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 | A | A | A | F(-1) | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 51 | 93 | 62 | 107 | 308 | 0 | 98 | 49 | 0 |
N.S. |
1 | 0.53 | 0.97 | 0.65 | 1.11 | 3.21 | 0.00 | 1.02 | 0.51 | 0.00 |
time (sec) |
N/A | 0.399 | 0.685 | 0.330 | 0.299 | 0.145 | 0.000 | 0.385 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 51 | 60 | 71 | 147 | 316 | 0 | 98 | 75 | 0 |
N.S. |
1 | 0.53 | 0.62 | 0.74 | 1.53 | 3.29 | 0.00 | 1.02 | 0.78 | 0.00 |
time (sec) |
N/A | 0.406 | 0.100 | 0.320 | 0.265 | 0.153 | 0.000 | 0.418 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 78 | 83 | 131 | 813 | 240 | 0 | 127 | 195 | 0 |
N.S. |
1 | 0.68 | 0.73 | 1.15 | 7.13 | 2.11 | 0.00 | 1.11 | 1.71 | 0.00 |
time (sec) |
N/A | 0.505 | 0.146 | 0.427 | 0.352 | 0.116 | 0.000 | 0.362 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 106 | 88 | 134 | 1044 | 272 | 0 | 189 | 184 | 0 |
N.S. |
1 | 0.68 | 0.56 | 0.86 | 6.69 | 1.74 | 0.00 | 1.21 | 1.18 | 0.00 |
time (sec) |
N/A | 0.627 | 0.180 | 0.352 | 0.342 | 0.116 | 0.000 | 0.484 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 121 | 111 | 201 | 2732 | 308 | 0 | 270 | 347 | 0 |
N.S. |
1 | 0.61 | 0.56 | 1.02 | 13.80 | 1.56 | 0.00 | 1.36 | 1.75 | 0.00 |
time (sec) |
N/A | 0.649 | 0.321 | 0.461 | 0.410 | 0.157 | 0.000 | 0.434 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 241 | 141 | 109 | 112 | 185 | 331 | 0 | 118 | 99 | 144 |
N.S. |
1 | 0.59 | 0.45 | 0.46 | 0.77 | 1.37 | 0.00 | 0.49 | 0.41 | 0.60 |
time (sec) |
N/A | 0.633 | 0.970 | 0.704 | 0.381 | 0.121 | 0.000 | 0.342 | 0.170 | 42.653 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 199 | 114 | 92 | 105 | 140 | 303 | 0 | 98 | 88 | 94 |
N.S. |
1 | 0.57 | 0.46 | 0.53 | 0.70 | 1.52 | 0.00 | 0.49 | 0.44 | 0.47 |
time (sec) |
N/A | 0.525 | 1.378 | 0.383 | 0.328 | 0.136 | 0.000 | 0.346 | 0.174 | 1.237 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 97 | 75 | 80 | 94 | 263 | 0 | 223 | 60 | 73 |
N.S. |
1 | 0.63 | 0.48 | 0.52 | 0.61 | 1.70 | 0.00 | 1.44 | 0.39 | 0.47 |
time (sec) |
N/A | 0.354 | 1.329 | 0.355 | 0.303 | 0.123 | 0.000 | 0.410 | 0.182 | 0.704 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 67 | 61 | 66 | 71 | 227 | 0 | 156 | 43 | 57 |
N.S. |
1 | 0.50 | 0.45 | 0.49 | 0.53 | 1.68 | 0.00 | 1.16 | 0.32 | 0.42 |
time (sec) |
N/A | 0.226 | 0.174 | 0.322 | 0.262 | 0.115 | 0.000 | 0.397 | 0.168 | 44.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 53 | 93 | 64 | 111 | 316 | 0 | 113 | 51 | 0 |
N.S. |
1 | 0.52 | 0.91 | 0.63 | 1.09 | 3.10 | 0.00 | 1.11 | 0.50 | 0.00 |
time (sec) |
N/A | 0.396 | 0.875 | 0.348 | 0.273 | 0.142 | 0.000 | 0.410 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 53 | 60 | 73 | 151 | 324 | 0 | 113 | 77 | 0 |
N.S. |
1 | 0.52 | 0.59 | 0.72 | 1.48 | 3.18 | 0.00 | 1.11 | 0.75 | 0.00 |
time (sec) |
N/A | 0.398 | 0.141 | 0.332 | 0.300 | 0.144 | 0.000 | 0.433 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 80 | 83 | 133 | 873 | 250 | 0 | 153 | 197 | 0 |
N.S. |
1 | 0.67 | 0.69 | 1.11 | 7.28 | 2.08 | 0.00 | 1.28 | 1.64 | 0.00 |
time (sec) |
N/A | 0.509 | 0.281 | 0.390 | 0.332 | 0.113 | 0.000 | 0.490 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 108 | 87 | 136 | 1112 | 286 | 0 | 219 | 186 | 0 |
N.S. |
1 | 0.66 | 0.53 | 0.83 | 6.78 | 1.74 | 0.00 | 1.34 | 1.13 | 0.00 |
time (sec) |
N/A | 0.619 | 0.575 | 0.348 | 0.330 | 0.123 | 0.000 | 0.471 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 123 | 110 | 203 | 2972 | 326 | 0 | 318 | 349 | 0 |
N.S. |
1 | 0.59 | 0.53 | 0.98 | 14.29 | 1.57 | 0.00 | 1.53 | 1.68 | 0.00 |
time (sec) |
N/A | 0.645 | 0.411 | 0.479 | 0.383 | 0.121 | 0.000 | 0.529 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 111 | 92 | 102 | 116 | 282 | 0 | 0 | 88 | 140 |
N.S. |
1 | 0.60 | 0.50 | 0.55 | 0.63 | 1.53 | 0.00 | 0.00 | 0.48 | 0.76 |
time (sec) |
N/A | 0.521 | 1.215 | 0.845 | 0.359 | 0.133 | 0.000 | 0.000 | 0.163 | 46.539 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 94 | 75 | 77 | 80 | 242 | 0 | 0 | 60 | 107 |
N.S. |
1 | 0.66 | 0.52 | 0.54 | 0.56 | 1.69 | 0.00 | 0.00 | 0.42 | 0.75 |
time (sec) |
N/A | 0.345 | 0.956 | 0.405 | 0.317 | 0.116 | 0.000 | 0.000 | 0.155 | 1.805 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 64 | 61 | 63 | 64 | 218 | 184 | 0 | 43 | 93 |
N.S. |
1 | 0.52 | 0.50 | 0.51 | 0.52 | 1.77 | 1.50 | 0.00 | 0.35 | 0.76 |
time (sec) |
N/A | 0.215 | 0.119 | 0.371 | 0.290 | 0.147 | 16.297 | 0.000 | 0.173 | 1.206 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 50 | 93 | 61 | 104 | 309 | 0 | 0 | 51 | 0 |
N.S. |
1 | 0.54 | 1.00 | 0.66 | 1.12 | 3.32 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.383 | 0.457 | 0.462 | 0.281 | 0.154 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 50 | 60 | 70 | 149 | 317 | 0 | 0 | 77 | 0 |
N.S. |
1 | 0.54 | 0.65 | 0.75 | 1.60 | 3.41 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.384 | 0.082 | 0.412 | 0.297 | 0.140 | 0.000 | 0.000 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 77 | 83 | 131 | 785 | 239 | 0 | 0 | 197 | 0 |
N.S. |
1 | 0.69 | 0.75 | 1.18 | 7.07 | 2.15 | 0.00 | 0.00 | 1.77 | 0.00 |
time (sec) |
N/A | 0.498 | 0.124 | 0.530 | 0.383 | 0.117 | 0.000 | 0.000 | 0.254 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 105 | 87 | 133 | 1014 | 271 | 0 | 0 | 186 | 0 |
N.S. |
1 | 0.69 | 0.57 | 0.88 | 6.67 | 1.78 | 0.00 | 0.00 | 1.22 | 0.00 |
time (sec) |
N/A | 0.613 | 0.345 | 0.542 | 0.351 | 0.136 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 120 | 110 | 200 | 2611 | 305 | 0 | 0 | 349 | 0 |
N.S. |
1 | 0.62 | 0.57 | 1.04 | 13.53 | 1.58 | 0.00 | 0.00 | 1.81 | 0.00 |
time (sec) |
N/A | 0.656 | 0.287 | 0.753 | 0.355 | 0.131 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 199 | 114 | 92 | 105 | 116 | 282 | 0 | 0 | 88 | 140 |
N.S. |
1 | 0.57 | 0.46 | 0.53 | 0.58 | 1.42 | 0.00 | 0.00 | 0.44 | 0.70 |
time (sec) |
N/A | 0.529 | 1.290 | 0.539 | 0.346 | 0.117 | 0.000 | 0.000 | 0.183 | 46.275 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 97 | 75 | 80 | 80 | 242 | 0 | 0 | 60 | 107 |
N.S. |
1 | 0.63 | 0.48 | 0.52 | 0.52 | 1.56 | 0.00 | 0.00 | 0.39 | 0.69 |
time (sec) |
N/A | 0.355 | 1.119 | 0.307 | 0.337 | 0.126 | 0.000 | 0.000 | 0.165 | 1.483 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 67 | 61 | 66 | 64 | 218 | 0 | 0 | 43 | 93 |
N.S. |
1 | 0.50 | 0.45 | 0.49 | 0.47 | 1.61 | 0.00 | 0.00 | 0.32 | 0.69 |
time (sec) |
N/A | 0.224 | 0.127 | 0.293 | 0.327 | 0.119 | 0.000 | 0.000 | 0.166 | 1.011 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 53 | 48 | 64 | 104 | 309 | 0 | 0 | 51 | 0 |
N.S. |
1 | 0.52 | 0.47 | 0.63 | 1.02 | 3.03 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.393 | 0.681 | 0.309 | 0.292 | 0.189 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 53 | 60 | 73 | 157 | 317 | 0 | 0 | 77 | 0 |
N.S. |
1 | 0.52 | 0.59 | 0.72 | 1.54 | 3.11 | 0.00 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 0.399 | 0.103 | 0.346 | 0.310 | 0.146 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 80 | 83 | 134 | 802 | 239 | 0 | 0 | 197 | 0 |
N.S. |
1 | 0.67 | 0.69 | 1.12 | 6.68 | 1.99 | 0.00 | 0.00 | 1.64 | 0.00 |
time (sec) |
N/A | 0.504 | 0.134 | 0.409 | 0.378 | 0.121 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 108 | 87 | 136 | 1048 | 271 | 0 | 0 | 186 | 0 |
N.S. |
1 | 0.66 | 0.53 | 0.83 | 6.39 | 1.65 | 0.00 | 0.00 | 1.13 | 0.00 |
time (sec) |
N/A | 0.628 | 0.348 | 0.360 | 0.385 | 0.123 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 123 | 110 | 203 | 2660 | 305 | 0 | 0 | 349 | 0 |
N.S. |
1 | 0.59 | 0.53 | 0.98 | 12.79 | 1.47 | 0.00 | 0.00 | 1.68 | 0.00 |
time (sec) |
N/A | 0.679 | 0.298 | 0.438 | 0.330 | 0.162 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 199 | 114 | 95 | 105 | 116 | 282 | 0 | 0 | 88 | 140 |
N.S. |
1 | 0.57 | 0.48 | 0.53 | 0.58 | 1.42 | 0.00 | 0.00 | 0.44 | 0.70 |
time (sec) |
N/A | 0.529 | 1.329 | 0.573 | 0.339 | 0.119 | 0.000 | 0.000 | 0.161 | 41.333 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 97 | 78 | 80 | 80 | 242 | 0 | 0 | 60 | 107 |
N.S. |
1 | 0.63 | 0.50 | 0.52 | 0.52 | 1.56 | 0.00 | 0.00 | 0.39 | 0.69 |
time (sec) |
N/A | 0.362 | 1.105 | 0.332 | 0.318 | 0.124 | 0.000 | 0.000 | 0.166 | 1.477 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 67 | 64 | 66 | 64 | 218 | 0 | 0 | 43 | 93 |
N.S. |
1 | 0.50 | 0.47 | 0.49 | 0.47 | 1.61 | 0.00 | 0.00 | 0.32 | 0.69 |
time (sec) |
N/A | 0.225 | 0.158 | 0.303 | 0.295 | 0.122 | 0.000 | 0.000 | 0.174 | 1.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 53 | 53 | 64 | 104 | 309 | 0 | 0 | 51 | 0 |
N.S. |
1 | 0.52 | 0.52 | 0.63 | 1.02 | 3.03 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.404 | 0.702 | 0.310 | 0.307 | 0.166 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 53 | 60 | 73 | 157 | 317 | 0 | 0 | 77 | 0 |
N.S. |
1 | 0.52 | 0.59 | 0.72 | 1.54 | 3.11 | 0.00 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 0.410 | 0.100 | 0.312 | 0.291 | 0.151 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 80 | 83 | 134 | 820 | 239 | 0 | 0 | 197 | 0 |
N.S. |
1 | 0.67 | 0.69 | 1.12 | 6.83 | 1.99 | 0.00 | 0.00 | 1.64 | 0.00 |
time (sec) |
N/A | 0.505 | 0.121 | 0.419 | 0.323 | 0.114 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 108 | 87 | 136 | 1098 | 271 | 0 | 0 | 186 | 0 |
N.S. |
1 | 0.66 | 0.53 | 0.83 | 6.70 | 1.65 | 0.00 | 0.00 | 1.13 | 0.00 |
time (sec) |
N/A | 0.624 | 0.255 | 0.373 | 0.324 | 0.145 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 123 | 110 | 203 | 2760 | 305 | 0 | 0 | 349 | 0 |
N.S. |
1 | 0.59 | 0.53 | 0.98 | 13.27 | 1.47 | 0.00 | 0.00 | 1.68 | 0.00 |
time (sec) |
N/A | 0.656 | 0.249 | 0.503 | 0.411 | 0.129 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 161 | 117 | 0 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.05 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.524 | 0.357 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 157 | 121 | 0 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.02 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.489 | 0.749 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 159 | 122 | 0 | 0 | 0 | 0 | 0 | 62 | 0 |
N.S. |
1 | 1.07 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.556 | 0.611 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.279 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 156 | 116 | 0 | 0 | 0 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.06 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.577 | 0.398 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.315 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 157 | 123 | 0 | 0 | 0 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.08 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.591 | 0.249 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.307 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 159 | 123 | 0 | 0 | 0 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.05 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.572 | 0.236 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.312 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 161 | 117 | 0 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.05 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.539 | 0.407 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 157 | 114 | 0 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.02 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.502 | 0.328 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 159 | 121 | 0 | 0 | 0 | 0 | 0 | 62 | 0 |
N.S. |
1 | 1.07 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.560 | 0.695 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.341 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 157 | 122 | 0 | 0 | 0 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.08 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.577 | 0.947 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.342 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 157 | 117 | 0 | 0 | 0 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.08 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.571 | 0.266 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.339 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 159 | 124 | 0 | 0 | 0 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.05 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.586 | 0.228 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.358 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 161 | 133 | 0 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.05 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.521 | 1.403 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 161 | 124 | 0 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.05 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.499 | 0.037 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 157 | 121 | 0 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.02 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.460 | 0.218 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.191 | 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 | 149 | 154 | 116 | 0 | 0 | 0 | 0 | 0 | 62 | 0 |
N.S. |
1 | 1.03 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.534 | 0.631 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.210 | 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 | 157 | 116 | 0 | 0 | 0 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.08 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.560 | 0.687 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 159 | 118 | 0 | 0 | 0 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.07 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.545 | 0.266 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 161 | 122 | 0 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.05 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.504 | 0.355 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 161 | 122 | 0 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.05 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.501 | 0.373 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 161 | 124 | 0 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.05 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.492 | 0.023 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 152 | 115 | 0 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.00 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.476 | 0.236 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 155 | 115 | 0 | 0 | 0 | 0 | 0 | 62 | 0 |
N.S. |
1 | 1.05 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.536 | 0.017 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 159 | 118 | 0 | 0 | 0 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.07 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.555 | 0.295 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 232 | 218 | 178 | 0 | 0 | 0 | 0 | 0 | 72 | 0 |
N.S. |
1 | 0.94 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.695 | 0.837 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 217 | 175 | 0 | 0 | 0 | 0 | 0 | 63 | 0 |
N.S. |
1 | 0.95 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.645 | 0.603 | 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 | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 217 | 175 | 0 | 0 | 0 | 0 | 0 | 63 | 0 |
N.S. |
1 | 0.95 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.605 | 0.559 | 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 | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 217 | 175 | 0 | 0 | 0 | 0 | 0 | 68 | 0 |
N.S. |
1 | 0.95 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.642 | 0.573 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.190 | 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 | 227 | 215 | 173 | 0 | 0 | 0 | 0 | 0 | 68 | 0 |
N.S. |
1 | 0.95 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.626 | 0.560 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 0 | 175 | 0 | 0 | 0 | 0 | 0 | 68 | 0 |
N.S. |
1 | 0.00 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.000 | 0.669 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 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 | 227 | 219 | 157 | 0 | 0 | 0 | 0 | 0 | 66 | 0 |
N.S. |
1 | 0.96 | 0.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.634 | 0.558 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 188 | 153 | 0 | 0 | 0 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.01 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.591 | 0.431 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 188 | 151 | 0 | 0 | 0 | 0 | 0 | 66 | 0 |
N.S. |
1 | 1.01 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.569 | 0.395 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.255 | 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 | 187 | 184 | 144 | 0 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 0.98 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.540 | 0.385 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.253 | 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 | 170 | 175 | 138 | 0 | 0 | 0 | 0 | 0 | 76 | 0 |
N.S. |
1 | 1.03 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.563 | 0.657 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.309 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 182 | 130 | 0 | 0 | 0 | 0 | 0 | 82 | 0 |
N.S. |
1 | 1.05 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.615 | 0.956 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 195 | 150 | 0 | 0 | 0 | 0 | 0 | 82 | 0 |
N.S. |
1 | 1.01 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.655 | 0.395 | 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(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 195 | 150 | 0 | 0 | 0 | 0 | 0 | 82 | 0 |
N.S. |
1 | 0.99 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.661 | 0.395 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 215 | 173 | 0 | 0 | 0 | 0 | 0 | 72 | 0 |
N.S. |
1 | 0.96 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.651 | 0.513 | 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 | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 215 | 173 | 0 | 0 | 0 | 0 | 0 | 63 | 0 |
N.S. |
1 | 0.96 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.635 | 0.527 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.224 | 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 | 221 | 213 | 171 | 0 | 0 | 0 | 0 | 0 | 63 | 0 |
N.S. |
1 | 0.96 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.626 | 0.521 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.251 | 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 | 217 | 214 | 166 | 0 | 0 | 0 | 0 | 0 | 65 | 0 |
N.S. |
1 | 0.99 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.648 | 0.510 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 213 | 173 | 0 | 0 | 0 | 0 | 0 | 74 | 0 |
N.S. |
1 | 0.96 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.654 | 0.507 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 215 | 173 | 0 | 0 | 0 | 0 | 0 | 74 | 0 |
N.S. |
1 | 0.96 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.639 | 0.506 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.205 | 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 | 183 | 185 | 376 | 0 | 0 | 0 | 0 | 0 | 65 | 0 |
N.S. |
1 | 1.01 | 2.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.713 | 3.119 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.190 | 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 | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 154 | 137 | 0 | 0 | 0 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.07 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.653 | 1.658 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 154 | 0 | 0 | 0 | 0 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.634 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 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 | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 151 | 105 | 0 | 0 | 0 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.05 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.643 | 1.404 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 148 | 0 | 0 | 0 | 0 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.643 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 287 | 292 | 296 | 0 | 0 | 0 | 0 | 0 | 65 | 0 |
N.S. |
1 | 1.02 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.700 | 5.357 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.194 | 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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 287 | 292 | 294 | 0 | 0 | 0 | 0 | 0 | 65 | 0 |
N.S. |
1 | 1.02 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.663 | 5.258 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.186 | 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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 287 | 289 | 268 | 0 | 0 | 0 | 0 | 0 | 65 | 0 |
N.S. |
1 | 1.01 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.690 | 3.908 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.208 | 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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 286 | 288 | 266 | 0 | 0 | 0 | 0 | 0 | 65 | 0 |
N.S. |
1 | 1.01 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.675 | 3.883 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 215 | 215 | 0 | 0 | 0 | 0 | 0 | 0 | 88 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.567 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 304 | 303 | 16142 | 0 | 0 | 0 | 0 | 0 | 65 | 0 |
N.S. |
1 | 1.00 | 53.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.709 | 28.779 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 0.000 |