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 | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 49 | 1911 | 6135 | 617 | 0 | 195 | 1825 | 209 |
N.S. |
1 | 1.00 | 1.00 | 39.00 | 125.20 | 12.59 | 0.00 | 3.98 | 37.24 | 4.27 |
time (sec) |
N/A | 0.343 | 0.860 | 2.985 | 2.099 | 0.087 | 0.000 | 0.168 | 0.184 | 0.376 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 49 | 1374 | 4471 | 456 | 0 | 174 | 1300 | 730 |
N.S. |
1 | 1.00 | 1.00 | 28.04 | 91.24 | 9.31 | 0.00 | 3.55 | 26.53 | 14.90 |
time (sec) |
N/A | 0.350 | 0.739 | 1.564 | 1.529 | 0.084 | 0.000 | 0.160 | 0.173 | 0.396 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 215 | 153 | 929 | 3066 | 323 | 0 | 153 | 865 | 533 |
N.S. |
1 | 1.20 | 0.85 | 5.19 | 17.13 | 1.80 | 0.00 | 0.85 | 4.83 | 2.98 |
time (sec) |
N/A | 1.032 | 0.984 | 0.786 | 1.110 | 0.089 | 0.000 | 0.144 | 0.167 | 0.285 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 169 | 126 | 576 | 1922 | 218 | 0 | 132 | 520 | 378 |
N.S. |
1 | 1.17 | 0.87 | 3.97 | 13.26 | 1.50 | 0.00 | 0.91 | 3.59 | 2.61 |
time (sec) |
N/A | 0.802 | 0.502 | 0.401 | 0.719 | 0.083 | 0.000 | 0.141 | 0.159 | 0.232 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 123 | 90 | 315 | 1037 | 141 | 0 | 111 | 265 | 243 |
N.S. |
1 | 1.11 | 0.81 | 2.84 | 9.34 | 1.27 | 0.00 | 1.00 | 2.39 | 2.19 |
time (sec) |
N/A | 0.594 | 0.380 | 0.192 | 0.432 | 0.080 | 0.000 | 0.147 | 0.149 | 0.177 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 77 | 146 | 413 | 88 | 0 | 91 | 115 | 130 |
N.S. |
1 | 1.00 | 1.00 | 1.90 | 5.36 | 1.14 | 0.00 | 1.18 | 1.49 | 1.69 |
time (sec) |
N/A | 0.415 | 0.292 | 0.101 | 0.216 | 0.079 | 0.000 | 0.129 | 0.148 | 0.154 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 44 | 58 | 58 | 48 | 0 | 36 | 45 | 48 |
N.S. |
1 | 1.00 | 1.00 | 1.32 | 1.32 | 1.09 | 0.00 | 0.82 | 1.02 | 1.09 |
time (sec) |
N/A | 0.258 | 0.096 | 0.037 | 0.035 | 0.076 | 0.000 | 0.116 | 0.154 | 0.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 63 | 62 | 0 | 83 | 0 | 0 | 48 | 86 |
N.S. |
1 | 1.00 | 0.94 | 0.93 | 0.00 | 1.24 | 0.00 | 0.00 | 0.72 | 1.28 |
time (sec) |
N/A | 0.407 | 0.376 | 0.109 | 0.000 | 0.087 | 0.000 | 0.000 | 0.152 | 0.355 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 102 | 81 | 96 | 0 | 163 | 0 | 0 | 0 | 201 |
N.S. |
1 | 1.00 | 0.79 | 0.94 | 0.00 | 1.60 | 0.00 | 0.00 | 0.00 | 1.97 |
time (sec) |
N/A | 0.550 | 0.452 | 0.157 | 0.000 | 0.079 | 0.000 | 0.000 | 0.168 | 0.860 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 137 | 97 | 129 | 0 | 288 | 0 | 0 | 0 | 168 |
N.S. |
1 | 1.01 | 0.71 | 0.95 | 0.00 | 2.12 | 0.00 | 0.00 | 0.00 | 1.24 |
time (sec) |
N/A | 0.717 | 0.501 | 0.274 | 0.000 | 0.080 | 0.000 | 0.000 | 0.219 | 0.772 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 172 | 112 | 162 | 0 | 429 | 0 | 0 | 0 | 201 |
N.S. |
1 | 1.01 | 0.66 | 0.95 | 0.00 | 2.52 | 0.00 | 0.00 | 0.00 | 1.18 |
time (sec) |
N/A | 0.899 | 0.579 | 0.482 | 0.000 | 0.086 | 0.000 | 0.000 | 0.251 | 0.421 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 49 | 195 | 0 | 598 | 0 | 0 | 0 | 234 |
N.S. |
1 | 1.00 | 1.00 | 3.98 | 0.00 | 12.20 | 0.00 | 0.00 | 0.00 | 4.78 |
time (sec) |
N/A | 0.341 | 0.474 | 0.807 | 0.000 | 0.093 | 0.000 | 0.000 | 0.199 | 0.416 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 49 | 228 | 0 | 795 | 0 | 0 | 0 | 267 |
N.S. |
1 | 1.00 | 1.00 | 4.65 | 0.00 | 16.22 | 0.00 | 0.00 | 0.00 | 5.45 |
time (sec) |
N/A | 0.340 | 0.567 | 1.301 | 0.000 | 0.092 | 0.000 | 0.000 | 0.214 | 0.482 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 61 | 0 | 0 | 71 | 0 | 0 | 49 | 75 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 1.16 | 0.00 | 0.00 | 0.80 | 1.23 |
time (sec) |
N/A | 0.359 | 0.231 | 0.000 | 0.000 | 0.079 | 0.000 | 0.000 | 0.160 | 0.202 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | B | B | B | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 31 | 835 | 1268 | 688 | 1170 | 0 | 856 | 685 |
N.S. |
1 | 1.00 | 0.30 | 7.95 | 12.08 | 6.55 | 11.14 | 0.00 | 8.15 | 6.52 |
time (sec) |
N/A | 0.455 | 0.367 | 5.595 | 0.247 | 0.092 | 0.322 | 0.000 | 0.167 | 0.526 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | B | B | B | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 31 | 562 | 874 | 474 | 821 | 0 | 583 | 487 |
N.S. |
1 | 1.00 | 0.35 | 6.39 | 9.93 | 5.39 | 9.33 | 0.00 | 6.62 | 5.53 |
time (sec) |
N/A | 0.457 | 0.327 | 2.855 | 0.176 | 0.097 | 0.251 | 0.000 | 0.176 | 0.388 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 150 | 75 | 343 | 555 | 302 | 536 | 1320 | 364 | 323 |
N.S. |
1 | 1.21 | 0.60 | 2.77 | 4.48 | 2.44 | 4.32 | 10.65 | 2.94 | 2.60 |
time (sec) |
N/A | 0.927 | 0.372 | 1.237 | 0.166 | 0.084 | 0.204 | 0.601 | 0.161 | 0.279 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 106 | 56 | 178 | 308 | 172 | 304 | 705 | 199 | 196 |
N.S. |
1 | 1.10 | 0.58 | 1.85 | 3.21 | 1.79 | 3.17 | 7.34 | 2.07 | 2.04 |
time (sec) |
N/A | 0.691 | 0.337 | 0.500 | 0.164 | 0.082 | 0.131 | 0.364 | 0.159 | 0.186 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 40 | 67 | 133 | 84 | 143 | 1014 | 88 | 95 |
N.S. |
1 | 1.00 | 0.65 | 1.08 | 2.15 | 1.35 | 2.31 | 16.35 | 1.42 | 1.53 |
time (sec) |
N/A | 0.492 | 0.293 | 0.171 | 0.161 | 0.088 | 0.097 | 0.202 | 0.159 | 0.174 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 26 | 25 | 47 | 44 | 47 | 47 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 0.93 | 1.74 | 1.63 | 1.74 | 1.74 | 0.93 |
time (sec) |
N/A | 0.336 | 0.047 | 0.073 | 0.030 | 0.087 | 0.067 | 0.135 | 0.153 | 0.091 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 0 | 0 | 44 | 0 | 0 | 49 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 2.00 | 0.00 | 0.00 | 2.23 | 0.91 |
time (sec) |
N/A | 0.330 | 0.325 | 0.000 | 0.000 | 0.079 | 0.000 | 0.000 | 0.163 | 0.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 47 | 0 | 0 | 147 | 0 | 0 | 0 | 51 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 2.77 | 0.00 | 0.00 | 0.00 | 0.96 |
time (sec) |
N/A | 0.474 | 0.338 | 0.000 | 0.000 | 0.076 | 0.000 | 0.000 | 0.195 | 0.310 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 88 | 64 | 0 | 0 | 269 | 0 | 0 | 0 | 76 |
N.S. |
1 | 1.01 | 0.74 | 0.00 | 0.00 | 3.09 | 0.00 | 0.00 | 0.00 | 0.87 |
time (sec) |
N/A | 0.650 | 0.373 | 0.000 | 0.000 | 0.080 | 0.000 | 0.000 | 0.215 | 0.746 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 123 | 80 | 0 | 0 | 431 | 0 | 0 | 0 | 104 |
N.S. |
1 | 1.02 | 0.66 | 0.00 | 0.00 | 3.56 | 0.00 | 0.00 | 0.00 | 0.86 |
time (sec) |
N/A | 0.797 | 0.399 | 0.000 | 0.000 | 0.082 | 0.000 | 0.000 | 0.242 | 0.285 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 31 | 0 | 0 | 636 | 0 | 0 | 0 | 120 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 20.52 | 0.00 | 0.00 | 0.00 | 3.87 |
time (sec) |
N/A | 0.336 | 0.327 | 0.000 | 0.000 | 0.092 | 0.000 | 0.000 | 0.306 | 0.359 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 31 | 0 | 0 | 883 | 0 | 0 | 0 | 136 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 28.48 | 0.00 | 0.00 | 0.00 | 4.39 |
time (sec) |
N/A | 0.337 | 0.341 | 0.000 | 0.000 | 0.097 | 0.000 | 0.000 | 0.331 | 0.518 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 49 | 0 | 0 | 118 | 0 | 0 | 119 | 112 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 2.41 | 0.00 | 0.00 | 2.43 | 2.29 |
time (sec) |
N/A | 0.350 | 0.364 | 0.000 | 0.000 | 0.088 | 0.000 | 0.000 | 0.255 | 0.293 |
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 | 49 | 49 | 49 | 0 | 0 | 63 | 0 | 0 | 79 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 1.29 | 0.00 | 0.00 | 1.61 | 0.00 |
time (sec) |
N/A | 0.314 | 0.271 | 0.000 | 0.000 | 0.085 | 0.000 | 0.000 | 0.211 | 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 | 47 | 47 | 47 | 0 | 0 | 63 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 1.34 | 0.00 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.263 | 0.147 | 0.000 | 0.000 | 0.076 | 0.000 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 49 | 0 | 0 | 110 | 0 | 0 | 60 | 74 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 2.24 | 0.00 | 0.00 | 1.22 | 1.51 |
time (sec) |
N/A | 0.337 | 0.524 | 0.000 | 0.000 | 0.080 | 0.000 | 0.000 | 0.185 | 0.223 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 49 | 0 | 0 | 135 | 0 | 0 | 71 | 87 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 2.76 | 0.00 | 0.00 | 1.45 | 1.78 |
time (sec) |
N/A | 0.332 | 0.553 | 0.000 | 0.000 | 0.080 | 0.000 | 0.000 | 0.183 | 0.246 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 49 | 0 | 0 | 226 | 0 | 0 | 0 | 130 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 4.61 | 0.00 | 0.00 | 0.00 | 2.65 |
time (sec) |
N/A | 0.336 | 0.598 | 0.000 | 0.000 | 0.080 | 0.000 | 0.000 | 0.239 | 0.550 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | A | C | B | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 62 | 42 | 0 | 43 | 42 | 73 | 781 | 36 | 38 |
N.S. |
1 | 0.97 | 0.66 | 0.00 | 0.67 | 0.66 | 1.14 | 12.20 | 0.56 | 0.59 |
time (sec) |
N/A | 0.354 | 0.072 | 0.000 | 0.035 | 0.084 | 0.181 | 0.156 | 0.212 | 0.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | C | B | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 104 | 60 | 0 | 62 | 58 | 0 | 1338 | 54 | 54 |
N.S. |
1 | 1.04 | 0.60 | 0.00 | 0.62 | 0.58 | 0.00 | 13.38 | 0.54 | 0.54 |
time (sec) |
N/A | 0.449 | 0.062 | 0.000 | 0.034 | 0.087 | 0.000 | 0.197 | 0.214 | 0.127 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 50 | 0 | 0 | 0 | 0 | 0 | 0 | 73 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.46 |
time (sec) |
N/A | 0.338 | 0.025 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.197 | 0.184 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 534 | 0 | 244 | 0 | 0 | 827 | 181 |
N.S. |
1 | 1.00 | 1.00 | 18.41 | 0.00 | 8.41 | 0.00 | 0.00 | 28.52 | 6.24 |
time (sec) |
N/A | 0.315 | 0.010 | 0.431 | 0.000 | 0.076 | 0.000 | 0.000 | 0.195 | 0.186 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 368 | 0 | 175 | 0 | 0 | 594 | 148 |
N.S. |
1 | 1.00 | 1.00 | 13.14 | 0.00 | 6.25 | 0.00 | 0.00 | 21.21 | 5.29 |
time (sec) |
N/A | 0.310 | 0.010 | 0.297 | 0.000 | 0.080 | 0.000 | 0.000 | 0.190 | 0.179 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 116 | 76 | 234 | 0 | 120 | 0 | 0 | 402 | 89 |
N.S. |
1 | 0.97 | 0.64 | 1.97 | 0.00 | 1.01 | 0.00 | 0.00 | 3.38 | 0.75 |
time (sec) |
N/A | 0.623 | 0.084 | 0.224 | 0.000 | 0.084 | 0.000 | 0.000 | 0.192 | 0.257 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 81 | 58 | 133 | 0 | 77 | 0 | 0 | 248 | 82 |
N.S. |
1 | 0.95 | 0.68 | 1.56 | 0.00 | 0.91 | 0.00 | 0.00 | 2.92 | 0.96 |
time (sec) |
N/A | 0.505 | 0.060 | 0.131 | 0.000 | 0.081 | 0.000 | 0.000 | 0.191 | 1.351 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 42 | 61 | 0 | 51 | 0 | 0 | 230 | 47 |
N.S. |
1 | 1.00 | 0.91 | 1.33 | 0.00 | 1.11 | 0.00 | 0.00 | 5.00 | 1.02 |
time (sec) |
N/A | 0.367 | 0.033 | 0.099 | 0.000 | 0.085 | 0.000 | 0.000 | 0.191 | 0.471 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 22 | 0 | 20 | 0 | 0 | 29 | 20 |
N.S. |
1 | 1.00 | 1.00 | 1.10 | 0.00 | 1.00 | 0.00 | 0.00 | 1.45 | 1.00 |
time (sec) |
N/A | 0.300 | 0.009 | 0.151 | 0.000 | 0.078 | 0.000 | 0.000 | 0.192 | 0.150 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 26 | 25 | 31 | 34 | 31 | 31 | 25 |
N.S. |
1 | 1.00 | 1.00 | 1.04 | 1.00 | 1.24 | 1.36 | 1.24 | 1.24 | 1.00 |
time (sec) |
N/A | 0.303 | 0.012 | 0.118 | 0.027 | 0.074 | 0.098 | 0.121 | 0.185 | 0.806 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 41 | 51 | 0 | 51 | 44 | 0 | 47 | 41 |
N.S. |
1 | 1.00 | 0.72 | 0.89 | 0.00 | 0.89 | 0.77 | 0.00 | 0.82 | 0.72 |
time (sec) |
N/A | 0.422 | 0.025 | 0.167 | 0.000 | 0.077 | 0.081 | 0.000 | 0.204 | 1.438 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 99 | 60 | 79 | 0 | 95 | 102 | 0 | 89 | 104 |
N.S. |
1 | 1.10 | 0.67 | 0.88 | 0.00 | 1.06 | 1.13 | 0.00 | 0.99 | 1.16 |
time (sec) |
N/A | 0.563 | 0.034 | 0.236 | 0.000 | 0.078 | 0.104 | 0.000 | 0.206 | 1.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 141 | 76 | 125 | 0 | 150 | 177 | 0 | 146 | 161 |
N.S. |
1 | 1.16 | 0.62 | 1.02 | 0.00 | 1.23 | 1.45 | 0.00 | 1.20 | 1.32 |
time (sec) |
N/A | 0.727 | 0.045 | 0.347 | 0.000 | 0.080 | 0.123 | 0.000 | 0.203 | 0.227 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 29 | 189 | 0 | 219 | 272 | 0 | 221 | 231 |
N.S. |
1 | 1.00 | 0.32 | 2.05 | 0.00 | 2.38 | 2.96 | 0.00 | 2.40 | 2.51 |
time (sec) |
N/A | 0.402 | 0.011 | 0.458 | 0.000 | 0.083 | 0.143 | 0.000 | 0.217 | 0.276 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 108 | 28 | 271 | 0 | 302 | 388 | 0 | 314 | 315 |
N.S. |
1 | 1.00 | 0.26 | 2.51 | 0.00 | 2.80 | 3.59 | 0.00 | 2.91 | 2.92 |
time (sec) |
N/A | 0.420 | 0.010 | 0.643 | 0.000 | 0.086 | 0.169 | 0.000 | 0.216 | 0.329 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 61 | 0 | 0 | 0 | 0 | 0 | 0 | 73 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.20 |
time (sec) |
N/A | 0.340 | 0.042 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.194 | 0.223 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 31 | 961 | 0 | 465 | 0 | 0 | 0 | 136 |
N.S. |
1 | 1.00 | 1.00 | 31.00 | 0.00 | 15.00 | 0.00 | 0.00 | 0.00 | 4.39 |
time (sec) |
N/A | 0.314 | 0.013 | 3.441 | 0.000 | 0.092 | 0.000 | 0.000 | 0.204 | 0.295 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 31 | 646 | 0 | 331 | 0 | 0 | 0 | 120 |
N.S. |
1 | 1.00 | 1.00 | 20.84 | 0.00 | 10.68 | 0.00 | 0.00 | 0.00 | 3.87 |
time (sec) |
N/A | 0.310 | 0.012 | 1.783 | 0.000 | 0.092 | 0.000 | 0.000 | 0.216 | 0.231 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 123 | 96 | 395 | 0 | 225 | 0 | 0 | 0 | 92 |
N.S. |
1 | 1.02 | 0.79 | 3.26 | 0.00 | 1.86 | 0.00 | 0.00 | 0.00 | 0.76 |
time (sec) |
N/A | 0.693 | 0.180 | 0.908 | 0.000 | 0.087 | 0.000 | 0.000 | 0.215 | 0.220 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 88 | 71 | 208 | 0 | 145 | 0 | 0 | 0 | 76 |
N.S. |
1 | 1.01 | 0.82 | 2.39 | 0.00 | 1.67 | 0.00 | 0.00 | 0.00 | 0.87 |
time (sec) |
N/A | 0.546 | 0.051 | 0.393 | 0.000 | 0.085 | 0.000 | 0.000 | 0.216 | 0.173 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 47 | 86 | 0 | 96 | 0 | 0 | 0 | 51 |
N.S. |
1 | 1.00 | 0.89 | 1.62 | 0.00 | 1.81 | 0.00 | 0.00 | 0.00 | 0.96 |
time (sec) |
N/A | 0.400 | 0.030 | 0.157 | 0.000 | 0.090 | 0.000 | 0.000 | 0.221 | 1.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 23 | 0 | 31 | 0 | 0 | 52 | 20 |
N.S. |
1 | 1.00 | 1.00 | 1.05 | 0.00 | 1.41 | 0.00 | 0.00 | 2.36 | 0.91 |
time (sec) |
N/A | 0.298 | 0.010 | 0.153 | 0.000 | 0.083 | 0.000 | 0.000 | 0.204 | 0.204 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 26 | 25 | 54 | 53 | 54 | 54 | 37 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 0.93 | 2.00 | 1.96 | 2.00 | 2.00 | 1.37 |
time (sec) |
N/A | 0.300 | 0.014 | 0.260 | 0.025 | 0.074 | 0.136 | 0.136 | 0.190 | 0.112 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 47 | 74 | 101 | 100 | 82 | 0 | 93 | 97 |
N.S. |
1 | 1.00 | 0.76 | 1.19 | 1.63 | 1.61 | 1.32 | 0.00 | 1.50 | 1.56 |
time (sec) |
N/A | 0.427 | 0.031 | 0.490 | 0.045 | 0.082 | 0.112 | 0.000 | 0.210 | 0.181 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 106 | 64 | 127 | 208 | 180 | 189 | 1703 | 171 | 183 |
N.S. |
1 | 1.16 | 0.70 | 1.40 | 2.29 | 1.98 | 2.08 | 18.71 | 1.88 | 2.01 |
time (sec) |
N/A | 0.576 | 0.042 | 0.988 | 0.042 | 0.081 | 0.149 | 0.201 | 0.198 | 0.287 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 150 | 81 | 216 | 349 | 287 | 333 | 0 | 282 | 292 |
N.S. |
1 | 1.19 | 0.64 | 1.71 | 2.77 | 2.28 | 2.64 | 0.00 | 2.24 | 2.32 |
time (sec) |
N/A | 0.751 | 0.053 | 1.709 | 0.041 | 0.086 | 0.174 | 0.000 | 0.200 | 0.452 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 96 | 31 | 341 | 526 | 420 | 518 | 0 | 429 | 427 |
N.S. |
1 | 1.00 | 0.32 | 3.55 | 5.48 | 4.38 | 5.40 | 0.00 | 4.47 | 4.45 |
time (sec) |
N/A | 0.410 | 0.011 | 2.923 | 0.049 | 0.093 | 0.300 | 0.000 | 0.196 | 0.636 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 31 | 502 | 740 | 583 | 745 | 0 | 612 | 583 |
N.S. |
1 | 1.00 | 0.27 | 4.44 | 6.55 | 5.16 | 6.59 | 0.00 | 5.42 | 5.16 |
time (sec) |
N/A | 0.436 | 0.012 | 4.691 | 0.056 | 0.110 | 0.412 | 0.000 | 0.214 | 0.867 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 49 | 1173 | 0 | 561 | 0 | 0 | 0 | 265 |
N.S. |
1 | 1.00 | 1.00 | 23.94 | 0.00 | 11.45 | 0.00 | 0.00 | 0.00 | 5.41 |
time (sec) |
N/A | 0.331 | 0.037 | 4.255 | 0.000 | 0.093 | 0.000 | 0.000 | 0.192 | 0.488 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 49 | 826 | 0 | 413 | 0 | 0 | 0 | 232 |
N.S. |
1 | 1.00 | 1.00 | 16.86 | 0.00 | 8.43 | 0.00 | 0.00 | 0.00 | 4.73 |
time (sec) |
N/A | 0.328 | 0.034 | 2.378 | 0.000 | 0.089 | 0.000 | 0.000 | 0.202 | 0.414 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 172 | 113 | 543 | 0 | 293 | 0 | 0 | 0 | 199 |
N.S. |
1 | 1.01 | 0.66 | 3.19 | 0.00 | 1.72 | 0.00 | 0.00 | 0.00 | 1.17 |
time (sec) |
N/A | 0.925 | 0.164 | 1.210 | 0.000 | 0.091 | 0.000 | 0.000 | 0.196 | 0.557 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 137 | 97 | 324 | 0 | 201 | 0 | 0 | 0 | 166 |
N.S. |
1 | 1.01 | 0.71 | 2.38 | 0.00 | 1.48 | 0.00 | 0.00 | 0.00 | 1.22 |
time (sec) |
N/A | 0.735 | 0.123 | 0.612 | 0.000 | 0.086 | 0.000 | 0.000 | 0.191 | 0.334 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 102 | 79 | 169 | 0 | 130 | 0 | 0 | 0 | 97 |
N.S. |
1 | 1.00 | 0.77 | 1.66 | 0.00 | 1.27 | 0.00 | 0.00 | 0.00 | 0.95 |
time (sec) |
N/A | 0.565 | 0.100 | 0.294 | 0.000 | 0.086 | 0.000 | 0.000 | 0.213 | 0.497 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 63 | 74 | 0 | 91 | 0 | 0 | 1286 | 62 |
N.S. |
1 | 1.00 | 0.94 | 1.10 | 0.00 | 1.36 | 0.00 | 0.00 | 19.19 | 0.93 |
time (sec) |
N/A | 0.419 | 0.055 | 0.110 | 0.000 | 0.079 | 0.000 | 0.000 | 0.200 | 0.691 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 46 | 35 | 0 | 45 | 0 | 0 | 1242 | 35 |
N.S. |
1 | 1.00 | 1.00 | 0.76 | 0.00 | 0.98 | 0.00 | 0.00 | 27.00 | 0.76 |
time (sec) |
N/A | 0.340 | 0.015 | 0.265 | 0.000 | 0.084 | 0.000 | 0.000 | 0.191 | 0.205 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 81 | 76 | 0 | 117 | 0 | 0 | 1118 | 76 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.00 | 1.44 | 0.00 | 0.00 | 13.80 | 0.94 |
time (sec) |
N/A | 0.495 | 0.059 | 0.561 | 0.000 | 0.093 | 0.000 | 0.000 | 0.196 | 0.326 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 127 | 95 | 109 | 0 | 199 | 0 | 0 | 1610 | 105 |
N.S. |
1 | 1.10 | 0.83 | 0.95 | 0.00 | 1.73 | 0.00 | 0.00 | 14.00 | 0.91 |
time (sec) |
N/A | 0.654 | 0.112 | 1.143 | 0.000 | 0.089 | 0.000 | 0.000 | 0.205 | 0.416 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 173 | 111 | 142 | 0 | 305 | 0 | 0 | 0 | 142 |
N.S. |
1 | 1.16 | 0.74 | 0.95 | 0.00 | 2.05 | 0.00 | 0.00 | 0.00 | 0.95 |
time (sec) |
N/A | 0.835 | 0.156 | 2.238 | 0.000 | 0.093 | 0.000 | 0.000 | 0.210 | 0.541 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 219 | 127 | 175 | 0 | 439 | 0 | 0 | 0 | 160 |
N.S. |
1 | 1.20 | 0.69 | 0.96 | 0.00 | 2.40 | 0.00 | 0.00 | 0.00 | 0.87 |
time (sec) |
N/A | 1.030 | 0.202 | 3.967 | 0.000 | 0.100 | 0.000 | 0.000 | 0.206 | 0.687 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 49 | 208 | 0 | 601 | 0 | 0 | 0 | 189 |
N.S. |
1 | 1.00 | 1.00 | 4.24 | 0.00 | 12.27 | 0.00 | 0.00 | 0.00 | 3.86 |
time (sec) |
N/A | 0.317 | 0.054 | 6.711 | 0.000 | 0.108 | 0.000 | 0.000 | 0.210 | 0.850 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 49 | 241 | 0 | 791 | 0 | 0 | 0 | 217 |
N.S. |
1 | 1.00 | 1.00 | 4.92 | 0.00 | 16.14 | 0.00 | 0.00 | 0.00 | 4.43 |
time (sec) |
N/A | 0.324 | 0.035 | 10.398 | 0.000 | 0.124 | 0.000 | 0.000 | 0.242 | 0.971 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 61 | 0 | 0 | 0 | 0 | 0 | 0 | 73 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.20 |
time (sec) |
N/A | 0.342 | 0.053 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.212 | 0.245 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 31 | 0 | 0 | 686 | 0 | 0 | 0 | 136 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 22.13 | 0.00 | 0.00 | 0.00 | 4.39 |
time (sec) |
N/A | 0.309 | 0.016 | 0.000 | 0.000 | 0.100 | 0.000 | 0.000 | 0.255 | 0.356 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 31 | 0 | 0 | 487 | 0 | 0 | 0 | 120 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 15.71 | 0.00 | 0.00 | 0.00 | 3.87 |
time (sec) |
N/A | 0.308 | 0.014 | 0.000 | 0.000 | 0.099 | 0.000 | 0.000 | 0.229 | 0.302 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 123 | 96 | 0 | 0 | 330 | 0 | 0 | 0 | 92 |
N.S. |
1 | 1.02 | 0.79 | 0.00 | 0.00 | 2.73 | 0.00 | 0.00 | 0.00 | 0.76 |
time (sec) |
N/A | 0.702 | 0.233 | 0.000 | 0.000 | 0.090 | 0.000 | 0.000 | 0.218 | 0.308 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 88 | 71 | 0 | 0 | 213 | 0 | 0 | 0 | 76 |
N.S. |
1 | 1.01 | 0.82 | 0.00 | 0.00 | 2.45 | 0.00 | 0.00 | 0.00 | 0.87 |
time (sec) |
N/A | 0.571 | 0.086 | 0.000 | 0.000 | 0.091 | 0.000 | 0.000 | 0.197 | 0.225 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 47 | 0 | 0 | 141 | 0 | 0 | 0 | 51 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 2.66 | 0.00 | 0.00 | 0.00 | 0.96 |
time (sec) |
N/A | 0.418 | 0.041 | 0.000 | 0.000 | 0.084 | 0.000 | 0.000 | 0.204 | 0.182 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 0 | 0 | 42 | 0 | 0 | 75 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 1.91 | 0.00 | 0.00 | 3.41 | 0.91 |
time (sec) |
N/A | 0.295 | 0.013 | 0.000 | 0.000 | 0.083 | 0.000 | 0.000 | 0.169 | 0.165 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 26 | 25 | 77 | 65 | 77 | 77 | 48 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 0.93 | 2.85 | 2.41 | 2.85 | 2.85 | 1.78 |
time (sec) |
N/A | 0.303 | 0.018 | 0.499 | 0.025 | 0.081 | 0.188 | 0.143 | 0.185 | 0.147 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 47 | 97 | 144 | 148 | 114 | 0 | 138 | 136 |
N.S. |
1 | 1.00 | 0.76 | 1.56 | 2.32 | 2.39 | 1.84 | 0.00 | 2.23 | 2.19 |
time (sec) |
N/A | 0.429 | 0.036 | 1.263 | 0.041 | 0.080 | 0.142 | 0.000 | 0.268 | 0.247 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 106 | 64 | 175 | 300 | 265 | 270 | 0 | 252 | 263 |
N.S. |
1 | 1.10 | 0.67 | 1.82 | 3.12 | 2.76 | 2.81 | 0.00 | 2.62 | 2.74 |
time (sec) |
N/A | 0.576 | 0.055 | 2.883 | 0.044 | 0.087 | 0.194 | 0.000 | 0.211 | 0.399 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 150 | 73 | 307 | 507 | 423 | 484 | 0 | 417 | 422 |
N.S. |
1 | 1.22 | 0.59 | 2.50 | 4.12 | 3.44 | 3.93 | 0.00 | 3.39 | 3.43 |
time (sec) |
N/A | 0.733 | 0.042 | 5.802 | 0.047 | 0.105 | 0.267 | 0.000 | 0.194 | 0.685 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 96 | 31 | 493 | 770 | 621 | 760 | 0 | 636 | 620 |
N.S. |
1 | 1.00 | 0.32 | 5.14 | 8.02 | 6.47 | 7.92 | 0.00 | 6.62 | 6.46 |
time (sec) |
N/A | 0.408 | 0.015 | 10.549 | 0.060 | 0.123 | 0.568 | 0.000 | 0.236 | 0.991 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 31 | 733 | 1085 | 863 | 1096 | 0 | 909 | 854 |
N.S. |
1 | 1.00 | 0.27 | 6.49 | 9.60 | 7.64 | 9.70 | 0.00 | 8.04 | 7.56 |
time (sec) |
N/A | 0.452 | 0.013 | 18.087 | 0.069 | 0.170 | 2.625 | 0.000 | 0.309 | 1.399 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 49 | 0 | 0 | 178 | 0 | 0 | 0 | 128 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 3.63 | 0.00 | 0.00 | 0.00 | 2.61 |
time (sec) |
N/A | 0.324 | 0.035 | 0.000 | 0.000 | 0.108 | 0.000 | 0.000 | 0.283 | 0.390 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 49 | 0 | 0 | 142 | 0 | 0 | 0 | 107 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 2.90 | 0.00 | 0.00 | 0.00 | 2.18 |
time (sec) |
N/A | 0.302 | 0.029 | 0.000 | 0.000 | 0.082 | 0.000 | 0.000 | 0.271 | 0.940 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 47 | 0 | 0 | 129 | 0 | 0 | 0 | 71 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 2.74 | 0.00 | 0.00 | 0.00 | 1.51 |
time (sec) |
N/A | 0.263 | 0.017 | 0.000 | 0.000 | 0.081 | 0.000 | 0.000 | 0.299 | 0.341 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 49 | 0 | 0 | 59 | 0 | 0 | 0 | 58 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 1.20 | 0.00 | 0.00 | 0.00 | 1.18 |
time (sec) |
N/A | 0.317 | 0.035 | 0.000 | 0.000 | 0.082 | 0.000 | 0.000 | 0.241 | 0.251 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 49 | 0 | 0 | 58 | 0 | 0 | 0 | 48 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 1.18 | 0.00 | 0.00 | 0.00 | 0.98 |
time (sec) |
N/A | 0.317 | 0.035 | 0.000 | 0.000 | 0.080 | 0.000 | 0.000 | 0.269 | 0.229 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 49 | 0 | 0 | 155 | 0 | 0 | 0 | 114 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 3.16 | 0.00 | 0.00 | 0.00 | 2.33 |
time (sec) |
N/A | 0.315 | 0.041 | 0.000 | 0.000 | 0.083 | 0.000 | 0.000 | 0.176 | 0.427 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 61 | 0 | 0 | 0 | 0 | 0 | 25 | 93 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.41 | 1.52 |
time (sec) |
N/A | 0.331 | 0.027 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 0.460 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 54 | 0 | 0 | 0 | 0 | 0 | 87 | 73 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.61 | 1.35 |
time (sec) |
N/A | 0.325 | 0.022 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.168 | 0.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 54 | 0 | 0 | 0 | 0 | 0 | 62 | 73 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.15 | 1.35 |
time (sec) |
N/A | 0.324 | 0.021 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 0.297 |
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 | 54 | 54 | 54 | 0 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.307 | 0.017 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.163 | 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 | 50 | 50 | 50 | 0 | 0 | 0 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.281 | 0.014 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 26 | 0 | 22 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.18 | 0.00 | 1.00 | 0.00 | 0.00 | 1.14 | 0.00 |
time (sec) |
N/A | 0.288 | 0.008 | 0.193 | 0.000 | 0.073 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 52 | 0 | 0 | 0 | 0 | 0 | 36 | 71 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.69 | 1.37 |
time (sec) |
N/A | 0.318 | 0.017 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.155 | 0.174 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 54 | 0 | 0 | 0 | 0 | 0 | 47 | 67 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.87 | 1.24 |
time (sec) |
N/A | 0.312 | 0.015 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.152 | 0.173 |