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 | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 81 | 82 | 73 | 66 | 66 | 90 | 80 | 71 | 69 |
N.S. |
1 | 1.01 | 0.90 | 0.81 | 0.81 | 1.11 | 0.99 | 0.88 | 0.85 |
time (sec) |
N/A | 0.347 | 0.022 | 0.063 | 0.266 | 0.244 | 0.078 | 0.433 | 0.033 |
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 | 74 | 75 | 66 | 62 | 59 | 85 | 73 | 66 | 65 |
N.S. |
1 | 1.01 | 0.89 | 0.84 | 0.80 | 1.15 | 0.99 | 0.89 | 0.88 |
time (sec) |
N/A | 0.338 | 0.021 | 0.079 | 0.267 | 0.251 | 0.076 | 0.523 | 0.027 |
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 | 65 | 68 | 61 | 56 | 54 | 80 | 68 | 54 | 60 |
N.S. |
1 | 1.05 | 0.94 | 0.86 | 0.83 | 1.23 | 1.05 | 0.83 | 0.92 |
time (sec) |
N/A | 0.314 | 0.020 | 0.071 | 0.279 | 0.251 | 0.078 | 0.470 | 8.608 |
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 | 58 | 68 | 58 | 51 | 49 | 70 | 60 | 49 | 69 |
N.S. |
1 | 1.17 | 1.00 | 0.88 | 0.84 | 1.21 | 1.03 | 0.84 | 1.19 |
time (sec) |
N/A | 0.281 | 0.016 | 0.054 | 0.272 | 0.249 | 0.076 | 0.460 | 0.030 |
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 | 66 | 77 | 72 | 58 | 55 | 84 | 65 | 62 | 59 |
N.S. |
1 | 1.17 | 1.09 | 0.88 | 0.83 | 1.27 | 0.98 | 0.94 | 0.89 |
time (sec) |
N/A | 0.308 | 0.067 | 0.068 | 0.267 | 0.255 | 0.083 | 0.451 | 8.656 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 71 | 80 | 101 | 63 | 66 | 105 | 76 | 66 | 68 |
N.S. |
1 | 1.13 | 1.42 | 0.89 | 0.93 | 1.48 | 1.07 | 0.93 | 0.96 |
time (sec) |
N/A | 0.347 | 0.045 | 0.073 | 0.270 | 0.246 | 0.097 | 0.438 | 0.037 |
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 | 80 | 81 | 82 | 68 | 71 | 110 | 80 | 79 | 72 |
N.S. |
1 | 1.01 | 1.02 | 0.85 | 0.89 | 1.38 | 1.00 | 0.99 | 0.90 |
time (sec) |
N/A | 0.365 | 0.068 | 0.072 | 0.285 | 0.252 | 0.095 | 0.438 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 87 | 92 | 114 | 73 | 76 | 115 | 85 | 84 | 78 |
N.S. |
1 | 1.06 | 1.31 | 0.84 | 0.87 | 1.32 | 0.98 | 0.97 | 0.90 |
time (sec) |
N/A | 0.384 | 0.055 | 0.072 | 0.275 | 0.241 | 0.112 | 0.441 | 8.641 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 248 | 253 | 145 | 79 | 0 | 215 | 71 | 585 | 171 |
N.S. |
1 | 1.02 | 0.58 | 0.32 | 0.00 | 0.87 | 0.29 | 2.36 | 0.69 |
time (sec) |
N/A | 0.578 | 0.126 | 0.174 | 0.000 | 0.249 | 0.344 | 0.594 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 237 | 244 | 132 | 72 | 0 | 210 | 1205 | 576 | 164 |
N.S. |
1 | 1.03 | 0.56 | 0.30 | 0.00 | 0.89 | 5.08 | 2.43 | 0.69 |
time (sec) |
N/A | 0.532 | 0.105 | 0.087 | 0.000 | 0.247 | 0.739 | 0.628 | 8.618 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 232 | 237 | 129 | 69 | 0 | 205 | 60 | 573 | 162 |
N.S. |
1 | 1.02 | 0.56 | 0.30 | 0.00 | 0.88 | 0.26 | 2.47 | 0.70 |
time (sec) |
N/A | 0.497 | 0.105 | 0.081 | 0.000 | 0.251 | 0.329 | 0.593 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 225 | 230 | 121 | 64 | 0 | 222 | 51 | 566 | 156 |
N.S. |
1 | 1.02 | 0.54 | 0.28 | 0.00 | 0.99 | 0.23 | 2.52 | 0.69 |
time (sec) |
N/A | 0.480 | 0.109 | 0.076 | 0.000 | 0.270 | 0.330 | 0.611 | 0.089 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 224 | 263 | 115 | 61 | 0 | 217 | 1185 | 565 | 153 |
N.S. |
1 | 1.17 | 0.51 | 0.27 | 0.00 | 0.97 | 5.29 | 2.52 | 0.68 |
time (sec) |
N/A | 0.490 | 0.189 | 0.075 | 0.000 | 0.256 | 0.694 | 0.582 | 8.652 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 229 | 232 | 126 | 63 | 0 | 230 | 1192 | 572 | 159 |
N.S. |
1 | 1.01 | 0.55 | 0.28 | 0.00 | 1.00 | 5.21 | 2.50 | 0.69 |
time (sec) |
N/A | 0.555 | 0.121 | 0.099 | 0.000 | 0.253 | 0.765 | 0.577 | 0.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 238 | 239 | 131 | 68 | 0 | 245 | 60 | 579 | 165 |
N.S. |
1 | 1.00 | 0.55 | 0.29 | 0.00 | 1.03 | 0.25 | 2.43 | 0.69 |
time (sec) |
N/A | 0.528 | 0.210 | 0.099 | 0.000 | 0.246 | 0.353 | 0.595 | 0.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 245 | 246 | 140 | 73 | 0 | 252 | 1202 | 584 | 171 |
N.S. |
1 | 1.00 | 0.57 | 0.30 | 0.00 | 1.03 | 4.91 | 2.38 | 0.70 |
time (sec) |
N/A | 0.563 | 0.207 | 0.106 | 0.000 | 0.257 | 0.772 | 0.625 | 8.765 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 243 | 255 | 156 | 82 | 0 | 282 | 1204 | 588 | 184 |
N.S. |
1 | 1.05 | 0.64 | 0.34 | 0.00 | 1.16 | 4.95 | 2.42 | 0.76 |
time (sec) |
N/A | 0.641 | 0.154 | 0.095 | 0.000 | 0.257 | 0.754 | 0.729 | 0.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 242 | 252 | 155 | 79 | 0 | 279 | 82 | 585 | 182 |
N.S. |
1 | 1.04 | 0.64 | 0.33 | 0.00 | 1.15 | 0.34 | 2.42 | 0.75 |
time (sec) |
N/A | 0.612 | 0.136 | 0.076 | 0.000 | 0.252 | 0.369 | 0.751 | 8.896 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 235 | 245 | 138 | 74 | 0 | 272 | 71 | 580 | 176 |
N.S. |
1 | 1.04 | 0.59 | 0.31 | 0.00 | 1.16 | 0.30 | 2.47 | 0.75 |
time (sec) |
N/A | 0.583 | 0.222 | 0.077 | 0.000 | 0.248 | 0.344 | 0.722 | 8.853 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 238 | 292 | 129 | 71 | 0 | 267 | 1198 | 577 | 173 |
N.S. |
1 | 1.23 | 0.54 | 0.30 | 0.00 | 1.12 | 5.03 | 2.42 | 0.73 |
time (sec) |
N/A | 0.574 | 0.204 | 0.075 | 0.000 | 0.256 | 0.697 | 0.874 | 0.127 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 246 | 290 | 133 | 71 | 0 | 277 | 1200 | 577 | 174 |
N.S. |
1 | 1.18 | 0.54 | 0.29 | 0.00 | 1.13 | 4.88 | 2.35 | 0.71 |
time (sec) |
N/A | 0.581 | 0.201 | 0.079 | 0.000 | 0.250 | 0.721 | 0.754 | 0.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 248 | 294 | 129 | 71 | 0 | 277 | 1195 | 577 | 173 |
N.S. |
1 | 1.19 | 0.52 | 0.29 | 0.00 | 1.12 | 4.82 | 2.33 | 0.70 |
time (sec) |
N/A | 0.540 | 0.192 | 0.070 | 0.000 | 0.251 | 0.701 | 0.720 | 8.700 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 253 | 253 | 140 | 73 | 0 | 290 | 75 | 582 | 179 |
N.S. |
1 | 1.00 | 0.55 | 0.29 | 0.00 | 1.15 | 0.30 | 2.30 | 0.71 |
time (sec) |
N/A | 0.644 | 0.263 | 0.096 | 0.000 | 0.270 | 0.364 | 0.738 | 8.872 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 262 | 268 | 139 | 78 | 0 | 305 | 80 | 589 | 185 |
N.S. |
1 | 1.02 | 0.53 | 0.30 | 0.00 | 1.16 | 0.31 | 2.25 | 0.71 |
time (sec) |
N/A | 0.632 | 0.233 | 0.098 | 0.000 | 0.261 | 0.367 | 0.768 | 8.752 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 149 | 148 | 142 | 151 | 0 | 486 | 0 | 144 | 1834 |
N.S. |
1 | 0.99 | 0.95 | 1.01 | 0.00 | 3.26 | 0.00 | 0.97 | 12.31 |
time (sec) |
N/A | 0.443 | 0.075 | 0.256 | 0.000 | 0.335 | 0.000 | 0.638 | 9.001 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F(-1) | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 594 | 607 | 721 | 348 | 0 | 0 | 0 | 10752 | 47339 |
N.S. |
1 | 1.02 | 1.21 | 0.59 | 0.00 | 0.00 | 0.00 | 18.10 | 79.70 |
time (sec) |
N/A | 8.038 | 1.562 | 0.183 | 0.000 | 0.000 | 0.000 | 2.341 | 10.708 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 471 | 477 | 575 | 274 | 0 | 23774 | 0 | 9152 | 36589 |
N.S. |
1 | 1.01 | 1.22 | 0.58 | 0.00 | 50.48 | 0.00 | 19.43 | 77.68 |
time (sec) |
N/A | 3.931 | 1.164 | 0.160 | 0.000 | 181.702 | 0.000 | 2.044 | 10.390 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 449 | 435 | 512 | 269 | 0 | 19375 | 0 | 8905 | 32587 |
N.S. |
1 | 0.97 | 1.14 | 0.60 | 0.00 | 43.15 | 0.00 | 19.83 | 72.58 |
time (sec) |
N/A | 0.949 | 1.012 | 0.148 | 0.000 | 151.256 | 0.000 | 1.895 | 11.165 |
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 | 460 | 462 | 529 | 550 | 0 | 23991 | 0 | 9167 | 40860 |
N.S. |
1 | 1.00 | 1.15 | 1.20 | 0.00 | 52.15 | 0.00 | 19.93 | 88.83 |
time (sec) |
N/A | 2.694 | 1.611 | 0.255 | 0.000 | 144.800 | 0.000 | 1.747 | 12.149 |
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 | 542 | 551 | 612 | 629 | 0 | 33432 | 0 | 10411 | 51386 |
N.S. |
1 | 1.02 | 1.13 | 1.16 | 0.00 | 61.68 | 0.00 | 19.21 | 94.81 |
time (sec) |
N/A | 3.946 | 1.362 | 0.272 | 0.000 | 297.365 | 0.000 | 1.799 | 12.571 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 21 | 31 | 31 | 54 | 58 | 31 |
N.S. |
1 | 1.00 | 1.00 | 1.05 | 1.55 | 1.55 | 2.70 | 2.90 | 1.55 |
time (sec) |
N/A | 0.195 | 0.449 | 0.273 | 0.239 | 0.248 | 158.450 | 0.346 | 8.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 210 | 234 | 149 | 145 | 295 | 138 | 367 | 228 | 287 |
N.S. |
1 | 1.11 | 0.71 | 0.69 | 1.40 | 0.66 | 1.75 | 1.09 | 1.37 |
time (sec) |
N/A | 0.459 | 0.362 | 0.461 | 0.284 | 0.263 | 19.879 | 0.372 | 8.419 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 159 | 186 | 116 | 109 | 217 | 104 | 367 | 164 | 215 |
N.S. |
1 | 1.17 | 0.73 | 0.69 | 1.36 | 0.65 | 2.31 | 1.03 | 1.35 |
time (sec) |
N/A | 0.404 | 0.271 | 0.423 | 0.281 | 0.261 | 11.903 | 0.324 | 8.289 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 109 | 139 | 80 | 73 | 139 | 71 | 350 | 102 | 143 |
N.S. |
1 | 1.28 | 0.73 | 0.67 | 1.28 | 0.65 | 3.21 | 0.94 | 1.31 |
time (sec) |
N/A | 0.333 | 0.196 | 0.435 | 0.284 | 0.274 | 7.520 | 0.337 | 8.359 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | C | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 93 | 107 | 106 | 143 | 105 | 80 | 304 | 189 | 161 |
N.S. |
1 | 1.15 | 1.14 | 1.54 | 1.13 | 0.86 | 3.27 | 2.03 | 1.73 |
time (sec) |
N/A | 0.368 | 0.260 | 0.442 | 0.313 | 0.268 | 18.143 | 0.440 | 9.754 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 99 | 149 | 85 | 137 | 123 | 98 | 0 | 374 | 422 |
N.S. |
1 | 1.51 | 0.86 | 1.38 | 1.24 | 0.99 | 0.00 | 3.78 | 4.26 |
time (sec) |
N/A | 0.371 | 0.278 | 0.434 | 0.278 | 0.275 | 0.000 | 0.462 | 10.856 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 126 | 180 | 102 | 143 | 193 | 102 | 0 | 767 | 932 |
N.S. |
1 | 1.43 | 0.81 | 1.13 | 1.53 | 0.81 | 0.00 | 6.09 | 7.40 |
time (sec) |
N/A | 0.393 | 0.304 | 0.444 | 0.290 | 0.268 | 0.000 | 0.607 | 15.498 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 212 | 226 | 141 | 179 | 271 | 137 | 0 | 1434 | 1621 |
N.S. |
1 | 1.07 | 0.67 | 0.84 | 1.28 | 0.65 | 0.00 | 6.76 | 7.65 |
time (sec) |
N/A | 0.422 | 0.390 | 0.441 | 0.279 | 0.273 | 0.000 | 0.770 | 24.813 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 216 | 192 | 134 | 161 | 226 | 134 | 0 | 177 | 1132 |
N.S. |
1 | 0.89 | 0.62 | 0.75 | 1.05 | 0.62 | 0.00 | 0.82 | 5.24 |
time (sec) |
N/A | 0.370 | 0.317 | 0.436 | 0.281 | 0.284 | 0.000 | 0.340 | 27.906 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 128 | 155 | 98 | 128 | 146 | 100 | 0 | 115 | 651 |
N.S. |
1 | 1.21 | 0.77 | 1.00 | 1.14 | 0.78 | 0.00 | 0.90 | 5.09 |
time (sec) |
N/A | 0.307 | 0.230 | 0.444 | 0.287 | 0.266 | 0.000 | 0.334 | 17.263 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 126 | 86 | 116 | 94 | 90 | 0 | 239 | 306 |
N.S. |
1 | 1.24 | 0.84 | 1.14 | 0.92 | 0.88 | 0.00 | 2.34 | 3.00 |
time (sec) |
N/A | 0.305 | 0.203 | 0.441 | 0.293 | 0.271 | 0.000 | 0.372 | 11.990 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 157 | 135 | 81 | 107 | 94 | 90 | 257 | 530 | 138 |
N.S. |
1 | 0.86 | 0.52 | 0.68 | 0.60 | 0.57 | 1.64 | 3.38 | 0.88 |
time (sec) |
N/A | 0.315 | 0.196 | 0.440 | 0.278 | 0.282 | 18.200 | 0.414 | 8.747 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 160 | 156 | 87 | 82 | 148 | 76 | 0 | 1055 | 146 |
N.S. |
1 | 0.98 | 0.54 | 0.51 | 0.92 | 0.48 | 0.00 | 6.59 | 0.91 |
time (sec) |
N/A | 0.326 | 0.166 | 0.447 | 0.279 | 0.269 | 0.000 | 0.528 | 8.491 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 226 | 193 | 124 | 118 | 226 | 110 | 0 | 1451 | 218 |
N.S. |
1 | 0.85 | 0.55 | 0.52 | 1.00 | 0.49 | 0.00 | 6.42 | 0.96 |
time (sec) |
N/A | 0.352 | 0.216 | 0.441 | 0.289 | 0.317 | 0.000 | 0.692 | 8.531 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 292 | 230 | 158 | 154 | 304 | 144 | 0 | 1847 | 290 |
N.S. |
1 | 0.79 | 0.54 | 0.53 | 1.04 | 0.49 | 0.00 | 6.33 | 0.99 |
time (sec) |
N/A | 0.382 | 0.257 | 0.441 | 0.280 | 0.352 | 0.000 | 0.936 | 8.564 |