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 | B | F(-1) | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 80 | 80 | 0 | 1574 | 0 | 379 | 83 |
N.S. |
1 | 1.00 | 0.82 | 0.82 | 0.00 | 16.23 | 0.00 | 3.91 | 0.86 |
time (sec) |
N/A | 0.387 | 0.388 | 0.200 | 0.000 | 0.282 | 0.000 | 0.443 | 2.364 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 78 | 74 | 66 | 63 | 0 | 988 | 0 | 224 | 62 |
N.S. |
1 | 0.95 | 0.85 | 0.81 | 0.00 | 12.67 | 0.00 | 2.87 | 0.79 |
time (sec) |
N/A | 0.307 | 0.169 | 0.155 | 0.000 | 0.274 | 0.000 | 0.404 | 2.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 72 | 66 | 62 | 0 | 637 | 0 | 168 | 61 |
N.S. |
1 | 0.96 | 0.88 | 0.83 | 0.00 | 8.49 | 0.00 | 2.24 | 0.81 |
time (sec) |
N/A | 0.301 | 0.079 | 0.123 | 0.000 | 0.272 | 0.000 | 0.341 | 2.005 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 58 | 51 | 52 | 47 | 0 | 594 | 0 | 101 | 41 |
N.S. |
1 | 0.88 | 0.90 | 0.81 | 0.00 | 10.24 | 0.00 | 1.74 | 0.71 |
time (sec) |
N/A | 0.225 | 0.043 | 0.197 | 0.000 | 0.276 | 0.000 | 0.329 | 1.919 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-2) | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 51 | 49 | 46 | 0 | 598 | 0 | 0 | 38 |
N.S. |
1 | 0.89 | 0.86 | 0.81 | 0.00 | 10.49 | 0.00 | 0.00 | 0.67 |
time (sec) |
N/A | 0.230 | 0.041 | 0.184 | 0.000 | 0.287 | 0.000 | 0.000 | 1.974 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-2) | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 78 | 74 | 74 | 65 | 0 | 923 | 0 | 0 | 64 |
N.S. |
1 | 0.95 | 0.95 | 0.83 | 0.00 | 11.83 | 0.00 | 0.00 | 0.82 |
time (sec) |
N/A | 0.312 | 0.093 | 0.142 | 0.000 | 0.282 | 0.000 | 0.000 | 2.006 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-2) | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 79 | 76 | 78 | 64 | 0 | 1428 | 0 | 0 | 63 |
N.S. |
1 | 0.96 | 0.99 | 0.81 | 0.00 | 18.08 | 0.00 | 0.00 | 0.80 |
time (sec) |
N/A | 0.306 | 0.118 | 0.140 | 0.000 | 0.277 | 0.000 | 0.000 | 2.125 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-2) | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 101 | 90 | 83 | 0 | 2132 | 0 | 0 | 80 |
N.S. |
1 | 1.01 | 0.90 | 0.83 | 0.00 | 21.32 | 0.00 | 0.00 | 0.80 |
time (sec) |
N/A | 0.406 | 0.283 | 0.146 | 0.000 | 0.298 | 0.000 | 0.000 | 2.301 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 236 | 198 | 193 | 209 | 0 | 292 | 0 | 0 | 249 |
N.S. |
1 | 0.84 | 0.82 | 0.89 | 0.00 | 1.24 | 0.00 | 0.00 | 1.06 |
time (sec) |
N/A | 0.464 | 0.319 | 0.070 | 0.000 | 0.300 | 0.000 | 0.000 | 2.425 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 218 | 177 | 149 | 181 | 0 | 310 | 0 | 0 | 233 |
N.S. |
1 | 0.81 | 0.68 | 0.83 | 0.00 | 1.42 | 0.00 | 0.00 | 1.07 |
time (sec) |
N/A | 0.394 | 0.199 | 0.108 | 0.000 | 0.265 | 0.000 | 0.000 | 2.207 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 132 | 111 | 108 | 109 | 0 | 291 | 0 | 217 | 146 |
N.S. |
1 | 0.84 | 0.82 | 0.83 | 0.00 | 2.20 | 0.00 | 1.64 | 1.11 |
time (sec) |
N/A | 0.329 | 0.204 | 0.080 | 0.000 | 0.267 | 0.000 | 0.425 | 2.236 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 132 | 111 | 98 | 109 | 0 | 1598 | 0 | 216 | 147 |
N.S. |
1 | 0.84 | 0.74 | 0.83 | 0.00 | 12.11 | 0.00 | 1.64 | 1.11 |
time (sec) |
N/A | 0.320 | 0.123 | 0.074 | 0.000 | 0.295 | 0.000 | 0.387 | 2.313 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-2) | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 218 | 177 | 177 | 193 | 0 | 356 | 0 | 0 | 197 |
N.S. |
1 | 0.81 | 0.81 | 0.89 | 0.00 | 1.63 | 0.00 | 0.00 | 0.90 |
time (sec) |
N/A | 0.380 | 0.254 | 0.104 | 0.000 | 0.261 | 0.000 | 0.000 | 2.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-2) | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 238 | 200 | 243 | 211 | 0 | 3348 | 0 | 0 | 165 |
N.S. |
1 | 0.84 | 1.02 | 0.89 | 0.00 | 14.07 | 0.00 | 0.00 | 0.69 |
time (sec) |
N/A | 0.455 | 0.401 | 0.080 | 0.000 | 0.332 | 0.000 | 0.000 | 2.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 43 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.208 | 0.133 | 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 | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 49 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.214 | 0.126 | 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 | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 49 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.300 | 0.111 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 56 | 53 | 97 | 823 | 0 | 90 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.87 | 1.59 | 13.49 | 0.00 | 1.48 | 0.00 |
time (sec) |
N/A | 0.330 | 0.134 | 0.145 | 0.273 | 0.280 | 0.000 | 0.303 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 35 | 39 | 45 | 54 | 125 | 0 | 54 | 0 |
N.S. |
1 | 1.13 | 1.26 | 1.45 | 1.74 | 4.03 | 0.00 | 1.74 | 0.00 |
time (sec) |
N/A | 0.257 | 0.049 | 0.111 | 0.263 | 0.287 | 0.000 | 0.278 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 31 | 52 | 34 | 128 | 0 | 60 | 30 |
N.S. |
1 | 1.00 | 1.00 | 1.68 | 1.10 | 4.13 | 0.00 | 1.94 | 0.97 |
time (sec) |
N/A | 0.247 | 0.068 | 0.107 | 0.269 | 0.257 | 0.000 | 0.294 | 1.947 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 59 | 48 | 79 | 84 | 817 | 0 | 104 | 0 |
N.S. |
1 | 0.91 | 0.74 | 1.22 | 1.29 | 12.57 | 0.00 | 1.60 | 0.00 |
time (sec) |
N/A | 0.328 | 0.152 | 0.103 | 0.266 | 0.272 | 0.000 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 297 | 187 | 166 | 0 | 0 | 1994 | 0 | 0 | 0 |
N.S. |
1 | 0.63 | 0.56 | 0.00 | 0.00 | 6.71 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.484 | 0.357 | 0.000 | 0.000 | 0.294 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 289 | 182 | 200 | 0 | 0 | 2037 | 0 | 0 | 0 |
N.S. |
1 | 0.63 | 0.69 | 0.00 | 0.00 | 7.05 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.513 | 0.151 | 0.000 | 0.000 | 0.315 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 264 | 167 | 151 | 0 | 0 | 1618 | 0 | 0 | 0 |
N.S. |
1 | 0.63 | 0.57 | 0.00 | 0.00 | 6.13 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.412 | 0.117 | 0.000 | 0.000 | 0.283 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 264 | 165 | 182 | 0 | 0 | 8338 | 0 | 0 | 0 |
N.S. |
1 | 0.62 | 0.69 | 0.00 | 0.00 | 31.58 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.399 | 0.248 | 0.000 | 0.000 | 0.408 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 289 | 184 | 248 | 0 | 0 | 2066 | 0 | 0 | 0 |
N.S. |
1 | 0.64 | 0.86 | 0.00 | 0.00 | 7.15 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.499 | 0.279 | 0.000 | 0.000 | 0.313 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 309 | 187 | 251 | 0 | 0 | 14359 | 0 | 0 | 0 |
N.S. |
1 | 0.61 | 0.81 | 0.00 | 0.00 | 46.47 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.476 | 0.614 | 0.000 | 0.000 | 0.434 | 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 | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 55 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.299 | 0.130 | 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 | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 134 | 97 | 82 | 107 | 0 | 2152 | 0 | 788 | 0 |
N.S. |
1 | 0.72 | 0.61 | 0.80 | 0.00 | 16.06 | 0.00 | 5.88 | 0.00 |
time (sec) |
N/A | 0.452 | 0.556 | 0.193 | 0.000 | 0.323 | 0.000 | 0.582 | 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 | 104 | 77 | 63 | 89 | 0 | 633 | 0 | 269 | 0 |
N.S. |
1 | 0.74 | 0.61 | 0.86 | 0.00 | 6.09 | 0.00 | 2.59 | 0.00 |
time (sec) |
N/A | 0.388 | 0.094 | 0.161 | 0.000 | 0.289 | 0.000 | 0.387 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 105 | 77 | 80 | 91 | 0 | 907 | 0 | 0 | 0 |
N.S. |
1 | 0.73 | 0.76 | 0.87 | 0.00 | 8.64 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.383 | 0.089 | 0.170 | 0.000 | 0.300 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 141 | 99 | 90 | 106 | 0 | 3022 | 0 | 0 | 0 |
N.S. |
1 | 0.70 | 0.64 | 0.75 | 0.00 | 21.43 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.444 | 0.217 | 0.150 | 0.000 | 0.338 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 50 | 43 | 130 | 87 | 1046 | 151 | 0 | 0 |
N.S. |
1 | 0.68 | 0.58 | 1.76 | 1.18 | 14.14 | 2.04 | 0.00 | 0.00 |
time (sec) |
N/A | 0.327 | 0.083 | 0.153 | 0.276 | 0.298 | 68.065 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | A | B | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 38 | 41 | 119 | 34 | 392 | 126 | 0 | 0 |
N.S. |
1 | 0.76 | 0.82 | 2.38 | 0.68 | 7.84 | 2.52 | 0.00 | 0.00 |
time (sec) |
N/A | 0.267 | 0.031 | 0.154 | 0.278 | 0.264 | 6.192 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | B | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 35 | 39 | 192 | 51 | 148 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 1.26 | 6.19 | 1.65 | 4.77 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.260 | 0.032 | 0.154 | 0.273 | 0.264 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 31 | 192 | 32 | 187 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 6.19 | 1.03 | 6.03 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.245 | 0.034 | 0.157 | 0.282 | 0.255 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 38 | 40 | 89 | 37 | 287 | 0 | 0 | 0 |
N.S. |
1 | 0.76 | 0.80 | 1.78 | 0.74 | 5.74 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.255 | 0.072 | 0.147 | 0.271 | 0.262 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 52 | 51 | 132 | 89 | 1579 | 0 | 0 | 0 |
N.S. |
1 | 0.65 | 0.64 | 1.65 | 1.11 | 19.74 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.333 | 0.097 | 0.165 | 0.269 | 0.278 | 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 | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 53 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.303 | 0.112 | 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 | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 69 | 43 | 77 | 137 | 3421 | 0 | 77 | 0 |
N.S. |
1 | 0.63 | 0.39 | 0.70 | 1.25 | 31.10 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 0.425 | 0.073 | 0.156 | 0.277 | 0.331 | 0.000 | 0.319 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 38 | 41 | 55 | 34 | 415 | 0 | 27 | 0 |
N.S. |
1 | 0.76 | 0.82 | 1.10 | 0.68 | 8.30 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.257 | 0.037 | 0.113 | 0.272 | 0.258 | 0.000 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 38 | 40 | 59 | 36 | 422 | 0 | 32 | 0 |
N.S. |
1 | 0.76 | 0.80 | 1.18 | 0.72 | 8.44 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.248 | 0.066 | 0.116 | 0.272 | 0.275 | 0.000 | 0.289 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 118 | 71 | 68 | 84 | 155 | 3473 | 0 | 83 | 0 |
N.S. |
1 | 0.60 | 0.58 | 0.71 | 1.31 | 29.43 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 0.410 | 0.253 | 0.109 | 0.274 | 0.319 | 0.000 | 0.335 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 353 | 217 | 244 | 0 | 0 | 2864 | 0 | 0 | 0 |
N.S. |
1 | 0.61 | 0.69 | 0.00 | 0.00 | 8.11 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.647 | 2.076 | 0.000 | 0.000 | 0.319 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 291 | 186 | 166 | 0 | 0 | 618 | 0 | 0 | 0 |
N.S. |
1 | 0.64 | 0.57 | 0.00 | 0.00 | 2.12 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.511 | 0.396 | 0.000 | 0.000 | 0.278 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 289 | 182 | 200 | 0 | 0 | 288 | 0 | 0 | 0 |
N.S. |
1 | 0.63 | 0.69 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.474 | 0.182 | 0.000 | 0.000 | 0.272 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 289 | 184 | 248 | 0 | 0 | 3316 | 0 | 0 | 0 |
N.S. |
1 | 0.64 | 0.86 | 0.00 | 0.00 | 11.47 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.464 | 0.154 | 0.000 | 0.000 | 0.332 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 291 | 184 | 251 | 0 | 0 | 1159 | 0 | 0 | 0 |
N.S. |
1 | 0.63 | 0.86 | 0.00 | 0.00 | 3.98 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.507 | 0.302 | 0.000 | 0.000 | 0.278 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 369 | 221 | 274 | 0 | 0 | 15579 | 0 | 0 | 0 |
N.S. |
1 | 0.60 | 0.74 | 0.00 | 0.00 | 42.22 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.657 | 1.745 | 0.000 | 0.000 | 0.539 | 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 | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 57 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.304 | 0.116 | 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(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 59 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.304 | 0.130 | 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(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 54 | 68 | 54 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.26 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.297 | 0.104 | 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(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 58 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.305 | 0.115 | 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(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 59 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.302 | 0.139 | 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(-2) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 61 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.304 | 0.127 | 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(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 61 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.305 | 0.113 | 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(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 54 | 68 | 54 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.26 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.296 | 0.105 | 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(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 58 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.298 | 0.116 | 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(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 61 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.306 | 0.124 | 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(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 61 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.299 | 0.136 | 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 | A | B | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 52 | 94 | 31 | 140 | 448 | 48 | 41 | 88 |
N.S. |
1 | 1.27 | 2.29 | 0.76 | 3.41 | 10.93 | 1.17 | 1.00 | 2.15 |
time (sec) |
N/A | 0.429 | 0.270 | 0.105 | 0.199 | 0.255 | 0.669 | 0.284 | 1.868 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | B | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 39 | 84 | 25 | 95 | 273 | 37 | 35 | 60 |
N.S. |
1 | 1.26 | 2.71 | 0.81 | 3.06 | 8.81 | 1.19 | 1.13 | 1.94 |
time (sec) |
N/A | 0.349 | 0.198 | 0.077 | 0.204 | 0.244 | 0.453 | 0.279 | 1.902 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | B | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 26 | 61 | 19 | 55 | 142 | 31 | 29 | 36 |
N.S. |
1 | 1.13 | 2.65 | 0.83 | 2.39 | 6.17 | 1.35 | 1.26 | 1.57 |
time (sec) |
N/A | 0.280 | 0.161 | 0.073 | 0.178 | 0.244 | 0.355 | 0.269 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 28 | 13 | 19 | 53 | 22 | 21 | 20 |
N.S. |
1 | 1.00 | 2.15 | 1.00 | 1.46 | 4.08 | 1.69 | 1.62 | 1.54 |
time (sec) |
N/A | 0.213 | 0.015 | 0.047 | 0.184 | 0.235 | 0.193 | 0.286 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 14 | 11 | 10 | 26 | 27 | 10 | 14 |
N.S. |
1 | 1.00 | 0.88 | 0.69 | 0.62 | 1.62 | 1.69 | 0.62 | 0.88 |
time (sec) |
N/A | 0.171 | 0.115 | 0.050 | 0.181 | 0.244 | 0.258 | 0.264 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 31 | 28 | 17 | 16 | 52 | 88 | 18 | 16 |
N.S. |
1 | 1.19 | 1.08 | 0.65 | 0.62 | 2.00 | 3.38 | 0.69 | 0.62 |
time (sec) |
N/A | 0.229 | 0.701 | 0.074 | 0.183 | 0.250 | 0.484 | 0.264 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 46 | 33 | 23 | 22 | 86 | 182 | 24 | 22 |
N.S. |
1 | 1.28 | 0.92 | 0.64 | 0.61 | 2.39 | 5.06 | 0.67 | 0.61 |
time (sec) |
N/A | 0.301 | 0.292 | 0.079 | 0.185 | 0.242 | 0.567 | 0.277 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 61 | 35 | 29 | 28 | 121 | 299 | 30 | 28 |
N.S. |
1 | 1.33 | 0.76 | 0.63 | 0.61 | 2.63 | 6.50 | 0.65 | 0.61 |
time (sec) |
N/A | 0.383 | 0.352 | 0.084 | 0.186 | 0.257 | 0.733 | 0.274 | 1.826 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 76 | 41 | 35 | 34 | 159 | 444 | 36 | 34 |
N.S. |
1 | 1.36 | 0.73 | 0.62 | 0.61 | 2.84 | 7.93 | 0.64 | 0.61 |
time (sec) |
N/A | 0.444 | 0.496 | 0.096 | 0.182 | 0.265 | 0.929 | 0.274 | 1.865 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 63 | 47 | 43 | 0 | 438 | 0 | 160 | 44 |
N.S. |
1 | 1.11 | 0.82 | 0.75 | 0.00 | 7.68 | 0.00 | 2.81 | 0.77 |
time (sec) |
N/A | 0.377 | 0.848 | 0.119 | 0.000 | 0.263 | 0.000 | 0.290 | 1.941 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 48 | 39 | 35 | 0 | 259 | 0 | 112 | 54 |
N.S. |
1 | 1.07 | 0.87 | 0.78 | 0.00 | 5.76 | 0.00 | 2.49 | 1.20 |
time (sec) |
N/A | 0.305 | 0.705 | 0.086 | 0.000 | 0.265 | 0.000 | 0.288 | 1.880 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 27 | 0 | 131 | 0 | 63 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.00 | 3.97 | 0.00 | 1.91 | 0.79 |
time (sec) |
N/A | 0.238 | 0.553 | 0.063 | 0.000 | 0.255 | 0.000 | 0.278 | 1.881 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 17 | 0 | 50 | 0 | 37 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.00 | 2.38 | 0.00 | 1.76 | 0.76 |
time (sec) |
N/A | 0.186 | 0.418 | 0.093 | 0.000 | 0.255 | 0.000 | 0.276 | 1.909 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 26 | 27 | 0 | 85 | 0 | 66 | 26 |
N.S. |
1 | 1.00 | 0.81 | 0.84 | 0.00 | 2.66 | 0.00 | 2.06 | 0.81 |
time (sec) |
N/A | 0.242 | 0.450 | 0.084 | 0.000 | 0.260 | 0.000 | 0.286 | 1.894 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 28 | 35 | 0 | 168 | 0 | 113 | 32 |
N.S. |
1 | 1.00 | 0.57 | 0.71 | 0.00 | 3.43 | 0.00 | 2.31 | 0.65 |
time (sec) |
N/A | 0.305 | 0.557 | 0.077 | 0.000 | 0.266 | 0.000 | 0.280 | 1.907 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 66 | 28 | 43 | 0 | 266 | 0 | 161 | 40 |
N.S. |
1 | 1.08 | 0.46 | 0.70 | 0.00 | 4.36 | 0.00 | 2.64 | 0.66 |
time (sec) |
N/A | 0.379 | 0.629 | 0.075 | 0.000 | 0.265 | 0.000 | 0.277 | 1.899 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 142 | 146 | 141 | 150 | 348 | 2748 | 588 | 226 | 244 |
N.S. |
1 | 1.03 | 0.99 | 1.06 | 2.45 | 19.35 | 4.14 | 1.59 | 1.72 |
time (sec) |
N/A | 0.769 | 0.852 | 0.269 | 0.200 | 0.275 | 1.792 | 0.290 | 1.975 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 105 | 109 | 113 | 219 | 1396 | 444 | 153 | 158 |
N.S. |
1 | 1.04 | 1.08 | 1.12 | 2.17 | 13.82 | 4.40 | 1.51 | 1.56 |
time (sec) |
N/A | 0.538 | 0.946 | 0.187 | 0.188 | 0.272 | 1.198 | 0.288 | 1.942 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 69 | 73 | 86 | 87 | 136 | 654 | 333 | 99 | 97 |
N.S. |
1 | 1.06 | 1.25 | 1.26 | 1.97 | 9.48 | 4.83 | 1.43 | 1.41 |
time (sec) |
N/A | 0.387 | 0.425 | 0.146 | 0.188 | 0.262 | 0.830 | 0.290 | 0.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 42 | 65 | 59 | 49 | 205 | 209 | 57 | 51 |
N.S. |
1 | 1.11 | 1.71 | 1.55 | 1.29 | 5.39 | 5.50 | 1.50 | 1.34 |
time (sec) |
N/A | 0.265 | 0.132 | 0.085 | 0.193 | 0.258 | 0.574 | 0.280 | 0.113 |
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 | 50 | 50 | 64 | 50 | 52 | 62 | 236 | 62 | 55 |
N.S. |
1 | 1.00 | 1.28 | 1.00 | 1.04 | 1.24 | 4.72 | 1.24 | 1.10 |
time (sec) |
N/A | 0.322 | 0.112 | 0.126 | 0.181 | 0.249 | 1.527 | 0.271 | 1.894 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-2) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 98 | 100 | 93 | 124 | 426 | 0 | 130 | 104 |
N.S. |
1 | 1.15 | 1.18 | 1.09 | 1.46 | 5.01 | 0.00 | 1.53 | 1.22 |
time (sec) |
N/A | 0.475 | 1.585 | 0.112 | 0.193 | 0.264 | 0.000 | 0.299 | 2.005 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F(-2) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 129 | 155 | 134 | 130 | 322 | 1431 | 0 | 203 | 195 |
N.S. |
1 | 1.20 | 1.04 | 1.01 | 2.50 | 11.09 | 0.00 | 1.57 | 1.51 |
time (sec) |
N/A | 0.694 | 3.563 | 0.252 | 0.202 | 0.280 | 0.000 | 0.289 | 2.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F(-2) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 169 | 208 | 214 | 163 | 522 | 3698 | 0 | 303 | 310 |
N.S. |
1 | 1.23 | 1.27 | 0.96 | 3.09 | 21.88 | 0.00 | 1.79 | 1.83 |
time (sec) |
N/A | 0.971 | 6.244 | 0.349 | 0.236 | 0.324 | 0.000 | 0.306 | 2.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 53 | 28 | 28 | 49 | 42 | 29 | 22 |
N.S. |
1 | 1.00 | 1.71 | 0.90 | 0.90 | 1.58 | 1.35 | 0.94 | 0.71 |
time (sec) |
N/A | 0.282 | 0.045 | 0.080 | 0.185 | 0.266 | 0.414 | 0.294 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 53 | 28 | 29 | 48 | 42 | 24 | 22 |
N.S. |
1 | 1.00 | 1.71 | 0.90 | 0.94 | 1.55 | 1.35 | 0.77 | 0.71 |
time (sec) |
N/A | 0.287 | 0.043 | 0.072 | 0.179 | 0.255 | 0.425 | 0.258 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 90 | 128 | 63 | 0 | 2231 | 0 | 0 | 151 |
N.S. |
1 | 1.22 | 1.73 | 0.85 | 0.00 | 30.15 | 0.00 | 0.00 | 2.04 |
time (sec) |
N/A | 0.277 | 6.820 | 0.217 | 0.000 | 0.306 | 0.000 | 0.000 | 2.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 85 | 74 | 62 | 0 | 2307 | 0 | 0 | 242 |
N.S. |
1 | 1.15 | 1.00 | 0.84 | 0.00 | 31.18 | 0.00 | 0.00 | 3.27 |
time (sec) |
N/A | 0.254 | 0.175 | 0.154 | 0.000 | 0.316 | 0.000 | 0.000 | 2.149 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 60 | 62 | 42 | 35 | 36 | 93 | 0 | 42 | 34 |
N.S. |
1 | 1.03 | 0.70 | 0.58 | 0.60 | 1.55 | 0.00 | 0.70 | 0.57 |
time (sec) |
N/A | 0.253 | 0.238 | 1.625 | 0.193 | 0.244 | 0.000 | 0.270 | 2.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 38 | 36 | 30 | 33 | 60 | 0 | 31 | 29 |
N.S. |
1 | 1.31 | 1.24 | 1.03 | 1.14 | 2.07 | 0.00 | 1.07 | 1.00 |
time (sec) |
N/A | 0.276 | 0.233 | 0.560 | 0.196 | 0.250 | 0.000 | 0.268 | 1.928 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 40 | 30 | 23 | 22 | 50 | 0 | 30 | 22 |
N.S. |
1 | 1.05 | 0.79 | 0.61 | 0.58 | 1.32 | 0.00 | 0.79 | 0.58 |
time (sec) |
N/A | 0.241 | 0.191 | 0.267 | 0.197 | 0.247 | 0.000 | 0.268 | 1.913 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 27 | 21 | 18 | 17 | 25 | 0 | 19 | 17 |
N.S. |
1 | 1.42 | 1.11 | 0.95 | 0.89 | 1.32 | 0.00 | 1.00 | 0.89 |
time (sec) |
N/A | 0.250 | 0.154 | 0.141 | 0.190 | 0.246 | 0.000 | 0.275 | 1.883 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 7 | 7 | 6 | 9 | 0 | 6 | 6 |
N.S. |
1 | 1.00 | 0.70 | 0.70 | 0.60 | 0.90 | 0.00 | 0.60 | 0.60 |
time (sec) |
N/A | 0.187 | 0.004 | 0.099 | 0.188 | 0.263 | 0.000 | 0.262 | 1.810 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 7 | 7 | 10 | 8 | 7 | 18 | 0 | 12 | 11 |
N.S. |
1 | 1.00 | 1.43 | 1.14 | 1.00 | 2.57 | 0.00 | 1.71 | 1.57 |
time (sec) |
N/A | 0.200 | 0.010 | 0.161 | 0.176 | 0.247 | 0.000 | 0.269 | 1.858 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | B | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 8 | 18 | 21 | 23 | 31 | 77 | 0 | 26 | 29 |
N.S. |
1 | 2.25 | 2.62 | 2.88 | 3.88 | 9.62 | 0.00 | 3.25 | 3.62 |
time (sec) |
N/A | 0.239 | 0.322 | 0.309 | 0.183 | 0.255 | 0.000 | 0.279 | 0.081 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 11 | 12 | 11 | 10 | 41 | 55 | 0 | 10 | 16 |
N.S. |
1 | 1.09 | 1.00 | 0.91 | 3.73 | 5.00 | 0.00 | 0.91 | 1.45 |
time (sec) |
N/A | 0.199 | 5.085 | 0.684 | 0.192 | 0.241 | 0.000 | 0.272 | 1.856 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 155 | 195 | 156 | 192 | 166 | 1279 | 0 | 229 | 143 |
N.S. |
1 | 1.26 | 1.01 | 1.24 | 1.07 | 8.25 | 0.00 | 1.48 | 0.92 |
time (sec) |
N/A | 0.490 | 0.548 | 5.862 | 0.198 | 0.267 | 0.000 | 0.276 | 2.315 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 134 | 132 | 171 | 172 | 0 | 1859 | 0 | 163 | 172 |
N.S. |
1 | 0.99 | 1.28 | 1.28 | 0.00 | 13.87 | 0.00 | 1.22 | 1.28 |
time (sec) |
N/A | 0.942 | 1.101 | 2.014 | 0.000 | 0.287 | 0.000 | 0.279 | 2.519 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 118 | 75 | 107 | 83 | 331 | 0 | 114 | 85 |
N.S. |
1 | 1.28 | 0.82 | 1.16 | 0.90 | 3.60 | 0.00 | 1.24 | 0.92 |
time (sec) |
N/A | 0.367 | 0.458 | 0.611 | 0.196 | 0.259 | 0.000 | 0.267 | 2.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 75 | 80 | 93 | 0 | 431 | 0 | 72 | 156 |
N.S. |
1 | 1.03 | 1.10 | 1.27 | 0.00 | 5.90 | 0.00 | 0.99 | 2.14 |
time (sec) |
N/A | 0.496 | 0.738 | 0.266 | 0.000 | 0.285 | 0.000 | 0.304 | 2.121 |