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 | B | B | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 41 | 128 | 174 | 68 | 0 | 44 | 41 | 0 |
N.S. |
1 | 1.00 | 0.73 | 2.29 | 3.11 | 1.21 | 0.00 | 0.79 | 0.73 | 0.00 |
time (sec) |
N/A | 0.329 | 0.027 | 0.913 | 0.208 | 0.104 | 0.000 | 0.116 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 44 | 159 | 300 | 197 | 0 | 78 | 53 | 0 |
N.S. |
1 | 1.00 | 0.68 | 2.45 | 4.62 | 3.03 | 0.00 | 1.20 | 0.82 | 0.00 |
time (sec) |
N/A | 0.336 | 0.058 | 0.992 | 0.250 | 0.105 | 0.000 | 0.114 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 91 | 57 | 209 | 427 | 514 | 0 | 118 | 65 | 0 |
N.S. |
1 | 0.98 | 0.61 | 2.25 | 4.59 | 5.53 | 0.00 | 1.27 | 0.70 | 0.00 |
time (sec) |
N/A | 0.444 | 0.103 | 1.020 | 0.225 | 0.097 | 0.000 | 0.122 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 51 | 63 | 0 | 99 | 0 | 84 | 46 | 0 |
N.S. |
1 | 1.00 | 0.89 | 1.11 | 0.00 | 1.74 | 0.00 | 1.47 | 0.81 | 0.00 |
time (sec) |
N/A | 0.307 | 0.184 | 0.857 | 0.000 | 0.081 | 0.000 | 0.119 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 81 | 83 | 0 | 217 | 0 | 111 | 57 | 0 |
N.S. |
1 | 1.00 | 1.25 | 1.28 | 0.00 | 3.34 | 0.00 | 1.71 | 0.88 | 0.00 |
time (sec) |
N/A | 0.320 | 0.282 | 0.945 | 0.000 | 0.097 | 0.000 | 0.121 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 92 | 118 | 118 | 0 | 548 | 0 | 189 | 70 | 0 |
N.S. |
1 | 0.98 | 1.26 | 1.26 | 0.00 | 5.83 | 0.00 | 2.01 | 0.74 | 0.00 |
time (sec) |
N/A | 0.420 | 0.448 | 0.962 | 0.000 | 0.086 | 0.000 | 0.135 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 244 | 203 | 1365 | 0 | 1123 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.05 | 0.87 | 5.86 | 0.00 | 4.82 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 1.426 | 0.412 | 25.397 | 0.000 | 0.103 | 0.000 | 0.000 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 187 | 124 | 973 | 0 | 623 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.03 | 0.69 | 5.38 | 0.00 | 3.44 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 1.038 | 0.470 | 18.359 | 0.000 | 0.102 | 0.000 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 139 | 123 | 599 | 0 | 319 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.01 | 0.89 | 4.34 | 0.00 | 2.31 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.770 | 0.250 | 14.028 | 0.000 | 0.084 | 0.000 | 0.000 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 59 | 73 | 0 | 240 | 403 | 50 | 1 | 242 |
N.S. |
1 | 1.00 | 0.98 | 1.22 | 0.00 | 4.00 | 6.72 | 0.83 | 0.02 | 4.03 |
time (sec) |
N/A | 0.304 | 0.085 | 0.306 | 0.000 | 0.106 | 14.935 | 0.112 | 0.193 | 2.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 93 | 81 | 108 | 0 | 828 | 0 | 107 | 44 | 246 |
N.S. |
1 | 1.13 | 0.99 | 1.32 | 0.00 | 10.10 | 0.00 | 1.30 | 0.54 | 3.00 |
time (sec) |
N/A | 0.381 | 0.140 | 0.400 | 0.000 | 0.098 | 0.000 | 0.115 | 0.210 | 2.393 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 161 | 134 | 207 | 0 | 3166 | 0 | 249 | 225 | 0 |
N.S. |
1 | 1.19 | 0.99 | 1.53 | 0.00 | 23.45 | 0.00 | 1.84 | 1.67 | 0.00 |
time (sec) |
N/A | 0.639 | 0.288 | 0.644 | 0.000 | 0.159 | 0.000 | 0.119 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 239 | 196 | 342 | 0 | 7603 | 0 | 453 | 817 | 0 |
N.S. |
1 | 1.21 | 0.99 | 1.74 | 0.00 | 38.59 | 0.00 | 2.30 | 4.15 | 0.00 |
time (sec) |
N/A | 0.949 | 0.486 | 1.071 | 0.000 | 0.329 | 0.000 | 0.124 | 0.252 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 63 | 56 | 81 | 0 | 190 | 168 | 57 | 41 | 205 |
N.S. |
1 | 1.12 | 1.00 | 1.45 | 0.00 | 3.39 | 3.00 | 1.02 | 0.73 | 3.66 |
time (sec) |
N/A | 0.350 | 0.071 | 0.382 | 0.000 | 0.102 | 14.514 | 0.110 | 0.245 | 0.515 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 6 | 6 | 6 | 7 | 0 | 6 | 3 | 6 | 1 | 6 |
N.S. |
1 | 1.00 | 1.00 | 1.17 | 0.00 | 1.00 | 0.50 | 1.00 | 0.17 | 1.00 |
time (sec) |
N/A | 0.169 | 0.000 | 0.123 | 0.000 | 0.070 | 0.083 | 0.108 | 0.220 | 0.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 12 | 0 | 54 | 0 | 26 | 25 | 51 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 0.00 | 4.91 | 0.00 | 2.36 | 2.27 | 4.64 |
time (sec) |
N/A | 0.220 | 0.012 | 0.324 | 0.000 | 0.075 | 0.000 | 0.117 | 0.270 | 1.952 |
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 | 38 | 24 | 32 | 34 | 45 | 44 | 37 | 30 | 48 |
N.S. |
1 | 1.06 | 0.67 | 0.89 | 0.94 | 1.25 | 1.22 | 1.03 | 0.83 | 1.33 |
time (sec) |
N/A | 0.295 | 0.046 | 0.253 | 0.107 | 0.092 | 0.356 | 0.114 | 0.226 | 0.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 108 | 80 | 218 | 0 | 184 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.00 | 0.74 | 2.02 | 0.00 | 1.70 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.640 | 0.319 | 6.933 | 0.000 | 0.085 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 163 | 133 | 485 | 0 | 601 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.07 | 0.88 | 3.19 | 0.00 | 3.95 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.834 | 0.279 | 7.425 | 0.000 | 0.092 | 0.000 | 0.000 | 0.248 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 241 | 172 | 797 | 0 | 2053 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.04 | 0.74 | 3.45 | 0.00 | 8.89 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 1.223 | 0.618 | 11.669 | 0.000 | 0.184 | 0.000 | 0.000 | 0.262 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 78 | 39 | 38 | 71 | 817 | 0 | 79 | 65 | 0 |
N.S. |
1 | 1.08 | 0.54 | 0.53 | 0.99 | 11.35 | 0.00 | 1.10 | 0.90 | 0.00 |
time (sec) |
N/A | 0.470 | 0.018 | 0.896 | 0.125 | 0.125 | 0.000 | 0.111 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 56 | 33 | 32 | 53 | 501 | 0 | 41 | 51 | 0 |
N.S. |
1 | 1.06 | 0.62 | 0.60 | 1.00 | 9.45 | 0.00 | 0.77 | 0.96 | 0.00 |
time (sec) |
N/A | 0.386 | 0.014 | 0.809 | 0.138 | 0.094 | 0.000 | 0.111 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 23 | 24 | 35 | 222 | 0 | 29 | 33 | 0 |
N.S. |
1 | 1.00 | 0.68 | 0.71 | 1.03 | 6.53 | 0.00 | 0.85 | 0.97 | 0.00 |
time (sec) |
N/A | 0.286 | 0.008 | 0.297 | 0.150 | 0.098 | 0.000 | 0.112 | 0.262 | 0.000 |
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 | 13 | 13 | 13 | 15 | 17 | 69 | 15 | 14 | 5 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.15 | 1.31 | 5.31 | 1.15 | 1.08 | 0.38 | 1.31 |
time (sec) |
N/A | 0.218 | 0.016 | 0.269 | 0.128 | 0.079 | 0.200 | 0.112 | 0.224 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 17 | 55 | 8 | 186 | 0 | 0 | 11 | 0 |
N.S. |
1 | 1.00 | 1.06 | 3.44 | 0.50 | 11.62 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.230 | 0.005 | 0.296 | 0.173 | 0.081 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 26 | 82 | 41 | 299 | 0 | 56 | 58 | 0 |
N.S. |
1 | 1.00 | 0.62 | 1.95 | 0.98 | 7.12 | 0.00 | 1.33 | 1.38 | 0.00 |
time (sec) |
N/A | 0.311 | 0.012 | 0.375 | 0.181 | 0.082 | 0.000 | 0.118 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 69 | 36 | 102 | 75 | 837 | 0 | 72 | 114 | 0 |
N.S. |
1 | 1.13 | 0.59 | 1.67 | 1.23 | 13.72 | 0.00 | 1.18 | 1.87 | 0.00 |
time (sec) |
N/A | 0.411 | 0.025 | 0.374 | 0.190 | 0.093 | 0.000 | 0.114 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 99 | 65 | 0 | 0 | 802 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.82 | 0.54 | 0.00 | 0.00 | 6.63 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.561 | 0.095 | 0.000 | 0.000 | 0.107 | 0.000 | 0.000 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 63 | 54 | 0 | 0 | 305 | 0 | 0 | 14 | 0 |
N.S. |
1 | 0.89 | 0.76 | 0.00 | 0.00 | 4.30 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.393 | 0.064 | 0.000 | 0.000 | 0.087 | 0.000 | 0.000 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 45 | 59 | 0 | 0 | 54 | 0 | 0 | 11 | 0 |
N.S. |
1 | 0.94 | 1.23 | 0.00 | 0.00 | 1.12 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.315 | 0.053 | 0.000 | 0.000 | 0.090 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 41 | 36 | 0 | 0 | 82 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.89 | 0.78 | 0.00 | 0.00 | 1.78 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.337 | 0.029 | 0.000 | 0.000 | 0.082 | 0.000 | 0.000 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 65 | 48 | 0 | 0 | 554 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.87 | 0.64 | 0.00 | 0.00 | 7.39 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.374 | 0.056 | 0.000 | 0.000 | 0.127 | 0.000 | 0.000 | 0.274 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 95 | 61 | 0 | 0 | 1473 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.79 | 0.50 | 0.00 | 0.00 | 12.17 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.555 | 0.085 | 0.000 | 0.000 | 0.148 | 0.000 | 0.000 | 0.235 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 92 | 53 | 171 | 100 | 1597 | 0 | 76 | 87 | 0 |
N.S. |
1 | 0.70 | 0.40 | 1.30 | 0.76 | 12.10 | 0.00 | 0.58 | 0.66 | 0.00 |
time (sec) |
N/A | 0.542 | 0.097 | 15.123 | 0.121 | 0.153 | 0.000 | 0.112 | 0.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 60 | 38 | 125 | 62 | 659 | 0 | 52 | 55 | 0 |
N.S. |
1 | 0.77 | 0.49 | 1.60 | 0.79 | 8.45 | 0.00 | 0.67 | 0.71 | 0.00 |
time (sec) |
N/A | 0.405 | 0.062 | 0.572 | 0.134 | 0.156 | 0.000 | 0.117 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F(-1) | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 29 | 25 | 83 | 27 | 180 | 0 | 28 | 26 | 0 |
N.S. |
1 | 0.81 | 0.69 | 2.31 | 0.75 | 5.00 | 0.00 | 0.78 | 0.72 | 0.00 |
time (sec) |
N/A | 0.240 | 0.024 | 0.564 | 0.118 | 0.095 | 0.000 | 0.112 | 0.263 | 0.000 |
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 | 15 | 15 | 15 | 29 | 16 | 116 | 0 | 13 | 21 | 39 |
N.S. |
1 | 1.00 | 1.00 | 1.93 | 1.07 | 7.73 | 0.00 | 0.87 | 1.40 | 2.60 |
time (sec) |
N/A | 0.232 | 0.005 | 0.491 | 0.121 | 0.083 | 0.000 | 0.112 | 0.216 | 0.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 48 | 30 | 48 | 165 | 1137 | 0 | 27 | 60 | 48 |
N.S. |
1 | 0.72 | 0.45 | 0.72 | 2.46 | 16.97 | 0.00 | 0.40 | 0.90 | 0.72 |
time (sec) |
N/A | 0.252 | 0.024 | 0.528 | 0.121 | 0.105 | 0.000 | 0.118 | 0.300 | 0.133 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 68 | 47 | 60 | 457 | 3065 | 0 | 39 | 102 | 256 |
N.S. |
1 | 0.58 | 0.40 | 0.51 | 3.91 | 26.20 | 0.00 | 0.33 | 0.87 | 2.19 |
time (sec) |
N/A | 0.279 | 0.041 | 0.549 | 0.146 | 0.181 | 0.000 | 0.117 | 0.260 | 1.911 |
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 | 8 | 8 | 12 | 9 | 8 | 31 | 7 | 10 | 9 | 8 |
N.S. |
1 | 1.00 | 1.50 | 1.12 | 1.00 | 3.88 | 0.88 | 1.25 | 1.12 | 1.00 |
time (sec) |
N/A | 0.190 | 0.009 | 0.277 | 0.032 | 0.082 | 0.181 | 0.107 | 0.251 | 0.078 |
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 | 8 | 8 | 12 | 9 | 8 | 31 | 7 | 10 | 10 | 8 |
N.S. |
1 | 1.00 | 1.50 | 1.12 | 1.00 | 3.88 | 0.88 | 1.25 | 1.25 | 1.00 |
time (sec) |
N/A | 0.199 | 0.009 | 0.310 | 0.025 | 0.065 | 0.169 | 0.109 | 0.237 | 1.828 |
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 | 12 | 12 | 18 | 11 | 12 | 20 | 7 | 10 | 20 | 10 |
N.S. |
1 | 1.00 | 1.50 | 0.92 | 1.00 | 1.67 | 0.58 | 0.83 | 1.67 | 0.83 |
time (sec) |
N/A | 0.203 | 0.001 | 0.404 | 0.037 | 0.075 | 0.211 | 0.105 | 0.226 | 1.830 |
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 | 14 | 14 | 24 | 11 | 12 | 22 | 7 | 10 | 22 | 10 |
N.S. |
1 | 1.00 | 1.71 | 0.79 | 0.86 | 1.57 | 0.50 | 0.71 | 1.57 | 0.71 |
time (sec) |
N/A | 0.203 | 0.001 | 0.457 | 0.031 | 0.081 | 0.345 | 0.110 | 0.220 | 0.048 |
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 | 10 | 10 | 13 | 11 | 23 | 48 | 58 | 21 | 40 | 10 |
N.S. |
1 | 1.00 | 1.30 | 1.10 | 2.30 | 4.80 | 5.80 | 2.10 | 4.00 | 1.00 |
time (sec) |
N/A | 0.221 | 0.015 | 1.264 | 0.033 | 0.090 | 0.209 | 0.105 | 0.286 | 2.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 13 | 11 | 23 | 54 | 58 | 22 | 40 | 10 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.92 | 4.50 | 4.83 | 1.83 | 3.33 | 0.83 |
time (sec) |
N/A | 0.221 | 0.014 | 1.245 | 0.027 | 0.081 | 0.213 | 0.104 | 0.227 | 2.041 |
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 | 10 | 10 | 12 | 9 | 8 | 55 | 15 | 12 | 16 | 8 |
N.S. |
1 | 1.00 | 1.20 | 0.90 | 0.80 | 5.50 | 1.50 | 1.20 | 1.60 | 0.80 |
time (sec) |
N/A | 0.199 | 0.008 | 0.477 | 0.036 | 0.075 | 0.262 | 0.110 | 0.265 | 2.089 |
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 | 12 | 12 | 12 | 11 | 8 | 55 | 14 | 12 | 14 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.67 | 4.58 | 1.17 | 1.00 | 1.17 | 0.67 |
time (sec) |
N/A | 0.193 | 0.009 | 0.563 | 0.047 | 0.070 | 0.251 | 0.106 | 0.208 | 0.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 12 | 9 | 49 | 33 | 7 | 16 | 35 | 16 |
N.S. |
1 | 1.00 | 0.86 | 0.64 | 3.50 | 2.36 | 0.50 | 1.14 | 2.50 | 1.14 |
time (sec) |
N/A | 0.208 | 0.076 | 0.689 | 0.039 | 0.071 | 0.296 | 0.109 | 0.275 | 0.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 12 | 9 | 49 | 33 | 8 | 16 | 35 | 16 |
N.S. |
1 | 1.00 | 0.75 | 0.56 | 3.06 | 2.06 | 0.50 | 1.00 | 2.19 | 1.00 |
time (sec) |
N/A | 0.205 | 0.069 | 0.872 | 0.038 | 0.071 | 0.502 | 0.107 | 0.252 | 2.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 18 | 15 | 31 | 89 | 126 | 21 | 56 | 14 |
N.S. |
1 | 1.00 | 1.29 | 1.07 | 2.21 | 6.36 | 9.00 | 1.50 | 4.00 | 1.00 |
time (sec) |
N/A | 0.223 | 0.009 | 1.056 | 0.033 | 0.101 | 0.269 | 0.114 | 0.253 | 2.183 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 18 | 17 | 35 | 90 | 126 | 20 | 52 | 16 |
N.S. |
1 | 1.00 | 0.90 | 0.85 | 1.75 | 4.50 | 6.30 | 1.00 | 2.60 | 0.80 |
time (sec) |
N/A | 0.224 | 0.008 | 1.270 | 0.037 | 0.078 | 0.259 | 0.114 | 0.260 | 1.976 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 60 | 51 | 165 | 102 | 101 | 1253 | 90 | 111 | 131 |
N.S. |
1 | 1.05 | 0.89 | 2.89 | 1.79 | 1.77 | 21.98 | 1.58 | 1.95 | 2.30 |
time (sec) |
N/A | 0.374 | 0.154 | 0.145 | 0.034 | 0.079 | 2.983 | 0.111 | 0.263 | 2.248 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 47 | 27 | 40 | 84 | 94 | 284 | 75 | 89 | 107 |
N.S. |
1 | 1.02 | 0.59 | 0.87 | 1.83 | 2.04 | 6.17 | 1.63 | 1.93 | 2.33 |
time (sec) |
N/A | 0.269 | 0.021 | 157.084 | 0.045 | 0.080 | 1.995 | 0.117 | 0.257 | 2.169 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 46 | 39 | 96 | 78 | 57 | 692 | 66 | 83 | 95 |
N.S. |
1 | 1.05 | 0.89 | 2.18 | 1.77 | 1.30 | 15.73 | 1.50 | 1.89 | 2.16 |
time (sec) |
N/A | 0.330 | 0.167 | 61.892 | 0.028 | 0.092 | 1.248 | 0.109 | 0.267 | 2.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 32 | 21 | 26 | 60 | 52 | 150 | 51 | 61 | 71 |
N.S. |
1 | 0.97 | 0.64 | 0.79 | 1.82 | 1.58 | 4.55 | 1.55 | 1.85 | 2.15 |
time (sec) |
N/A | 0.241 | 0.015 | 22.314 | 0.039 | 0.080 | 0.835 | 0.109 | 0.239 | 2.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 30 | 25 | 60 | 54 | 27 | 294 | 40 | 53 | 59 |
N.S. |
1 | 0.97 | 0.81 | 1.94 | 1.74 | 0.87 | 9.48 | 1.29 | 1.71 | 1.90 |
time (sec) |
N/A | 0.257 | 0.113 | 7.096 | 0.037 | 0.075 | 0.471 | 0.117 | 0.231 | 1.954 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 13 | 16 | 36 | 18 | 49 | 27 | 31 | 35 |
N.S. |
1 | 1.00 | 0.81 | 1.00 | 2.25 | 1.12 | 3.06 | 1.69 | 1.94 | 2.19 |
time (sec) |
N/A | 0.222 | 0.011 | 2.323 | 0.030 | 0.079 | 0.296 | 0.114 | 0.236 | 2.001 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 17 | 24 | 23 | 11 | 46 | 17 | 23 | 23 |
N.S. |
1 | 1.00 | 1.31 | 1.85 | 1.77 | 0.85 | 3.54 | 1.31 | 1.77 | 1.77 |
time (sec) |
N/A | 0.213 | 0.039 | 0.567 | 0.038 | 0.080 | 0.188 | 0.111 | 0.254 | 1.974 |
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 | 9 | 11 | 12 | 12 | 11 | 16 | 7 | 17 | 9 | 9 |
N.S. |
1 | 1.22 | 1.33 | 1.33 | 1.22 | 1.78 | 0.78 | 1.89 | 1.00 | 1.00 |
time (sec) |
N/A | 0.214 | 0.007 | 0.181 | 0.032 | 0.085 | 0.061 | 0.106 | 0.283 | 1.943 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 29 | 42 | 20 | 47 | 103 | 0 | 52 | 89 | 51 |
N.S. |
1 | 1.26 | 1.83 | 0.87 | 2.04 | 4.48 | 0.00 | 2.26 | 3.87 | 2.22 |
time (sec) |
N/A | 0.289 | 0.022 | 0.582 | 0.034 | 0.082 | 0.000 | 0.112 | 0.262 | 1.987 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 30 | 24 | 59 | 94 | 0 | 35 | 33 | 89 |
N.S. |
1 | 1.00 | 1.25 | 1.00 | 2.46 | 3.92 | 0.00 | 1.46 | 1.38 | 3.71 |
time (sec) |
N/A | 0.324 | 0.170 | 0.973 | 0.035 | 0.075 | 0.000 | 0.110 | 0.265 | 1.994 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 61 | 60 | 38 | 103 | 631 | 0 | 94 | 245 | 114 |
N.S. |
1 | 1.11 | 1.09 | 0.69 | 1.87 | 11.47 | 0.00 | 1.71 | 4.45 | 2.07 |
time (sec) |
N/A | 0.322 | 0.102 | 2.277 | 0.031 | 0.084 | 0.000 | 0.108 | 0.257 | 2.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 43 | 38 | 36 | 233 | 250 | 0 | 59 | 75 | 263 |
N.S. |
1 | 1.16 | 1.03 | 0.97 | 6.30 | 6.76 | 0.00 | 1.59 | 2.03 | 7.11 |
time (sec) |
N/A | 0.337 | 0.124 | 5.173 | 0.035 | 0.076 | 0.000 | 0.113 | 0.276 | 1.995 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 93 | 89 | 54 | 155 | 1551 | 0 | 116 | 405 | 244 |
N.S. |
1 | 0.99 | 0.95 | 0.57 | 1.65 | 16.50 | 0.00 | 1.23 | 4.31 | 2.60 |
time (sec) |
N/A | 0.351 | 0.187 | 10.963 | 0.038 | 0.097 | 0.000 | 0.111 | 0.273 | 2.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 140 | 144 | 148 | 310 | 2134 | 0 | 229 | 444 | 289 |
N.S. |
1 | 1.00 | 1.03 | 1.06 | 2.21 | 15.24 | 0.00 | 1.64 | 3.17 | 2.06 |
time (sec) |
N/A | 0.438 | 0.157 | 0.092 | 0.045 | 0.108 | 0.000 | 0.122 | 0.326 | 2.771 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 184 | 154 | 409 | 0 | 2913 | 0 | 266 | 373 | 348 |
N.S. |
1 | 1.19 | 1.00 | 2.66 | 0.00 | 18.92 | 0.00 | 1.73 | 2.42 | 2.26 |
time (sec) |
N/A | 1.127 | 0.188 | 0.109 | 0.000 | 0.129 | 0.000 | 0.112 | 0.240 | 2.772 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 82 | 84 | 82 | 178 | 866 | 0 | 124 | 255 | 169 |
N.S. |
1 | 0.99 | 1.01 | 0.99 | 2.14 | 10.43 | 0.00 | 1.49 | 3.07 | 2.04 |
time (sec) |
N/A | 0.348 | 0.115 | 112.233 | 0.037 | 0.096 | 0.000 | 0.117 | 0.235 | 2.311 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 125 | 95 | 223 | 0 | 1099 | 0 | 146 | 194 | 222 |
N.S. |
1 | 1.20 | 0.91 | 2.14 | 0.00 | 10.57 | 0.00 | 1.40 | 1.87 | 2.13 |
time (sec) |
N/A | 0.642 | 0.138 | 30.005 | 0.000 | 0.099 | 0.000 | 0.111 | 0.255 | 2.355 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 40 | 39 | 84 | 234 | 0 | 56 | 115 | 79 |
N.S. |
1 | 1.00 | 1.00 | 0.98 | 2.10 | 5.85 | 0.00 | 1.40 | 2.88 | 1.98 |
time (sec) |
N/A | 0.255 | 0.066 | 6.921 | 0.040 | 0.091 | 0.000 | 0.113 | 0.275 | 2.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 73 | 54 | 100 | 0 | 279 | 892 | 68 | 64 | 139 |
N.S. |
1 | 1.24 | 0.92 | 1.69 | 0.00 | 4.73 | 15.12 | 1.15 | 1.08 | 2.36 |
time (sec) |
N/A | 0.413 | 0.089 | 1.334 | 0.000 | 0.111 | 52.895 | 0.116 | 0.258 | 2.071 |
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 | 11 | 11 | 11 | 12 | 11 | 27 | 14 | 19 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 1.00 | 2.45 | 1.27 | 1.73 | 1.00 | 1.00 |
time (sec) |
N/A | 0.201 | 0.028 | 0.250 | 0.027 | 0.091 | 0.084 | 0.111 | 0.261 | 0.063 |
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 | 53 | 66 | 49 | 52 | 59 | 58 | 0 | 67 | 66 | 160 |
N.S. |
1 | 1.25 | 0.92 | 0.98 | 1.11 | 1.09 | 0.00 | 1.26 | 1.25 | 3.02 |
time (sec) |
N/A | 0.311 | 0.071 | 0.680 | 0.030 | 0.103 | 0.000 | 0.114 | 0.248 | 2.357 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 78 | 77 | 78 | 0 | 470 | 0 | 76 | 167 | 327 |
N.S. |
1 | 1.16 | 1.15 | 1.16 | 0.00 | 7.01 | 0.00 | 1.13 | 2.49 | 4.88 |
time (sec) |
N/A | 0.337 | 0.175 | 1.240 | 0.000 | 0.084 | 0.000 | 0.117 | 0.237 | 2.605 |
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 | 99 | 117 | 100 | 90 | 154 | 818 | 0 | 179 | 494 | 291 |
N.S. |
1 | 1.18 | 1.01 | 0.91 | 1.56 | 8.26 | 0.00 | 1.81 | 4.99 | 2.94 |
time (sec) |
N/A | 0.394 | 0.334 | 2.883 | 0.050 | 0.107 | 0.000 | 0.109 | 0.237 | 2.547 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 134 | 141 | 127 | 0 | 2339 | 0 | 156 | 481 | 642 |
N.S. |
1 | 1.22 | 1.28 | 1.15 | 0.00 | 21.26 | 0.00 | 1.42 | 4.37 | 5.84 |
time (sec) |
N/A | 0.600 | 0.388 | 6.718 | 0.000 | 0.136 | 0.000 | 0.114 | 0.269 | 3.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 196 | 165 | 138 | 348 | 3450 | 0 | 338 | 1180 | 559 |
N.S. |
1 | 1.17 | 0.99 | 0.83 | 2.08 | 20.66 | 0.00 | 2.02 | 7.07 | 3.35 |
time (sec) |
N/A | 0.526 | 0.471 | 14.531 | 0.049 | 0.186 | 0.000 | 0.124 | 0.240 | 2.886 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 200 | 201 | 213 | 0 | 6381 | 0 | 303 | 919 | 1031 |
N.S. |
1 | 1.26 | 1.26 | 1.34 | 0.00 | 40.13 | 0.00 | 1.91 | 5.78 | 6.48 |
time (sec) |
N/A | 0.966 | 1.210 | 29.243 | 0.000 | 0.165 | 0.000 | 0.124 | 0.247 | 3.641 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 72 | 61 | 99 | 0 | 700 | 0 | 68 | 252 | 139 |
N.S. |
1 | 1.07 | 0.91 | 1.48 | 0.00 | 10.45 | 0.00 | 1.01 | 3.76 | 2.07 |
time (sec) |
N/A | 0.396 | 0.099 | 1.328 | 0.000 | 0.102 | 0.000 | 0.122 | 0.268 | 2.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 133 | 100 | 154 | 0 | 2003 | 0 | 144 | 516 | 722 |
N.S. |
1 | 1.18 | 0.88 | 1.36 | 0.00 | 17.73 | 0.00 | 1.27 | 4.57 | 6.39 |
time (sec) |
N/A | 1.000 | 0.308 | 1.379 | 0.000 | 0.155 | 0.000 | 0.115 | 0.242 | 7.269 |
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 | 57 | 59 | 46 | 95 | 96 | 450 | 0 | 115 | 292 | 1221 |
N.S. |
1 | 1.04 | 0.81 | 1.67 | 1.68 | 7.89 | 0.00 | 2.02 | 5.12 | 21.42 |
time (sec) |
N/A | 0.344 | 0.098 | 0.766 | 0.125 | 0.102 | 0.000 | 0.114 | 0.230 | 2.607 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 75 | 61 | 78 | 0 | 326 | 0 | 67 | 111 | 285 |
N.S. |
1 | 1.23 | 1.00 | 1.28 | 0.00 | 5.34 | 0.00 | 1.10 | 1.82 | 4.67 |
time (sec) |
N/A | 0.693 | 0.112 | 0.582 | 0.000 | 0.115 | 0.000 | 0.121 | 0.212 | 4.605 |
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 | 20 | 22 | 20 | 33 | 33 | 40 | 0 | 33 | 31 | 201 |
N.S. |
1 | 1.10 | 1.00 | 1.65 | 1.65 | 2.00 | 0.00 | 1.65 | 1.55 | 10.05 |
time (sec) |
N/A | 0.235 | 0.008 | 0.336 | 0.114 | 0.084 | 0.000 | 0.108 | 0.296 | 0.452 |
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 | 54 | 59 | 50 | 53 | 59 | 60 | 0 | 67 | 65 | 148 |
N.S. |
1 | 1.09 | 0.93 | 0.98 | 1.09 | 1.11 | 0.00 | 1.24 | 1.20 | 2.74 |
time (sec) |
N/A | 0.286 | 0.073 | 0.523 | 0.039 | 0.083 | 0.000 | 0.107 | 0.221 | 0.446 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 88 | 77 | 78 | 0 | 470 | 0 | 76 | 167 | 337 |
N.S. |
1 | 1.14 | 1.00 | 1.01 | 0.00 | 6.10 | 0.00 | 0.99 | 2.17 | 4.38 |
time (sec) |
N/A | 0.487 | 0.172 | 0.820 | 0.000 | 0.113 | 0.000 | 0.112 | 0.240 | 2.363 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 135 | 101 | 91 | 156 | 839 | 0 | 178 | 494 | 291 |
N.S. |
1 | 1.44 | 1.07 | 0.97 | 1.66 | 8.93 | 0.00 | 1.89 | 5.26 | 3.10 |
time (sec) |
N/A | 0.439 | 0.281 | 1.292 | 0.044 | 0.105 | 0.000 | 0.119 | 0.327 | 2.510 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 158 | 131 | 127 | 0 | 2417 | 0 | 172 | 496 | 666 |
N.S. |
1 | 1.15 | 0.96 | 0.93 | 0.00 | 17.64 | 0.00 | 1.26 | 3.62 | 4.86 |
time (sec) |
N/A | 0.906 | 0.370 | 2.085 | 0.000 | 0.111 | 0.000 | 0.122 | 0.276 | 2.736 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 47 | 58 | 64 | 89 | 750 | 0 | 58 | 151 | 183 |
N.S. |
1 | 1.02 | 1.26 | 1.39 | 1.93 | 16.30 | 0.00 | 1.26 | 3.28 | 3.98 |
time (sec) |
N/A | 0.481 | 0.219 | 1.257 | 0.114 | 0.087 | 0.000 | 0.116 | 0.218 | 1.993 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 38 | 25 | 43 | 223 | 174 | 0 | 48 | 77 | 117 |
N.S. |
1 | 1.27 | 0.83 | 1.43 | 7.43 | 5.80 | 0.00 | 1.60 | 2.57 | 3.90 |
time (sec) |
N/A | 0.365 | 0.022 | 0.844 | 0.034 | 0.072 | 0.000 | 0.114 | 0.269 | 1.933 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 46 | 48 | 57 | 315 | 0 | 39 | 94 | 95 |
N.S. |
1 | 1.00 | 1.39 | 1.45 | 1.73 | 9.55 | 0.00 | 1.18 | 2.85 | 2.88 |
time (sec) |
N/A | 0.394 | 0.141 | 0.634 | 0.116 | 0.094 | 0.000 | 0.113 | 0.255 | 1.868 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 27 | 17 | 26 | 70 | 66 | 0 | 22 | 41 | 25 |
N.S. |
1 | 1.42 | 0.89 | 1.37 | 3.68 | 3.47 | 0.00 | 1.16 | 2.16 | 1.32 |
time (sec) |
N/A | 0.286 | 0.017 | 0.426 | 0.035 | 0.076 | 0.000 | 0.107 | 0.248 | 1.849 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 18 | 30 | 23 | 50 | 0 | 22 | 36 | 33 |
N.S. |
1 | 1.00 | 1.20 | 2.00 | 1.53 | 3.33 | 0.00 | 1.47 | 2.40 | 2.20 |
time (sec) |
N/A | 0.299 | 0.167 | 0.352 | 0.132 | 0.088 | 0.000 | 0.118 | 0.255 | 1.923 |
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 | 18 | 22 | 12 | 14 | 24 | 28 | 0 | 22 | 21 | 26 |
N.S. |
1 | 1.22 | 0.67 | 0.78 | 1.33 | 1.56 | 0.00 | 1.22 | 1.17 | 1.44 |
time (sec) |
N/A | 0.217 | 0.015 | 0.274 | 0.027 | 0.078 | 0.000 | 0.106 | 0.258 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 42 | 42 | 20 | 48 | 103 | 0 | 52 | 87 | 51 |
N.S. |
1 | 1.27 | 1.27 | 0.61 | 1.45 | 3.12 | 0.00 | 1.58 | 2.64 | 1.55 |
time (sec) |
N/A | 0.385 | 0.029 | 0.272 | 0.027 | 0.076 | 0.000 | 0.108 | 0.233 | 1.882 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 36 | 25 | 29 | 121 | 91 | 0 | 35 | 47 | 92 |
N.S. |
1 | 1.20 | 0.83 | 0.97 | 4.03 | 3.03 | 0.00 | 1.17 | 1.57 | 3.07 |
time (sec) |
N/A | 0.366 | 0.180 | 0.317 | 0.032 | 0.081 | 0.000 | 0.111 | 0.224 | 1.893 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 59 | 60 | 38 | 103 | 631 | 0 | 94 | 245 | 132 |
N.S. |
1 | 1.28 | 1.30 | 0.83 | 2.24 | 13.72 | 0.00 | 2.04 | 5.33 | 2.87 |
time (sec) |
N/A | 0.493 | 0.075 | 0.385 | 0.042 | 0.076 | 0.000 | 0.110 | 0.251 | 1.944 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 46 | 41 | 45 | 469 | 224 | 0 | 59 | 103 | 263 |
N.S. |
1 | 1.12 | 1.00 | 1.10 | 11.44 | 5.46 | 0.00 | 1.44 | 2.51 | 6.41 |
time (sec) |
N/A | 0.386 | 0.148 | 0.487 | 0.039 | 0.075 | 0.000 | 0.111 | 0.266 | 2.005 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 37 | 125 | 0 | 376 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.00 | 1.00 | 3.38 | 0.00 | 10.16 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.246 | 0.017 | 0.461 | 0.000 | 0.262 | 0.000 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 104 | 0 | 356 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 1.00 | 4.33 | 0.00 | 14.83 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.238 | 0.010 | 0.433 | 0.000 | 0.118 | 0.000 | 0.000 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 55 | 112 | 0 | 291 | 741 | 60 | 99 | 197 |
N.S. |
1 | 1.00 | 0.98 | 2.00 | 0.00 | 5.20 | 13.23 | 1.07 | 1.77 | 3.52 |
time (sec) |
N/A | 0.336 | 0.076 | 0.614 | 0.000 | 0.107 | 13.298 | 0.110 | 0.249 | 4.046 |
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 | 18 | 18 | 19 | 23 | 19 | 46 | 20 | 22 | 47 | 22 |
N.S. |
1 | 1.00 | 1.06 | 1.28 | 1.06 | 2.56 | 1.11 | 1.22 | 2.61 | 1.22 |
time (sec) |
N/A | 0.276 | 0.024 | 0.316 | 0.025 | 0.091 | 0.145 | 0.104 | 0.235 | 0.059 |