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 | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 324 | 344 | 235 | 938 | 0 | 1067 | 0 | 395 | 39 | 0 |
N.S. |
1 | 1.06 | 0.73 | 2.90 | 0.00 | 3.29 | 0.00 | 1.22 | 0.12 | 0.00 |
time (sec) |
N/A | 1.238 | 1.446 | 0.362 | 0.000 | 0.133 | 0.000 | 0.139 | 200.036 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 386 | 391 | 268 | 1146 | 0 | 1259 | 0 | 494 | 929 | 0 |
N.S. |
1 | 1.01 | 0.69 | 2.97 | 0.00 | 3.26 | 0.00 | 1.28 | 2.41 | 0.00 |
time (sec) |
N/A | 1.348 | 1.686 | 0.372 | 0.000 | 0.159 | 0.000 | 0.145 | 0.396 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 368 | 312 | 203 | 251 | 389 | 322 | 0 | 2288 | 231 | 0 |
N.S. |
1 | 0.85 | 0.55 | 0.68 | 1.06 | 0.88 | 0.00 | 6.22 | 0.63 | 0.00 |
time (sec) |
N/A | 1.219 | 2.756 | 0.368 | 0.084 | 0.100 | 0.000 | 0.136 | 0.243 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 306 | 274 | 170 | 203 | 345 | 280 | 0 | 1017 | 196 | 0 |
N.S. |
1 | 0.90 | 0.56 | 0.66 | 1.13 | 0.92 | 0.00 | 3.32 | 0.64 | 0.00 |
time (sec) |
N/A | 1.129 | 2.463 | 0.366 | 0.083 | 0.087 | 0.000 | 0.120 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 244 | 236 | 136 | 155 | 243 | 237 | 0 | 567 | 161 | 0 |
N.S. |
1 | 0.97 | 0.56 | 0.64 | 1.00 | 0.97 | 0.00 | 2.32 | 0.66 | 0.00 |
time (sec) |
N/A | 1.051 | 2.422 | 0.369 | 0.066 | 0.080 | 0.000 | 0.134 | 0.254 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 256 | 198 | 107 | 111 | 195 | 196 | 0 | 470 | 126 | 0 |
N.S. |
1 | 0.77 | 0.42 | 0.43 | 0.76 | 0.77 | 0.00 | 1.84 | 0.49 | 0.00 |
time (sec) |
N/A | 1.021 | 2.367 | 0.356 | 0.067 | 0.081 | 0.000 | 0.131 | 0.283 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 315 | 285 | 204 | 380 | 0 | 570 | 0 | 292 | 247 | 0 |
N.S. |
1 | 0.90 | 0.65 | 1.21 | 0.00 | 1.81 | 0.00 | 0.93 | 0.78 | 0.00 |
time (sec) |
N/A | 1.231 | 2.985 | 0.371 | 0.000 | 0.104 | 0.000 | 0.144 | 0.297 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 315 | 300 | 206 | 519 | 0 | 675 | 0 | 295 | 411 | 0 |
N.S. |
1 | 0.95 | 0.65 | 1.65 | 0.00 | 2.14 | 0.00 | 0.94 | 1.30 | 0.00 |
time (sec) |
N/A | 1.238 | 3.097 | 0.369 | 0.000 | 0.108 | 0.000 | 0.150 | 0.354 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 321 | 297 | 205 | 642 | 0 | 811 | 0 | 276 | 588 | 0 |
N.S. |
1 | 0.93 | 0.64 | 2.00 | 0.00 | 2.53 | 0.00 | 0.86 | 1.83 | 0.00 |
time (sec) |
N/A | 1.187 | 3.274 | 0.370 | 0.000 | 0.112 | 0.000 | 0.150 | 1.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 332 | 298 | 221 | 790 | 0 | 941 | 0 | 330 | 776 | 0 |
N.S. |
1 | 0.90 | 0.67 | 2.38 | 0.00 | 2.83 | 0.00 | 0.99 | 2.34 | 0.00 |
time (sec) |
N/A | 1.203 | 3.481 | 0.365 | 0.000 | 0.125 | 0.000 | 0.141 | 0.301 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 353 | 336 | 239 | 958 | 0 | 1091 | 0 | 406 | 909 | 0 |
N.S. |
1 | 0.95 | 0.68 | 2.71 | 0.00 | 3.09 | 0.00 | 1.15 | 2.58 | 0.00 |
time (sec) |
N/A | 1.318 | 3.817 | 0.369 | 0.000 | 0.143 | 0.000 | 0.146 | 0.461 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 384 | 384 | 266 | 1146 | 0 | 1259 | 0 | 494 | 929 | 0 |
N.S. |
1 | 1.00 | 0.69 | 2.98 | 0.00 | 3.28 | 0.00 | 1.29 | 2.42 | 0.00 |
time (sec) |
N/A | 1.333 | 3.731 | 0.371 | 0.000 | 0.161 | 0.000 | 0.157 | 0.422 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 306 | 274 | 157 | 197 | 243 | 196 | 0 | 354 | 126 | 0 |
N.S. |
1 | 0.90 | 0.51 | 0.64 | 0.79 | 0.64 | 0.00 | 1.16 | 0.41 | 0.00 |
time (sec) |
N/A | 1.132 | 0.611 | 0.371 | 0.066 | 0.082 | 0.000 | 0.115 | 0.257 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 244 | 236 | 126 | 149 | 197 | 154 | 0 | 255 | 91 | 0 |
N.S. |
1 | 0.97 | 0.52 | 0.61 | 0.81 | 0.63 | 0.00 | 1.05 | 0.37 | 0.00 |
time (sec) |
N/A | 1.065 | 0.502 | 0.368 | 0.065 | 0.082 | 0.000 | 0.133 | 0.265 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 198 | 98 | 105 | 150 | 114 | 0 | 167 | 60 | 0 |
N.S. |
1 | 1.08 | 0.53 | 0.57 | 0.82 | 0.62 | 0.00 | 0.91 | 0.33 | 0.00 |
time (sec) |
N/A | 1.000 | 0.448 | 0.357 | 0.064 | 0.088 | 0.000 | 0.130 | 0.271 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 214 | 145 | 245 | 0 | 414 | 0 | 132 | 159 | 0 |
N.S. |
1 | 1.06 | 0.72 | 1.21 | 0.00 | 2.05 | 0.00 | 0.65 | 0.79 | 0.00 |
time (sec) |
N/A | 1.059 | 0.638 | 0.365 | 0.000 | 0.134 | 0.000 | 0.123 | 0.331 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 226 | 161 | 378 | 0 | 563 | 0 | 168 | 378 | 0 |
N.S. |
1 | 1.05 | 0.75 | 1.75 | 0.00 | 2.61 | 0.00 | 0.78 | 1.75 | 0.00 |
time (sec) |
N/A | 1.039 | 0.975 | 0.362 | 0.000 | 0.105 | 0.000 | 0.126 | 0.455 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 262 | 175 | 542 | 0 | 707 | 0 | 207 | 618 | 0 |
N.S. |
1 | 1.11 | 0.74 | 2.31 | 0.00 | 3.01 | 0.00 | 0.88 | 2.63 | 0.00 |
time (sec) |
N/A | 1.149 | 1.140 | 0.363 | 0.000 | 0.120 | 0.000 | 0.137 | 0.263 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 266 | 309 | 203 | 730 | 0 | 879 | 0 | 296 | 848 | 0 |
N.S. |
1 | 1.16 | 0.76 | 2.74 | 0.00 | 3.30 | 0.00 | 1.11 | 3.19 | 0.00 |
time (sec) |
N/A | 1.178 | 1.351 | 0.365 | 0.000 | 0.146 | 0.000 | 0.141 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 311 | 283 | 166 | 203 | 198 | 199 | 0 | 324 | 128 | 0 |
N.S. |
1 | 0.91 | 0.53 | 0.65 | 0.64 | 0.64 | 0.00 | 1.04 | 0.41 | 0.00 |
time (sec) |
N/A | 1.245 | 2.832 | 0.375 | 0.074 | 0.092 | 0.000 | 0.140 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 245 | 135 | 155 | 152 | 158 | 0 | 229 | 93 | 0 |
N.S. |
1 | 0.98 | 0.54 | 0.62 | 0.61 | 0.63 | 0.00 | 0.91 | 0.37 | 0.00 |
time (sec) |
N/A | 1.182 | 2.640 | 0.371 | 0.071 | 0.087 | 0.000 | 0.129 | 0.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 207 | 106 | 111 | 111 | 118 | 0 | 145 | 62 | 0 |
N.S. |
1 | 1.08 | 0.55 | 0.58 | 0.58 | 0.61 | 0.00 | 0.76 | 0.32 | 0.00 |
time (sec) |
N/A | 1.111 | 2.519 | 0.362 | 0.067 | 0.084 | 0.000 | 0.123 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 222 | 167 | 238 | 0 | 475 | 0 | 153 | 179 | 0 |
N.S. |
1 | 1.08 | 0.81 | 1.16 | 0.00 | 2.31 | 0.00 | 0.74 | 0.87 | 0.00 |
time (sec) |
N/A | 1.143 | 2.951 | 0.367 | 0.000 | 0.103 | 0.000 | 0.124 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 257 | 178 | 404 | 0 | 699 | 0 | 192 | 468 | 0 |
N.S. |
1 | 1.10 | 0.76 | 1.73 | 0.00 | 3.00 | 0.00 | 0.82 | 2.01 | 0.00 |
time (sec) |
N/A | 1.089 | 3.284 | 0.365 | 0.000 | 0.116 | 0.000 | 0.133 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 264 | 304 | 210 | 602 | 0 | 767 | 0 | 239 | 728 | 0 |
N.S. |
1 | 1.15 | 0.80 | 2.28 | 0.00 | 2.91 | 0.00 | 0.91 | 2.76 | 0.00 |
time (sec) |
N/A | 1.200 | 3.576 | 0.365 | 0.000 | 0.109 | 0.000 | 0.142 | 0.235 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 328 | 354 | 240 | 810 | 0 | 1069 | 0 | 341 | 997 | 0 |
N.S. |
1 | 1.08 | 0.73 | 2.47 | 0.00 | 3.26 | 0.00 | 1.04 | 3.04 | 0.00 |
time (sec) |
N/A | 1.311 | 3.956 | 0.371 | 0.000 | 0.141 | 0.000 | 0.144 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 336 | 307 | 168 | 203 | 240 | 218 | 0 | 297 | 136 | 0 |
N.S. |
1 | 0.91 | 0.50 | 0.60 | 0.71 | 0.65 | 0.00 | 0.88 | 0.40 | 0.00 |
time (sec) |
N/A | 1.278 | 2.904 | 0.383 | 0.076 | 0.089 | 0.000 | 0.142 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 277 | 269 | 134 | 155 | 196 | 176 | 0 | 215 | 101 | 0 |
N.S. |
1 | 0.97 | 0.48 | 0.56 | 0.71 | 0.64 | 0.00 | 0.78 | 0.36 | 0.00 |
time (sec) |
N/A | 1.206 | 2.779 | 0.375 | 0.074 | 0.089 | 0.000 | 0.137 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 228 | 101 | 110 | 155 | 134 | 0 | 136 | 69 | 0 |
N.S. |
1 | 1.06 | 0.47 | 0.51 | 0.72 | 0.62 | 0.00 | 0.63 | 0.32 | 0.00 |
time (sec) |
N/A | 1.137 | 2.657 | 0.370 | 0.072 | 0.092 | 0.000 | 0.128 | 0.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 230 | 247 | 183 | 406 | 0 | 693 | 0 | 189 | 345 | 0 |
N.S. |
1 | 1.07 | 0.80 | 1.77 | 0.00 | 3.01 | 0.00 | 0.82 | 1.50 | 0.00 |
time (sec) |
N/A | 1.130 | 3.272 | 0.374 | 0.000 | 0.107 | 0.000 | 0.134 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 262 | 284 | 211 | 454 | 0 | 677 | 0 | 231 | 521 | 0 |
N.S. |
1 | 1.08 | 0.81 | 1.73 | 0.00 | 2.58 | 0.00 | 0.88 | 1.99 | 0.00 |
time (sec) |
N/A | 1.255 | 3.910 | 0.369 | 0.000 | 0.116 | 0.000 | 0.136 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 326 | 350 | 241 | 810 | 0 | 1059 | 0 | 312 | 997 | 0 |
N.S. |
1 | 1.07 | 0.74 | 2.48 | 0.00 | 3.25 | 0.00 | 0.96 | 3.06 | 0.00 |
time (sec) |
N/A | 1.276 | 4.044 | 0.374 | 0.000 | 0.128 | 0.000 | 0.131 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 334 | 397 | 273 | 858 | 0 | 1259 | 0 | 383 | 1033 | 0 |
N.S. |
1 | 1.19 | 0.82 | 2.57 | 0.00 | 3.77 | 0.00 | 1.15 | 3.09 | 0.00 |
time (sec) |
N/A | 1.406 | 4.708 | 0.368 | 0.000 | 0.145 | 0.000 | 0.147 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 495 | 599 | 397 | 0 | 0 | 0 | 3728 | 0 | 0 | 0 |
N.S. |
1 | 1.21 | 0.80 | 0.00 | 0.00 | 0.00 | 7.53 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 6.406 | 3.995 | 0.000 | 0.000 | 0.000 | 7.283 | 0.000 | 0.287 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 355 | 439 | 338 | 0 | 0 | 0 | 2343 | 0 | 0 | 0 |
N.S. |
1 | 1.24 | 0.95 | 0.00 | 0.00 | 0.00 | 6.60 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.811 | 1.769 | 0.000 | 0.000 | 0.000 | 5.511 | 0.000 | 0.262 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 296 | 329 | 232 | 0 | 0 | 0 | 950 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 0.78 | 0.00 | 0.00 | 0.00 | 3.21 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.534 | 1.444 | 0.000 | 0.000 | 0.000 | 3.344 | 0.000 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 201 | 168 | 0 | 0 | 0 | 466 | 0 | 1566 | 0 |
N.S. |
1 | 1.19 | 0.99 | 0.00 | 0.00 | 0.00 | 2.76 | 0.00 | 9.27 | 0.00 |
time (sec) |
N/A | 0.765 | 0.683 | 0.000 | 0.000 | 0.000 | 1.991 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 286 | 257 | 0 | 0 | 0 | 0 | 0 | 1164 | 0 |
N.S. |
1 | 1.16 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 4.73 | 0.00 |
time (sec) |
N/A | 1.234 | 1.767 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 286 | 289 | 255 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.208 | 2.376 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 329 | 314 | 265 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.349 | 2.882 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.241 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 372 | 359 | 686 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 1.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.547 | 4.380 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.786 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 371 | 358 | 325 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.510 | 3.124 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.544 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 373 | 360 | 306 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.493 | 2.298 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.421 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 374 | 361 | 310 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.477 | 2.454 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.385 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 342 | 353 | 313 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.501 | 3.628 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.408 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 367 | 354 | 313 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.557 | 4.643 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.430 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 365 | 347 | 313 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.525 | 4.718 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.500 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 367 | 350 | 313 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.570 | 4.984 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.565 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 85 | 0 | 0 | 0 | 0 | 0 | 476 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 5.60 | 0.00 |
time (sec) |
N/A | 0.371 | 0.077 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.276 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 140 | 131 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.453 | 0.091 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.277 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 253 | 250 | 193 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.877 | 0.767 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.357 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 462 | 447 | 269 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 0.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.711 | 0.960 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.450 | 0.000 |