | 0 |
N.S. |
1 | 0.96 | 0.65 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.215 | 10.029 | 0.000 | 0.000 | 0.000 | 1.094 | 0.000 | 0.262 | 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 | 151 | 145 | 78 | 0 | 0 | 0 | 68 | 0 | 35 | 0 |
N.S. |
1 | 0.96 | 0.52 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.239 | 10.027 | 0.000 | 0.000 | 0.000 | 1.233 | 0.000 | 0.235 | 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 | 101 | 105 | 80 | 77 | 118 | 88 | 121 | 114 | 270 | 76 |
N.S. |
1 | 1.04 | 0.79 | 0.76 | 1.17 | 0.87 | 1.20 | 1.13 | 2.67 | 0.75 |
time (sec) |
N/A | 0.233 | 0.064 | 0.437 | 0.036 | 0.077 | 3.830 | 0.125 | 0.207 | 0.687 |
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 | 71 | 75 | 56 | 49 | 83 | 63 | 88 | 78 | 202 | 62 |
N.S. |
1 | 1.06 | 0.79 | 0.69 | 1.17 | 0.89 | 1.24 | 1.10 | 2.85 | 0.87 |
time (sec) |
N/A | 0.209 | 0.052 | 0.529 | 0.034 | 0.077 | 3.234 | 0.124 | 0.219 | 0.556 |
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 | 44 | 48 | 33 | 30 | 48 | 41 | 58 | 38 | 135 | 33 |
N.S. |
1 | 1.09 | 0.75 | 0.68 | 1.09 | 0.93 | 1.32 | 0.86 | 3.07 | 0.75 |
time (sec) |
N/A | 0.189 | 0.037 | 0.424 | 0.044 | 0.107 | 2.472 | 0.123 | 0.224 | 0.470 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 93 | 79 | 87 | 94 | 256 | 68 | 215 | 221 | 70 |
N.S. |
1 | 1.18 | 1.00 | 1.10 | 1.19 | 3.24 | 0.86 | 2.72 | 2.80 | 0.89 |
time (sec) |
N/A | 0.214 | 0.120 | 0.439 | 0.190 | 0.096 | 8.607 | 0.127 | 0.243 | 0.803 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | C | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 118 | 105 | 110 | 192 | 797 | 85 | 285 | 69 | 146 |
N.S. |
1 | 0.99 | 0.88 | 0.92 | 1.61 | 6.70 | 0.71 | 2.39 | 0.58 | 1.23 |
time (sec) |
N/A | 0.234 | 0.250 | 0.799 | 0.120 | 0.126 | 15.845 | 0.131 | 0.242 | 1.171 |
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 | 182 | 173 | 125 | 0 | 0 | 0 | 60 | 0 | 73 | 0 |
N.S. |
1 | 0.95 | 0.69 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.259 | 10.078 | 0.000 | 0.000 | 0.000 | 2.555 | 0.000 | 0.257 | 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 | 149 | 143 | 102 | 0 | 0 | 0 | 60 | 0 | 73 | 0 |
N.S. |
1 | 0.96 | 0.68 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.235 | 10.064 | 0.000 | 0.000 | 0.000 | 2.106 | 0.000 | 0.263 | 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 | 118 | 113 | 77 | 0 | 0 | 0 | 60 | 0 | 73 | 0 |
N.S. |
1 | 0.96 | 0.65 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.209 | 10.049 | 0.000 | 0.000 | 0.000 | 1.874 | 0.000 | 0.247 | 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 | 83 | 119 | 74 | 0 | 0 | 0 | 56 | 0 | 69 | 0 |
N.S. |
1 | 1.43 | 0.89 | 0.00 | 0.00 | 0.00 | 0.67 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.212 | 0.017 | 0.000 | 0.000 | 0.000 | 1.796 | 0.000 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 86 | 0 | 0 | 0 | 54 | 0 | 68 | 80 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.63 | 0.00 | 0.79 | 0.93 |
time (sec) |
N/A | 0.197 | 10.027 | 0.000 | 0.000 | 0.000 | 2.580 | 0.000 | 0.227 | 1.036 |
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 | 120 | 115 | 72 | 0 | 0 | 0 | 63 | 0 | 71 | 0 |
N.S. |
1 | 0.96 | 0.60 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.217 | 10.027 | 0.000 | 0.000 | 0.000 | 3.195 | 0.000 | 0.247 | 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 | 151 | 145 | 72 | 0 | 0 | 0 | 68 | 0 | 71 | 0 |
N.S. |
1 | 0.96 | 0.48 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.234 | 10.029 | 0.000 | 0.000 | 0.000 | 3.810 | 0.000 | 0.236 | 0.000 |