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 | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 17 | 15 | 18 | 17 | 17 | 15 | 20 | 15 |
N.S. |
1 | 0.85 | 0.75 | 0.90 | 0.85 | 0.85 | 0.75 | 1.00 | 0.75 |
time (sec) |
N/A | 0.028 | 0.007 | 0.033 | 0.192 | 0.243 | 0.051 | 0.272 | 0.104 |
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 | 20 | 20 | 20 | 16 | 148 | 48 | 17 | 48 | 36 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 7.40 | 2.40 | 0.85 | 2.40 | 1.80 |
time (sec) |
N/A | 0.238 | 0.200 | 8.788 | 0.353 | 0.249 | 0.262 | 0.379 | 14.780 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 19 | 18 | 47 | 20 | 0 | 19 |
N.S. |
1 | 0.00 | 1.00 | 0.83 | 0.78 | 2.04 | 0.87 | 0.00 | 0.83 |
time (sec) |
N/A | 0.000 | 0.853 | 0.573 | 0.423 | 0.253 | 0.306 | 0.000 | 14.427 |
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 | 33 | 37 | 43 | 34 | 35 | 35 | 36 | 38 | 33 |
N.S. |
1 | 1.12 | 1.30 | 1.03 | 1.06 | 1.06 | 1.09 | 1.15 | 1.00 |
time (sec) |
N/A | 0.094 | 0.019 | 0.095 | 0.228 | 0.247 | 0.091 | 0.274 | 0.142 |
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 | 33 | 34 | 30 | 35 | 35 | 20 | 35 | 26 |
N.S. |
1 | 1.18 | 1.21 | 1.07 | 1.25 | 1.25 | 0.71 | 1.25 | 0.93 |
time (sec) |
N/A | 0.031 | 0.059 | 0.264 | 0.202 | 0.252 | 0.102 | 0.286 | 13.905 |
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 | 20 | 19 | 14 | 16 | 13 | 10 | 16 | 13 |
N.S. |
1 | 1.05 | 1.00 | 0.74 | 0.84 | 0.68 | 0.53 | 0.84 | 0.68 |
time (sec) |
N/A | 0.237 | 1.114 | 0.284 | 0.261 | 0.262 | 0.043 | 0.287 | 0.133 |
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 | 30 | 0 | 24 | 32 | 396 | 30 | 27 | 30 | 53 |
N.S. |
1 | 0.00 | 0.80 | 1.07 | 13.20 | 1.00 | 0.90 | 1.00 | 1.77 |
time (sec) |
N/A | 0.000 | 0.113 | 1.209 | 0.397 | 0.253 | 0.211 | 0.414 | 14.713 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 47 | 65 | 41 | 40 | 48 | 44 | 50 | 30 |
N.S. |
1 | 1.74 | 2.41 | 1.52 | 1.48 | 1.78 | 1.63 | 1.85 | 1.11 |
time (sec) |
N/A | 0.080 | 0.034 | 0.258 | 0.199 | 0.269 | 0.082 | 0.279 | 14.360 |
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 | 19 | 18 | 18 | 20 | 18 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.90 | 0.90 | 1.00 | 0.90 | 0.90 |
time (sec) |
N/A | 0.087 | 0.073 | 0.145 | 0.271 | 0.256 | 0.071 | 0.274 | 14.478 |
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 | 13 | 13 | 13 | 12 | 12 | 12 | 13 | 12 |
N.S. |
1 | 0.54 | 0.54 | 0.54 | 0.50 | 0.50 | 0.50 | 0.54 | 0.50 |
time (sec) |
N/A | 0.006 | 0.005 | 0.753 | 0.205 | 0.265 | 0.059 | 0.268 | 0.067 |
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 | 19 | 19 | 18 | 18 | 14 | 18 | 38 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 0.95 | 0.95 | 0.74 | 0.95 | 2.00 |
time (sec) |
N/A | 0.000 | 0.150 | 4.749 | 0.243 | 0.256 | 0.055 | 0.269 | 14.480 |
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 | 20 | 0 | 20 | 18 | 0 | 17 | 17 | 35 | 17 |
N.S. |
1 | 0.00 | 1.00 | 0.90 | 0.00 | 0.85 | 0.85 | 1.75 | 0.85 |
time (sec) |
N/A | 0.000 | 1.131 | 1.717 | 0.000 | 0.253 | 0.144 | 0.300 | 14.478 |
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 | 15 | 14 | 13 | 20 | 12 | 13 | 13 |
N.S. |
1 | 1.20 | 0.75 | 0.70 | 0.65 | 1.00 | 0.60 | 0.65 | 0.65 |
time (sec) |
N/A | 0.009 | 0.009 | 0.102 | 0.206 | 0.245 | 0.049 | 0.268 | 0.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | B | B | B | B | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 0 | 51 | 75 | 62 | 54 | 62 | 73 |
N.S. |
1 | 0.00 | 0.00 | 2.12 | 3.12 | 2.58 | 2.25 | 2.58 | 3.04 |
time (sec) |
N/A | 0.000 | 0.000 | 5.946 | 0.409 | 0.301 | 0.311 | 0.293 | 14.329 |
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 | 21 | 27 | 21 | 14 | 18 | 18 | 24 | 0 | 18 |
N.S. |
1 | 1.29 | 1.00 | 0.67 | 0.86 | 0.86 | 1.14 | 0.00 | 0.86 |
time (sec) |
N/A | 0.105 | 0.419 | 0.437 | 0.293 | 0.238 | 0.111 | 0.000 | 0.160 |
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 | 10 | 10 | 10 | 9 | 9 | 8 | 9 | 9 |
N.S. |
1 | 0.83 | 0.83 | 0.83 | 0.75 | 0.75 | 0.67 | 0.75 | 0.75 |
time (sec) |
N/A | 0.001 | 0.000 | 0.041 | 0.182 | 0.245 | 0.015 | 0.272 | 0.003 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 192 | 21 | 43 | 0 | 53 | 27 | 32 | 19 |
N.S. |
1 | 7.68 | 0.84 | 1.72 | 0.00 | 2.12 | 1.08 | 1.28 | 0.76 |
time (sec) |
N/A | 0.265 | 0.360 | 0.377 | 0.000 | 0.246 | 0.102 | 0.277 | 0.534 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 19 | 19 | 42 | 3532 | 40 | 41 | 40 | 0 |
N.S. |
1 | 0.68 | 0.68 | 1.50 | 126.14 | 1.43 | 1.46 | 1.43 | 0.00 |
time (sec) |
N/A | 0.129 | 0.042 | 0.847 | 0.317 | 0.269 | 0.098 | 0.325 | 0.000 |
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 | 19 | 0 | 21 | 19 | 39 | 17 | 20 | 17 | 17 |
N.S. |
1 | 0.00 | 1.11 | 1.00 | 2.05 | 0.89 | 1.05 | 0.89 | 0.89 |
time (sec) |
N/A | 0.000 | 0.546 | 1.347 | 0.317 | 0.246 | 0.097 | 0.275 | 14.441 |
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 | 23 | 26 | 23 | 28 | 28 | 22 | 28 | 21 |
N.S. |
1 | 0.85 | 0.96 | 0.85 | 1.04 | 1.04 | 0.81 | 1.04 | 0.78 |
time (sec) |
N/A | 0.006 | 0.000 | 0.088 | 0.181 | 0.239 | 0.022 | 0.279 | 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 | 30 | 26 | 25 | 21 | 20 | 42 | 19 | 20 | 20 |
N.S. |
1 | 0.87 | 0.83 | 0.70 | 0.67 | 1.40 | 0.63 | 0.67 | 0.67 |
time (sec) |
N/A | 0.242 | 0.200 | 0.312 | 0.400 | 0.249 | 0.206 | 0.313 | 15.393 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | B | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 40 | 40 | 59 | 40 | 54 | 35 | 0 |
N.S. |
1 | 0.00 | 1.29 | 1.29 | 1.90 | 1.29 | 1.74 | 1.13 | 0.00 |
time (sec) |
N/A | 0.000 | 0.424 | 2.037 | 0.414 | 0.261 | 6.474 | 0.290 | 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 | 12 | 11 | 10 | 9 | 9 | 8 | 9 | 9 |
N.S. |
1 | 0.60 | 0.55 | 0.50 | 0.45 | 0.45 | 0.40 | 0.45 | 0.45 |
time (sec) |
N/A | 0.001 | 0.003 | 0.050 | 0.188 | 0.246 | 0.031 | 0.270 | 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 | 14 | 15 | 14 | 14 | 13 | 13 | 10 | 13 | 13 |
N.S. |
1 | 1.07 | 1.00 | 1.00 | 0.93 | 0.93 | 0.71 | 0.93 | 0.93 |
time (sec) |
N/A | 0.006 | 0.005 | 0.092 | 0.181 | 0.262 | 0.050 | 0.274 | 14.233 |
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 | 15 | 15 | 14 | 13 | 16 | 12 | 13 | 13 |
N.S. |
1 | 0.94 | 0.94 | 0.88 | 0.81 | 1.00 | 0.75 | 0.81 | 0.81 |
time (sec) |
N/A | 0.011 | 0.005 | 0.275 | 0.182 | 0.264 | 0.046 | 0.273 | 14.432 |
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 | 27 | 26 | 27 | 27 | 29 | 24 | 29 | 28 |
N.S. |
1 | 0.96 | 0.93 | 0.96 | 0.96 | 1.04 | 0.86 | 1.04 | 1.00 |
time (sec) |
N/A | 0.350 | 0.070 | 1.832 | 0.317 | 0.257 | 0.092 | 0.293 | 15.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | F(-1) | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 20 | 16 | 15 | 0 | 19 | 15 | 18 |
N.S. |
1 | 0.00 | 0.95 | 0.76 | 0.71 | 0.00 | 0.90 | 0.71 | 0.86 |
time (sec) |
N/A | 0.000 | 0.658 | 0.406 | 0.407 | 0.000 | 0.855 | 0.297 | 14.445 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | B | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 60 | 55 | 73 | 174 | 60 | 47 | 75 |
N.S. |
1 | 0.00 | 1.71 | 1.57 | 2.09 | 4.97 | 1.71 | 1.34 | 2.14 |
time (sec) |
N/A | 0.000 | 0.398 | 1.109 | 1.833 | 0.305 | 0.220 | 0.386 | 15.993 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | C | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 45 | 61 | 36 | 104 | 41 | 48 | 100 | 24 |
N.S. |
1 | 2.14 | 2.90 | 1.71 | 4.95 | 1.95 | 2.29 | 4.76 | 1.14 |
time (sec) |
N/A | 0.170 | 0.065 | 0.359 | 0.309 | 0.292 | 0.119 | 0.303 | 0.284 |
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 | 7 | 7 | 6 | 5 | 5 | 3 | 5 | 5 |
N.S. |
1 | 0.44 | 0.44 | 0.38 | 0.31 | 0.31 | 0.19 | 0.31 | 0.31 |
time (sec) |
N/A | 0.000 | 0.000 | 0.010 | 0.186 | 0.256 | 0.020 | 0.267 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 19 | 19 | 18 | 18 | 0 | 0 | 18 |
N.S. |
1 | 0.00 | 0.86 | 0.86 | 0.82 | 0.82 | 0.00 | 0.00 | 0.82 |
time (sec) |
N/A | 0.000 | 0.109 | 14.794 | 0.286 | 0.259 | 0.000 | 0.000 | 13.930 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | F(-2) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 38 | 27 | 82 | 28 | 26 | 0 | 59 |
N.S. |
1 | 0.00 | 1.15 | 0.82 | 2.48 | 0.85 | 0.79 | 0.00 | 1.79 |
time (sec) |
N/A | 0.000 | 0.358 | 203.392 | 0.353 | 0.275 | 1.184 | 0.000 | 14.511 |
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 | 17 | 16 | 23 | 19 | 25 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.74 | 0.70 | 1.00 | 0.83 | 1.09 | 0.91 |
time (sec) |
N/A | 0.016 | 0.013 | 0.037 | 0.179 | 0.267 | 0.061 | 0.268 | 13.744 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 93 | 43 | 145 | 157 | 170 | 191 | 0 |
N.S. |
1 | 0.00 | 2.74 | 1.26 | 4.26 | 4.62 | 5.00 | 5.62 | 0.00 |
time (sec) |
N/A | 0.000 | 3.328 | 1.217 | 1.117 | 0.286 | 0.632 | 0.642 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | B | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 259 | 20 | 22 | 34 | 33 | 34 | 0 | 21 |
N.S. |
1 | 11.77 | 0.91 | 1.00 | 1.55 | 1.50 | 1.55 | 0.00 | 0.95 |
time (sec) |
N/A | 0.772 | 0.070 | 0.402 | 0.188 | 0.267 | 1.446 | 0.000 | 0.251 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 29 | 26 | 55 | 54 | 24 | 0 | 47 |
N.S. |
1 | 0.00 | 1.04 | 0.93 | 1.96 | 1.93 | 0.86 | 0.00 | 1.68 |
time (sec) |
N/A | 0.000 | 1.444 | 0.910 | 0.437 | 0.266 | 0.148 | 0.000 | 14.102 |
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 | 24 | 90 | 23 | 39 | 493 | 26 | 39 | 40 | 27 |
N.S. |
1 | 3.75 | 0.96 | 1.62 | 20.54 | 1.08 | 1.62 | 1.67 | 1.12 |
time (sec) |
N/A | 0.292 | 0.111 | 1.277 | 0.357 | 0.270 | 0.196 | 0.318 | 0.573 |
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 | 22 | 22 | 19 | 18 | 18 | 19 | 18 | 23 |
N.S. |
1 | 0.96 | 0.96 | 0.83 | 0.78 | 0.78 | 0.83 | 0.78 | 1.00 |
time (sec) |
N/A | 0.056 | 0.158 | 0.148 | 0.195 | 0.264 | 0.094 | 0.290 | 13.737 |
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 | 18 | 17 | 17 | 18 | 18 | 17 | 19 | 16 |
N.S. |
1 | 0.95 | 0.89 | 0.89 | 0.95 | 0.95 | 0.89 | 1.00 | 0.84 |
time (sec) |
N/A | 0.012 | 0.011 | 0.124 | 0.192 | 0.260 | 0.050 | 0.273 | 13.254 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 30 | 28 | 24 | 34 | 26 | 29 | 48 | 17 |
N.S. |
1 | 1.07 | 1.00 | 0.86 | 1.21 | 0.93 | 1.04 | 1.71 | 0.61 |
time (sec) |
N/A | 0.064 | 0.023 | 0.848 | 0.216 | 0.297 | 0.066 | 0.271 | 13.439 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 56 | 27 | 25 | 24 | 23 | 27 | 40 | 27 |
N.S. |
1 | 2.55 | 1.23 | 1.14 | 1.09 | 1.05 | 1.23 | 1.82 | 1.23 |
time (sec) |
N/A | 0.064 | 0.020 | 0.125 | 0.184 | 0.244 | 0.563 | 0.264 | 0.143 |
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 | 28 | 28 | 28 | 29 | 44 | 54 | 26 | 72 | 28 |
N.S. |
1 | 1.00 | 1.00 | 1.04 | 1.57 | 1.93 | 0.93 | 2.57 | 1.00 |
time (sec) |
N/A | 0.035 | 0.057 | 0.201 | 0.188 | 0.271 | 0.111 | 0.270 | 0.175 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 24 | 33 | 33 | 0 | 25 | 590 | 159 | 132 |
N.S. |
1 | 0.96 | 1.32 | 1.32 | 0.00 | 1.00 | 23.60 | 6.36 | 5.28 |
time (sec) |
N/A | 0.499 | 8.136 | 0.724 | 0.000 | 0.270 | 4.417 | 0.283 | 0.205 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 132 | 22 | 20 | 28 | 37 | 31 | 0 | 0 |
N.S. |
1 | 5.50 | 0.92 | 0.83 | 1.17 | 1.54 | 1.29 | 0.00 | 0.00 |
time (sec) |
N/A | 0.204 | 0.174 | 4.636 | 0.211 | 0.265 | 3.221 | 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 | 19 | 26 | 19 | 30 | 18 | 27 | 26 | 18 | 19 |
N.S. |
1 | 1.37 | 1.00 | 1.58 | 0.95 | 1.42 | 1.37 | 0.95 | 1.00 |
time (sec) |
N/A | 0.193 | 0.113 | 0.205 | 0.412 | 0.269 | 0.102 | 0.296 | 14.406 |
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 | 17 | 23 | 15 | 16 | 16 | 17 | 18 | 14 |
N.S. |
1 | 0.89 | 1.21 | 0.79 | 0.84 | 0.84 | 0.89 | 0.95 | 0.74 |
time (sec) |
N/A | 0.008 | 0.012 | 0.687 | 0.207 | 0.275 | 0.097 | 0.307 | 14.557 |
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 | 9 | 9 | 9 | 10 | 9 | 9 | 7 | 9 | 9 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 1.00 | 1.00 | 0.78 | 1.00 | 1.00 |
time (sec) |
N/A | 0.001 | 0.000 | 0.115 | 0.205 | 0.262 | 0.020 | 0.279 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 40 | 17 | 41 | 42 | 75 | 42 | 17 | 17 |
N.S. |
1 | 1.82 | 0.77 | 1.86 | 1.91 | 3.41 | 1.91 | 0.77 | 0.77 |
time (sec) |
N/A | 0.087 | 0.035 | 0.224 | 0.203 | 0.260 | 0.133 | 0.275 | 0.181 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 25 | 27 | 105 | 105 | 44 | 148 | 1690 |
N.S. |
1 | 0.00 | 0.93 | 1.00 | 3.89 | 3.89 | 1.63 | 5.48 | 62.59 |
time (sec) |
N/A | 0.000 | 0.198 | 8.847 | 0.391 | 0.287 | 0.294 | 1.540 | 19.357 |
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 | 14 | 98 | 70 | 74 | 70 | 70 | 73 | 70 | 88 |
N.S. |
1 | 7.00 | 5.00 | 5.29 | 5.00 | 5.00 | 5.21 | 5.00 | 6.29 |
time (sec) |
N/A | 0.263 | 0.184 | 0.175 | 0.198 | 0.293 | 0.085 | 0.282 | 14.028 |
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 | 5 | 5 | 5 | 5 | 4 | 4 | 3 | 4 | 4 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.80 | 0.80 | 0.60 | 0.80 | 0.80 |
time (sec) |
N/A | 0.001 | 0.000 | 0.151 | 0.199 | 0.255 | 0.029 | 0.279 | 0.011 |
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 | 25 | 27 | 18 | 18 | 18 | 20 | 18 | 17 |
N.S. |
1 | 0.89 | 0.96 | 0.64 | 0.64 | 0.64 | 0.71 | 0.64 | 0.61 |
time (sec) |
N/A | 0.006 | 0.000 | 0.135 | 0.194 | 0.262 | 0.020 | 0.285 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | F(-1) | B | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 69 | 186 | 0 | 140 | 134 | 0 | 697 |
N.S. |
1 | 0.00 | 2.30 | 6.20 | 0.00 | 4.67 | 4.47 | 0.00 | 23.23 |
time (sec) |
N/A | 0.000 | 0.464 | 1.727 | 0.000 | 0.298 | 2.765 | 0.000 | 15.462 |
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 | 27 | 0 | 25 | 26 | 24 | 41 | 44 | 0 | 29 |
N.S. |
1 | 0.00 | 0.93 | 0.96 | 0.89 | 1.52 | 1.63 | 0.00 | 1.07 |
time (sec) |
N/A | 0.000 | 0.522 | 5.667 | 0.354 | 0.275 | 0.252 | 0.000 | 14.264 |
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 | 25 | 19 | 16 | 16 | 22 | 20 | 24 | 15 |
N.S. |
1 | 1.09 | 0.83 | 0.70 | 0.70 | 0.96 | 0.87 | 1.04 | 0.65 |
time (sec) |
N/A | 0.098 | 0.074 | 0.344 | 0.279 | 0.279 | 1.497 | 0.283 | 13.896 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 25 | 27 | 0 | 30 | 19 | 0 | 22 |
N.S. |
1 | 0.00 | 0.89 | 0.96 | 0.00 | 1.07 | 0.68 | 0.00 | 0.79 |
time (sec) |
N/A | 0.000 | 2.082 | 2.612 | 0.000 | 0.261 | 0.107 | 0.000 | 14.198 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 27 | 12 | 12 | 268 | 14 | 12 | 24 | 14 |
N.S. |
1 | 2.25 | 1.00 | 1.00 | 22.33 | 1.17 | 1.00 | 2.00 | 1.17 |
time (sec) |
N/A | 0.030 | 0.043 | 0.143 | 0.341 | 0.261 | 0.042 | 0.275 | 0.080 |
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 | 28 | 29 | 28 | 49 | 45 | 17 | 60 | 27 |
N.S. |
1 | 0.78 | 0.81 | 0.78 | 1.36 | 1.25 | 0.47 | 1.67 | 0.75 |
time (sec) |
N/A | 0.168 | 0.043 | 0.323 | 0.256 | 0.266 | 0.101 | 0.289 | 13.968 |
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 | 18 | 0 | 22 | 18 | 23 | 21 | 15 | 23 | 17 |
N.S. |
1 | 0.00 | 1.22 | 1.00 | 1.28 | 1.17 | 0.83 | 1.28 | 0.94 |
time (sec) |
N/A | 0.000 | 0.236 | 0.688 | 0.245 | 0.270 | 0.078 | 0.274 | 14.279 |
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 | 26 | 0 | 24 | 25 | 28 | 24 | 24 | 28 | 25 |
N.S. |
1 | 0.00 | 0.92 | 0.96 | 1.08 | 0.92 | 0.92 | 1.08 | 0.96 |
time (sec) |
N/A | 0.000 | 0.196 | 1.232 | 0.380 | 0.287 | 0.101 | 0.271 | 14.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 27 | 64 | 54 | 1721 | 63 | 71 | 268 | 133 |
N.S. |
1 | 1.50 | 3.56 | 3.00 | 95.61 | 3.50 | 3.94 | 14.89 | 7.39 |
time (sec) |
N/A | 0.147 | 1.350 | 1.056 | 0.212 | 0.292 | 0.107 | 0.570 | 13.685 |
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 | 30 | 29 | 20 | 32 | 31 | 26 | 102 |
N.S. |
1 | 0.00 | 1.20 | 1.16 | 0.80 | 1.28 | 1.24 | 1.04 | 4.08 |
time (sec) |
N/A | 0.000 | 5.113 | 1.800 | 0.233 | 0.267 | 0.140 | 0.268 | 0.464 |
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 | 11 | 11 | 9 | 9 | 9 | 5 | 9 | 8 |
N.S. |
1 | 0.37 | 0.37 | 0.30 | 0.30 | 0.30 | 0.17 | 0.30 | 0.27 |
time (sec) |
N/A | 0.001 | 0.001 | 0.044 | 0.224 | 0.244 | 0.019 | 0.272 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 77 | 42 | 62 | 0 | 106 | 87 | 137 | 79 |
N.S. |
1 | 2.75 | 1.50 | 2.21 | 0.00 | 3.79 | 3.11 | 4.89 | 2.82 |
time (sec) |
N/A | 1.288 | 0.076 | 0.866 | 0.000 | 0.273 | 0.154 | 0.270 | 14.405 |
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 | 17 | 962 | 21 | 20 | 423 | 20 | 19 | 20 | 19 |
N.S. |
1 | 56.59 | 1.24 | 1.18 | 24.88 | 1.18 | 1.12 | 1.18 | 1.12 |
time (sec) |
N/A | 0.924 | 0.472 | 0.577 | 1.520 | 0.270 | 0.112 | 0.274 | 13.751 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 27 | 29 | 34 | 35 | 32 | 628 | 0 |
N.S. |
1 | 0.00 | 0.90 | 0.97 | 1.13 | 1.17 | 1.07 | 20.93 | 0.00 |
time (sec) |
N/A | 0.000 | 0.353 | 0.355 | 0.245 | 0.290 | 0.108 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 49 | 23 | 24 | 0 | 23 | 17 | 31 | 23 |
N.S. |
1 | 1.75 | 0.82 | 0.86 | 0.00 | 0.82 | 0.61 | 1.11 | 0.82 |
time (sec) |
N/A | 0.138 | 0.103 | 1.394 | 0.000 | 0.280 | 0.115 | 0.276 | 12.812 |
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 | 26 | 21 | 27 | 24 | 25 | 27 | 37 | 21 |
N.S. |
1 | 0.96 | 0.78 | 1.00 | 0.89 | 0.93 | 1.00 | 1.37 | 0.78 |
time (sec) |
N/A | 0.171 | 0.156 | 1.203 | 0.299 | 0.273 | 0.086 | 0.267 | 13.574 |
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 | 31 | 31 | 31 | 185 | 30 | 39 | 0 | 1938 | 0 |
N.S. |
1 | 1.00 | 1.00 | 5.97 | 0.97 | 1.26 | 0.00 | 62.52 | 0.00 |
time (sec) |
N/A | 2.624 | 0.505 | 0.256 | 0.437 | 0.262 | 0.000 | 24.854 | 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 | 33 | 46 | 38 | 35 | 34 | 35 | 32 | 35 | 35 |
N.S. |
1 | 1.39 | 1.15 | 1.06 | 1.03 | 1.06 | 0.97 | 1.06 | 1.06 |
time (sec) |
N/A | 1.310 | 0.088 | 1.185 | 0.255 | 0.253 | 0.192 | 0.333 | 13.217 |
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 | 29 | 0 | 30 | 36 | 47 | 33 | 61 | 36 | 49 |
N.S. |
1 | 0.00 | 1.03 | 1.24 | 1.62 | 1.14 | 2.10 | 1.24 | 1.69 |
time (sec) |
N/A | 0.000 | 5.082 | 1.238 | 0.358 | 0.261 | 0.132 | 0.324 | 12.822 |
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 | 35 | 35 | 47 | 36 | 29 | 38 | 35 |
N.S. |
1 | 0.00 | 1.21 | 1.21 | 1.62 | 1.24 | 1.00 | 1.31 | 1.21 |
time (sec) |
N/A | 0.000 | 0.134 | 0.613 | 0.480 | 0.285 | 0.372 | 0.526 | 13.820 |
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 | 15 | 14 | 14 | 14 | 14 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.74 | 0.74 | 0.74 | 0.74 | 0.84 |
time (sec) |
N/A | 0.003 | 0.019 | 0.089 | 0.191 | 0.261 | 0.033 | 0.262 | 0.043 |
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 | 20 | 21 | 20 | 20 | 56 | 22 | 19 | 22 | 16 |
N.S. |
1 | 1.05 | 1.00 | 1.00 | 2.80 | 1.10 | 0.95 | 1.10 | 0.80 |
time (sec) |
N/A | 0.035 | 0.023 | 0.279 | 0.231 | 0.264 | 0.073 | 0.268 | 12.438 |
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 | 24 | 34 | 32 | 27 | 35 | 36 | 34 | 57 | 26 |
N.S. |
1 | 1.42 | 1.33 | 1.12 | 1.46 | 1.50 | 1.42 | 2.38 | 1.08 |
time (sec) |
N/A | 0.078 | 2.496 | 0.231 | 0.238 | 0.269 | 0.120 | 0.285 | 13.548 |
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 | 16 | 0 | 13 | 13 | 12 | 12 | 10 | 12 | 12 |
N.S. |
1 | 0.00 | 0.81 | 0.81 | 0.75 | 0.75 | 0.62 | 0.75 | 0.75 |
time (sec) |
N/A | 0.000 | 0.139 | 0.063 | 0.218 | 0.271 | 0.048 | 0.269 | 0.089 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 22 | 20 | 25 | 27 | 0 | 35 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.91 | 1.14 | 1.23 | 0.00 | 1.59 | 0.00 |
time (sec) |
N/A | 0.000 | 0.167 | 65.451 | 0.260 | 0.290 | 0.000 | 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 | 20 | 8 | 8 | 9 | 8 | 8 | 7 | 9 | 8 |
N.S. |
1 | 0.40 | 0.40 | 0.45 | 0.40 | 0.40 | 0.35 | 0.45 | 0.40 |
time (sec) |
N/A | 0.002 | 0.001 | 0.060 | 0.184 | 0.260 | 0.027 | 0.266 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | C | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 56 | 54 | 57 | 68 | 64 | 65 | 143 | 56 |
N.S. |
1 | 2.80 | 2.70 | 2.85 | 3.40 | 3.20 | 3.25 | 7.15 | 2.80 |
time (sec) |
N/A | 0.095 | 2.192 | 0.345 | 0.227 | 0.251 | 0.115 | 0.278 | 0.160 |
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 | 15 | 15 | 14 | 13 | 17 | 10 | 13 | 13 |
N.S. |
1 | 0.94 | 0.94 | 0.88 | 0.81 | 1.06 | 0.62 | 0.81 | 0.81 |
time (sec) |
N/A | 0.014 | 0.014 | 0.181 | 0.179 | 0.269 | 0.042 | 0.270 | 12.509 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 24 | 23 | 50 | 1942 | 50 | 44 | 746 | 1018 |
N.S. |
1 | 0.86 | 0.82 | 1.79 | 69.36 | 1.79 | 1.57 | 26.64 | 36.36 |
time (sec) |
N/A | 0.171 | 0.058 | 0.736 | 0.324 | 0.272 | 0.101 | 0.298 | 45.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 18 | 24 | 0 | 23 | 19 | 17 | 17 |
N.S. |
1 | 0.00 | 1.00 | 1.33 | 0.00 | 1.28 | 1.06 | 0.94 | 0.94 |
time (sec) |
N/A | 0.000 | 0.268 | 0.773 | 0.000 | 0.240 | 0.123 | 0.289 | 13.143 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 80 | 34 | 52 | 0 | 42 | 82 | 56 | 30 |
N.S. |
1 | 3.33 | 1.42 | 2.17 | 0.00 | 1.75 | 3.42 | 2.33 | 1.25 |
time (sec) |
N/A | 0.456 | 0.323 | 0.183 | 0.000 | 0.307 | 0.246 | 0.264 | 13.151 |
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 | 34 | 36 | 29 | 26 | 34 | 29 | 26 | 26 |
N.S. |
1 | 1.17 | 1.24 | 1.00 | 0.90 | 1.17 | 1.00 | 0.90 | 0.90 |
time (sec) |
N/A | 0.034 | 0.030 | 0.365 | 0.192 | 0.264 | 0.059 | 0.273 | 12.457 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 27 | 27 | 25 | 54 | 32 | 24 | 25 | 25 |
N.S. |
1 | 1.23 | 1.23 | 1.14 | 2.45 | 1.45 | 1.09 | 1.14 | 1.14 |
time (sec) |
N/A | 0.110 | 0.046 | 0.059 | 0.198 | 0.252 | 0.059 | 0.248 | 13.510 |
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 | 26 | 0 | 26 | 28 | 21 | 30 | 24 | 24 | 22 |
N.S. |
1 | 0.00 | 1.00 | 1.08 | 0.81 | 1.15 | 0.92 | 0.92 | 0.85 |
time (sec) |
N/A | 0.000 | 0.625 | 0.260 | 0.307 | 0.254 | 0.147 | 0.272 | 12.487 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | B | B | A | F | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 11 | 0 | 0 | 25 | 34 | 34 | 29 | 0 | 24 |
N.S. |
1 | 0.00 | 0.00 | 2.27 | 3.09 | 3.09 | 2.64 | 0.00 | 2.18 |
time (sec) |
N/A | 0.000 | 0.000 | 0.565 | 0.311 | 0.259 | 0.157 | 0.000 | 12.426 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 21 | 19 | 18 | 61 | 19 | 0 | 20 |
N.S. |
1 | 0.00 | 0.88 | 0.79 | 0.75 | 2.54 | 0.79 | 0.00 | 0.83 |
time (sec) |
N/A | 0.000 | 0.766 | 0.215 | 0.405 | 0.291 | 0.288 | 0.000 | 12.869 |
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 | 27 | 32 | 29 | 23 | 0 | 23 | 26 | 23 | 25 |
N.S. |
1 | 1.19 | 1.07 | 0.85 | 0.00 | 0.85 | 0.96 | 0.85 | 0.93 |
time (sec) |
N/A | 0.187 | 1.496 | 0.712 | 0.000 | 0.256 | 0.177 | 0.311 | 0.261 |
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 | 30 | 25 | 27 | 21 | 26 | 22 | 21 | 24 |
N.S. |
1 | 1.11 | 0.93 | 1.00 | 0.78 | 0.96 | 0.81 | 0.78 | 0.89 |
time (sec) |
N/A | 0.272 | 0.562 | 0.850 | 0.318 | 0.249 | 0.130 | 0.274 | 12.593 |
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 | 18 | 0 | 16 | 17 | 19 | 16 | 12 | 44 | 17 |
N.S. |
1 | 0.00 | 0.89 | 0.94 | 1.06 | 0.89 | 0.67 | 2.44 | 0.94 |
time (sec) |
N/A | 0.000 | 0.087 | 1.053 | 0.318 | 0.283 | 0.060 | 0.275 | 13.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 34 | 45 | 31 | 54 | 28 | 27 | 28 | 28 |
N.S. |
1 | 1.48 | 1.96 | 1.35 | 2.35 | 1.22 | 1.17 | 1.22 | 1.22 |
time (sec) |
N/A | 0.058 | 10.619 | 0.475 | 0.327 | 0.262 | 0.091 | 0.285 | 0.210 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 32 | 36 | 42 | 0 | 30 | 26 | 59 | 52 |
N.S. |
1 | 1.33 | 1.50 | 1.75 | 0.00 | 1.25 | 1.08 | 2.46 | 2.17 |
time (sec) |
N/A | 0.086 | 0.320 | 0.730 | 0.000 | 0.265 | 0.146 | 0.284 | 12.693 |
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 | 27 | 22 | 30 | 40 | 20 | 40 | 21 |
N.S. |
1 | 0.00 | 0.93 | 0.76 | 1.03 | 1.38 | 0.69 | 1.38 | 0.72 |
time (sec) |
N/A | 0.000 | 0.171 | 0.158 | 0.267 | 0.279 | 0.152 | 0.267 | 13.250 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 18 | 19 | 189 | 18 | 17 | 17 | 16 |
N.S. |
1 | 1.00 | 0.86 | 0.90 | 9.00 | 0.86 | 0.81 | 0.81 | 0.76 |
time (sec) |
N/A | 0.174 | 0.070 | 0.576 | 0.211 | 0.260 | 0.118 | 0.270 | 13.729 |
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 | 27 | 27 | 20 | 31 | 22 | 22 | 25 | 19 |
N.S. |
1 | 1.59 | 1.59 | 1.18 | 1.82 | 1.29 | 1.29 | 1.47 | 1.12 |
time (sec) |
N/A | 0.029 | 0.006 | 0.026 | 0.189 | 0.265 | 0.069 | 0.267 | 13.812 |
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 | 18 | 16 | 14 | 17 | 17 | 17 | 14 | 0 | 14 |
N.S. |
1 | 0.89 | 0.78 | 0.94 | 0.94 | 0.94 | 0.78 | 0.00 | 0.78 |
time (sec) |
N/A | 0.100 | 0.107 | 0.665 | 0.217 | 0.257 | 0.112 | 0.000 | 14.625 |
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 | 20 | 20 | 22 | 32 | 22 | 20 | 24 | 20 |
N.S. |
1 | 1.05 | 1.05 | 1.16 | 1.68 | 1.16 | 1.05 | 1.26 | 1.05 |
time (sec) |
N/A | 0.311 | 0.265 | 26.389 | 0.328 | 0.258 | 0.115 | 0.302 | 13.913 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 42 | 166 | 48 | 33 | 26 | 44 | 47 | 42 |
N.S. |
1 | 1.83 | 7.22 | 2.09 | 1.43 | 1.13 | 1.91 | 2.04 | 1.83 |
time (sec) |
N/A | 4.032 | 0.148 | 0.204 | 0.270 | 0.267 | 0.099 | 0.307 | 13.500 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 126 | 37 | 30 | 34 | 31 | 22 | 0 | 29 |
N.S. |
1 | 3.71 | 1.09 | 0.88 | 1.00 | 0.91 | 0.65 | 0.00 | 0.85 |
time (sec) |
N/A | 0.386 | 0.243 | 1.624 | 0.373 | 0.270 | 0.100 | 0.000 | 13.554 |