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 | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 137 | 141 | 138 | 0 | 0 | 96 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 1.01 | 0.00 | 0.00 | 0.70 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.365 | 0.414 | 0.000 | 0.000 | 0.095 | 0.000 | 0.000 | 0.000 |
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 | 158 | 86 | 178 | 586 | 255 | 502 | 181 | 245 |
N.S. |
1 | 1.01 | 0.55 | 1.14 | 3.76 | 1.63 | 3.22 | 1.16 | 1.57 |
time (sec) |
N/A | 0.433 | 0.450 | 0.637 | 0.236 | 0.238 | 0.467 | 0.286 | 23.322 |
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 | 120 | 128 | 71 | 118 | 342 | 166 | 342 | 121 | 165 |
N.S. |
1 | 1.07 | 0.59 | 0.98 | 2.85 | 1.38 | 2.85 | 1.01 | 1.38 |
time (sec) |
N/A | 0.379 | 0.278 | 0.437 | 0.238 | 0.242 | 0.343 | 0.287 | 22.514 |
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 | 84 | 50 | 69 | 171 | 92 | 175 | 73 | 100 |
N.S. |
1 | 0.94 | 0.56 | 0.78 | 1.92 | 1.03 | 1.97 | 0.82 | 1.12 |
time (sec) |
N/A | 0.268 | 0.218 | 0.347 | 0.234 | 0.252 | 0.249 | 0.281 | 0.167 |
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 | 50 | 54 | 34 | 36 | 65 | 42 | 80 | 38 | 47 |
N.S. |
1 | 1.08 | 0.68 | 0.72 | 1.30 | 0.84 | 1.60 | 0.76 | 0.94 |
time (sec) |
N/A | 0.224 | 0.189 | 0.258 | 0.206 | 0.238 | 0.183 | 0.287 | 22.279 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 63 | 60 | 84 | 143 | 64 | 0 | 569 | 0 |
N.S. |
1 | 0.97 | 0.92 | 1.29 | 2.20 | 0.98 | 0.00 | 8.75 | 0.00 |
time (sec) |
N/A | 0.432 | 0.109 | 0.371 | 0.267 | 0.243 | 0.000 | 0.312 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 92 | 80 | 124 | 166 | 105 | 0 | 2870 | 0 |
N.S. |
1 | 1.08 | 0.94 | 1.46 | 1.95 | 1.24 | 0.00 | 33.76 | 0.00 |
time (sec) |
N/A | 0.552 | 0.357 | 0.431 | 0.295 | 0.247 | 0.000 | 0.506 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 114 | 120 | 102 | 162 | 201 | 187 | 0 | 5398 | 0 |
N.S. |
1 | 1.05 | 0.89 | 1.42 | 1.76 | 1.64 | 0.00 | 47.35 | 0.00 |
time (sec) |
N/A | 0.660 | 1.102 | 0.582 | 0.339 | 0.244 | 0.000 | 0.465 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 144 | 154 | 164 | 200 | 251 | 263 | 0 | 7592 | 0 |
N.S. |
1 | 1.07 | 1.14 | 1.39 | 1.74 | 1.83 | 0.00 | 52.72 | 0.00 |
time (sec) |
N/A | 0.794 | 0.617 | 0.767 | 0.398 | 0.240 | 0.000 | 0.577 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 8 | 7 | 13 | 6 | 5 | 6 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 1.62 | 0.75 | 0.62 | 0.75 | 0.00 |
time (sec) |
N/A | 0.197 | 0.010 | 0.210 | 0.247 | 0.235 | 0.600 | 0.269 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 20 | 16 | 15 | 15 | 17 | 22 | 19 | 0 |
N.S. |
1 | 1.25 | 1.00 | 0.94 | 0.94 | 1.06 | 1.38 | 1.19 | 0.00 |
time (sec) |
N/A | 0.262 | 0.011 | 0.536 | 0.246 | 0.229 | 1.012 | 0.268 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 31 | 29 | 26 | 15 | 30 | 24 | 26 | 0 |
N.S. |
1 | 1.07 | 1.00 | 0.90 | 0.52 | 1.03 | 0.83 | 0.90 | 0.00 |
time (sec) |
N/A | 0.328 | 0.012 | 0.616 | 0.253 | 0.232 | 0.756 | 0.283 | 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 | 275 | 275 | 237 | 0 | 0 | 188 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.68 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.513 | 1.144 | 0.000 | 0.000 | 0.094 | 0.000 | 0.000 | 0.000 |
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 | 205 | 249 | 385 | 173 | 880 | 352 | 646 | 350 | 448 |
N.S. |
1 | 1.21 | 1.88 | 0.84 | 4.29 | 1.72 | 3.15 | 1.71 | 2.19 |
time (sec) |
N/A | 1.283 | 1.640 | 1.428 | 0.251 | 0.250 | 0.625 | 0.306 | 24.745 |
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 | 151 | 164 | 121 | 224 | 499 | 227 | 391 | 231 | 289 |
N.S. |
1 | 1.09 | 0.80 | 1.48 | 3.30 | 1.50 | 2.59 | 1.53 | 1.91 |
time (sec) |
N/A | 0.736 | 1.193 | 0.879 | 0.238 | 0.248 | 0.455 | 0.297 | 23.323 |
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 | 106 | 93 | 128 | 240 | 130 | 216 | 137 | 161 |
N.S. |
1 | 1.03 | 0.90 | 1.24 | 2.33 | 1.26 | 2.10 | 1.33 | 1.56 |
time (sec) |
N/A | 0.447 | 0.658 | 1.037 | 0.211 | 0.261 | 0.322 | 0.301 | 22.969 |
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 | 51 | 48 | 44 | 56 | 85 | 59 | 85 | 69 | 59 |
N.S. |
1 | 0.94 | 0.86 | 1.10 | 1.67 | 1.16 | 1.67 | 1.35 | 1.16 |
time (sec) |
N/A | 0.256 | 0.215 | 0.648 | 0.199 | 0.248 | 0.224 | 0.292 | 0.201 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 102 | 171 | 276 | 122 | 0 | 6059 | 0 |
N.S. |
1 | 1.00 | 0.84 | 1.41 | 2.28 | 1.01 | 0.00 | 50.07 | 0.00 |
time (sec) |
N/A | 0.445 | 0.625 | 0.620 | 0.291 | 0.248 | 0.000 | 0.504 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 168 | 168 | 139 | 247 | 305 | 186 | 0 | 67350 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.47 | 1.82 | 1.11 | 0.00 | 400.89 | 0.00 |
time (sec) |
N/A | 0.487 | 1.643 | 0.580 | 0.346 | 0.254 | 0.000 | 2.409 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 221 | 221 | 183 | 316 | 340 | 312 | 0 | 114422 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.43 | 1.54 | 1.41 | 0.00 | 517.75 | 0.00 |
time (sec) |
N/A | 0.555 | 2.169 | 1.493 | 0.424 | 0.269 | 0.000 | 3.323 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 270 | 270 | 298 | 389 | 390 | 450 | 0 | 168646 | 0 |
N.S. |
1 | 1.00 | 1.10 | 1.44 | 1.44 | 1.67 | 0.00 | 624.61 | 0.00 |
time (sec) |
N/A | 0.635 | 1.508 | 1.769 | 0.584 | 0.277 | 0.000 | 4.616 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 271 | 271 | 246 | 0 | 0 | 190 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.00 | 0.00 | 0.70 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.525 | 1.478 | 0.000 | 0.000 | 0.095 | 0.000 | 0.000 | 0.000 |
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 | 260 | 326 | 158 | 187 | 967 | 434 | 935 | 361 | 576 |
N.S. |
1 | 1.25 | 0.61 | 0.72 | 3.72 | 1.67 | 3.60 | 1.39 | 2.22 |
time (sec) |
N/A | 1.000 | 2.117 | 1.988 | 0.254 | 0.257 | 0.878 | 0.314 | 24.220 |
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 | 196 | 243 | 135 | 148 | 549 | 283 | 602 | 241 | 366 |
N.S. |
1 | 1.24 | 0.69 | 0.76 | 2.80 | 1.44 | 3.07 | 1.23 | 1.87 |
time (sec) |
N/A | 0.774 | 0.988 | 1.541 | 0.246 | 0.259 | 0.609 | 0.305 | 24.998 |
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 | 134 | 133 | 91 | 111 | 263 | 159 | 320 | 145 | 202 |
N.S. |
1 | 0.99 | 0.68 | 0.83 | 1.96 | 1.19 | 2.39 | 1.08 | 1.51 |
time (sec) |
N/A | 0.388 | 0.525 | 1.278 | 0.217 | 0.252 | 0.427 | 0.289 | 24.528 |
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 | 72 | 80 | 75 | 69 | 92 | 76 | 138 | 75 | 94 |
N.S. |
1 | 1.11 | 1.04 | 0.96 | 1.28 | 1.06 | 1.92 | 1.04 | 1.31 |
time (sec) |
N/A | 0.305 | 0.154 | 0.984 | 0.206 | 0.247 | 0.309 | 0.281 | 0.319 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 129 | 129 | 110 | 178 | 281 | 126 | 0 | 6046 | 0 |
N.S. |
1 | 1.00 | 0.85 | 1.38 | 2.18 | 0.98 | 0.00 | 46.87 | 0.00 |
time (sec) |
N/A | 0.427 | 0.345 | 0.995 | 0.296 | 0.250 | 0.000 | 0.514 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 179 | 179 | 151 | 256 | 308 | 194 | 0 | 63510 | 0 |
N.S. |
1 | 1.00 | 0.84 | 1.43 | 1.72 | 1.08 | 0.00 | 354.80 | 0.00 |
time (sec) |
N/A | 0.497 | 1.329 | 1.333 | 0.354 | 0.253 | 0.000 | 2.655 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 229 | 229 | 199 | 329 | 343 | 334 | 0 | 111694 | 0 |
N.S. |
1 | 1.00 | 0.87 | 1.44 | 1.50 | 1.46 | 0.00 | 487.75 | 0.00 |
time (sec) |
N/A | 0.565 | 3.119 | 1.645 | 0.436 | 0.259 | 0.000 | 3.336 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 287 | 287 | 316 | 404 | 393 | 474 | 0 | 157526 | 0 |
N.S. |
1 | 1.00 | 1.10 | 1.41 | 1.37 | 1.65 | 0.00 | 548.87 | 0.00 |
time (sec) |
N/A | 0.644 | 2.281 | 2.125 | 0.614 | 0.272 | 0.000 | 4.529 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 20 | 22 | 22 | 20 | 22 | 24 |
N.S. |
1 | 1.00 | 1.14 | 1.43 | 1.57 | 1.57 | 1.43 | 1.57 | 1.71 |
time (sec) |
N/A | 0.199 | 3.546 | 0.286 | 0.380 | 0.233 | 18.240 | 0.288 | 23.551 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 151 | 215 | 799 | 1159 | 1281 | 1204 | 0 | 0 | 0 |
N.S. |
1 | 1.42 | 5.29 | 7.68 | 8.48 | 7.97 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.869 | 6.270 | 1.206 | 0.411 | 0.313 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 171 | 560 | 792 | 759 | 818 | 0 | 0 | 0 |
N.S. |
1 | 1.35 | 4.41 | 6.24 | 5.98 | 6.44 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.680 | 2.858 | 1.157 | 0.339 | 0.310 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 93 | 125 | 356 | 477 | 411 | 502 | 0 | 0 | 0 |
N.S. |
1 | 1.34 | 3.83 | 5.13 | 4.42 | 5.40 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.530 | 1.610 | 1.127 | 0.299 | 0.274 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 81 | 192 | 215 | 190 | 250 | 0 | 0 | 0 |
N.S. |
1 | 1.25 | 2.95 | 3.31 | 2.92 | 3.85 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.357 | 5.467 | 0.996 | 0.305 | 0.269 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 20 | 22 | 22 | 19 | 22 | 24 |
N.S. |
1 | 1.00 | 1.14 | 1.43 | 1.57 | 1.57 | 1.36 | 1.57 | 1.71 |
time (sec) |
N/A | 0.196 | 4.960 | 0.560 | 0.418 | 0.257 | 0.557 | 0.295 | 22.966 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 20 | 22 | 33 | 20 | 22 | 24 |
N.S. |
1 | 1.00 | 1.14 | 1.43 | 1.57 | 2.36 | 1.43 | 1.57 | 1.71 |
time (sec) |
N/A | 0.198 | 9.022 | 0.537 | 0.668 | 0.251 | 0.812 | 2.059 | 21.856 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 22 | 24 | 24 | 22 | 24 | 24 |
N.S. |
1 | 1.00 | 1.10 | 1.10 | 1.20 | 1.20 | 1.10 | 1.20 | 1.20 |
time (sec) |
N/A | 0.318 | 3.159 | 0.303 | 0.712 | 0.251 | 66.692 | 0.304 | 21.340 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 208 | 228 | 308 | 716 | 2948 | 1021 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 1.48 | 3.44 | 14.17 | 4.91 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.802 | 1.534 | 1.232 | 0.585 | 0.307 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 146 | 156 | 311 | 433 | 1770 | 669 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 2.13 | 2.97 | 12.12 | 4.58 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.558 | 1.342 | 1.128 | 0.382 | 0.288 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 90 | 92 | 234 | 212 | 553 | 375 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 2.60 | 2.36 | 6.14 | 4.17 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.358 | 2.371 | 0.778 | 0.350 | 0.275 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 131 | 46 | 259 | 62 | 0 | 697 | 88 |
N.S. |
1 | 1.00 | 4.37 | 1.53 | 8.63 | 2.07 | 0.00 | 23.23 | 2.93 |
time (sec) |
N/A | 0.227 | 0.114 | 0.507 | 0.232 | 0.268 | 0.000 | 0.537 | 24.281 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 22 | 508 | 24 | 20 | 24 | 24 |
N.S. |
1 | 1.00 | 1.10 | 1.10 | 25.40 | 1.20 | 1.00 | 1.20 | 1.20 |
time (sec) |
N/A | 0.256 | 19.170 | 0.527 | 0.583 | 0.257 | 0.953 | 0.890 | 23.853 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 22 | 745 | 35 | 22 | 24 | 24 |
N.S. |
1 | 1.00 | 1.10 | 1.10 | 37.25 | 1.75 | 1.10 | 1.20 | 1.20 |
time (sec) |
N/A | 0.277 | 22.944 | 0.539 | 1.281 | 0.247 | 1.367 | 2.878 | 23.867 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 22 | 24 | 24 | 0 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.00 | 1.09 | 1.09 |
time (sec) |
N/A | 0.331 | 7.834 | 0.288 | 0.747 | 0.250 | 0.000 | 0.296 | 23.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 179 | 512 | 716 | 4551 | 1075 | 0 | 0 | 0 |
N.S. |
1 | 1.31 | 3.74 | 5.23 | 33.22 | 7.85 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.818 | 6.640 | 1.822 | 0.555 | 0.298 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 137 | 277 | 409 | 1044 | 591 | 0 | 0 | 0 |
N.S. |
1 | 1.19 | 2.41 | 3.56 | 9.08 | 5.14 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.596 | 6.457 | 1.668 | 0.493 | 0.273 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | B | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 59 | 94 | 136 | 1130 | 102 | 0 | 2978 | 147 |
N.S. |
1 | 1.09 | 1.74 | 2.52 | 20.93 | 1.89 | 0.00 | 55.15 | 2.72 |
time (sec) |
N/A | 0.346 | 1.057 | 1.310 | 0.291 | 0.275 | 0.000 | 1.214 | 25.391 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 48 | 61 | 287 | 44 | 0 | 526 | 53 |
N.S. |
1 | 1.00 | 1.37 | 1.74 | 8.20 | 1.26 | 0.00 | 15.03 | 1.51 |
time (sec) |
N/A | 0.244 | 0.338 | 1.029 | 0.245 | 0.242 | 0.000 | 0.351 | 24.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 22 | 1664 | 24 | 20 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 75.64 | 1.09 | 0.91 | 1.09 | 1.09 |
time (sec) |
N/A | 0.269 | 13.138 | 0.569 | 1.151 | 0.250 | 2.074 | 0.332 | 23.320 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 22 | 2153 | 35 | 22 | 0 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 97.86 | 1.59 | 1.00 | 0.00 | 1.09 |
time (sec) |
N/A | 0.287 | 12.396 | 0.562 | 2.661 | 0.257 | 3.141 | 0.000 | 23.274 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 196 | 218 | 144 | 234 | 277 | 222 | 0 | 1205 | 0 |
N.S. |
1 | 1.11 | 0.73 | 1.19 | 1.41 | 1.13 | 0.00 | 6.15 | 0.00 |
time (sec) |
N/A | 1.078 | 0.682 | 0.889 | 0.403 | 0.259 | 0.000 | 0.597 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 168 | 183 | 128 | 187 | 256 | 167 | 0 | 747 | 0 |
N.S. |
1 | 1.09 | 0.76 | 1.11 | 1.52 | 0.99 | 0.00 | 4.45 | 0.00 |
time (sec) |
N/A | 0.866 | 0.601 | 0.618 | 0.372 | 0.247 | 0.000 | 0.454 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 142 | 150 | 145 | 142 | 209 | 125 | 0 | 406 | 0 |
N.S. |
1 | 1.06 | 1.02 | 1.00 | 1.47 | 0.88 | 0.00 | 2.86 | 0.00 |
time (sec) |
N/A | 0.694 | 0.402 | 0.611 | 0.398 | 0.240 | 0.000 | 0.384 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 142 | 150 | 145 | 142 | 209 | 125 | 0 | 406 | 0 |
N.S. |
1 | 1.06 | 1.02 | 1.00 | 1.47 | 0.88 | 0.00 | 2.86 | 0.00 |
time (sec) |
N/A | 0.687 | 0.009 | 0.556 | 0.389 | 0.244 | 0.000 | 0.382 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 168 | 183 | 128 | 187 | 256 | 167 | 0 | 747 | 0 |
N.S. |
1 | 1.09 | 0.76 | 1.11 | 1.52 | 0.99 | 0.00 | 4.45 | 0.00 |
time (sec) |
N/A | 0.833 | 0.024 | 0.556 | 0.383 | 0.256 | 0.000 | 0.471 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 196 | 218 | 144 | 234 | 277 | 222 | 0 | 1205 | 0 |
N.S. |
1 | 1.11 | 0.73 | 1.19 | 1.41 | 1.13 | 0.00 | 6.15 | 0.00 |
time (sec) |
N/A | 0.981 | 0.084 | 0.753 | 0.382 | 0.248 | 0.000 | 0.607 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 406 | 406 | 1418 | 474 | 547 | 370 | 0 | 2478 | 0 |
N.S. |
1 | 1.00 | 3.49 | 1.17 | 1.35 | 0.91 | 0.00 | 6.10 | 0.00 |
time (sec) |
N/A | 1.365 | 12.503 | 1.444 | 0.409 | 0.273 | 0.000 | 1.002 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 353 | 353 | 730 | 386 | 497 | 298 | 0 | 1547 | 0 |
N.S. |
1 | 1.00 | 2.07 | 1.09 | 1.41 | 0.84 | 0.00 | 4.38 | 0.00 |
time (sec) |
N/A | 0.978 | 1.293 | 0.806 | 0.408 | 0.262 | 0.000 | 0.810 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 304 | 304 | 251 | 294 | 424 | 245 | 0 | 848 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.97 | 1.39 | 0.81 | 0.00 | 2.79 | 0.00 |
time (sec) |
N/A | 0.757 | 0.244 | 0.694 | 0.365 | 0.263 | 0.000 | 0.550 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 304 | 304 | 251 | 294 | 424 | 245 | 0 | 848 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.97 | 1.39 | 0.81 | 0.00 | 2.79 | 0.00 |
time (sec) |
N/A | 0.723 | 0.008 | 0.470 | 0.384 | 0.268 | 0.000 | 0.548 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 353 | 353 | 730 | 386 | 497 | 298 | 0 | 1547 | 0 |
N.S. |
1 | 1.00 | 2.07 | 1.09 | 1.41 | 0.84 | 0.00 | 4.38 | 0.00 |
time (sec) |
N/A | 0.842 | 0.011 | 0.482 | 0.354 | 0.271 | 0.000 | 0.819 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 406 | 406 | 1418 | 474 | 547 | 370 | 0 | 2478 | 0 |
N.S. |
1 | 1.00 | 3.49 | 1.17 | 1.35 | 0.91 | 0.00 | 6.10 | 0.00 |
time (sec) |
N/A | 0.958 | 0.012 | 1.228 | 0.374 | 0.261 | 0.000 | 1.006 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 407 | 407 | 1332 | 470 | 551 | 406 | 0 | 2435 | 0 |
N.S. |
1 | 1.00 | 3.27 | 1.15 | 1.35 | 1.00 | 0.00 | 5.98 | 0.00 |
time (sec) |
N/A | 1.238 | 14.414 | 3.852 | 0.386 | 0.276 | 0.000 | 1.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 351 | 351 | 693 | 376 | 503 | 316 | 0 | 1515 | 0 |
N.S. |
1 | 1.00 | 1.97 | 1.07 | 1.43 | 0.90 | 0.00 | 4.32 | 0.00 |
time (sec) |
N/A | 0.903 | 1.937 | 0.760 | 0.377 | 0.268 | 0.000 | 0.895 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 299 | 299 | 252 | 286 | 429 | 244 | 0 | 826 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.96 | 1.43 | 0.82 | 0.00 | 2.76 | 0.00 |
time (sec) |
N/A | 0.675 | 0.380 | 0.762 | 0.363 | 0.267 | 0.000 | 0.622 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 299 | 299 | 252 | 286 | 429 | 244 | 0 | 826 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.96 | 1.43 | 0.82 | 0.00 | 2.76 | 0.00 |
time (sec) |
N/A | 0.647 | 0.140 | 0.473 | 0.371 | 0.297 | 0.000 | 0.611 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 351 | 351 | 693 | 376 | 503 | 316 | 0 | 1515 | 0 |
N.S. |
1 | 1.00 | 1.97 | 1.07 | 1.43 | 0.90 | 0.00 | 4.32 | 0.00 |
time (sec) |
N/A | 0.770 | 1.536 | 0.531 | 0.390 | 0.269 | 0.000 | 0.854 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 407 | 407 | 1332 | 470 | 551 | 406 | 0 | 2435 | 0 |
N.S. |
1 | 1.00 | 3.27 | 1.15 | 1.35 | 1.00 | 0.00 | 5.98 | 0.00 |
time (sec) |
N/A | 0.872 | 6.027 | 3.559 | 0.397 | 0.296 | 0.000 | 1.136 | 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 | 267 | 267 | 250 | 0 | 0 | 186 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.00 | 0.00 | 0.70 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.483 | 0.770 | 0.000 | 0.000 | 0.098 | 0.000 | 0.000 | 0.000 |
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 | 205 | 247 | 150 | 181 | 889 | 294 | 646 | 350 | 448 |
N.S. |
1 | 1.20 | 0.73 | 0.88 | 4.34 | 1.43 | 3.15 | 1.71 | 2.19 |
time (sec) |
N/A | 1.221 | 1.782 | 1.773 | 0.301 | 0.254 | 0.638 | 0.308 | 25.722 |
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 | 151 | 165 | 127 | 224 | 505 | 183 | 391 | 231 | 290 |
N.S. |
1 | 1.09 | 0.84 | 1.48 | 3.34 | 1.21 | 2.59 | 1.53 | 1.92 |
time (sec) |
N/A | 0.718 | 0.839 | 1.439 | 0.266 | 0.245 | 0.453 | 0.293 | 24.406 |
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 | 105 | 86 | 128 | 243 | 100 | 216 | 137 | 145 |
N.S. |
1 | 1.02 | 0.83 | 1.24 | 2.36 | 0.97 | 2.10 | 1.33 | 1.41 |
time (sec) |
N/A | 0.451 | 0.486 | 1.315 | 0.256 | 0.248 | 0.338 | 0.295 | 24.426 |
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 | 51 | 50 | 71 | 64 | 86 | 46 | 85 | 69 | 58 |
N.S. |
1 | 0.98 | 1.39 | 1.25 | 1.69 | 0.90 | 1.67 | 1.35 | 1.14 |
time (sec) |
N/A | 0.244 | 0.138 | 1.070 | 0.225 | 0.237 | 0.250 | 0.277 | 24.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 100 | 172 | 275 | 120 | 0 | 6279 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.42 | 2.27 | 0.99 | 0.00 | 51.89 | 0.00 |
time (sec) |
N/A | 0.401 | 0.332 | 0.780 | 0.329 | 0.238 | 0.000 | 0.508 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 168 | 168 | 139 | 245 | 302 | 182 | 0 | 66726 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.46 | 1.80 | 1.08 | 0.00 | 397.18 | 0.00 |
time (sec) |
N/A | 0.469 | 1.220 | 1.020 | 0.367 | 0.254 | 0.000 | 2.454 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 221 | 221 | 181 | 318 | 337 | 306 | 0 | 118262 | 0 |
N.S. |
1 | 1.00 | 0.82 | 1.44 | 1.52 | 1.38 | 0.00 | 535.12 | 0.00 |
time (sec) |
N/A | 0.538 | 2.686 | 1.514 | 0.446 | 0.267 | 0.000 | 3.479 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 270 | 270 | 300 | 386 | 387 | 444 | 0 | 166374 | 0 |
N.S. |
1 | 1.00 | 1.11 | 1.43 | 1.43 | 1.64 | 0.00 | 616.20 | 0.00 |
time (sec) |
N/A | 0.611 | 1.861 | 1.710 | 0.663 | 0.274 | 0.000 | 4.747 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 162 | 162 | 155 | 0 | 0 | 136 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.84 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.391 | 3.785 | 0.000 | 0.000 | 0.090 | 0.000 | 0.000 | 0.000 |
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 | 131 | 131 | 132 | 146 | 735 | 466 | 1231 | 224 | 349 |
N.S. |
1 | 1.00 | 1.01 | 1.11 | 5.61 | 3.56 | 9.40 | 1.71 | 2.66 |
time (sec) |
N/A | 0.360 | 1.254 | 2.628 | 0.273 | 0.256 | 0.906 | 0.318 | 23.662 |
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 | 105 | 105 | 106 | 121 | 442 | 308 | 835 | 153 | 329 |
N.S. |
1 | 1.00 | 1.01 | 1.15 | 4.21 | 2.93 | 7.95 | 1.46 | 3.13 |
time (sec) |
N/A | 0.312 | 0.663 | 1.810 | 0.254 | 0.248 | 0.632 | 0.313 | 1.204 |
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 | 79 | 79 | 77 | 79 | 232 | 180 | 493 | 94 | 179 |
N.S. |
1 | 1.00 | 0.97 | 1.00 | 2.94 | 2.28 | 6.24 | 1.19 | 2.27 |
time (sec) |
N/A | 0.298 | 0.411 | 1.458 | 0.240 | 0.257 | 0.471 | 0.312 | 23.133 |
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 | 53 | 53 | 54 | 46 | 96 | 85 | 238 | 48 | 57 |
N.S. |
1 | 1.00 | 1.02 | 0.87 | 1.81 | 1.60 | 4.49 | 0.91 | 1.08 |
time (sec) |
N/A | 0.223 | 0.597 | 0.971 | 0.233 | 0.254 | 0.325 | 0.293 | 23.133 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 65 | 107 | 162 | 73 | 0 | 669 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.37 | 2.08 | 0.94 | 0.00 | 8.58 | 0.00 |
time (sec) |
N/A | 0.318 | 0.158 | 0.921 | 0.294 | 0.252 | 0.000 | 0.329 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 104 | 81 | 155 | 171 | 112 | 0 | 3218 | 0 |
N.S. |
1 | 1.00 | 0.78 | 1.49 | 1.64 | 1.08 | 0.00 | 30.94 | 0.00 |
time (sec) |
N/A | 0.352 | 0.465 | 1.234 | 0.312 | 0.256 | 0.000 | 0.755 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 127 | 105 | 193 | 206 | 213 | 0 | 5600 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.52 | 1.62 | 1.68 | 0.00 | 44.09 | 0.00 |
time (sec) |
N/A | 0.387 | 0.941 | 1.533 | 0.381 | 0.263 | 0.000 | 0.489 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | B | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 158 | 158 | 123 | 230 | 258 | 349 | 0 | 8508 | 0 |
N.S. |
1 | 1.00 | 0.78 | 1.46 | 1.63 | 2.21 | 0.00 | 53.85 | 0.00 |
time (sec) |
N/A | 0.427 | 1.795 | 2.017 | 0.456 | 0.267 | 0.000 | 0.568 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 407 | 407 | 376 | 0 | 0 | 280 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.69 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.644 | 1.040 | 0.000 | 0.000 | 0.103 | 0.000 | 0.000 | 0.000 |
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 | 330 | 330 | 238 | 259 | 1339 | 471 | 1098 | 531 | 816 |
N.S. |
1 | 1.00 | 0.72 | 0.78 | 4.06 | 1.43 | 3.33 | 1.61 | 2.47 |
time (sec) |
N/A | 0.611 | 3.576 | 2.979 | 0.310 | 0.264 | 1.134 | 0.360 | 27.718 |
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 | 259 | 259 | 369 | 205 | 766 | 296 | 690 | 351 | 516 |
N.S. |
1 | 1.00 | 1.42 | 0.79 | 2.96 | 1.14 | 2.66 | 1.36 | 1.99 |
time (sec) |
N/A | 0.517 | 1.510 | 2.246 | 0.270 | 0.260 | 0.840 | 0.338 | 2.999 |
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 | 184 | 184 | 127 | 152 | 375 | 166 | 382 | 209 | 249 |
N.S. |
1 | 1.00 | 0.69 | 0.83 | 2.04 | 0.90 | 2.08 | 1.14 | 1.35 |
time (sec) |
N/A | 0.409 | 0.844 | 2.140 | 0.261 | 0.252 | 0.583 | 0.317 | 1.063 |
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 | 109 | 109 | 94 | 92 | 139 | 76 | 163 | 106 | 99 |
N.S. |
1 | 1.00 | 0.86 | 0.84 | 1.28 | 0.70 | 1.50 | 0.97 | 0.91 |
time (sec) |
N/A | 0.282 | 0.284 | 1.703 | 0.246 | 0.239 | 0.395 | 0.302 | 23.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 185 | 185 | 154 | 258 | 414 | 182 | 0 | 46675 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.39 | 2.24 | 0.98 | 0.00 | 252.30 | 0.00 |
time (sec) |
N/A | 0.525 | 0.419 | 1.236 | 0.353 | 0.252 | 0.000 | 1.762 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 257 | 257 | 213 | 370 | 445 | 272 | 0 | 1014406 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.44 | 1.73 | 1.06 | 0.00 | 3947.11 | 0.00 |
time (sec) |
N/A | 0.625 | 1.588 | 1.543 | 0.414 | 0.267 | 0.000 | 47.389 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 338 | 338 | 279 | 480 | 480 | 456 | 0 | 1737414 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.42 | 1.42 | 1.35 | 0.00 | 5140.28 | 0.00 |
time (sec) |
N/A | 0.719 | 3.969 | 2.226 | 0.566 | 0.285 | 0.000 | 99.433 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 413 | 413 | 457 | 585 | 530 | 653 | 0 | 2449286 | 0 |
N.S. |
1 | 1.00 | 1.11 | 1.42 | 1.28 | 1.58 | 0.00 | 5930.47 | 0.00 |
time (sec) |
N/A | 0.859 | 2.545 | 2.894 | 0.850 | 0.295 | 0.000 | 207.311 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 22 | 22 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 1.00 | 1.10 | 1.10 |
time (sec) |
N/A | 0.457 | 11.866 | 0.315 | 0.683 | 0.237 | 7.834 | 0.298 | 23.982 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 333 | 376 | 837 | 1295 | 1548 | 1367 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 2.51 | 3.89 | 4.65 | 4.11 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.669 | 1.334 | 2.605 | 0.525 | 0.329 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 254 | 278 | 330 | 847 | 929 | 925 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 1.30 | 3.33 | 3.66 | 3.64 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.233 | 0.867 | 1.793 | 0.375 | 0.317 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 181 | 221 | 479 | 513 | 562 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 1.29 | 2.80 | 3.00 | 3.29 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.811 | 0.838 | 1.432 | 0.297 | 0.301 | 0.000 | 0.000 | 0.000 |