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 | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 212 | 161 | 272 | 0 | 316 | 0 | 0 | 108 | 0 |
N.S. |
1 | 1.05 | 0.80 | 1.35 | 0.00 | 1.56 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 1.044 | 4.565 | 5.877 | 0.000 | 0.093 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 182 | 89 | 134 | 0 | 258 | 0 | 0 | 108 | 0 |
N.S. |
1 | 1.04 | 0.51 | 0.77 | 0.00 | 1.47 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.887 | 2.589 | 5.246 | 0.000 | 0.099 | 0.000 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 178 | 129 | 242 | 0 | 208 | 0 | 0 | 98 | 0 |
N.S. |
1 | 1.02 | 0.74 | 1.38 | 0.00 | 1.19 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.838 | 3.192 | 8.317 | 0.000 | 0.078 | 0.000 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 147 | 79 | 103 | 0 | 148 | 0 | 0 | 72 | 0 |
N.S. |
1 | 1.06 | 0.57 | 0.74 | 0.00 | 1.06 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.687 | 2.304 | 7.858 | 0.000 | 0.110 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 154 | 101 | 473 | 0 | 123 | 0 | 0 | 112 | 0 |
N.S. |
1 | 1.24 | 0.81 | 3.81 | 0.00 | 0.99 | 0.00 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.722 | 2.532 | 7.257 | 0.000 | 0.086 | 0.000 | 0.000 | 0.230 | 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 | 111 | 108 | 123 | 115 | 0 | 82 | 0 | 0 | 112 | 0 |
N.S. |
1 | 0.97 | 1.11 | 1.04 | 0.00 | 0.74 | 0.00 | 0.00 | 1.01 | 0.00 |
time (sec) |
N/A | 0.519 | 1.872 | 7.197 | 0.000 | 0.101 | 0.000 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 108 | 108 | 324 | 0 | 94 | 0 | 0 | 112 | 0 |
N.S. |
1 | 0.97 | 0.97 | 2.92 | 0.00 | 0.85 | 0.00 | 0.00 | 1.01 | 0.00 |
time (sec) |
N/A | 0.527 | 2.256 | 8.454 | 0.000 | 0.077 | 0.000 | 0.000 | 0.238 | 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 | 124 | 130 | 133 | 129 | 0 | 96 | 0 | 0 | 112 | 0 |
N.S. |
1 | 1.05 | 1.07 | 1.04 | 0.00 | 0.77 | 0.00 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.610 | 1.781 | 11.739 | 0.000 | 0.082 | 0.000 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 130 | 118 | 258 | 0 | 108 | 0 | 0 | 112 | 0 |
N.S. |
1 | 1.05 | 0.95 | 2.08 | 0.00 | 0.87 | 0.00 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.635 | 2.869 | 18.480 | 0.000 | 0.083 | 0.000 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 166 | 148 | 139 | 0 | 110 | 0 | 0 | 112 | 0 |
N.S. |
1 | 1.07 | 0.95 | 0.90 | 0.00 | 0.71 | 0.00 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 0.801 | 2.002 | 21.196 | 0.000 | 0.109 | 0.000 | 0.000 | 0.235 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 166 | 145 | 282 | 0 | 145 | 0 | 0 | 112 | 0 |
N.S. |
1 | 1.07 | 0.94 | 1.82 | 0.00 | 0.94 | 0.00 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 0.770 | 4.171 | 30.819 | 0.000 | 0.093 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 202 | 170 | 151 | 0 | 156 | 0 | 0 | 112 | 0 |
N.S. |
1 | 1.09 | 0.91 | 0.81 | 0.00 | 0.84 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.923 | 2.499 | 32.798 | 0.000 | 0.092 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 215 | 221 | 327 | 269 | 0 | 250 | 0 | 0 | 125 | 0 |
N.S. |
1 | 1.03 | 1.52 | 1.25 | 0.00 | 1.16 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 1.048 | 6.914 | 17.098 | 0.000 | 0.106 | 0.000 | 0.000 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 190 | 101 | 119 | 0 | 188 | 0 | 0 | 93 | 0 |
N.S. |
1 | 1.04 | 0.55 | 0.65 | 0.00 | 1.03 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.867 | 2.677 | 14.788 | 0.000 | 0.088 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 179 | 123 | 498 | 0 | 164 | 0 | 0 | 138 | 0 |
N.S. |
1 | 1.01 | 0.69 | 2.80 | 0.00 | 0.92 | 0.00 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.838 | 4.792 | 13.465 | 0.000 | 0.109 | 0.000 | 0.000 | 0.238 | 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 | 146 | 150 | 130 | 129 | 0 | 129 | 0 | 0 | 138 | 0 |
N.S. |
1 | 1.03 | 0.89 | 0.88 | 0.00 | 0.88 | 0.00 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 0.692 | 2.830 | 12.387 | 0.000 | 0.095 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 159 | 110 | 496 | 0 | 94 | 0 | 0 | 138 | 0 |
N.S. |
1 | 1.02 | 0.71 | 3.18 | 0.00 | 0.60 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.712 | 3.766 | 14.069 | 0.000 | 0.106 | 0.000 | 0.000 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 133 | 133 | 129 | 0 | 96 | 0 | 0 | 138 | 0 |
N.S. |
1 | 1.06 | 1.06 | 1.03 | 0.00 | 0.77 | 0.00 | 0.00 | 1.10 | 0.00 |
time (sec) |
N/A | 0.573 | 2.552 | 17.347 | 0.000 | 0.111 | 0.000 | 0.000 | 0.235 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 133 | 108 | 270 | 0 | 108 | 0 | 0 | 138 | 0 |
N.S. |
1 | 1.06 | 0.86 | 2.16 | 0.00 | 0.86 | 0.00 | 0.00 | 1.10 | 0.00 |
time (sec) |
N/A | 0.577 | 3.978 | 26.880 | 0.000 | 0.081 | 0.000 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 169 | 148 | 139 | 0 | 110 | 0 | 0 | 138 | 0 |
N.S. |
1 | 1.08 | 0.95 | 0.89 | 0.00 | 0.71 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.722 | 2.403 | 31.253 | 0.000 | 0.092 | 0.000 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 169 | 121 | 278 | 0 | 122 | 0 | 0 | 138 | 0 |
N.S. |
1 | 1.08 | 0.78 | 1.78 | 0.00 | 0.78 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.711 | 7.971 | 42.074 | 0.000 | 0.094 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 205 | 155 | 151 | 0 | 124 | 0 | 0 | 138 | 0 |
N.S. |
1 | 1.10 | 0.83 | 0.81 | 0.00 | 0.66 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.870 | 3.002 | 46.421 | 0.000 | 0.099 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 135 | 128 | 235 | 0 | 205 | 0 | 0 | 39 | 0 |
N.S. |
1 | 0.99 | 0.94 | 1.73 | 0.00 | 1.51 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.636 | 2.148 | 4.261 | 0.000 | 0.086 | 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(-2) | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 62 | 105 | 0 | 152 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.00 | 0.59 | 1.00 | 0.00 | 1.45 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.500 | 1.531 | 3.804 | 0.000 | 0.103 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 102 | 200 | 0 | 123 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.00 | 1.01 | 1.98 | 0.00 | 1.22 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.505 | 1.694 | 2.863 | 0.000 | 0.087 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 49 | 87 | 0 | 63 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.00 | 0.70 | 1.24 | 0.00 | 0.90 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.386 | 1.208 | 2.237 | 0.000 | 0.083 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 74 | 477 | 0 | 96 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 1.06 | 6.81 | 0.00 | 1.37 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.391 | 1.238 | 1.967 | 0.000 | 0.078 | 0.000 | 0.000 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 83 | 161 | 0 | 90 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 1.04 | 2.01 | 0.00 | 1.12 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.386 | 0.964 | 2.804 | 0.000 | 0.093 | 0.000 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 109 | 407 | 0 | 107 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.00 | 1.36 | 5.09 | 0.00 | 1.34 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.391 | 1.443 | 3.683 | 0.000 | 0.090 | 0.000 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 116 | 125 | 118 | 0 | 115 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.02 | 1.10 | 1.04 | 0.00 | 1.01 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.520 | 1.424 | 3.772 | 0.000 | 0.091 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 116 | 134 | 444 | 0 | 129 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.02 | 1.18 | 3.89 | 0.00 | 1.13 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.519 | 1.903 | 4.197 | 0.000 | 0.095 | 0.000 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 152 | 142 | 128 | 0 | 137 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.05 | 0.98 | 0.88 | 0.00 | 0.94 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.648 | 1.739 | 10.991 | 0.000 | 0.090 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 188 | 302 | 258 | 0 | 256 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.03 | 1.65 | 1.41 | 0.00 | 1.40 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.819 | 2.755 | 5.671 | 0.000 | 0.082 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 158 | 85 | 121 | 0 | 201 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.04 | 0.56 | 0.80 | 0.00 | 1.32 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.670 | 1.456 | 5.110 | 0.000 | 0.090 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 154 | 123 | 222 | 0 | 170 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.01 | 0.81 | 1.46 | 0.00 | 1.12 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.671 | 1.823 | 3.956 | 0.000 | 0.080 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 120 | 67 | 95 | 0 | 115 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.01 | 0.56 | 0.80 | 0.00 | 0.97 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.502 | 1.322 | 3.188 | 0.000 | 0.092 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 116 | 80 | 219 | 0 | 100 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.01 | 0.70 | 1.90 | 0.00 | 0.87 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.530 | 1.436 | 4.126 | 0.000 | 0.082 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 101 | 164 | 0 | 97 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.00 | 1.12 | 1.82 | 0.00 | 1.08 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.396 | 1.267 | 3.485 | 0.000 | 0.133 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 102 | 428 | 0 | 108 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.00 | 1.13 | 4.76 | 0.00 | 1.20 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.418 | 1.217 | 3.408 | 0.000 | 0.079 | 0.000 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 126 | 112 | 177 | 0 | 101 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.09 | 0.97 | 1.53 | 0.00 | 0.87 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.525 | 1.047 | 3.358 | 0.000 | 0.079 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 126 | 123 | 480 | 0 | 118 | 0 | 0 | 55 | 0 |
N.S. |
1 | 1.09 | 1.06 | 4.14 | 0.00 | 1.02 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.549 | 1.969 | 4.465 | 0.000 | 0.103 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 162 | 134 | 128 | 0 | 126 | 0 | 0 | 76 | 0 |
N.S. |
1 | 1.08 | 0.89 | 0.85 | 0.00 | 0.84 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.688 | 1.461 | 4.245 | 0.000 | 0.106 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 162 | 149 | 520 | 0 | 140 | 0 | 0 | 82 | 0 |
N.S. |
1 | 1.08 | 0.99 | 3.47 | 0.00 | 0.93 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.678 | 2.655 | 4.533 | 0.000 | 0.094 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 198 | 151 | 138 | 0 | 148 | 0 | 0 | 82 | 0 |
N.S. |
1 | 1.09 | 0.83 | 0.76 | 0.00 | 0.82 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.838 | 1.829 | 17.704 | 0.000 | 0.098 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 188 | 128 | 246 | 0 | 213 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.06 | 0.72 | 1.38 | 0.00 | 1.20 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.931 | 2.173 | 4.781 | 0.000 | 0.085 | 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(-2) | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 154 | 74 | 107 | 0 | 158 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.09 | 0.52 | 0.76 | 0.00 | 1.12 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.735 | 1.557 | 3.793 | 0.000 | 0.095 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 150 | 93 | 229 | 0 | 150 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.06 | 0.66 | 1.62 | 0.00 | 1.06 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.701 | 1.796 | 4.223 | 0.000 | 0.078 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 123 | 125 | 117 | 0 | 97 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.06 | 1.08 | 1.01 | 0.00 | 0.84 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.580 | 1.403 | 4.008 | 0.000 | 0.081 | 0.000 | 0.000 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 123 | 117 | 446 | 0 | 114 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.06 | 1.01 | 3.84 | 0.00 | 0.98 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.583 | 1.546 | 3.633 | 0.000 | 0.079 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 133 | 104 | 191 | 0 | 111 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.01 | 0.79 | 1.45 | 0.00 | 0.84 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.568 | 1.469 | 3.197 | 0.000 | 0.086 | 0.000 | 0.000 | 0.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 133 | 140 | 497 | 0 | 120 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.01 | 1.06 | 3.77 | 0.00 | 0.91 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.583 | 1.591 | 3.572 | 0.000 | 0.077 | 0.000 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 170 | 129 | 143 | 0 | 112 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.12 | 0.85 | 0.94 | 0.00 | 0.74 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.703 | 1.225 | 3.405 | 0.000 | 0.088 | 0.000 | 0.000 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 170 | 145 | 279 | 0 | 129 | 0 | 0 | 78 | 0 |
N.S. |
1 | 1.12 | 0.95 | 1.84 | 0.00 | 0.85 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.724 | 1.998 | 4.492 | 0.000 | 0.098 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 206 | 151 | 151 | 0 | 137 | 0 | 0 | 86 | 0 |
N.S. |
1 | 1.11 | 0.81 | 0.81 | 0.00 | 0.74 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.942 | 1.587 | 4.589 | 0.000 | 0.093 | 0.000 | 0.000 | 0.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 203 | 124 | 257 | 0 | 193 | 0 | 0 | 69 | 0 |
N.S. |
1 | 1.06 | 0.65 | 1.34 | 0.00 | 1.01 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.902 | 2.044 | 5.438 | 0.000 | 0.081 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 171 | 134 | 122 | 0 | 147 | 0 | 0 | 69 | 0 |
N.S. |
1 | 1.09 | 0.85 | 0.78 | 0.00 | 0.94 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.718 | 1.489 | 4.748 | 0.000 | 0.110 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 169 | 106 | 444 | 0 | 114 | 0 | 0 | 69 | 0 |
N.S. |
1 | 1.04 | 0.65 | 2.72 | 0.00 | 0.70 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.726 | 1.538 | 4.493 | 0.000 | 0.078 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 143 | 137 | 191 | 0 | 111 | 0 | 0 | 69 | 0 |
N.S. |
1 | 1.08 | 1.04 | 1.45 | 0.00 | 0.84 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.589 | 1.446 | 3.801 | 0.000 | 0.088 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 143 | 149 | 501 | 0 | 128 | 0 | 0 | 69 | 0 |
N.S. |
1 | 1.08 | 1.13 | 3.80 | 0.00 | 0.97 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.590 | 1.661 | 3.726 | 0.000 | 0.080 | 0.000 | 0.000 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 179 | 144 | 144 | 0 | 125 | 0 | 0 | 69 | 0 |
N.S. |
1 | 1.10 | 0.88 | 0.88 | 0.00 | 0.77 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.726 | 1.411 | 3.616 | 0.000 | 0.100 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 179 | 142 | 291 | 0 | 132 | 0 | 0 | 65 | 0 |
N.S. |
1 | 1.10 | 0.87 | 1.79 | 0.00 | 0.81 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.732 | 1.898 | 3.863 | 0.000 | 0.088 | 0.000 | 0.000 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 214 | 137 | 153 | 0 | 123 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.12 | 0.72 | 0.80 | 0.00 | 0.64 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.914 | 1.148 | 3.807 | 0.000 | 0.077 | 0.000 | 0.000 | 0.235 | 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 | 69 | 69 | 71 | 0 | 0 | 0 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.455 | 0.242 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.232 | 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 | 67 | 67 | 61 | 0 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.430 | 0.156 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.232 | 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 | 67 | 67 | 61 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.456 | 0.124 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.170 | 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 | 69 | 69 | 63 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.443 | 0.207 | 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 | 71 | 71 | 111 | 0 | 0 | 0 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.00 | 1.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.82 | 0.00 |
time (sec) |
N/A | 0.463 | 0.397 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.240 | 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 | 69 | 69 | 102 | 0 | 0 | 0 | 0 | 0 | 56 | 0 |
N.S. |
1 | 1.00 | 1.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.446 | 0.340 | 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 | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 80 | 103 | 0 | 0 | 0 | 0 | 0 | 59 | 0 |
N.S. |
1 | 0.96 | 1.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.449 | 0.321 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 82 | 105 | 0 | 0 | 0 | 0 | 0 | 59 | 0 |
N.S. |
1 | 0.96 | 1.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.453 | 0.472 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 83 | 84 | 0 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 0.99 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.469 | 1.432 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 81 | 103 | 0 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 0.99 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.448 | 1.179 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 112 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.00 | 1.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.439 | 1.587 | 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(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 119 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.00 | 1.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.471 | 1.791 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 86 | 128 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.02 | 1.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.470 | 1.495 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 86 | 121 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.02 | 1.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.462 | 1.265 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 141 | 0 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.00 | 1.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.468 | 1.998 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 143 | 0 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.00 | 2.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.472 | 1.736 | 0.000 | 0.000 | 0.000 | 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) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 102 | 70 | 82 | 76 | 154 | 0 | 0 | 60 | 474 |
N.S. |
1 | 0.87 | 0.60 | 0.70 | 0.65 | 1.32 | 0.00 | 0.00 | 0.51 | 4.05 |
time (sec) |
N/A | 0.281 | 0.304 | 0.913 | 0.030 | 0.094 | 0.000 | 0.000 | 0.235 | 9.403 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 78 | 58 | 63 | 58 | 119 | 0 | 0 | 60 | 352 |
N.S. |
1 | 0.89 | 0.66 | 0.72 | 0.66 | 1.35 | 0.00 | 0.00 | 0.68 | 4.00 |
time (sec) |
N/A | 0.276 | 0.190 | 0.503 | 0.035 | 0.085 | 0.000 | 0.000 | 0.216 | 4.240 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 54 | 48 | 44 | 40 | 84 | 0 | 0 | 60 | 230 |
N.S. |
1 | 0.92 | 0.81 | 0.75 | 0.68 | 1.42 | 0.00 | 0.00 | 1.02 | 3.90 |
time (sec) |
N/A | 0.267 | 0.143 | 0.504 | 0.055 | 0.102 | 0.000 | 0.000 | 0.195 | 3.482 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 24 | 21 | 46 | 0 | 0 | 60 | 82 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.72 | 1.59 | 0.00 | 0.00 | 2.07 | 2.83 |
time (sec) |
N/A | 0.254 | 0.063 | 0.366 | 0.028 | 0.087 | 0.000 | 0.000 | 0.191 | 0.652 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | B | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 112 | 51 | 328 | 122 | 253 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.90 | 0.41 | 2.65 | 0.98 | 2.04 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.290 | 0.110 | 4.437 | 0.116 | 0.088 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 191 | 53 | 351 | 176 | 275 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.97 | 0.27 | 1.78 | 0.89 | 1.40 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.321 | 0.113 | 4.237 | 0.131 | 0.110 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 274 | 270 | 53 | 371 | 230 | 297 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.99 | 0.19 | 1.35 | 0.84 | 1.08 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.351 | 0.223 | 4.659 | 0.137 | 0.100 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 155 | 95 | 115 | 0 | 132 | 0 | 0 | 60 | 289 |
N.S. |
1 | 1.05 | 0.65 | 0.78 | 0.00 | 0.90 | 0.00 | 0.00 | 0.41 | 1.97 |
time (sec) |
N/A | 0.687 | 0.875 | 3.222 | 0.000 | 0.116 | 0.000 | 0.000 | 0.216 | 5.593 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 114 | 77 | 89 | 0 | 97 | 0 | 0 | 60 | 102 |
N.S. |
1 | 1.04 | 0.70 | 0.81 | 0.00 | 0.88 | 0.00 | 0.00 | 0.55 | 0.93 |
time (sec) |
N/A | 0.518 | 0.597 | 2.811 | 0.000 | 0.126 | 0.000 | 0.000 | 0.245 | 3.318 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 63 | 63 | 222 | 62 | 0 | 0 | 60 | 88 |
N.S. |
1 | 1.00 | 0.86 | 0.86 | 3.04 | 0.85 | 0.00 | 0.00 | 0.82 | 1.21 |
time (sec) |
N/A | 0.364 | 0.480 | 2.664 | 16.067 | 0.089 | 0.000 | 0.000 | 0.242 | 3.264 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 39 | 52 | 0 | 25 | 0 | 0 | 56 | 61 |
N.S. |
1 | 1.00 | 1.26 | 1.68 | 0.00 | 0.81 | 0.00 | 0.00 | 1.81 | 1.97 |
time (sec) |
N/A | 0.215 | 0.262 | 2.600 | 0.000 | 0.075 | 0.000 | 0.000 | 0.219 | 0.375 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 87 | 320 | 774 | 184 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 1.05 | 3.86 | 9.33 | 2.22 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.352 | 0.598 | 4.364 | 0.250 | 0.092 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 163 | 126 | 340 | 935 | 245 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.06 | 0.82 | 2.21 | 6.07 | 1.59 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.645 | 0.649 | 4.665 | 0.270 | 0.095 | 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) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 245 | 152 | 361 | 2220 | 267 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.10 | 0.68 | 1.62 | 9.96 | 1.20 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 1.021 | 0.844 | 4.475 | 0.404 | 0.105 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 102 | 73 | 82 | 76 | 170 | 0 | 0 | 62 | 544 |
N.S. |
1 | 0.87 | 0.62 | 0.70 | 0.65 | 1.45 | 0.00 | 0.00 | 0.53 | 4.65 |
time (sec) |
N/A | 0.274 | 0.380 | 0.549 | 0.034 | 0.117 | 0.000 | 0.000 | 0.217 | 12.431 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 78 | 61 | 63 | 58 | 134 | 0 | 0 | 62 | 420 |
N.S. |
1 | 0.89 | 0.69 | 0.72 | 0.66 | 1.52 | 0.00 | 0.00 | 0.70 | 4.77 |
time (sec) |
N/A | 0.265 | 0.236 | 0.553 | 0.042 | 0.096 | 0.000 | 0.000 | 0.207 | 4.512 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 54 | 51 | 44 | 40 | 98 | 0 | 0 | 62 | 296 |
N.S. |
1 | 0.92 | 0.86 | 0.75 | 0.68 | 1.66 | 0.00 | 0.00 | 1.05 | 5.02 |
time (sec) |
N/A | 0.265 | 0.149 | 0.555 | 0.043 | 0.093 | 0.000 | 0.000 | 0.225 | 3.514 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 24 | 21 | 59 | 0 | 0 | 62 | 153 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.72 | 2.03 | 0.00 | 0.00 | 2.14 | 5.28 |
time (sec) |
N/A | 0.221 | 0.092 | 0.483 | 0.044 | 0.078 | 0.000 | 0.000 | 0.201 | 1.513 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 84 | 92 | 396 | 98 | 244 | 0 | 0 | 57 | 0 |
N.S. |
1 | 0.87 | 0.95 | 4.08 | 1.01 | 2.52 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.259 | 0.154 | 4.713 | 0.144 | 0.082 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 159 | 53 | 772 | 158 | 287 | 0 | 0 | 57 | 0 |
N.S. |
1 | 0.94 | 0.31 | 4.54 | 0.93 | 1.69 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.314 | 0.103 | 4.344 | 0.138 | 0.086 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 247 | 238 | 53 | 815 | 212 | 311 | 0 | 0 | 57 | 0 |
N.S. |
1 | 0.96 | 0.21 | 3.30 | 0.86 | 1.26 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.357 | 0.135 | 5.057 | 0.117 | 0.090 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 155 | 109 | 100 | 994 | 125 | 0 | 0 | 62 | 293 |
N.S. |
1 | 1.05 | 0.74 | 0.68 | 6.76 | 0.85 | 0.00 | 0.00 | 0.42 | 1.99 |
time (sec) |
N/A | 0.717 | 1.160 | 2.872 | 9.297 | 0.102 | 0.000 | 0.000 | 0.245 | 4.656 |