Detailed conclusion table per each integral is given by 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 just an F.
In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 38 | 20 | 19 | 30 | 37 | 15 | 12 |
N.S. | 1 | 1.00 | 3.17 | 1.67 | 1.58 | 2.50 | 3.08 | 1.25 | 1.00 |
time (sec) |
N/A | 0.003 | 0.018 | 0.019 | 0.297 | 2.578 | 1.024 | 0.475 | 0.401 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 12 | 13 | 19 | 0 | 13 | 11 |
N.S. | 1 | 1.00 | 1.00 | 1.09 | 1.18 | 1.73 | 0.00 | 1.18 | 1.00 |
time (sec) |
N/A | 0.007 | 0.015 | 0.032 | 0.278 | 3.027 | 0.000 | 0.453 | 0.104 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 75 | 38 | 46 | 72 | 0 | 92 | 36 |
N.S. | 1 | 1.00 | 2.21 | 1.12 | 1.35 | 2.12 | 0.00 | 2.71 | 1.06 |
time (sec) |
N/A | 0.010 | 0.019 | 0.067 | 0.292 | 3.348 | 0.000 | 0.435 | 0.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 35 | 23 | 25 | 45 | 0 | 25 | 21 |
N.S. | 1 | 1.00 | 1.30 | 0.85 | 0.93 | 1.67 | 0.00 | 0.93 | 0.78 |
time (sec) |
N/A | 0.009 | 0.016 | 0.043 | 0.279 | 2.889 | 0.000 | 0.433 | 0.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 113 | 50 | 71 | 112 | 0 | 138 | 59 |
N.S. | 1 | 1.00 | 2.05 | 0.91 | 1.29 | 2.04 | 0.00 | 2.51 | 1.07 |
time (sec) |
N/A | 0.019 | 0.021 | 0.072 | 0.287 | 4.424 | 0.000 | 0.445 | 0.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 56 | 33 | 35 | 64 | 0 | 35 | 38 |
N.S. | 1 | 1.00 | 1.33 | 0.79 | 0.83 | 1.52 | 0.00 | 0.83 | 0.90 |
time (sec) |
N/A | 0.011 | 0.020 | 0.052 | 0.294 | 2.922 | 0.000 | 0.439 | 0.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 151 | 60 | 91 | 155 | 0 | 182 | 78 |
N.S. | 1 | 1.00 | 1.99 | 0.79 | 1.20 | 2.04 | 0.00 | 2.39 | 1.03 |
time (sec) |
N/A | 0.030 | 0.019 | 0.088 | 0.330 | 3.652 | 0.000 | 0.479 | 0.155 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 77 | 43 | 45 | 87 | 0 | 45 | 41 |
N.S. | 1 | 1.00 | 1.40 | 0.78 | 0.82 | 1.58 | 0.00 | 0.82 | 0.75 |
time (sec) |
N/A | 0.013 | 0.016 | 0.053 | 0.329 | 3.179 | 0.000 | 0.455 | 0.127 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | C | F(-2) | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 63 | 160 | 0 | 120 | 0 | 0 | -1 |
N.S. |
1 | 1.00 | 0.70 | 1.78 | 0.00 | 1.33 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.027 | 0.207 | 0.136 | 0.000 | 0.764 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 50 | 88 | 0 | 88 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.75 | 1.31 | 0.00 | 1.31 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.021 | 0.092 | 0.094 | 0.000 | 0.723 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 49 | 132 | 0 | 72 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.78 | 2.10 | 0.00 | 1.14 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A | 0.022 | 0.064 | 0.106 | 0.000 | 0.371 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | C | F | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 40 | 69 | 0 | 51 | 0 | 0 | 61 |
N.S. | 1 | 1.00 | 0.98 | 1.68 | 0.00 | 1.24 | 0.00 | 0.00 | 1.49 |
time (sec) |
N/A | 0.013 | 0.041 | 0.099 | 0.000 | 0.752 | 0.000 | 0.000 | 0.121 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 40 | 91 | 0 | 55 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.98 | 2.22 | 0.00 | 1.34 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A | 0.012 | 0.044 | 0.135 | 0.000 | 1.205 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 53 | 88 | 0 | 68 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.79 | 1.31 | 0.00 | 1.01 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.023 | 0.066 | 0.122 | 0.000 | 0.440 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 60 | 142 | 0 | 85 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.90 | 2.12 | 0.00 | 1.27 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.020 | 0.112 | 0.108 | 0.000 | 0.654 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 65 | 104 | 0 | 81 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.72 | 1.16 | 0.00 | 0.90 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.029 | 0.170 | 0.112 | 0.000 | 0.776 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | C | F(-2) | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 67 | 1052 | 0 | 150 | 0 | 0 | -1 |
N.S. |
1 | 1.00 | 0.65 | 10.21 | 0.00 | 1.46 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.041 | 0.206 | 1.236 | 0.000 | 0.834 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 55 | 313 | 0 | 105 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.73 | 4.17 | 0.00 | 1.40 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.024 | 0.192 | 1.131 | 0.000 | 0.670 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 54 | 508 | 0 | 83 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.76 | 7.15 | 0.00 | 1.17 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.028 | 0.128 | 1.191 | 0.000 | 0.884 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | C | F | F | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 42 | 165 | 0 | 55 | 0 | 0 | 63 |
N.S. | 1 | 1.00 | 0.98 | 3.84 | 0.00 | 1.28 | 0.00 | 0.00 | 1.47 |
time (sec) |
N/A | 0.015 | 0.035 | 1.101 | 0.000 | 0.648 | 0.000 | 0.000 | 0.199 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 42 | 533 | 0 | 62 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.98 | 12.40 | 0.00 | 1.44 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A | 0.015 | 0.039 | 1.214 | 0.000 | 0.898 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 63 | 189 | 0 | 85 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.82 | 2.45 | 0.00 | 1.10 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.025 | 0.089 | 1.131 | 0.000 | 0.802 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 60 | 547 | 0 | 96 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.78 | 7.10 | 0.00 | 1.25 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.024 | 0.158 | 1.118 | 0.000 | 0.335 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 70 | 213 | 0 | 98 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.67 | 2.03 | 0.00 | 0.93 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.038 | 0.145 | 1.350 | 0.000 | 1.174 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 54 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A | 0.018 | 0.084 | 0.036 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 51 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A | 0.018 | 0.062 | 0.029 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 51 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A | 0.017 | 0.063 | 0.030 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 51 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A | 0.017 | 0.057 | 0.028 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 51 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A | 0.017 | 0.056 | 0.029 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 68 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A | 0.018 | 0.128 | 0.028 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 57 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A | 0.021 | 0.055 | 0.031 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 59 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.09 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A | 0.021 | 0.074 | 0.032 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 59 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A | 0.020 | 0.072 | 0.033 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 59 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A | 0.021 | 0.075 | 0.025 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 59 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A | 0.021 | 0.072 | 0.026 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 76 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 1.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A | 0.022 | 0.168 | 0.028 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 59 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.029 | 0.104 | 0.039 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 65 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.027 | 0.085 | 0.037 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | B | F(-2) | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 92 | 101 | 1669 | 93 | 0 | 129 | -1 |
N.S. |
1 | 1.00 | 1.84 | 2.02 | 33.38 | 1.86 | 0.00 | 2.58 | -0.02 |
time (sec) |
N/A | 0.013 | 0.271 | 0.126 | 0.609 | 4.046 | 0.000 | 0.470 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | B | F | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 72 | 78 | 869 | 69 | 0 | 100 | -1 |
N.S. | 1 | 1.00 | 2.00 | 2.17 | 24.14 | 1.92 | 0.00 | 2.78 | -0.03 |
time (sec) |
N/A | 0.010 | 0.280 | 0.096 | 0.561 | 3.701 | 0.000 | 0.457 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | B | B | B | F | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 51 | 52 | 300 | 44 | 0 | 69 | -1 |
N.S. | 1 | 1.00 | 2.32 | 2.36 | 13.64 | 2.00 | 0.00 | 3.14 | -0.05 |
time (sec) |
N/A | 0.008 | 0.104 | 0.084 | 0.558 | 3.217 | 0.000 | 0.444 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | B | B | B | F | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 5 | 5 | 28 | 31 | 35 | 19 | 0 | 12 | -1 |
N.S. | 1 | 1.00 | 5.60 | 6.20 | 7.00 | 3.80 | 0.00 | 2.40 | -0.20 |
time (sec) |
N/A | 0.005 | 0.016 | 0.083 | 0.536 | 3.571 | 0.000 | 0.465 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | A | A | A | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 26 | 10 | 4 | 12 | 11 | 12 |
N.S. | 1 | 1.00 | 1.00 | 2.17 | 0.83 | 0.33 | 1.00 | 0.92 | 1.00 |
time (sec) |
N/A | 0.007 | 0.010 | 0.076 | 0.498 | 3.831 | 0.162 | 0.436 | 0.170 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 23 | 30 | 11 | 11 | 29 | 44 | -1 |
N.S. | 1 | 1.00 | 0.79 | 1.03 | 0.38 | 0.38 | 1.00 | 1.52 | -0.03 |
time (sec) |
N/A | 0.008 | 0.020 | 0.076 | 0.543 | 2.862 | 0.303 | 0.447 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 31 | 38 | 17 | 17 | 46 | 61 | -1 |
N.S. | 1 | 1.00 | 0.72 | 0.88 | 0.40 | 0.40 | 1.07 | 1.42 | -0.02 |
time (sec) |
N/A | 0.012 | 0.031 | 0.082 | 0.539 | 3.685 | 1.510 | 0.429 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 37 | 44 | 23 | 21 | 61 | 78 | -1 |
N.S. | 1 | 1.00 | 0.65 | 0.77 | 0.40 | 0.37 | 1.07 | 1.37 | -0.02 |
time (sec) |
N/A | 0.014 | 0.046 | 0.083 | 0.559 | 4.683 | 11.922 | 0.466 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F(-2) | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 61 | 102 | 2183 | 106 | 0 | 164 | -1 |
N.S. |
1 | 1.00 | 0.73 | 1.21 | 25.99 | 1.26 | 0.00 | 1.95 | -0.01 |
time (sec) |
N/A | 0.029 | 0.363 | 0.122 | 4.488 | 4.076 | 0.000 | 0.503 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 51 | 79 | 1113 | 80 | 0 | 124 | -1 |
N.S. | 1 | 1.00 | 0.78 | 1.22 | 17.12 | 1.23 | 0.00 | 1.91 | -0.02 |
time (sec) |
N/A | 0.024 | 0.240 | 0.098 | 0.858 | 4.014 | 0.000 | 0.443 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 39 | 53 | 318 | 49 | 0 | 72 | -1 |
N.S. | 1 | 1.00 | 0.85 | 1.15 | 6.91 | 1.07 | 0.00 | 1.57 | -0.02 |
time (sec) |
N/A | 0.017 | 0.082 | 0.087 | 0.543 | 3.422 | 0.000 | 0.430 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 30 | 32 | 24 | 64 | 0 | 13 | -1 |
N.S. | 1 | 1.00 | 1.15 | 1.23 | 0.92 | 2.46 | 0.00 | 0.50 | -0.04 |
time (sec) |
N/A | 0.012 | 0.020 | 0.086 | 0.558 | 2.565 | 0.000 | 0.414 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 27 | 13 | 22 | 14 | 34 | 15 |
N.S. | 1 | 1.00 | 1.00 | 1.93 | 0.93 | 1.57 | 1.00 | 2.43 | 1.07 |
time (sec) |
N/A | 0.010 | 0.009 | 0.076 | 0.514 | 2.807 | 0.204 | 0.463 | 0.220 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | A | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 27 | 31 | 0 | 29 | 32 | 52 | -1 |
N.S. | 1 | 1.00 | 0.75 | 0.86 | 0.00 | 0.81 | 0.89 | 1.44 | -0.03 |
time (sec) |
N/A | 0.013 | 0.021 | 0.083 | 0.000 | 2.422 | 0.342 | 0.433 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | A | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 36 | 39 | 0 | 37 | 51 | 62 | -1 |
N.S. | 1 | 1.00 | 0.65 | 0.71 | 0.00 | 0.67 | 0.93 | 1.13 | -0.02 |
time (sec) |
N/A | 0.020 | 0.034 | 0.080 | 0.000 | 2.624 | 1.604 | 0.426 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | A | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 42 | 45 | 0 | 43 | 68 | 76 | -1 |
N.S. | 1 | 1.00 | 0.57 | 0.61 | 0.00 | 0.58 | 0.92 | 1.03 | -0.01 |
time (sec) |
N/A | 0.026 | 0.052 | 0.086 | 0.000 | 3.159 | 11.730 | 0.418 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 123 | 58 | 1313 | 0 | 161 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.47 | 10.67 | 0.00 | 1.31 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.043 | 0.211 | 0.228 | 0.000 | 0.810 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 46 | 372 | 0 | 99 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.65 | 5.24 | 0.00 | 1.39 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.029 | 0.126 | 0.188 | 0.000 | 1.102 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 46 | 343 | 0 | 64 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.96 | 7.15 | 0.00 | 1.33 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A | 0.021 | 0.047 | 0.155 | 0.000 | 0.383 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 38 | 125 | 0 | 68 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.76 | 2.50 | 0.00 | 1.36 | 0.00 | 0.00 | -0.02 |
time (sec) |
N/A | 0.022 | 0.056 | 0.164 | 0.000 | 0.876 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 52 | 349 | 0 | 84 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.66 | 4.42 | 0.00 | 1.06 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.028 | 0.107 | 0.174 | 0.000 | 0.595 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | C | F | C | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 123 | 63 | 158 | 0 | 88 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.51 | 1.28 | 0.00 | 0.72 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.043 | 0.162 | 0.182 | 0.000 | 1.192 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 164 | 59 | 53 | 66 | 118 | 0 | 69 | 603 |
N.S. |
1 | 1.00 | 0.36 | 0.32 | 0.40 | 0.72 | 0.00 | 0.42 | 3.68 |
time (sec) |
N/A | 0.026 | 0.076 | 0.241 | 0.472 | 3.850 | 0.000 | 0.473 | 5.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 47 | 41 | 48 | 88 | 0 | 51 | 121 |
N.S. | 1 | 1.00 | 0.40 | 0.35 | 0.41 | 0.75 | 0.00 | 0.43 | 1.03 |
time (sec) |
N/A | 0.023 | 0.048 | 0.150 | 0.486 | 2.630 | 0.000 | 0.572 | 2.419 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 33 | 29 | 30 | 52 | 0 | 23 | 44 |
N.S. | 1 | 1.00 | 0.53 | 0.47 | 0.48 | 0.84 | 0.00 | 0.37 | 0.71 |
time (sec) |
N/A | 0.015 | 0.023 | 0.104 | 0.482 | 2.461 | 0.000 | 0.474 | 0.674 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 18 | 9 | 24 | 0 | 9 | 7 |
N.S. | 1 | 1.00 | 1.00 | 1.12 | 0.56 | 1.50 | 0.00 | 0.56 | 0.44 |
time (sec) |
N/A | 0.010 | 0.008 | 0.094 | 0.479 | 3.004 | 0.000 | 0.435 | 0.178 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 25 | 24 | 25 | 46 | 0 | 22 | -1 |
N.S. | 1 | 1.00 | 0.69 | 0.67 | 0.69 | 1.28 | 0.00 | 0.61 | -0.03 |
time (sec) |
N/A | 0.011 | 0.030 | 0.089 | 0.492 | 2.002 | 0.000 | 0.437 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 38 | 41 | 58 | 61 | 0 | 42 | -1 |
N.S. | 1 | 1.00 | 0.44 | 0.48 | 0.67 | 0.71 | 0.00 | 0.49 | -0.01 |
time (sec) |
N/A | 0.024 | 0.050 | 0.127 | 0.497 | 2.449 | 0.000 | 0.443 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 132 | 55 | 57 | 88 | 73 | 0 | 49 | -1 |
N.S. | 1 | 1.00 | 0.42 | 0.43 | 0.67 | 0.55 | 0.00 | 0.37 | -0.01 |
time (sec) |
N/A | 0.033 | 0.110 | 0.236 | 0.491 | 3.123 | 0.000 | 0.443 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 71 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.041 | 0.128 | 0.079 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 73 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.039 | 0.089 | 0.046 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | F | F | F | F | F | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 77 | 0 | 0 | 0 | 0 | 0 | -1 |
N.S. | 1 | 1.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | -0.01 |
time (sec) |
N/A | 0.035 | 0.156 | 0.063 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |