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 | Mupad | |
grade |
N/A | A | A | B | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 34 | 76 | 55 | 47 | 0 | 33 | 24 |
N.S. |
1 | 1.00 | 1.48 | 3.30 | 2.39 | 2.04 | 0.00 | 1.43 | 1.04 |
time (sec) |
N/A | 0.223 | 0.117 | 0.426 | 0.209 | 0.247 | 0.000 | 0.282 | 4.475 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 27 | 36 | 23 | 39 | 0 | 0 | 23 |
N.S. |
1 | 1.00 | 0.96 | 1.29 | 0.82 | 1.39 | 0.00 | 0.00 | 0.82 |
time (sec) |
N/A | 0.223 | 0.132 | 0.426 | 0.202 | 0.241 | 0.000 | 0.000 | 4.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 62 | 66 | 34 | 41 | 39 | 57 | 0 | 45 | 38 |
N.S. |
1 | 1.06 | 0.55 | 0.66 | 0.63 | 0.92 | 0.00 | 0.73 | 0.61 |
time (sec) |
N/A | 0.248 | 0.145 | 0.435 | 0.199 | 0.241 | 0.000 | 0.291 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 95 | 130 | 43 | 50 | 55 | 77 | 0 | 65 | 55 |
N.S. |
1 | 1.37 | 0.45 | 0.53 | 0.58 | 0.81 | 0.00 | 0.68 | 0.58 |
time (sec) |
N/A | 0.329 | 0.144 | 0.425 | 0.212 | 0.254 | 0.000 | 0.304 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 128 | 167 | 51 | 58 | 71 | 95 | 0 | 85 | 71 |
N.S. |
1 | 1.30 | 0.40 | 0.45 | 0.55 | 0.74 | 0.00 | 0.66 | 0.55 |
time (sec) |
N/A | 0.360 | 0.157 | 0.420 | 0.209 | 0.246 | 0.000 | 0.331 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 44 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.283 | 0.023 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 78 | 56 | 50 | 63 | 68 | 68 | 75 | 63 |
N.S. |
1 | 0.86 | 0.62 | 0.55 | 0.69 | 0.75 | 0.75 | 0.82 | 0.69 |
time (sec) |
N/A | 0.323 | 0.025 | 0.498 | 0.200 | 0.237 | 0.099 | 0.256 | 4.192 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 63 | 48 | 42 | 52 | 57 | 56 | 64 | 52 |
N.S. |
1 | 0.86 | 0.66 | 0.58 | 0.71 | 0.78 | 0.77 | 0.88 | 0.71 |
time (sec) |
N/A | 0.310 | 0.022 | 0.524 | 0.200 | 0.238 | 0.089 | 0.279 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 47 | 39 | 34 | 41 | 45 | 41 | 52 | 41 |
N.S. |
1 | 0.85 | 0.71 | 0.62 | 0.75 | 0.82 | 0.75 | 0.95 | 0.75 |
time (sec) |
N/A | 0.300 | 0.020 | 0.486 | 0.211 | 0.256 | 0.076 | 0.252 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 24 | 24 | 28 | 24 | 35 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.92 | 1.08 | 0.92 | 1.35 | 1.00 |
time (sec) |
N/A | 0.270 | 0.013 | 0.421 | 0.191 | 0.241 | 0.075 | 0.262 | 0.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 15 | 14 | 14 | 12 | 15 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.00 | 1.00 | 0.86 | 1.07 | 1.00 |
time (sec) |
N/A | 0.259 | 0.012 | 0.475 | 0.200 | 0.245 | 0.030 | 0.270 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 24 | 29 | 23 | 20 | 25 | 12 |
N.S. |
1 | 1.00 | 1.00 | 2.00 | 2.42 | 1.92 | 1.67 | 2.08 | 1.00 |
time (sec) |
N/A | 0.261 | 0.012 | 0.477 | 0.208 | 0.239 | 0.096 | 0.266 | 0.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 32 | 32 | 40 | 48 | 46 | 39 | 46 | 31 |
N.S. |
1 | 0.97 | 0.97 | 1.21 | 1.45 | 1.39 | 1.18 | 1.39 | 0.94 |
time (sec) |
N/A | 0.293 | 0.026 | 0.498 | 0.216 | 0.248 | 0.153 | 0.256 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 47 | 35 | 51 | 63 | 76 | 54 | 51 | 46 |
N.S. |
1 | 0.92 | 0.69 | 1.00 | 1.24 | 1.49 | 1.06 | 1.00 | 0.90 |
time (sec) |
N/A | 0.303 | 0.032 | 0.500 | 0.202 | 0.255 | 0.182 | 0.253 | 0.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 69 | 62 | 44 | 57 | 84 | 113 | 78 | 89 | 65 |
N.S. |
1 | 0.90 | 0.64 | 0.83 | 1.22 | 1.64 | 1.13 | 1.29 | 0.94 |
time (sec) |
N/A | 0.320 | 0.037 | 0.490 | 0.211 | 0.236 | 0.258 | 0.252 | 4.427 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 96 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.268 | 0.079 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 152 | 152 | 86 | 157 | 244 | 114 | 0 | 0 | 199 |
N.S. |
1 | 1.00 | 0.57 | 1.03 | 1.61 | 0.75 | 0.00 | 0.00 | 1.31 |
time (sec) |
N/A | 0.695 | 0.286 | 0.422 | 0.202 | 0.252 | 0.000 | 0.000 | 0.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 129 | 131 | 78 | 148 | 204 | 104 | 0 | 0 | 163 |
N.S. |
1 | 1.02 | 0.60 | 1.15 | 1.58 | 0.81 | 0.00 | 0.00 | 1.26 |
time (sec) |
N/A | 0.556 | 0.219 | 0.412 | 0.205 | 0.251 | 0.000 | 0.000 | 4.544 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 99 | 68 | 136 | 156 | 81 | 0 | 0 | 117 |
N.S. |
1 | 1.08 | 0.74 | 1.48 | 1.70 | 0.88 | 0.00 | 0.00 | 1.27 |
time (sec) |
N/A | 0.409 | 0.182 | 0.129 | 0.207 | 0.245 | 0.000 | 0.000 | 0.084 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 52 | 54 | 248 | 78 | 63 | 0 | 0 | 48 |
N.S. |
1 | 0.98 | 1.02 | 4.68 | 1.47 | 1.19 | 0.00 | 0.00 | 0.91 |
time (sec) |
N/A | 0.274 | 0.169 | 0.413 | 0.219 | 0.244 | 0.000 | 0.000 | 4.202 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 26 | 25 | 22 | 22 | 0 | 0 | 22 |
N.S. |
1 | 1.00 | 0.93 | 0.89 | 0.79 | 0.79 | 0.00 | 0.00 | 0.79 |
time (sec) |
N/A | 0.222 | 0.145 | 0.425 | 0.197 | 0.235 | 0.000 | 0.000 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 33 | 30 | 48 | 31 | 0 | 22 | 38 |
N.S. |
1 | 1.00 | 1.57 | 1.43 | 2.29 | 1.48 | 0.00 | 1.05 | 1.81 |
time (sec) |
N/A | 0.215 | 0.156 | 0.424 | 0.203 | 0.249 | 0.000 | 0.279 | 4.202 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 50 | 45 | 65 | 58 | 0 | 0 | 50 |
N.S. |
1 | 1.00 | 0.82 | 0.74 | 1.07 | 0.95 | 0.00 | 0.00 | 0.82 |
time (sec) |
N/A | 0.259 | 0.163 | 0.411 | 0.206 | 0.247 | 0.000 | 0.000 | 4.545 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 57 | 54 | 82 | 77 | 0 | 0 | 51 |
N.S. |
1 | 1.00 | 0.61 | 0.57 | 0.87 | 0.82 | 0.00 | 0.00 | 0.54 |
time (sec) |
N/A | 0.391 | 0.172 | 0.408 | 0.200 | 0.248 | 0.000 | 0.000 | 4.154 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 125 | 129 | 66 | 63 | 97 | 96 | 0 | 0 | 60 |
N.S. |
1 | 1.03 | 0.53 | 0.50 | 0.78 | 0.77 | 0.00 | 0.00 | 0.48 |
time (sec) |
N/A | 0.566 | 0.173 | 0.451 | 0.203 | 0.240 | 0.000 | 0.000 | 0.076 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 254 | 195 | 86 | 69 | 99 | 105 | 0 | 147 | 76 |
N.S. |
1 | 0.77 | 0.34 | 0.27 | 0.39 | 0.41 | 0.00 | 0.58 | 0.30 |
time (sec) |
N/A | 0.313 | 0.076 | 0.411 | 0.223 | 0.244 | 0.000 | 0.290 | 4.528 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 197 | 157 | 78 | 61 | 83 | 94 | 0 | 0 | 102 |
N.S. |
1 | 0.80 | 0.40 | 0.31 | 0.42 | 0.48 | 0.00 | 0.00 | 0.52 |
time (sec) |
N/A | 0.297 | 0.062 | 0.418 | 0.218 | 0.244 | 0.000 | 0.000 | 4.446 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 119 | 70 | 53 | 67 | 83 | 0 | 97 | 60 |
N.S. |
1 | 1.03 | 0.61 | 0.46 | 0.58 | 0.72 | 0.00 | 0.84 | 0.52 |
time (sec) |
N/A | 0.262 | 0.054 | 0.409 | 0.214 | 0.259 | 0.000 | 0.286 | 4.397 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 87 | 57 | 43 | 45 | 64 | 0 | 0 | 50 |
N.S. |
1 | 1.13 | 0.74 | 0.56 | 0.58 | 0.83 | 0.00 | 0.00 | 0.65 |
time (sec) |
N/A | 0.251 | 0.036 | 0.415 | 0.214 | 0.253 | 0.000 | 0.000 | 4.320 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 43 | 35 | 26 | 50 | 0 | 49 | 43 |
N.S. |
1 | 1.00 | 1.48 | 1.21 | 0.90 | 1.72 | 0.00 | 1.69 | 1.48 |
time (sec) |
N/A | 0.208 | 0.025 | 0.407 | 0.211 | 0.248 | 0.000 | 0.269 | 4.388 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 118 | 105 | 99 | 83 | 0 | 239 | 0 | 94 | 0 |
N.S. |
1 | 0.89 | 0.84 | 0.70 | 0.00 | 2.03 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.272 | 0.072 | 0.445 | 0.000 | 0.258 | 0.000 | 0.272 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 128 | 114 | 116 | 118 | 0 | 281 | 0 | 60 | 0 |
N.S. |
1 | 0.89 | 0.91 | 0.92 | 0.00 | 2.20 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.272 | 0.079 | 0.446 | 0.000 | 0.254 | 0.000 | 0.295 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 193 | 154 | 123 | 167 | 0 | 337 | 0 | 78 | 0 |
N.S. |
1 | 0.80 | 0.64 | 0.87 | 0.00 | 1.75 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.298 | 0.174 | 0.438 | 0.000 | 0.255 | 0.000 | 0.306 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 250 | 190 | 139 | 219 | 0 | 393 | 0 | 105 | 0 |
N.S. |
1 | 0.76 | 0.56 | 0.88 | 0.00 | 1.57 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.317 | 0.176 | 0.426 | 0.000 | 0.272 | 0.000 | 0.325 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 46 | 34 | 21 | 32 | 60 | 58 | 205 | 32 |
N.S. |
1 | 1.15 | 0.85 | 0.52 | 0.80 | 1.50 | 1.45 | 5.12 | 0.80 |
time (sec) |
N/A | 0.321 | 0.049 | 0.501 | 0.198 | 0.245 | 2.210 | 0.257 | 4.171 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 46 | 34 | 21 | 32 | 49 | 58 | 141 | 32 |
N.S. |
1 | 1.15 | 0.85 | 0.52 | 0.80 | 1.22 | 1.45 | 3.52 | 0.80 |
time (sec) |
N/A | 0.319 | 0.047 | 0.523 | 0.194 | 0.245 | 2.139 | 0.261 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 46 | 30 | 21 | 32 | 32 | 58 | 71 | 32 |
N.S. |
1 | 1.15 | 0.75 | 0.52 | 0.80 | 0.80 | 1.45 | 1.78 | 0.80 |
time (sec) |
N/A | 0.319 | 0.039 | 0.521 | 0.195 | 0.248 | 2.023 | 0.260 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 44 | 23 | 20 | 30 | 19 | 56 | 44 | 32 |
N.S. |
1 | 1.16 | 0.61 | 0.53 | 0.79 | 0.50 | 1.47 | 1.16 | 0.84 |
time (sec) |
N/A | 0.309 | 0.031 | 0.483 | 0.206 | 0.244 | 2.057 | 0.263 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 42 | 21 | 20 | 30 | 29 | 54 | 32 | 19 |
N.S. |
1 | 1.17 | 0.58 | 0.56 | 0.83 | 0.81 | 1.50 | 0.89 | 0.53 |
time (sec) |
N/A | 0.312 | 0.028 | 0.509 | 0.206 | 0.247 | 1.721 | 0.265 | 4.162 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 44 | 34 | 21 | 26 | 44 | 56 | 36 | 20 |
N.S. |
1 | 1.16 | 0.89 | 0.55 | 0.68 | 1.16 | 1.47 | 0.95 | 0.53 |
time (sec) |
N/A | 0.325 | 0.064 | 0.518 | 0.197 | 0.248 | 1.752 | 0.259 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 46 | 34 | 21 | 24 | 56 | 58 | 34 | 20 |
N.S. |
1 | 1.15 | 0.85 | 0.52 | 0.60 | 1.40 | 1.45 | 0.85 | 0.50 |
time (sec) |
N/A | 0.316 | 0.070 | 0.484 | 0.213 | 0.239 | 1.736 | 0.265 | 4.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 46 | 34 | 21 | 26 | 66 | 58 | 36 | 20 |
N.S. |
1 | 1.15 | 0.85 | 0.52 | 0.65 | 1.65 | 1.45 | 0.90 | 0.50 |
time (sec) |
N/A | 0.316 | 0.071 | 0.508 | 0.196 | 0.250 | 1.924 | 0.270 | 3.934 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 197 | 157 | 77 | 64 | 106 | 105 | 0 | 130 | 110 |
N.S. |
1 | 0.80 | 0.39 | 0.32 | 0.54 | 0.53 | 0.00 | 0.66 | 0.56 |
time (sec) |
N/A | 0.289 | 0.058 | 0.421 | 0.253 | 0.257 | 0.000 | 0.290 | 4.305 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 119 | 69 | 56 | 90 | 94 | 0 | 0 | 102 |
N.S. |
1 | 0.87 | 0.50 | 0.41 | 0.66 | 0.69 | 0.00 | 0.00 | 0.74 |
time (sec) |
N/A | 0.272 | 0.048 | 0.429 | 0.216 | 0.240 | 0.000 | 0.000 | 4.296 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 87 | 59 | 48 | 74 | 83 | 0 | 80 | 93 |
N.S. |
1 | 0.98 | 0.66 | 0.54 | 0.83 | 0.93 | 0.00 | 0.90 | 1.04 |
time (sec) |
N/A | 0.248 | 0.045 | 0.422 | 0.240 | 0.244 | 0.000 | 0.284 | 4.230 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 43 | 35 | 41 | 61 | 0 | 0 | 81 |
N.S. |
1 | 1.00 | 1.39 | 1.13 | 1.32 | 1.97 | 0.00 | 0.00 | 2.61 |
time (sec) |
N/A | 0.214 | 0.040 | 0.418 | 0.279 | 0.245 | 0.000 | 0.000 | 4.679 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 163 | 138 | 105 | 107 | 0 | 250 | 0 | 0 | 0 |
N.S. |
1 | 0.85 | 0.64 | 0.66 | 0.00 | 1.53 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.284 | 0.076 | 0.452 | 0.000 | 0.268 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 177 | 148 | 116 | 136 | 0 | 288 | 0 | 75 | 0 |
N.S. |
1 | 0.84 | 0.66 | 0.77 | 0.00 | 1.63 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.289 | 0.159 | 0.452 | 0.000 | 0.265 | 0.000 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 187 | 158 | 125 | 174 | 0 | 341 | 0 | 78 | 0 |
N.S. |
1 | 0.84 | 0.67 | 0.93 | 0.00 | 1.82 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.299 | 0.165 | 0.426 | 0.000 | 0.266 | 0.000 | 0.303 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 250 | 196 | 142 | 226 | 0 | 393 | 0 | 105 | 0 |
N.S. |
1 | 0.78 | 0.57 | 0.90 | 0.00 | 1.57 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.324 | 0.160 | 0.434 | 0.000 | 0.254 | 0.000 | 0.304 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 307 | 234 | 147 | 278 | 0 | 449 | 0 | 129 | 0 |
N.S. |
1 | 0.76 | 0.48 | 0.91 | 0.00 | 1.46 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.336 | 0.220 | 0.442 | 0.000 | 0.273 | 0.000 | 0.339 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 194 | 233 | 86 | 77 | 128 | 105 | 0 | 0 | 110 |
N.S. |
1 | 1.20 | 0.44 | 0.40 | 0.66 | 0.54 | 0.00 | 0.00 | 0.57 |
time (sec) |
N/A | 0.323 | 0.074 | 0.421 | 0.242 | 0.248 | 0.000 | 0.000 | 4.323 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 161 | 195 | 78 | 69 | 112 | 94 | 0 | 0 | 102 |
N.S. |
1 | 1.21 | 0.48 | 0.43 | 0.70 | 0.58 | 0.00 | 0.00 | 0.63 |
time (sec) |
N/A | 0.305 | 0.060 | 0.429 | 0.222 | 0.248 | 0.000 | 0.000 | 4.345 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 128 | 157 | 70 | 61 | 96 | 83 | 0 | 0 | 94 |
N.S. |
1 | 1.23 | 0.55 | 0.48 | 0.75 | 0.65 | 0.00 | 0.00 | 0.73 |
time (sec) |
N/A | 0.288 | 0.053 | 0.429 | 0.230 | 0.246 | 0.000 | 0.000 | 4.299 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 95 | 119 | 60 | 53 | 72 | 64 | 0 | 0 | 82 |
N.S. |
1 | 1.25 | 0.63 | 0.56 | 0.76 | 0.67 | 0.00 | 0.00 | 0.86 |
time (sec) |
N/A | 0.266 | 0.047 | 0.408 | 0.232 | 0.257 | 0.000 | 0.000 | 4.398 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 62 | 87 | 50 | 42 | 54 | 50 | 0 | 43 | 71 |
N.S. |
1 | 1.40 | 0.81 | 0.68 | 0.87 | 0.81 | 0.00 | 0.69 | 1.15 |
time (sec) |
N/A | 0.244 | 0.037 | 0.434 | 0.216 | 0.246 | 0.000 | 0.274 | 4.413 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 28 | 35 | 29 | 44 | 0 | 0 | 34 |
N.S. |
1 | 1.00 | 0.97 | 1.21 | 1.00 | 1.52 | 0.00 | 0.00 | 1.17 |
time (sec) |
N/A | 0.211 | 0.028 | 0.412 | 0.214 | 0.253 | 0.000 | 0.000 | 3.990 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 76 | 78 | 0 | 141 | 0 | 64 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 0.00 | 1.86 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.249 | 0.056 | 0.451 | 0.000 | 0.254 | 0.000 | 0.277 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 136 | 117 | 116 | 123 | 0 | 281 | 0 | 0 | 0 |
N.S. |
1 | 0.86 | 0.85 | 0.90 | 0.00 | 2.07 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.275 | 0.087 | 0.433 | 0.000 | 0.259 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 193 | 155 | 125 | 172 | 0 | 341 | 0 | 88 | 0 |
N.S. |
1 | 0.80 | 0.65 | 0.89 | 0.00 | 1.77 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.295 | 0.121 | 0.435 | 0.000 | 0.260 | 0.000 | 0.301 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 148 | 88 | 78 | 123 | 204 | 150 | 161 | 112 |
N.S. |
1 | 1.08 | 0.64 | 0.57 | 0.90 | 1.49 | 1.09 | 1.18 | 0.82 |
time (sec) |
N/A | 0.388 | 0.089 | 0.574 | 0.296 | 0.248 | 2.900 | 0.269 | 0.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 116 | 126 | 80 | 71 | 109 | 182 | 133 | 134 | 95 |
N.S. |
1 | 1.09 | 0.69 | 0.61 | 0.94 | 1.57 | 1.15 | 1.16 | 0.82 |
time (sec) |
N/A | 0.353 | 0.070 | 0.566 | 0.304 | 0.268 | 2.749 | 0.267 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 95 | 104 | 71 | 61 | 95 | 146 | 116 | 107 | 78 |
N.S. |
1 | 1.09 | 0.75 | 0.64 | 1.00 | 1.54 | 1.22 | 1.13 | 0.82 |
time (sec) |
N/A | 0.343 | 0.052 | 0.556 | 0.295 | 0.266 | 2.612 | 0.271 | 4.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 76 | 82 | 61 | 57 | 79 | 119 | 99 | 77 | 61 |
N.S. |
1 | 1.08 | 0.80 | 0.75 | 1.04 | 1.57 | 1.30 | 1.01 | 0.80 |
time (sec) |
N/A | 0.321 | 0.038 | 0.533 | 0.291 | 0.255 | 2.577 | 0.269 | 4.517 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 58 | 60 | 58 | 45 | 68 | 118 | 82 | 51 | 47 |
N.S. |
1 | 1.03 | 1.00 | 0.78 | 1.17 | 2.03 | 1.41 | 0.88 | 0.81 |
time (sec) |
N/A | 0.318 | 0.031 | 0.546 | 0.299 | 0.248 | 1.734 | 0.267 | 4.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 37 | 29 | 52 | 88 | 66 | 36 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 1.41 | 2.38 | 1.78 | 0.97 | 0.76 |
time (sec) |
N/A | 0.309 | 0.022 | 0.494 | 0.300 | 0.260 | 1.839 | 0.266 | 0.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 62 | 37 | 50 | 71 | 146 | 83 | 54 | 47 |
N.S. |
1 | 1.09 | 0.65 | 0.88 | 1.25 | 2.56 | 1.46 | 0.95 | 0.82 |
time (sec) |
N/A | 0.320 | 0.029 | 0.513 | 0.287 | 0.264 | 1.970 | 0.260 | 4.259 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 83 | 91 | 39 | 64 | 81 | 196 | 104 | 73 | 65 |
N.S. |
1 | 1.10 | 0.47 | 0.77 | 0.98 | 2.36 | 1.25 | 0.88 | 0.78 |
time (sec) |
N/A | 0.332 | 0.031 | 0.532 | 0.322 | 0.256 | 2.241 | 0.263 | 0.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 120 | 39 | 78 | 101 | 252 | 121 | 93 | 79 |
N.S. |
1 | 1.15 | 0.38 | 0.75 | 0.97 | 2.42 | 1.16 | 0.89 | 0.76 |
time (sec) |
N/A | 0.349 | 0.036 | 0.550 | 0.293 | 0.261 | 2.466 | 0.266 | 0.102 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 368 | 267 | 84 | 88 | 152 | 105 | 0 | 0 | 110 |
N.S. |
1 | 0.73 | 0.23 | 0.24 | 0.41 | 0.29 | 0.00 | 0.00 | 0.30 |
time (sec) |
N/A | 0.346 | 0.060 | 0.463 | 0.230 | 0.271 | 0.000 | 0.000 | 4.466 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 311 | 229 | 76 | 80 | 136 | 94 | 0 | 0 | 102 |
N.S. |
1 | 0.74 | 0.24 | 0.26 | 0.44 | 0.30 | 0.00 | 0.00 | 0.33 |
time (sec) |
N/A | 0.329 | 0.053 | 0.448 | 0.220 | 0.245 | 0.000 | 0.000 | 4.854 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 254 | 191 | 68 | 72 | 120 | 83 | 0 | 0 | 94 |
N.S. |
1 | 0.75 | 0.27 | 0.28 | 0.47 | 0.33 | 0.00 | 0.00 | 0.37 |
time (sec) |
N/A | 0.311 | 0.046 | 0.467 | 0.216 | 0.256 | 0.000 | 0.000 | 4.462 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 195 | 153 | 57 | 63 | 93 | 63 | 0 | 0 | 81 |
N.S. |
1 | 0.78 | 0.29 | 0.32 | 0.48 | 0.32 | 0.00 | 0.00 | 0.42 |
time (sec) |
N/A | 0.287 | 0.040 | 0.482 | 0.219 | 0.243 | 0.000 | 0.000 | 4.418 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 115 | 48 | 55 | 75 | 50 | 0 | 0 | 71 |
N.S. |
1 | 0.84 | 0.35 | 0.40 | 0.55 | 0.36 | 0.00 | 0.00 | 0.52 |
time (sec) |
N/A | 0.264 | 0.031 | 0.464 | 0.223 | 0.251 | 0.000 | 0.000 | 4.266 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 83 | 48 | 47 | 48 | 44 | 0 | 42 | 34 |
N.S. |
1 | 0.98 | 0.56 | 0.55 | 0.56 | 0.52 | 0.00 | 0.49 | 0.40 |
time (sec) |
N/A | 0.242 | 0.035 | 0.460 | 0.220 | 0.251 | 0.000 | 0.276 | 4.406 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 41 | 35 | 45 | 43 | 0 | 41 | 32 |
N.S. |
1 | 1.00 | 1.41 | 1.21 | 1.55 | 1.48 | 0.00 | 1.41 | 1.10 |
time (sec) |
N/A | 0.212 | 0.033 | 0.451 | 0.222 | 0.257 | 0.000 | 0.272 | 4.234 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 120 | 101 | 122 | 85 | 0 | 235 | 0 | 0 | 0 |
N.S. |
1 | 0.84 | 1.02 | 0.71 | 0.00 | 1.96 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.265 | 0.096 | 0.461 | 0.000 | 0.265 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 184 | 141 | 130 | 129 | 0 | 285 | 0 | 90 | 0 |
N.S. |
1 | 0.77 | 0.71 | 0.70 | 0.00 | 1.55 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.290 | 0.315 | 0.467 | 0.000 | 0.282 | 0.000 | 0.299 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 99 | 112 | 41 | 62 | 110 | 57 | 0 | 59 | 94 |
N.S. |
1 | 1.13 | 0.41 | 0.63 | 1.11 | 0.58 | 0.00 | 0.60 | 0.95 |
time (sec) |
N/A | 0.254 | 0.043 | 0.127 | 0.212 | 0.250 | 0.000 | 0.259 | 0.089 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 79 | 80 | 40 | 57 | 87 | 54 | 0 | 48 | 68 |
N.S. |
1 | 1.01 | 0.51 | 0.72 | 1.10 | 0.68 | 0.00 | 0.61 | 0.86 |
time (sec) |
N/A | 0.226 | 0.029 | 0.098 | 0.223 | 0.245 | 0.000 | 0.268 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 21 | 22 | 50 | 24 | 0 | 15 | 18 |
N.S. |
1 | 1.00 | 1.17 | 1.22 | 2.78 | 1.33 | 0.00 | 0.83 | 1.00 |
time (sec) |
N/A | 0.197 | 0.025 | 0.039 | 0.203 | 0.239 | 0.000 | 0.254 | 4.448 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 31 | 39 | 48 | 83 | 51 | 0 | 38 | 63 |
N.S. |
1 | 0.89 | 1.11 | 1.37 | 2.37 | 1.46 | 0.00 | 1.09 | 1.80 |
time (sec) |
N/A | 0.206 | 0.023 | 0.094 | 0.208 | 0.243 | 0.000 | 0.266 | 4.011 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 133 | 144 | 52 | 70 | 138 | 66 | 0 | 71 | 118 |
N.S. |
1 | 1.08 | 0.39 | 0.53 | 1.04 | 0.50 | 0.00 | 0.53 | 0.89 |
time (sec) |
N/A | 0.283 | 0.048 | 0.443 | 0.210 | 0.248 | 0.000 | 0.271 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 106 | 112 | 47 | 65 | 112 | 61 | 0 | 60 | 94 |
N.S. |
1 | 1.06 | 0.44 | 0.61 | 1.06 | 0.58 | 0.00 | 0.57 | 0.89 |
time (sec) |
N/A | 0.240 | 0.035 | 0.443 | 0.233 | 0.250 | 0.000 | 0.266 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 71 | 74 | 52 | 70 | 138 | 66 | 0 | 72 | 118 |
N.S. |
1 | 1.04 | 0.73 | 0.99 | 1.94 | 0.93 | 0.00 | 1.01 | 1.66 |
time (sec) |
N/A | 0.269 | 0.042 | 0.462 | 0.214 | 0.257 | 0.000 | 0.265 | 4.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 50 | 47 | 60 | 112 | 61 | 0 | 60 | 90 |
N.S. |
1 | 0.94 | 0.89 | 1.13 | 2.11 | 1.15 | 0.00 | 1.13 | 1.70 |
time (sec) |
N/A | 0.238 | 0.032 | 0.478 | 0.205 | 0.254 | 0.000 | 0.270 | 4.274 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 15 | 16 | 26 | 15 | 0 | 14 | 26 |
N.S. |
1 | 1.00 | 0.68 | 0.73 | 1.18 | 0.68 | 0.00 | 0.64 | 1.18 |
time (sec) |
N/A | 0.212 | 0.025 | 0.430 | 0.218 | 0.236 | 0.000 | 0.270 | 0.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 18 | 35 | 31 | 31 | 26 | 21 | 14 |
N.S. |
1 | 1.00 | 0.82 | 1.59 | 1.41 | 1.41 | 1.18 | 0.95 | 0.64 |
time (sec) |
N/A | 0.200 | 0.016 | 0.438 | 0.199 | 0.245 | 2.091 | 0.264 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 51 | 41 | 64 | 74 | 66 | 0 | 65 | 43 |
N.S. |
1 | 1.09 | 0.87 | 1.36 | 1.57 | 1.40 | 0.00 | 1.38 | 0.91 |
time (sec) |
N/A | 0.261 | 0.076 | 0.467 | 0.208 | 0.251 | 0.000 | 0.272 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 37 | 38 | 52 | 44 | 61 | 0 | 49 | 28 |
N.S. |
1 | 1.12 | 1.15 | 1.58 | 1.33 | 1.85 | 0.00 | 1.48 | 0.85 |
time (sec) |
N/A | 0.233 | 0.045 | 0.459 | 0.257 | 0.253 | 0.000 | 0.267 | 4.249 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 36 | 56 | 44 | 44 | 0 | 44 | 28 |
N.S. |
1 | 1.00 | 0.80 | 1.24 | 0.98 | 0.98 | 0.00 | 0.98 | 0.62 |
time (sec) |
N/A | 0.223 | 0.047 | 0.440 | 0.260 | 0.253 | 0.000 | 0.275 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 18 | 12 | 11 | 11 | 8 | 22 | 11 |
N.S. |
1 | 1.00 | 0.86 | 0.57 | 0.52 | 0.52 | 0.38 | 1.05 | 0.52 |
time (sec) |
N/A | 0.187 | 0.016 | 0.437 | 0.213 | 0.239 | 3.339 | 0.275 | 0.190 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 60 | 43 | 64 | 56 | 84 | 0 | 79 | 40 |
N.S. |
1 | 1.09 | 0.78 | 1.16 | 1.02 | 1.53 | 0.00 | 1.44 | 0.73 |
time (sec) |
N/A | 0.283 | 0.062 | 0.482 | 0.209 | 0.239 | 0.000 | 0.272 | 4.623 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 22 | 13 | 31 | 0 | 46 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.54 | 1.29 | 0.00 | 1.92 | 0.54 |
time (sec) |
N/A | 0.202 | 0.020 | 0.464 | 0.223 | 0.266 | 0.000 | 0.264 | 0.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 67 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.294 | 0.034 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 140 | 118 | 67 | 49 | 55 | 69 | 0 | 0 | 57 |
N.S. |
1 | 0.84 | 0.48 | 0.35 | 0.39 | 0.49 | 0.00 | 0.00 | 0.41 |
time (sec) |
N/A | 0.300 | 0.050 | 0.444 | 0.240 | 0.243 | 0.000 | 0.000 | 4.653 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 86 | 56 | 41 | 41 | 61 | 0 | 81 | 49 |
N.S. |
1 | 0.93 | 0.61 | 0.45 | 0.45 | 0.66 | 0.00 | 0.88 | 0.53 |
time (sec) |
N/A | 0.259 | 0.032 | 0.454 | 0.240 | 0.250 | 0.000 | 0.274 | 4.585 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 43 | 35 | 26 | 50 | 0 | 49 | 43 |
N.S. |
1 | 1.00 | 1.48 | 1.21 | 0.90 | 1.72 | 0.00 | 1.69 | 1.48 |
time (sec) |
N/A | 0.205 | 0.014 | 0.432 | 0.257 | 0.246 | 0.000 | 0.267 | 0.003 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 94 | 78 | 75 | 70 | 0 | 207 | 0 | 88 | 0 |
N.S. |
1 | 0.83 | 0.80 | 0.74 | 0.00 | 2.20 | 0.00 | 0.94 | 0.00 |
time (sec) |
N/A | 0.284 | 0.050 | 0.472 | 0.000 | 0.266 | 0.000 | 0.276 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 76 | 76 | 78 | 0 | 229 | 0 | 101 | 0 |
N.S. |
1 | 0.78 | 0.78 | 0.80 | 0.00 | 2.36 | 0.00 | 1.04 | 0.00 |
time (sec) |
N/A | 0.284 | 0.045 | 0.468 | 0.000 | 0.280 | 0.000 | 0.289 | 0.000 |