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 | B | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 73 | 49 | 0 | 114 | 0 | 101 | 0 |
N.S. |
1 | 1.00 | 2.03 | 1.36 | 0.00 | 3.17 | 0.00 | 2.81 | 0.00 |
time (sec) |
N/A | 0.091 | 0.418 | 1.766 | 0.000 | 0.266 | 0.000 | 0.345 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 115 | 125 | 112 | 0 | 238 | 0 | 210 | 0 |
N.S. |
1 | 1.11 | 1.20 | 1.08 | 0.00 | 2.29 | 0.00 | 2.02 | 0.00 |
time (sec) |
N/A | 0.174 | 0.979 | 2.322 | 0.000 | 0.284 | 0.000 | 0.341 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 107 | 115 | 146 | 145 | 0 | 299 | 0 | 297 | 0 |
N.S. |
1 | 1.07 | 1.36 | 1.36 | 0.00 | 2.79 | 0.00 | 2.78 | 0.00 |
time (sec) |
N/A | 0.176 | 0.771 | 2.197 | 0.000 | 0.269 | 0.000 | 0.357 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 113 | 122 | 160 | 191 | 0 | 362 | 0 | 320 | 0 |
N.S. |
1 | 1.08 | 1.42 | 1.69 | 0.00 | 3.20 | 0.00 | 2.83 | 0.00 |
time (sec) |
N/A | 0.175 | 0.962 | 2.712 | 0.000 | 0.270 | 0.000 | 0.386 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 142 | 156 | 271 | 245 | 0 | 440 | 0 | 386 | 0 |
N.S. |
1 | 1.10 | 1.91 | 1.73 | 0.00 | 3.10 | 0.00 | 2.72 | 0.00 |
time (sec) |
N/A | 0.196 | 1.096 | 3.247 | 0.000 | 0.276 | 0.000 | 0.408 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 175 | 190 | 335 | 299 | 0 | 523 | 0 | 327 | 0 |
N.S. |
1 | 1.09 | 1.91 | 1.71 | 0.00 | 2.99 | 0.00 | 1.87 | 0.00 |
time (sec) |
N/A | 0.214 | 1.396 | 3.030 | 0.000 | 0.274 | 0.000 | 0.455 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 133 | 145 | 73 | 81 | 0 | 265 | 0 | 243 | 0 |
N.S. |
1 | 1.09 | 0.55 | 0.61 | 0.00 | 1.99 | 0.00 | 1.83 | 0.00 |
time (sec) |
N/A | 0.244 | 2.472 | 38.374 | 0.000 | 0.261 | 0.000 | 0.387 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 109 | 93 | 71 | 0 | 234 | 0 | 210 | 0 |
N.S. |
1 | 1.09 | 0.93 | 0.71 | 0.00 | 2.34 | 0.00 | 2.10 | 0.00 |
time (sec) |
N/A | 0.190 | 4.185 | 37.120 | 0.000 | 0.256 | 0.000 | 0.423 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 73 | 49 | 61 | 0 | 179 | 0 | 136 | 0 |
N.S. |
1 | 1.12 | 0.75 | 0.94 | 0.00 | 2.75 | 0.00 | 2.09 | 0.00 |
time (sec) |
N/A | 0.139 | 1.268 | 2.178 | 0.000 | 0.266 | 0.000 | 0.377 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 36 | 70 | 49 | 0 | 141 | 0 | 131 | 0 |
N.S. |
1 | 1.09 | 2.12 | 1.48 | 0.00 | 4.27 | 0.00 | 3.97 | 0.00 |
time (sec) |
N/A | 0.090 | 0.444 | 2.082 | 0.000 | 0.279 | 0.000 | 0.373 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 151 | 153 | 129 | 0 | 265 | 0 | 290 | 0 |
N.S. |
1 | 1.10 | 1.12 | 0.94 | 0.00 | 1.93 | 0.00 | 2.12 | 0.00 |
time (sec) |
N/A | 0.225 | 0.737 | 2.410 | 0.000 | 0.285 | 0.000 | 0.333 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 150 | 170 | 189 | 0 | 326 | 0 | 358 | 0 |
N.S. |
1 | 1.09 | 1.24 | 1.38 | 0.00 | 2.38 | 0.00 | 2.61 | 0.00 |
time (sec) |
N/A | 0.229 | 0.816 | 2.895 | 0.000 | 0.294 | 0.000 | 0.371 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 145 | 157 | 184 | 239 | 0 | 388 | 0 | 381 | 0 |
N.S. |
1 | 1.08 | 1.27 | 1.65 | 0.00 | 2.68 | 0.00 | 2.63 | 0.00 |
time (sec) |
N/A | 0.233 | 0.801 | 3.432 | 0.000 | 0.280 | 0.000 | 0.406 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 143 | 157 | 271 | 245 | 0 | 440 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 1.90 | 1.71 | 0.00 | 3.08 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.226 | 1.038 | 3.509 | 0.000 | 0.265 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 176 | 191 | 335 | 299 | 0 | 523 | 0 | 513 | 0 |
N.S. |
1 | 1.09 | 1.90 | 1.70 | 0.00 | 2.97 | 0.00 | 2.91 | 0.00 |
time (sec) |
N/A | 0.265 | 1.335 | 3.830 | 0.000 | 0.289 | 0.000 | 0.448 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 207 | 225 | 399 | 353 | 0 | 600 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 1.93 | 1.71 | 0.00 | 2.90 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.281 | 2.221 | 4.194 | 0.000 | 0.292 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 120 | 132 | 109 | 69 | 238 | 74 | 0 | 325 | 0 |
N.S. |
1 | 1.10 | 0.91 | 0.58 | 1.98 | 0.62 | 0.00 | 2.71 | 0.00 |
time (sec) |
N/A | 0.239 | 7.462 | 1.707 | 0.343 | 0.260 | 0.000 | 0.364 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 98 | 99 | 59 | 192 | 58 | 0 | 225 | 0 |
N.S. |
1 | 1.10 | 1.11 | 0.66 | 2.16 | 0.65 | 0.00 | 2.53 | 0.00 |
time (sec) |
N/A | 0.204 | 6.468 | 1.601 | 0.318 | 0.267 | 0.000 | 0.347 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 58 | 60 | 87 | 49 | 146 | 41 | 0 | 64 | 90 |
N.S. |
1 | 1.03 | 1.50 | 0.84 | 2.52 | 0.71 | 0.00 | 1.10 | 1.55 |
time (sec) |
N/A | 0.149 | 0.983 | 0.555 | 0.345 | 0.262 | 0.000 | 0.321 | 7.465 |
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 | 28 | 29 | 28 | 39 | 76 | 29 | 0 | 62 | 40 |
N.S. |
1 | 1.04 | 1.00 | 1.39 | 2.71 | 1.04 | 0.00 | 2.21 | 1.43 |
time (sec) |
N/A | 0.096 | 0.467 | 0.559 | 0.335 | 0.251 | 0.000 | 0.307 | 0.226 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 83 | 96 | 86 | 0 | 154 | 0 | 125 | 0 |
N.S. |
1 | 1.01 | 1.17 | 1.05 | 0.00 | 1.88 | 0.00 | 1.52 | 0.00 |
time (sec) |
N/A | 0.123 | 1.216 | 0.908 | 0.000 | 0.285 | 0.000 | 0.334 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 117 | 122 | 134 | 0 | 207 | 0 | 289 | 0 |
N.S. |
1 | 1.06 | 1.11 | 1.22 | 0.00 | 1.88 | 0.00 | 2.63 | 0.00 |
time (sec) |
N/A | 0.140 | 1.604 | 0.927 | 0.000 | 0.288 | 0.000 | 0.331 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 144 | 156 | 159 | 210 | 0 | 241 | 0 | 375 | 0 |
N.S. |
1 | 1.08 | 1.10 | 1.46 | 0.00 | 1.67 | 0.00 | 2.60 | 0.00 |
time (sec) |
N/A | 0.193 | 1.951 | 0.915 | 0.000 | 0.270 | 0.000 | 0.395 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 161 | 176 | 121 | 91 | 380 | 104 | 0 | 426 | 0 |
N.S. |
1 | 1.09 | 0.75 | 0.57 | 2.36 | 0.65 | 0.00 | 2.65 | 0.00 |
time (sec) |
N/A | 0.297 | 8.879 | 20.086 | 0.338 | 0.269 | 0.000 | 0.409 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 128 | 136 | 109 | 79 | 334 | 91 | 0 | 119 | 0 |
N.S. |
1 | 1.06 | 0.85 | 0.62 | 2.61 | 0.71 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.251 | 6.592 | 19.949 | 0.326 | 0.393 | 0.000 | 0.345 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 95 | 100 | 101 | 71 | 288 | 76 | 0 | 225 | 360 |
N.S. |
1 | 1.05 | 1.06 | 0.75 | 3.03 | 0.80 | 0.00 | 2.37 | 3.79 |
time (sec) |
N/A | 0.200 | 1.487 | 19.856 | 0.329 | 0.266 | 0.000 | 0.404 | 11.991 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 64 | 68 | 89 | 61 | 239 | 57 | 0 | 111 | 120 |
N.S. |
1 | 1.06 | 1.39 | 0.95 | 3.73 | 0.89 | 0.00 | 1.73 | 1.88 |
time (sec) |
N/A | 0.152 | 1.069 | 0.522 | 0.317 | 0.288 | 0.000 | 0.380 | 10.496 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 36 | 70 | 49 | 149 | 46 | 0 | 110 | 227 |
N.S. |
1 | 1.09 | 2.12 | 1.48 | 4.52 | 1.39 | 0.00 | 3.33 | 6.88 |
time (sec) |
N/A | 0.092 | 0.497 | 0.571 | 0.395 | 0.256 | 0.000 | 0.316 | 9.348 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 124 | 106 | 109 | 0 | 204 | 0 | 201 | 0 |
N.S. |
1 | 1.08 | 0.92 | 0.95 | 0.00 | 1.77 | 0.00 | 1.75 | 0.00 |
time (sec) |
N/A | 0.168 | 1.446 | 0.913 | 0.000 | 0.276 | 0.000 | 0.377 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 143 | 155 | 161 | 157 | 0 | 186 | 0 | 350 | 0 |
N.S. |
1 | 1.08 | 1.13 | 1.10 | 0.00 | 1.30 | 0.00 | 2.45 | 0.00 |
time (sec) |
N/A | 0.192 | 1.920 | 0.861 | 0.000 | 0.264 | 0.000 | 0.499 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 177 | 192 | 153 | 233 | 0 | 241 | 0 | 457 | 0 |
N.S. |
1 | 1.08 | 0.86 | 1.32 | 0.00 | 1.36 | 0.00 | 2.58 | 0.00 |
time (sec) |
N/A | 0.246 | 2.437 | 0.796 | 0.000 | 0.271 | 0.000 | 0.364 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 161 | 174 | 121 | 91 | 472 | 119 | 0 | 426 | 0 |
N.S. |
1 | 1.08 | 0.75 | 0.57 | 2.93 | 0.74 | 0.00 | 2.65 | 0.00 |
time (sec) |
N/A | 0.298 | 8.234 | 179.742 | 0.300 | 0.272 | 0.000 | 0.393 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 128 | 134 | 111 | 81 | 426 | 106 | 0 | 325 | 542 |
N.S. |
1 | 1.05 | 0.87 | 0.63 | 3.33 | 0.83 | 0.00 | 2.54 | 4.23 |
time (sec) |
N/A | 0.262 | 2.160 | 182.349 | 0.296 | 0.275 | 0.000 | 0.380 | 16.695 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 104 | 101 | 71 | 380 | 91 | 0 | 165 | 453 |
N.S. |
1 | 1.07 | 1.04 | 0.73 | 3.92 | 0.94 | 0.00 | 1.70 | 4.67 |
time (sec) |
N/A | 0.193 | 1.766 | 180.855 | 0.295 | 0.266 | 0.000 | 0.352 | 11.845 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 73 | 89 | 61 | 331 | 74 | 0 | 207 | 355 |
N.S. |
1 | 1.09 | 1.33 | 0.91 | 4.94 | 1.10 | 0.00 | 3.09 | 5.30 |
time (sec) |
N/A | 0.143 | 1.239 | 0.758 | 0.294 | 0.256 | 0.000 | 0.322 | 10.375 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 36 | 70 | 49 | 218 | 61 | 0 | 157 | 90 |
N.S. |
1 | 1.09 | 2.12 | 1.48 | 6.61 | 1.85 | 0.00 | 4.76 | 2.73 |
time (sec) |
N/A | 0.088 | 0.658 | 0.633 | 0.293 | 0.251 | 0.000 | 0.325 | 9.660 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 148 | 160 | 186 | 122 | 0 | 241 | 0 | 278 | 0 |
N.S. |
1 | 1.08 | 1.26 | 0.82 | 0.00 | 1.63 | 0.00 | 1.88 | 0.00 |
time (sec) |
N/A | 0.221 | 1.617 | 0.912 | 0.000 | 0.276 | 0.000 | 0.399 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-1) | A | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 176 | 191 | 171 | 170 | 0 | 238 | 0 | 424 | 0 |
N.S. |
1 | 1.09 | 0.97 | 0.97 | 0.00 | 1.35 | 0.00 | 2.41 | 0.00 |
time (sec) |
N/A | 0.240 | 2.505 | 1.144 | 0.000 | 0.282 | 0.000 | 0.392 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-1) | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 210 | 228 | 440 | 246 | 0 | 208 | 0 | 531 | 0 |
N.S. |
1 | 1.09 | 2.10 | 1.17 | 0.00 | 0.99 | 0.00 | 2.53 | 0.00 |
time (sec) |
N/A | 0.288 | 3.355 | 1.016 | 0.000 | 0.283 | 0.000 | 0.423 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 43 | 86 | 81 | 0 | 95 | 0 | 51 | 99 |
N.S. |
1 | 1.02 | 2.05 | 1.93 | 0.00 | 2.26 | 0.00 | 1.21 | 2.36 |
time (sec) |
N/A | 0.061 | 1.164 | 3.066 | 0.000 | 0.278 | 0.000 | 0.358 | 8.163 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 43 | 77 | 72 | 0 | 83 | 0 | 51 | 88 |
N.S. |
1 | 1.08 | 1.92 | 1.80 | 0.00 | 2.08 | 0.00 | 1.28 | 2.20 |
time (sec) |
N/A | 0.063 | 0.897 | 3.050 | 0.000 | 0.285 | 0.000 | 0.344 | 7.596 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 43 | 63 | 55 | 0 | 61 | 0 | 51 | 71 |
N.S. |
1 | 1.02 | 1.50 | 1.31 | 0.00 | 1.45 | 0.00 | 1.21 | 1.69 |
time (sec) |
N/A | 0.062 | 0.714 | 2.807 | 0.000 | 0.275 | 0.000 | 0.325 | 0.945 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 41 | 82 | 36 | 0 | 43 | 0 | 51 | 47 |
N.S. |
1 | 1.02 | 2.05 | 0.90 | 0.00 | 1.08 | 0.00 | 1.28 | 1.18 |
time (sec) |
N/A | 0.055 | 0.064 | 3.262 | 0.000 | 0.269 | 0.000 | 0.302 | 6.759 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 52 | 117 | 96 | 63 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.02 | 2.29 | 1.88 | 1.24 | 0.00 | 0.00 | 1.04 | 0.00 |
time (sec) |
N/A | 0.076 | 1.025 | 2.199 | 0.288 | 0.000 | 0.000 | 0.443 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 87 | 39 | 0 | 59 | 0 | 53 | 0 |
N.S. |
1 | 1.00 | 2.18 | 0.98 | 0.00 | 1.48 | 0.00 | 1.32 | 0.00 |
time (sec) |
N/A | 0.065 | 0.716 | 3.213 | 0.000 | 0.248 | 0.000 | 0.308 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 43 | 90 | 67 | 0 | 73 | 0 | 53 | 142 |
N.S. |
1 | 1.02 | 2.14 | 1.60 | 0.00 | 1.74 | 0.00 | 1.26 | 3.38 |
time (sec) |
N/A | 0.066 | 0.802 | 2.474 | 0.000 | 0.268 | 0.000 | 0.330 | 8.966 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 43 | 87 | 92 | 0 | 90 | 0 | 53 | 190 |
N.S. |
1 | 1.10 | 2.23 | 2.36 | 0.00 | 2.31 | 0.00 | 1.36 | 4.87 |
time (sec) |
N/A | 0.063 | 1.283 | 3.639 | 0.000 | 0.262 | 0.000 | 0.343 | 11.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 89 | 149 | 92 | 0 | 101 | 0 | 104 | 111 |
N.S. |
1 | 1.05 | 1.75 | 1.08 | 0.00 | 1.19 | 0.00 | 1.22 | 1.31 |
time (sec) |
N/A | 0.133 | 3.850 | 2.827 | 0.000 | 0.291 | 0.000 | 0.363 | 8.647 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 89 | 140 | 76 | 0 | 87 | 0 | 104 | 100 |
N.S. |
1 | 1.05 | 1.65 | 0.89 | 0.00 | 1.02 | 0.00 | 1.22 | 1.18 |
time (sec) |
N/A | 0.132 | 2.950 | 2.933 | 0.000 | 0.269 | 0.000 | 0.377 | 8.425 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 81 | 89 | 69 | 49 | 0 | 60 | 0 | 100 | 66 |
N.S. |
1 | 1.10 | 0.85 | 0.60 | 0.00 | 0.74 | 0.00 | 1.23 | 0.81 |
time (sec) |
N/A | 0.139 | 0.684 | 2.983 | 0.000 | 0.266 | 0.000 | 0.335 | 0.958 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 62 | 55 | 0 | 61 | 0 | 51 | 71 |
N.S. |
1 | 1.00 | 1.44 | 1.28 | 0.00 | 1.42 | 0.00 | 1.19 | 1.65 |
time (sec) |
N/A | 0.064 | 5.529 | 2.901 | 0.000 | 0.297 | 0.000 | 0.336 | 7.116 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 96 | 116 | 203 | 0 | 0 | 0 | 96 | 0 |
N.S. |
1 | 1.04 | 1.26 | 2.21 | 0.00 | 0.00 | 0.00 | 1.04 | 0.00 |
time (sec) |
N/A | 0.152 | 1.626 | 2.654 | 0.000 | 0.000 | 0.000 | 0.333 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 95 | 97 | 155 | 128 | 137 | 0 | 0 | 110 | 0 |
N.S. |
1 | 1.02 | 1.63 | 1.35 | 1.44 | 0.00 | 0.00 | 1.16 | 0.00 |
time (sec) |
N/A | 0.168 | 6.143 | 3.250 | 0.292 | 0.000 | 0.000 | 0.372 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 102 | 51 | 0 | 80 | 0 | 87 | 0 |
N.S. |
1 | 1.00 | 2.43 | 1.21 | 0.00 | 1.90 | 0.00 | 2.07 | 0.00 |
time (sec) |
N/A | 0.070 | 2.431 | 3.068 | 0.000 | 0.278 | 0.000 | 0.340 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 108 | 93 | 0 | 101 | 0 | 93 | 124 |
N.S. |
1 | 1.00 | 1.23 | 1.06 | 0.00 | 1.15 | 0.00 | 1.06 | 1.41 |
time (sec) |
N/A | 0.140 | 1.583 | 3.138 | 0.000 | 0.269 | 0.000 | 0.331 | 10.658 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 92 | 108 | 119 | 0 | 114 | 0 | 87 | 195 |
N.S. |
1 | 1.05 | 1.23 | 1.35 | 0.00 | 1.30 | 0.00 | 0.99 | 2.22 |
time (sec) |
N/A | 0.136 | 2.117 | 3.116 | 0.000 | 0.277 | 0.000 | 0.338 | 11.909 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 92 | 108 | 146 | 0 | 131 | 0 | 93 | 225 |
N.S. |
1 | 1.05 | 1.23 | 1.66 | 0.00 | 1.49 | 0.00 | 1.06 | 2.56 |
time (sec) |
N/A | 0.135 | 3.109 | 3.265 | 0.000 | 0.276 | 0.000 | 0.338 | 13.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 134 | 159 | 94 | 0 | 112 | 0 | 156 | 124 |
N.S. |
1 | 1.06 | 1.25 | 0.74 | 0.00 | 0.88 | 0.00 | 1.23 | 0.98 |
time (sec) |
N/A | 0.197 | 4.792 | 4.670 | 0.000 | 0.285 | 0.000 | 0.354 | 10.591 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 134 | 88 | 65 | 0 | 85 | 0 | 156 | 83 |
N.S. |
1 | 1.06 | 0.69 | 0.51 | 0.00 | 0.67 | 0.00 | 1.23 | 0.65 |
time (sec) |
N/A | 0.205 | 0.930 | 4.645 | 0.000 | 0.267 | 0.000 | 0.342 | 1.609 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 136 | 76 | 0 | 87 | 0 | 150 | 100 |
N.S. |
1 | 1.00 | 1.53 | 0.85 | 0.00 | 0.98 | 0.00 | 1.69 | 1.12 |
time (sec) |
N/A | 0.129 | 2.759 | 2.941 | 0.000 | 0.273 | 0.000 | 0.330 | 8.362 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 72 | 72 | 0 | 82 | 0 | 51 | 86 |
N.S. |
1 | 1.00 | 1.67 | 1.67 | 0.00 | 1.91 | 0.00 | 1.19 | 2.00 |
time (sec) |
N/A | 0.063 | 5.599 | 3.285 | 0.000 | 0.261 | 0.000 | 0.309 | 7.479 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 134 | 141 | 130 | 241 | 0 | 0 | 0 | 128 | 0 |
N.S. |
1 | 1.05 | 0.97 | 1.80 | 0.00 | 0.00 | 0.00 | 0.96 | 0.00 |
time (sec) |
N/A | 0.226 | 11.946 | 3.138 | 0.000 | 0.000 | 0.000 | 0.329 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 138 | 144 | 169 | 140 | 0 | 0 | 0 | 135 | 0 |
N.S. |
1 | 1.04 | 1.22 | 1.01 | 0.00 | 0.00 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 0.234 | 6.846 | 3.016 | 0.000 | 0.000 | 0.000 | 0.364 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 140 | 147 | 191 | 195 | 184 | 0 | 0 | 125 | 0 |
N.S. |
1 | 1.05 | 1.36 | 1.39 | 1.31 | 0.00 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.238 | 6.630 | 3.033 | 0.327 | 0.000 | 0.000 | 0.347 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 110 | 73 | 0 | 109 | 0 | 131 | 0 |
N.S. |
1 | 1.00 | 2.62 | 1.74 | 0.00 | 2.60 | 0.00 | 3.12 | 0.00 |
time (sec) |
N/A | 0.071 | 12.740 | 3.023 | 0.000 | 0.266 | 0.000 | 0.316 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 118 | 121 | 0 | 133 | 0 | 123 | 242 |
N.S. |
1 | 1.00 | 1.34 | 1.38 | 0.00 | 1.51 | 0.00 | 1.40 | 2.75 |
time (sec) |
N/A | 0.146 | 3.952 | 3.263 | 0.000 | 0.283 | 0.000 | 0.331 | 11.662 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 133 | 133 | 118 | 148 | 0 | 148 | 0 | 132 | 273 |
N.S. |
1 | 1.00 | 0.89 | 1.11 | 0.00 | 1.11 | 0.00 | 0.99 | 2.05 |
time (sec) |
N/A | 0.214 | 5.674 | 3.036 | 0.000 | 0.281 | 0.000 | 0.323 | 12.450 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 133 | 140 | 118 | 175 | 0 | 162 | 0 | 123 | 287 |
N.S. |
1 | 1.05 | 0.89 | 1.32 | 0.00 | 1.22 | 0.00 | 0.92 | 2.16 |
time (sec) |
N/A | 0.203 | 8.534 | 3.403 | 0.000 | 0.281 | 0.000 | 0.361 | 13.227 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 169 | 179 | 179 | 110 | 0 | 128 | 0 | 204 | 376 |
N.S. |
1 | 1.06 | 1.06 | 0.65 | 0.00 | 0.76 | 0.00 | 1.21 | 2.22 |
time (sec) |
N/A | 0.253 | 8.952 | 4.646 | 0.000 | 0.279 | 0.000 | 0.336 | 11.494 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 169 | 179 | 98 | 75 | 0 | 101 | 0 | 204 | 179 |
N.S. |
1 | 1.06 | 0.58 | 0.44 | 0.00 | 0.60 | 0.00 | 1.21 | 1.06 |
time (sec) |
N/A | 0.261 | 1.483 | 4.845 | 0.000 | 0.288 | 0.000 | 0.328 | 11.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 134 | 134 | 159 | 94 | 0 | 112 | 0 | 204 | 124 |
N.S. |
1 | 1.00 | 1.19 | 0.70 | 0.00 | 0.84 | 0.00 | 1.52 | 0.93 |
time (sec) |
N/A | 0.209 | 4.539 | 4.092 | 0.000 | 0.282 | 0.000 | 0.411 | 10.948 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 145 | 92 | 0 | 101 | 0 | 104 | 109 |
N.S. |
1 | 1.00 | 1.63 | 1.03 | 0.00 | 1.13 | 0.00 | 1.17 | 1.22 |
time (sec) |
N/A | 0.129 | 3.521 | 2.824 | 0.000 | 0.262 | 0.000 | 0.337 | 2.656 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 82 | 81 | 0 | 95 | 0 | 51 | 99 |
N.S. |
1 | 1.00 | 1.91 | 1.88 | 0.00 | 2.21 | 0.00 | 1.19 | 2.30 |
time (sec) |
N/A | 0.063 | 5.629 | 3.096 | 0.000 | 0.272 | 0.000 | 0.307 | 8.617 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 172 | 184 | 140 | 270 | 0 | 0 | 0 | 141 | 0 |
N.S. |
1 | 1.07 | 0.81 | 1.57 | 0.00 | 0.00 | 0.00 | 0.82 | 0.00 |
time (sec) |
N/A | 0.281 | 6.806 | 2.722 | 0.000 | 0.000 | 0.000 | 0.334 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 183 | 192 | 179 | 158 | 0 | 0 | 0 | 170 | 0 |
N.S. |
1 | 1.05 | 0.98 | 0.86 | 0.00 | 0.00 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.283 | 7.888 | 2.615 | 0.000 | 0.000 | 0.000 | 0.344 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 185 | 195 | 207 | 218 | 0 | 0 | 0 | 153 | 0 |
N.S. |
1 | 1.05 | 1.12 | 1.18 | 0.00 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.303 | 8.656 | 3.279 | 0.000 | 0.000 | 0.000 | 0.327 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 182 | 193 | 232 | 291 | 336 | 0 | 0 | 145 | 0 |
N.S. |
1 | 1.06 | 1.27 | 1.60 | 1.85 | 0.00 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.297 | 8.421 | 2.947 | 0.303 | 0.000 | 0.000 | 0.328 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 115 | 90 | 0 | 127 | 0 | 155 | 0 |
N.S. |
1 | 1.00 | 2.74 | 2.14 | 0.00 | 3.02 | 0.00 | 3.69 | 0.00 |
time (sec) |
N/A | 0.068 | 16.034 | 3.467 | 0.000 | 0.284 | 0.000 | 0.337 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 331 | 147 | 0 | 163 | 0 | 167 | 317 |
N.S. |
1 | 1.00 | 3.76 | 1.67 | 0.00 | 1.85 | 0.00 | 1.90 | 3.60 |
time (sec) |
N/A | 0.142 | 8.398 | 3.128 | 0.000 | 0.283 | 0.000 | 0.353 | 12.714 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 133 | 133 | 335 | 175 | 0 | 178 | 0 | 155 | 330 |
N.S. |
1 | 1.00 | 2.52 | 1.32 | 0.00 | 1.34 | 0.00 | 1.17 | 2.48 |
time (sec) |
N/A | 0.221 | 9.071 | 3.323 | 0.000 | 0.281 | 0.000 | 0.364 | 13.315 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 178 | 178 | 333 | 200 | 0 | 192 | 0 | 167 | 647 |
N.S. |
1 | 1.00 | 1.87 | 1.12 | 0.00 | 1.08 | 0.00 | 0.94 | 3.63 |
time (sec) |
N/A | 0.291 | 10.331 | 3.447 | 0.000 | 0.311 | 0.000 | 0.359 | 14.651 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 178 | 188 | 329 | 227 | 0 | 204 | 0 | 155 | 673 |
N.S. |
1 | 1.06 | 1.85 | 1.28 | 0.00 | 1.15 | 0.00 | 0.87 | 3.78 |
time (sec) |
N/A | 0.289 | 11.150 | 3.569 | 0.000 | 0.304 | 0.000 | 0.346 | 15.332 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 139 | 139 | 139 | 243 | 0 | 0 | 0 | 128 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.75 | 0.00 | 0.00 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 0.210 | 12.224 | 3.141 | 0.000 | 0.000 | 0.000 | 0.335 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 122 | 207 | 0 | 0 | 0 | 96 | 0 |
N.S. |
1 | 1.00 | 1.31 | 2.23 | 0.00 | 0.00 | 0.00 | 1.03 | 0.00 |
time (sec) |
N/A | 0.143 | 1.683 | 3.384 | 0.000 | 0.000 | 0.000 | 0.334 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 119 | 95 | 64 | 0 | 0 | 219 | 0 |
N.S. |
1 | 1.00 | 2.43 | 1.94 | 1.31 | 0.00 | 0.00 | 4.47 | 0.00 |
time (sec) |
N/A | 0.084 | 1.192 | 2.283 | 0.297 | 0.000 | 0.000 | 0.365 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 112 | 74 | 0 | 160 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.43 | 1.61 | 0.00 | 3.48 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.064 | 0.393 | 4.793 | 0.000 | 0.302 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 95 | 95 | 158 | 247 | 0 | 311 | 0 | 172 | 0 |
N.S. |
1 | 1.00 | 1.66 | 2.60 | 0.00 | 3.27 | 0.00 | 1.81 | 0.00 |
time (sec) |
N/A | 0.140 | 0.891 | 3.299 | 0.000 | 0.345 | 0.000 | 0.317 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 140 | 140 | 213 | 424 | 0 | 376 | 0 | 184 | 0 |
N.S. |
1 | 1.00 | 1.52 | 3.03 | 0.00 | 2.69 | 0.00 | 1.31 | 0.00 |
time (sec) |
N/A | 0.217 | 0.793 | 2.970 | 0.000 | 0.334 | 0.000 | 0.343 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 182 | 191 | 165 | 158 | 0 | 0 | 0 | 170 | 0 |
N.S. |
1 | 1.05 | 0.91 | 0.87 | 0.00 | 0.00 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.304 | 7.705 | 2.878 | 0.000 | 0.000 | 0.000 | 0.334 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 141 | 143 | 156 | 141 | 0 | 0 | 0 | 131 | 0 |
N.S. |
1 | 1.01 | 1.11 | 1.00 | 0.00 | 0.00 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.210 | 6.662 | 3.214 | 0.000 | 0.000 | 0.000 | 0.602 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 96 | 97 | 139 | 130 | 136 | 0 | 0 | 110 | 0 |
N.S. |
1 | 1.01 | 1.45 | 1.35 | 1.42 | 0.00 | 0.00 | 1.15 | 0.00 |
time (sec) |
N/A | 0.147 | 1.232 | 2.815 | 0.296 | 0.000 | 0.000 | 0.514 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 87 | 39 | 0 | 58 | 0 | 53 | 52 |
N.S. |
1 | 1.00 | 2.12 | 0.95 | 0.00 | 1.41 | 0.00 | 1.29 | 1.27 |
time (sec) |
N/A | 0.066 | 1.016 | 2.847 | 0.000 | 0.282 | 0.000 | 0.507 | 7.834 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 95 | 145 | 242 | 0 | 305 | 0 | 165 | 0 |
N.S. |
1 | 1.03 | 1.58 | 2.63 | 0.00 | 3.32 | 0.00 | 1.79 | 0.00 |
time (sec) |
N/A | 0.134 | 0.762 | 3.041 | 0.000 | 0.314 | 0.000 | 0.734 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 143 | 175 | 95 | 0 | 262 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.28 | 0.69 | 0.00 | 1.91 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.221 | 0.795 | 3.238 | 0.000 | 0.313 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 182 | 191 | 274 | 202 | 0 | 377 | 0 | 218 | 0 |
N.S. |
1 | 1.05 | 1.51 | 1.11 | 0.00 | 2.07 | 0.00 | 1.20 | 0.00 |
time (sec) |
N/A | 0.308 | 1.155 | 2.890 | 0.000 | 0.334 | 0.000 | 0.361 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 233 | 237 | 205 | 227 | 0 | 0 | 0 | 188 | 0 |
N.S. |
1 | 1.02 | 0.88 | 0.97 | 0.00 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.371 | 11.133 | 2.896 | 0.000 | 0.000 | 0.000 | 0.329 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 188 | 193 | 190 | 217 | 0 | 0 | 0 | 154 | 0 |
N.S. |
1 | 1.03 | 1.01 | 1.15 | 0.00 | 0.00 | 0.00 | 0.82 | 0.00 |
time (sec) |
N/A | 0.302 | 7.663 | 2.992 | 0.000 | 0.000 | 0.000 | 0.324 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 143 | 143 | 178 | 193 | 183 | 0 | 0 | 129 | 0 |
N.S. |
1 | 1.00 | 1.24 | 1.35 | 1.28 | 0.00 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.214 | 1.791 | 3.214 | 0.293 | 0.000 | 0.000 | 0.324 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 92 | 50 | 0 | 80 | 0 | 93 | 118 |
N.S. |
1 | 1.00 | 2.19 | 1.19 | 0.00 | 1.90 | 0.00 | 2.21 | 2.81 |
time (sec) |
N/A | 0.067 | 1.195 | 3.141 | 0.000 | 0.278 | 0.000 | 0.540 | 8.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 87 | 67 | 0 | 73 | 0 | 53 | 103 |
N.S. |
1 | 1.00 | 2.02 | 1.56 | 0.00 | 1.70 | 0.00 | 1.23 | 2.40 |
time (sec) |
N/A | 0.065 | 1.072 | 2.743 | 0.000 | 0.262 | 0.000 | 0.501 | 7.336 |