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 | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 133 | 106 | 125 | 243 | 286 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.25 | 1.00 | 1.18 | 2.29 | 2.70 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.601 | 0.009 | 0.284 | 0.152 | 0.088 | 0.000 | 0.000 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 96 | 77 | 103 | 163 | 200 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.25 | 1.00 | 1.34 | 2.12 | 2.60 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.466 | 0.007 | 0.250 | 0.160 | 0.089 | 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 | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 61 | 54 | 78 | 92 | 122 | 0 | 0 | 10 | 129 |
N.S. |
1 | 1.13 | 1.00 | 1.44 | 1.70 | 2.26 | 0.00 | 0.00 | 0.19 | 2.39 |
time (sec) |
N/A | 0.337 | 0.005 | 0.281 | 0.161 | 0.080 | 0.000 | 0.000 | 0.149 | 8.481 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 12 | 12 | 8 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 0.80 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.183 | 1.357 | 0.121 | 0.284 | 0.070 | 0.263 | 0.189 | 0.167 | 8.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.184 | 2.245 | 0.130 | 0.280 | 0.067 | 0.225 | 0.354 | 0.149 | 7.781 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 122 | 115 | 133 | 639 | 225 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.24 | 1.17 | 1.36 | 6.52 | 2.30 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.596 | 0.562 | 0.330 | 0.240 | 0.084 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 87 | 160 | 108 | 257 | 144 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.19 | 2.19 | 1.48 | 3.52 | 1.97 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.431 | 4.548 | 0.307 | 0.236 | 0.078 | 0.000 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 43 | 34 | 214 | 38 | 41 | 162 | 37 | 35 |
N.S. |
1 | 1.00 | 1.43 | 1.13 | 7.13 | 1.27 | 1.37 | 5.40 | 1.23 | 1.17 |
time (sec) |
N/A | 0.259 | 0.141 | 0.262 | 0.146 | 0.074 | 0.168 | 0.397 | 0.150 | 0.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 12 | 243 | 14 | 10 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 20.25 | 1.17 | 0.83 | 1.17 | 1.17 | 1.17 |
time (sec) |
N/A | 0.197 | 2.884 | 0.204 | 0.304 | 0.068 | 0.289 | 0.563 | 0.165 | 8.716 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 12 | 250 | 14 | 12 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 20.83 | 1.17 | 1.00 | 1.17 | 1.17 | 1.17 |
time (sec) |
N/A | 0.190 | 2.106 | 0.215 | 0.325 | 0.079 | 0.221 | 0.362 | 0.150 | 8.336 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 245 | 370 | 251 | 1205 | 344 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.20 | 1.80 | 1.22 | 5.88 | 1.68 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 1.353 | 6.482 | 0.241 | 0.341 | 0.086 | 0.000 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 149 | 172 | 180 | 736 | 240 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.16 | 1.34 | 1.41 | 5.75 | 1.88 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.850 | 2.079 | 0.234 | 0.285 | 0.090 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 98 | 171 | 122 | 386 | 146 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.09 | 1.90 | 1.36 | 4.29 | 1.62 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.483 | 4.333 | 0.208 | 0.253 | 0.077 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 12 | 534 | 14 | 10 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 44.50 | 1.17 | 0.83 | 1.17 | 1.17 | 1.17 |
time (sec) |
N/A | 0.200 | 4.396 | 0.133 | 0.518 | 0.070 | 0.286 | 0.373 | 0.154 | 8.502 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 12 | 536 | 14 | 12 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 44.67 | 1.17 | 1.00 | 1.17 | 1.17 | 1.17 |
time (sec) |
N/A | 0.201 | 2.313 | 0.139 | 0.638 | 0.064 | 0.244 | 0.305 | 0.159 | 8.302 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 0 | 0 | 16 | 0 | 0 | 23 | 50 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.89 | 0.00 | 0.00 | 1.28 | 2.78 |
time (sec) |
N/A | 3.012 | 1.564 | 0.000 | 0.000 | 0.076 | 0.000 | 0.000 | 0.155 | 9.191 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | A | F | F(-2) | B | B |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 0 | 17 | 0 | 0 | 15 | 0 | 0 | 14 | 45 |
N.S. |
1 | 0.00 | 1.00 | 0.00 | 0.00 | 0.88 | 0.00 | 0.00 | 0.82 | 2.65 |
time (sec) |
N/A | 0.000 | 0.806 | 0.000 | 0.000 | 0.072 | 0.000 | 0.000 | 0.155 | 9.659 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 206 | 278 | 170 | 0 | 164 | 258 | 188 | 91 | 423 |
N.S. |
1 | 1.09 | 1.47 | 0.90 | 0.00 | 0.87 | 1.37 | 0.99 | 0.48 | 2.24 |
time (sec) |
N/A | 0.717 | 0.714 | 0.634 | 0.000 | 0.074 | 0.199 | 0.163 | 0.171 | 8.924 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 147 | 178 | 108 | 0 | 105 | 165 | 119 | 65 | 241 |
N.S. |
1 | 1.07 | 1.30 | 0.79 | 0.00 | 0.77 | 1.20 | 0.87 | 0.47 | 1.76 |
time (sec) |
N/A | 0.503 | 0.433 | 0.608 | 0.000 | 0.072 | 0.170 | 0.216 | 0.154 | 8.731 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 90 | 96 | 50 | 0 | 55 | 92 | 62 | 39 | 105 |
N.S. |
1 | 1.07 | 1.14 | 0.60 | 0.00 | 0.65 | 1.10 | 0.74 | 0.46 | 1.25 |
time (sec) |
N/A | 0.328 | 0.636 | 0.519 | 0.000 | 0.069 | 0.142 | 0.162 | 0.158 | 8.735 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 152 | 166 | 65 | 112 | 51 | 0 | 138 | 32 | 0 |
N.S. |
1 | 0.94 | 1.03 | 0.40 | 0.70 | 0.32 | 0.00 | 0.86 | 0.20 | 0.00 |
time (sec) |
N/A | 0.757 | 0.540 | 0.542 | 0.112 | 0.069 | 0.000 | 0.164 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 167 | 224 | 96 | 119 | 83 | 0 | 1013 | 61 | 0 |
N.S. |
1 | 0.99 | 1.33 | 0.57 | 0.71 | 0.49 | 0.00 | 6.03 | 0.36 | 0.00 |
time (sec) |
N/A | 0.757 | 0.686 | 0.560 | 0.132 | 0.071 | 0.000 | 2.127 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 225 | 285 | 216 | 158 | 130 | 0 | 532 | 90 | 0 |
N.S. |
1 | 0.99 | 1.26 | 0.95 | 0.70 | 0.57 | 0.00 | 2.34 | 0.40 | 0.00 |
time (sec) |
N/A | 0.982 | 0.914 | 0.612 | 0.229 | 0.088 | 0.000 | 0.241 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 270 | 473 | 283 | 0 | 267 | 665 | 368 | 129 | 289 |
N.S. |
1 | 1.00 | 1.75 | 1.05 | 0.00 | 0.99 | 2.46 | 1.36 | 0.48 | 1.07 |
time (sec) |
N/A | 0.545 | 2.277 | 0.968 | 0.000 | 0.073 | 0.356 | 0.247 | 0.160 | 9.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 202 | 282 | 173 | 0 | 163 | 418 | 217 | 94 | 183 |
N.S. |
1 | 1.00 | 1.40 | 0.86 | 0.00 | 0.81 | 2.07 | 1.07 | 0.47 | 0.91 |
time (sec) |
N/A | 0.445 | 1.451 | 0.943 | 0.000 | 0.076 | 0.274 | 0.241 | 0.154 | 8.262 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 151 | 130 | 82 | 0 | 79 | 226 | 101 | 59 | 103 |
N.S. |
1 | 1.00 | 0.86 | 0.54 | 0.00 | 0.52 | 1.50 | 0.67 | 0.39 | 0.68 |
time (sec) |
N/A | 0.392 | 0.964 | 0.698 | 0.000 | 0.074 | 0.224 | 0.194 | 0.165 | 8.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 305 | 305 | 211 | 114 | 194 | 84 | 0 | 404 | 59 | 0 |
N.S. |
1 | 1.00 | 0.69 | 0.37 | 0.64 | 0.28 | 0.00 | 1.32 | 0.19 | 0.00 |
time (sec) |
N/A | 1.061 | 0.763 | 0.837 | 0.144 | 0.076 | 0.000 | 0.271 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 436 | 436 | 467 | 175 | 211 | 142 | 0 | 1967 | 107 | 0 |
N.S. |
1 | 1.00 | 1.07 | 0.40 | 0.48 | 0.33 | 0.00 | 4.51 | 0.25 | 0.00 |
time (sec) |
N/A | 1.074 | 1.550 | 0.836 | 0.196 | 0.077 | 0.000 | 11.118 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 396 | 396 | 667 | 396 | 0 | 370 | 945 | 548 | 177 | 411 |
N.S. |
1 | 1.00 | 1.68 | 1.00 | 0.00 | 0.93 | 2.39 | 1.38 | 0.45 | 1.04 |
time (sec) |
N/A | 0.691 | 3.378 | 1.106 | 0.000 | 0.086 | 0.525 | 0.337 | 0.165 | 9.271 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 294 | 294 | 405 | 238 | 0 | 221 | 588 | 315 | 130 | 263 |
N.S. |
1 | 1.00 | 1.38 | 0.81 | 0.00 | 0.75 | 2.00 | 1.07 | 0.44 | 0.89 |
time (sec) |
N/A | 0.536 | 2.227 | 1.070 | 0.000 | 0.100 | 0.403 | 0.292 | 0.174 | 8.965 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 209 | 208 | 205 | 114 | 0 | 105 | 311 | 142 | 83 | 146 |
N.S. |
1 | 1.00 | 0.98 | 0.55 | 0.00 | 0.50 | 1.49 | 0.68 | 0.40 | 0.70 |
time (sec) |
N/A | 0.480 | 1.343 | 0.832 | 0.000 | 0.070 | 0.313 | 0.274 | 0.158 | 9.147 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 449 | 449 | 336 | 163 | 276 | 117 | 0 | 810 | 84 | 0 |
N.S. |
1 | 1.00 | 0.75 | 0.36 | 0.61 | 0.26 | 0.00 | 1.80 | 0.19 | 0.00 |
time (sec) |
N/A | 1.938 | 1.034 | 0.905 | 0.158 | 0.082 | 0.000 | 0.295 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 712 | 712 | 833 | 254 | 297 | 197 | 0 | 2915 | 152 | 0 |
N.S. |
1 | 1.00 | 1.17 | 0.36 | 0.42 | 0.28 | 0.00 | 4.09 | 0.21 | 0.00 |
time (sec) |
N/A | 2.051 | 2.551 | 1.046 | 0.278 | 0.072 | 0.000 | 28.907 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 21 | 520 | 115 | 51 | 23 | 252 | 24 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 22.61 | 5.00 | 2.22 | 1.00 | 10.96 | 1.04 |
time (sec) |
N/A | 0.226 | 40.379 | 0.263 | 0.844 | 0.072 | 3.417 | 0.410 | 0.171 | 8.611 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 23 | 19 | 79 | 34 | 29 | 21 | 69 | 22 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 3.76 | 1.62 | 1.38 | 1.00 | 3.29 | 1.05 |
time (sec) |
N/A | 0.208 | 8.801 | 0.180 | 0.237 | 0.077 | 2.252 | 0.224 | 0.152 | 8.561 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 133 | 0 | 0 | 85 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 1.36 | 0.00 | 0.00 | 0.87 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.333 | 1.589 | 0.000 | 0.000 | 0.074 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 171 | 192 | 0 | 0 | 144 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.00 | 1.12 | 0.00 | 0.00 | 0.84 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.427 | 3.637 | 0.000 | 0.000 | 0.080 | 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 | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 251 | 269 | 0 | 0 | 198 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.00 | 1.07 | 0.00 | 0.00 | 0.79 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.496 | 12.416 | 0.000 | 0.000 | 0.088 | 0.000 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 152 | 342 | 500 | 672 | 500 | 0 | 0 | 119 | 0 |
N.S. |
1 | 1.00 | 2.25 | 3.29 | 4.42 | 3.29 | 0.00 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.476 | 0.124 | 0.528 | 0.219 | 0.090 | 0.000 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 115 | 191 | 314 | 373 | 317 | 0 | 0 | 85 | 0 |
N.S. |
1 | 1.00 | 1.66 | 2.73 | 3.24 | 2.76 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.417 | 0.070 | 0.497 | 0.199 | 0.084 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 87 | 143 | 130 | 160 | 0 | 0 | 48 | 161 |
N.S. |
1 | 1.00 | 1.04 | 1.70 | 1.55 | 1.90 | 0.00 | 0.00 | 0.57 | 1.92 |
time (sec) |
N/A | 0.323 | 0.009 | 0.450 | 0.154 | 0.085 | 0.000 | 0.000 | 0.147 | 8.501 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 86 | 20 | 15 | 20 | 32 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 4.78 | 1.11 | 0.83 | 1.11 | 1.78 | 1.11 |
time (sec) |
N/A | 0.214 | 1.733 | 0.187 | 0.230 | 0.063 | 0.603 | 0.221 | 0.151 | 8.265 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 142 | 31 | 17 | 20 | 79 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 7.89 | 1.72 | 0.94 | 1.11 | 4.39 | 1.11 |
time (sec) |
N/A | 0.202 | 4.581 | 0.181 | 0.292 | 0.067 | 2.372 | 3.925 | 0.160 | 8.233 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 300 | 300 | 1337 | 952 | 2525 | 759 | 0 | 0 | 332 | 0 |
N.S. |
1 | 1.00 | 4.46 | 3.17 | 8.42 | 2.53 | 0.00 | 0.00 | 1.11 | 0.00 |
time (sec) |
N/A | 0.768 | 7.171 | 0.895 | 0.781 | 0.096 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 229 | 649 | 575 | 1263 | 450 | 0 | 0 | 228 | 0 |
N.S. |
1 | 1.00 | 2.83 | 2.51 | 5.52 | 1.97 | 0.00 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.612 | 6.718 | 0.856 | 0.317 | 0.092 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 135 | 200 | 238 | 527 | 219 | 0 | 0 | 128 | 0 |
N.S. |
1 | 1.00 | 1.48 | 1.76 | 3.90 | 1.62 | 0.00 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 0.401 | 7.169 | 0.865 | 0.184 | 0.086 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 491 | 36 | 17 | 22 | 59 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 24.55 | 1.80 | 0.85 | 1.10 | 2.95 | 1.10 |
time (sec) |
N/A | 0.234 | 19.012 | 0.473 | 0.579 | 0.080 | 0.928 | 0.365 | 0.152 | 8.897 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 609 | 47 | 19 | 22 | 157 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 30.45 | 2.35 | 0.95 | 1.10 | 7.85 | 1.10 |
time (sec) |
N/A | 0.224 | 12.250 | 0.386 | 1.036 | 0.096 | 2.020 | 15.150 | 0.155 | 10.233 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 612 | 612 | 2594 | 1930 | 6861 | 1177 | 0 | 0 | 463 | 0 |
N.S. |
1 | 1.00 | 4.24 | 3.15 | 11.21 | 1.92 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 1.289 | 7.323 | 0.995 | 8.171 | 0.109 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 427 | 427 | 1846 | 1138 | 3407 | 688 | 0 | 0 | 327 | 0 |
N.S. |
1 | 1.00 | 4.32 | 2.67 | 7.98 | 1.61 | 0.00 | 0.00 | 0.77 | 0.00 |
time (sec) |
N/A | 0.942 | 7.051 | 0.855 | 1.591 | 0.124 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 275 | 275 | 277 | 493 | 1319 | 327 | 0 | 0 | 190 | 0 |
N.S. |
1 | 1.00 | 1.01 | 1.79 | 4.80 | 1.19 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.590 | 8.102 | 0.767 | 0.430 | 0.084 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 1935 | 52 | 17 | 22 | 86 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 96.75 | 2.60 | 0.85 | 1.10 | 4.30 | 1.10 |
time (sec) |
N/A | 0.222 | 13.634 | 0.497 | 2.797 | 0.073 | 1.277 | 0.431 | 0.154 | 9.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 2194 | 63 | 19 | 22 | 237 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 109.70 | 3.15 | 0.95 | 1.10 | 11.85 | 1.10 |
time (sec) |
N/A | 0.225 | 16.869 | 0.605 | 9.601 | 0.078 | 2.382 | 25.522 | 0.166 | 9.214 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 243 | 246 | 297 | 1468 | 983 | 1183 | 0 | 0 | 219 | 0 |
N.S. |
1 | 1.01 | 1.22 | 6.04 | 4.05 | 4.87 | 0.00 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.978 | 1.446 | 0.612 | 0.481 | 0.107 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 188 | 236 | 940 | 715 | 834 | 0 | 0 | 159 | 0 |
N.S. |
1 | 1.04 | 1.30 | 5.19 | 3.95 | 4.61 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.738 | 1.297 | 0.548 | 0.401 | 0.119 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 132 | 177 | 462 | 399 | 527 | 0 | 0 | 97 | 0 |
N.S. |
1 | 1.06 | 1.42 | 3.70 | 3.19 | 4.22 | 0.00 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.494 | 1.405 | 0.493 | 0.295 | 0.089 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 279 | 27 | 17 | 22 | 31 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 13.95 | 1.35 | 0.85 | 1.10 | 1.55 | 1.10 |
time (sec) |
N/A | 0.236 | 2.145 | 0.368 | 0.771 | 0.068 | 0.947 | 0.296 | 0.172 | 9.312 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 424 | 51 | 19 | 22 | 61 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 21.20 | 2.55 | 0.95 | 1.10 | 3.05 | 1.10 |
time (sec) |
N/A | 0.237 | 4.074 | 0.355 | 1.791 | 0.068 | 1.745 | 4.191 | 0.158 | 9.511 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 848 | 848 | 1724 | 5959 | 4631 | 2537 | 0 | 0 | 1099 | 0 |
N.S. |
1 | 1.00 | 2.03 | 7.03 | 5.46 | 2.99 | 0.00 | 0.00 | 1.30 | 0.00 |
time (sec) |
N/A | 2.279 | 9.244 | 0.944 | 2.833 | 0.139 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 654 | 654 | 761 | 3901 | 2530 | 1576 | 0 | 0 | 794 | 0 |
N.S. |
1 | 1.00 | 1.16 | 5.96 | 3.87 | 2.41 | 0.00 | 0.00 | 1.21 | 0.00 |
time (sec) |
N/A | 1.791 | 6.111 | 0.789 | 0.919 | 0.115 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 228 | 745 | 2001 | 1156 | 843 | 0 | 0 | 481 | 0 |
N.S. |
1 | 1.07 | 3.48 | 9.35 | 5.40 | 3.94 | 0.00 | 0.00 | 2.25 | 0.00 |
time (sec) |
N/A | 0.784 | 7.467 | 0.699 | 0.534 | 0.121 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 1498 | 55 | 19 | 22 | 66 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 74.90 | 2.75 | 0.95 | 1.10 | 3.30 | 1.10 |
time (sec) |
N/A | 0.234 | 12.128 | 0.562 | 10.948 | 0.077 | 1.617 | 0.445 | 0.156 | 9.798 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 20 | 1977 | 96 | 20 | 22 | 121 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 98.85 | 4.80 | 1.00 | 1.10 | 6.05 | 1.10 |
time (sec) |
N/A | 0.235 | 13.832 | 0.454 | 28.357 | 0.082 | 3.107 | 22.715 | 0.174 | 9.501 |