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 | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 8 | 7 | 12 | 0 | 7 | 27 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.78 | 1.33 | 0.00 | 0.78 | 3.00 |
time (sec) |
N/A | 0.019 | 0.008 | 1.143 | 0.183 | 0.259 | 0.000 | 0.298 | 2.664 |
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 | 20 | 20 | 20 | 16 | 16 | 16 | 12 | 16 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.80 | 0.80 | 0.60 | 0.80 | 0.75 |
time (sec) |
N/A | 0.002 | 0.000 | 0.020 | 0.204 | 0.228 | 0.019 | 0.319 | 0.026 |
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 | 12 | 12 | 13 | 10 | 9 | 9 | 8 | 10 | 9 |
N.S. |
1 | 1.00 | 1.08 | 0.83 | 0.75 | 0.75 | 0.67 | 0.83 | 0.75 |
time (sec) |
N/A | 0.018 | 0.023 | 0.037 | 0.205 | 0.259 | 0.034 | 0.282 | 0.184 |
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 | 21 | 18 | 17 | 17 | 15 | 17 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.81 | 0.81 | 0.71 | 0.81 | 0.81 |
time (sec) |
N/A | 0.009 | 0.006 | 0.162 | 0.203 | 0.244 | 0.044 | 0.296 | 0.053 |
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 | 43 | 43 | 43 | 22 | 30 | 27 | 20 | 23 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.51 | 0.70 | 0.63 | 0.47 | 0.53 | 0.26 |
time (sec) |
N/A | 0.015 | 0.021 | 0.134 | 0.197 | 0.263 | 0.120 | 0.318 | 0.426 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 18 | 15 | 16 | 22 | 144 | 43 | 14 |
N.S. |
1 | 1.00 | 0.75 | 0.62 | 0.67 | 0.92 | 6.00 | 1.79 | 0.58 |
time (sec) |
N/A | 0.006 | 0.020 | 0.167 | 0.181 | 0.257 | 0.628 | 0.319 | 0.212 |
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 | 38 | 24 | 20 | 16 | 16 | 34 | 16 | 21 |
N.S. |
1 | 1.00 | 0.63 | 0.53 | 0.42 | 0.42 | 0.89 | 0.42 | 0.55 |
time (sec) |
N/A | 0.015 | 0.011 | 0.032 | 0.202 | 0.242 | 0.100 | 0.291 | 0.035 |
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 | 31 | 30 | 32 | 39 | 30 | 32 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.81 | 0.86 | 1.05 | 0.81 | 0.86 |
time (sec) |
N/A | 0.030 | 0.050 | 0.234 | 0.278 | 0.251 | 0.601 | 0.300 | 0.208 |
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 | 17 | 17 | 17 | 16 | 15 | 21 | 14 | 17 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.88 | 1.24 | 0.82 | 1.00 | 0.88 |
time (sec) |
N/A | 0.021 | 0.005 | 0.181 | 0.190 | 0.247 | 0.045 | 0.286 | 0.042 |
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 | 40 | 29 | 26 | 38 | 26 | 39 | 26 | 34 |
N.S. |
1 | 1.00 | 0.72 | 0.65 | 0.95 | 0.65 | 0.98 | 0.65 | 0.85 |
time (sec) |
N/A | 0.061 | 0.089 | 0.220 | 0.201 | 0.252 | 0.093 | 0.272 | 0.198 |
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 | 5 | 5 | 5 | 6 | 5 | 20 | 5 | 5 | 5 |
N.S. |
1 | 1.00 | 1.00 | 1.20 | 1.00 | 4.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.010 | 4.174 | 0.201 | 0.194 | 0.256 | 0.154 | 0.303 | 0.247 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 6 | 6 | 20 | 5 | 4 | 18 | 3 | 19 | 4 |
N.S. |
1 | 1.00 | 3.33 | 0.83 | 0.67 | 3.00 | 0.50 | 3.17 | 0.67 |
time (sec) |
N/A | 0.001 | 0.035 | 0.422 | 0.300 | 0.240 | 0.068 | 0.279 | 0.008 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 24 | 22 | 62 | 62 | 61 | 22 | 29 |
N.S. |
1 | 1.00 | 0.65 | 0.59 | 1.68 | 1.68 | 1.65 | 0.59 | 0.78 |
time (sec) |
N/A | 0.011 | 0.008 | 0.156 | 0.192 | 0.247 | 0.061 | 0.291 | 0.100 |
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 | 21 | 21 | 21 | 18 | 18 | 36 | 19 | 18 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.86 | 1.71 | 0.90 | 0.86 | 0.86 |
time (sec) |
N/A | 0.024 | 0.028 | 0.177 | 0.215 | 0.248 | 0.049 | 0.299 | 0.395 |
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 | 30 | 30 | 30 | 25 | 24 | 22 | 41 | 24 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.80 | 0.73 | 1.37 | 0.80 | 0.80 |
time (sec) |
N/A | 0.040 | 0.058 | 0.172 | 0.199 | 0.256 | 0.074 | 0.266 | 0.255 |
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 | 4 | 4 | 27 | 4 | 3 | 3 | 3 | 3 | 3 |
N.S. |
1 | 1.00 | 6.75 | 1.00 | 0.75 | 0.75 | 0.75 | 0.75 | 0.75 |
time (sec) |
N/A | 0.021 | 0.007 | 0.188 | 0.207 | 0.260 | 0.219 | 0.277 | 0.236 |
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 | 13 | 13 | 13 | 12 | 15 | 11 | 10 | 15 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 1.15 | 0.85 | 0.77 | 1.15 | 0.85 |
time (sec) |
N/A | 0.004 | 0.005 | 0.151 | 0.200 | 0.234 | 0.040 | 0.317 | 0.046 |
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 | 44 | 44 | 24 | 21 | 21 | 21 | 22 | 21 | 21 |
N.S. |
1 | 1.00 | 0.55 | 0.48 | 0.48 | 0.48 | 0.50 | 0.48 | 0.48 |
time (sec) |
N/A | 0.032 | 0.022 | 0.046 | 0.210 | 0.233 | 0.042 | 0.296 | 0.027 |
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 | 41 | 41 | 42 | 28 | 27 | 25 | 37 | 27 | 27 |
N.S. |
1 | 1.00 | 1.02 | 0.68 | 0.66 | 0.61 | 0.90 | 0.66 | 0.66 |
time (sec) |
N/A | 0.009 | 0.039 | 0.149 | 0.276 | 0.230 | 1.704 | 0.283 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 20 | 19 | 17 | 114 | 13 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.76 | 0.68 | 4.56 | 0.52 | 0.56 |
time (sec) |
N/A | 0.023 | 0.002 | 1.335 | 0.185 | 0.263 | 0.962 | 0.316 | 0.225 |
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 | 12 | 12 | 12 | 11 | 10 | 10 | 7 | 10 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.83 | 0.83 | 0.58 | 0.83 | 0.67 |
time (sec) |
N/A | 0.001 | 0.003 | 0.023 | 0.192 | 0.234 | 0.029 | 0.287 | 0.186 |
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 | 41 | 41 | 65 | 41 | 43 | 32 | 0 | 30 | 43 |
N.S. |
1 | 1.00 | 1.59 | 1.00 | 1.05 | 0.78 | 0.00 | 0.73 | 1.05 |
time (sec) |
N/A | 0.012 | 0.101 | 0.190 | 0.275 | 0.251 | 0.000 | 0.322 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 27 | 119 | 27 | 27 | 29 | 28 | 0 |
N.S. |
1 | 1.00 | 0.79 | 3.50 | 0.79 | 0.79 | 0.85 | 0.82 | 0.00 |
time (sec) |
N/A | 0.026 | 0.015 | 0.157 | 0.272 | 0.268 | 1.221 | 0.303 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 18 | 17 | 17 | 42 | 17 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.89 | 0.89 | 2.21 | 0.89 | 0.89 |
time (sec) |
N/A | 0.005 | 0.006 | 0.184 | 0.275 | 0.261 | 0.044 | 0.294 | 0.042 |
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 | 38 | 45 | 30 | 39 | 37 | 34 | 31 | 28 |
N.S. |
1 | 1.00 | 1.18 | 0.79 | 1.03 | 0.97 | 0.89 | 0.82 | 0.74 |
time (sec) |
N/A | 0.009 | 0.110 | 0.311 | 0.278 | 0.250 | 0.224 | 0.268 | 0.047 |
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 | 12 | 12 | 12 | 9 | 8 | 8 | 7 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 0.67 | 0.67 | 0.58 | 0.67 | 0.67 |
time (sec) |
N/A | 0.006 | 0.006 | 0.210 | 0.278 | 0.246 | 0.048 | 0.295 | 0.199 |
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 | 31 | 31 | 31 | 27 | 26 | 26 | 36 | 26 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.84 | 0.84 | 1.16 | 0.84 | 0.90 |
time (sec) |
N/A | 0.013 | 0.013 | 0.708 | 0.282 | 0.237 | 0.044 | 0.289 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 37 | 16 | 121 | 29 | 12 | 150 | 19 |
N.S. |
1 | 1.00 | 3.70 | 1.60 | 12.10 | 2.90 | 1.20 | 15.00 | 1.90 |
time (sec) |
N/A | 0.011 | 0.014 | 0.124 | 0.280 | 0.257 | 0.442 | 0.361 | 0.112 |
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 | 15 | 15 | 15 | 27 | 29 | 26 | 22 | 30 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.80 | 1.93 | 1.73 | 1.47 | 2.00 | 0.87 |
time (sec) |
N/A | 0.008 | 0.006 | 0.202 | 0.193 | 0.256 | 0.067 | 0.288 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 14 | 0 | 13 | 63 | 13 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.67 | 0.00 | 0.62 | 3.00 | 0.62 | 1.00 |
time (sec) |
N/A | 0.008 | 0.103 | 0.029 | 0.000 | 0.232 | 0.160 | 0.279 | 0.237 |
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 | 23 | 23 | 18 | 16 | 19 | 17 | 19 | 18 | 17 |
N.S. |
1 | 1.00 | 0.78 | 0.70 | 0.83 | 0.74 | 0.83 | 0.78 | 0.74 |
time (sec) |
N/A | 0.015 | 0.050 | 0.040 | 0.203 | 0.241 | 0.060 | 0.267 | 0.302 |
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 | 20 | 20 | 20 | 17 | 16 | 16 | 17 | 16 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.80 | 0.80 | 0.85 | 0.80 | 0.80 |
time (sec) |
N/A | 0.006 | 0.009 | 0.037 | 0.206 | 0.261 | 0.126 | 0.274 | 0.313 |
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 | 18 | 18 | 18 | 16 | 18 | 19 | 14 | 20 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 1.00 | 1.06 | 0.78 | 1.11 | 1.00 |
time (sec) |
N/A | 0.013 | 0.006 | 0.065 | 0.202 | 0.256 | 0.054 | 0.281 | 0.216 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 20 | 19 | 25 | 20 | 20 | 19 |
N.S. |
1 | 1.00 | 1.00 | 1.67 | 1.58 | 2.08 | 1.67 | 1.67 | 1.58 |
time (sec) |
N/A | 0.014 | 0.046 | 0.052 | 0.192 | 0.243 | 0.051 | 0.285 | 0.249 |
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 | 8 | 8 | 23 | 9 | 10 | 15 | 12 | 16 | 8 |
N.S. |
1 | 1.00 | 2.88 | 1.12 | 1.25 | 1.88 | 1.50 | 2.00 | 1.00 |
time (sec) |
N/A | 0.032 | 0.007 | 0.145 | 0.279 | 0.262 | 0.353 | 0.303 | 0.228 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 13 | 12 | 12 | 44 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.72 | 0.67 | 0.67 | 2.44 | 0.67 | 0.67 |
time (sec) |
N/A | 0.003 | 0.018 | 0.308 | 0.274 | 0.242 | 0.486 | 0.295 | 0.146 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 10 | 0 | 24 | 0 | 9 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.00 | 2.18 | 0.00 | 0.82 | 1.64 |
time (sec) |
N/A | 0.039 | 0.021 | 0.479 | 0.000 | 0.316 | 0.000 | 0.289 | 0.438 |
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 | 30 | 30 | 46 | 23 | 22 | 30 | 27 | 22 | 22 |
N.S. |
1 | 1.00 | 1.53 | 0.77 | 0.73 | 1.00 | 0.90 | 0.73 | 0.73 |
time (sec) |
N/A | 0.006 | 0.077 | 0.465 | 0.310 | 0.256 | 0.107 | 0.328 | 0.177 |
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 | 24 | 24 | 20 | 23 | 21 | 21 | 26 | 21 | 23 |
N.S. |
1 | 1.00 | 0.83 | 0.96 | 0.88 | 0.88 | 1.08 | 0.88 | 0.96 |
time (sec) |
N/A | 0.030 | 0.009 | 0.111 | 0.206 | 0.261 | 0.127 | 0.285 | 0.030 |
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 | 50 | 50 | 47 | 33 | 49 | 39 | 37 | 40 | 39 |
N.S. |
1 | 1.00 | 0.94 | 0.66 | 0.98 | 0.78 | 0.74 | 0.80 | 0.78 |
time (sec) |
N/A | 0.011 | 0.084 | 0.373 | 0.283 | 0.249 | 0.250 | 0.286 | 0.228 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 10 | 9 | 46 | 51 | 9 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.82 | 4.18 | 4.64 | 0.82 | 0.82 |
time (sec) |
N/A | 0.001 | 0.002 | 0.155 | 0.198 | 0.244 | 0.028 | 0.266 | 0.224 |
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 | 25 | 25 | 31 | 20 | 19 | 19 | 20 | 19 | 19 |
N.S. |
1 | 1.00 | 1.24 | 0.80 | 0.76 | 0.76 | 0.80 | 0.76 | 0.76 |
time (sec) |
N/A | 0.024 | 0.011 | 0.175 | 0.201 | 0.242 | 0.022 | 0.279 | 0.190 |
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 | 27 | 27 | 22 | 20 | 19 | 21 | 26 | 19 | 19 |
N.S. |
1 | 1.00 | 0.81 | 0.74 | 0.70 | 0.78 | 0.96 | 0.70 | 0.70 |
time (sec) |
N/A | 0.008 | 0.050 | 0.151 | 0.191 | 0.242 | 0.167 | 0.272 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 41 | 23 | 34 | 56 | 36 | 70 | 18 |
N.S. |
1 | 1.00 | 1.71 | 0.96 | 1.42 | 2.33 | 1.50 | 2.92 | 0.75 |
time (sec) |
N/A | 0.008 | 0.043 | 0.295 | 0.192 | 0.248 | 0.057 | 0.282 | 0.070 |
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 | 34 | 34 | 35 | 32 | 33 | 35 | 27 | 44 | 32 |
N.S. |
1 | 1.00 | 1.03 | 0.94 | 0.97 | 1.03 | 0.79 | 1.29 | 0.94 |
time (sec) |
N/A | 0.006 | 0.042 | 0.280 | 0.316 | 0.232 | 0.098 | 0.289 | 0.495 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 25 | 35 | 28 | 73 | 38 | 37 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 1.17 | 0.93 | 2.43 | 1.27 | 1.23 |
time (sec) |
N/A | 0.012 | 0.028 | 0.218 | 0.275 | 0.232 | 0.841 | 0.288 | 0.111 |
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 | 32 | 32 | 19 | 16 | 16 | 16 | 15 | 16 | 16 |
N.S. |
1 | 1.00 | 0.59 | 0.50 | 0.50 | 0.50 | 0.47 | 0.50 | 0.50 |
time (sec) |
N/A | 0.014 | 0.018 | 0.047 | 0.208 | 0.238 | 0.036 | 0.295 | 0.033 |
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 | 23 | 23 | 31 | 18 | 17 | 12 | 26 | 42 | 12 |
N.S. |
1 | 1.00 | 1.35 | 0.78 | 0.74 | 0.52 | 1.13 | 1.83 | 0.52 |
time (sec) |
N/A | 0.027 | 0.025 | 0.158 | 0.194 | 0.254 | 0.119 | 0.282 | 0.113 |
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 | 27 | 27 | 24 | 22 | 21 | 21 | 19 | 21 | 21 |
N.S. |
1 | 1.00 | 0.89 | 0.81 | 0.78 | 0.78 | 0.70 | 0.78 | 0.78 |
time (sec) |
N/A | 0.012 | 0.008 | 0.023 | 0.285 | 0.254 | 0.072 | 0.267 | 0.290 |
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 | 38 | 32 | 31 | 53 | 28 | 29 | 32 | 28 |
N.S. |
1 | 1.00 | 0.84 | 0.82 | 1.39 | 0.74 | 0.76 | 0.84 | 0.74 |
time (sec) |
N/A | 0.018 | 0.014 | 0.037 | 0.279 | 0.248 | 0.144 | 0.275 | 0.234 |
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 | 5 | 5 | 5 | 5 | 4 | 16 | 8 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.80 | 3.20 | 1.60 | 1.20 | 1.20 |
time (sec) |
N/A | 0.009 | 0.008 | 0.319 | 0.202 | 0.244 | 0.375 | 0.270 | 0.048 |
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 | 29 | 29 | 25 | 22 | 21 | 21 | 27 | 21 | 23 |
N.S. |
1 | 1.00 | 0.86 | 0.76 | 0.72 | 0.72 | 0.93 | 0.72 | 0.79 |
time (sec) |
N/A | 0.031 | 0.018 | 0.194 | 0.206 | 0.274 | 0.088 | 0.285 | 0.202 |
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 | 36 | 45 | 29 | 36 | 47 | 27 | 26 | 27 |
N.S. |
1 | 1.00 | 1.25 | 0.81 | 1.00 | 1.31 | 0.75 | 0.72 | 0.75 |
time (sec) |
N/A | 0.009 | 0.090 | 0.240 | 0.294 | 0.251 | 0.283 | 0.287 | 0.187 |
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 | 28 | 28 | 31 | 23 | 22 | 22 | 24 | 22 | 22 |
N.S. |
1 | 1.00 | 1.11 | 0.82 | 0.79 | 0.79 | 0.86 | 0.79 | 0.79 |
time (sec) |
N/A | 0.014 | 0.012 | 0.210 | 0.292 | 0.254 | 0.056 | 0.301 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 25 | 42 | 43 | 46 | 38 | 29 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 1.62 | 1.65 | 1.77 | 1.46 | 1.12 |
time (sec) |
N/A | 0.016 | 0.006 | 0.362 | 0.205 | 0.253 | 0.065 | 0.272 | 0.059 |
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 | 46 | 46 | 30 | 23 | 24 | 33 | 46 | 22 | 22 |
N.S. |
1 | 1.00 | 0.65 | 0.50 | 0.52 | 0.72 | 1.00 | 0.48 | 0.48 |
time (sec) |
N/A | 0.016 | 0.039 | 0.316 | 0.210 | 0.256 | 0.025 | 0.291 | 0.221 |
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 | 20 | 20 | 15 | 17 | 16 | 24 | 17 | 16 | 11 |
N.S. |
1 | 1.00 | 0.75 | 0.85 | 0.80 | 1.20 | 0.85 | 0.80 | 0.55 |
time (sec) |
N/A | 0.026 | 0.017 | 0.419 | 0.204 | 0.274 | 0.641 | 0.260 | 0.286 |
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 | 24 | 18 | 16 | 24 | 14 | 19 | 19 |
N.S. |
1 | 1.00 | 1.14 | 0.86 | 0.76 | 1.14 | 0.67 | 0.90 | 0.90 |
time (sec) |
N/A | 0.017 | 0.032 | 0.051 | 0.211 | 0.253 | 0.048 | 0.282 | 0.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 33 | 77 | 47 | 58 | 0 | 50 | 0 |
N.S. |
1 | 1.00 | 0.89 | 2.08 | 1.27 | 1.57 | 0.00 | 1.35 | 0.00 |
time (sec) |
N/A | 0.033 | 0.024 | 0.678 | 0.291 | 0.307 | 0.000 | 0.287 | 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 | 28 | 28 | 46 | 26 | 29 | 27 | 29 | 28 | 23 |
N.S. |
1 | 1.00 | 1.64 | 0.93 | 1.04 | 0.96 | 1.04 | 1.00 | 0.82 |
time (sec) |
N/A | 0.008 | 0.058 | 0.254 | 0.192 | 0.247 | 0.227 | 0.292 | 0.145 |
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 | 19 | 19 | 19 | 17 | 15 | 18 | 17 | 15 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.79 | 0.95 | 0.89 | 0.79 | 1.11 |
time (sec) |
N/A | 0.007 | 0.008 | 0.292 | 0.213 | 0.250 | 0.020 | 0.298 | 0.035 |
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 | 46 | 46 | 26 | 25 | 24 | 24 | 22 | 24 | 24 |
N.S. |
1 | 1.00 | 0.57 | 0.54 | 0.52 | 0.52 | 0.48 | 0.52 | 0.52 |
time (sec) |
N/A | 0.029 | 0.021 | 0.038 | 0.195 | 0.245 | 0.034 | 0.278 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 15 | 33 | 16 | 32 | 30 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 1.83 | 0.89 | 1.78 | 1.67 | 0.00 |
time (sec) |
N/A | 0.006 | 0.284 | 0.736 | 0.214 | 0.242 | 0.528 | 0.298 | 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 | 27 | 27 | 22 | 20 | 19 | 21 | 24 | 19 | 19 |
N.S. |
1 | 1.00 | 0.81 | 0.74 | 0.70 | 0.78 | 0.89 | 0.70 | 0.70 |
time (sec) |
N/A | 0.012 | 0.074 | 0.152 | 0.217 | 0.254 | 0.088 | 0.305 | 0.220 |
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 | 18 | 22 | 18 | 17 | 16 | 15 | 0 | 16 | 18 |
N.S. |
1 | 1.22 | 1.00 | 0.94 | 0.89 | 0.83 | 0.00 | 0.89 | 1.00 |
time (sec) |
N/A | 0.030 | 0.009 | 0.039 | 0.202 | 0.266 | 0.000 | 0.283 | 0.248 |
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 | 27 | 27 | 23 | 22 | 21 | 21 | 20 | 21 | 21 |
N.S. |
1 | 1.00 | 0.85 | 0.81 | 0.78 | 0.78 | 0.74 | 0.78 | 0.78 |
time (sec) |
N/A | 0.012 | 0.001 | 0.030 | 0.198 | 0.260 | 0.096 | 0.276 | 0.002 |
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 | 21 | 20 | 20 | 20 | 20 | 31 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.77 | 0.77 | 0.77 | 0.77 | 1.19 |
time (sec) |
N/A | 0.009 | 0.031 | 0.083 | 0.306 | 0.251 | 0.282 | 0.298 | 0.245 |
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 | 15 | 15 | 11 | 14 | 9 | 9 | 15 | 9 | 9 |
N.S. |
1 | 1.00 | 0.73 | 0.93 | 0.60 | 0.60 | 1.00 | 0.60 | 0.60 |
time (sec) |
N/A | 0.014 | 0.033 | 1.704 | 0.205 | 0.250 | 0.779 | 0.275 | 0.287 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 50 | 35 | 34 | 37 | 121 | 29 | 30 |
N.S. |
1 | 1.00 | 1.06 | 0.74 | 0.72 | 0.79 | 2.57 | 0.62 | 0.64 |
time (sec) |
N/A | 0.009 | 0.129 | 0.250 | 0.289 | 0.241 | 1.713 | 0.299 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 36 | 10 | 9 | 26 | 27 | 9 | 26 |
N.S. |
1 | 1.00 | 3.27 | 0.91 | 0.82 | 2.36 | 2.45 | 0.82 | 2.36 |
time (sec) |
N/A | 0.002 | 0.003 | 0.177 | 0.200 | 0.238 | 0.014 | 0.303 | 0.024 |
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 | 17 | 17 | 17 | 14 | 13 | 13 | 12 | 13 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.76 | 0.76 | 0.71 | 0.76 | 0.82 |
time (sec) |
N/A | 0.022 | 0.007 | 0.167 | 0.207 | 0.257 | 0.021 | 0.293 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 27 | 14 | 13 | 20 | 29 | 13 | 13 |
N.S. |
1 | 1.00 | 1.59 | 0.82 | 0.76 | 1.18 | 1.71 | 0.76 | 0.76 |
time (sec) |
N/A | 0.023 | 0.012 | 1.822 | 0.198 | 0.274 | 0.020 | 0.265 | 0.199 |
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 | 27 | 27 | 18 | 15 | 19 | 17 | 36 | 19 | 14 |
N.S. |
1 | 1.00 | 0.67 | 0.56 | 0.70 | 0.63 | 1.33 | 0.70 | 0.52 |
time (sec) |
N/A | 0.004 | 0.012 | 0.194 | 0.207 | 0.242 | 0.532 | 0.279 | 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 | 24 | 24 | 22 | 17 | 16 | 19 | 24 | 16 | 16 |
N.S. |
1 | 1.00 | 0.92 | 0.71 | 0.67 | 0.79 | 1.00 | 0.67 | 0.67 |
time (sec) |
N/A | 0.008 | 0.002 | 0.274 | 0.210 | 0.266 | 0.017 | 0.271 | 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 | 12 | 12 | 12 | 17 | 20 | 18 | 12 | 16 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.42 | 1.67 | 1.50 | 1.00 | 1.33 | 1.33 |
time (sec) |
N/A | 0.007 | 0.001 | 0.027 | 0.207 | 0.256 | 0.037 | 0.308 | 0.020 |
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 | 40 | 30 | 22 | 34 | 26 | 53 | 28 | 25 |
N.S. |
1 | 1.00 | 0.75 | 0.55 | 0.85 | 0.65 | 1.32 | 0.70 | 0.62 |
time (sec) |
N/A | 0.010 | 0.021 | 0.177 | 0.292 | 0.251 | 0.280 | 0.282 | 0.024 |