Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 130 | 72 | 120 | 221 | 114 | 0 | 109 | 100 | 176 |
N.S. |
1 | 1.02 | 0.57 | 0.94 | 1.74 | 0.90 | 0.00 | 0.86 | 0.79 | 1.39 |
time (sec) |
N/A | 0.896 | 0.261 | 0.128 | 0.036 | 0.072 | 0.000 | 0.137 | 0.151 | 13.557 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 102 | 64 | 112 | 181 | 104 | 0 | 90 | 80 | 140 |
N.S. |
1 | 1.02 | 0.64 | 1.12 | 1.81 | 1.04 | 0.00 | 0.90 | 0.80 | 1.40 |
time (sec) |
N/A | 0.681 | 0.184 | 0.121 | 0.031 | 0.077 | 0.000 | 0.144 | 0.143 | 13.727 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 70 | 53 | 99 | 135 | 81 | 0 | 68 | 58 | 96 |
N.S. |
1 | 1.08 | 0.82 | 1.52 | 2.08 | 1.25 | 0.00 | 1.05 | 0.89 | 1.48 |
time (sec) |
N/A | 0.479 | 0.122 | 0.080 | 0.034 | 0.077 | 0.000 | 0.118 | 0.145 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 34 | 76 | 55 | 47 | 0 | 33 | 27 | 24 |
N.S. |
1 | 1.00 | 1.48 | 3.30 | 2.39 | 2.04 | 0.00 | 1.43 | 1.17 | 1.04 |
time (sec) |
N/A | 0.377 | 0.134 | 0.121 | 0.034 | 0.071 | 0.000 | 0.127 | 0.149 | 13.350 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 27 | 36 | 23 | 39 | 0 | 0 | 32 | 23 |
N.S. |
1 | 1.00 | 0.96 | 1.29 | 0.82 | 1.39 | 0.00 | 0.00 | 1.14 | 0.82 |
time (sec) |
N/A | 0.375 | 0.145 | 0.125 | 0.033 | 0.067 | 0.000 | 0.000 | 0.142 | 0.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 66 | 34 | 41 | 39 | 57 | 0 | 45 | 59 | 38 |
N.S. |
1 | 1.06 | 0.55 | 0.66 | 0.63 | 0.92 | 0.00 | 0.73 | 0.95 | 0.61 |
time (sec) |
N/A | 0.415 | 0.149 | 0.128 | 0.029 | 0.084 | 0.000 | 0.164 | 0.153 | 13.294 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 130 | 43 | 50 | 55 | 77 | 0 | 65 | 96 | 55 |
N.S. |
1 | 1.37 | 0.45 | 0.53 | 0.58 | 0.81 | 0.00 | 0.68 | 1.01 | 0.58 |
time (sec) |
N/A | 0.569 | 0.170 | 0.125 | 0.036 | 0.075 | 0.000 | 0.155 | 0.145 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 167 | 51 | 58 | 71 | 95 | 0 | 85 | 132 | 71 |
N.S. |
1 | 1.30 | 0.40 | 0.45 | 0.55 | 0.74 | 0.00 | 0.66 | 1.03 | 0.55 |
time (sec) |
N/A | 0.621 | 0.165 | 0.139 | 0.038 | 0.096 | 0.000 | 0.178 | 0.147 | 0.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 78 | 56 | 50 | 63 | 68 | 68 | 75 | 53 | 63 |
N.S. |
1 | 0.86 | 0.62 | 0.55 | 0.69 | 0.75 | 0.75 | 0.82 | 0.58 | 0.69 |
time (sec) |
N/A | 0.552 | 0.025 | 0.144 | 0.028 | 0.070 | 0.078 | 0.113 | 0.150 | 0.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 63 | 48 | 42 | 52 | 57 | 56 | 64 | 45 | 52 |
N.S. |
1 | 0.86 | 0.66 | 0.58 | 0.71 | 0.78 | 0.77 | 0.88 | 0.62 | 0.71 |
time (sec) |
N/A | 0.529 | 0.023 | 0.154 | 0.033 | 0.083 | 0.071 | 0.111 | 0.152 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 47 | 39 | 34 | 41 | 45 | 41 | 52 | 36 | 41 |
N.S. |
1 | 0.85 | 0.71 | 0.62 | 0.75 | 0.82 | 0.75 | 0.95 | 0.65 | 0.75 |
time (sec) |
N/A | 0.512 | 0.019 | 0.133 | 0.033 | 0.085 | 0.070 | 0.128 | 0.144 | 0.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 24 | 24 | 28 | 24 | 35 | 27 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.92 | 1.08 | 0.92 | 1.35 | 1.04 | 1.00 |
time (sec) |
N/A | 0.457 | 0.013 | 0.121 | 0.026 | 0.092 | 0.061 | 0.135 | 0.151 | 13.310 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 15 | 14 | 14 | 12 | 15 | 14 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.00 | 1.00 | 0.86 | 1.07 | 1.00 | 1.00 |
time (sec) |
N/A | 0.447 | 0.012 | 0.129 | 0.025 | 0.090 | 0.025 | 0.136 | 0.147 | 0.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 24 | 29 | 23 | 20 | 25 | 29 | 12 |
N.S. |
1 | 1.00 | 1.00 | 2.00 | 2.42 | 1.92 | 1.67 | 2.08 | 2.42 | 1.00 |
time (sec) |
N/A | 0.451 | 0.014 | 0.129 | 0.028 | 0.083 | 0.076 | 0.134 | 0.141 | 13.339 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 32 | 32 | 40 | 48 | 46 | 39 | 46 | 53 | 31 |
N.S. |
1 | 0.97 | 0.97 | 1.21 | 1.45 | 1.39 | 1.18 | 1.39 | 1.61 | 0.94 |
time (sec) |
N/A | 0.495 | 0.029 | 0.141 | 0.035 | 0.068 | 0.124 | 0.114 | 0.144 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 47 | 35 | 51 | 63 | 76 | 54 | 51 | 93 | 46 |
N.S. |
1 | 0.92 | 0.69 | 1.00 | 1.24 | 1.49 | 1.06 | 1.00 | 1.82 | 0.90 |
time (sec) |
N/A | 0.514 | 0.035 | 0.144 | 0.027 | 0.084 | 0.155 | 0.137 | 0.146 | 13.308 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 62 | 44 | 57 | 84 | 113 | 78 | 89 | 137 | 65 |
N.S. |
1 | 0.90 | 0.64 | 0.83 | 1.22 | 1.64 | 1.13 | 1.29 | 1.99 | 0.94 |
time (sec) |
N/A | 0.531 | 0.041 | 0.145 | 0.028 | 0.111 | 0.216 | 0.134 | 0.141 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 131 | 78 | 148 | 204 | 104 | 0 | 0 | 135 | 163 |
N.S. |
1 | 1.02 | 0.60 | 1.15 | 1.58 | 0.81 | 0.00 | 0.00 | 1.05 | 1.26 |
time (sec) |
N/A | 0.944 | 0.245 | 0.129 | 0.036 | 0.077 | 0.000 | 0.000 | 0.144 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 99 | 68 | 136 | 156 | 81 | 0 | 0 | 113 | 117 |
N.S. |
1 | 1.08 | 0.74 | 1.48 | 1.70 | 0.88 | 0.00 | 0.00 | 1.23 | 1.27 |
time (sec) |
N/A | 0.694 | 0.193 | 0.099 | 0.036 | 0.084 | 0.000 | 0.000 | 0.142 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 52 | 54 | 248 | 78 | 63 | 0 | 0 | 77 | 48 |
N.S. |
1 | 0.98 | 1.02 | 4.68 | 1.47 | 1.19 | 0.00 | 0.00 | 1.45 | 0.91 |
time (sec) |
N/A | 0.458 | 0.186 | 0.122 | 0.029 | 0.085 | 0.000 | 0.000 | 0.145 | 13.325 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 26 | 25 | 22 | 22 | 0 | 0 | 32 | 22 |
N.S. |
1 | 1.00 | 0.93 | 0.89 | 0.79 | 0.79 | 0.00 | 0.00 | 1.14 | 0.79 |
time (sec) |
N/A | 0.370 | 0.157 | 0.125 | 0.035 | 0.105 | 0.000 | 0.000 | 0.147 | 0.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 33 | 30 | 48 | 31 | 0 | 22 | 47 | 38 |
N.S. |
1 | 1.00 | 1.57 | 1.43 | 2.29 | 1.48 | 0.00 | 1.05 | 2.24 | 1.81 |
time (sec) |
N/A | 0.355 | 0.163 | 0.123 | 0.029 | 0.090 | 0.000 | 0.124 | 0.150 | 13.372 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 50 | 45 | 65 | 58 | 0 | 0 | 82 | 50 |
N.S. |
1 | 1.00 | 0.82 | 0.74 | 1.07 | 0.95 | 0.00 | 0.00 | 1.34 | 0.82 |
time (sec) |
N/A | 0.439 | 0.176 | 0.122 | 0.034 | 0.086 | 0.000 | 0.000 | 0.144 | 13.292 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 94 | 57 | 54 | 82 | 77 | 0 | 0 | 131 | 51 |
N.S. |
1 | 0.85 | 0.52 | 0.49 | 0.75 | 0.70 | 0.00 | 0.00 | 1.19 | 0.46 |
time (sec) |
N/A | 0.662 | 0.171 | 0.129 | 0.033 | 0.091 | 0.000 | 0.000 | 0.148 | 13.356 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 129 | 66 | 63 | 97 | 96 | 0 | 0 | 146 | 60 |
N.S. |
1 | 0.90 | 0.46 | 0.44 | 0.68 | 0.67 | 0.00 | 0.00 | 1.02 | 0.42 |
time (sec) |
N/A | 0.963 | 0.192 | 0.141 | 0.039 | 0.078 | 0.000 | 0.000 | 0.150 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 254 | 195 | 86 | 69 | 99 | 105 | 0 | 147 | 55 | 76 |
N.S. |
1 | 0.77 | 0.34 | 0.27 | 0.39 | 0.41 | 0.00 | 0.58 | 0.22 | 0.30 |
time (sec) |
N/A | 0.543 | 0.087 | 0.141 | 0.044 | 0.078 | 0.000 | 0.146 | 0.149 | 13.468 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 157 | 78 | 61 | 83 | 94 | 0 | 0 | 47 | 102 |
N.S. |
1 | 0.80 | 0.40 | 0.31 | 0.42 | 0.48 | 0.00 | 0.00 | 0.24 | 0.52 |
time (sec) |
N/A | 0.493 | 0.064 | 0.135 | 0.042 | 0.069 | 0.000 | 0.000 | 0.142 | 13.463 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 119 | 70 | 53 | 67 | 83 | 0 | 97 | 39 | 60 |
N.S. |
1 | 1.03 | 0.61 | 0.46 | 0.58 | 0.72 | 0.00 | 0.84 | 0.34 | 0.52 |
time (sec) |
N/A | 0.450 | 0.056 | 0.134 | 0.046 | 0.105 | 0.000 | 0.133 | 0.152 | 13.480 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 87 | 57 | 43 | 45 | 64 | 0 | 0 | 29 | 50 |
N.S. |
1 | 1.13 | 0.74 | 0.56 | 0.58 | 0.83 | 0.00 | 0.00 | 0.38 | 0.65 |
time (sec) |
N/A | 0.414 | 0.036 | 0.132 | 0.043 | 0.091 | 0.000 | 0.000 | 0.146 | 13.879 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 43 | 35 | 26 | 50 | 0 | 49 | 19 | 43 |
N.S. |
1 | 1.00 | 1.48 | 1.21 | 0.90 | 1.72 | 0.00 | 1.69 | 0.66 | 1.48 |
time (sec) |
N/A | 0.345 | 0.025 | 0.129 | 0.041 | 0.078 | 0.000 | 0.129 | 0.147 | 13.902 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 105 | 99 | 82 | 0 | 245 | 0 | 94 | 42 | 0 |
N.S. |
1 | 0.88 | 0.83 | 0.69 | 0.00 | 2.06 | 0.00 | 0.79 | 0.35 | 0.00 |
time (sec) |
N/A | 0.456 | 0.080 | 0.151 | 0.000 | 0.116 | 0.000 | 0.149 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 114 | 116 | 118 | 0 | 287 | 0 | 60 | 70 | 0 |
N.S. |
1 | 0.88 | 0.90 | 0.91 | 0.00 | 2.22 | 0.00 | 0.47 | 0.54 | 0.00 |
time (sec) |
N/A | 0.464 | 0.082 | 0.145 | 0.000 | 0.112 | 0.000 | 0.158 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 154 | 123 | 165 | 0 | 343 | 0 | 78 | 88 | 0 |
N.S. |
1 | 0.79 | 0.63 | 0.85 | 0.00 | 1.77 | 0.00 | 0.40 | 0.45 | 0.00 |
time (sec) |
N/A | 0.504 | 0.175 | 0.154 | 0.000 | 0.103 | 0.000 | 0.152 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 249 | 190 | 139 | 219 | 0 | 399 | 0 | 105 | 165 | 0 |
N.S. |
1 | 0.76 | 0.56 | 0.88 | 0.00 | 1.60 | 0.00 | 0.42 | 0.66 | 0.00 |
time (sec) |
N/A | 0.544 | 0.196 | 0.148 | 0.000 | 0.102 | 0.000 | 0.161 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 46 | 34 | 21 | 32 | 60 | 58 | 205 | 47 | 32 |
N.S. |
1 | 1.15 | 0.85 | 0.52 | 0.80 | 1.50 | 1.45 | 5.12 | 1.18 | 0.80 |
time (sec) |
N/A | 0.595 | 0.052 | 0.170 | 0.038 | 0.098 | 2.342 | 0.116 | 0.141 | 13.710 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 46 | 34 | 21 | 32 | 49 | 58 | 141 | 39 | 32 |
N.S. |
1 | 1.15 | 0.85 | 0.52 | 0.80 | 1.22 | 1.45 | 3.52 | 0.98 | 0.80 |
time (sec) |
N/A | 0.540 | 0.047 | 0.165 | 0.029 | 0.069 | 2.157 | 0.137 | 0.143 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 46 | 30 | 21 | 32 | 32 | 58 | 71 | 29 | 32 |
N.S. |
1 | 1.15 | 0.75 | 0.52 | 0.80 | 0.80 | 1.45 | 1.78 | 0.72 | 0.80 |
time (sec) |
N/A | 0.535 | 0.038 | 0.167 | 0.033 | 0.071 | 2.085 | 0.115 | 0.147 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 44 | 23 | 20 | 30 | 19 | 56 | 44 | 19 | 32 |
N.S. |
1 | 1.16 | 0.61 | 0.53 | 0.79 | 0.50 | 1.47 | 1.16 | 0.50 | 0.84 |
time (sec) |
N/A | 0.534 | 0.031 | 0.149 | 0.031 | 0.085 | 1.968 | 0.116 | 0.142 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 42 | 21 | 20 | 30 | 29 | 54 | 32 | 24 | 19 |
N.S. |
1 | 1.17 | 0.58 | 0.56 | 0.83 | 0.81 | 1.50 | 0.89 | 0.67 | 0.53 |
time (sec) |
N/A | 0.531 | 0.029 | 0.164 | 0.028 | 0.091 | 1.616 | 0.110 | 0.137 | 13.710 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 44 | 34 | 21 | 26 | 44 | 56 | 36 | 32 | 20 |
N.S. |
1 | 1.16 | 0.89 | 0.55 | 0.68 | 1.16 | 1.47 | 0.95 | 0.84 | 0.53 |
time (sec) |
N/A | 0.545 | 0.075 | 0.157 | 0.036 | 0.097 | 1.783 | 0.119 | 0.144 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 46 | 34 | 21 | 24 | 56 | 58 | 34 | 40 | 20 |
N.S. |
1 | 1.15 | 0.85 | 0.52 | 0.60 | 1.40 | 1.45 | 0.85 | 1.00 | 0.50 |
time (sec) |
N/A | 0.527 | 0.080 | 0.167 | 0.031 | 0.095 | 1.693 | 0.113 | 0.149 | 13.721 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 46 | 34 | 21 | 26 | 66 | 58 | 36 | 48 | 20 |
N.S. |
1 | 1.15 | 0.85 | 0.52 | 0.65 | 1.65 | 1.45 | 0.90 | 1.20 | 0.50 |
time (sec) |
N/A | 0.525 | 0.075 | 0.158 | 0.029 | 0.085 | 1.860 | 0.136 | 0.143 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 157 | 77 | 64 | 106 | 105 | 0 | 130 | 55 | 110 |
N.S. |
1 | 0.80 | 0.39 | 0.32 | 0.54 | 0.53 | 0.00 | 0.66 | 0.28 | 0.56 |
time (sec) |
N/A | 0.489 | 0.060 | 0.137 | 0.046 | 0.095 | 0.000 | 0.138 | 0.154 | 13.948 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 119 | 69 | 56 | 90 | 94 | 0 | 0 | 47 | 102 |
N.S. |
1 | 0.87 | 0.50 | 0.41 | 0.66 | 0.69 | 0.00 | 0.00 | 0.34 | 0.74 |
time (sec) |
N/A | 0.450 | 0.050 | 0.136 | 0.046 | 0.089 | 0.000 | 0.000 | 0.146 | 13.956 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 87 | 59 | 48 | 74 | 83 | 0 | 80 | 39 | 93 |
N.S. |
1 | 0.98 | 0.66 | 0.54 | 0.83 | 0.93 | 0.00 | 0.90 | 0.44 | 1.04 |
time (sec) |
N/A | 0.409 | 0.050 | 0.138 | 0.051 | 0.089 | 0.000 | 0.125 | 0.143 | 14.009 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 43 | 35 | 41 | 61 | 0 | 0 | 28 | 81 |
N.S. |
1 | 1.00 | 1.39 | 1.13 | 1.32 | 1.97 | 0.00 | 0.00 | 0.90 | 2.61 |
time (sec) |
N/A | 0.356 | 0.044 | 0.137 | 0.049 | 0.101 | 0.000 | 0.000 | 0.148 | 13.938 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 138 | 105 | 107 | 0 | 256 | 0 | 0 | 52 | 0 |
N.S. |
1 | 0.84 | 0.64 | 0.65 | 0.00 | 1.56 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.492 | 0.079 | 0.150 | 0.000 | 0.114 | 0.000 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 148 | 116 | 135 | 0 | 294 | 0 | 75 | 91 | 0 |
N.S. |
1 | 0.87 | 0.68 | 0.79 | 0.00 | 1.73 | 0.00 | 0.44 | 0.54 | 0.00 |
time (sec) |
N/A | 0.495 | 0.160 | 0.163 | 0.000 | 0.113 | 0.000 | 0.145 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 158 | 125 | 174 | 0 | 347 | 0 | 78 | 116 | 0 |
N.S. |
1 | 0.84 | 0.66 | 0.93 | 0.00 | 1.85 | 0.00 | 0.41 | 0.62 | 0.00 |
time (sec) |
N/A | 0.512 | 0.188 | 0.141 | 0.000 | 0.098 | 0.000 | 0.167 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 196 | 142 | 226 | 0 | 399 | 0 | 105 | 165 | 0 |
N.S. |
1 | 0.78 | 0.57 | 0.90 | 0.00 | 1.59 | 0.00 | 0.42 | 0.66 | 0.00 |
time (sec) |
N/A | 0.562 | 0.170 | 0.152 | 0.000 | 0.103 | 0.000 | 0.164 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 308 | 234 | 147 | 278 | 0 | 455 | 0 | 129 | 130 | 0 |
N.S. |
1 | 0.76 | 0.48 | 0.90 | 0.00 | 1.48 | 0.00 | 0.42 | 0.42 | 0.00 |
time (sec) |
N/A | 0.580 | 0.234 | 0.144 | 0.000 | 0.100 | 0.000 | 0.179 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 157 | 70 | 61 | 96 | 83 | 0 | 0 | 39 | 94 |
N.S. |
1 | 1.23 | 0.55 | 0.48 | 0.75 | 0.65 | 0.00 | 0.00 | 0.30 | 0.73 |
time (sec) |
N/A | 0.472 | 0.059 | 0.134 | 0.046 | 0.071 | 0.000 | 0.000 | 0.147 | 14.511 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 119 | 60 | 53 | 72 | 64 | 0 | 0 | 29 | 82 |
N.S. |
1 | 1.25 | 0.63 | 0.56 | 0.76 | 0.67 | 0.00 | 0.00 | 0.31 | 0.86 |
time (sec) |
N/A | 0.464 | 0.050 | 0.136 | 0.045 | 0.097 | 0.000 | 0.000 | 0.158 | 14.546 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 87 | 50 | 42 | 54 | 50 | 0 | 43 | 20 | 71 |
N.S. |
1 | 1.40 | 0.81 | 0.68 | 0.87 | 0.81 | 0.00 | 0.69 | 0.32 | 1.15 |
time (sec) |
N/A | 0.413 | 0.038 | 0.128 | 0.043 | 0.093 | 0.000 | 0.119 | 0.145 | 14.138 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 28 | 35 | 29 | 44 | 0 | 0 | 17 | 34 |
N.S. |
1 | 1.00 | 0.97 | 1.21 | 1.00 | 1.52 | 0.00 | 0.00 | 0.59 | 1.17 |
time (sec) |
N/A | 0.348 | 0.032 | 0.130 | 0.040 | 0.100 | 0.000 | 0.000 | 0.146 | 14.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 76 | 76 | 78 | 0 | 147 | 0 | 64 | 30 | 0 |
N.S. |
1 | 0.99 | 0.99 | 1.01 | 0.00 | 1.91 | 0.00 | 0.83 | 0.39 | 0.00 |
time (sec) |
N/A | 0.424 | 0.105 | 0.143 | 0.000 | 0.100 | 0.000 | 0.124 | 0.142 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 117 | 116 | 123 | 0 | 287 | 0 | 0 | 70 | 0 |
N.S. |
1 | 0.85 | 0.85 | 0.90 | 0.00 | 2.09 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.462 | 0.107 | 0.144 | 0.000 | 0.089 | 0.000 | 0.000 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 155 | 125 | 172 | 0 | 347 | 0 | 88 | 116 | 0 |
N.S. |
1 | 0.80 | 0.64 | 0.89 | 0.00 | 1.79 | 0.00 | 0.45 | 0.60 | 0.00 |
time (sec) |
N/A | 0.506 | 0.142 | 0.152 | 0.000 | 0.110 | 0.000 | 0.152 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 148 | 88 | 79 | 123 | 211 | 150 | 161 | 108 | 112 |
N.S. |
1 | 1.08 | 0.64 | 0.58 | 0.90 | 1.54 | 1.09 | 1.18 | 0.79 | 0.82 |
time (sec) |
N/A | 0.644 | 0.093 | 0.188 | 0.107 | 0.091 | 2.768 | 0.118 | 0.145 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 126 | 80 | 71 | 109 | 187 | 133 | 134 | 93 | 95 |
N.S. |
1 | 1.09 | 0.69 | 0.61 | 0.94 | 1.61 | 1.15 | 1.16 | 0.80 | 0.82 |
time (sec) |
N/A | 0.618 | 0.074 | 0.191 | 0.110 | 0.089 | 2.620 | 0.121 | 0.145 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 104 | 71 | 61 | 95 | 153 | 116 | 107 | 76 | 78 |
N.S. |
1 | 1.09 | 0.75 | 0.64 | 1.00 | 1.61 | 1.22 | 1.13 | 0.80 | 0.82 |
time (sec) |
N/A | 0.587 | 0.054 | 0.182 | 0.108 | 0.090 | 2.563 | 0.118 | 0.145 | 13.742 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 82 | 61 | 57 | 79 | 124 | 99 | 77 | 59 | 61 |
N.S. |
1 | 1.08 | 0.80 | 0.75 | 1.04 | 1.63 | 1.30 | 1.01 | 0.78 | 0.80 |
time (sec) |
N/A | 0.563 | 0.042 | 0.165 | 0.111 | 0.105 | 2.469 | 0.125 | 0.142 | 13.704 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 60 | 58 | 45 | 68 | 110 | 82 | 51 | 50 | 47 |
N.S. |
1 | 1.03 | 1.00 | 0.78 | 1.17 | 1.90 | 1.41 | 0.88 | 0.86 | 0.81 |
time (sec) |
N/A | 0.530 | 0.033 | 0.165 | 0.112 | 0.116 | 1.622 | 0.115 | 0.145 | 13.740 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 37 | 29 | 52 | 83 | 66 | 36 | 39 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 1.41 | 2.24 | 1.78 | 0.97 | 1.05 | 0.76 |
time (sec) |
N/A | 0.502 | 0.024 | 0.148 | 0.110 | 0.099 | 1.660 | 0.113 | 0.143 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 62 | 37 | 50 | 71 | 152 | 83 | 54 | 66 | 47 |
N.S. |
1 | 1.09 | 0.65 | 0.88 | 1.25 | 2.67 | 1.46 | 0.95 | 1.16 | 0.82 |
time (sec) |
N/A | 0.555 | 0.031 | 0.161 | 0.106 | 0.078 | 2.022 | 0.113 | 0.150 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 91 | 39 | 64 | 81 | 202 | 104 | 73 | 128 | 65 |
N.S. |
1 | 1.10 | 0.47 | 0.77 | 0.98 | 2.43 | 1.25 | 0.88 | 1.54 | 0.78 |
time (sec) |
N/A | 0.571 | 0.034 | 0.178 | 0.106 | 0.091 | 2.147 | 0.104 | 0.143 | 13.821 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 120 | 39 | 78 | 101 | 258 | 121 | 93 | 202 | 79 |
N.S. |
1 | 1.15 | 0.38 | 0.75 | 0.97 | 2.48 | 1.16 | 0.89 | 1.94 | 0.76 |
time (sec) |
N/A | 0.610 | 0.039 | 0.181 | 0.105 | 0.123 | 2.397 | 0.110 | 0.141 | 0.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 191 | 68 | 72 | 120 | 83 | 0 | 0 | 49 | 94 |
N.S. |
1 | 0.76 | 0.27 | 0.29 | 0.48 | 0.33 | 0.00 | 0.00 | 0.20 | 0.38 |
time (sec) |
N/A | 0.529 | 0.054 | 0.149 | 0.051 | 0.088 | 0.000 | 0.000 | 0.144 | 13.885 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 153 | 57 | 63 | 93 | 63 | 0 | 0 | 38 | 81 |
N.S. |
1 | 0.81 | 0.30 | 0.33 | 0.49 | 0.33 | 0.00 | 0.00 | 0.20 | 0.43 |
time (sec) |
N/A | 0.489 | 0.047 | 0.150 | 0.049 | 0.077 | 0.000 | 0.000 | 0.143 | 13.831 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 115 | 48 | 55 | 75 | 50 | 0 | 0 | 30 | 71 |
N.S. |
1 | 0.84 | 0.35 | 0.40 | 0.55 | 0.36 | 0.00 | 0.00 | 0.22 | 0.52 |
time (sec) |
N/A | 0.440 | 0.034 | 0.144 | 0.045 | 0.076 | 0.000 | 0.000 | 0.142 | 13.803 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 83 | 48 | 47 | 48 | 44 | 0 | 42 | 24 | 34 |
N.S. |
1 | 0.98 | 0.56 | 0.55 | 0.56 | 0.52 | 0.00 | 0.49 | 0.28 | 0.40 |
time (sec) |
N/A | 0.410 | 0.038 | 0.144 | 0.044 | 0.079 | 0.000 | 0.121 | 0.150 | 13.909 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 41 | 35 | 45 | 43 | 0 | 41 | 19 | 32 |
N.S. |
1 | 1.00 | 1.41 | 1.21 | 1.55 | 1.48 | 0.00 | 1.41 | 0.66 | 1.10 |
time (sec) |
N/A | 0.353 | 0.033 | 0.130 | 0.046 | 0.078 | 0.000 | 0.120 | 0.152 | 13.815 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 101 | 122 | 85 | 0 | 241 | 0 | 0 | 57 | 0 |
N.S. |
1 | 0.83 | 1.01 | 0.70 | 0.00 | 1.99 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.447 | 0.091 | 0.141 | 0.000 | 0.099 | 0.000 | 0.000 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 141 | 130 | 129 | 0 | 291 | 0 | 90 | 110 | 0 |
N.S. |
1 | 0.76 | 0.70 | 0.70 | 0.00 | 1.57 | 0.00 | 0.49 | 0.59 | 0.00 |
time (sec) |
N/A | 0.528 | 0.332 | 0.141 | 0.000 | 0.101 | 0.000 | 0.153 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 242 | 179 | 140 | 180 | 0 | 347 | 0 | 0 | 207 | 0 |
N.S. |
1 | 0.74 | 0.58 | 0.74 | 0.00 | 1.43 | 0.00 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.541 | 0.277 | 0.140 | 0.000 | 0.088 | 0.000 | 0.000 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 75 | 50 | 74 | 153 | 81 | 530 | 0 | 78 | 57 |
N.S. |
1 | 1.14 | 0.76 | 1.12 | 2.32 | 1.23 | 8.03 | 0.00 | 1.18 | 0.86 |
time (sec) |
N/A | 0.562 | 0.124 | 0.186 | 0.046 | 0.079 | 0.535 | 0.000 | 0.148 | 13.809 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 47 | 28 | 29 | 49 | 28 | 124 | 0 | 28 | 28 |
N.S. |
1 | 1.12 | 0.67 | 0.69 | 1.17 | 0.67 | 2.95 | 0.00 | 0.67 | 0.67 |
time (sec) |
N/A | 0.519 | 0.020 | 0.148 | 0.040 | 0.110 | 0.335 | 0.000 | 0.146 | 13.862 |
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 | 44 | 44 | 44 | 0 | 0 | 0 | 0 | 0 | 110 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.50 | 0.00 |
time (sec) |
N/A | 0.473 | 0.023 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 233 | 138 | 0 | 0 | 0 | 0 | 0 | 80 | 0 |
N.S. |
1 | 2.48 | 1.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.583 | 0.159 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 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 | 94 | 176 | 131 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.87 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.507 | 0.104 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.150 | 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 | 94 | 94 | 76 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.459 | 0.058 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 96 | 0 | 0 | 0 | 0 | 0 | 78 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.459 | 0.072 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.191 | 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 | 104 | 104 | 104 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.467 | 0.059 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 190 | 0 | 0 | 0 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.00 | 2.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.423 | 1.984 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.143 | 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 | 81 | 81 | 144 | 0 | 0 | 0 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.00 | 1.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.429 | 1.231 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.146 | 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 | 79 | 79 | 104 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 1.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.405 | 0.614 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.141 | 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 | 71 | 71 | 87 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 1.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.408 | 0.333 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.141 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 33 | 33 | 0 | 58 | 187 | 0 | 35 | 32 |
N.S. |
1 | 1.00 | 0.69 | 0.69 | 0.00 | 1.21 | 3.90 | 0.00 | 0.73 | 0.67 |
time (sec) |
N/A | 0.389 | 0.288 | 1.664 | 0.000 | 0.084 | 10.584 | 0.000 | 0.140 | 13.829 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 105 | 64 | 46 | 0 | 128 | 1112 | 0 | 90 | 113 |
N.S. |
1 | 1.01 | 0.62 | 0.44 | 0.00 | 1.23 | 10.69 | 0.00 | 0.87 | 1.09 |
time (sec) |
N/A | 0.464 | 0.368 | 5.191 | 0.000 | 0.087 | 55.945 | 0.000 | 0.143 | 13.929 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 224 | 208 | 83 | 68 | 0 | 228 | 0 | 0 | 180 | 180 |
N.S. |
1 | 0.93 | 0.37 | 0.30 | 0.00 | 1.02 | 0.00 | 0.00 | 0.80 | 0.80 |
time (sec) |
N/A | 0.641 | 0.424 | 13.991 | 0.000 | 0.088 | 0.000 | 0.000 | 0.141 | 13.949 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 106 | 103 | 0 | 0 | 0 | 0 | 0 | 72 | 0 |
N.S. |
1 | 1.08 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.478 | 0.123 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.149 | 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 | 98 | 106 | 101 | 0 | 0 | 0 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.08 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.474 | 0.087 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.148 | 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 | 98 | 106 | 98 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.08 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.464 | 0.081 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.139 | 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 | 96 | 104 | 96 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.08 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.460 | 0.072 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.141 | 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 | 96 | 104 | 94 | 0 | 0 | 0 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.08 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.463 | 0.053 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 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 | 98 | 187 | 117 | 0 | 0 | 0 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.91 | 1.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.532 | 0.135 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 249 | 138 | 0 | 0 | 0 | 0 | 0 | 72 | 0 |
N.S. |
1 | 2.54 | 1.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.608 | 0.204 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 278 | 226 | 116 | 104 | 122 | 185 | 0 | 0 | 82 | 223 |
N.S. |
1 | 0.81 | 0.42 | 0.37 | 0.44 | 0.67 | 0.00 | 0.00 | 0.29 | 0.80 |
time (sec) |
N/A | 0.631 | 0.086 | 1.479 | 0.044 | 0.087 | 0.000 | 0.000 | 0.158 | 13.762 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 129 | 78 | 61 | 68 | 93 | 0 | 0 | 51 | 140 |
N.S. |
1 | 1.02 | 0.61 | 0.48 | 0.54 | 0.73 | 0.00 | 0.00 | 0.40 | 1.10 |
time (sec) |
N/A | 0.463 | 0.061 | 0.989 | 0.039 | 0.118 | 0.000 | 0.000 | 0.152 | 13.779 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 58 | 34 | 37 | 44 | 0 | 0 | 22 | 55 |
N.S. |
1 | 1.00 | 1.61 | 0.94 | 1.03 | 1.22 | 0.00 | 0.00 | 0.61 | 1.53 |
time (sec) |
N/A | 0.358 | 0.025 | 0.971 | 0.037 | 0.099 | 0.000 | 0.000 | 0.146 | 13.653 |