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 | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 220 | 200 | 183 | 472 | 0 | 416 | 0 | 0 | 0 |
| N.S. |
1 | 0.91 | 0.83 | 2.15 | 0.00 | 1.89 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.199 | 4.469 | 3.815 | 0.000 | 0.119 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 254 | 227 | 200 | 491 | 0 | 435 | 0 | 0 | 0 |
| N.S. |
1 | 0.89 | 0.79 | 1.93 | 0.00 | 1.71 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.259 | 5.371 | 4.306 | 0.000 | 0.131 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 310 | 286 | 249 | 1013 | 0 | 595 | 0 | 0 | 0 |
| N.S. |
1 | 0.92 | 0.80 | 3.27 | 0.00 | 1.92 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.647 | 6.331 | 34.848 | 0.000 | 0.139 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
| size | 277 | 261 | 215 | 793 | 0 | 536 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 0.78 | 2.86 | 0.00 | 1.94 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.614 | 3.893 | 3.293 | 0.000 | 0.110 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 233 | 229 | 188 | 624 | 0 | 533 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 0.81 | 2.68 | 0.00 | 2.29 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.419 | 3.640 | 3.966 | 0.000 | 0.107 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 231 | 227 | 188 | 624 | 0 | 529 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 0.81 | 2.70 | 0.00 | 2.29 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.427 | 3.300 | 3.925 | 0.000 | 0.129 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 235 | 231 | 190 | 624 | 0 | 531 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 0.81 | 2.66 | 0.00 | 2.26 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.417 | 4.809 | 4.165 | 0.000 | 0.120 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 272 | 260 | 206 | 638 | 0 | 546 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 0.76 | 2.35 | 0.00 | 2.01 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.621 | 5.888 | 4.456 | 0.000 | 0.145 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 313 | 293 | 229 | 666 | 0 | 563 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 0.73 | 2.13 | 0.00 | 1.80 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.674 | 6.896 | 4.770 | 0.000 | 0.147 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 226 | 248 | 155 | 151 | 986 | 130 | 0 | 0 | 599 |
| N.S. |
1 | 1.10 | 0.69 | 0.67 | 4.36 | 0.58 | 0.00 | 0.00 | 2.65 |
| time (sec) |
N/A | 1.341 | 0.555 | 1.855 | 0.390 | 0.272 | 0.000 | 0.000 | 7.906 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 178 | 205 | 121 | 121 | 848 | 109 | 0 | 0 | 465 |
| N.S. |
1 | 1.15 | 0.68 | 0.68 | 4.76 | 0.61 | 0.00 | 0.00 | 2.61 |
| time (sec) |
N/A | 1.094 | 0.528 | 1.734 | 0.566 | 0.278 | 0.000 | 0.000 | 6.848 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 130 | 163 | 85 | 95 | 709 | 88 | 0 | 0 | 229 |
| N.S. |
1 | 1.25 | 0.65 | 0.73 | 5.45 | 0.68 | 0.00 | 0.00 | 1.76 |
| time (sec) |
N/A | 0.913 | 0.249 | 1.685 | 0.519 | 0.257 | 0.000 | 0.000 | 3.620 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 140 | 149 | 105 | 180 | 1547 | 125 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 0.75 | 1.29 | 11.05 | 0.89 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.906 | 0.276 | 1.849 | 0.700 | 0.275 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 141 | 149 | 104 | 271 | 1695 | 109 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 0.74 | 1.92 | 12.02 | 0.77 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.932 | 0.218 | 4.620 | 0.566 | 0.303 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 151 | 156 | 123 | 242 | 1996 | 133 | 0 | 0 | 0 |
| N.S. |
1 | 1.03 | 0.81 | 1.60 | 13.22 | 0.88 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.917 | 0.298 | 4.842 | 1.073 | 0.438 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 199 | 200 | 144 | 334 | 3770 | 155 | 0 | 0 | 0 |
| N.S. |
1 | 1.01 | 0.72 | 1.68 | 18.94 | 0.78 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.114 | 0.560 | 4.241 | 1.167 | 0.438 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 247 | 243 | 164 | 436 | 9619 | 175 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 0.66 | 1.77 | 38.94 | 0.71 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.300 | 0.712 | 4.169 | 1.044 | 0.581 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 284 | 307 | 187 | 182 | 1065 | 156 | 0 | 0 | 399 |
| N.S. |
1 | 1.08 | 0.66 | 0.64 | 3.75 | 0.55 | 0.00 | 0.00 | 1.40 |
| time (sec) |
N/A | 1.750 | 0.725 | 2.217 | 0.392 | 0.283 | 0.000 | 0.000 | 7.997 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 232 | 262 | 157 | 152 | 926 | 134 | 0 | 0 | 335 |
| N.S. |
1 | 1.13 | 0.68 | 0.66 | 3.99 | 0.58 | 0.00 | 0.00 | 1.44 |
| time (sec) |
N/A | 1.507 | 0.665 | 2.135 | 0.390 | 0.270 | 0.000 | 0.000 | 7.658 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 184 | 220 | 122 | 122 | 788 | 112 | 0 | 0 | 308 |
| N.S. |
1 | 1.20 | 0.66 | 0.66 | 4.28 | 0.61 | 0.00 | 0.00 | 1.67 |
| time (sec) |
N/A | 1.314 | 0.509 | 2.163 | 0.392 | 0.268 | 0.000 | 0.000 | 7.665 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 192 | 206 | 134 | 252 | 1915 | 155 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 0.70 | 1.31 | 9.97 | 0.81 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.248 | 0.647 | 1.940 | 0.564 | 0.284 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 191 | 201 | 128 | 332 | 2726 | 156 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.67 | 1.74 | 14.27 | 0.82 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.291 | 0.516 | 4.821 | 0.640 | 0.326 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 201 | 209 | 127 | 412 | 0 | 143 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 0.63 | 2.05 | 0.00 | 0.71 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.299 | 0.429 | 4.612 | 0.000 | 0.442 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 201 | 212 | 145 | 341 | 3824 | 162 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.72 | 1.70 | 19.02 | 0.81 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.296 | 0.637 | 4.379 | 0.913 | 0.424 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 253 | 259 | 165 | 441 | 9940 | 183 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 0.65 | 1.74 | 39.29 | 0.72 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.512 | 0.825 | 4.991 | 1.233 | 0.564 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 303 | 302 | 190 | 543 | 11425 | 204 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.63 | 1.79 | 37.71 | 0.67 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.752 | 1.313 | 4.556 | 2.135 | 0.574 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 334 | 362 | 224 | 214 | 1142 | 191 | 0 | 0 | 927 |
| N.S. |
1 | 1.08 | 0.67 | 0.64 | 3.42 | 0.57 | 0.00 | 0.00 | 2.78 |
| time (sec) |
N/A | 2.235 | 1.249 | 0.849 | 0.837 | 0.281 | 0.000 | 0.000 | 8.944 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 284 | 319 | 190 | 184 | 1005 | 167 | 0 | 0 | 787 |
| N.S. |
1 | 1.12 | 0.67 | 0.65 | 3.54 | 0.59 | 0.00 | 0.00 | 2.77 |
| time (sec) |
N/A | 1.965 | 0.957 | 0.774 | 0.455 | 0.285 | 0.000 | 0.000 | 8.078 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 234 | 271 | 158 | 154 | 866 | 143 | 0 | 0 | 749 |
| N.S. |
1 | 1.16 | 0.68 | 0.66 | 3.70 | 0.61 | 0.00 | 0.00 | 3.20 |
| time (sec) |
N/A | 1.683 | 0.861 | 0.720 | 0.420 | 0.283 | 0.000 | 0.000 | 8.301 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 242 | 261 | 172 | 305 | 2584 | 188 | 0 | 0 | 0 |
| N.S. |
1 | 1.08 | 0.71 | 1.26 | 10.68 | 0.78 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.606 | 1.218 | 0.794 | 0.618 | 0.300 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 243 | 256 | 156 | 385 | 3231 | 193 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 0.64 | 1.58 | 13.30 | 0.79 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.711 | 0.985 | 1.594 | 0.741 | 0.318 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 253 | 263 | 156 | 482 | 0 | 192 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 0.62 | 1.91 | 0.00 | 0.76 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.672 | 0.808 | 1.459 | 0.000 | 0.467 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 251 | 265 | 156 | 463 | 0 | 178 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 0.62 | 1.84 | 0.00 | 0.71 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.689 | 0.722 | 4.867 | 0.000 | 0.446 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 253 | 269 | 166 | 449 | 10517 | 195 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 0.66 | 1.77 | 41.57 | 0.77 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.686 | 1.005 | 4.899 | 1.132 | 0.568 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 301 | 312 | 191 | 551 | 11979 | 218 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 0.63 | 1.83 | 39.80 | 0.72 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.925 | 1.775 | 5.112 | 1.214 | 0.584 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | B | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 353 | 354 | 225 | 653 | 45124 | 241 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.64 | 1.85 | 127.83 | 0.68 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.195 | 2.912 | 5.117 | 3.124 | 0.594 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 305 | 346 | 199 | 557 | 0 | 209 | 0 | 0 | 0 |
| N.S. |
1 | 1.13 | 0.65 | 1.83 | 0.00 | 0.69 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.037 | 13.771 | 1.641 | 0.000 | 0.331 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 257 | 288 | 2607 | 497 | 0 | 189 | 0 | 0 | 0 |
| N.S. |
1 | 1.12 | 10.14 | 1.93 | 0.00 | 0.74 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.664 | 8.205 | 1.865 | 0.000 | 0.307 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 211 | 230 | 1843 | 437 | 0 | 169 | 0 | 0 | 0 |
| N.S. |
1 | 1.09 | 8.73 | 2.07 | 0.00 | 0.80 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.264 | 7.212 | 2.054 | 0.000 | 0.291 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 163 | 172 | 661 | 376 | 0 | 145 | 0 | 0 | 0 |
| N.S. |
1 | 1.06 | 4.06 | 2.31 | 0.00 | 0.89 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.002 | 6.576 | 1.973 | 0.000 | 0.324 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 178 | 164 | 277 | 315 | 0 | 162 | 0 | 0 | 0 |
| N.S. |
1 | 0.92 | 1.56 | 1.77 | 0.00 | 0.91 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.053 | 2.741 | 1.849 | 0.000 | 4.649 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 181 | 172 | 132 | 221 | 0 | 171 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 0.73 | 1.22 | 0.00 | 0.94 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.085 | 0.284 | 5.081 | 0.000 | 6.060 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 235 | 228 | 211 | 317 | 0 | 203 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 0.90 | 1.35 | 0.00 | 0.86 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.402 | 2.294 | 5.192 | 0.000 | 15.897 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | A | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 281 | 286 | 234 | 424 | 0 | 224 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 0.83 | 1.51 | 0.00 | 0.80 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.791 | 2.656 | 4.457 | 0.000 | 15.876 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 192 | 183 | 143 | 281 | 0 | 208 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 0.74 | 1.46 | 0.00 | 1.08 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.157 | 0.223 | 5.185 | 0.000 | 13.956 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-1) | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 333 | 360 | 3137 | 695 | 0 | 255 | 0 | 0 | 0 |
| N.S. |
1 | 1.08 | 9.42 | 2.09 | 0.00 | 0.77 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.144 | 8.653 | 2.047 | 0.000 | 0.332 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-1) | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 283 | 302 | 2296 | 635 | 0 | 235 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 8.11 | 2.24 | 0.00 | 0.83 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.719 | 7.512 | 1.691 | 0.000 | 0.336 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 233 | 244 | 1070 | 575 | 0 | 209 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 4.59 | 2.47 | 0.00 | 0.90 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.314 | 6.725 | 1.950 | 0.000 | 0.298 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 181 | 184 | 481 | 498 | 0 | 173 | 0 | 0 | 0 |
| N.S. |
1 | 1.02 | 2.66 | 2.75 | 0.00 | 0.96 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.979 | 4.357 | 2.185 | 0.000 | 0.290 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 189 | 175 | 171 | 361 | 0 | 213 | 0 | 0 | 0 |
| N.S. |
1 | 0.93 | 0.90 | 1.91 | 0.00 | 1.13 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.076 | 3.284 | 2.098 | 0.000 | 17.127 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 242 | 230 | 225 | 467 | 0 | 251 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 0.93 | 1.93 | 0.00 | 1.04 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.438 | 3.373 | 5.380 | 0.000 | 21.962 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 300 | 293 | 250 | 602 | 0 | 284 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 0.83 | 2.01 | 0.00 | 0.95 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.865 | 3.973 | 5.195 | 0.000 | 43.407 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 333 | 360 | 266 | 833 | 0 | 287 | 0 | 0 | 0 |
| N.S. |
1 | 1.08 | 0.80 | 2.50 | 0.00 | 0.86 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.100 | 13.750 | 2.009 | 0.000 | 0.319 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-1) | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 281 | 300 | 1374 | 773 | 0 | 264 | 0 | 0 | 0 |
| N.S. |
1 | 1.07 | 4.89 | 2.75 | 0.00 | 0.94 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.728 | 8.600 | 2.301 | 0.000 | 0.317 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F(-1) | A | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 231 | 242 | 952 | 744 | 0 | 226 | 0 | 0 | 0 |
| N.S. |
1 | 1.05 | 4.12 | 3.22 | 0.00 | 0.98 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.361 | 7.475 | 2.247 | 0.000 | 0.289 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 183 | 190 | 696 | 479 | 0 | 225 | 0 | 0 | 0 |
| N.S. |
1 | 1.04 | 3.80 | 2.62 | 0.00 | 1.23 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.995 | 6.600 | 1.982 | 0.000 | 0.323 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
| size | 241 | 233 | 232 | 579 | 0 | 293 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 0.96 | 2.40 | 0.00 | 1.22 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.429 | 5.126 | 1.888 | 0.000 | 36.824 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 294 | 290 | 251 | 714 | 0 | 329 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 0.85 | 2.43 | 0.00 | 1.12 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.884 | 5.740 | 5.464 | 0.000 | 47.652 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | A | F(-1) | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 352 | 350 | 270 | 917 | 0 | 360 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 0.77 | 2.61 | 0.00 | 1.02 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.287 | 7.363 | 4.616 | 0.000 | 84.101 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 205 | 182 | 155 | 814 | 0 | 243 | 0 | 0 | 0 |
| N.S. |
1 | 0.89 | 0.76 | 3.97 | 0.00 | 1.19 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.936 | 3.386 | 314.253 | 0.000 | 0.104 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 172 | 152 | 122 | 705 | 0 | 221 | 0 | 0 | 0 |
| N.S. |
1 | 0.88 | 0.71 | 4.10 | 0.00 | 1.28 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.892 | 2.460 | 318.714 | 0.000 | 0.097 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 135 | 119 | 96 | 613 | 0 | 190 | 0 | 0 | 0 |
| N.S. |
1 | 0.88 | 0.71 | 4.54 | 0.00 | 1.41 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.754 | 1.500 | 326.646 | 0.000 | 0.109 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 135 | 119 | 98 | 295 | 0 | 158 | 0 | 0 | 0 |
| N.S. |
1 | 0.88 | 0.73 | 2.19 | 0.00 | 1.17 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.741 | 1.303 | 5.492 | 0.000 | 0.100 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 141 | 128 | 101 | 399 | 0 | 171 | 0 | 0 | 0 |
| N.S. |
1 | 0.91 | 0.72 | 2.83 | 0.00 | 1.21 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.768 | 1.235 | 6.023 | 0.000 | 0.106 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 174 | 158 | 120 | 401 | 0 | 193 | 0 | 0 | 0 |
| N.S. |
1 | 0.91 | 0.69 | 2.30 | 0.00 | 1.11 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.881 | 1.613 | 7.835 | 0.000 | 0.104 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 205 | 186 | 141 | 443 | 0 | 211 | 0 | 0 | 0 |
| N.S. |
1 | 0.91 | 0.69 | 2.16 | 0.00 | 1.03 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.916 | 2.139 | 9.227 | 0.000 | 0.110 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 292 | 257 | 217 | 1152 | 0 | 327 | 0 | 0 | 0 |
| N.S. |
1 | 0.88 | 0.74 | 3.95 | 0.00 | 1.12 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.421 | 6.532 | 1435.885 | 0.000 | 0.118 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 243 | 227 | 218 | 903 | 0 | 289 | 0 | 0 | 0 |
| N.S. |
1 | 0.93 | 0.90 | 3.72 | 0.00 | 1.19 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.372 | 2.378 | 1406.651 | 0.000 | 0.110 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 209 | 194 | 147 | 886 | 0 | 266 | 0 | 0 | 0 |
| N.S. |
1 | 0.93 | 0.70 | 4.24 | 0.00 | 1.27 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.224 | 3.812 | 1367.630 | 0.000 | 0.120 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 194 | 174 | 133 | 862 | 0 | 236 | 0 | 0 | 0 |
| N.S. |
1 | 0.90 | 0.69 | 4.44 | 0.00 | 1.22 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.163 | 3.117 | 1456.075 | 0.000 | 0.111 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 206 | 193 | 139 | 481 | 0 | 212 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 0.67 | 2.33 | 0.00 | 1.03 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.230 | 2.763 | 7.659 | 0.000 | 0.122 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 211 | 203 | 148 | 532 | 0 | 238 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 0.70 | 2.52 | 0.00 | 1.13 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.221 | 2.858 | 8.567 | 0.000 | 0.121 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 245 | 233 | 170 | 587 | 0 | 261 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 0.69 | 2.40 | 0.00 | 1.07 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.365 | 3.103 | 10.671 | 0.000 | 0.128 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 294 | 262 | 209 | 649 | 0 | 296 | 0 | 0 | 0 |
| N.S. |
1 | 0.89 | 0.71 | 2.21 | 0.00 | 1.01 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.416 | 3.726 | 11.401 | 0.000 | 0.141 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 333 | 302 | 324 | 1243 | 0 | 374 | 0 | 0 | 0 |
| N.S. |
1 | 0.91 | 0.97 | 3.73 | 0.00 | 1.12 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.982 | 8.083 | 4660.674 | 0.000 | 0.128 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F(-1) | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 283 | 273 | 261 | 0 | 0 | 335 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 0.92 | 0.00 | 0.00 | 1.18 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.782 | 4.291 | 180.000 | 0.000 | 0.135 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F(-1) | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 269 | 252 | 216 | 0 | 0 | 315 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 0.80 | 0.00 | 0.00 | 1.17 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.695 | 3.896 | 180.000 | 0.000 | 0.130 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F(-1) | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 258 | 245 | 179 | 0 | 0 | 293 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 0.69 | 0.00 | 0.00 | 1.14 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.699 | 4.159 | 180.000 | 0.000 | 0.128 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 284 | 276 | 193 | 943 | 0 | 279 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 0.68 | 3.32 | 0.00 | 0.98 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.782 | 3.791 | 9.964 | 0.000 | 0.141 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 285 | 278 | 203 | 718 | 0 | 307 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 0.71 | 2.52 | 0.00 | 1.08 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.739 | 3.607 | 10.838 | 0.000 | 0.137 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 335 | 311 | 236 | 793 | 0 | 346 | 0 | 0 | 0 |
| N.S. |
1 | 0.93 | 0.70 | 2.37 | 0.00 | 1.03 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.916 | 4.236 | 11.135 | 0.000 | 0.156 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 386 | 341 | 276 | 873 | 0 | 383 | 0 | 0 | 0 |
| N.S. |
1 | 0.88 | 0.72 | 2.26 | 0.00 | 0.99 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.956 | 4.661 | 13.112 | 0.000 | 0.167 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F(-1) | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 417 | 390 | 425 | 0 | 0 | 451 | 0 | 0 | 0 |
| N.S. |
1 | 0.94 | 1.02 | 0.00 | 0.00 | 1.08 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.668 | 8.723 | 180.000 | 0.000 | 0.151 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F(-1) | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 365 | 356 | 356 | 0 | 0 | 410 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 0.98 | 0.00 | 0.00 | 1.12 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.462 | 9.603 | 180.000 | 0.000 | 0.164 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F(-1) | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 356 | 344 | 296 | 0 | 0 | 377 | 0 | 0 | 0 |
| N.S. |
1 | 0.97 | 0.83 | 0.00 | 0.00 | 1.06 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.463 | 5.247 | 180.000 | 0.000 | 0.159 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F(-1) | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 361 | 342 | 233 | 0 | 0 | 362 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 0.65 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.414 | 5.064 | 180.000 | 0.000 | 0.149 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F(-1) | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 340 | 328 | 243 | 0 | 0 | 354 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 0.71 | 0.00 | 0.00 | 1.04 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.358 | 4.215 | 180.000 | 0.000 | 0.157 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 360 | 353 | 252 | 1209 | 0 | 341 | 0 | 0 | 0 |
| N.S. |
1 | 0.98 | 0.70 | 3.36 | 0.00 | 0.95 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.453 | 4.084 | 10.712 | 0.000 | 0.151 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 369 | 367 | 265 | 924 | 0 | 383 | 0 | 0 | 0 |
| N.S. |
1 | 0.99 | 0.72 | 2.50 | 0.00 | 1.04 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.380 | 4.113 | 12.388 | 0.000 | 0.152 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | C | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 422 | 402 | 303 | 1017 | 0 | 424 | 0 | 0 | 0 |
| N.S. |
1 | 0.95 | 0.72 | 2.41 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.614 | 5.135 | 18.213 | 0.000 | 0.161 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 266 | 245 | 642 | 759 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.92 | 2.41 | 2.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.213 | 8.141 | 158.191 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 200 | 172 | 216 | 436 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.86 | 1.08 | 2.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.621 | 3.579 | 166.990 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 172 | 133 | 126 | 380 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.77 | 0.73 | 2.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.187 | 2.172 | 2.891 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 145 | 111 | 238 | 259 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.77 | 1.64 | 1.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.864 | 2.194 | 2.878 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 190 | 162 | 533 | 722 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.85 | 2.81 | 3.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.249 | 7.163 | 3.023 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 241 | 220 | 597 | 948 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.91 | 2.48 | 3.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.712 | 7.473 | 3.515 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 299 | 286 | 343 | 1244 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.96 | 1.15 | 4.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.259 | 5.588 | 4.334 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 396 | 337 | 718 | 992 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.85 | 1.81 | 2.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.794 | 8.499 | 37.324 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F(-1) | F(-1) | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 330 | 270 | 524 | 872 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.82 | 1.59 | 2.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 2.110 | 7.125 | 4.895 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | F(-1) | F | F | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 274 | 225 | 488 | 804 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 0.82 | 1.78 | 2.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 1.525 | 5.560 | 4.417 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |