Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 46 | 48 | 0 | 6 | 66 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 1.77 | 1.85 | 0.00 | 0.23 | 2.54 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.140 | 0.010 | 0.311 | 0.000 | 0.067 | 10.186 | 0.000 | 0.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 27 | 0 | 14 | 76 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.17 | 0.00 | 0.61 | 3.30 | 0.00 | 1.35 | 0.00 |
time (sec) |
N/A | 0.135 | 10.026 | 0.607 | 0.000 | 0.078 | 10.471 | 0.000 | 0.271 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 55 | 50 | 57 | 0 | 14 | 71 | 0 | 30 | 0 |
N.S. |
1 | 1.10 | 1.00 | 1.14 | 0.00 | 0.28 | 1.42 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.150 | 0.012 | 0.556 | 0.000 | 0.071 | 10.566 | 0.000 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 39 | 48 | 38 | 0 | 9 | 71 | 0 | 28 | 0 |
N.S. |
1 | 0.95 | 1.17 | 0.93 | 0.00 | 0.22 | 1.73 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.144 | 0.010 | 0.513 | 0.000 | 0.072 | 10.561 | 0.000 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 52 | 50 | 0 | 9 | 76 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 1.33 | 1.28 | 0.00 | 0.23 | 1.95 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.143 | 0.397 | 0.478 | 0.000 | 0.070 | 10.979 | 0.000 | 0.249 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 38 | 0 | 9 | 76 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 1.10 | 1.90 | 0.00 | 0.45 | 3.80 | 0.00 | 1.20 | 0.00 |
time (sec) |
N/A | 0.131 | 10.019 | 0.271 | 0.000 | 0.095 | 103.732 | 0.000 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 47 | 49 | 71 | 0 | 9 | 71 | 0 | 23 | 0 |
N.S. |
1 | 0.63 | 0.65 | 0.95 | 0.00 | 0.12 | 0.95 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.159 | 0.424 | 0.273 | 0.000 | 0.093 | 103.406 | 0.000 | 0.271 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 46 | 47 | 50 | 0 | 9 | 71 | 0 | 20 | 0 |
N.S. |
1 | 0.87 | 0.89 | 0.94 | 0.00 | 0.17 | 1.34 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.158 | 0.388 | 0.243 | 0.000 | 0.086 | 104.407 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 36 | 51 | 65 | 0 | 9 | 76 | 0 | 24 | 0 |
N.S. |
1 | 0.68 | 0.96 | 1.23 | 0.00 | 0.17 | 1.43 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.163 | 0.425 | 0.243 | 0.000 | 0.087 | 102.066 | 0.000 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 32 | 25 | 42 | 0 | 14 | 87 | 0 | 26 | 0 |
N.S. |
1 | 0.68 | 0.53 | 0.89 | 0.00 | 0.30 | 1.85 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.148 | 10.019 | 0.444 | 0.000 | 0.077 | 102.085 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 59 | 52 | 75 | 0 | 14 | 82 | 0 | 25 | 0 |
N.S. |
1 | 0.58 | 0.51 | 0.74 | 0.00 | 0.14 | 0.81 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.169 | 0.010 | 0.467 | 0.000 | 0.071 | 99.965 | 0.000 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 48 | 50 | 55 | 0 | 12 | 82 | 0 | 23 | 0 |
N.S. |
1 | 0.61 | 0.63 | 0.70 | 0.00 | 0.15 | 1.04 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.154 | 0.009 | 0.398 | 0.000 | 0.079 | 103.029 | 0.000 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 48 | 54 | 70 | 0 | 12 | 87 | 0 | 26 | 0 |
N.S. |
1 | 0.61 | 0.68 | 0.89 | 0.00 | 0.15 | 1.10 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.154 | 0.008 | 0.389 | 0.000 | 0.082 | 103.391 | 0.000 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 27 | 32 | 0 | 24 | 94 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.97 | 0.00 | 0.73 | 2.85 | 0.00 | 1.15 | 0.00 |
time (sec) |
N/A | 0.144 | 10.022 | 0.777 | 0.000 | 0.076 | 10.905 | 0.000 | 0.265 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 89 | 57 | 0 | 86 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.00 | 2.34 | 1.50 | 0.00 | 2.26 | 0.00 | 0.00 | 1.26 | 0.00 |
time (sec) |
N/A | 0.143 | 3.279 | 1.428 | 0.000 | 0.091 | 0.000 | 0.000 | 0.289 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 38 | 0 | 0 | 0 | 206 | 0 | 207 | 0 |
N.S. |
1 | 1.00 | 1.06 | 0.00 | 0.00 | 0.00 | 5.72 | 0.00 | 5.75 | 0.00 |
time (sec) |
N/A | 0.152 | 0.055 | 0.000 | 0.000 | 0.000 | 14.301 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 39 | 0 | 0 | 0 | 212 | 0 | 211 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 5.44 | 0.00 | 5.41 | 0.00 |
time (sec) |
N/A | 0.154 | 0.072 | 0.000 | 0.000 | 0.000 | 14.568 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 44 | 0 | 0 | 0 | 224 | 0 | 207 | 0 |
N.S. |
1 | 1.00 | 1.05 | 0.00 | 0.00 | 0.00 | 5.33 | 0.00 | 4.93 | 0.00 |
time (sec) |
N/A | 0.158 | 0.056 | 0.000 | 0.000 | 0.000 | 14.619 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 42 | 0 | 0 | 0 | 0 | 0 | 212 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 5.05 | 0.00 |
time (sec) |
N/A | 0.153 | 0.075 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 44 | 0 | 0 | 0 | 138 | 0 | 91 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.00 | 0.00 | 0.00 | 2.76 | 0.00 | 1.82 | 0.00 |
time (sec) |
N/A | 0.165 | 0.084 | 0.000 | 0.000 | 0.000 | 12.024 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 27 | 26 | 67 | 67 | 70 | 77 | 66 | 70 |
N.S. |
1 | 1.00 | 0.96 | 0.93 | 2.39 | 2.39 | 2.50 | 2.75 | 2.36 | 2.50 |
time (sec) |
N/A | 0.139 | 0.013 | 0.177 | 0.045 | 0.076 | 0.306 | 0.131 | 0.185 | 0.705 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 27 | 26 | 123 | 123 | 129 | 133 | 122 | 124 |
N.S. |
1 | 1.00 | 0.96 | 0.93 | 4.39 | 4.39 | 4.61 | 4.75 | 4.36 | 4.43 |
time (sec) |
N/A | 0.139 | 0.017 | 0.239 | 0.067 | 0.077 | 0.588 | 0.123 | 0.197 | 2.570 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 27 | 26 | 197 | 197 | 204 | 205 | 194 | 197 |
N.S. |
1 | 1.00 | 0.96 | 0.93 | 7.04 | 7.04 | 7.29 | 7.32 | 6.93 | 7.04 |
time (sec) |
N/A | 0.140 | 0.031 | 0.407 | 0.111 | 0.122 | 0.969 | 0.126 | 0.195 | 56.604 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 176 | 57 | 52 | 0 | 93 | 0 | 107 | 126 | 104 |
N.S. |
1 | 1.48 | 0.48 | 0.44 | 0.00 | 0.78 | 0.00 | 0.90 | 1.06 | 0.87 |
time (sec) |
N/A | 0.244 | 0.157 | 0.191 | 0.000 | 0.072 | 0.000 | 0.176 | 0.225 | 0.717 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 166 | 70 | 65 | 253 | 172 | 0 | 309 | 95 | 117 |
N.S. |
1 | 1.35 | 0.57 | 0.53 | 2.06 | 1.40 | 0.00 | 2.51 | 0.77 | 0.95 |
time (sec) |
N/A | 0.229 | 0.083 | 0.364 | 0.035 | 0.082 | 0.000 | 0.193 | 0.216 | 0.715 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 126 | 58 | 53 | 157 | 117 | 0 | 243 | 72 | 105 |
N.S. |
1 | 1.38 | 0.64 | 0.58 | 1.73 | 1.29 | 0.00 | 2.67 | 0.79 | 1.15 |
time (sec) |
N/A | 0.203 | 0.077 | 0.364 | 0.036 | 0.118 | 0.000 | 0.167 | 0.217 | 0.675 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 54 | 48 | 43 | 86 | 104 | 0 | 180 | 51 | 51 |
N.S. |
1 | 0.92 | 0.81 | 0.73 | 1.46 | 1.76 | 0.00 | 3.05 | 0.86 | 0.86 |
time (sec) |
N/A | 0.162 | 0.070 | 0.349 | 0.033 | 0.101 | 0.000 | 0.154 | 0.195 | 0.635 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 20 | 18 | 51 | 92 | 105 | 21 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.78 | 2.22 | 4.00 | 4.57 | 0.91 | 0.83 |
time (sec) |
N/A | 0.138 | 0.008 | 0.326 | 0.039 | 0.082 | 2.316 | 0.137 | 0.195 | 0.623 |
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 | 26 | 26 | 26 | 23 | 31 | 40 | 0 | 32 | 22 | 47 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 1.19 | 1.54 | 0.00 | 1.23 | 0.85 | 1.81 |
time (sec) |
N/A | 0.138 | 0.023 | 0.196 | 0.118 | 0.079 | 0.000 | 0.125 | 0.203 | 0.591 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 75 | 113 | 75 | 71 | 0 | 0 | 160 | 0 |
N.S. |
1 | 1.00 | 1.39 | 2.09 | 1.39 | 1.31 | 0.00 | 0.00 | 2.96 | 0.00 |
time (sec) |
N/A | 0.165 | 0.080 | 0.260 | 0.049 | 0.109 | 0.000 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 85 | 87 | 141 | 99 | 95 | 0 | 0 | 184 | 0 |
N.S. |
1 | 1.02 | 1.05 | 1.70 | 1.19 | 1.14 | 0.00 | 0.00 | 2.22 | 0.00 |
time (sec) |
N/A | 0.182 | 0.284 | 0.305 | 0.036 | 0.082 | 0.000 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 120 | 105 | 150 | 126 | 117 | 0 | 0 | 218 | 0 |
N.S. |
1 | 0.99 | 0.87 | 1.24 | 1.04 | 0.97 | 0.00 | 0.00 | 1.80 | 0.00 |
time (sec) |
N/A | 0.201 | 0.161 | 0.305 | 0.038 | 0.077 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 81 | 56 | 89 | 0 | 80 | 0 | 49 | 88 | 0 |
N.S. |
1 | 1.09 | 0.76 | 1.20 | 0.00 | 1.08 | 0.00 | 0.66 | 1.19 | 0.00 |
time (sec) |
N/A | 0.175 | 0.086 | 0.162 | 0.000 | 0.071 | 0.000 | 0.134 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 57 | 51 | 78 | 0 | 75 | 0 | 44 | 79 | 0 |
N.S. |
1 | 0.93 | 0.84 | 1.28 | 0.00 | 1.23 | 0.00 | 0.72 | 1.30 | 0.00 |
time (sec) |
N/A | 0.159 | 0.069 | 0.159 | 0.000 | 0.104 | 0.000 | 0.124 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 46 | 64 | 0 | 71 | 0 | 38 | 70 | 0 |
N.S. |
1 | 1.00 | 1.12 | 1.56 | 0.00 | 1.73 | 0.00 | 0.93 | 1.71 | 0.00 |
time (sec) |
N/A | 0.147 | 0.055 | 0.155 | 0.000 | 0.078 | 0.000 | 0.131 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 15 | 38 | 33 | 60 | 19 | 22 | 34 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 1.90 | 1.65 | 3.00 | 0.95 | 1.10 | 1.70 |
time (sec) |
N/A | 0.135 | 0.002 | 0.138 | 0.028 | 0.084 | 0.670 | 0.127 | 0.192 | 0.486 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 59 | 46 | 87 | 70 | 71 | 0 | 117 | 265 | 0 |
N.S. |
1 | 1.07 | 0.84 | 1.58 | 1.27 | 1.29 | 0.00 | 2.13 | 4.82 | 0.00 |
time (sec) |
N/A | 0.163 | 0.069 | 0.159 | 0.027 | 0.082 | 0.000 | 0.162 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 88 | 54 | 95 | 86 | 84 | 0 | 211 | 289 | 0 |
N.S. |
1 | 1.16 | 0.71 | 1.25 | 1.13 | 1.11 | 0.00 | 2.78 | 3.80 | 0.00 |
time (sec) |
N/A | 0.187 | 0.095 | 0.162 | 0.026 | 0.076 | 0.000 | 0.192 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 116 | 59 | 100 | 100 | 95 | 0 | 258 | 306 | 0 |
N.S. |
1 | 1.15 | 0.58 | 0.99 | 0.99 | 0.94 | 0.00 | 2.55 | 3.03 | 0.00 |
time (sec) |
N/A | 0.209 | 0.134 | 0.158 | 0.047 | 0.079 | 0.000 | 0.208 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 119 | 68 | 87 | 70 | 57 | 0 | 52 | 85 | 0 |
N.S. |
1 | 1.11 | 0.64 | 0.81 | 0.65 | 0.53 | 0.00 | 0.49 | 0.79 | 0.00 |
time (sec) |
N/A | 0.193 | 0.094 | 0.155 | 0.111 | 0.083 | 0.000 | 0.131 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 92 | 63 | 80 | 56 | 52 | 0 | 46 | 70 | 0 |
N.S. |
1 | 1.06 | 0.72 | 0.92 | 0.64 | 0.60 | 0.00 | 0.53 | 0.80 | 0.00 |
time (sec) |
N/A | 0.175 | 0.078 | 0.162 | 0.111 | 0.083 | 0.000 | 0.127 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 66 | 54 | 66 | 40 | 45 | 0 | 37 | 55 | 0 |
N.S. |
1 | 1.08 | 0.89 | 1.08 | 0.66 | 0.74 | 0.00 | 0.61 | 0.90 | 0.00 |
time (sec) |
N/A | 0.160 | 0.065 | 0.159 | 0.109 | 0.091 | 0.000 | 0.135 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 41 | 39 | 57 | 28 | 40 | 134 | 31 | 40 | 0 |
N.S. |
1 | 0.87 | 0.83 | 1.21 | 0.60 | 0.85 | 2.85 | 0.66 | 0.85 | 0.00 |
time (sec) |
N/A | 0.144 | 0.006 | 0.142 | 0.118 | 0.086 | 2.191 | 0.122 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 43 | 54 | 51 | 41 | 57 | 0 | 158 | 115 | 0 |
N.S. |
1 | 1.16 | 1.46 | 1.38 | 1.11 | 1.54 | 0.00 | 4.27 | 3.11 | 0.00 |
time (sec) |
N/A | 0.166 | 0.065 | 0.150 | 0.111 | 0.081 | 0.000 | 0.157 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 44 | 59 | 55 | 42 | 65 | 0 | 236 | 128 | 0 |
N.S. |
1 | 1.16 | 1.55 | 1.45 | 1.11 | 1.71 | 0.00 | 6.21 | 3.37 | 0.00 |
time (sec) |
N/A | 0.158 | 0.083 | 0.163 | 0.117 | 0.079 | 0.000 | 0.167 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 70 | 54 | 64 | 54 | 50 | 0 | 234 | 135 | 0 |
N.S. |
1 | 1.21 | 0.93 | 1.10 | 0.93 | 0.86 | 0.00 | 4.03 | 2.33 | 0.00 |
time (sec) |
N/A | 0.162 | 0.111 | 0.162 | 0.107 | 0.083 | 0.000 | 0.181 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 98 | 59 | 78 | 68 | 55 | 0 | 278 | 150 | 0 |
N.S. |
1 | 1.27 | 0.77 | 1.01 | 0.88 | 0.71 | 0.00 | 3.61 | 1.95 | 0.00 |
time (sec) |
N/A | 0.175 | 0.105 | 0.158 | 0.113 | 0.085 | 0.000 | 0.242 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 126 | 66 | 93 | 82 | 60 | 0 | 326 | 165 | 0 |
N.S. |
1 | 1.34 | 0.70 | 0.99 | 0.87 | 0.64 | 0.00 | 3.47 | 1.76 | 0.00 |
time (sec) |
N/A | 0.206 | 0.167 | 0.161 | 0.117 | 0.160 | 0.000 | 0.184 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 151 | 106 | 127 | 104 | 97 | 0 | 228 | 133 | 0 |
N.S. |
1 | 1.05 | 0.74 | 0.88 | 0.72 | 0.67 | 0.00 | 1.58 | 0.92 | 0.00 |
time (sec) |
N/A | 0.221 | 0.142 | 0.247 | 0.117 | 0.115 | 0.000 | 0.234 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 118 | 95 | 116 | 79 | 86 | 0 | 189 | 109 | 0 |
N.S. |
1 | 1.03 | 0.83 | 1.01 | 0.69 | 0.75 | 0.00 | 1.64 | 0.95 | 0.00 |
time (sec) |
N/A | 0.192 | 0.123 | 0.214 | 0.106 | 0.095 | 0.000 | 0.227 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 83 | 74 | 102 | 53 | 75 | 0 | 153 | 85 | 0 |
N.S. |
1 | 1.04 | 0.92 | 1.28 | 0.66 | 0.94 | 0.00 | 1.91 | 1.06 | 0.00 |
time (sec) |
N/A | 0.174 | 0.097 | 0.206 | 0.112 | 0.075 | 0.000 | 0.185 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 102 | 94 | 138 | 84 | 87 | 0 | 232 | 177 | 0 |
N.S. |
1 | 1.00 | 0.92 | 1.35 | 0.82 | 0.85 | 0.00 | 2.27 | 1.74 | 0.00 |
time (sec) |
N/A | 0.228 | 0.113 | 0.215 | 0.125 | 0.122 | 0.000 | 0.368 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 101 | 78 | 141 | 84 | 94 | 0 | 348 | 181 | 0 |
N.S. |
1 | 1.01 | 0.78 | 1.41 | 0.84 | 0.94 | 0.00 | 3.48 | 1.81 | 0.00 |
time (sec) |
N/A | 0.226 | 0.127 | 0.245 | 0.131 | 0.100 | 0.000 | 0.405 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 110 | 84 | 134 | 114 | 98 | 0 | 390 | 198 | 0 |
N.S. |
1 | 1.00 | 0.76 | 1.22 | 1.04 | 0.89 | 0.00 | 3.55 | 1.80 | 0.00 |
time (sec) |
N/A | 0.245 | 0.149 | 0.236 | 0.116 | 0.080 | 0.000 | 0.393 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 128 | 87 | 115 | 108 | 78 | 0 | 395 | 202 | 0 |
N.S. |
1 | 1.41 | 0.96 | 1.26 | 1.19 | 0.86 | 0.00 | 4.34 | 2.22 | 0.00 |
time (sec) |
N/A | 0.203 | 0.109 | 0.230 | 0.111 | 0.077 | 0.000 | 0.393 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 166 | 98 | 129 | 133 | 89 | 0 | 458 | 226 | 0 |
N.S. |
1 | 1.34 | 0.79 | 1.04 | 1.07 | 0.72 | 0.00 | 3.69 | 1.82 | 0.00 |
time (sec) |
N/A | 0.230 | 0.113 | 0.236 | 0.113 | 0.077 | 0.000 | 0.425 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 198 | 109 | 140 | 158 | 100 | 0 | 521 | 250 | 0 |
N.S. |
1 | 1.28 | 0.70 | 0.90 | 1.02 | 0.65 | 0.00 | 3.36 | 1.61 | 0.00 |
time (sec) |
N/A | 0.293 | 0.128 | 0.238 | 0.136 | 0.080 | 0.000 | 0.432 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 236 | 120 | 151 | 183 | 111 | 0 | 584 | 274 | 0 |
N.S. |
1 | 1.26 | 0.64 | 0.80 | 0.97 | 0.59 | 0.00 | 3.11 | 1.46 | 0.00 |
time (sec) |
N/A | 0.323 | 0.138 | 0.235 | 0.115 | 0.090 | 0.000 | 0.456 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 100 | 32 | 32 | 54 | 31 | 94 | 48 | 29 | 298 |
N.S. |
1 | 1.82 | 0.58 | 0.58 | 0.98 | 0.56 | 1.71 | 0.87 | 0.53 | 5.42 |
time (sec) |
N/A | 0.187 | 0.016 | 0.165 | 0.105 | 0.143 | 3.756 | 0.126 | 0.180 | 1.614 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 72 | 27 | 27 | 40 | 26 | 94 | 36 | 24 | 317 |
N.S. |
1 | 1.64 | 0.61 | 0.61 | 0.91 | 0.59 | 2.14 | 0.82 | 0.55 | 7.20 |
time (sec) |
N/A | 0.165 | 0.014 | 0.172 | 0.106 | 0.081 | 2.341 | 0.131 | 0.195 | 1.857 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 44 | 22 | 20 | 26 | 19 | 94 | 23 | 19 | 108 |
N.S. |
1 | 1.52 | 0.76 | 0.69 | 0.90 | 0.66 | 3.24 | 0.79 | 0.66 | 3.72 |
time (sec) |
N/A | 0.146 | 0.012 | 0.148 | 0.113 | 0.098 | 1.680 | 0.122 | 0.214 | 0.908 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 18 | 13 | 15 | 11 | 14 | 80 | 14 | 12 | 44 |
N.S. |
1 | 1.38 | 1.00 | 1.15 | 0.85 | 1.08 | 6.15 | 1.08 | 0.92 | 3.38 |
time (sec) |
N/A | 0.132 | 0.001 | 0.173 | 0.128 | 0.066 | 1.510 | 0.125 | 0.207 | 0.672 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 20 | 14 | 34 | 25 | 20 | 58 | 93 | 89 | 47 |
N.S. |
1 | 1.43 | 1.00 | 2.43 | 1.79 | 1.43 | 4.14 | 6.64 | 6.36 | 3.36 |
time (sec) |
N/A | 0.135 | 0.014 | 0.139 | 0.040 | 0.072 | 12.192 | 0.146 | 0.191 | 1.439 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 46 | 35 | 51 | 40 | 44 | 0 | 232 | 120 | 186 |
N.S. |
1 | 1.31 | 1.00 | 1.46 | 1.14 | 1.26 | 0.00 | 6.63 | 3.43 | 5.31 |
time (sec) |
N/A | 0.149 | 0.029 | 0.165 | 0.122 | 0.072 | 0.000 | 0.166 | 0.190 | 1.447 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 74 | 42 | 68 | 54 | 52 | 0 | 326 | 137 | 317 |
N.S. |
1 | 1.40 | 0.79 | 1.28 | 1.02 | 0.98 | 0.00 | 6.15 | 2.58 | 5.98 |
time (sec) |
N/A | 0.165 | 0.040 | 0.157 | 0.107 | 0.084 | 0.000 | 0.202 | 0.211 | 1.671 |
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 | 59 | 84 | 51 | 69 | 45 | 51 | 0 | 57 | 58 | 556 |
N.S. |
1 | 1.42 | 0.86 | 1.17 | 0.76 | 0.86 | 0.00 | 0.97 | 0.98 | 9.42 |
time (sec) |
N/A | 0.167 | 0.080 | 0.156 | 0.110 | 0.077 | 0.000 | 0.143 | 0.211 | 4.499 |
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 | 41 | 56 | 46 | 55 | 31 | 46 | 0 | 44 | 43 | 380 |
N.S. |
1 | 1.37 | 1.12 | 1.34 | 0.76 | 1.12 | 0.00 | 1.07 | 1.05 | 9.27 |
time (sec) |
N/A | 0.160 | 0.059 | 0.155 | 0.113 | 0.072 | 0.000 | 0.122 | 0.204 | 3.798 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 28 | 35 | 39 | 17 | 38 | 0 | 27 | 28 | 202 |
N.S. |
1 | 1.22 | 1.52 | 1.70 | 0.74 | 1.65 | 0.00 | 1.17 | 1.22 | 8.78 |
time (sec) |
N/A | 0.138 | 0.041 | 0.157 | 0.116 | 0.075 | 0.000 | 0.125 | 0.204 | 3.225 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | A | B | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 2 | 2 | 20 | 27 | 2 | 22 | 39 | 13 | 14 | 22 |
N.S. |
1 | 1.00 | 10.00 | 13.50 | 1.00 | 11.00 | 19.50 | 6.50 | 7.00 | 11.00 |
time (sec) |
N/A | 0.121 | 0.001 | 0.138 | 0.151 | 0.071 | 0.482 | 0.122 | 0.207 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 21 | 16 | 18 | 14 | 17 | 58 | 92 | 15 | 17 |
N.S. |
1 | 1.31 | 1.00 | 1.12 | 0.88 | 1.06 | 3.62 | 5.75 | 0.94 | 1.06 |
time (sec) |
N/A | 0.131 | 0.021 | 0.163 | 0.110 | 0.077 | 4.668 | 0.131 | 0.206 | 0.609 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 47 | 25 | 25 | 29 | 24 | 58 | 185 | 22 | 32 |
N.S. |
1 | 1.27 | 0.68 | 0.68 | 0.78 | 0.65 | 1.57 | 5.00 | 0.59 | 0.86 |
time (sec) |
N/A | 0.147 | 0.027 | 0.167 | 0.105 | 0.087 | 4.522 | 0.136 | 0.248 | 0.569 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 75 | 30 | 30 | 43 | 29 | 58 | 277 | 27 | 42 |
N.S. |
1 | 1.36 | 0.55 | 0.55 | 0.78 | 0.53 | 1.05 | 5.04 | 0.49 | 0.76 |
time (sec) |
N/A | 0.163 | 0.031 | 0.160 | 0.108 | 0.071 | 11.025 | 0.290 | 0.205 | 0.573 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 50 | 51 | 52 | 37 | 40 | 0 | 70 | 42 | 362 |
N.S. |
1 | 1.06 | 1.09 | 1.11 | 0.79 | 0.85 | 0.00 | 1.49 | 0.89 | 7.70 |
time (sec) |
N/A | 0.147 | 0.076 | 0.167 | 0.047 | 0.080 | 0.000 | 0.134 | 0.210 | 4.808 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 13 | 9 | 17 | 0 | 39 | 15 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.72 | 0.50 | 0.94 | 0.00 | 2.17 | 0.83 | 0.94 |
time (sec) |
N/A | 0.130 | 0.030 | 0.158 | 0.030 | 0.068 | 0.000 | 0.136 | 0.208 | 0.507 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 38 | 46 | 27 | 32 | 131 | 41 | 29 | 30 |
N.S. |
1 | 1.00 | 1.46 | 1.77 | 1.04 | 1.23 | 5.04 | 1.58 | 1.12 | 1.15 |
time (sec) |
N/A | 0.132 | 0.038 | 0.169 | 0.033 | 0.102 | 1.581 | 0.135 | 0.209 | 0.515 |
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 | 34 | 34 | 32 | 35 | 13 | 30 | 0 | 32 | 36 | 116 |
N.S. |
1 | 1.00 | 0.94 | 1.03 | 0.38 | 0.88 | 0.00 | 0.94 | 1.06 | 3.41 |
time (sec) |
N/A | 0.143 | 0.039 | 0.165 | 0.106 | 0.095 | 0.000 | 0.129 | 0.180 | 1.888 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 36 | 44 | 27 | 36 | 0 | 40 | 36 | 109 |
N.S. |
1 | 1.00 | 1.64 | 2.00 | 1.23 | 1.64 | 0.00 | 1.82 | 1.64 | 4.95 |
time (sec) |
N/A | 0.134 | 0.048 | 0.174 | 0.140 | 0.072 | 0.000 | 0.139 | 0.196 | 1.207 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 13 | 34 | 31 | 60 | 12 | 38 | 27 |
N.S. |
1 | 1.00 | 1.00 | 0.72 | 1.89 | 1.72 | 3.33 | 0.67 | 2.11 | 1.50 |
time (sec) |
N/A | 0.122 | 0.012 | 0.163 | 0.034 | 0.077 | 0.669 | 0.127 | 0.208 | 0.533 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 34 | 40 | 27 | 32 | 0 | 30 | 27 | 194 |
N.S. |
1 | 1.00 | 1.31 | 1.54 | 1.04 | 1.23 | 0.00 | 1.15 | 1.04 | 7.46 |
time (sec) |
N/A | 0.130 | 0.058 | 0.170 | 0.037 | 0.077 | 0.000 | 0.118 | 0.221 | 4.885 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 12 | 7 | 11 | 76 | 11 | 9 | 67 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.47 | 0.73 | 5.07 | 0.73 | 0.60 | 4.47 |
time (sec) |
N/A | 0.124 | 0.028 | 0.174 | 0.030 | 0.081 | 1.442 | 0.116 | 0.247 | 1.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 2 | 2 | 18 | 31 | 14 | 18 | 39 | 16 | 17 | 2 |
N.S. |
1 | 1.00 | 9.00 | 15.50 | 7.00 | 9.00 | 19.50 | 8.00 | 8.50 | 1.00 |
time (sec) |
N/A | 0.114 | 0.017 | 0.161 | 0.043 | 0.079 | 0.493 | 0.127 | 0.196 | 0.008 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 28 | 7 | 18 | 56 | 20 | 27 | 49 |
N.S. |
1 | 1.00 | 1.12 | 1.75 | 0.44 | 1.12 | 3.50 | 1.25 | 1.69 | 3.06 |
time (sec) |
N/A | 0.127 | 0.027 | 0.165 | 0.134 | 0.088 | 12.388 | 0.118 | 0.223 | 0.847 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 15 | 11 | 17 | 58 | 21 | 15 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.61 | 0.94 | 3.22 | 1.17 | 0.83 | 0.78 |
time (sec) |
N/A | 0.123 | 0.034 | 0.164 | 0.109 | 0.079 | 4.291 | 0.126 | 0.195 | 0.589 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 33 | 42 | 15 | 44 | 58 | 54 | 89 | 0 |
N.S. |
1 | 1.00 | 0.94 | 1.20 | 0.43 | 1.26 | 1.66 | 1.54 | 2.54 | 0.00 |
time (sec) |
N/A | 0.137 | 0.055 | 0.182 | 0.105 | 0.082 | 74.048 | 0.134 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 43 | 27 | 0 | 30 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 1.87 | 1.17 | 0.00 | 1.30 | 0.00 | 0.00 | 1.35 | 0.00 |
time (sec) |
N/A | 0.131 | 0.450 | 0.424 | 0.000 | 0.076 | 0.000 | 0.000 | 0.270 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 27 | 43 | 43 | 0 | 29 | 0 | 0 | 28 | 0 |
N.S. |
1 | 0.57 | 0.91 | 0.91 | 0.00 | 0.62 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.138 | 0.441 | 0.339 | 0.000 | 0.072 | 0.000 | 0.000 | 0.270 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 52 | 49 | 0 | 52 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.00 | 1.58 | 1.48 | 0.00 | 1.58 | 0.00 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.143 | 0.671 | 0.562 | 0.000 | 0.071 | 0.000 | 0.000 | 0.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 37 | 52 | 33 | 0 | 51 | 0 | 0 | 33 | 0 |
N.S. |
1 | 0.55 | 0.78 | 0.49 | 0.00 | 0.76 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.151 | 0.671 | 0.424 | 0.000 | 0.116 | 0.000 | 0.000 | 0.299 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 402 | 417 | 103 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.04 | 0.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.350 | 10.048 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.308 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 373 | 384 | 89 | 0 | 0 | 0 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.03 | 0.24 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.308 | 10.047 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 344 | 349 | 67 | 0 | 0 | 0 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.01 | 0.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.283 | 0.014 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 79 | 138 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.03 | 1.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.232 | 10.085 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.048 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F(-1) | F | F | B | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 80 | 268 | 0 | 0 | 0 | 0 | 0 | 77 | 0 |
N.S. |
1 | 1.03 | 3.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.99 | 0.00 |
time (sec) |
N/A | 0.231 | 10.558 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.552 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F(-1) | F | F | B | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 82 | 281 | 0 | 0 | 0 | 0 | 0 | 103 | 0 |
N.S. |
1 | 1.02 | 3.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.29 | 0.00 |
time (sec) |
N/A | 0.235 | 10.564 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.688 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 156 | 100 | 155 | 149 | 514 | 4027 | 969 | 630 | 683 |
N.S. |
1 | 1.00 | 0.64 | 0.99 | 0.96 | 3.29 | 25.81 | 6.21 | 4.04 | 4.38 |
time (sec) |
N/A | 0.293 | 0.107 | 0.207 | 0.047 | 0.108 | 0.606 | 0.132 | 0.195 | 0.788 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 116 | 72 | 115 | 111 | 288 | 1867 | 533 | 340 | 367 |
N.S. |
1 | 1.00 | 0.62 | 0.99 | 0.96 | 2.48 | 16.09 | 4.59 | 2.93 | 3.16 |
time (sec) |
N/A | 0.241 | 0.056 | 0.166 | 0.043 | 0.100 | 0.428 | 0.130 | 0.192 | 0.641 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 83 | 75 | 73 | 130 | 641 | 229 | 142 | 165 |
N.S. |
1 | 1.00 | 1.09 | 0.99 | 0.96 | 1.71 | 8.43 | 3.01 | 1.87 | 2.17 |
time (sec) |
N/A | 0.201 | 0.069 | 0.131 | 0.040 | 0.084 | 0.293 | 0.126 | 0.189 | 0.536 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 77 | 0 | 0 | 0 | 337 | 0 | 34 | 0 |
N.S. |
1 | 1.00 | 0.90 | 0.00 | 0.00 | 0.00 | 3.92 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.192 | 0.067 | 0.000 | 0.000 | 0.000 | 1.230 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 77 | 0 | 0 | 0 | 1972 | 0 | 49 | 0 |
N.S. |
1 | 1.00 | 0.90 | 0.00 | 0.00 | 0.00 | 22.93 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.187 | 0.066 | 0.000 | 0.000 | 0.000 | 2.228 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 77 | 0 | 0 | 0 | 5872 | 0 | 66 | 0 |
N.S. |
1 | 1.00 | 0.90 | 0.00 | 0.00 | 0.00 | 68.28 | 0.00 | 0.77 | 0.00 |
time (sec) |
N/A | 0.184 | 0.078 | 0.000 | 0.000 | 0.000 | 4.045 | 0.000 | 0.208 | 0.000 |