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 | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 20 | 14 | 15 | 14 | 17 | 10 | 14 | 25 | 14 |
N.S. |
1 | 1.43 | 1.00 | 1.07 | 1.00 | 1.21 | 0.71 | 1.00 | 1.79 | 1.00 |
time (sec) |
N/A | 0.169 | 0.012 | 3.210 | 0.111 | 0.058 | 0.058 | 0.104 | 0.203 | 0.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 40 | 125 | 37 | 53 | 61 | 230 | 108 | 64 | 48 |
N.S. |
1 | 1.14 | 3.57 | 1.06 | 1.51 | 1.74 | 6.57 | 3.09 | 1.83 | 1.37 |
time (sec) |
N/A | 0.202 | 0.398 | 0.923 | 0.066 | 0.070 | 3.438 | 0.111 | 0.211 | 15.666 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 41 | 118 | 36 | 54 | 64 | 207 | 130 | 68 | 76 |
N.S. |
1 | 1.17 | 3.37 | 1.03 | 1.54 | 1.83 | 5.91 | 3.71 | 1.94 | 2.17 |
time (sec) |
N/A | 0.205 | 0.381 | 0.871 | 0.066 | 0.072 | 3.379 | 0.116 | 0.203 | 15.368 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 67 | 209 | 55 | 61 | 93 | 374 | 269 | 70 | 123 |
N.S. |
1 | 1.24 | 3.87 | 1.02 | 1.13 | 1.72 | 6.93 | 4.98 | 1.30 | 2.28 |
time (sec) |
N/A | 0.231 | 6.184 | 0.965 | 0.084 | 0.074 | 21.712 | 0.175 | 0.194 | 15.428 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 55 | 73 | 67 | 72 | 72 | 80 | 72 | 67 | 72 |
N.S. |
1 | 2.50 | 3.32 | 3.05 | 3.27 | 3.27 | 3.64 | 3.27 | 3.05 | 3.27 |
time (sec) |
N/A | 0.263 | 0.007 | 0.812 | 0.035 | 0.057 | 0.022 | 0.105 | 0.200 | 15.178 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 50 | 47 | 43 | 48 | 48 | 54 | 48 | 43 | 48 |
N.S. |
1 | 2.27 | 2.14 | 1.95 | 2.18 | 2.18 | 2.45 | 2.18 | 1.95 | 2.18 |
time (sec) |
N/A | 0.255 | 0.005 | 0.510 | 0.035 | 0.059 | 0.019 | 0.104 | 0.196 | 15.250 |
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 | 24 | 24 | 24 | 21 | 24 | 24 | 27 | 24 | 20 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 1.00 | 1.00 | 1.12 | 1.00 | 0.83 | 0.83 |
time (sec) |
N/A | 0.166 | 0.000 | 0.086 | 0.026 | 0.059 | 0.017 | 0.106 | 0.188 | 15.383 |
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 | 18 | 18 | 24 | 19 | 18 | 18 | 19 | 18 | 18 | 18 |
N.S. |
1 | 1.00 | 1.33 | 1.06 | 1.00 | 1.00 | 1.06 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.198 | 0.012 | 0.941 | 0.028 | 0.061 | 0.064 | 0.106 | 0.298 | 0.050 |
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 | 19 | 19 | 19 | 20 | 21 | 21 | 15 | 21 | 20 | 19 |
N.S. |
1 | 1.00 | 1.00 | 1.05 | 1.11 | 1.11 | 0.79 | 1.11 | 1.05 | 1.00 |
time (sec) |
N/A | 0.175 | 0.019 | 0.865 | 0.032 | 0.061 | 0.184 | 0.114 | 0.199 | 15.181 |
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 | 22 | 22 | 23 | 21 | 32 | 32 | 31 | 21 | 33 | 35 |
N.S. |
1 | 1.00 | 1.05 | 0.95 | 1.45 | 1.45 | 1.41 | 0.95 | 1.50 | 1.59 |
time (sec) |
N/A | 0.177 | 0.018 | 1.032 | 0.033 | 0.061 | 0.302 | 0.119 | 0.187 | 15.196 |
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 | 22 | 22 | 23 | 21 | 43 | 43 | 42 | 21 | 44 | 33 |
N.S. |
1 | 1.00 | 1.05 | 0.95 | 1.95 | 1.95 | 1.91 | 0.95 | 2.00 | 1.50 |
time (sec) |
N/A | 0.177 | 0.019 | 0.862 | 0.029 | 0.063 | 0.418 | 0.114 | 0.190 | 15.469 |
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 | 22 | 22 | 23 | 21 | 54 | 54 | 54 | 21 | 55 | 33 |
N.S. |
1 | 1.00 | 1.05 | 0.95 | 2.45 | 2.45 | 2.45 | 0.95 | 2.50 | 1.50 |
time (sec) |
N/A | 0.178 | 0.018 | 0.845 | 0.036 | 0.060 | 0.543 | 0.128 | 0.194 | 0.071 |
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 | 34 | 45 | 33 | 38 | 68 | 82 | 280 | 182 | 76 | 79 |
N.S. |
1 | 1.32 | 0.97 | 1.12 | 2.00 | 2.41 | 8.24 | 5.35 | 2.24 | 2.32 |
time (sec) |
N/A | 0.235 | 0.580 | 1.466 | 0.068 | 0.093 | 56.590 | 0.149 | 0.196 | 15.979 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 171 | 118 | 133 | 356 | 300 | 0 | 1690 | 275 | 276 |
N.S. |
1 | 1.44 | 0.99 | 1.12 | 2.99 | 2.52 | 0.00 | 14.20 | 2.31 | 2.32 |
time (sec) |
N/A | 0.362 | 0.841 | 1.743 | 0.141 | 0.077 | 0.000 | 0.531 | 0.179 | 16.371 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 116 | 75 | 120 | 125 | 125 | 143 | 134 | 119 | 115 |
N.S. |
1 | 4.64 | 3.00 | 4.80 | 5.00 | 5.00 | 5.72 | 5.36 | 4.76 | 4.60 |
time (sec) |
N/A | 0.409 | 0.028 | 1.290 | 0.027 | 0.056 | 0.033 | 0.131 | 0.191 | 16.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 69 | 51 | 65 | 70 | 70 | 78 | 73 | 64 | 69 |
N.S. |
1 | 2.76 | 2.04 | 2.60 | 2.80 | 2.80 | 3.12 | 2.92 | 2.56 | 2.76 |
time (sec) |
N/A | 0.289 | 0.018 | 0.494 | 0.034 | 0.056 | 0.030 | 0.106 | 0.202 | 0.044 |
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 | 22 | 22 | 23 | 21 | 22 | 22 | 24 | 22 | 20 | 24 |
N.S. |
1 | 1.00 | 1.05 | 0.95 | 1.00 | 1.00 | 1.09 | 1.00 | 0.91 | 1.09 |
time (sec) |
N/A | 0.166 | 0.000 | 0.092 | 0.030 | 0.055 | 0.048 | 0.109 | 0.186 | 0.029 |
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 | 20 | 20 | 20 | 21 | 20 | 20 | 20 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.00 | 1.05 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.202 | 0.013 | 1.489 | 0.027 | 0.061 | 0.127 | 0.106 | 0.175 | 0.062 |
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 | 17 | 17 | 17 | 18 | 17 | 17 | 17 | 17 | 26 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.00 | 1.00 | 1.00 | 1.53 | 1.00 |
time (sec) |
N/A | 0.163 | 0.015 | 1.392 | 0.028 | 0.060 | 0.286 | 0.109 | 0.175 | 0.057 |
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 | 23 | 23 | 22 | 22 | 49 | 49 | 51 | 24 | 51 | 48 |
N.S. |
1 | 1.00 | 0.96 | 0.96 | 2.13 | 2.13 | 2.22 | 1.04 | 2.22 | 2.09 |
time (sec) |
N/A | 0.190 | 0.023 | 1.477 | 0.037 | 0.063 | 0.701 | 0.140 | 0.172 | 0.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 50 | 22 | 22 | 86 | 86 | 92 | 24 | 93 | 87 |
N.S. |
1 | 2.17 | 0.96 | 0.96 | 3.74 | 3.74 | 4.00 | 1.04 | 4.04 | 3.78 |
time (sec) |
N/A | 0.210 | 0.024 | 1.393 | 0.042 | 0.063 | 0.986 | 0.114 | 0.176 | 0.163 |
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 | 25 | 25 | 25 | 24 | 140 | 140 | 143 | 24 | 149 | 137 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 5.60 | 5.60 | 5.72 | 0.96 | 5.96 | 5.48 |
time (sec) |
N/A | 0.194 | 0.026 | 1.464 | 0.050 | 0.066 | 1.452 | 0.138 | 0.173 | 16.951 |
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 | 46 | 59 | 45 | 57 | 106 | 126 | 507 | 321 | 136 | 115 |
N.S. |
1 | 1.28 | 0.98 | 1.24 | 2.30 | 2.74 | 11.02 | 6.98 | 2.96 | 2.50 |
time (sec) |
N/A | 0.286 | 1.081 | 1.496 | 0.072 | 0.082 | 69.176 | 0.134 | 0.180 | 17.096 |
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 | 44 | 56 | 44 | 50 | 99 | 122 | 483 | 297 | 127 | 121 |
N.S. |
1 | 1.27 | 1.00 | 1.14 | 2.25 | 2.77 | 10.98 | 6.75 | 2.89 | 2.75 |
time (sec) |
N/A | 0.287 | 1.027 | 1.458 | 0.069 | 0.075 | 61.659 | 0.129 | 0.169 | 17.317 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 212 | 146 | 174 | 566 | 518 | 0 | 3983 | 881 | 348 |
N.S. |
1 | 1.43 | 0.99 | 1.18 | 3.82 | 3.50 | 0.00 | 26.91 | 5.95 | 2.35 |
time (sec) |
N/A | 0.404 | 1.028 | 1.776 | 0.215 | 0.087 | 0.000 | 1.405 | 0.261 | 17.488 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 205 | 110 | 222 | 237 | 237 | 245 | 259 | 255 | 209 |
N.S. |
1 | 5.54 | 2.97 | 6.00 | 6.41 | 6.41 | 6.62 | 7.00 | 6.89 | 5.65 |
time (sec) |
N/A | 0.537 | 0.060 | 1.299 | 0.033 | 0.059 | 0.047 | 0.113 | 0.203 | 15.620 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 108 | 72 | 121 | 128 | 128 | 131 | 138 | 135 | 112 |
N.S. |
1 | 2.92 | 1.95 | 3.27 | 3.46 | 3.46 | 3.54 | 3.73 | 3.65 | 3.03 |
time (sec) |
N/A | 0.371 | 0.039 | 0.460 | 0.026 | 0.059 | 0.030 | 0.121 | 0.957 | 15.379 |
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 | 41 | 41 | 46 | 45 | 41 | 43 | 42 | 41 | 42 | 44 |
N.S. |
1 | 1.00 | 1.12 | 1.10 | 1.00 | 1.05 | 1.02 | 1.00 | 1.02 | 1.07 |
time (sec) |
N/A | 0.194 | 0.000 | 0.093 | 0.028 | 0.085 | 0.028 | 0.130 | 0.178 | 0.051 |
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 | 33 | 31 | 31 | 33 | 33 | 27 | 40 | 39 | 40 |
N.S. |
1 | 1.00 | 0.94 | 0.94 | 1.00 | 1.00 | 0.82 | 1.21 | 1.18 | 1.21 |
time (sec) |
N/A | 0.225 | 0.026 | 1.476 | 0.035 | 0.060 | 0.256 | 0.115 | 0.199 | 0.091 |
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 | 29 | 55 | 26 | 27 | 29 | 29 | 24 | 29 | 36 | 27 |
N.S. |
1 | 1.90 | 0.90 | 0.93 | 1.00 | 1.00 | 0.83 | 1.00 | 1.24 | 0.93 |
time (sec) |
N/A | 0.226 | 0.028 | 1.382 | 0.034 | 0.065 | 0.736 | 0.113 | 0.194 | 0.068 |
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 | 35 | 35 | 32 | 32 | 58 | 58 | 61 | 33 | 61 | 57 |
N.S. |
1 | 1.00 | 0.91 | 0.91 | 1.66 | 1.66 | 1.74 | 0.94 | 1.74 | 1.63 |
time (sec) |
N/A | 0.224 | 0.044 | 1.389 | 0.036 | 0.067 | 3.683 | 0.108 | 0.183 | 15.263 |
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 | 36 | 36 | 35 | 33 | 96 | 96 | 102 | 33 | 103 | 96 |
N.S. |
1 | 1.00 | 0.97 | 0.92 | 2.67 | 2.67 | 2.83 | 0.92 | 2.86 | 2.67 |
time (sec) |
N/A | 0.217 | 0.040 | 1.412 | 0.047 | 0.075 | 8.931 | 0.111 | 0.192 | 15.747 |
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 | 36 | 36 | 35 | 33 | 150 | 150 | 153 | 33 | 158 | 146 |
N.S. |
1 | 1.00 | 0.97 | 0.92 | 4.17 | 4.17 | 4.25 | 0.92 | 4.39 | 4.06 |
time (sec) |
N/A | 0.223 | 0.045 | 1.427 | 0.055 | 0.072 | 17.971 | 0.158 | 0.194 | 0.312 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 103 | 87 | 79 | 0 | 205 | 214 | 81 | 173 | 0 |
N.S. |
1 | 1.01 | 0.85 | 0.77 | 0.00 | 2.01 | 2.10 | 0.79 | 1.70 | 0.00 |
time (sec) |
N/A | 0.282 | 0.961 | 1.608 | 0.000 | 0.086 | 0.467 | 0.139 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 204 | 491 | 0 | 1079 | 0 | 851 | 316 | 0 |
N.S. |
1 | 1.00 | 2.49 | 5.99 | 0.00 | 13.16 | 0.00 | 10.38 | 3.85 | 0.00 |
time (sec) |
N/A | 0.251 | 0.471 | 4.470 | 0.000 | 0.227 | 0.000 | 0.258 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 189 | 307 | 0 | 813 | 0 | 703 | 225 | 0 |
N.S. |
1 | 1.00 | 2.86 | 4.65 | 0.00 | 12.32 | 0.00 | 10.65 | 3.41 | 0.00 |
time (sec) |
N/A | 0.230 | 0.454 | 2.582 | 0.000 | 0.119 | 0.000 | 0.217 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 129 | 1333 | 827 | 0 | 1544 | 0 | 1170 | 2661 | 0 |
N.S. |
1 | 1.00 | 10.33 | 6.41 | 0.00 | 11.97 | 0.00 | 9.07 | 20.63 | 0.00 |
time (sec) |
N/A | 0.310 | 4.598 | 2.621 | 0.000 | 0.315 | 0.000 | 0.304 | 0.277 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 224 | 243 | 1746 | 1868 | 0 | 3818 | 0 | 2986 | 18107 | 0 |
N.S. |
1 | 1.08 | 7.79 | 8.34 | 0.00 | 17.04 | 0.00 | 13.33 | 80.83 | 0.00 |
time (sec) |
N/A | 0.601 | 16.586 | 3.131 | 0.000 | 2.529 | 0.000 | 0.930 | 2.915 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 328 | 374 | 3382 | 3649 | 0 | 8134 | 0 | 30280 | 27811 | 0 |
N.S. |
1 | 1.14 | 10.31 | 11.12 | 0.00 | 24.80 | 0.00 | 92.32 | 84.79 | 0.00 |
time (sec) |
N/A | 1.157 | 16.662 | 3.701 | 0.000 | 10.771 | 0.000 | 4.014 | 22.694 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 162 | 1420 | 1352 | 0 | 2005 | 0 | 1305 | 3406 | 0 |
N.S. |
1 | 1.00 | 8.77 | 8.35 | 0.00 | 12.38 | 0.00 | 8.06 | 21.02 | 0.00 |
time (sec) |
N/A | 0.388 | 3.254 | 4.974 | 0.000 | 0.772 | 0.000 | 0.321 | 0.321 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 39 | 27 | 0 | 38 | 0 | 52 | 42 | 0 |
N.S. |
1 | 1.00 | 1.39 | 0.96 | 0.00 | 1.36 | 0.00 | 1.86 | 1.50 | 0.00 |
time (sec) |
N/A | 0.167 | 0.241 | 2.638 | 0.000 | 0.066 | 0.000 | 0.116 | 0.190 | 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 | 108 | 136 | 142 | 0 | 0 | 0 | 0 | 0 | 803 | 0 |
N.S. |
1 | 1.26 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 7.44 | 0.00 |
time (sec) |
N/A | 0.267 | 0.238 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.213 | 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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 200 | 172 | 0 | 0 | 0 | 0 | 0 | 925 | 0 |
N.S. |
1 | 1.52 | 1.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 7.01 | 0.00 |
time (sec) |
N/A | 0.329 | 0.678 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.203 | 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 | 68 | 68 | 68 | 54 | 54 | 54 | 65 | 54 | 53 | 54 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.79 | 0.79 | 0.96 | 0.79 | 0.78 | 0.79 |
time (sec) |
N/A | 0.258 | 0.005 | 1.102 | 0.031 | 0.056 | 0.038 | 0.124 | 0.190 | 0.086 |
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 | 56 | 56 | 56 | 44 | 44 | 44 | 53 | 44 | 43 | 44 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.79 | 0.79 | 0.95 | 0.79 | 0.77 | 0.79 |
time (sec) |
N/A | 0.236 | 0.002 | 1.133 | 0.026 | 0.056 | 0.031 | 0.137 | 0.194 | 0.035 |
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 | 44 | 44 | 44 | 34 | 34 | 34 | 41 | 34 | 33 | 34 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.77 | 0.77 | 0.93 | 0.77 | 0.75 | 0.77 |
time (sec) |
N/A | 0.217 | 0.002 | 1.109 | 0.030 | 0.058 | 0.034 | 0.106 | 0.189 | 0.026 |
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 | 30 | 30 | 30 | 24 | 24 | 24 | 26 | 24 | 23 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.80 | 0.80 | 0.87 | 0.80 | 0.77 | 0.80 |
time (sec) |
N/A | 0.193 | 0.001 | 0.168 | 0.026 | 0.058 | 0.027 | 0.111 | 0.185 | 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 | 42 | 42 | 42 | 34 | 33 | 33 | 49 | 33 | 32 | 35 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.79 | 0.79 | 1.17 | 0.79 | 0.76 | 0.83 |
time (sec) |
N/A | 0.208 | 0.021 | 1.825 | 0.118 | 0.063 | 0.076 | 0.108 | 0.194 | 15.821 |
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 | 43 | 43 | 43 | 34 | 36 | 45 | 42 | 36 | 69 | 35 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.84 | 1.05 | 0.98 | 0.84 | 1.60 | 0.81 |
time (sec) |
N/A | 0.192 | 0.017 | 1.817 | 0.110 | 0.063 | 0.078 | 0.148 | 0.188 | 0.045 |
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 | 64 | 69 | 53 | 47 | 56 | 75 | 63 | 46 | 123 | 55 |
N.S. |
1 | 1.08 | 0.83 | 0.73 | 0.88 | 1.17 | 0.98 | 0.72 | 1.92 | 0.86 |
time (sec) |
N/A | 0.217 | 0.029 | 1.827 | 0.109 | 0.062 | 0.097 | 0.121 | 0.190 | 15.806 |
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 | 80 | 80 | 80 | 64 | 64 | 64 | 76 | 64 | 63 | 64 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.80 | 0.80 | 0.95 | 0.80 | 0.79 | 0.80 |
time (sec) |
N/A | 0.272 | 0.005 | 1.687 | 0.030 | 0.060 | 0.068 | 0.131 | 0.189 | 0.106 |
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 | 66 | 66 | 66 | 54 | 54 | 54 | 63 | 54 | 53 | 54 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.82 | 0.82 | 0.95 | 0.82 | 0.80 | 0.82 |
time (sec) |
N/A | 0.259 | 0.003 | 1.651 | 0.036 | 0.056 | 0.038 | 0.128 | 0.197 | 0.077 |
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 | 54 | 54 | 54 | 44 | 44 | 44 | 51 | 44 | 43 | 44 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.81 | 0.81 | 0.94 | 0.81 | 0.80 | 0.81 |
time (sec) |
N/A | 0.233 | 0.003 | 1.676 | 0.033 | 0.056 | 0.028 | 0.118 | 0.193 | 0.035 |
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 | 46 | 46 | 46 | 34 | 34 | 34 | 41 | 34 | 33 | 34 |
N.S. |
1 | 1.00 | 1.00 | 0.74 | 0.74 | 0.74 | 0.89 | 0.74 | 0.72 | 0.74 |
time (sec) |
N/A | 0.216 | 0.001 | 1.101 | 0.045 | 0.055 | 0.023 | 0.159 | 0.188 | 0.027 |
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 | 56 | 56 | 53 | 44 | 43 | 43 | 63 | 43 | 42 | 45 |
N.S. |
1 | 1.00 | 0.95 | 0.79 | 0.77 | 0.77 | 1.12 | 0.77 | 0.75 | 0.80 |
time (sec) |
N/A | 0.222 | 0.024 | 2.360 | 0.108 | 0.064 | 0.078 | 0.112 | 0.191 | 15.236 |
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 | 63 | 66 | 59 | 50 | 52 | 78 | 65 | 52 | 117 | 51 |
N.S. |
1 | 1.05 | 0.94 | 0.79 | 0.83 | 1.24 | 1.03 | 0.83 | 1.86 | 0.81 |
time (sec) |
N/A | 0.271 | 0.035 | 2.378 | 0.108 | 0.073 | 0.093 | 0.108 | 0.189 | 0.052 |
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 | 64 | 69 | 53 | 47 | 56 | 75 | 63 | 46 | 123 | 55 |
N.S. |
1 | 1.08 | 0.83 | 0.73 | 0.88 | 1.17 | 0.98 | 0.72 | 1.92 | 0.86 |
time (sec) |
N/A | 0.250 | 0.027 | 2.068 | 0.112 | 0.064 | 0.099 | 0.115 | 0.196 | 15.105 |
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 | 85 | 95 | 63 | 57 | 76 | 105 | 83 | 56 | 179 | 75 |
N.S. |
1 | 1.12 | 0.74 | 0.67 | 0.89 | 1.24 | 0.98 | 0.66 | 2.11 | 0.88 |
time (sec) |
N/A | 0.279 | 0.048 | 2.312 | 0.111 | 0.064 | 0.107 | 0.121 | 0.193 | 15.423 |
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 | 96 | 96 | 96 | 74 | 74 | 74 | 92 | 74 | 73 | 74 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.77 | 0.77 | 0.96 | 0.77 | 0.76 | 0.77 |
time (sec) |
N/A | 0.301 | 0.004 | 1.708 | 0.031 | 0.058 | 0.049 | 0.137 | 0.191 | 0.143 |
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 | 82 | 82 | 82 | 64 | 64 | 64 | 78 | 64 | 63 | 64 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 0.78 | 0.78 | 0.95 | 0.78 | 0.77 | 0.78 |
time (sec) |
N/A | 0.261 | 0.003 | 1.723 | 0.031 | 0.056 | 0.032 | 0.110 | 0.190 | 0.108 |
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 | 68 | 68 | 68 | 54 | 54 | 54 | 65 | 54 | 53 | 54 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.79 | 0.79 | 0.96 | 0.79 | 0.78 | 0.79 |
time (sec) |
N/A | 0.264 | 0.003 | 1.707 | 0.029 | 0.060 | 0.032 | 0.119 | 0.189 | 0.077 |
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 | 56 | 56 | 56 | 44 | 44 | 44 | 53 | 44 | 43 | 44 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.79 | 0.79 | 0.95 | 0.79 | 0.77 | 0.79 |
time (sec) |
N/A | 0.236 | 0.002 | 1.125 | 0.026 | 0.057 | 0.028 | 0.139 | 0.186 | 0.038 |
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 | 70 | 70 | 63 | 54 | 53 | 53 | 76 | 53 | 52 | 55 |
N.S. |
1 | 1.00 | 0.90 | 0.77 | 0.76 | 0.76 | 1.09 | 0.76 | 0.74 | 0.79 |
time (sec) |
N/A | 0.243 | 0.025 | 2.467 | 0.111 | 0.064 | 0.080 | 0.152 | 0.189 | 0.045 |
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 | 77 | 78 | 77 | 60 | 62 | 88 | 78 | 62 | 127 | 61 |
N.S. |
1 | 1.01 | 1.00 | 0.78 | 0.81 | 1.14 | 1.01 | 0.81 | 1.65 | 0.79 |
time (sec) |
N/A | 0.297 | 0.031 | 2.415 | 0.114 | 0.069 | 0.090 | 0.106 | 0.197 | 15.336 |
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 | 84 | 92 | 78 | 63 | 72 | 118 | 85 | 62 | 203 | 71 |
N.S. |
1 | 1.10 | 0.93 | 0.75 | 0.86 | 1.40 | 1.01 | 0.74 | 2.42 | 0.85 |
time (sec) |
N/A | 0.329 | 0.043 | 2.441 | 0.109 | 0.077 | 0.115 | 0.118 | 0.189 | 16.270 |
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 | 84 | 84 | 72 | 64 | 63 | 63 | 87 | 63 | 62 | 65 |
N.S. |
1 | 1.00 | 0.86 | 0.76 | 0.75 | 0.75 | 1.04 | 0.75 | 0.74 | 0.77 |
time (sec) |
N/A | 0.243 | 0.032 | 4.191 | 0.108 | 0.067 | 0.079 | 0.113 | 0.175 | 16.266 |
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 | 70 | 70 | 63 | 54 | 53 | 53 | 73 | 53 | 52 | 55 |
N.S. |
1 | 1.00 | 0.90 | 0.77 | 0.76 | 0.76 | 1.04 | 0.76 | 0.74 | 0.79 |
time (sec) |
N/A | 0.234 | 0.026 | 2.359 | 0.107 | 0.069 | 0.099 | 0.133 | 0.194 | 0.047 |
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 | 56 | 56 | 52 | 44 | 43 | 43 | 60 | 43 | 42 | 45 |
N.S. |
1 | 1.00 | 0.93 | 0.79 | 0.77 | 0.77 | 1.07 | 0.77 | 0.75 | 0.80 |
time (sec) |
N/A | 0.220 | 0.024 | 2.339 | 0.106 | 0.067 | 0.069 | 0.110 | 0.192 | 0.043 |
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 | 42 | 42 | 42 | 34 | 33 | 33 | 46 | 33 | 32 | 35 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.79 | 0.79 | 1.10 | 0.79 | 0.76 | 0.83 |
time (sec) |
N/A | 0.199 | 0.013 | 1.830 | 0.113 | 0.073 | 0.085 | 0.126 | 0.198 | 0.041 |
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 | 79 | 73 | 60 | 59 | 59 | 83 | 59 | 57 | 79 |
N.S. |
1 | 1.08 | 1.00 | 0.82 | 0.81 | 0.81 | 1.14 | 0.81 | 0.78 | 1.08 |
time (sec) |
N/A | 0.251 | 0.036 | 3.071 | 0.107 | 0.076 | 0.121 | 0.109 | 0.178 | 16.722 |
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 | 94 | 105 | 94 | 76 | 78 | 117 | 102 | 78 | 204 | 95 |
N.S. |
1 | 1.12 | 1.00 | 0.81 | 0.83 | 1.24 | 1.09 | 0.83 | 2.17 | 1.01 |
time (sec) |
N/A | 0.342 | 0.085 | 2.905 | 0.111 | 0.067 | 0.154 | 0.110 | 0.198 | 16.640 |
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 | 115 | 131 | 104 | 89 | 98 | 177 | 119 | 88 | 358 | 115 |
N.S. |
1 | 1.14 | 0.90 | 0.77 | 0.85 | 1.54 | 1.03 | 0.77 | 3.11 | 1.00 |
time (sec) |
N/A | 0.440 | 0.161 | 2.920 | 0.108 | 0.070 | 0.195 | 0.138 | 0.199 | 0.191 |
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 | 86 | 91 | 70 | 72 | 98 | 90 | 72 | 137 | 72 |
N.S. |
1 | 0.95 | 1.00 | 0.77 | 0.79 | 1.08 | 0.99 | 0.79 | 1.51 | 0.79 |
time (sec) |
N/A | 0.300 | 0.059 | 2.246 | 0.109 | 0.060 | 0.095 | 0.127 | 0.182 | 15.776 |
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 | 77 | 76 | 77 | 60 | 62 | 88 | 75 | 62 | 127 | 61 |
N.S. |
1 | 0.99 | 1.00 | 0.78 | 0.81 | 1.14 | 0.97 | 0.81 | 1.65 | 0.79 |
time (sec) |
N/A | 0.288 | 0.035 | 2.345 | 0.106 | 0.060 | 0.105 | 0.110 | 0.197 | 16.126 |
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 | 63 | 64 | 63 | 50 | 52 | 78 | 61 | 52 | 117 | 52 |
N.S. |
1 | 1.02 | 1.00 | 0.79 | 0.83 | 1.24 | 0.97 | 0.83 | 1.86 | 0.83 |
time (sec) |
N/A | 0.263 | 0.038 | 2.365 | 0.109 | 0.063 | 0.084 | 0.118 | 0.196 | 0.050 |
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 | 43 | 43 | 43 | 34 | 36 | 45 | 42 | 36 | 69 | 36 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.84 | 1.05 | 0.98 | 0.84 | 1.60 | 0.84 |
time (sec) |
N/A | 0.191 | 0.017 | 1.781 | 0.107 | 0.062 | 0.081 | 0.103 | 0.193 | 15.558 |
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 | 94 | 105 | 94 | 76 | 78 | 117 | 102 | 78 | 204 | 96 |
N.S. |
1 | 1.12 | 1.00 | 0.81 | 0.83 | 1.24 | 1.09 | 0.83 | 2.17 | 1.02 |
time (sec) |
N/A | 0.345 | 0.064 | 2.742 | 0.120 | 0.071 | 0.165 | 0.113 | 0.175 | 0.190 |
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 | 127 | 143 | 106 | 94 | 96 | 167 | 122 | 96 | 358 | 115 |
N.S. |
1 | 1.13 | 0.83 | 0.74 | 0.76 | 1.31 | 0.96 | 0.76 | 2.82 | 0.91 |
time (sec) |
N/A | 0.443 | 0.061 | 3.079 | 0.108 | 0.070 | 0.179 | 0.111 | 0.196 | 0.200 |
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 | 148 | 169 | 136 | 106 | 118 | 237 | 143 | 110 | 514 | 135 |
N.S. |
1 | 1.14 | 0.92 | 0.72 | 0.80 | 1.60 | 0.97 | 0.74 | 3.47 | 0.91 |
time (sec) |
N/A | 0.553 | 0.068 | 2.958 | 0.107 | 0.073 | 0.192 | 0.114 | 0.189 | 15.257 |
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 | 98 | 106 | 98 | 73 | 82 | 128 | 95 | 72 | 213 | 81 |
N.S. |
1 | 1.08 | 1.00 | 0.74 | 0.84 | 1.31 | 0.97 | 0.73 | 2.17 | 0.83 |
time (sec) |
N/A | 0.379 | 0.040 | 2.343 | 0.109 | 0.063 | 0.123 | 0.109 | 0.184 | 15.271 |
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 | 84 | 94 | 84 | 63 | 72 | 118 | 82 | 62 | 203 | 72 |
N.S. |
1 | 1.12 | 1.00 | 0.75 | 0.86 | 1.40 | 0.98 | 0.74 | 2.42 | 0.86 |
time (sec) |
N/A | 0.339 | 0.040 | 2.368 | 0.105 | 0.066 | 0.112 | 0.111 | 0.193 | 15.582 |
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 | 64 | 69 | 51 | 47 | 56 | 75 | 63 | 46 | 123 | 56 |
N.S. |
1 | 1.08 | 0.80 | 0.73 | 0.88 | 1.17 | 0.98 | 0.72 | 1.92 | 0.88 |
time (sec) |
N/A | 0.253 | 0.033 | 2.399 | 0.109 | 0.064 | 0.095 | 0.118 | 0.191 | 0.055 |
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 | 64 | 69 | 51 | 47 | 56 | 75 | 61 | 46 | 123 | 55 |
N.S. |
1 | 1.08 | 0.80 | 0.73 | 0.88 | 1.17 | 0.95 | 0.72 | 1.92 | 0.86 |
time (sec) |
N/A | 0.217 | 0.031 | 1.661 | 0.109 | 0.066 | 0.090 | 0.109 | 0.199 | 15.333 |
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 | 115 | 131 | 99 | 89 | 98 | 177 | 122 | 88 | 358 | 116 |
N.S. |
1 | 1.14 | 0.86 | 0.77 | 0.85 | 1.54 | 1.06 | 0.77 | 3.11 | 1.01 |
time (sec) |
N/A | 0.434 | 0.166 | 3.237 | 0.114 | 0.070 | 0.193 | 0.113 | 0.169 | 15.939 |
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 | 160 | 181 | 136 | 106 | 116 | 227 | 143 | 110 | 514 | 136 |
N.S. |
1 | 1.13 | 0.85 | 0.66 | 0.72 | 1.42 | 0.89 | 0.69 | 3.21 | 0.85 |
time (sec) |
N/A | 0.565 | 0.114 | 2.783 | 0.106 | 0.071 | 0.200 | 0.129 | 0.194 | 0.192 |
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 | 181 | 207 | 151 | 118 | 138 | 297 | 163 | 116 | 670 | 155 |
N.S. |
1 | 1.14 | 0.83 | 0.65 | 0.76 | 1.64 | 0.90 | 0.64 | 3.70 | 0.86 |
time (sec) |
N/A | 0.670 | 0.087 | 2.715 | 0.110 | 0.070 | 0.218 | 0.109 | 0.195 | 15.558 |
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 | 69 | 68 | 65 | 62 | 195 | 116 | 60 | 120 | 60 |
N.S. |
1 | 1.00 | 0.99 | 0.94 | 0.90 | 2.83 | 1.68 | 0.87 | 1.74 | 0.87 |
time (sec) |
N/A | 0.212 | 0.059 | 0.873 | 0.107 | 0.071 | 0.377 | 0.109 | 0.184 | 0.111 |
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 | 69 | 68 | 65 | 62 | 195 | 116 | 60 | 120 | 60 |
N.S. |
1 | 1.00 | 0.99 | 0.94 | 0.90 | 2.83 | 1.68 | 0.87 | 1.74 | 0.87 |
time (sec) |
N/A | 0.230 | 0.016 | 0.853 | 0.118 | 0.068 | 0.386 | 0.137 | 0.175 | 15.711 |
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 | 159 | 159 | 164 | 158 | 0 | 553 | 0 | 172 | 419 | 2331 |
N.S. |
1 | 1.00 | 1.03 | 0.99 | 0.00 | 3.48 | 0.00 | 1.08 | 2.64 | 14.66 |
time (sec) |
N/A | 0.416 | 0.160 | 1.937 | 0.000 | 1.815 | 0.000 | 0.110 | 0.172 | 20.080 |
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 | 159 | 164 | 152 | 158 | 0 | 553 | 0 | 172 | 419 | 2331 |
N.S. |
1 | 1.03 | 0.96 | 0.99 | 0.00 | 3.48 | 0.00 | 1.08 | 2.64 | 14.66 |
time (sec) |
N/A | 0.380 | 0.195 | 2.129 | 0.000 | 1.791 | 0.000 | 0.127 | 0.170 | 19.342 |
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 | 13 | 12 | 12 | 10 | 14 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.86 | 0.86 | 0.71 | 1.00 | 0.86 | 0.86 |
time (sec) |
N/A | 0.176 | 0.006 | 0.757 | 0.025 | 0.060 | 0.059 | 0.106 | 0.166 | 0.058 |
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 | 208 | 248 | 95 | 75 | 177 | 98 | 97 | 93 | 186 | 221 |
N.S. |
1 | 1.19 | 0.46 | 0.36 | 0.85 | 0.47 | 0.47 | 0.45 | 0.89 | 1.06 |
time (sec) |
N/A | 0.757 | 1.226 | 2.418 | 0.118 | 0.070 | 0.467 | 0.118 | 0.236 | 18.125 |
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 | 166 | 196 | 85 | 65 | 143 | 88 | 83 | 83 | 154 | 187 |
N.S. |
1 | 1.18 | 0.51 | 0.39 | 0.86 | 0.53 | 0.50 | 0.50 | 0.93 | 1.13 |
time (sec) |
N/A | 0.554 | 0.993 | 2.409 | 0.118 | 0.069 | 0.409 | 0.120 | 0.200 | 17.121 |
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 | 124 | 144 | 75 | 55 | 109 | 78 | 70 | 73 | 122 | 153 |
N.S. |
1 | 1.16 | 0.60 | 0.44 | 0.88 | 0.63 | 0.56 | 0.59 | 0.98 | 1.23 |
time (sec) |
N/A | 0.379 | 0.654 | 2.381 | 0.117 | 0.069 | 0.387 | 0.143 | 0.175 | 16.178 |
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 | 82 | 92 | 65 | 45 | 75 | 68 | 56 | 63 | 90 | 119 |
N.S. |
1 | 1.12 | 0.79 | 0.55 | 0.91 | 0.83 | 0.68 | 0.77 | 1.10 | 1.45 |
time (sec) |
N/A | 0.241 | 0.372 | 1.958 | 0.108 | 0.073 | 0.351 | 0.116 | 0.198 | 16.328 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 180 | 206 | 483 | 0 | 492 | 0 | 0 | 99 | 0 |
N.S. |
1 | 1.03 | 1.18 | 2.78 | 0.00 | 2.83 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.520 | 0.329 | 4.688 | 0.000 | 0.091 | 0.000 | 0.000 | 0.411 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 194 | 419 | 473 | 0 | 526 | 0 | 0 | 346 | 0 |
N.S. |
1 | 1.03 | 2.23 | 2.52 | 0.00 | 2.80 | 0.00 | 0.00 | 1.84 | 0.00 |
time (sec) |
N/A | 0.528 | 0.781 | 5.298 | 0.000 | 0.087 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 234 | 392 | 483 | 0 | 586 | 0 | 0 | 698 | 0 |
N.S. |
1 | 1.05 | 1.76 | 2.17 | 0.00 | 2.63 | 0.00 | 0.00 | 3.13 | 0.00 |
time (sec) |
N/A | 0.640 | 0.975 | 5.586 | 0.000 | 0.099 | 0.000 | 0.000 | 0.248 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 276 | 105 | 85 | 206 | 108 | 110 | 103 | 218 | 0 |
N.S. |
1 | 1.19 | 0.45 | 0.37 | 0.89 | 0.47 | 0.48 | 0.45 | 0.94 | 0.00 |
time (sec) |
N/A | 0.842 | 1.568 | 2.427 | 0.119 | 0.073 | 0.596 | 0.124 | 0.314 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 224 | 95 | 75 | 172 | 98 | 95 | 93 | 186 | 0 |
N.S. |
1 | 1.19 | 0.50 | 0.40 | 0.91 | 0.52 | 0.50 | 0.49 | 0.98 | 0.00 |
time (sec) |
N/A | 0.586 | 1.273 | 2.431 | 0.121 | 0.071 | 0.601 | 0.125 | 0.270 | 0.000 |