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 | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 179 | 199 | 158 | 149 | 142 | 149 | 219 | 139 | 0 |
N.S. |
1 | 1.11 | 0.88 | 0.83 | 0.79 | 0.83 | 1.22 | 0.78 | 0.00 |
time (sec) |
N/A | 0.274 | 1.006 | 2.234 | 0.279 | 0.306 | 0.793 | 0.293 | 0.000 |
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 | 148 | 165 | 155 | 138 | 122 | 138 | 197 | 129 | 67 |
N.S. |
1 | 1.11 | 1.05 | 0.93 | 0.82 | 0.93 | 1.33 | 0.87 | 0.45 |
time (sec) |
N/A | 0.244 | 0.522 | 2.222 | 0.293 | 0.287 | 0.649 | 0.284 | 9.905 |
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 | 124 | 136 | 133 | 116 | 129 | 116 | 520 | 103 | 0 |
N.S. |
1 | 1.10 | 1.07 | 0.94 | 1.04 | 0.94 | 4.19 | 0.83 | 0.00 |
time (sec) |
N/A | 0.230 | 0.411 | 2.229 | 0.284 | 0.382 | 1.613 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 132 | 142 | 114 | 105 | 139 | 105 | 328 | 248 | 0 |
N.S. |
1 | 1.08 | 0.86 | 0.80 | 1.05 | 0.80 | 2.48 | 1.88 | 0.00 |
time (sec) |
N/A | 0.238 | 0.634 | 2.211 | 0.273 | 0.398 | 2.126 | 0.317 | 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 | 142 | 150 | 111 | 94 | 160 | 94 | 316 | 80 | 0 |
N.S. |
1 | 1.06 | 0.78 | 0.66 | 1.13 | 0.66 | 2.23 | 0.56 | 0.00 |
time (sec) |
N/A | 0.257 | 0.448 | 2.445 | 0.297 | 0.389 | 3.332 | 0.276 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 136 | 144 | 92 | 83 | 156 | 83 | 0 | 69 | 0 |
N.S. |
1 | 1.06 | 0.68 | 0.61 | 1.15 | 0.61 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.255 | 0.523 | 2.729 | 0.275 | 0.413 | 0.000 | 0.288 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 132 | 147 | 107 | 117 | 197 | 110 | 0 | 185 | 0 |
N.S. |
1 | 1.11 | 0.81 | 0.89 | 1.49 | 0.83 | 0.00 | 1.40 | 0.00 |
time (sec) |
N/A | 0.390 | 0.469 | 2.369 | 0.285 | 0.658 | 0.000 | 0.323 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 145 | 141 | 101 | 151 | 271 | 144 | 0 | 155 | 0 |
N.S. |
1 | 0.97 | 0.70 | 1.04 | 1.87 | 0.99 | 0.00 | 1.07 | 0.00 |
time (sec) |
N/A | 0.306 | 0.552 | 2.484 | 0.298 | 0.299 | 0.000 | 0.448 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 138 | 147 | 103 | 184 | 401 | 172 | 0 | 206 | 0 |
N.S. |
1 | 1.07 | 0.75 | 1.33 | 2.91 | 1.25 | 0.00 | 1.49 | 0.00 |
time (sec) |
N/A | 0.256 | 0.575 | 2.611 | 0.284 | 0.295 | 0.000 | 0.392 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 143 | 143 | 98 | 611 | 623 | 200 | 0 | 210 | 0 |
N.S. |
1 | 1.00 | 0.69 | 4.27 | 4.36 | 1.40 | 0.00 | 1.47 | 0.00 |
time (sec) |
N/A | 0.260 | 0.606 | 2.740 | 0.274 | 0.287 | 0.000 | 0.407 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 41 | 36 | 539 | 162 | 0 | 167 | 141 |
N.S. |
1 | 1.00 | 1.24 | 1.09 | 16.33 | 4.91 | 0.00 | 5.06 | 4.27 |
time (sec) |
N/A | 0.147 | 0.651 | 3.134 | 0.199 | 0.296 | 0.000 | 0.290 | 10.619 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 48 | 43 | 659 | 202 | 0 | 351 | 170 |
N.S. |
1 | 1.00 | 0.72 | 0.64 | 9.84 | 3.01 | 0.00 | 5.24 | 2.54 |
time (sec) |
N/A | 0.182 | 0.704 | 3.608 | 0.197 | 0.339 | 0.000 | 0.305 | 11.530 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 108 | 60 | 55 | 790 | 236 | 0 | 413 | 199 |
N.S. |
1 | 1.08 | 0.60 | 0.55 | 7.90 | 2.36 | 0.00 | 4.13 | 1.99 |
time (sec) |
N/A | 0.215 | 0.866 | 4.355 | 0.223 | 0.389 | 0.000 | 0.306 | 11.580 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 133 | 149 | 71 | 66 | 932 | 269 | 0 | 475 | 228 |
N.S. |
1 | 1.12 | 0.53 | 0.50 | 7.01 | 2.02 | 0.00 | 3.57 | 1.71 |
time (sec) |
N/A | 0.244 | 1.027 | 5.961 | 0.199 | 0.522 | 0.000 | 0.300 | 12.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 166 | 190 | 82 | 77 | 1085 | 302 | 0 | 537 | 257 |
N.S. |
1 | 1.14 | 0.49 | 0.46 | 6.54 | 1.82 | 0.00 | 3.23 | 1.55 |
time (sec) |
N/A | 0.295 | 1.120 | 7.424 | 0.209 | 0.703 | 0.000 | 0.302 | 12.647 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 64 | 50 | 32 | 50 | 0 | 37 | 0 |
N.S. |
1 | 1.00 | 1.36 | 1.06 | 0.68 | 1.06 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.170 | 0.215 | 2.384 | 0.287 | 0.281 | 0.000 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 130 | 135 | 116 | 181 | 113 | 238 | 148 | 101 | 0 |
N.S. |
1 | 1.04 | 0.89 | 1.39 | 0.87 | 1.83 | 1.14 | 0.78 | 0.00 |
time (sec) |
N/A | 0.233 | 0.420 | 2.384 | 0.189 | 0.277 | 0.513 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 167 | 175 | 127 | 197 | 144 | 260 | 160 | 113 | 0 |
N.S. |
1 | 1.05 | 0.76 | 1.18 | 0.86 | 1.56 | 0.96 | 0.68 | 0.00 |
time (sec) |
N/A | 0.284 | 0.421 | 2.365 | 0.192 | 0.276 | 0.576 | 0.296 | 0.000 |
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 | 44 | 44 | 42 | 32 | 36 | 34 | 48 | 34 | 32 |
N.S. |
1 | 1.00 | 0.95 | 0.73 | 0.82 | 0.77 | 1.09 | 0.77 | 0.73 |
time (sec) |
N/A | 0.155 | 0.118 | 2.246 | 0.191 | 0.252 | 0.089 | 0.270 | 9.824 |
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 | 38 | 38 | 46 | 29 | 28 | 40 | 39 | 25 | 25 |
N.S. |
1 | 1.00 | 1.21 | 0.76 | 0.74 | 1.05 | 1.03 | 0.66 | 0.66 |
time (sec) |
N/A | 0.156 | 0.135 | 2.244 | 0.277 | 0.264 | 0.080 | 0.261 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 32 | 18 | 12 | 28 | 15 | 12 | 12 |
N.S. |
1 | 1.00 | 2.29 | 1.29 | 0.86 | 2.00 | 1.07 | 0.86 | 0.86 |
time (sec) |
N/A | 0.146 | 0.116 | 2.296 | 0.282 | 0.260 | 1.042 | 0.266 | 0.125 |
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 | 38 | 38 | 46 | 29 | 28 | 40 | 39 | 25 | 25 |
N.S. |
1 | 1.00 | 1.21 | 0.76 | 0.74 | 1.05 | 1.03 | 0.66 | 0.66 |
time (sec) |
N/A | 0.162 | 0.122 | 2.284 | 0.274 | 0.260 | 0.084 | 0.271 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 34 | 19 | 14 | 30 | 17 | 14 | 14 |
N.S. |
1 | 1.00 | 2.12 | 1.19 | 0.88 | 1.88 | 1.06 | 0.88 | 0.88 |
time (sec) |
N/A | 0.144 | 0.112 | 2.474 | 0.276 | 0.274 | 1.171 | 0.274 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 39 | 20 | 21 | 41 | 0 | 0 | 21 |
N.S. |
1 | 1.00 | 1.56 | 0.80 | 0.84 | 1.64 | 0.00 | 0.00 | 0.84 |
time (sec) |
N/A | 0.151 | 0.185 | 2.808 | 0.284 | 0.280 | 0.000 | 0.000 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 25 | 20 | 38 | 33 | 0 | 41 | 19 |
N.S. |
1 | 1.00 | 1.14 | 0.91 | 1.73 | 1.50 | 0.00 | 1.86 | 0.86 |
time (sec) |
N/A | 0.138 | 0.233 | 2.235 | 0.195 | 0.272 | 0.000 | 0.284 | 9.408 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 182 | 189 | 103 | 94 | 135 | 94 | 153 | 79 | 0 |
N.S. |
1 | 1.04 | 0.57 | 0.52 | 0.74 | 0.52 | 0.84 | 0.43 | 0.00 |
time (sec) |
N/A | 0.284 | 0.597 | 2.396 | 0.269 | 0.286 | 0.587 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 149 | 153 | 92 | 83 | 110 | 83 | 139 | 68 | 0 |
N.S. |
1 | 1.03 | 0.62 | 0.56 | 0.74 | 0.56 | 0.93 | 0.46 | 0.00 |
time (sec) |
N/A | 0.258 | 0.558 | 2.351 | 0.285 | 0.275 | 0.555 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 116 | 117 | 83 | 72 | 85 | 72 | 126 | 56 | 0 |
N.S. |
1 | 1.01 | 0.72 | 0.62 | 0.73 | 0.62 | 1.09 | 0.48 | 0.00 |
time (sec) |
N/A | 0.225 | 0.411 | 2.483 | 0.277 | 0.278 | 0.523 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 81 | 69 | 60 | 62 | 60 | 112 | 45 | 0 |
N.S. |
1 | 1.09 | 0.93 | 0.81 | 0.84 | 0.81 | 1.51 | 0.61 | 0.00 |
time (sec) |
N/A | 0.198 | 0.335 | 2.283 | 0.275 | 0.270 | 0.490 | 0.296 | 0.000 |
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 | 47 | 47 | 57 | 50 | 41 | 50 | 94 | 37 | 54 |
N.S. |
1 | 1.00 | 1.21 | 1.06 | 0.87 | 1.06 | 2.00 | 0.79 | 1.15 |
time (sec) |
N/A | 0.174 | 0.190 | 2.160 | 0.268 | 0.287 | 0.392 | 0.295 | 9.963 |
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 | 31 | 31 | 31 | 29 | 30 | 35 | 0 | 41 | 29 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.97 | 1.13 | 0.00 | 1.32 | 0.94 |
time (sec) |
N/A | 0.152 | 0.202 | 2.222 | 0.280 | 0.279 | 0.000 | 0.283 | 9.667 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 41 | 37 | 74 | 70 | 0 | 74 | 36 |
N.S. |
1 | 1.00 | 0.61 | 0.55 | 1.10 | 1.04 | 0.00 | 1.10 | 0.54 |
time (sec) |
N/A | 0.190 | 0.330 | 2.378 | 0.276 | 0.261 | 0.000 | 0.286 | 9.535 |
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 | 100 | 108 | 52 | 49 | 128 | 104 | 0 | 165 | 48 |
N.S. |
1 | 1.08 | 0.52 | 0.49 | 1.28 | 1.04 | 0.00 | 1.65 | 0.48 |
time (sec) |
N/A | 0.211 | 0.458 | 2.658 | 0.284 | 0.374 | 0.000 | 0.291 | 9.513 |
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 | 133 | 149 | 63 | 60 | 193 | 137 | 0 | 227 | 117 |
N.S. |
1 | 1.12 | 0.47 | 0.45 | 1.45 | 1.03 | 0.00 | 1.71 | 0.88 |
time (sec) |
N/A | 0.237 | 0.494 | 2.352 | 0.278 | 0.355 | 0.000 | 0.291 | 9.561 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 166 | 190 | 74 | 71 | 269 | 170 | 0 | 121 | 146 |
N.S. |
1 | 1.14 | 0.45 | 0.43 | 1.62 | 1.02 | 0.00 | 0.73 | 0.88 |
time (sec) |
N/A | 0.269 | 0.593 | 2.273 | 0.274 | 0.409 | 0.000 | 0.288 | 9.773 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 143 | 139 | 100 | 156 | 209 | 143 | 0 | 155 | 0 |
N.S. |
1 | 0.97 | 0.70 | 1.09 | 1.46 | 1.00 | 0.00 | 1.08 | 0.00 |
time (sec) |
N/A | 0.306 | 0.622 | 2.335 | 0.288 | 0.374 | 0.000 | 0.299 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 108 | 109 | 94 | 145 | 180 | 128 | 0 | 142 | 0 |
N.S. |
1 | 1.01 | 0.87 | 1.34 | 1.67 | 1.19 | 0.00 | 1.31 | 0.00 |
time (sec) |
N/A | 0.225 | 0.488 | 2.341 | 0.287 | 0.484 | 0.000 | 0.301 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 74 | 281 | 152 | 112 | 0 | 86 | 0 |
N.S. |
1 | 1.00 | 0.91 | 3.47 | 1.88 | 1.38 | 0.00 | 1.06 | 0.00 |
time (sec) |
N/A | 0.195 | 0.452 | 2.323 | 0.281 | 0.355 | 0.000 | 0.300 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 39 | 36 | 80 | 63 | 0 | 74 | 35 |
N.S. |
1 | 1.00 | 1.18 | 1.09 | 2.42 | 1.91 | 0.00 | 2.24 | 1.06 |
time (sec) |
N/A | 0.157 | 0.355 | 2.341 | 0.192 | 0.274 | 0.000 | 0.288 | 9.700 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 42 | 39 | 58 | 71 | 0 | 103 | 38 |
N.S. |
1 | 1.00 | 0.79 | 0.74 | 1.09 | 1.34 | 0.00 | 1.94 | 0.72 |
time (sec) |
N/A | 0.162 | 0.325 | 2.316 | 0.193 | 0.274 | 0.000 | 0.297 | 9.805 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | C | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 58 | 53 | 60 | 102 | 296 | 0 | 54 |
N.S. |
1 | 1.00 | 1.04 | 0.95 | 1.07 | 1.82 | 5.29 | 0.00 | 0.96 |
time (sec) |
N/A | 0.163 | 0.317 | 2.311 | 0.190 | 0.286 | 3.659 | 0.000 | 9.806 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 90 | 82 | 70 | 85 | 168 | 0 | 0 | 78 |
N.S. |
1 | 1.10 | 1.00 | 0.85 | 1.04 | 2.05 | 0.00 | 0.00 | 0.95 |
time (sec) |
N/A | 0.187 | 0.448 | 2.644 | 0.192 | 0.300 | 0.000 | 0.000 | 10.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 131 | 93 | 88 | 156 | 203 | 0 | 242 | 139 |
N.S. |
1 | 1.14 | 0.81 | 0.77 | 1.36 | 1.77 | 0.00 | 2.10 | 1.21 |
time (sec) |
N/A | 0.222 | 0.520 | 2.390 | 0.196 | 0.293 | 0.000 | 0.317 | 9.886 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 148 | 172 | 104 | 99 | 252 | 234 | 0 | 0 | 168 |
N.S. |
1 | 1.16 | 0.70 | 0.67 | 1.70 | 1.58 | 0.00 | 0.00 | 1.14 |
time (sec) |
N/A | 0.250 | 0.596 | 2.350 | 0.198 | 0.350 | 0.000 | 0.000 | 10.197 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 181 | 213 | 115 | 110 | 373 | 269 | 0 | 0 | 197 |
N.S. |
1 | 1.18 | 0.64 | 0.61 | 2.06 | 1.49 | 0.00 | 0.00 | 1.09 |
time (sec) |
N/A | 0.282 | 0.747 | 2.354 | 0.201 | 0.438 | 0.000 | 0.000 | 10.212 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 206 | 213 | 131 | 216 | 383 | 201 | 0 | 234 | 0 |
N.S. |
1 | 1.03 | 0.64 | 1.05 | 1.86 | 0.98 | 0.00 | 1.14 | 0.00 |
time (sec) |
N/A | 0.456 | 0.659 | 2.597 | 0.378 | 0.305 | 0.000 | 0.313 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 173 | 174 | 111 | 204 | 358 | 190 | 0 | 223 | 0 |
N.S. |
1 | 1.01 | 0.64 | 1.18 | 2.07 | 1.10 | 0.00 | 1.29 | 0.00 |
time (sec) |
N/A | 0.346 | 0.657 | 2.502 | 0.331 | 0.313 | 0.000 | 0.329 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 138 | 144 | 105 | 192 | 327 | 175 | 0 | 205 | 0 |
N.S. |
1 | 1.04 | 0.76 | 1.39 | 2.37 | 1.27 | 0.00 | 1.49 | 0.00 |
time (sec) |
N/A | 0.254 | 0.580 | 2.499 | 0.314 | 0.285 | 0.000 | 0.299 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 112 | 86 | 580 | 299 | 159 | 0 | 180 | 0 |
N.S. |
1 | 1.00 | 0.77 | 5.18 | 2.67 | 1.42 | 0.00 | 1.61 | 0.00 |
time (sec) |
N/A | 0.226 | 0.559 | 2.558 | 0.301 | 0.285 | 0.000 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 41 | 36 | 148 | 100 | 0 | 105 | 37 |
N.S. |
1 | 1.00 | 1.24 | 1.09 | 4.48 | 3.03 | 0.00 | 3.18 | 1.12 |
time (sec) |
N/A | 0.150 | 0.444 | 2.545 | 0.252 | 0.289 | 0.000 | 0.303 | 10.449 |
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 | 67 | 67 | 53 | 44 | 123 | 104 | 0 | 165 | 49 |
N.S. |
1 | 1.00 | 0.79 | 0.66 | 1.84 | 1.55 | 0.00 | 2.46 | 0.73 |
time (sec) |
N/A | 0.175 | 0.432 | 2.847 | 0.199 | 0.277 | 0.000 | 0.292 | 10.040 |
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 | 103 | 111 | 53 | 50 | 101 | 106 | 0 | 165 | 49 |
N.S. |
1 | 1.08 | 0.51 | 0.49 | 0.98 | 1.03 | 0.00 | 1.60 | 0.48 |
time (sec) |
N/A | 0.222 | 0.458 | 2.563 | 0.205 | 0.267 | 0.000 | 0.297 | 9.868 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 82 | 70 | 65 | 78 | 116 | 0 | 0 | 66 |
N.S. |
1 | 1.06 | 0.91 | 0.84 | 1.01 | 1.51 | 0.00 | 0.00 | 0.86 |
time (sec) |
N/A | 0.194 | 0.439 | 2.460 | 0.213 | 0.292 | 0.000 | 0.000 | 10.247 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | C | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 88 | 82 | 77 | 80 | 171 | 604 | 0 | 78 |
N.S. |
1 | 1.10 | 1.02 | 0.96 | 1.00 | 2.14 | 7.55 | 0.00 | 0.98 |
time (sec) |
N/A | 0.196 | 0.418 | 2.212 | 0.197 | 0.299 | 7.234 | 0.000 | 9.868 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 106 | 122 | 104 | 92 | 105 | 236 | 0 | 0 | 155 |
N.S. |
1 | 1.15 | 0.98 | 0.87 | 0.99 | 2.23 | 0.00 | 0.00 | 1.46 |
time (sec) |
N/A | 0.213 | 0.512 | 2.358 | 0.226 | 0.532 | 0.000 | 0.000 | 9.750 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 139 | 163 | 115 | 110 | 176 | 248 | 0 | 294 | 184 |
N.S. |
1 | 1.17 | 0.83 | 0.79 | 1.27 | 1.78 | 0.00 | 2.12 | 1.32 |
time (sec) |
N/A | 0.239 | 0.633 | 2.455 | 0.197 | 0.593 | 0.000 | 0.322 | 9.951 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 172 | 204 | 126 | 121 | 272 | 259 | 0 | 0 | 213 |
N.S. |
1 | 1.19 | 0.73 | 0.70 | 1.58 | 1.51 | 0.00 | 0.00 | 1.24 |
time (sec) |
N/A | 0.266 | 0.685 | 2.503 | 0.222 | 0.845 | 0.000 | 0.000 | 10.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 205 | 245 | 137 | 132 | 393 | 314 | 0 | 0 | 242 |
N.S. |
1 | 1.20 | 0.67 | 0.64 | 1.92 | 1.53 | 0.00 | 0.00 | 1.18 |
time (sec) |
N/A | 0.299 | 0.931 | 2.476 | 0.203 | 1.219 | 0.000 | 0.000 | 10.340 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 238 | 286 | 148 | 143 | 539 | 369 | 0 | 402 | 271 |
N.S. |
1 | 1.20 | 0.62 | 0.60 | 2.26 | 1.55 | 0.00 | 1.69 | 1.14 |
time (sec) |
N/A | 0.350 | 0.908 | 2.540 | 0.209 | 1.030 | 0.000 | 0.337 | 10.313 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 34 | 15 | 14 | 30 | 10 | 14 | 14 |
N.S. |
1 | 1.00 | 2.12 | 0.94 | 0.88 | 1.88 | 0.62 | 0.88 | 0.88 |
time (sec) |
N/A | 0.145 | 0.122 | 2.684 | 0.267 | 0.281 | 0.061 | 0.291 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 32 | 13 | 12 | 28 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 2.29 | 0.93 | 0.86 | 2.00 | 0.71 | 0.86 | 0.86 |
time (sec) |
N/A | 0.141 | 0.102 | 2.217 | 0.269 | 0.269 | 0.061 | 0.279 | 0.104 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 160 | 166 | 75 | 65 | 82 | 78 | 0 | 390 | 103 |
N.S. |
1 | 1.04 | 0.47 | 0.41 | 0.51 | 0.49 | 0.00 | 2.44 | 0.64 |
time (sec) |
N/A | 0.264 | 0.172 | 2.415 | 0.206 | 0.293 | 0.000 | 0.296 | 9.916 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 122 | 64 | 54 | 68 | 67 | 0 | 232 | 85 |
N.S. |
1 | 1.03 | 0.54 | 0.45 | 0.57 | 0.56 | 0.00 | 1.95 | 0.71 |
time (sec) |
N/A | 0.228 | 0.155 | 2.332 | 0.203 | 0.282 | 0.000 | 0.301 | 9.577 |
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 | 78 | 78 | 53 | 43 | 54 | 56 | 0 | 109 | 69 |
N.S. |
1 | 1.00 | 0.68 | 0.55 | 0.69 | 0.72 | 0.00 | 1.40 | 0.88 |
time (sec) |
N/A | 0.186 | 0.131 | 2.360 | 0.208 | 0.278 | 0.000 | 0.283 | 10.012 |
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 | 38 | 40 | 35 | 26 | 44 | 0 | 37 | 35 |
N.S. |
1 | 1.00 | 1.05 | 0.92 | 0.68 | 1.16 | 0.00 | 0.97 | 0.92 |
time (sec) |
N/A | 0.155 | 0.108 | 2.474 | 0.199 | 0.379 | 0.000 | 0.277 | 9.810 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 99 | 99 | 98 | 89 | 0 | 237 | 0 | 111 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.90 | 0.00 | 2.39 | 0.00 | 1.12 | 0.00 |
time (sec) |
N/A | 0.214 | 0.273 | 2.488 | 0.000 | 0.421 | 0.000 | 0.297 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 101 | 117 | 0 | 292 | 0 | 68 | 0 |
N.S. |
1 | 1.00 | 1.03 | 1.19 | 0.00 | 2.98 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.210 | 0.374 | 2.389 | 0.000 | 0.401 | 0.000 | 0.295 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 141 | 150 | 113 | 176 | 0 | 356 | 0 | 101 | 0 |
N.S. |
1 | 1.06 | 0.80 | 1.25 | 0.00 | 2.52 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 0.244 | 0.423 | 2.546 | 0.000 | 0.493 | 0.000 | 0.301 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 201 | 210 | 84 | 77 | 110 | 107 | 0 | 822 | 116 |
N.S. |
1 | 1.04 | 0.42 | 0.38 | 0.55 | 0.53 | 0.00 | 4.09 | 0.58 |
time (sec) |
N/A | 0.290 | 0.458 | 2.936 | 0.209 | 0.331 | 0.000 | 0.315 | 10.252 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 160 | 166 | 73 | 66 | 96 | 95 | 0 | 468 | 128 |
N.S. |
1 | 1.04 | 0.46 | 0.41 | 0.60 | 0.59 | 0.00 | 2.92 | 0.80 |
time (sec) |
N/A | 0.256 | 0.419 | 2.431 | 0.200 | 0.270 | 0.000 | 0.296 | 10.531 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 122 | 62 | 55 | 82 | 83 | 0 | 393 | 109 |
N.S. |
1 | 1.03 | 0.52 | 0.46 | 0.69 | 0.70 | 0.00 | 3.30 | 0.92 |
time (sec) |
N/A | 0.221 | 0.374 | 2.490 | 0.209 | 0.264 | 0.000 | 0.291 | 10.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 51 | 44 | 55 | 71 | 0 | 163 | 60 |
N.S. |
1 | 1.00 | 0.65 | 0.56 | 0.71 | 0.91 | 0.00 | 2.09 | 0.77 |
time (sec) |
N/A | 0.189 | 0.365 | 2.677 | 0.200 | 0.290 | 0.000 | 0.276 | 9.946 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 43 | 36 | 39 | 57 | 0 | 113 | 48 |
N.S. |
1 | 1.00 | 1.13 | 0.95 | 1.03 | 1.50 | 0.00 | 2.97 | 1.26 |
time (sec) |
N/A | 0.157 | 0.358 | 2.468 | 0.196 | 0.323 | 0.000 | 0.283 | 9.898 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 136 | 139 | 110 | 112 | 0 | 269 | 0 | 146 | 0 |
N.S. |
1 | 1.02 | 0.81 | 0.82 | 0.00 | 1.98 | 0.00 | 1.07 | 0.00 |
time (sec) |
N/A | 0.251 | 0.623 | 2.587 | 0.000 | 0.274 | 0.000 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 133 | 138 | 107 | 142 | 0 | 309 | 0 | 92 | 0 |
N.S. |
1 | 1.04 | 0.80 | 1.07 | 0.00 | 2.32 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.242 | 0.678 | 2.397 | 0.000 | 0.286 | 0.000 | 0.298 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 139 | 139 | 109 | 176 | 0 | 367 | 0 | 101 | 0 |
N.S. |
1 | 1.00 | 0.78 | 1.27 | 0.00 | 2.64 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.238 | 0.752 | 2.347 | 0.000 | 0.397 | 0.000 | 0.316 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 178 | 191 | 151 | 241 | 0 | 444 | 0 | 144 | 0 |
N.S. |
1 | 1.07 | 0.85 | 1.35 | 0.00 | 2.49 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.279 | 0.795 | 2.364 | 0.000 | 0.448 | 0.000 | 0.324 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 217 | 240 | 153 | 303 | 0 | 518 | 0 | 181 | 0 |
N.S. |
1 | 1.11 | 0.71 | 1.40 | 0.00 | 2.39 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.331 | 0.857 | 2.782 | 0.000 | 0.399 | 0.000 | 0.335 | 0.000 |
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 | 160 | 166 | 67 | 62 | 57 | 69 | 0 | 137 | 98 |
N.S. |
1 | 1.04 | 0.42 | 0.39 | 0.36 | 0.43 | 0.00 | 0.86 | 0.61 |
time (sec) |
N/A | 0.251 | 0.194 | 2.253 | 0.212 | 0.370 | 0.000 | 0.290 | 9.990 |
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 | 119 | 122 | 56 | 51 | 58 | 58 | 0 | 100 | 79 |
N.S. |
1 | 1.03 | 0.47 | 0.43 | 0.49 | 0.49 | 0.00 | 0.84 | 0.66 |
time (sec) |
N/A | 0.203 | 0.180 | 2.303 | 0.214 | 0.316 | 0.000 | 0.281 | 10.237 |
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 | 78 | 78 | 44 | 39 | 34 | 46 | 0 | 60 | 61 |
N.S. |
1 | 1.00 | 0.56 | 0.50 | 0.44 | 0.59 | 0.00 | 0.77 | 0.78 |
time (sec) |
N/A | 0.176 | 0.156 | 2.399 | 0.202 | 0.292 | 0.000 | 0.276 | 10.037 |
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 | 36 | 36 | 35 | 32 | 29 | 39 | 0 | 38 | 32 |
N.S. |
1 | 1.00 | 0.97 | 0.89 | 0.81 | 1.08 | 0.00 | 1.06 | 0.89 |
time (sec) |
N/A | 0.150 | 0.126 | 2.279 | 0.226 | 0.266 | 0.000 | 0.276 | 9.920 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 86 | 68 | 0 | 169 | 0 | 66 | 0 |
N.S. |
1 | 1.00 | 1.32 | 1.05 | 0.00 | 2.60 | 0.00 | 1.02 | 0.00 |
time (sec) |
N/A | 0.177 | 0.182 | 2.341 | 0.000 | 0.285 | 0.000 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 109 | 109 | 122 | 123 | 0 | 300 | 0 | 77 | 0 |
N.S. |
1 | 1.00 | 1.12 | 1.13 | 0.00 | 2.75 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.206 | 0.315 | 2.280 | 0.000 | 0.339 | 0.000 | 0.326 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 150 | 158 | 135 | 181 | 0 | 368 | 0 | 106 | 0 |
N.S. |
1 | 1.05 | 0.90 | 1.21 | 0.00 | 2.45 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.243 | 0.364 | 2.356 | 0.000 | 0.282 | 0.000 | 0.317 | 0.000 |
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 | 160 | 162 | 66 | 66 | 45 | 77 | 0 | 141 | 104 |
N.S. |
1 | 1.01 | 0.41 | 0.41 | 0.28 | 0.48 | 0.00 | 0.88 | 0.65 |
time (sec) |
N/A | 0.258 | 0.590 | 2.404 | 0.208 | 0.285 | 0.000 | 0.285 | 10.283 |
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 | 119 | 118 | 55 | 55 | 43 | 66 | 0 | 102 | 86 |
N.S. |
1 | 0.99 | 0.46 | 0.46 | 0.36 | 0.55 | 0.00 | 0.86 | 0.72 |
time (sec) |
N/A | 0.221 | 0.516 | 2.724 | 0.198 | 0.408 | 0.000 | 0.287 | 9.869 |
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 | 74 | 74 | 43 | 44 | 23 | 55 | 0 | 67 | 66 |
N.S. |
1 | 1.00 | 0.58 | 0.59 | 0.31 | 0.74 | 0.00 | 0.91 | 0.89 |
time (sec) |
N/A | 0.191 | 0.474 | 2.469 | 0.207 | 0.374 | 0.000 | 0.288 | 9.898 |
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 | 36 | 36 | 35 | 36 | 16 | 48 | 0 | 40 | 50 |
N.S. |
1 | 1.00 | 0.97 | 1.00 | 0.44 | 1.33 | 0.00 | 1.11 | 1.39 |
time (sec) |
N/A | 0.165 | 0.430 | 2.227 | 0.201 | 0.361 | 0.000 | 0.276 | 9.921 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 104 | 124 | 91 | 0 | 284 | 0 | 124 | 0 |
N.S. |
1 | 1.00 | 1.19 | 0.88 | 0.00 | 2.73 | 0.00 | 1.19 | 0.00 |
time (sec) |
N/A | 0.214 | 0.600 | 2.239 | 0.000 | 0.387 | 0.000 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 150 | 153 | 125 | 141 | 0 | 382 | 0 | 111 | 0 |
N.S. |
1 | 1.02 | 0.83 | 0.94 | 0.00 | 2.55 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.247 | 0.750 | 2.222 | 0.000 | 0.521 | 0.000 | 0.318 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 191 | 202 | 138 | 202 | 0 | 412 | 0 | 129 | 0 |
N.S. |
1 | 1.06 | 0.72 | 1.06 | 0.00 | 2.16 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.291 | 0.891 | 2.226 | 0.000 | 0.298 | 0.000 | 0.307 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 32 | 39 | 0 | 30 | 0 | 36 | 0 |
N.S. |
1 | 1.00 | 1.03 | 1.26 | 0.00 | 0.97 | 0.00 | 1.16 | 0.00 |
time (sec) |
N/A | 0.152 | 0.109 | 2.235 | 0.000 | 0.287 | 0.000 | 0.273 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F(-1) | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 87 | 87 | 58 | 52 | 71 | 62 | 0 | 0 | 54 |
N.S. |
1 | 1.00 | 0.67 | 0.60 | 0.82 | 0.71 | 0.00 | 0.00 | 0.62 |
time (sec) |
N/A | 0.202 | 0.326 | 2.201 | 0.288 | 0.287 | 0.000 | 0.000 | 0.308 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 50 | 44 | 60 | 54 | 0 | 96 | 73 |
N.S. |
1 | 1.00 | 0.77 | 0.68 | 0.92 | 0.83 | 0.00 | 1.48 | 1.12 |
time (sec) |
N/A | 0.185 | 0.295 | 2.270 | 0.290 | 0.292 | 0.000 | 0.275 | 9.892 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | F | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 42 | 36 | 49 | 46 | 0 | 0 | 60 |
N.S. |
1 | 1.00 | 0.98 | 0.84 | 1.14 | 1.07 | 0.00 | 0.00 | 1.40 |
time (sec) |
N/A | 0.168 | 0.264 | 2.640 | 0.315 | 0.281 | 0.000 | 0.000 | 9.702 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 33 | 30 | 25 | 37 | 0 | 18 | 29 |
N.S. |
1 | 1.00 | 1.65 | 1.50 | 1.25 | 1.85 | 0.00 | 0.90 | 1.45 |
time (sec) |
N/A | 0.141 | 0.246 | 2.173 | 0.308 | 0.289 | 0.000 | 0.272 | 0.107 |
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 | 46 | 46 | 63 | 66 | 0 | 99 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.37 | 1.43 | 0.00 | 2.15 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.173 | 0.360 | 2.216 | 0.000 | 0.285 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 64 | 86 | 0 | 116 | 0 | 52 | 0 |
N.S. |
1 | 1.00 | 1.16 | 1.56 | 0.00 | 2.11 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 0.173 | 0.419 | 2.179 | 0.000 | 0.379 | 0.000 | 0.279 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 101 | 123 | 0 | 137 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.17 | 1.43 | 0.00 | 1.59 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.189 | 0.478 | 2.211 | 0.000 | 0.381 | 0.000 | 0.000 | 0.000 |