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 | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 102 | 105 | 77 | 0 | 0 | 0 | 78 | 0 | 0 |
N.S. |
1 | 1.03 | 0.75 | 0.00 | 0.00 | 0.00 | 0.76 | 0.00 | 0.00 |
time (sec) |
N/A | 0.282 | 10.046 | 0.000 | 0.000 | 0.000 | 2.414 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 107 | 110 | 84 | 0 | 0 | 0 | 82 | 0 | 0 |
N.S. |
1 | 1.03 | 0.79 | 0.00 | 0.00 | 0.00 | 0.77 | 0.00 | 0.00 |
time (sec) |
N/A | 0.281 | 10.041 | 0.000 | 0.000 | 0.000 | 9.409 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 144 | 149 | 88 | 0 | 0 | 0 | 85 | 0 | 0 |
N.S. |
1 | 1.03 | 0.61 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 | 0.00 |
time (sec) |
N/A | 0.318 | 10.063 | 0.000 | 0.000 | 0.000 | 100.432 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 182 | 189 | 88 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.372 | 10.055 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | C | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 171 | 166 | 148 | 0 | 0 | 810 | 94 | 0 | 0 |
N.S. |
1 | 0.97 | 0.87 | 0.00 | 0.00 | 4.74 | 0.55 | 0.00 | 0.00 |
time (sec) |
N/A | 0.279 | 1.029 | 0.000 | 0.000 | 0.313 | 14.243 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | C | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 122 | 136 | 103 | 0 | 0 | 389 | 83 | 0 | 0 |
N.S. |
1 | 1.11 | 0.84 | 0.00 | 0.00 | 3.19 | 0.68 | 0.00 | 0.00 |
time (sec) |
N/A | 0.252 | 0.538 | 0.000 | 0.000 | 0.301 | 9.933 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 45 | 39 | 0 | 57 | 117 | 0 | 70 |
N.S. |
1 | 1.00 | 0.67 | 0.58 | 0.00 | 0.85 | 1.75 | 0.00 | 1.04 |
time (sec) |
N/A | 0.191 | 0.353 | 3.189 | 0.000 | 0.287 | 30.963 | 0.000 | 5.493 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 104 | 67 | 62 | 0 | 80 | 0 | 0 | 101 |
N.S. |
1 | 1.00 | 0.64 | 0.60 | 0.00 | 0.77 | 0.00 | 0.00 | 0.97 |
time (sec) |
N/A | 0.214 | 0.554 | 3.202 | 0.000 | 0.284 | 0.000 | 0.000 | 5.752 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 141 | 138 | 91 | 86 | 0 | 105 | 0 | 0 | 125 |
N.S. |
1 | 0.98 | 0.65 | 0.61 | 0.00 | 0.74 | 0.00 | 0.00 | 0.89 |
time (sec) |
N/A | 0.234 | 0.841 | 3.262 | 0.000 | 0.287 | 0.000 | 0.000 | 5.820 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 180 | 176 | 112 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.293 | 10.100 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 142 | 138 | 85 | 0 | 0 | 0 | 94 | 0 | 0 |
N.S. |
1 | 0.97 | 0.60 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 | 0.00 |
time (sec) |
N/A | 0.261 | 10.079 | 0.000 | 0.000 | 0.000 | 42.935 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 99 | 101 | 77 | 0 | 0 | 0 | 94 | 0 | 0 |
N.S. |
1 | 1.02 | 0.78 | 0.00 | 0.00 | 0.00 | 0.95 | 0.00 | 0.00 |
time (sec) |
N/A | 0.231 | 10.073 | 0.000 | 0.000 | 0.000 | 6.824 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 103 | 105 | 77 | 0 | 0 | 0 | 82 | 0 | 0 |
N.S. |
1 | 1.02 | 0.75 | 0.00 | 0.00 | 0.00 | 0.80 | 0.00 | 0.00 |
time (sec) |
N/A | 0.234 | 10.032 | 0.000 | 0.000 | 0.000 | 15.391 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 144 | 144 | 78 | 0 | 0 | 0 | 85 | 0 | 0 |
N.S. |
1 | 1.00 | 0.54 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 | 0.00 |
time (sec) |
N/A | 0.275 | 10.034 | 0.000 | 0.000 | 0.000 | 77.570 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 182 | 184 | 82 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.301 | 10.052 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 184 | 186 | 129 | 0 | 0 | 0 | 94 | 0 | 0 |
N.S. |
1 | 1.01 | 0.70 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 | 0.00 |
time (sec) |
N/A | 0.311 | 0.997 | 0.000 | 0.000 | 0.000 | 49.355 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 125 | 136 | 108 | 0 | 0 | 0 | 87 | 0 | 0 |
N.S. |
1 | 1.09 | 0.86 | 0.00 | 0.00 | 0.00 | 0.70 | 0.00 | 0.00 |
time (sec) |
N/A | 0.273 | 0.753 | 0.000 | 0.000 | 0.000 | 12.726 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 44 | 40 | 0 | 56 | 119 | 0 | 69 |
N.S. |
1 | 1.00 | 0.68 | 0.62 | 0.00 | 0.86 | 1.83 | 0.00 | 1.06 |
time (sec) |
N/A | 0.186 | 0.464 | 3.206 | 0.000 | 0.319 | 31.599 | 0.000 | 5.612 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 106 | 67 | 62 | 0 | 81 | 469 | 0 | 101 |
N.S. |
1 | 1.02 | 0.64 | 0.60 | 0.00 | 0.78 | 4.51 | 0.00 | 0.97 |
time (sec) |
N/A | 0.210 | 0.545 | 3.250 | 0.000 | 0.308 | 138.648 | 0.000 | 5.764 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 141 | 140 | 91 | 86 | 0 | 105 | 0 | 0 | 125 |
N.S. |
1 | 0.99 | 0.65 | 0.61 | 0.00 | 0.74 | 0.00 | 0.00 | 0.89 |
time (sec) |
N/A | 0.233 | 0.917 | 3.213 | 0.000 | 0.343 | 0.000 | 0.000 | 5.846 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 192 | 184 | 110 | 0 | 0 | 0 | 94 | 0 | 0 |
N.S. |
1 | 0.96 | 0.57 | 0.00 | 0.00 | 0.00 | 0.49 | 0.00 | 0.00 |
time (sec) |
N/A | 0.359 | 10.095 | 0.000 | 0.000 | 0.000 | 149.191 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 152 | 148 | 85 | 0 | 0 | 0 | 94 | 0 | 0 |
N.S. |
1 | 0.97 | 0.56 | 0.00 | 0.00 | 0.00 | 0.62 | 0.00 | 0.00 |
time (sec) |
N/A | 0.323 | 10.074 | 0.000 | 0.000 | 0.000 | 20.357 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 116 | 119 | 79 | 0 | 0 | 0 | 78 | 0 | 0 |
N.S. |
1 | 1.03 | 0.68 | 0.00 | 0.00 | 0.00 | 0.67 | 0.00 | 0.00 |
time (sec) |
N/A | 0.287 | 10.047 | 0.000 | 0.000 | 0.000 | 18.124 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 144 | 147 | 91 | 0 | 0 | 0 | 97 | 0 | 0 |
N.S. |
1 | 1.02 | 0.63 | 0.00 | 0.00 | 0.00 | 0.67 | 0.00 | 0.00 |
time (sec) |
N/A | 0.318 | 10.040 | 0.000 | 0.000 | 0.000 | 55.221 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 181 | 183 | 82 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.351 | 10.052 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 221 | 217 | 150 | 0 | 0 | 904 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.68 | 0.00 | 0.00 | 4.09 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.332 | 1.897 | 0.000 | 0.000 | 0.312 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | C | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 149 | 165 | 124 | 0 | 0 | 468 | 116 | 0 | 0 |
N.S. |
1 | 1.11 | 0.83 | 0.00 | 0.00 | 3.14 | 0.78 | 0.00 | 0.00 |
time (sec) |
N/A | 0.277 | 1.321 | 0.000 | 0.000 | 0.298 | 67.625 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 44 | 39 | 0 | 62 | 230 | 0 | 79 |
N.S. |
1 | 1.00 | 0.56 | 0.49 | 0.00 | 0.78 | 2.91 | 0.00 | 1.00 |
time (sec) |
N/A | 0.195 | 0.610 | 3.295 | 0.000 | 0.279 | 69.403 | 0.000 | 5.864 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 106 | 67 | 62 | 0 | 95 | 0 | 0 | 115 |
N.S. |
1 | 1.02 | 0.64 | 0.60 | 0.00 | 0.91 | 0.00 | 0.00 | 1.11 |
time (sec) |
N/A | 0.215 | 0.550 | 3.382 | 0.000 | 0.290 | 0.000 | 0.000 | 5.910 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 141 | 140 | 88 | 86 | 0 | 119 | 0 | 0 | 144 |
N.S. |
1 | 0.99 | 0.62 | 0.61 | 0.00 | 0.84 | 0.00 | 0.00 | 1.02 |
time (sec) |
N/A | 0.246 | 0.765 | 3.254 | 0.000 | 0.278 | 0.000 | 0.000 | 6.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 178 | 174 | 115 | 110 | 0 | 143 | 0 | 0 | 156 |
N.S. |
1 | 0.98 | 0.65 | 0.62 | 0.00 | 0.80 | 0.00 | 0.00 | 0.88 |
time (sec) |
N/A | 0.265 | 1.291 | 3.242 | 0.000 | 0.279 | 0.000 | 0.000 | 6.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 230 | 225 | 140 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.329 | 10.153 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 192 | 189 | 116 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.303 | 10.104 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 155 | 151 | 98 | 0 | 0 | 0 | 94 | 0 | 0 |
N.S. |
1 | 0.97 | 0.63 | 0.00 | 0.00 | 0.00 | 0.61 | 0.00 | 0.00 |
time (sec) |
N/A | 0.276 | 10.088 | 0.000 | 0.000 | 0.000 | 154.706 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 114 | 116 | 86 | 0 | 0 | 0 | 94 | 0 | 0 |
N.S. |
1 | 1.02 | 0.75 | 0.00 | 0.00 | 0.00 | 0.82 | 0.00 | 0.00 |
time (sec) |
N/A | 0.242 | 10.077 | 0.000 | 0.000 | 0.000 | 45.738 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 142 | 141 | 85 | 0 | 0 | 0 | 97 | 0 | 0 |
N.S. |
1 | 0.99 | 0.60 | 0.00 | 0.00 | 0.00 | 0.68 | 0.00 | 0.00 |
time (sec) |
N/A | 0.271 | 10.033 | 0.000 | 0.000 | 0.000 | 119.178 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 181 | 178 | 86 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.284 | 10.033 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 219 | 218 | 87 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.327 | 10.068 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 97 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.245 | 0.166 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 86 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.223 | 0.075 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 86 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.222 | 0.059 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 172 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.197 | 0.049 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 84 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.217 | 0.082 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 86 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.216 | 0.090 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 242 | 232 | 195 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.371 | 0.229 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 146 | 145 | 118 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.245 | 0.125 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 84 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.201 | 0.045 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 95 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.228 | 0.082 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 100 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.223 | 0.082 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 100 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.228 | 0.105 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 91 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.234 | 0.414 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 91 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.225 | 0.369 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 91 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.224 | 0.250 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 89 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.228 | 0.281 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 89 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.229 | 0.422 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 91 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.222 | 0.450 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |