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 | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 373 | 373 | 248 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.593 | 1.520 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 277 | 277 | 204 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.347 | 0.978 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 191 | 191 | 145 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.158 | 0.664 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 202 | 202 | 159 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.167 | 0.502 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 279 | 279 | 220 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.355 | 2.578 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 362 | 362 | 288 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.608 | 5.871 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 336 | 336 | 596 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.619 | 25.418 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 229 | 229 | 478 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.352 | 20.872 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 137 | 137 | 409 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.152 | 2.167 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | F | F | F(-1) | F(-1) |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 152 | 152 | 250 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 1.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.287 | 12.005 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | F | F | F(-1) | F(-1) |
| verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 226 | 226 | 523 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 2.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.452 | 27.192 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 221 | 221 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.301 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F | F | F | F | F | F | F(-1) |
| verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 114 | 114 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| time (sec) |
N/A | 0.101 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | F | F | A | F | B | B |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 37 | 37 | 107 | 0 | 0 | 41 | 0 | 9496 | 61 |
| N.S. |
1 | 1.00 | 2.89 | 0.00 | 0.00 | 1.11 | 0.00 | 256.65 | 1.65 |
| time (sec) |
N/A | 0.081 | 5.069 | 0.000 | 0.000 | 0.288 | 0.000 | 84.241 | 12.925 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | F | F | A | F | B | B |
| verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
| size | 35 | 35 | 35 | 0 | 0 | 41 | 0 | 5502 | 38 |
| N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 1.17 | 0.00 | 157.20 | 1.09 |
| time (sec) |
N/A | 0.061 | 1.446 | 0.000 | 0.000 | 0.267 | 0.000 | 40.100 | 14.390 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 153 | 153 | 147 | 212 | 0 | 804 | 0 | 356 | 3718 |
| N.S. |
1 | 1.00 | 0.96 | 1.39 | 0.00 | 5.25 | 0.00 | 2.33 | 24.30 |
| time (sec) |
N/A | 0.263 | 1.969 | 0.903 | 0.000 | 0.332 | 0.000 | 0.661 | 17.913 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 182 | 182 | 141 | 119 | 336 | 123 | 853 | 178 | 454 |
| N.S. |
1 | 1.00 | 0.77 | 0.65 | 1.85 | 0.68 | 4.69 | 0.98 | 2.49 |
| time (sec) |
N/A | 0.206 | 1.354 | 2.016 | 0.228 | 0.262 | 0.442 | 0.313 | 15.295 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 142 | 142 | 123 | 98 | 200 | 102 | 486 | 140 | 389 |
| N.S. |
1 | 1.00 | 0.87 | 0.69 | 1.41 | 0.72 | 3.42 | 0.99 | 2.74 |
| time (sec) |
N/A | 0.166 | 1.279 | 1.497 | 0.210 | 0.264 | 0.299 | 0.319 | 14.194 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 97 | 105 | 105 | 78 | 179 | 82 | 396 | 110 | 345 |
| N.S. |
1 | 1.08 | 1.08 | 0.80 | 1.85 | 0.85 | 4.08 | 1.13 | 3.56 |
| time (sec) |
N/A | 0.117 | 0.804 | 1.261 | 0.211 | 0.263 | 0.204 | 0.318 | 13.867 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 49 | 49 | 48 | 50 | 73 | 43 | 138 | 55 | 122 |
| N.S. |
1 | 1.00 | 0.98 | 1.02 | 1.49 | 0.88 | 2.82 | 1.12 | 2.49 |
| time (sec) |
N/A | 0.047 | 0.248 | 0.742 | 0.225 | 0.255 | 0.125 | 0.295 | 14.573 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 56 | 56 | 107 | 67 | 265 | 116 | 828 | 117 | 111 |
| N.S. |
1 | 1.00 | 1.91 | 1.20 | 4.73 | 2.07 | 14.79 | 2.09 | 1.98 |
| time (sec) |
N/A | 0.112 | 5.167 | 0.592 | 0.299 | 0.266 | 1.027 | 0.306 | 12.744 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | C | B | B | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 72 | 72 | 160 | 80 | 456 | 162 | 700 | 87 | 132 |
| N.S. |
1 | 1.00 | 2.22 | 1.11 | 6.33 | 2.25 | 9.72 | 1.21 | 1.83 |
| time (sec) |
N/A | 0.149 | 6.011 | 0.642 | 0.321 | 0.260 | 2.034 | 0.321 | 12.125 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 104 | 104 | 147 | 94 | 737 | 183 | 1035 | 131 | 172 |
| N.S. |
1 | 1.00 | 1.41 | 0.90 | 7.09 | 1.76 | 9.95 | 1.26 | 1.65 |
| time (sec) |
N/A | 0.156 | 6.277 | 0.750 | 0.230 | 0.271 | 4.342 | 0.327 | 12.455 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 142 | 142 | 174 | 130 | 1080 | 251 | 1831 | 176 | 228 |
| N.S. |
1 | 1.00 | 1.23 | 0.92 | 7.61 | 1.77 | 12.89 | 1.24 | 1.61 |
| time (sec) |
N/A | 0.190 | 6.165 | 0.914 | 0.238 | 0.250 | 8.618 | 0.359 | 12.495 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 176 | 176 | 200 | 166 | 1425 | 305 | 3232 | 251 | 310 |
| N.S. |
1 | 1.00 | 1.14 | 0.94 | 8.10 | 1.73 | 18.36 | 1.43 | 1.76 |
| time (sec) |
N/A | 0.215 | 6.468 | 1.039 | 0.263 | 0.256 | 15.825 | 0.375 | 13.045 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 229 | 229 | 219 | 159 | 571 | 158 | 1586 | 270 | 661 |
| N.S. |
1 | 1.00 | 0.96 | 0.69 | 2.49 | 0.69 | 6.93 | 1.18 | 2.89 |
| time (sec) |
N/A | 0.242 | 3.280 | 3.059 | 0.231 | 0.275 | 0.872 | 0.381 | 14.881 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 189 | 189 | 163 | 137 | 460 | 135 | 1210 | 237 | 553 |
| N.S. |
1 | 1.00 | 0.86 | 0.72 | 2.43 | 0.71 | 6.40 | 1.25 | 2.93 |
| time (sec) |
N/A | 0.204 | 5.482 | 2.321 | 0.239 | 0.284 | 0.616 | 0.381 | 15.146 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 147 | 147 | 137 | 119 | 360 | 114 | 910 | 202 | 542 |
| N.S. |
1 | 1.00 | 0.93 | 0.81 | 2.45 | 0.78 | 6.19 | 1.37 | 3.69 |
| time (sec) |
N/A | 0.146 | 7.029 | 2.126 | 0.226 | 0.279 | 0.441 | 0.357 | 14.575 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 89 | 89 | 54 | 78 | 164 | 75 | 372 | 113 | 238 |
| N.S. |
1 | 1.00 | 0.61 | 0.88 | 1.84 | 0.84 | 4.18 | 1.27 | 2.67 |
| time (sec) |
N/A | 0.087 | 0.113 | 1.165 | 0.221 | 0.275 | 0.278 | 0.333 | 14.882 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 98 | 98 | 115 | 82 | 179 | 77 | 396 | 107 | 339 |
| N.S. |
1 | 1.00 | 1.17 | 0.84 | 1.83 | 0.79 | 4.04 | 1.09 | 3.46 |
| time (sec) |
N/A | 0.101 | 0.696 | 1.186 | 0.203 | 0.257 | 0.201 | 0.319 | 13.880 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 117 | 117 | 191 | 92 | 624 | 177 | 2365 | 156 | 244 |
| N.S. |
1 | 1.00 | 1.63 | 0.79 | 5.33 | 1.51 | 20.21 | 1.33 | 2.09 |
| time (sec) |
N/A | 0.192 | 9.819 | 0.602 | 0.306 | 0.274 | 1.977 | 0.334 | 15.250 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | B | B | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 109 | 109 | 238 | 107 | 839 | 237 | 2474 | 129 | 246 |
| N.S. |
1 | 1.00 | 2.18 | 0.98 | 7.70 | 2.17 | 22.70 | 1.18 | 2.26 |
| time (sec) |
N/A | 0.192 | 11.230 | 0.769 | 0.314 | 0.269 | 3.927 | 0.320 | 15.255 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | B | B | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 112 | 112 | 278 | 126 | 1139 | 277 | 1647 | 151 | 233 |
| N.S. |
1 | 1.00 | 2.48 | 1.12 | 10.17 | 2.47 | 14.71 | 1.35 | 2.08 |
| time (sec) |
N/A | 0.187 | 11.275 | 0.769 | 0.332 | 0.260 | 7.776 | 0.322 | 15.853 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 75 | 75 | 191 | 133 | 1571 | 263 | 2008 | 217 | 269 |
| N.S. |
1 | 1.00 | 2.55 | 1.77 | 20.95 | 3.51 | 26.77 | 2.89 | 3.59 |
| time (sec) |
N/A | 0.155 | 8.251 | 1.024 | 0.271 | 0.260 | 14.429 | 0.343 | 14.132 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 115 | 115 | 261 | 171 | 2087 | 335 | 3262 | 285 | 331 |
| N.S. |
1 | 1.00 | 2.27 | 1.49 | 18.15 | 2.91 | 28.37 | 2.48 | 2.88 |
| time (sec) |
N/A | 0.196 | 8.308 | 0.987 | 0.275 | 0.260 | 25.838 | 0.354 | 15.177 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 156 | 156 | 285 | 219 | 2604 | 407 | 4816 | 353 | 423 |
| N.S. |
1 | 1.00 | 1.83 | 1.40 | 16.69 | 2.61 | 30.87 | 2.26 | 2.71 |
| time (sec) |
N/A | 0.230 | 8.592 | 1.491 | 0.313 | 0.254 | 44.161 | 0.356 | 15.724 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 197 | 197 | 313 | 248 | 3120 | 475 | 6669 | 421 | 500 |
| N.S. |
1 | 1.00 | 1.59 | 1.26 | 15.84 | 2.41 | 33.85 | 2.14 | 2.54 |
| time (sec) |
N/A | 0.283 | 10.419 | 1.562 | 0.338 | 0.273 | 71.059 | 0.403 | 14.894 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 265 | 265 | 255 | 189 | 661 | 181 | 1948 | 337 | 812 |
| N.S. |
1 | 1.00 | 0.96 | 0.71 | 2.49 | 0.68 | 7.35 | 1.27 | 3.06 |
| time (sec) |
N/A | 0.265 | 9.459 | 4.209 | 0.229 | 0.292 | 1.514 | 0.376 | 16.014 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 222 | 222 | 232 | 164 | 617 | 158 | 1753 | 292 | 705 |
| N.S. |
1 | 1.00 | 1.05 | 0.74 | 2.78 | 0.71 | 7.90 | 1.32 | 3.18 |
| time (sec) |
N/A | 0.244 | 8.776 | 2.642 | 0.324 | 0.301 | 1.143 | 0.370 | 15.153 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 181 | 181 | 209 | 149 | 571 | 137 | 1579 | 265 | 661 |
| N.S. |
1 | 1.00 | 1.15 | 0.82 | 3.15 | 0.76 | 8.72 | 1.46 | 3.65 |
| time (sec) |
N/A | 0.170 | 7.467 | 2.940 | 0.244 | 0.278 | 0.874 | 0.356 | 15.200 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 117 | 117 | 64 | 102 | 264 | 92 | 682 | 155 | 325 |
| N.S. |
1 | 1.00 | 0.55 | 0.87 | 2.26 | 0.79 | 5.83 | 1.32 | 2.78 |
| time (sec) |
N/A | 0.111 | 0.166 | 1.955 | 0.218 | 0.266 | 0.540 | 0.320 | 14.899 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 138 | 138 | 133 | 115 | 360 | 106 | 910 | 198 | 536 |
| N.S. |
1 | 1.00 | 0.96 | 0.83 | 2.61 | 0.77 | 6.59 | 1.43 | 3.88 |
| time (sec) |
N/A | 0.147 | 6.886 | 2.080 | 0.221 | 0.273 | 0.452 | 0.321 | 14.056 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 140 | 140 | 141 | 97 | 200 | 100 | 486 | 140 | 390 |
| N.S. |
1 | 1.00 | 1.01 | 0.69 | 1.43 | 0.71 | 3.47 | 1.00 | 2.79 |
| time (sec) |
N/A | 0.158 | 0.894 | 1.395 | 0.208 | 0.263 | 0.299 | 0.437 | 14.337 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 156 | 156 | 223 | 110 | 1139 | 218 | 4255 | 223 | 323 |
| N.S. |
1 | 1.00 | 1.43 | 0.71 | 7.30 | 1.40 | 27.28 | 1.43 | 2.07 |
| time (sec) |
N/A | 0.222 | 11.644 | 0.655 | 0.348 | 0.260 | 3.789 | 0.384 | 14.853 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 163 | 163 | 280 | 166 | 1386 | 286 | 4665 | 222 | 341 |
| N.S. |
1 | 1.00 | 1.72 | 1.02 | 8.50 | 1.75 | 28.62 | 1.36 | 2.09 |
| time (sec) |
N/A | 0.243 | 11.291 | 0.788 | 0.339 | 0.261 | 7.398 | 0.435 | 14.918 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | B | B | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 153 | 153 | 316 | 157 | 1685 | 337 | 4665 | 215 | 336 |
| N.S. |
1 | 1.00 | 2.07 | 1.03 | 11.01 | 2.20 | 30.49 | 1.41 | 2.20 |
| time (sec) |
N/A | 0.247 | 11.412 | 0.918 | 0.346 | 0.262 | 13.602 | 0.440 | 14.757 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | B | B | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 151 | 151 | 356 | 177 | 2118 | 363 | 2951 | 202 | 316 |
| N.S. |
1 | 1.00 | 2.36 | 1.17 | 14.03 | 2.40 | 19.54 | 1.34 | 2.09 |
| time (sec) |
N/A | 0.236 | 11.472 | 1.033 | 0.392 | 0.266 | 23.735 | 0.499 | 16.544 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | B | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 77 | 77 | 283 | 173 | 2701 | 331 | 3262 | 285 | 346 |
| N.S. |
1 | 1.00 | 3.68 | 2.25 | 35.08 | 4.30 | 42.36 | 3.70 | 4.49 |
| time (sec) |
N/A | 0.162 | 12.042 | 1.164 | 0.304 | 0.263 | 40.133 | 0.502 | 14.760 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 118 | 118 | 313 | 211 | 3390 | 405 | 4816 | 353 | 408 |
| N.S. |
1 | 1.00 | 2.65 | 1.79 | 28.73 | 3.43 | 40.81 | 2.99 | 3.46 |
| time (sec) |
N/A | 0.190 | 12.462 | 1.305 | 0.314 | 0.273 | 64.758 | 0.758 | 14.776 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 156 | 156 | 339 | 250 | 4078 | 475 | 6669 | 421 | 500 |
| N.S. |
1 | 1.00 | 2.17 | 1.60 | 26.14 | 3.04 | 42.75 | 2.70 | 3.21 |
| time (sec) |
N/A | 0.240 | 13.834 | 1.690 | 0.388 | 0.266 | 102.643 | 0.432 | 14.357 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 197 | 197 | 365 | 298 | 4765 | 541 | 8821 | 489 | 577 |
| N.S. |
1 | 1.00 | 1.85 | 1.51 | 24.19 | 2.75 | 44.78 | 2.48 | 2.93 |
| time (sec) |
N/A | 0.305 | 14.866 | 2.005 | 0.409 | 0.286 | 162.970 | 0.453 | 14.899 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 190 | 190 | 274 | 209 | 1796 | 261 | 6690 | 326 | 397 |
| N.S. |
1 | 1.00 | 1.44 | 1.10 | 9.45 | 1.37 | 35.21 | 1.72 | 2.09 |
| time (sec) |
N/A | 0.255 | 12.479 | 0.808 | 0.327 | 0.275 | 6.941 | 0.323 | 15.293 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 157 | 157 | 220 | 110 | 1120 | 218 | 4255 | 224 | 319 |
| N.S. |
1 | 1.00 | 1.40 | 0.70 | 7.13 | 1.39 | 27.10 | 1.43 | 2.03 |
| time (sec) |
N/A | 0.209 | 11.649 | 0.753 | 0.328 | 0.277 | 3.833 | 0.323 | 14.872 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 118 | 118 | 188 | 94 | 608 | 179 | 2365 | 157 | 241 |
| N.S. |
1 | 1.00 | 1.59 | 0.80 | 5.15 | 1.52 | 20.04 | 1.33 | 2.04 |
| time (sec) |
N/A | 0.190 | 8.656 | 0.638 | 0.313 | 0.270 | 2.031 | 0.309 | 15.332 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | B | B | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 57 | 57 | 127 | 67 | 256 | 117 | 828 | 115 | 110 |
| N.S. |
1 | 1.00 | 2.23 | 1.18 | 4.49 | 2.05 | 14.53 | 2.02 | 1.93 |
| time (sec) |
N/A | 0.108 | 5.372 | 0.602 | 0.403 | 0.261 | 1.063 | 0.463 | 13.592 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 35 | 35 | 35 | 42 | 35 | 28 | 83 | 39 | 39 |
| N.S. |
1 | 1.00 | 1.00 | 1.20 | 1.00 | 0.80 | 2.37 | 1.11 | 1.11 |
| time (sec) |
N/A | 0.097 | 0.022 | 0.529 | 0.204 | 0.239 | 0.717 | 0.333 | 12.487 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 63 | 63 | 108 | 86 | 266 | 73 | 578 | 97 | 118 |
| N.S. |
1 | 1.00 | 1.71 | 1.37 | 4.22 | 1.16 | 9.17 | 1.54 | 1.87 |
| time (sec) |
N/A | 0.144 | 1.279 | 0.713 | 0.228 | 0.256 | 2.234 | 0.351 | 12.206 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 102 | 102 | 157 | 111 | 423 | 107 | 1236 | 167 | 178 |
| N.S. |
1 | 1.00 | 1.54 | 1.09 | 4.15 | 1.05 | 12.12 | 1.64 | 1.75 |
| time (sec) |
N/A | 0.197 | 1.640 | 0.997 | 0.226 | 0.249 | 4.554 | 0.319 | 12.237 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 142 | 142 | 240 | 136 | 619 | 141 | 2468 | 223 | 239 |
| N.S. |
1 | 1.00 | 1.69 | 0.96 | 4.36 | 0.99 | 17.38 | 1.57 | 1.68 |
| time (sec) |
N/A | 0.235 | 2.022 | 0.964 | 0.236 | 0.253 | 9.496 | 0.324 | 13.141 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 240 | 240 | 354 | 252 | 2982 | 370 | 10608 | 391 | 500 |
| N.S. |
1 | 1.00 | 1.48 | 1.05 | 12.42 | 1.54 | 44.20 | 1.63 | 2.08 |
| time (sec) |
N/A | 0.309 | 11.800 | 1.368 | 0.362 | 0.276 | 21.523 | 0.367 | 15.165 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 180 | 180 | 311 | 193 | 2094 | 322 | 7337 | 349 | 414 |
| N.S. |
1 | 1.00 | 1.73 | 1.07 | 11.63 | 1.79 | 40.76 | 1.94 | 2.30 |
| time (sec) |
N/A | 0.241 | 11.466 | 1.124 | 0.350 | 0.290 | 12.857 | 0.331 | 15.039 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 162 | 162 | 274 | 162 | 1378 | 291 | 4665 | 222 | 336 |
| N.S. |
1 | 1.00 | 1.69 | 1.00 | 8.51 | 1.80 | 28.80 | 1.37 | 2.07 |
| time (sec) |
N/A | 0.230 | 11.303 | 0.940 | 0.327 | 0.268 | 7.416 | 0.315 | 14.789 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | B | B | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 108 | 108 | 234 | 107 | 833 | 242 | 2474 | 130 | 242 |
| N.S. |
1 | 1.00 | 2.17 | 0.99 | 7.71 | 2.24 | 22.91 | 1.20 | 2.24 |
| time (sec) |
N/A | 0.190 | 11.225 | 0.739 | 0.323 | 0.260 | 3.979 | 0.329 | 14.634 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | C | B | B | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 72 | 72 | 156 | 81 | 452 | 166 | 702 | 87 | 133 |
| N.S. |
1 | 1.00 | 2.17 | 1.12 | 6.28 | 2.31 | 9.75 | 1.21 | 1.85 |
| time (sec) |
N/A | 0.141 | 6.303 | 0.687 | 0.297 | 0.263 | 2.094 | 0.340 | 12.677 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 62 | 62 | 110 | 86 | 265 | 69 | 578 | 97 | 117 |
| N.S. |
1 | 1.00 | 1.77 | 1.39 | 4.27 | 1.11 | 9.32 | 1.56 | 1.89 |
| time (sec) |
N/A | 0.134 | 1.266 | 0.664 | 0.220 | 0.249 | 2.225 | 0.333 | 12.714 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 62 | 62 | 53 | 70 | 47 | 41 | 469 | 82 | 82 |
| N.S. |
1 | 1.00 | 0.85 | 1.13 | 0.76 | 0.66 | 7.56 | 1.32 | 1.32 |
| time (sec) |
N/A | 0.095 | 0.087 | 0.720 | 0.213 | 0.251 | 2.043 | 0.325 | 12.461 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | C | B | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 93 | 93 | 237 | 136 | 651 | 116 | 2674 | 221 | 183 |
| N.S. |
1 | 1.00 | 2.55 | 1.46 | 7.00 | 1.25 | 28.75 | 2.38 | 1.97 |
| time (sec) |
N/A | 0.149 | 2.003 | 1.235 | 0.238 | 0.253 | 9.027 | 0.341 | 12.537 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | C | B | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 135 | 135 | 285 | 161 | 835 | 151 | 4228 | 277 | 197 |
| N.S. |
1 | 1.00 | 2.11 | 1.19 | 6.19 | 1.12 | 31.32 | 2.05 | 1.46 |
| time (sec) |
N/A | 0.197 | 2.395 | 1.780 | 0.246 | 0.255 | 17.577 | 0.462 | 12.666 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 175 | 175 | 329 | 184 | 998 | 187 | 5868 | 333 | 337 |
| N.S. |
1 | 1.00 | 1.88 | 1.05 | 5.70 | 1.07 | 33.53 | 1.90 | 1.93 |
| time (sec) |
N/A | 0.246 | 3.147 | 2.380 | 0.296 | 0.253 | 33.910 | 0.529 | 13.105 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 243 | 243 | 388 | 240 | 3282 | 429 | 10608 | 357 | 501 |
| N.S. |
1 | 1.00 | 1.60 | 0.99 | 13.51 | 1.77 | 43.65 | 1.47 | 2.06 |
| time (sec) |
N/A | 0.293 | 12.081 | 1.412 | 0.378 | 0.273 | 37.877 | 0.507 | 15.073 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | B | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 201 | 201 | 348 | 201 | 2394 | 392 | 7337 | 290 | 419 |
| N.S. |
1 | 1.00 | 1.73 | 1.00 | 11.91 | 1.95 | 36.50 | 1.44 | 2.08 |
| time (sec) |
N/A | 0.275 | 11.630 | 1.102 | 0.354 | 0.269 | 23.489 | 0.509 | 15.723 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | B | B | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 153 | 153 | 308 | 157 | 1679 | 338 | 4665 | 215 | 333 |
| N.S. |
1 | 1.00 | 2.01 | 1.03 | 10.97 | 2.21 | 30.49 | 1.41 | 2.18 |
| time (sec) |
N/A | 0.229 | 11.419 | 1.007 | 0.351 | 0.269 | 13.774 | 0.449 | 15.367 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | B | B | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 110 | 110 | 272 | 127 | 1134 | 279 | 1647 | 151 | 230 |
| N.S. |
1 | 1.00 | 2.47 | 1.15 | 10.31 | 2.54 | 14.97 | 1.37 | 2.09 |
| time (sec) |
N/A | 0.181 | 11.252 | 0.783 | 0.313 | 0.280 | 7.716 | 0.437 | 16.202 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 103 | 103 | 139 | 92 | 733 | 191 | 1035 | 130 | 172 |
| N.S. |
1 | 1.00 | 1.35 | 0.89 | 7.12 | 1.85 | 10.05 | 1.26 | 1.67 |
| time (sec) |
N/A | 0.154 | 6.473 | 0.762 | 0.213 | 0.261 | 4.419 | 0.655 | 13.632 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | B | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 102 | 102 | 156 | 111 | 423 | 106 | 1236 | 165 | 178 |
| N.S. |
1 | 1.00 | 1.53 | 1.09 | 4.15 | 1.04 | 12.12 | 1.62 | 1.75 |
| time (sec) |
N/A | 0.172 | 1.684 | 0.933 | 0.213 | 0.259 | 4.536 | 0.328 | 12.985 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | C | B | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 90 | 90 | 237 | 136 | 650 | 108 | 2674 | 221 | 183 |
| N.S. |
1 | 1.00 | 2.63 | 1.51 | 7.22 | 1.20 | 29.71 | 2.46 | 2.03 |
| time (sec) |
N/A | 0.148 | 1.991 | 1.174 | 0.225 | 0.268 | 9.003 | 0.466 | 13.083 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | A | A | B | A | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 84 | 84 | 65 | 83 | 60 | 56 | 1098 | 126 | 126 |
| N.S. |
1 | 1.00 | 0.77 | 0.99 | 0.71 | 0.67 | 13.07 | 1.50 | 1.50 |
| time (sec) |
N/A | 0.114 | 0.138 | 1.166 | 0.241 | 0.266 | 6.104 | 0.353 | 15.425 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | C | B | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 121 | 121 | 325 | 186 | 1019 | 150 | 6135 | 333 | 217 |
| N.S. |
1 | 1.00 | 2.69 | 1.54 | 8.42 | 1.24 | 50.70 | 2.75 | 1.79 |
| time (sec) |
N/A | 0.160 | 2.893 | 2.396 | 0.244 | 0.261 | 33.492 | 0.378 | 13.098 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | C | B | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 162 | 162 | 373 | 211 | 1201 | 185 | 8396 | 389 | 231 |
| N.S. |
1 | 1.00 | 2.30 | 1.30 | 7.41 | 1.14 | 51.83 | 2.40 | 1.43 |
| time (sec) |
N/A | 0.202 | 3.746 | 3.192 | 0.255 | 0.261 | 59.132 | 0.366 | 13.689 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | C | B | A | B | B | B |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 205 | 205 | 401 | 236 | 1387 | 221 | 11011 | 445 | 474 |
| N.S. |
1 | 1.00 | 1.96 | 1.15 | 6.77 | 1.08 | 53.71 | 2.17 | 2.31 |
| time (sec) |
N/A | 0.238 | 5.412 | 4.121 | 0.274 | 0.280 | 100.070 | 0.382 | 14.671 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F(-1) | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 198 | 198 | 149 | 119 | 0 | 287 | 0 | 296 | 0 |
| N.S. |
1 | 1.00 | 0.75 | 0.60 | 0.00 | 1.45 | 0.00 | 1.49 | 0.00 |
| time (sec) |
N/A | 0.362 | 4.164 | 7.458 | 0.000 | 0.273 | 0.000 | 0.457 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 157 | 157 | 123 | 103 | 0 | 243 | 0 | 262 | 0 |
| N.S. |
1 | 1.00 | 0.78 | 0.66 | 0.00 | 1.55 | 0.00 | 1.67 | 0.00 |
| time (sec) |
N/A | 0.278 | 2.966 | 7.356 | 0.000 | 0.257 | 0.000 | 0.495 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 116 | 116 | 104 | 81 | 0 | 184 | 0 | 194 | 0 |
| N.S. |
1 | 1.00 | 0.90 | 0.70 | 0.00 | 1.59 | 0.00 | 1.67 | 0.00 |
| time (sec) |
N/A | 0.211 | 2.451 | 1.601 | 0.000 | 0.272 | 0.000 | 0.374 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | F | A | F | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 73 | 73 | 191 | 63 | 0 | 130 | 0 | 118 | 0 |
| N.S. |
1 | 1.00 | 2.62 | 0.86 | 0.00 | 1.78 | 0.00 | 1.62 | 0.00 |
| time (sec) |
N/A | 0.169 | 1.153 | 1.698 | 0.000 | 0.254 | 0.000 | 0.383 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 122 | 122 | 166 | 159 | 0 | 254 | 0 | 300 | 0 |
| N.S. |
1 | 1.00 | 1.36 | 1.30 | 0.00 | 2.08 | 0.00 | 2.46 | 0.00 |
| time (sec) |
N/A | 0.236 | 2.941 | 1.879 | 0.000 | 0.281 | 0.000 | 0.330 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 115 | 115 | 157 | 227 | 0 | 318 | 0 | 390 | 0 |
| N.S. |
1 | 1.00 | 1.37 | 1.97 | 0.00 | 2.77 | 0.00 | 3.39 | 0.00 |
| time (sec) |
N/A | 0.237 | 3.312 | 1.687 | 0.000 | 0.268 | 0.000 | 0.362 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 126 | 126 | 199 | 267 | 0 | 394 | 0 | 419 | 0 |
| N.S. |
1 | 1.00 | 1.58 | 2.12 | 0.00 | 3.13 | 0.00 | 3.33 | 0.00 |
| time (sec) |
N/A | 0.237 | 4.284 | 2.642 | 0.000 | 0.273 | 0.000 | 0.379 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | B | F | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 163 | 163 | 217 | 352 | 0 | 490 | 0 | 628 | 0 |
| N.S. |
1 | 1.00 | 1.33 | 2.16 | 0.00 | 3.01 | 0.00 | 3.85 | 0.00 |
| time (sec) |
N/A | 0.271 | 6.370 | 2.974 | 0.000 | 0.282 | 0.000 | 0.448 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | F | A | F(-1) | A | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 210 | 210 | 1355 | 121 | 0 | 358 | 0 | 373 | 0 |
| N.S. |
1 | 1.00 | 6.45 | 0.58 | 0.00 | 1.70 | 0.00 | 1.78 | 0.00 |
| time (sec) |
N/A | 0.389 | 10.716 | 36.968 | 0.000 | 0.272 | 0.000 | 0.526 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | F | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 167 | 167 | 1173 | 105 | 0 | 313 | 0 | 340 | 0 |
| N.S. |
1 | 1.00 | 7.02 | 0.63 | 0.00 | 1.87 | 0.00 | 2.04 | 0.00 |
| time (sec) |
N/A | 0.312 | 12.620 | 36.990 | 0.000 | 0.279 | 0.000 | 0.620 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 120 | 120 | 106 | 83 | 0 | 228 | 0 | 238 | 0 |
| N.S. |
1 | 1.00 | 0.88 | 0.69 | 0.00 | 1.90 | 0.00 | 1.98 | 0.00 |
| time (sec) |
N/A | 0.274 | 9.196 | 2.052 | 0.000 | 0.264 | 0.000 | 0.651 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 81 | 81 | 89 | 65 | 0 | 193 | 0 | 200 | 0 |
| N.S. |
1 | 1.00 | 1.10 | 0.80 | 0.00 | 2.38 | 0.00 | 2.47 | 0.00 |
| time (sec) |
N/A | 0.219 | 0.822 | 1.367 | 0.000 | 0.269 | 0.000 | 0.540 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | F(-1) | A | F | B | F | B | F(-1) |
| verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 161 | 161 | 0 | 197 | 0 | 310 | 0 | 480 | 0 |
| N.S. |
1 | 1.00 | 0.00 | 1.22 | 0.00 | 1.93 | 0.00 | 2.98 | 0.00 |
| time (sec) |
N/A | 0.314 | 0.000 | 2.360 | 0.000 | 0.285 | 0.000 | 0.478 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | A | F | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 176 | 176 | 355 | 282 | 0 | 385 | 0 | 566 | 0 |
| N.S. |
1 | 1.00 | 2.02 | 1.60 | 0.00 | 2.19 | 0.00 | 3.22 | 0.00 |
| time (sec) |
N/A | 0.338 | 11.348 | 2.579 | 0.000 | 0.275 | 0.000 | 0.520 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 175 | 175 | 344 | 386 | 0 | 449 | 0 | 601 | 0 |
| N.S. |
1 | 1.00 | 1.97 | 2.21 | 0.00 | 2.57 | 0.00 | 3.43 | 0.00 |
| time (sec) |
N/A | 0.328 | 11.511 | 3.296 | 0.000 | 0.283 | 0.000 | 0.675 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 175 | 175 | 342 | 354 | 0 | 521 | 0 | 658 | 0 |
| N.S. |
1 | 1.00 | 1.95 | 2.02 | 0.00 | 2.98 | 0.00 | 3.76 | 0.00 |
| time (sec) |
N/A | 0.328 | 11.883 | 3.256 | 0.000 | 0.271 | 0.000 | 0.738 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | C | B | F | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 222 | 222 | 357 | 440 | 0 | 654 | 0 | 745 | 0 |
| N.S. |
1 | 1.00 | 1.61 | 1.98 | 0.00 | 2.95 | 0.00 | 3.36 | 0.00 |
| time (sec) |
N/A | 0.361 | 12.355 | 3.725 | 0.000 | 0.287 | 0.000 | 0.538 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | F | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 210 | 210 | 1569 | 121 | 0 | 405 | 0 | 458 | 0 |
| N.S. |
1 | 1.00 | 7.47 | 0.58 | 0.00 | 1.93 | 0.00 | 2.18 | 0.00 |
| time (sec) |
N/A | 0.378 | 11.611 | 167.160 | 0.000 | 0.280 | 0.000 | 0.561 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | A | A | F | B | F(-1) | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 161 | 161 | 143 | 105 | 0 | 334 | 0 | 372 | 0 |
| N.S. |
1 | 1.00 | 0.89 | 0.65 | 0.00 | 2.07 | 0.00 | 2.31 | 0.00 |
| time (sec) |
N/A | 0.332 | 10.180 | 168.774 | 0.000 | 0.275 | 0.000 | 0.591 | 0.000 |
| Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
| grade |
N/A | A | B | A | F | B | F | B | F(-1) |
| verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
| size | 124 | 124 | 1157 | 83 | 0 | 287 | 0 | 294 | 0 |
| N.S. |
1 | 1.00 | 9.33 | 0.67 | 0.00 | 2.31 | 0.00 | 2.37 | 0.00 |
| time (sec) |
N/A | 0.294 | 12.547 | 2.448 | 0.000 | 0.277 | 0.000 | 0.488 | 0.000 |