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 | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 56 | 36 | 32 | 0 | 43 | 0 | 45 | 0 |
N.S. |
1 | 1.06 | 0.68 | 0.60 | 0.00 | 0.81 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.333 | 0.036 | 1.010 | 0.000 | 0.272 | 0.000 | 0.329 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 26 | 24 | 0 | 29 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.76 | 0.71 | 0.00 | 0.85 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.267 | 0.039 | 0.476 | 0.000 | 0.269 | 0.000 | 0.336 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 16 | 13 | 19 | 17 | 17 | 40 |
N.S. |
1 | 1.00 | 1.00 | 1.14 | 0.93 | 1.36 | 1.21 | 1.21 | 2.86 |
time (sec) |
N/A | 0.194 | 0.013 | 0.493 | 0.399 | 0.260 | 0.113 | 0.339 | 13.751 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 30 | 49 | 26 | 70 | 0 | 15 | 0 |
N.S. |
1 | 1.00 | 1.76 | 2.88 | 1.53 | 4.12 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.199 | 0.023 | 0.722 | 0.456 | 0.272 | 0.000 | 0.362 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 55 | 70 | 314 | 58 | 0 | 81 | 0 |
N.S. |
1 | 1.00 | 1.31 | 1.67 | 7.48 | 1.38 | 0.00 | 1.93 | 0.00 |
time (sec) |
N/A | 0.280 | 0.057 | 0.841 | 0.463 | 0.253 | 0.000 | 0.359 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 69 | 77 | 89 | 931 | 78 | 0 | 118 | 0 |
N.S. |
1 | 1.13 | 1.26 | 1.46 | 15.26 | 1.28 | 0.00 | 1.93 | 0.00 |
time (sec) |
N/A | 0.368 | 0.147 | 0.832 | 0.630 | 0.277 | 0.000 | 0.371 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 123 | 101 | 65 | 192 | 0 | 110 | 0 | 0 | 0 |
N.S. |
1 | 0.82 | 0.53 | 1.56 | 0.00 | 0.89 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.461 | 0.127 | 4.465 | 0.000 | 0.105 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 65 | 54 | 302 | 0 | 80 | 0 | 0 | 0 |
N.S. |
1 | 0.89 | 0.74 | 4.14 | 0.00 | 1.10 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.330 | 0.078 | 1.448 | 0.000 | 0.095 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 47 | 41 | 163 | 0 | 69 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 0.82 | 3.26 | 0.00 | 1.38 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.263 | 0.040 | 1.411 | 0.000 | 0.091 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 48 | 43 | 37 | 274 | 0 | 102 | 0 | 0 | 0 |
N.S. |
1 | 0.90 | 0.77 | 5.71 | 0.00 | 2.12 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.266 | 0.036 | 1.169 | 0.000 | 0.100 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 67 | 48 | 239 | 0 | 139 | 0 | 0 | 0 |
N.S. |
1 | 0.87 | 0.62 | 3.10 | 0.00 | 1.81 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.335 | 0.068 | 1.472 | 0.000 | 0.085 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 123 | 97 | 60 | 314 | 0 | 209 | 0 | 0 | 0 |
N.S. |
1 | 0.79 | 0.49 | 2.55 | 0.00 | 1.70 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.460 | 0.162 | 1.368 | 0.000 | 0.099 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 132 | 92 | 53 | 61 | 85 | 82 | 0 | 57 | 0 |
N.S. |
1 | 0.70 | 0.40 | 0.46 | 0.64 | 0.62 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.469 | 0.127 | 10.176 | 0.311 | 0.279 | 0.000 | 0.319 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 78 | 60 | 38 | 43 | 55 | 56 | 0 | 27 | 0 |
N.S. |
1 | 0.77 | 0.49 | 0.55 | 0.71 | 0.72 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.327 | 0.080 | 0.577 | 0.320 | 0.269 | 0.000 | 0.308 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 29 | 25 | 24 | 22 | 36 | 0 | 15 | 0 |
N.S. |
1 | 0.81 | 0.69 | 0.67 | 0.61 | 1.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.213 | 0.024 | 0.605 | 0.317 | 0.272 | 0.000 | 0.411 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 18 | 9 | 36 | 0 | 9 | 7 |
N.S. |
1 | 1.00 | 1.00 | 1.12 | 0.56 | 2.25 | 0.00 | 0.56 | 0.44 |
time (sec) |
N/A | 0.217 | 0.018 | 0.559 | 0.296 | 0.272 | 0.000 | 0.413 | 13.215 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 68 | 38 | 34 | 37 | 23 | 74 | 0 | 23 | 44 |
N.S. |
1 | 0.56 | 0.50 | 0.54 | 0.34 | 1.09 | 0.00 | 0.34 | 0.65 |
time (sec) |
N/A | 0.242 | 0.036 | 0.528 | 0.299 | 0.261 | 0.000 | 0.420 | 13.792 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 118 | 54 | 47 | 49 | 35 | 104 | 0 | 35 | 117 |
N.S. |
1 | 0.46 | 0.40 | 0.42 | 0.30 | 0.88 | 0.00 | 0.30 | 0.99 |
time (sec) |
N/A | 0.254 | 0.054 | 0.641 | 0.324 | 0.279 | 0.000 | 0.405 | 15.910 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 74 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.279 | 0.122 | 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(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 72 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.270 | 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(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 74 | 88 | 68 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.19 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.262 | 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(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 72 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.269 | 0.052 | 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(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 71 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.276 | 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(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 73 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.276 | 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 | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 71 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.272 | 0.043 | 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 | 77 | 77 | 61 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.261 | 0.050 | 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 | 75 | 75 | 67 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.270 | 0.054 | 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 | 77 | 77 | 65 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.273 | 0.061 | 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 | A | F | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 29 | 0 | 16 | 58 | 384 | 36 |
N.S. |
1 | 1.00 | 1.00 | 1.16 | 0.00 | 0.64 | 2.32 | 15.36 | 1.44 |
time (sec) |
N/A | 0.232 | 0.035 | 1.102 | 0.000 | 0.264 | 0.356 | 0.738 | 14.438 |
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 | 79 | 79 | 73 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.280 | 0.036 | 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 | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 13 | 17 | 12 | 15 | 17 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 1.06 | 0.75 | 0.94 | 1.06 | 0.69 |
time (sec) |
N/A | 0.144 | 0.007 | 0.194 | 0.287 | 0.274 | 0.020 | 0.326 | 13.574 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 26 | 20 | 40 | 28 | 110 | 25 | 33 |
N.S. |
1 | 1.00 | 0.79 | 0.61 | 1.21 | 0.85 | 3.33 | 0.76 | 1.00 |
time (sec) |
N/A | 0.255 | 0.002 | 0.651 | 0.279 | 0.278 | 0.129 | 0.302 | 13.533 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 48 | 34 | 26 | 69 | 37 | 233 | 34 | 42 |
N.S. |
1 | 1.04 | 0.74 | 0.57 | 1.50 | 0.80 | 5.07 | 0.74 | 0.91 |
time (sec) |
N/A | 0.309 | 0.002 | 1.046 | 0.298 | 0.272 | 0.259 | 0.307 | 14.012 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 63 | 42 | 34 | 104 | 46 | 376 | 43 | 51 |
N.S. |
1 | 1.07 | 0.71 | 0.58 | 1.76 | 0.78 | 6.37 | 0.73 | 0.86 |
time (sec) |
N/A | 0.373 | 0.006 | 1.359 | 0.286 | 0.271 | 0.489 | 0.310 | 13.919 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 62 | 45 | 58 | 45 | 50 | 46 | 314 | 149 | 54 |
N.S. |
1 | 0.73 | 0.94 | 0.73 | 0.81 | 0.74 | 5.06 | 2.40 | 0.87 |
time (sec) |
N/A | 0.307 | 0.139 | 0.719 | 0.264 | 0.269 | 10.455 | 0.309 | 0.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 37 | 43 | 35 | 40 | 36 | 143 | 105 | 38 |
N.S. |
1 | 0.80 | 0.93 | 0.76 | 0.87 | 0.78 | 3.11 | 2.28 | 0.83 |
time (sec) |
N/A | 0.304 | 0.081 | 0.506 | 0.275 | 0.258 | 4.102 | 0.302 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 25 | 25 | 23 | 27 | 25 | 36 | 29 | 25 |
N.S. |
1 | 0.93 | 0.93 | 0.85 | 1.00 | 0.93 | 1.33 | 1.07 | 0.93 |
time (sec) |
N/A | 0.287 | 0.055 | 0.400 | 0.283 | 0.264 | 1.515 | 0.308 | 13.946 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 16 | 15 | 15 | 34 | 15 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.23 | 1.15 | 1.15 | 2.62 | 1.15 | 1.15 |
time (sec) |
N/A | 0.243 | 0.010 | 0.526 | 0.290 | 0.249 | 0.592 | 0.300 | 13.810 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 23 | 46 | 39 | 46 | 55 | 0 | 62 | 31 |
N.S. |
1 | 0.79 | 1.59 | 1.34 | 1.59 | 1.90 | 0.00 | 2.14 | 1.07 |
time (sec) |
N/A | 0.267 | 0.090 | 0.550 | 0.291 | 0.252 | 0.000 | 0.305 | 0.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 58 | 54 | 146 | 63 | 70 | 98 | 0 | 149 | 55 |
N.S. |
1 | 0.93 | 2.52 | 1.09 | 1.21 | 1.69 | 0.00 | 2.57 | 0.95 |
time (sec) |
N/A | 0.303 | 0.265 | 0.639 | 0.315 | 0.266 | 0.000 | 0.329 | 14.181 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 85 | 132 | 87 | 90 | 135 | 0 | 181 | 74 |
N.S. |
1 | 1.04 | 1.61 | 1.06 | 1.10 | 1.65 | 0.00 | 2.21 | 0.90 |
time (sec) |
N/A | 0.310 | 2.744 | 0.815 | 0.303 | 0.274 | 0.000 | 0.333 | 0.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 81 | 44 | 57 | 72 | 56 | 1161 | 63 | 68 |
N.S. |
1 | 1.11 | 0.60 | 0.78 | 0.99 | 0.77 | 15.90 | 0.86 | 0.93 |
time (sec) |
N/A | 0.309 | 0.207 | 0.627 | 0.392 | 0.276 | 6.573 | 0.301 | 14.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 52 | 34 | 44 | 49 | 45 | 502 | 50 | 45 |
N.S. |
1 | 1.06 | 0.69 | 0.90 | 1.00 | 0.92 | 10.24 | 1.02 | 0.92 |
time (sec) |
N/A | 0.299 | 0.152 | 0.463 | 0.383 | 0.273 | 2.564 | 0.305 | 13.719 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 27 | 24 | 26 | 34 | 100 | 26 | 20 |
N.S. |
1 | 1.00 | 1.35 | 1.20 | 1.30 | 1.70 | 5.00 | 1.30 | 1.00 |
time (sec) |
N/A | 0.322 | 0.010 | 0.398 | 0.363 | 0.256 | 0.924 | 0.304 | 13.749 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 14 | 13 | 21 | 41 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.00 | 1.62 | 3.15 | 1.00 | 1.00 |
time (sec) |
N/A | 0.224 | 0.005 | 0.336 | 0.295 | 0.238 | 0.467 | 0.296 | 13.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 22 | 16 | 25 | 28 | 36 | 0 | 19 | 17 |
N.S. |
1 | 0.79 | 0.57 | 0.89 | 1.00 | 1.29 | 0.00 | 0.68 | 0.61 |
time (sec) |
N/A | 0.288 | 0.044 | 0.515 | 0.266 | 0.262 | 0.000 | 0.318 | 14.112 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 34 | 49 | 35 | 42 | 56 | 0 | 42 | 38 |
N.S. |
1 | 0.74 | 1.07 | 0.76 | 0.91 | 1.22 | 0.00 | 0.91 | 0.83 |
time (sec) |
N/A | 0.298 | 0.111 | 0.596 | 0.341 | 0.259 | 0.000 | 0.335 | 13.850 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 62 | 44 | 70 | 45 | 52 | 77 | 0 | 52 | 50 |
N.S. |
1 | 0.71 | 1.13 | 0.73 | 0.84 | 1.24 | 0.00 | 0.84 | 0.81 |
time (sec) |
N/A | 0.310 | 0.096 | 0.879 | 0.282 | 0.245 | 0.000 | 0.312 | 13.875 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 49 | 59 | 47 | 52 | 46 | 156 | 57 | 48 |
N.S. |
1 | 0.75 | 0.91 | 0.72 | 0.80 | 0.71 | 2.40 | 0.88 | 0.74 |
time (sec) |
N/A | 0.311 | 0.110 | 0.722 | 0.266 | 0.254 | 24.600 | 0.337 | 13.236 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 35 | 42 | 37 | 41 | 38 | 156 | 106 | 36 |
N.S. |
1 | 0.74 | 0.89 | 0.79 | 0.87 | 0.81 | 3.32 | 2.26 | 0.77 |
time (sec) |
N/A | 0.286 | 0.067 | 0.634 | 0.283 | 0.256 | 10.897 | 0.339 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 28 | 31 | 29 | 28 | 28 | 156 | 28 | 26 |
N.S. |
1 | 0.85 | 0.94 | 0.88 | 0.85 | 0.85 | 4.73 | 0.85 | 0.79 |
time (sec) |
N/A | 0.283 | 0.068 | 0.543 | 0.284 | 0.260 | 3.916 | 0.326 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 17 | 16 | 16 | 156 | 16 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.89 | 0.89 | 8.67 | 0.89 | 0.89 |
time (sec) |
N/A | 0.258 | 0.009 | 0.549 | 0.277 | 0.263 | 1.920 | 0.314 | 12.979 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 35 | 61 | 49 | 59 | 70 | 0 | 107 | 41 |
N.S. |
1 | 0.74 | 1.30 | 1.04 | 1.26 | 1.49 | 0.00 | 2.28 | 0.87 |
time (sec) |
N/A | 0.287 | 0.075 | 0.756 | 0.250 | 0.256 | 0.000 | 0.296 | 0.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 78 | 66 | 208 | 75 | 86 | 118 | 0 | 175 | 70 |
N.S. |
1 | 0.85 | 2.67 | 0.96 | 1.10 | 1.51 | 0.00 | 2.24 | 0.90 |
time (sec) |
N/A | 0.313 | 0.380 | 0.889 | 0.230 | 0.253 | 0.000 | 0.330 | 12.938 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 69 | 64 | 46 | 56 | 64 | 59 | 1275 | 68 | 66 |
N.S. |
1 | 0.93 | 0.67 | 0.81 | 0.93 | 0.86 | 18.48 | 0.99 | 0.96 |
time (sec) |
N/A | 0.314 | 0.206 | 0.743 | 0.357 | 0.275 | 16.725 | 0.293 | 13.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 32 | 42 | 34 | 37 | 49 | 551 | 44 | 31 |
N.S. |
1 | 0.84 | 1.11 | 0.89 | 0.97 | 1.29 | 14.50 | 1.16 | 0.82 |
time (sec) |
N/A | 0.318 | 0.011 | 0.668 | 0.355 | 0.273 | 7.023 | 0.304 | 13.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 17 | 16 | 32 | 94 | 16 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.89 | 1.78 | 5.22 | 0.89 | 0.89 |
time (sec) |
N/A | 0.272 | 0.012 | 0.516 | 0.258 | 0.267 | 2.790 | 0.306 | 12.596 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 29 | 26 | 25 | 25 | 34 | 238 | 25 | 24 |
N.S. |
1 | 0.91 | 0.81 | 0.78 | 0.78 | 1.06 | 7.44 | 0.78 | 0.75 |
time (sec) |
N/A | 0.245 | 0.029 | 0.454 | 0.309 | 0.246 | 1.187 | 0.293 | 12.694 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 36 | 50 | 37 | 40 | 46 | 0 | 48 | 36 |
N.S. |
1 | 0.77 | 1.06 | 0.79 | 0.85 | 0.98 | 0.00 | 1.02 | 0.77 |
time (sec) |
N/A | 0.294 | 0.101 | 0.698 | 0.306 | 0.244 | 0.000 | 0.309 | 12.699 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 48 | 46 | 47 | 52 | 72 | 0 | 34 | 48 |
N.S. |
1 | 0.74 | 0.71 | 0.72 | 0.80 | 1.11 | 0.00 | 0.52 | 0.74 |
time (sec) |
N/A | 0.308 | 0.041 | 0.939 | 0.314 | 0.266 | 0.000 | 0.306 | 13.135 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 26 | 23 | 20 | 22 | 25 | 362 | 22 | 21 |
N.S. |
1 | 0.90 | 0.79 | 0.69 | 0.76 | 0.86 | 12.48 | 0.76 | 0.72 |
time (sec) |
N/A | 0.239 | 0.005 | 0.579 | 0.311 | 0.264 | 1.810 | 0.285 | 12.891 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 32 | 27 | 24 | 28 | 31 | 675 | 28 | 33 |
N.S. |
1 | 0.86 | 0.73 | 0.65 | 0.76 | 0.84 | 18.24 | 0.76 | 0.89 |
time (sec) |
N/A | 0.244 | 0.006 | 0.926 | 0.497 | 0.272 | 5.396 | 0.288 | 12.853 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 42 | 39 | 32 | 34 | 37 | 1083 | 34 | 43 |
N.S. |
1 | 0.82 | 0.76 | 0.63 | 0.67 | 0.73 | 21.24 | 0.67 | 0.84 |
time (sec) |
N/A | 0.250 | 0.007 | 1.460 | 0.313 | 0.248 | 14.843 | 0.280 | 13.138 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 46 | 77 | 54 | 43 | 43 | 107 | 67 | 44 |
N.S. |
1 | 0.90 | 1.51 | 1.06 | 0.84 | 0.84 | 2.10 | 1.31 | 0.86 |
time (sec) |
N/A | 0.233 | 0.075 | 1.370 | 0.383 | 0.247 | 0.221 | 0.308 | 13.143 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 29 | 54 | 34 | 34 | 27 | 58 | 40 | 27 |
N.S. |
1 | 0.94 | 1.74 | 1.10 | 1.10 | 0.87 | 1.87 | 1.29 | 0.87 |
time (sec) |
N/A | 0.205 | 0.046 | 0.810 | 0.303 | 0.267 | 0.111 | 0.295 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 63 | 28 | 38 | 42 | 0 | 58 | 23 |
N.S. |
1 | 1.00 | 2.42 | 1.08 | 1.46 | 1.62 | 0.00 | 2.23 | 0.88 |
time (sec) |
N/A | 0.241 | 0.049 | 0.524 | 0.293 | 0.267 | 0.000 | 0.294 | 12.974 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 118 | 52 | 58 | 95 | 0 | 121 | 42 |
N.S. |
1 | 1.00 | 2.95 | 1.30 | 1.45 | 2.38 | 0.00 | 3.02 | 1.05 |
time (sec) |
N/A | 0.262 | 0.070 | 0.883 | 0.285 | 0.251 | 0.000 | 0.301 | 0.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 85 | 70 | 62 | 104 | 69 | 258 | 68 | 92 |
N.S. |
1 | 0.96 | 0.79 | 0.70 | 1.17 | 0.78 | 2.90 | 0.76 | 1.03 |
time (sec) |
N/A | 0.344 | 0.124 | 1.265 | 0.362 | 0.256 | 0.329 | 0.298 | 14.219 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 59 | 45 | 44 | 74 | 50 | 158 | 43 | 68 |
N.S. |
1 | 0.97 | 0.74 | 0.72 | 1.21 | 0.82 | 2.59 | 0.70 | 1.11 |
time (sec) |
N/A | 0.270 | 0.109 | 0.959 | 0.361 | 0.261 | 0.159 | 0.279 | 13.832 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 33 | 24 | 29 | 29 | 51 | 25 | 27 |
N.S. |
1 | 1.00 | 1.10 | 0.80 | 0.97 | 0.97 | 1.70 | 0.83 | 0.90 |
time (sec) |
N/A | 0.155 | 0.042 | 0.387 | 0.297 | 0.267 | 0.081 | 0.279 | 13.514 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 22 | 23 | 32 | 0 | 39 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.38 | 1.44 | 2.00 | 0.00 | 2.44 | 1.00 |
time (sec) |
N/A | 0.184 | 0.034 | 0.881 | 0.401 | 0.266 | 0.000 | 0.412 | 13.617 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 49 | 35 | 28 | 54 | 0 | 37 | 29 |
N.S. |
1 | 1.00 | 1.14 | 0.81 | 0.65 | 1.26 | 0.00 | 0.86 | 0.67 |
time (sec) |
N/A | 0.272 | 0.065 | 1.090 | 0.280 | 0.250 | 0.000 | 0.405 | 13.875 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 56 | 95 | 56 | 45 | 81 | 0 | 61 | 49 |
N.S. |
1 | 0.86 | 1.46 | 0.86 | 0.69 | 1.25 | 0.00 | 0.94 | 0.75 |
time (sec) |
N/A | 0.290 | 0.068 | 1.111 | 0.290 | 0.255 | 0.000 | 0.432 | 14.089 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 16 | 17 | 16 | 15 | 17 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.89 | 0.84 | 0.79 | 0.89 | 0.79 |
time (sec) |
N/A | 0.146 | 0.021 | 0.219 | 0.248 | 0.257 | 0.021 | 0.376 | 13.518 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 43 | 41 | 39 | 47 | 110 | 42 | 44 |
N.S. |
1 | 1.00 | 0.86 | 0.82 | 0.78 | 0.94 | 2.20 | 0.84 | 0.88 |
time (sec) |
N/A | 0.193 | 0.046 | 0.671 | 0.242 | 0.271 | 0.132 | 0.379 | 13.890 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 87 | 92 | 80 | 70 | 71 | 81 | 246 | 76 | 118 |
N.S. |
1 | 1.06 | 0.92 | 0.80 | 0.82 | 0.93 | 2.83 | 0.87 | 1.36 |
time (sec) |
N/A | 0.319 | 0.070 | 1.008 | 0.236 | 0.269 | 0.274 | 0.384 | 13.981 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 140 | 150 | 113 | 110 | 108 | 123 | 410 | 118 | 147 |
N.S. |
1 | 1.07 | 0.81 | 0.79 | 0.77 | 0.88 | 2.93 | 0.84 | 1.05 |
time (sec) |
N/A | 0.496 | 0.110 | 1.439 | 0.272 | 0.258 | 0.496 | 0.403 | 13.570 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 106 | 99 | 180 | 110 | 116 | 272 | 0 | 332 | 112 |
N.S. |
1 | 0.93 | 1.70 | 1.04 | 1.09 | 2.57 | 0.00 | 3.13 | 1.06 |
time (sec) |
N/A | 0.296 | 1.273 | 1.322 | 0.373 | 0.297 | 0.000 | 0.429 | 0.172 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 73 | 150 | 70 | 88 | 218 | 0 | 173 | 72 |
N.S. |
1 | 0.95 | 1.95 | 0.91 | 1.14 | 2.83 | 0.00 | 2.25 | 0.94 |
time (sec) |
N/A | 0.273 | 0.483 | 0.970 | 0.389 | 0.293 | 0.000 | 0.418 | 13.421 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 52 | 51 | 125 | 45 | 67 | 165 | 0 | 57 | 44 |
N.S. |
1 | 0.98 | 2.40 | 0.87 | 1.29 | 3.17 | 0.00 | 1.10 | 0.85 |
time (sec) |
N/A | 0.238 | 0.265 | 0.556 | 0.319 | 0.284 | 0.000 | 0.390 | 0.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 97 | 29 | 50 | 117 | 367693 | 37 | 29 |
N.S. |
1 | 1.00 | 2.62 | 0.78 | 1.35 | 3.16 | 9937.65 | 1.00 | 0.78 |
time (sec) |
N/A | 0.214 | 0.864 | 0.391 | 0.396 | 0.280 | 76.845 | 0.383 | 0.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 54 | 143 | 62 | 83 | 161 | 0 | 100 | 457 |
N.S. |
1 | 0.98 | 2.60 | 1.13 | 1.51 | 2.93 | 0.00 | 1.82 | 8.31 |
time (sec) |
N/A | 0.241 | 0.535 | 0.628 | 0.406 | 0.281 | 0.000 | 0.398 | 14.661 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 94 | 224 | 107 | 120 | 327 | 0 | 196 | 592 |
N.S. |
1 | 1.11 | 2.64 | 1.26 | 1.41 | 3.85 | 0.00 | 2.31 | 6.96 |
time (sec) |
N/A | 0.286 | 1.815 | 0.848 | 0.454 | 0.284 | 0.000 | 0.413 | 13.808 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 125 | 146 | 657 | 168 | 181 | 612 | 0 | 334 | 1105 |
N.S. |
1 | 1.17 | 5.26 | 1.34 | 1.45 | 4.90 | 0.00 | 2.67 | 8.84 |
time (sec) |
N/A | 0.344 | 6.632 | 0.993 | 0.334 | 0.339 | 0.000 | 0.440 | 13.558 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 163 | 202 | 133 | 168 | 192 | 453 | 0 | 233 | 2244 |
N.S. |
1 | 1.24 | 0.82 | 1.03 | 1.18 | 2.78 | 0.00 | 1.43 | 13.77 |
time (sec) |
N/A | 0.476 | 1.175 | 1.628 | 0.329 | 0.327 | 0.000 | 0.448 | 15.307 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 117 | 144 | 95 | 118 | 128 | 372 | 0 | 157 | 1892 |
N.S. |
1 | 1.23 | 0.81 | 1.01 | 1.09 | 3.18 | 0.00 | 1.34 | 16.17 |
time (sec) |
N/A | 0.386 | 0.512 | 1.049 | 0.361 | 0.303 | 0.000 | 0.433 | 14.189 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 94 | 69 | 81 | 78 | 305 | 0 | 114 | 481 |
N.S. |
1 | 1.22 | 0.90 | 1.05 | 1.01 | 3.96 | 0.00 | 1.48 | 6.25 |
time (sec) |
N/A | 0.288 | 0.349 | 0.709 | 0.345 | 0.284 | 0.000 | 0.431 | 14.138 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 46 | 48 | 46 | 260 | 0 | 81 | 104 |
N.S. |
1 | 1.00 | 1.00 | 1.04 | 1.00 | 5.65 | 0.00 | 1.76 | 2.26 |
time (sec) |
N/A | 0.291 | 1.407 | 0.409 | 0.396 | 0.291 | 0.000 | 0.397 | 13.852 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 36 | 30 | 29 | 236 | 16298 | 64 | 33 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.81 | 6.56 | 452.72 | 1.78 | 0.92 |
time (sec) |
N/A | 0.199 | 0.733 | 0.386 | 0.324 | 0.282 | 13.057 | 0.438 | 14.950 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 51 | 53 | 50 | 48 | 313 | 0 | 83 | 45 |
N.S. |
1 | 0.96 | 1.00 | 0.94 | 0.91 | 5.91 | 0.00 | 1.57 | 0.85 |
time (sec) |
N/A | 0.241 | 0.551 | 0.630 | 0.301 | 0.293 | 0.000 | 0.494 | 14.008 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 72 | 119 | 69 | 69 | 451 | 0 | 111 | 68 |
N.S. |
1 | 0.94 | 1.55 | 0.90 | 0.90 | 5.86 | 0.00 | 1.44 | 0.88 |
time (sec) |
N/A | 0.287 | 0.804 | 0.844 | 0.313 | 0.271 | 0.000 | 0.460 | 13.885 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 109 | 101 | 147 | 96 | 98 | 595 | 0 | 155 | 95 |
N.S. |
1 | 0.93 | 1.35 | 0.88 | 0.90 | 5.46 | 0.00 | 1.42 | 0.87 |
time (sec) |
N/A | 0.310 | 2.311 | 1.129 | 0.356 | 0.289 | 0.000 | 0.472 | 13.775 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 140 | 129 | 137 | 130 | 137 | 789 | 0 | 215 | 130 |
N.S. |
1 | 0.92 | 0.98 | 0.93 | 0.98 | 5.64 | 0.00 | 1.54 | 0.93 |
time (sec) |
N/A | 0.340 | 5.818 | 1.531 | 0.370 | 0.310 | 0.000 | 0.481 | 15.183 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 128 | 122 | 194 | 116 | 154 | 529 | 0 | 322 | 123 |
N.S. |
1 | 0.95 | 1.52 | 0.91 | 1.20 | 4.13 | 0.00 | 2.52 | 0.96 |
time (sec) |
N/A | 0.341 | 1.307 | 1.603 | 0.363 | 0.313 | 0.000 | 0.476 | 0.222 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 97 | 172 | 90 | 131 | 427 | 0 | 342 | 95 |
N.S. |
1 | 0.95 | 1.69 | 0.88 | 1.28 | 4.19 | 0.00 | 3.35 | 0.93 |
time (sec) |
N/A | 0.307 | 0.899 | 1.105 | 0.323 | 0.283 | 0.000 | 0.362 | 0.187 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 83 | 82 | 160 | 77 | 111 | 327 | 0 | 93 | 71 |
N.S. |
1 | 0.99 | 1.93 | 0.93 | 1.34 | 3.94 | 0.00 | 1.12 | 0.86 |
time (sec) |
N/A | 0.258 | 0.527 | 0.716 | 0.328 | 0.282 | 0.000 | 0.429 | 13.527 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 73 | 149 | 65 | 98 | 282 | 0 | 79 | 62 |
N.S. |
1 | 0.99 | 2.01 | 0.88 | 1.32 | 3.81 | 0.00 | 1.07 | 0.84 |
time (sec) |
N/A | 0.227 | 0.259 | 0.585 | 0.392 | 0.276 | 0.000 | 0.469 | 0.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 103 | 113 | 194 | 107 | 149 | 455 | 0 | 246 | 2039 |
N.S. |
1 | 1.10 | 1.88 | 1.04 | 1.45 | 4.42 | 0.00 | 2.39 | 19.80 |
time (sec) |
N/A | 0.288 | 1.149 | 0.916 | 0.354 | 0.315 | 0.000 | 0.425 | 14.481 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 153 | 166 | 390 | 152 | 223 | 838 | 0 | 512 | 2338 |
N.S. |
1 | 1.08 | 2.55 | 0.99 | 1.46 | 5.48 | 0.00 | 3.35 | 15.28 |
time (sec) |
N/A | 0.372 | 1.650 | 1.137 | 0.403 | 0.350 | 0.000 | 0.421 | 15.462 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 148 | 169 | 106 | 134 | 181 | 623 | 0 | 223 | 2295 |
N.S. |
1 | 1.14 | 0.72 | 0.91 | 1.22 | 4.21 | 0.00 | 1.51 | 15.51 |
time (sec) |
N/A | 0.398 | 1.191 | 1.245 | 0.332 | 0.318 | 0.000 | 0.397 | 16.770 |