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 | F | A | A | A | A | A | F(-2) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 27 | 36 | 24 | 35 | 32 | 0 | 69 |
N.S. |
1 | 0.00 | 0.84 | 1.12 | 0.75 | 1.09 | 1.00 | 0.00 | 2.16 |
time (sec) |
N/A | 0.000 | 0.202 | 0.152 | 0.243 | 0.262 | 0.232 | 0.000 | 8.393 |
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 | 22 | 22 | 22 | 20 | 21 | 43 | 19 | 21 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.95 | 1.95 | 0.86 | 0.95 | 0.95 |
time (sec) |
N/A | 2.119 | 0.387 | 0.620 | 0.285 | 0.263 | 0.112 | 0.284 | 8.244 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 29 | 25 | 32 | 35 | 39 | 39 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.86 | 1.10 | 1.21 | 1.34 | 1.34 | 0.00 |
time (sec) |
N/A | 0.000 | 0.111 | 5.194 | 0.345 | 0.272 | 0.159 | 0.334 | 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 | 16 | 17 | 17 | 16 | 15 | 17 | 14 | 17 | 15 |
N.S. |
1 | 1.06 | 1.06 | 1.00 | 0.94 | 1.06 | 0.88 | 1.06 | 0.94 |
time (sec) |
N/A | 0.203 | 0.008 | 0.361 | 0.196 | 0.245 | 0.057 | 0.258 | 8.119 |
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 | 22 | 20 | 19 | 18 | 18 | 19 | 19 | 18 |
N.S. |
1 | 0.88 | 0.80 | 0.76 | 0.72 | 0.72 | 0.76 | 0.76 | 0.72 |
time (sec) |
N/A | 0.171 | 0.003 | 0.071 | 0.189 | 0.255 | 0.037 | 0.266 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | C | A | B | F(-1) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 71 | 59 | 111 | 64 | 100 | 0 | 67 |
N.S. |
1 | 0.00 | 2.03 | 1.69 | 3.17 | 1.83 | 2.86 | 0.00 | 1.91 |
time (sec) |
N/A | 0.000 | 0.162 | 0.463 | 0.376 | 0.269 | 0.186 | 0.000 | 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 | 20 | 22 | 20 | 17 | 16 | 16 | 17 | 16 | 17 |
N.S. |
1 | 1.10 | 1.00 | 0.85 | 0.80 | 0.80 | 0.85 | 0.80 | 0.85 |
time (sec) |
N/A | 0.158 | 0.025 | 0.062 | 0.196 | 0.269 | 0.045 | 0.266 | 0.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 47 | 73 | 61 | 58 | 70 | 259 | 59 |
N.S. |
1 | 0.00 | 1.62 | 2.52 | 2.10 | 2.00 | 2.41 | 8.93 | 2.03 |
time (sec) |
N/A | 0.000 | 2.214 | 0.660 | 0.251 | 0.262 | 0.276 | 0.619 | 8.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 26 | 27 | 30 | 30 | 22 | 26 | 26 |
N.S. |
1 | 0.00 | 1.08 | 1.12 | 1.25 | 1.25 | 0.92 | 1.08 | 1.08 |
time (sec) |
N/A | 0.000 | 0.067 | 1.212 | 0.420 | 0.249 | 0.265 | 0.282 | 8.847 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 48 | 43 | 44 | 44 | 42 | 44 | 44 |
N.S. |
1 | 0.00 | 1.66 | 1.48 | 1.52 | 1.52 | 1.45 | 1.52 | 1.52 |
time (sec) |
N/A | 0.000 | 0.821 | 1.160 | 0.271 | 0.263 | 0.409 | 1.015 | 9.204 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 89 | 111 | 89 | 92 | 97 | 105 | 107 | 90 |
N.S. |
1 | 2.78 | 3.47 | 2.78 | 2.88 | 3.03 | 3.28 | 3.34 | 2.81 |
time (sec) |
N/A | 0.340 | 0.039 | 0.176 | 0.201 | 0.246 | 2.695 | 0.267 | 8.567 |
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 | 34 | 25 | 33 | 24 | 30 | 26 | 22 | 26 |
N.S. |
1 | 1.36 | 1.00 | 1.32 | 0.96 | 1.20 | 1.04 | 0.88 | 1.04 |
time (sec) |
N/A | 0.790 | 0.223 | 1.686 | 0.302 | 0.246 | 0.437 | 0.373 | 8.588 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 15 | 14 | 33 | 30 | 27 | 14 | 14 |
N.S. |
1 | 0.00 | 0.79 | 0.74 | 1.74 | 1.58 | 1.42 | 0.74 | 0.74 |
time (sec) |
N/A | 0.000 | 0.222 | 0.072 | 0.255 | 0.267 | 0.167 | 0.269 | 8.692 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | C | A | B | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 223 | 42 | 62 | 41 | 39 | 79 | 39 |
N.S. |
1 | 0.00 | 8.26 | 1.56 | 2.30 | 1.52 | 1.44 | 2.93 | 1.44 |
time (sec) |
N/A | 0.000 | 1.853 | 0.425 | 0.280 | 0.260 | 0.112 | 0.907 | 8.816 |
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 | 22 | 24 | 18 | 17 | 17 | 15 | 17 | 18 |
N.S. |
1 | 0.79 | 0.86 | 0.64 | 0.61 | 0.61 | 0.54 | 0.61 | 0.64 |
time (sec) |
N/A | 0.159 | 0.005 | 0.108 | 0.197 | 0.255 | 0.044 | 0.263 | 8.257 |
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 | 7 | 7 | 7 | 6 | 6 | 5 | 6 | 7 |
N.S. |
1 | 0.50 | 0.50 | 0.50 | 0.43 | 0.43 | 0.36 | 0.43 | 0.50 |
time (sec) |
N/A | 0.136 | 0.020 | 0.072 | 0.192 | 0.258 | 0.033 | 0.257 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | C | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 0 | 21 | 17 | 30 | 20 | 12 | 16 | 16 |
N.S. |
1 | 0.00 | 1.31 | 1.06 | 1.88 | 1.25 | 0.75 | 1.00 | 1.00 |
time (sec) |
N/A | 0.000 | 0.094 | 0.048 | 0.236 | 0.258 | 0.041 | 0.254 | 8.425 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 31 | 45 | 76 | 101 | 94 | 107 | 0 |
N.S. |
1 | 0.00 | 1.35 | 1.96 | 3.30 | 4.39 | 4.09 | 4.65 | 0.00 |
time (sec) |
N/A | 0.000 | 5.160 | 11.526 | 0.459 | 0.270 | 0.371 | 1.704 | 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 | 22 | 22 | 20 | 37 | 19 | 17 | 28 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 1.68 | 0.86 | 0.77 | 1.27 | 0.86 |
time (sec) |
N/A | 1.209 | 0.373 | 1.273 | 0.330 | 0.250 | 5.152 | 0.287 | 8.635 |
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 | 31 | 18 | 29 | 28 | 28 | 26 | 28 | 33 |
N.S. |
1 | 1.72 | 1.00 | 1.61 | 1.56 | 1.56 | 1.44 | 1.56 | 1.83 |
time (sec) |
N/A | 0.269 | 0.035 | 0.074 | 0.197 | 0.253 | 0.059 | 0.262 | 0.156 |
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 | 12 | 12 | 13 | 12 | 10 | 10 | 12 | 12 |
N.S. |
1 | 1.09 | 1.09 | 1.18 | 1.09 | 0.91 | 0.91 | 1.09 | 1.09 |
time (sec) |
N/A | 0.153 | 0.001 | 0.051 | 0.205 | 0.256 | 0.053 | 0.260 | 8.462 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 28 | 29 | 26 | 80 | 52 | 27 | 60 | 69 |
N.S. |
1 | 1.17 | 1.21 | 1.08 | 3.33 | 2.17 | 1.12 | 2.50 | 2.88 |
time (sec) |
N/A | 0.780 | 0.119 | 0.180 | 0.328 | 0.263 | 0.122 | 0.262 | 8.932 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 26 | 25 | 24 | 24 | 24 | 0 | 24 |
N.S. |
1 | 0.00 | 1.13 | 1.09 | 1.04 | 1.04 | 1.04 | 0.00 | 1.04 |
time (sec) |
N/A | 0.000 | 3.695 | 1.075 | 0.246 | 0.281 | 0.522 | 0.000 | 8.737 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 19 | 23 | 22 | 22 | 29 | 22 | 22 |
N.S. |
1 | 0.00 | 0.86 | 1.05 | 1.00 | 1.00 | 1.32 | 1.00 | 1.00 |
time (sec) |
N/A | 0.000 | 0.099 | 0.963 | 0.320 | 0.259 | 0.085 | 0.266 | 9.427 |
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 | 39 | 28 | 46 | 34 | 34 | 29 | 49 | 31 |
N.S. |
1 | 1.30 | 0.93 | 1.53 | 1.13 | 1.13 | 0.97 | 1.63 | 1.03 |
time (sec) |
N/A | 1.412 | 0.191 | 0.920 | 0.268 | 0.257 | 0.166 | 0.377 | 8.658 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 55 | 22 | 39 | 19 | 22 | 78 |
N.S. |
1 | 0.00 | 1.00 | 2.39 | 0.96 | 1.70 | 0.83 | 0.96 | 3.39 |
time (sec) |
N/A | 0.000 | 0.121 | 0.455 | 0.323 | 0.262 | 0.106 | 0.379 | 9.006 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 49 | 24 | 42 | 26 | 29 | 501 | 40 |
N.S. |
1 | 0.00 | 1.96 | 0.96 | 1.68 | 1.04 | 1.16 | 20.04 | 1.60 |
time (sec) |
N/A | 0.000 | 8.483 | 0.333 | 0.261 | 0.244 | 0.085 | 0.279 | 9.799 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 38 | 53 | 39 | 35 | 46 | 51 | 55 | 54 |
N.S. |
1 | 1.65 | 2.30 | 1.70 | 1.52 | 2.00 | 2.22 | 2.39 | 2.35 |
time (sec) |
N/A | 0.696 | 0.048 | 142.325 | 0.320 | 0.268 | 0.159 | 0.272 | 8.683 |
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 | 25 | 47 | 31 | 35 | 30 | 50 | 27 | 54 | 56 |
N.S. |
1 | 1.88 | 1.24 | 1.40 | 1.20 | 2.00 | 1.08 | 2.16 | 2.24 |
time (sec) |
N/A | 1.744 | 6.845 | 0.234 | 0.234 | 0.269 | 0.079 | 0.254 | 8.401 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 182 | 163 | 155 | 149 | 240 | 168 | 93 | 640 |
N.S. |
1 | 6.28 | 5.62 | 5.34 | 5.14 | 8.28 | 5.79 | 3.21 | 22.07 |
time (sec) |
N/A | 0.903 | 0.202 | 2.735 | 0.228 | 0.265 | 17.355 | 0.276 | 31.897 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 64 | 96 | 34 | 317 | 31 | 27 | 45 | 32 |
N.S. |
1 | 1.94 | 2.91 | 1.03 | 9.61 | 0.94 | 0.82 | 1.36 | 0.97 |
time (sec) |
N/A | 0.967 | 0.174 | 0.279 | 0.357 | 0.253 | 0.117 | 0.311 | 9.057 |
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 | 21 | 15 | 15 | 15 | 15 | 15 | 14 |
N.S. |
1 | 1.00 | 0.84 | 0.60 | 0.60 | 0.60 | 0.60 | 0.60 | 0.56 |
time (sec) |
N/A | 0.153 | 0.007 | 0.079 | 0.197 | 0.250 | 0.045 | 0.258 | 0.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | A | B | B | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 64 | 97 | 104 | 52 | 82 | 58 | 0 | 48 |
N.S. |
1 | 2.13 | 3.23 | 3.47 | 1.73 | 2.73 | 1.93 | 0.00 | 1.60 |
time (sec) |
N/A | 0.726 | 0.138 | 0.287 | 0.200 | 0.268 | 0.855 | 0.000 | 0.443 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 23 | 27 | 37 | 21 | 27 | 0 | 34 |
N.S. |
1 | 0.00 | 0.88 | 1.04 | 1.42 | 0.81 | 1.04 | 0.00 | 1.31 |
time (sec) |
N/A | 0.000 | 0.174 | 0.137 | 0.323 | 0.260 | 0.100 | 0.000 | 0.185 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 31 | 14 | 12 | 25 | 11 | 10 | 11 | 9 |
N.S. |
1 | 2.38 | 1.08 | 0.92 | 1.92 | 0.85 | 0.77 | 0.85 | 0.69 |
time (sec) |
N/A | 0.166 | 0.044 | 0.111 | 0.203 | 0.240 | 0.035 | 0.250 | 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 | 17 | 17 | 20 | 23 | 17 | 17 | 24 | 18 | 35 |
N.S. |
1 | 1.00 | 1.18 | 1.35 | 1.00 | 1.00 | 1.41 | 1.06 | 2.06 |
time (sec) |
N/A | 0.143 | 0.015 | 0.392 | 0.209 | 0.262 | 0.047 | 0.247 | 0.312 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | B | B | B | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 0 | 33 | 174 | 85 | 87 | 174 | 155 |
N.S. |
1 | 0.00 | 0.00 | 1.06 | 5.61 | 2.74 | 2.81 | 5.61 | 5.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.086 | 0.831 | 0.264 | 1.049 | 0.634 | 9.207 |
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 | 20 | 26 | 20 | 15 | 14 | 22 | 14 | 59 | 14 |
N.S. |
1 | 1.30 | 1.00 | 0.75 | 0.70 | 1.10 | 0.70 | 2.95 | 0.70 |
time (sec) |
N/A | 0.188 | 0.044 | 0.189 | 0.215 | 0.258 | 0.057 | 0.266 | 8.469 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 28 | 26 | 27 | 47 | 46 | 27 | 47 | 0 |
N.S. |
1 | 1.17 | 1.08 | 1.12 | 1.96 | 1.92 | 1.12 | 1.96 | 0.00 |
time (sec) |
N/A | 0.887 | 1.137 | 1.045 | 0.313 | 0.261 | 0.066 | 0.261 | 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 | 14 | 12 | 10 | 9 | 9 | 10 | 9 | 11 |
N.S. |
1 | 0.64 | 0.55 | 0.45 | 0.41 | 0.41 | 0.45 | 0.41 | 0.50 |
time (sec) |
N/A | 0.136 | 0.002 | 0.505 | 0.193 | 0.238 | 0.042 | 0.244 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 37 | 27 | 47 | 28 | 22 | 26 | 26 |
N.S. |
1 | 0.00 | 1.48 | 1.08 | 1.88 | 1.12 | 0.88 | 1.04 | 1.04 |
time (sec) |
N/A | 0.000 | 11.335 | 0.206 | 0.240 | 0.261 | 0.115 | 0.267 | 0.277 |
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 | 6 | 5 | 5 | 7 | 5 | 5 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.71 | 0.71 | 1.00 | 0.71 | 0.71 |
time (sec) |
N/A | 0.121 | 0.000 | 0.003 | 0.190 | 0.245 | 0.017 | 0.250 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 57 | 30 | 32 | 57 | 30 | 29 | 0 | 34 |
N.S. |
1 | 2.19 | 1.15 | 1.23 | 2.19 | 1.15 | 1.12 | 0.00 | 1.31 |
time (sec) |
N/A | 0.590 | 0.383 | 0.957 | 0.338 | 0.263 | 0.133 | 0.000 | 8.616 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 23 | 34 | 86 | 26 | 20 | 36 | 0 |
N.S. |
1 | 0.00 | 0.96 | 1.42 | 3.58 | 1.08 | 0.83 | 1.50 | 0.00 |
time (sec) |
N/A | 0.000 | 0.411 | 0.681 | 0.332 | 0.247 | 0.146 | 0.425 | 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 | 20 | 22 | 22 | 20 | 25 | 19 | 19 | 19 | 19 |
N.S. |
1 | 1.10 | 1.10 | 1.00 | 1.25 | 0.95 | 0.95 | 0.95 | 0.95 |
time (sec) |
N/A | 0.764 | 0.209 | 0.204 | 0.355 | 0.271 | 0.143 | 0.261 | 8.534 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 25 | 23 | 26 | 23 | 36 | 62 | 22 |
N.S. |
1 | 0.00 | 0.89 | 0.82 | 0.93 | 0.82 | 1.29 | 2.21 | 0.79 |
time (sec) |
N/A | 0.000 | 0.701 | 37.289 | 0.347 | 0.249 | 0.153 | 0.277 | 9.281 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 152 | 26 | 93 | 120 | 120 | 153 | 120 | 96 |
N.S. |
1 | 5.43 | 0.93 | 3.32 | 4.29 | 4.29 | 5.46 | 4.29 | 3.43 |
time (sec) |
N/A | 0.281 | 0.033 | 0.299 | 0.197 | 0.256 | 0.039 | 0.255 | 8.252 |
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 | 22 | 25 | 19 | 18 | 26 | 17 | 18 | 17 |
N.S. |
1 | 1.22 | 1.39 | 1.06 | 1.00 | 1.44 | 0.94 | 1.00 | 0.94 |
time (sec) |
N/A | 0.270 | 0.043 | 0.217 | 0.363 | 0.253 | 1.119 | 0.250 | 8.436 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | C | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 88 | 198 | 51 | 1477 | 193 | 291 | 415 | 586 |
N.S. |
1 | 2.75 | 6.19 | 1.59 | 46.16 | 6.03 | 9.09 | 12.97 | 18.31 |
time (sec) |
N/A | 1.792 | 0.601 | 0.831 | 0.327 | 0.288 | 1.396 | 0.276 | 0.361 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 27 | 23 | 24 | 28 | 22 | 28 | 22 |
N.S. |
1 | 0.00 | 0.87 | 0.74 | 0.77 | 0.90 | 0.71 | 0.90 | 0.71 |
time (sec) |
N/A | 0.000 | 0.260 | 0.066 | 0.199 | 0.256 | 0.079 | 0.255 | 8.425 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 31 | 31 | 26 | 32 | 29 | 26 | 30 | 26 |
N.S. |
1 | 1.24 | 1.24 | 1.04 | 1.28 | 1.16 | 1.04 | 1.20 | 1.04 |
time (sec) |
N/A | 0.258 | 0.055 | 0.234 | 0.228 | 0.250 | 0.064 | 0.254 | 0.089 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 20 | 23 | 23 | 0 | 51 | 22 | 77 | 22 |
N.S. |
1 | 0.95 | 1.10 | 1.10 | 0.00 | 2.43 | 1.05 | 3.67 | 1.05 |
time (sec) |
N/A | 0.595 | 0.029 | 0.226 | 0.000 | 0.254 | 0.099 | 0.252 | 0.127 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 120 | 23 | 23 | 51 | 39 | 20 | 47 | 22 |
N.S. |
1 | 3.87 | 0.74 | 0.74 | 1.65 | 1.26 | 0.65 | 1.52 | 0.71 |
time (sec) |
N/A | 1.590 | 1.345 | 0.140 | 0.316 | 0.267 | 0.110 | 0.252 | 8.897 |
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 | 32 | 21 | 22 | 16 | 21 | 27 | 16 | 18 |
N.S. |
1 | 1.52 | 1.00 | 1.05 | 0.76 | 1.00 | 1.29 | 0.76 | 0.86 |
time (sec) |
N/A | 0.302 | 0.208 | 0.227 | 0.324 | 0.250 | 0.110 | 0.284 | 0.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 38 | 48 | 43 | 43 | 41 | 38 | 60 |
N.S. |
1 | 0.00 | 1.46 | 1.85 | 1.65 | 1.65 | 1.58 | 1.46 | 2.31 |
time (sec) |
N/A | 0.000 | 1.325 | 1.927 | 0.237 | 0.257 | 0.181 | 0.264 | 8.750 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 26 | 31 | 0 | 50 | 31 | 70 | 27 |
N.S. |
1 | 0.00 | 0.96 | 1.15 | 0.00 | 1.85 | 1.15 | 2.59 | 1.00 |
time (sec) |
N/A | 0.000 | 0.176 | 0.847 | 0.000 | 0.255 | 0.241 | 0.266 | 9.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 28 | 26 | 37 | 55 | 20 | 37 | 31 |
N.S. |
1 | 0.00 | 0.85 | 0.79 | 1.12 | 1.67 | 0.61 | 1.12 | 0.94 |
time (sec) |
N/A | 0.000 | 4.148 | 0.331 | 0.236 | 0.278 | 0.071 | 0.269 | 8.931 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 46 | 20 | 26 | 22 | 48 | 26 | 19 |
N.S. |
1 | 0.00 | 1.92 | 0.83 | 1.08 | 0.92 | 2.00 | 1.08 | 0.79 |
time (sec) |
N/A | 0.000 | 2.451 | 0.296 | 0.324 | 0.260 | 0.122 | 0.258 | 0.352 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 0 | 13 | 13 | 12 | 12 | 14 | 12 | 12 |
N.S. |
1 | 0.00 | 0.93 | 0.93 | 0.86 | 0.86 | 1.00 | 0.86 | 0.86 |
time (sec) |
N/A | 0.000 | 0.168 | 0.326 | 0.235 | 0.252 | 0.161 | 0.287 | 9.181 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | C | F | A | B | F | F(-1) |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 77 | 266 | 0 | 66 | 100 | 0 | 0 |
N.S. |
1 | 0.00 | 2.20 | 7.60 | 0.00 | 1.89 | 2.86 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.372 | 0.041 | 0.000 | 0.265 | 0.661 | 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 | 29 | 25 | 23 | 22 | 21 | 21 | 22 | 21 | 21 |
N.S. |
1 | 0.86 | 0.79 | 0.76 | 0.72 | 0.72 | 0.76 | 0.72 | 0.72 |
time (sec) |
N/A | 0.154 | 0.005 | 0.069 | 0.202 | 0.286 | 0.056 | 0.251 | 8.794 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 24 | 67 | 98 | 43 | 22 | 1320 | 118 |
N.S. |
1 | 0.00 | 0.96 | 2.68 | 3.92 | 1.72 | 0.88 | 52.80 | 4.72 |
time (sec) |
N/A | 0.000 | 0.141 | 53.385 | 0.326 | 0.265 | 0.265 | 2.935 | 10.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 28 | 30 | 33 | 33 | 27 | 34 | 402 |
N.S. |
1 | 0.00 | 1.27 | 1.36 | 1.50 | 1.50 | 1.23 | 1.55 | 18.27 |
time (sec) |
N/A | 0.000 | 0.093 | 1.401 | 0.270 | 0.255 | 0.110 | 0.272 | 10.217 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | F(-1) | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 32 | 30 | 29 | 0 | 31 | 0 | 32 |
N.S. |
1 | 0.00 | 1.10 | 1.03 | 1.00 | 0.00 | 1.07 | 0.00 | 1.10 |
time (sec) |
N/A | 0.000 | 3.054 | 0.943 | 0.527 | 0.000 | 0.174 | 0.000 | 9.376 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 40 | 42 | 41 | 40 | 37 | 38 | 39 |
N.S. |
1 | 0.00 | 1.33 | 1.40 | 1.37 | 1.33 | 1.23 | 1.27 | 1.30 |
time (sec) |
N/A | 0.000 | 0.181 | 9.565 | 0.358 | 0.249 | 0.176 | 0.385 | 9.228 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 582 | 31 | 28 | 308 | 34 | 27 | 38 | 27 |
N.S. |
1 | 18.19 | 0.97 | 0.88 | 9.62 | 1.06 | 0.84 | 1.19 | 0.84 |
time (sec) |
N/A | 2.426 | 0.227 | 0.466 | 0.337 | 0.262 | 0.124 | 0.264 | 9.275 |
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 | 27 | 25 | 17 | 18 | 19 | 14 | 18 | 18 |
N.S. |
1 | 1.08 | 1.00 | 0.68 | 0.72 | 0.76 | 0.56 | 0.72 | 0.72 |
time (sec) |
N/A | 0.379 | 0.082 | 0.168 | 0.229 | 0.244 | 0.098 | 0.246 | 9.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 15 | 16 | 25 | 20 | 20 | 0 | 20 |
N.S. |
1 | 0.00 | 0.83 | 0.89 | 1.39 | 1.11 | 1.11 | 0.00 | 1.11 |
time (sec) |
N/A | 0.000 | 0.096 | 0.164 | 0.282 | 0.245 | 0.114 | 0.000 | 9.249 |
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 | 45 | 25 | 32 | 39 | 33 | 32 | 33 | 37 |
N.S. |
1 | 1.80 | 1.00 | 1.28 | 1.56 | 1.32 | 1.28 | 1.32 | 1.48 |
time (sec) |
N/A | 0.188 | 0.159 | 0.101 | 0.198 | 0.252 | 0.091 | 0.255 | 9.354 |
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 | 28 | 17 | 15 | 15 | 15 | 19 | 15 | 15 |
N.S. |
1 | 1.40 | 0.85 | 0.75 | 0.75 | 0.75 | 0.95 | 0.75 | 0.75 |
time (sec) |
N/A | 0.184 | 0.032 | 0.051 | 0.192 | 0.250 | 0.048 | 0.259 | 0.096 |
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 | 38 | 40 | 35 | 47 | 39 | 48 | 48 | 39 | 0 |
N.S. |
1 | 1.05 | 0.92 | 1.24 | 1.03 | 1.26 | 1.26 | 1.03 | 0.00 |
time (sec) |
N/A | 3.448 | 0.270 | 0.511 | 0.296 | 0.261 | 0.418 | 0.294 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 24 | 19 | 19 | 20 | 19 | 19 | 18 |
N.S. |
1 | 0.00 | 1.00 | 0.79 | 0.79 | 0.83 | 0.79 | 0.79 | 0.75 |
time (sec) |
N/A | 0.000 | 0.157 | 0.249 | 0.272 | 0.249 | 0.243 | 0.285 | 9.824 |
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 | 24 | 14 | 14 | 22 | 21 | 20 | 22 | 16 |
N.S. |
1 | 1.20 | 0.70 | 0.70 | 1.10 | 1.05 | 1.00 | 1.10 | 0.80 |
time (sec) |
N/A | 0.160 | 0.010 | 0.138 | 0.210 | 0.243 | 0.045 | 0.251 | 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 | 18 | 19 | 24 | 19 | 18 | 18 | 15 | 18 | 18 |
N.S. |
1 | 1.06 | 1.33 | 1.06 | 1.00 | 1.00 | 0.83 | 1.00 | 1.00 |
time (sec) |
N/A | 0.698 | 0.715 | 0.093 | 0.223 | 0.244 | 0.068 | 0.251 | 0.169 |
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 | 24 | 19 | 17 | 21 | 21 | 14 | 21 | 16 |
N.S. |
1 | 1.33 | 1.06 | 0.94 | 1.17 | 1.17 | 0.78 | 1.17 | 0.89 |
time (sec) |
N/A | 0.149 | 0.007 | 0.077 | 0.226 | 0.234 | 0.019 | 0.253 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 20 | 11 | 10 | 71 | 9 | 10 | 9 | 9 |
N.S. |
1 | 1.54 | 0.85 | 0.77 | 5.46 | 0.69 | 0.77 | 0.69 | 0.69 |
time (sec) |
N/A | 0.388 | 0.077 | 0.318 | 0.368 | 0.251 | 0.058 | 0.262 | 9.244 |
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 | 12 | 21 | 21 | 20 | 19 | 19 | 17 | 21 | 19 |
N.S. |
1 | 1.75 | 1.75 | 1.67 | 1.58 | 1.58 | 1.42 | 1.75 | 1.58 |
time (sec) |
N/A | 0.325 | 0.010 | 0.047 | 0.205 | 0.250 | 0.065 | 0.253 | 0.150 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 87 | 20 | 57 | 87 | 70 | 85 | 107 | 21 |
N.S. |
1 | 4.35 | 1.00 | 2.85 | 4.35 | 3.50 | 4.25 | 5.35 | 1.05 |
time (sec) |
N/A | 1.047 | 0.313 | 0.272 | 0.346 | 0.256 | 0.219 | 0.256 | 9.314 |
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 | 23 | 23 | 24 | 23 | 34 | 19 | 24 | 23 |
N.S. |
1 | 0.82 | 0.82 | 0.86 | 0.82 | 1.21 | 0.68 | 0.86 | 0.82 |
time (sec) |
N/A | 0.262 | 0.014 | 0.076 | 0.199 | 0.237 | 0.045 | 0.248 | 0.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | B | A | A | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 0 | 45 | 64 | 47 | 48 | 65 | 44688 |
N.S. |
1 | 0.00 | 0.00 | 1.32 | 1.88 | 1.38 | 1.41 | 1.91 | 1314.35 |
time (sec) |
N/A | 0.000 | 0.000 | 8.183 | 0.342 | 0.252 | 0.141 | 0.293 | 13.535 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 29 | 38 | 96 | 41 | 24 | 40 | 54 |
N.S. |
1 | 0.00 | 1.00 | 1.31 | 3.31 | 1.41 | 0.83 | 1.38 | 1.86 |
time (sec) |
N/A | 0.000 | 0.087 | 2.059 | 0.323 | 0.256 | 0.179 | 0.278 | 9.836 |
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 | 31 | 30 | 27 | 26 | 26 | 27 | 26 | 28 |
N.S. |
1 | 1.07 | 1.03 | 0.93 | 0.90 | 0.90 | 0.93 | 0.90 | 0.97 |
time (sec) |
N/A | 0.317 | 1.013 | 0.122 | 0.292 | 0.243 | 0.131 | 0.287 | 9.361 |
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 | 10 | 10 | 12 | 11 | 10 | 10 | 8 | 11 | 10 |
N.S. |
1 | 1.00 | 1.20 | 1.10 | 1.00 | 1.00 | 0.80 | 1.10 | 1.00 |
time (sec) |
N/A | 0.150 | 0.005 | 0.317 | 0.217 | 0.237 | 0.033 | 0.262 | 0.039 |
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 | 24 | 26 | 19 | 20 | 26 | 17 | 20 | 20 |
N.S. |
1 | 0.73 | 0.79 | 0.58 | 0.61 | 0.79 | 0.52 | 0.61 | 0.61 |
time (sec) |
N/A | 0.247 | 0.013 | 0.044 | 0.199 | 0.240 | 0.039 | 0.254 | 9.157 |
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 | 26 | 52 | 24 | 27 | 37 | 26 | 24 | 54 | 29 |
N.S. |
1 | 2.00 | 0.92 | 1.04 | 1.42 | 1.00 | 0.92 | 2.08 | 1.12 |
time (sec) |
N/A | 0.194 | 0.086 | 0.198 | 0.200 | 0.246 | 0.071 | 0.248 | 0.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 86 | 101 | 74 | 78 | 80 | 117 | 81 | 73 |
N.S. |
1 | 3.44 | 4.04 | 2.96 | 3.12 | 3.20 | 4.68 | 3.24 | 2.92 |
time (sec) |
N/A | 0.258 | 0.259 | 0.134 | 0.196 | 0.255 | 0.139 | 0.252 | 9.470 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 135 | 31 | 27 | 89 | 37 | 24 | 41 | 26 |
N.S. |
1 | 4.82 | 1.11 | 0.96 | 3.18 | 1.32 | 0.86 | 1.46 | 0.93 |
time (sec) |
N/A | 1.113 | 0.041 | 0.074 | 0.241 | 0.247 | 0.097 | 0.267 | 9.596 |
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 | 31 | 27 | 25 | 27 | 26 | 27 | 35 | 25 |
N.S. |
1 | 1.15 | 1.00 | 0.93 | 1.00 | 0.96 | 1.00 | 1.30 | 0.93 |
time (sec) |
N/A | 0.556 | 0.087 | 6.767 | 0.400 | 0.247 | 112.832 | 0.792 | 9.649 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 20 | 23 | 18 | 22 | 19 | 18 | 19 |
N.S. |
1 | 0.00 | 0.80 | 0.92 | 0.72 | 0.88 | 0.76 | 0.72 | 0.76 |
time (sec) |
N/A | 0.000 | 0.437 | 0.358 | 0.320 | 0.252 | 0.145 | 0.324 | 9.323 |
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 | 12 | 12 | 13 | 12 | 12 | 10 | 12 | 12 |
N.S. |
1 | 0.67 | 0.67 | 0.72 | 0.67 | 0.67 | 0.56 | 0.67 | 0.67 |
time (sec) |
N/A | 0.144 | 0.000 | 0.012 | 0.213 | 0.231 | 0.017 | 0.260 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 29 | 29 | 27 | 39 | 33 | 26 | 33 | 26 |
N.S. |
1 | 0.91 | 0.91 | 0.84 | 1.22 | 1.03 | 0.81 | 1.03 | 0.81 |
time (sec) |
N/A | 0.514 | 0.193 | 0.094 | 0.233 | 0.257 | 0.085 | 0.255 | 9.064 |
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 | 21 | 15 | 15 | 14 | 18 | 15 | 18 | 14 |
N.S. |
1 | 1.24 | 0.88 | 0.88 | 0.82 | 1.06 | 0.88 | 1.06 | 0.82 |
time (sec) |
N/A | 0.235 | 0.014 | 0.292 | 0.280 | 0.238 | 0.075 | 0.251 | 9.343 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 32 | 32 | 301 | 41 | 39 | 76 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 9.41 | 1.28 | 1.22 | 2.38 | 0.00 |
time (sec) |
N/A | 0.000 | 0.094 | 2.717 | 2.230 | 0.256 | 5.223 | 0.265 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 79 | 19 | 18 | 21 | 35 | 29 | 27 | 17 |
N.S. |
1 | 3.76 | 0.90 | 0.86 | 1.00 | 1.67 | 1.38 | 1.29 | 0.81 |
time (sec) |
N/A | 0.471 | 0.172 | 0.997 | 0.326 | 0.241 | 0.073 | 0.252 | 8.954 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 128 | 23 | 23 | 141 | 33 | 29 | 0 | 0 |
N.S. |
1 | 4.92 | 0.88 | 0.88 | 5.42 | 1.27 | 1.12 | 0.00 | 0.00 |
time (sec) |
N/A | 13.540 | 0.208 | 24.064 | 1.181 | 0.253 | 0.399 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 26 | 22 | 75 | 21 | 15 | 0 | 21 |
N.S. |
1 | 0.00 | 1.08 | 0.92 | 3.12 | 0.88 | 0.62 | 0.00 | 0.88 |
time (sec) |
N/A | 0.000 | 0.588 | 1.003 | 0.459 | 0.247 | 0.170 | 0.000 | 9.473 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F(-2) | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 34 | 32 | 0 | 31 | 42 | 35 | 29 |
N.S. |
1 | 0.00 | 1.10 | 1.03 | 0.00 | 1.00 | 1.35 | 1.13 | 0.94 |
time (sec) |
N/A | 0.000 | 0.816 | 16.277 | 0.000 | 0.253 | 0.271 | 0.273 | 9.774 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 22 | 21 | 21 | 21 | 17 | 21 | 18 |
N.S. |
1 | 0.00 | 1.00 | 0.95 | 0.95 | 0.95 | 0.77 | 0.95 | 0.82 |
time (sec) |
N/A | 0.000 | 0.221 | 1.067 | 0.312 | 0.240 | 0.061 | 0.259 | 9.302 |
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 | 29 | 40 | 38 | 38 | 47 | 48 | 37 | 77 | 0 |
N.S. |
1 | 1.38 | 1.31 | 1.31 | 1.62 | 1.66 | 1.28 | 2.66 | 0.00 |
time (sec) |
N/A | 1.291 | 0.108 | 1.436 | 0.252 | 0.258 | 0.246 | 0.307 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 45 | 35 | 33 | 109 | 39 | 37 | 37 | 23 |
N.S. |
1 | 2.05 | 1.59 | 1.50 | 4.95 | 1.77 | 1.68 | 1.68 | 1.05 |
time (sec) |
N/A | 0.655 | 0.064 | 0.140 | 0.214 | 0.244 | 0.111 | 0.267 | 8.994 |