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 | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 9 | 75 | 102 | 0 | 10 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.69 | 5.77 | 7.85 | 0.00 | 0.77 | 1.46 |
time (sec) |
N/A | 0.148 | 0.008 | 0.619 | 0.202 | 0.250 | 0.000 | 0.286 | 0.348 |
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 | 9 | 9 | 9 | 7 | 6 | 16 | 12 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 0.67 | 1.78 | 1.33 | 0.67 | 0.67 |
time (sec) |
N/A | 0.142 | 0.001 | 0.596 | 0.194 | 0.228 | 0.211 | 0.275 | 0.365 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 19 | 18 | 13 | 0 | 25 | 32 | 16 | 14 |
N.S. |
1 | 1.46 | 1.38 | 1.00 | 0.00 | 1.92 | 2.46 | 1.23 | 1.08 |
time (sec) |
N/A | 0.186 | 0.020 | 0.555 | 0.000 | 0.242 | 0.225 | 0.287 | 0.112 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 1 | 4 | 1 | 2 | 1 | 1 | 10 | 1 | 1 |
N.S. |
1 | 4.00 | 1.00 | 2.00 | 1.00 | 1.00 | 10.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.137 | 0.000 | 0.509 | 0.199 | 0.221 | 0.174 | 0.277 | 0.320 |
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 | 22 | 20 | 36 | 17 | 16 | 26 | 0 | 17 | 16 |
N.S. |
1 | 0.91 | 1.64 | 0.77 | 0.73 | 1.18 | 0.00 | 0.77 | 0.73 |
time (sec) |
N/A | 0.168 | 0.021 | 0.092 | 0.205 | 0.242 | 0.000 | 0.285 | 0.064 |
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 | 13 | 13 | 18 | 12 | 11 | 21 | 0 | 11 | 11 |
N.S. |
1 | 1.00 | 1.38 | 0.92 | 0.85 | 1.62 | 0.00 | 0.85 | 0.85 |
time (sec) |
N/A | 0.178 | 0.018 | 0.187 | 0.197 | 0.232 | 0.000 | 0.279 | 0.351 |
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 | 15 | 15 | 20 | 12 | 11 | 22 | 0 | 11 | 11 |
N.S. |
1 | 1.00 | 1.33 | 0.80 | 0.73 | 1.47 | 0.00 | 0.73 | 0.73 |
time (sec) |
N/A | 0.185 | 0.018 | 0.234 | 0.204 | 0.237 | 0.000 | 0.286 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 19 | 19 | 26 | 25 | 56 | 0 | 32 |
N.S. |
1 | 1.00 | 0.73 | 0.73 | 1.00 | 0.96 | 2.15 | 0.00 | 1.23 |
time (sec) |
N/A | 0.149 | 0.007 | 0.030 | 0.200 | 0.241 | 0.275 | 0.000 | 0.450 |
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 | 42 | 49 | 30 | 41 | 42 | 45 | 155 | 84 | 43 |
N.S. |
1 | 1.17 | 0.71 | 0.98 | 1.00 | 1.07 | 3.69 | 2.00 | 1.02 |
time (sec) |
N/A | 0.187 | 0.008 | 0.045 | 0.203 | 0.247 | 0.355 | 0.289 | 0.396 |
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 | 39 | 21 | 23 | 22 | 17 | 34 | 22 | 17 |
N.S. |
1 | 1.15 | 0.62 | 0.68 | 0.65 | 0.50 | 1.00 | 0.65 | 0.50 |
time (sec) |
N/A | 0.167 | 0.004 | 0.085 | 0.198 | 0.247 | 0.724 | 0.275 | 0.037 |
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 | 46 | 28 | 25 | 25 | 25 | 22 | 24 | 21 |
N.S. |
1 | 1.64 | 1.00 | 0.89 | 0.89 | 0.89 | 0.79 | 0.86 | 0.75 |
time (sec) |
N/A | 0.175 | 0.004 | 0.024 | 0.204 | 0.256 | 0.047 | 0.300 | 0.375 |
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 | 67 | 70 | 81 | 58 | 69 | 69 | 71 | 71 | 71 |
N.S. |
1 | 1.04 | 1.21 | 0.87 | 1.03 | 1.03 | 1.06 | 1.06 | 1.06 |
time (sec) |
N/A | 0.199 | 0.012 | 0.302 | 0.204 | 0.233 | 0.062 | 0.285 | 0.439 |
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 | 23 | 24 | 36 | 23 | 26 | 23 | 20 |
N.S. |
1 | 1.00 | 1.00 | 1.04 | 1.57 | 1.00 | 1.13 | 1.00 | 0.87 |
time (sec) |
N/A | 0.148 | 0.004 | 0.021 | 0.205 | 0.238 | 0.049 | 0.281 | 0.422 |
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 | 60 | 60 | 60 | 48 | 66 | 48 | 51 | 52 | 51 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 1.10 | 0.80 | 0.85 | 0.87 | 0.85 |
time (sec) |
N/A | 0.273 | 0.008 | 0.030 | 0.211 | 0.236 | 0.069 | 0.299 | 0.458 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 43 | 31 | 8 | 34 | 32 | 0 | 29 |
N.S. |
1 | 1.00 | 1.00 | 0.72 | 0.19 | 0.79 | 0.74 | 0.00 | 0.67 |
time (sec) |
N/A | 0.266 | 0.025 | 0.036 | 0.225 | 0.236 | 0.280 | 0.000 | 0.330 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 30 | 32 | 25 | 0 | 177 | 0 | 0 |
N.S. |
1 | 1.00 | 1.03 | 1.10 | 0.86 | 0.00 | 6.10 | 0.00 | 0.00 |
time (sec) |
N/A | 0.176 | 0.004 | 0.356 | 0.197 | 0.000 | 3.779 | 0.000 | 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 | 29 | 29 | 27 | 30 | 38 | 34 | 24 | 138 | 35 |
N.S. |
1 | 1.00 | 0.93 | 1.03 | 1.31 | 1.17 | 0.83 | 4.76 | 1.21 |
time (sec) |
N/A | 0.155 | 0.011 | 0.278 | 0.195 | 0.248 | 0.109 | 0.307 | 0.475 |
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 | 13 | 12 | 12 | 15 | 12 | 22 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.00 | 1.00 | 1.25 | 1.00 | 1.83 |
time (sec) |
N/A | 0.148 | 0.004 | 0.036 | 0.188 | 0.247 | 0.369 | 0.314 | 0.385 |
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 | 20 | 19 | 22 | 36 | 19 | 19 |
N.S. |
1 | 1.00 | 1.00 | 1.05 | 1.00 | 1.16 | 1.89 | 1.00 | 1.00 |
time (sec) |
N/A | 0.160 | 0.007 | 0.063 | 0.189 | 0.243 | 0.465 | 0.287 | 0.501 |
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 | 11 | 11 | 11 | 12 | 11 | 11 | 8 | 30 | 11 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 1.00 | 1.00 | 0.73 | 2.73 | 1.00 |
time (sec) |
N/A | 0.158 | 0.020 | 0.029 | 0.197 | 0.230 | 0.048 | 0.269 | 0.345 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 24 | 0 | 27 | 71 | 22 | 22 |
N.S. |
1 | 1.00 | 1.00 | 1.04 | 0.00 | 1.17 | 3.09 | 0.96 | 0.96 |
time (sec) |
N/A | 0.167 | 0.007 | 0.101 | 0.000 | 0.242 | 5.322 | 0.264 | 0.487 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 46 | 15 | 7 | 18 | 0 | 18 | 14 |
N.S. |
1 | 1.00 | 2.88 | 0.94 | 0.44 | 1.12 | 0.00 | 1.12 | 0.88 |
time (sec) |
N/A | 0.175 | 0.014 | 0.026 | 0.202 | 0.230 | 0.000 | 0.282 | 0.473 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 50 | 17 | 20 | 20 | 0 | 0 | 16 |
N.S. |
1 | 1.00 | 2.78 | 0.94 | 1.11 | 1.11 | 0.00 | 0.00 | 0.89 |
time (sec) |
N/A | 0.175 | 0.015 | 0.028 | 0.194 | 0.236 | 0.000 | 0.000 | 0.449 |
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 | 18 | 18 | 18 | 17 | 7 | 25 | 0 | 10 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.39 | 1.39 | 0.00 | 0.56 | 0.89 |
time (sec) |
N/A | 0.174 | 0.015 | 0.027 | 0.286 | 0.248 | 0.000 | 0.301 | 0.656 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 37 | 13 | 44 | 0 | 0 | 27 |
N.S. |
1 | 1.00 | 1.00 | 1.68 | 0.59 | 2.00 | 0.00 | 0.00 | 1.23 |
time (sec) |
N/A | 0.214 | 0.011 | 0.027 | 0.192 | 0.245 | 0.000 | 0.000 | 0.638 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 39 | 37 | 27 | 0 | 0 | 22 |
N.S. |
1 | 1.00 | 1.00 | 1.62 | 1.54 | 1.12 | 0.00 | 0.00 | 0.92 |
time (sec) |
N/A | 0.228 | 0.013 | 0.026 | 0.185 | 0.256 | 0.000 | 0.000 | 0.689 |
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 | 23 | 23 | 23 | 43 | 13 | 27 | 0 | 21 | 25 |
N.S. |
1 | 1.00 | 1.00 | 1.87 | 0.57 | 1.17 | 0.00 | 0.91 | 1.09 |
time (sec) |
N/A | 0.238 | 0.012 | 0.024 | 0.279 | 0.249 | 0.000 | 0.332 | 0.659 |
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 | 11 | 11 | 11 | 12 | 11 | 11 | 10 | 11 | 8 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 1.00 | 1.00 | 0.91 | 1.00 | 0.73 |
time (sec) |
N/A | 0.137 | 0.004 | 0.027 | 0.194 | 0.246 | 0.065 | 0.331 | 0.390 |
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 | 22 | 20 | 21 | 15 | 20 | 24 | 20 | 15 |
N.S. |
1 | 1.10 | 1.00 | 1.05 | 0.75 | 1.00 | 1.20 | 1.00 | 0.75 |
time (sec) |
N/A | 0.183 | 0.005 | 0.046 | 0.191 | 0.243 | 0.094 | 0.290 | 0.500 |
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 | 33 | 29 | 30 | 22 | 29 | 36 | 29 | 29 |
N.S. |
1 | 1.14 | 1.00 | 1.03 | 0.76 | 1.00 | 1.24 | 1.00 | 1.00 |
time (sec) |
N/A | 0.198 | 0.005 | 0.057 | 0.193 | 0.239 | 0.124 | 0.297 | 0.409 |
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 | 38 | 39 | 29 | 38 | 48 | 38 | 38 |
N.S. |
1 | 1.16 | 1.00 | 1.03 | 0.76 | 1.00 | 1.26 | 1.00 | 1.00 |
time (sec) |
N/A | 0.220 | 0.007 | 0.060 | 0.194 | 0.256 | 0.151 | 0.309 | 0.420 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | C | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 0 | 29 | 15 | 24 | 0 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 1.21 | 0.62 | 1.00 | 0.00 | 1.00 |
time (sec) |
N/A | 0.188 | 0.023 | 0.000 | 0.048 | 0.074 | 0.703 | 0.000 | 0.479 |
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 | 4 | 4 | 4 | 5 | 4 | 4 | 0 | 5 | 4 |
N.S. |
1 | 1.00 | 1.00 | 1.25 | 1.00 | 1.00 | 0.00 | 1.25 | 1.00 |
time (sec) |
N/A | 0.168 | 0.012 | 0.197 | 0.191 | 0.244 | 0.000 | 0.275 | 0.433 |
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 | 7 | 7 | 7 | 10 | 9 | 12 | 7 | 9 | 9 |
N.S. |
1 | 1.00 | 1.00 | 1.43 | 1.29 | 1.71 | 1.00 | 1.29 | 1.29 |
time (sec) |
N/A | 0.239 | 0.003 | 0.663 | 0.207 | 0.253 | 0.681 | 0.297 | 0.430 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 12 | 11 | 46 | 10 | 38 | 8 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 1.00 | 4.18 | 0.91 | 3.45 | 0.73 |
time (sec) |
N/A | 0.170 | 0.006 | 4.227 | 0.192 | 0.233 | 0.195 | 0.290 | 0.374 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 8 | 7 | 7 | 7 | 0 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.78 | 0.78 | 0.78 | 0.00 | 1.78 |
time (sec) |
N/A | 0.159 | 0.004 | 1.256 | 0.190 | 0.232 | 1.632 | 0.000 | 0.514 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 23 | 0 | 22 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.00 | 0.85 | 0.77 | 0.85 | 0.85 |
time (sec) |
N/A | 0.142 | 0.014 | 0.017 | 0.000 | 0.251 | 2.612 | 0.307 | 0.083 |
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 | 35 | 30 | 27 | 26 | 25 | 26 | 26 | 27 | 25 |
N.S. |
1 | 0.86 | 0.77 | 0.74 | 0.71 | 0.74 | 0.74 | 0.77 | 0.71 |
time (sec) |
N/A | 0.162 | 0.009 | 0.046 | 0.191 | 0.234 | 0.063 | 0.315 | 0.068 |
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 | 24 | 24 | 20 | 26 | 27 | 20 | 24 |
N.S. |
1 | 1.00 | 0.75 | 0.75 | 0.62 | 0.81 | 0.84 | 0.62 | 0.75 |
time (sec) |
N/A | 0.220 | 0.019 | 0.083 | 0.208 | 0.237 | 81.280 | 0.290 | 0.438 |
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 | 52 | 51 | 42 | 43 | 42 | 42 | 0 | 43 | 31 |
N.S. |
1 | 0.98 | 0.81 | 0.83 | 0.81 | 0.81 | 0.00 | 0.83 | 0.60 |
time (sec) |
N/A | 0.216 | 0.021 | 0.052 | 0.196 | 0.259 | 0.000 | 0.278 | 0.613 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 35 | 30 | 26 | 25 | 24 | 42 | 26 | 0 |
N.S. |
1 | 1.17 | 1.00 | 0.87 | 0.83 | 0.80 | 1.40 | 0.87 | 0.00 |
time (sec) |
N/A | 0.239 | 0.006 | 0.384 | 0.196 | 0.239 | 0.662 | 0.302 | 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 | 30 | 35 | 29 | 27 | 25 | 39 | 46 | 26 | 148 |
N.S. |
1 | 1.17 | 0.97 | 0.90 | 0.83 | 1.30 | 1.53 | 0.87 | 4.93 |
time (sec) |
N/A | 0.260 | 0.047 | 10.178 | 0.204 | 0.245 | 10.177 | 0.293 | 2.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | A | F | A | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 28 | 33 | 32 | 164 | 56 | 32 | 0 | 43 | 39 |
N.S. |
1 | 1.18 | 1.14 | 5.86 | 2.00 | 1.14 | 0.00 | 1.54 | 1.39 |
time (sec) |
N/A | 0.215 | 0.078 | 0.668 | 0.204 | 0.245 | 0.000 | 0.307 | 0.644 |
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 | 60 | 66 | 56 | 55 | 86 | 53 | 88 | 36 | 164 |
N.S. |
1 | 1.10 | 0.93 | 0.92 | 1.43 | 0.88 | 1.47 | 0.60 | 2.73 |
time (sec) |
N/A | 0.487 | 0.108 | 0.592 | 0.273 | 0.250 | 2.715 | 0.351 | 0.938 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 71 | 52 | 52 | 51 | 44 | 0 | 104 | 0 |
N.S. |
1 | 1.09 | 0.80 | 0.80 | 0.78 | 0.68 | 0.00 | 1.60 | 0.00 |
time (sec) |
N/A | 0.325 | 0.022 | 0.122 | 0.273 | 0.256 | 0.000 | 0.304 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 65 | 42 | 37 | 47 | 36 | 54 | 57 | 0 |
N.S. |
1 | 1.07 | 0.69 | 0.61 | 0.77 | 0.59 | 0.89 | 0.93 | 0.00 |
time (sec) |
N/A | 0.310 | 0.014 | 0.392 | 0.279 | 0.256 | 0.135 | 0.305 | 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 | 53 | 64 | 37 | 42 | 44 | 36 | 44 | 41 | 41 |
N.S. |
1 | 1.21 | 0.70 | 0.79 | 0.83 | 0.68 | 0.83 | 0.77 | 0.77 |
time (sec) |
N/A | 0.523 | 0.010 | 0.096 | 0.285 | 0.242 | 0.138 | 0.286 | 0.413 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 79 | 56 | 48 | 64 | 53 | 53 | 0 | 44 |
N.S. |
1 | 1.30 | 0.92 | 0.79 | 1.05 | 0.87 | 0.87 | 0.00 | 0.72 |
time (sec) |
N/A | 0.555 | 0.011 | 0.139 | 0.278 | 0.247 | 0.230 | 0.000 | 0.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 69 | 42 | 56 | 95 | 35 | 0 | 106 | 0 |
N.S. |
1 | 1.10 | 0.67 | 0.89 | 1.51 | 0.56 | 0.00 | 1.68 | 0.00 |
time (sec) |
N/A | 0.390 | 0.026 | 0.108 | 0.375 | 0.264 | 0.000 | 0.306 | 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 | 148 | 203 | 92 | 174 | 0 | 77 | 0 | 137 | 0 |
N.S. |
1 | 1.37 | 0.62 | 1.18 | 0.00 | 0.52 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.652 | 0.041 | 0.464 | 0.000 | 0.261 | 0.000 | 0.313 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 30 | 31 | 30 | 26 | 31 | 27 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.91 | 0.88 | 0.76 | 0.91 | 0.79 | 0.00 |
time (sec) |
N/A | 0.219 | 0.006 | 0.322 | 0.271 | 0.256 | 0.535 | 0.307 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 30 | 33 | 30 | 26 | 31 | 27 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.97 | 0.88 | 0.76 | 0.91 | 0.79 | 0.00 |
time (sec) |
N/A | 0.212 | 0.011 | 0.302 | 0.280 | 0.257 | 0.607 | 0.320 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 33 | 26 | 28 | 22 | 27 | 37 | 22 | 0 |
N.S. |
1 | 1.10 | 0.87 | 0.93 | 0.73 | 0.90 | 1.23 | 0.73 | 0.00 |
time (sec) |
N/A | 0.187 | 0.016 | 0.385 | 0.275 | 0.241 | 0.162 | 0.325 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 76 | 42 | 54 | 50 | 39 | 53 | 50 | 0 |
N.S. |
1 | 1.29 | 0.71 | 0.92 | 0.85 | 0.66 | 0.90 | 0.85 | 0.00 |
time (sec) |
N/A | 0.310 | 0.019 | 0.439 | 0.280 | 0.245 | 0.280 | 0.320 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 38 | 35 | 37 | 27 | 37 | 63 | 34 | 0 |
N.S. |
1 | 1.03 | 0.95 | 1.00 | 0.73 | 1.00 | 1.70 | 0.92 | 0.00 |
time (sec) |
N/A | 0.196 | 0.011 | 0.403 | 0.293 | 0.256 | 0.378 | 0.294 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 64 | 47 | 77 | 49 | 47 | 88 | 60 | 0 |
N.S. |
1 | 1.05 | 0.77 | 1.26 | 0.80 | 0.77 | 1.44 | 0.98 | 0.00 |
time (sec) |
N/A | 0.251 | 0.032 | 0.500 | 0.296 | 0.264 | 6.920 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 95 | 97 | 119 | 155 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.25 | 1.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.522 | 0.204 | 0.591 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 42 | 36 | 201 | 35 | 44 | 0 | 135 | 0 |
N.S. |
1 | 1.02 | 0.88 | 4.90 | 0.85 | 1.07 | 0.00 | 3.29 | 0.00 |
time (sec) |
N/A | 0.225 | 0.023 | 0.589 | 0.274 | 0.260 | 0.000 | 0.345 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 28 | 32 | 32 | 26 | 26 | 27 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.94 | 0.94 | 0.76 | 0.76 | 0.79 | 0.00 |
time (sec) |
N/A | 0.238 | 0.007 | 0.296 | 0.276 | 0.242 | 0.105 | 0.327 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 66 | 43 | 54 | 52 | 39 | 53 | 50 | 0 |
N.S. |
1 | 1.08 | 0.70 | 0.89 | 0.85 | 0.64 | 0.87 | 0.82 | 0.00 |
time (sec) |
N/A | 0.329 | 0.014 | 0.453 | 0.285 | 0.255 | 0.212 | 0.328 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 46 | 25 | 44 | 24 | 27 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.42 | 1.32 | 2.32 | 1.26 | 1.42 | 0.00 |
time (sec) |
N/A | 0.179 | 0.009 | 0.306 | 0.279 | 0.254 | 3.930 | 0.300 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 32 | 47 | 25 | 44 | 24 | 27 | 0 |
N.S. |
1 | 1.00 | 1.88 | 2.76 | 1.47 | 2.59 | 1.41 | 1.59 | 0.00 |
time (sec) |
N/A | 0.174 | 0.027 | 0.316 | 0.276 | 0.259 | 4.144 | 0.292 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 62 | 64 | 45 | 63 | 48 | 61 | 78 | 54 | 0 |
N.S. |
1 | 1.03 | 0.73 | 1.02 | 0.77 | 0.98 | 1.26 | 0.87 | 0.00 |
time (sec) |
N/A | 0.243 | 0.046 | 0.319 | 0.295 | 0.266 | 12.590 | 0.316 | 0.000 |
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 | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 40 | 102 | 45 | 57 | 37 | 40 | 0 |
N.S. |
1 | 1.00 | 1.11 | 2.83 | 1.25 | 1.58 | 1.03 | 1.11 | 0.00 |
time (sec) |
N/A | 0.220 | 0.034 | 0.632 | 0.279 | 0.263 | 6.021 | 0.295 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 112 | 430 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.81 | 6.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.395 | 0.156 | 0.691 | 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 | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 55 | 38 | 43 | 42 | 36 | 49 | 95 | 0 |
N.S. |
1 | 1.02 | 0.70 | 0.80 | 0.78 | 0.67 | 0.91 | 1.76 | 0.00 |
time (sec) |
N/A | 0.273 | 0.025 | 0.269 | 0.276 | 0.251 | 5.063 | 0.333 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 66 | 71 | 50 | 59 | 52 | 41 | 78 | 53 | 0 |
N.S. |
1 | 1.08 | 0.76 | 0.89 | 0.79 | 0.62 | 1.18 | 0.80 | 0.00 |
time (sec) |
N/A | 0.274 | 0.031 | 0.470 | 0.278 | 0.245 | 0.309 | 0.304 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 78 | 60 | 69 | 0 | 49 | 66 | 60 | 0 |
N.S. |
1 | 1.07 | 0.82 | 0.95 | 0.00 | 0.67 | 0.90 | 0.82 | 0.00 |
time (sec) |
N/A | 0.516 | 0.015 | 0.342 | 0.000 | 0.253 | 0.205 | 0.305 | 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 | 32 | 37 | 21 | 22 | 26 | 19 | 31 | 26 | 21 |
N.S. |
1 | 1.16 | 0.66 | 0.69 | 0.81 | 0.59 | 0.97 | 0.81 | 0.66 |
time (sec) |
N/A | 0.177 | 0.012 | 0.326 | 0.276 | 0.258 | 0.205 | 0.298 | 0.090 |
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 | 44 | 54 | 36 | 37 | 39 | 38 | 88 | 34 | 26 |
N.S. |
1 | 1.23 | 0.82 | 0.84 | 0.89 | 0.86 | 2.00 | 0.77 | 0.59 |
time (sec) |
N/A | 0.185 | 0.013 | 0.342 | 0.279 | 0.244 | 0.312 | 0.282 | 0.453 |
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 | 23 | 20 | 24 | 19 | 19 | 19 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 1.04 | 0.83 | 0.83 | 0.83 | 0.83 |
time (sec) |
N/A | 0.258 | 0.003 | 0.281 | 0.278 | 0.251 | 0.110 | 0.318 | 0.368 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 66 | 57 | 126 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.85 | 1.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.413 | 0.018 | 0.444 | 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(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 28 | 29 | 40 | 26 | 0 | 0 | 23 |
N.S. |
1 | 1.00 | 0.82 | 0.85 | 1.18 | 0.76 | 0.00 | 0.00 | 0.68 |
time (sec) |
N/A | 0.236 | 0.017 | 0.509 | 0.293 | 0.240 | 0.000 | 0.000 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 79 | 84 | 64 | 137 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.81 | 1.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.502 | 0.043 | 0.349 | 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 | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 99 | 70 | 147 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 0.79 | 1.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.078 | 0.137 | 0.539 | 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 | 22 | 39 | 22 | 23 | 21 | 26 | 19 | 25 | 22 |
N.S. |
1 | 1.77 | 1.00 | 1.05 | 0.95 | 1.18 | 0.86 | 1.14 | 1.00 |
time (sec) |
N/A | 0.251 | 0.003 | 0.080 | 0.300 | 0.243 | 0.109 | 0.285 | 0.070 |
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 | 31 | 34 | 59 | 30 | 31 | 26 | 34 | 31 | 30 |
N.S. |
1 | 1.10 | 1.90 | 0.97 | 1.00 | 0.84 | 1.10 | 1.00 | 0.97 |
time (sec) |
N/A | 0.185 | 0.006 | 0.076 | 0.294 | 0.245 | 0.216 | 0.276 | 0.378 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 81 | 79 | 71 | 0 | 0 | 0 | 53 |
N.S. |
1 | 1.00 | 1.29 | 1.25 | 1.13 | 0.00 | 0.00 | 0.00 | 0.84 |
time (sec) |
N/A | 0.247 | 0.004 | 0.355 | 0.323 | 0.000 | 0.000 | 0.000 | 0.513 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 33 | 28 | 25 | 27 | 29 | 22 | 0 | 24 |
N.S. |
1 | 1.18 | 1.00 | 0.89 | 0.96 | 1.04 | 0.79 | 0.00 | 0.86 |
time (sec) |
N/A | 0.280 | 0.006 | 0.342 | 0.281 | 0.258 | 0.154 | 0.000 | 0.089 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 44 | 38 | 34 | 36 | 38 | 32 | 0 | 31 |
N.S. |
1 | 1.13 | 0.97 | 0.87 | 0.92 | 0.97 | 0.82 | 0.00 | 0.79 |
time (sec) |
N/A | 0.342 | 0.011 | 0.090 | 0.270 | 0.242 | 0.185 | 0.000 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 60 | 79 | 56 | 57 | 71 | 54 | 61 | 0 | 51 |
N.S. |
1 | 1.32 | 0.93 | 0.95 | 1.18 | 0.90 | 1.02 | 0.00 | 0.85 |
time (sec) |
N/A | 0.326 | 0.011 | 0.123 | 0.285 | 0.255 | 0.236 | 0.000 | 0.117 |
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 | 79 | 92 | 47 | 78 | 94 | 51 | 0 | 0 | 56 |
N.S. |
1 | 1.16 | 0.59 | 0.99 | 1.19 | 0.65 | 0.00 | 0.00 | 0.71 |
time (sec) |
N/A | 0.428 | 0.034 | 0.555 | 0.277 | 0.238 | 0.000 | 0.000 | 0.404 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 107 | 91 | 116 | 194 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.85 | 1.08 | 1.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.493 | 0.163 | 0.658 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 106 | 128 | 86 | 274 | 0 | 51 | 0 | 0 | 0 |
N.S. |
1 | 1.21 | 0.81 | 2.58 | 0.00 | 0.48 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.631 | 0.232 | 0.504 | 0.000 | 0.253 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 41 | 42 | 48 | 85 | 27 | 23 | 0 | 75 | 0 |
N.S. |
1 | 1.02 | 1.17 | 2.07 | 0.66 | 0.56 | 0.00 | 1.83 | 0.00 |
time (sec) |
N/A | 0.206 | 0.029 | 0.485 | 0.281 | 0.258 | 0.000 | 0.338 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 65 | 66 | 67 | 127 | 48 | 75 | 0 | 58 | 0 |
N.S. |
1 | 1.02 | 1.03 | 1.95 | 0.74 | 1.15 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.189 | 0.078 | 0.698 | 0.249 | 0.271 | 0.000 | 0.347 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 51 | 52 | 61 | 134 | 46 | 68 | 0 | 53 | 0 |
N.S. |
1 | 1.02 | 1.20 | 2.63 | 0.90 | 1.33 | 0.00 | 1.04 | 0.00 |
time (sec) |
N/A | 0.217 | 0.070 | 0.493 | 0.243 | 0.253 | 0.000 | 0.333 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 82 | 65 | 75 | 101 | 0 | 69 | 0 | 64 | 0 |
N.S. |
1 | 0.79 | 0.91 | 1.23 | 0.00 | 0.84 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.264 | 0.177 | 0.361 | 0.000 | 0.266 | 0.000 | 0.324 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | C | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 175 | 198 | 383 | 246 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 2.19 | 1.41 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.906 | 1.248 | 0.832 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 35 | 56 | 17 | 16 | 0 | 50 | 0 |
N.S. |
1 | 1.00 | 1.52 | 2.43 | 0.74 | 0.70 | 0.00 | 2.17 | 0.00 |
time (sec) |
N/A | 0.194 | 0.026 | 0.352 | 0.295 | 0.248 | 0.000 | 0.316 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 70 | 89 | 79 | 204 | 123 | 81 | 0 | 105 | 0 |
N.S. |
1 | 1.27 | 1.13 | 2.91 | 1.76 | 1.16 | 0.00 | 1.50 | 0.00 |
time (sec) |
N/A | 0.276 | 0.086 | 0.721 | 0.553 | 0.255 | 0.000 | 0.348 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 74 | 89 | 76 | 102 | 58 | 37 | 0 | 0 | 0 |
N.S. |
1 | 1.20 | 1.03 | 1.38 | 0.78 | 0.50 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.490 | 0.040 | 0.329 | 0.286 | 0.247 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 133 | 194 | 84 | 114 | 0 | 59 | 0 | 0 | 0 |
N.S. |
1 | 1.46 | 0.63 | 0.86 | 0.00 | 0.44 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.703 | 0.176 | 0.529 | 0.000 | 0.251 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 110 | 135 | 92 | 147 | 93 | 57 | 0 | 0 | 0 |
N.S. |
1 | 1.23 | 0.84 | 1.34 | 0.85 | 0.52 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.589 | 0.052 | 0.540 | 0.528 | 0.259 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | F | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 136 | 99 | 86 | 103 | 51 | 0 | 94 | 0 |
N.S. |
1 | 2.47 | 1.80 | 1.56 | 1.87 | 0.93 | 0.00 | 1.71 | 0.00 |
time (sec) |
N/A | 0.776 | 0.107 | 0.078 | 0.294 | 0.267 | 0.000 | 0.417 | 0.000 |
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 | 40 | 40 | 71 | 66 | 89 | 58 | 0 | 49 | 36 |
N.S. |
1 | 1.00 | 1.78 | 1.65 | 2.22 | 1.45 | 0.00 | 1.22 | 0.90 |
time (sec) |
N/A | 0.223 | 0.054 | 0.079 | 0.283 | 0.261 | 0.000 | 0.320 | 0.426 |
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 | 39 | 45 | 35 | 32 | 31 | 50 | 153 | 32 | 31 |
N.S. |
1 | 1.15 | 0.90 | 0.82 | 0.79 | 1.28 | 3.92 | 0.82 | 0.79 |
time (sec) |
N/A | 0.207 | 0.021 | 0.356 | 0.289 | 0.248 | 0.235 | 0.296 | 0.408 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 122 | 122 | 105 | 102 | 118 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.84 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.413 | 0.019 | 0.391 | 0.322 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 0 | 0 | 14 | 27 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.50 | 0.96 | 0.00 | 0.00 |
time (sec) |
N/A | 0.222 | 0.012 | 0.000 | 0.000 | 0.256 | 0.434 | 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 | 31 | 31 | 31 | 26 | 25 | 25 | 26 | 25 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.81 | 0.81 | 0.84 | 0.81 | 0.81 |
time (sec) |
N/A | 0.195 | 0.017 | 0.294 | 0.199 | 0.250 | 0.566 | 0.278 | 0.637 |