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 | C | A | F(-1) | C | A | B | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 141 | 18 | 0 | 114 | 21 | 128 | 0 | 17 |
N.S. |
1 | 7.83 | 1.00 | 0.00 | 6.33 | 1.17 | 7.11 | 0.00 | 0.94 |
time (sec) |
N/A | 0.547 | 0.131 | 0.000 | 0.302 | 0.252 | 1.992 | 0.000 | 8.415 |
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 | 24 | 23 | 104 | 22 | 19 | 0 | 23 |
N.S. |
1 | 0.00 | 1.00 | 0.96 | 4.33 | 0.92 | 0.79 | 0.00 | 0.96 |
time (sec) |
N/A | 0.000 | 0.105 | 30.014 | 0.292 | 0.258 | 0.770 | 0.000 | 9.911 |
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 | 7 | 9 | 7 | 6 | 8 | 5 | 6 | 6 |
N.S. |
1 | 0.39 | 0.50 | 0.39 | 0.33 | 0.44 | 0.28 | 0.33 | 0.33 |
time (sec) |
N/A | 0.123 | 0.000 | 0.010 | 0.197 | 0.238 | 0.014 | 0.267 | 0.002 |
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 | 36 | 43 | 36 | 40 | 39 | 41 | 42 |
N.S. |
1 | 0.00 | 1.24 | 1.48 | 1.24 | 1.38 | 1.34 | 1.41 | 1.45 |
time (sec) |
N/A | 0.000 | 0.038 | 0.274 | 0.189 | 0.260 | 1.361 | 0.277 | 8.418 |
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 | 30 | 0 | 56 | 49 | 62 | 53 | 54 | 49 | 0 |
N.S. |
1 | 0.00 | 1.87 | 1.63 | 2.07 | 1.77 | 1.80 | 1.63 | 0.00 |
time (sec) |
N/A | 0.000 | 0.168 | 0.303 | 0.250 | 0.266 | 0.325 | 3.997 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 35 | 41 | 33 | 32 | 32 | 32 | 32 | 31 |
N.S. |
1 | 1.75 | 2.05 | 1.65 | 1.60 | 1.60 | 1.60 | 1.60 | 1.55 |
time (sec) |
N/A | 0.212 | 0.006 | 0.046 | 0.223 | 0.247 | 0.045 | 0.272 | 0.102 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 24 | 14 | 16 | 27 | 15 | 17 | 15 | 13 |
N.S. |
1 | 0.92 | 0.54 | 0.62 | 1.04 | 0.58 | 0.65 | 0.58 | 0.50 |
time (sec) |
N/A | 0.162 | 0.008 | 0.031 | 0.182 | 0.255 | 0.045 | 0.272 | 0.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 84 | 79 | 26 | 130 | 58 | 66 | 75 | 67 |
N.S. |
1 | 3.36 | 3.16 | 1.04 | 5.20 | 2.32 | 2.64 | 3.00 | 2.68 |
time (sec) |
N/A | 0.377 | 0.047 | 0.102 | 0.193 | 0.264 | 0.115 | 0.280 | 8.616 |
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 | 33 | 70 | 47 | 55 | 0 | 45 | 49 | 70 | 55 |
N.S. |
1 | 2.12 | 1.42 | 1.67 | 0.00 | 1.36 | 1.48 | 2.12 | 1.67 |
time (sec) |
N/A | 0.663 | 2.872 | 0.163 | 0.000 | 0.251 | 0.115 | 0.284 | 8.484 |
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 | 26 | 27 | 46 | 46 | 20 | 46 | 26 |
N.S. |
1 | 0.00 | 0.90 | 0.93 | 1.59 | 1.59 | 0.69 | 1.59 | 0.90 |
time (sec) |
N/A | 0.000 | 3.870 | 0.209 | 0.249 | 0.260 | 0.061 | 0.290 | 8.777 |
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 | 23 | 0 | 9 | 10 | 9 | 9 | 7 | 9 | 9 |
N.S. |
1 | 0.00 | 0.39 | 0.43 | 0.39 | 0.39 | 0.30 | 0.39 | 0.39 |
time (sec) |
N/A | 0.000 | 0.028 | 0.151 | 0.220 | 0.247 | 0.043 | 0.275 | 8.460 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 26 | 26 | 14 | 13 | 12 | 14 | 13 | 12 |
N.S. |
1 | 2.00 | 2.00 | 1.08 | 1.00 | 0.92 | 1.08 | 1.00 | 0.92 |
time (sec) |
N/A | 0.407 | 0.031 | 0.130 | 0.211 | 0.254 | 0.112 | 0.287 | 8.343 |
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 | 28 | 0 | 50 | 36 | 50 | 49 | 46 | 54 | 99 |
N.S. |
1 | 0.00 | 1.79 | 1.29 | 1.79 | 1.75 | 1.64 | 1.93 | 3.54 |
time (sec) |
N/A | 0.000 | 0.099 | 0.421 | 0.219 | 0.256 | 0.187 | 0.314 | 8.425 |
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 | 64 | 32 | 35 | 44 | 33 | 44 | 33 | 41 |
N.S. |
1 | 1.83 | 0.91 | 1.00 | 1.26 | 0.94 | 1.26 | 0.94 | 1.17 |
time (sec) |
N/A | 0.603 | 0.142 | 0.135 | 0.225 | 0.253 | 0.414 | 0.273 | 8.493 |
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 | 25 | 28 | 26 | 29 | 29 | 29 | 29 |
N.S. |
1 | 0.00 | 1.14 | 1.27 | 1.18 | 1.32 | 1.32 | 1.32 | 1.32 |
time (sec) |
N/A | 0.000 | 0.057 | 2.769 | 0.243 | 0.261 | 0.204 | 14.240 | 9.974 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 34 | 34 | 61 | 37 | 70 | 70 | 71 | 71 |
N.S. |
1 | 1.36 | 1.36 | 2.44 | 1.48 | 2.80 | 2.80 | 2.84 | 2.84 |
time (sec) |
N/A | 1.231 | 7.516 | 0.516 | 0.328 | 0.278 | 0.307 | 0.699 | 8.981 |
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 | 24 | 0 | 20 | 26 | 20 | 20 | 0 | 32 | 0 |
N.S. |
1 | 0.00 | 0.83 | 1.08 | 0.83 | 0.83 | 0.00 | 1.33 | 0.00 |
time (sec) |
N/A | 0.000 | 0.391 | 0.227 | 0.226 | 0.267 | 0.000 | 0.284 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 24 | 24 | 25 | 43 | 26 | 20 | 24 | 21 |
N.S. |
1 | 0.89 | 0.89 | 0.93 | 1.59 | 0.96 | 0.74 | 0.89 | 0.78 |
time (sec) |
N/A | 0.201 | 0.013 | 0.036 | 0.176 | 0.254 | 0.058 | 0.283 | 8.935 |
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 | 17 | 13 | 14 | 14 | 24 | 14 | 14 |
N.S. |
1 | 1.06 | 0.94 | 0.72 | 0.78 | 0.78 | 1.33 | 0.78 | 0.78 |
time (sec) |
N/A | 0.142 | 0.005 | 0.100 | 0.237 | 0.270 | 0.070 | 0.280 | 0.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 18 | 19 | 17 | 17 | 19 | 17 | 16 |
N.S. |
1 | 1.00 | 1.20 | 1.27 | 1.13 | 1.13 | 1.27 | 1.13 | 1.07 |
time (sec) |
N/A | 0.147 | 0.006 | 0.032 | 0.220 | 0.248 | 0.037 | 0.272 | 8.970 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 118 | 39 | 46 | 73 | 45 | 53 | 0 | 37 |
N.S. |
1 | 4.07 | 1.34 | 1.59 | 2.52 | 1.55 | 1.83 | 0.00 | 1.28 |
time (sec) |
N/A | 2.395 | 0.121 | 1.795 | 0.315 | 0.261 | 0.387 | 0.000 | 9.378 |
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 | 21 | 46 | 24 | 23 | 73 | 25 | 22 | 43 | 22 |
N.S. |
1 | 2.19 | 1.14 | 1.10 | 3.48 | 1.19 | 1.05 | 2.05 | 1.05 |
time (sec) |
N/A | 0.460 | 0.128 | 0.055 | 0.263 | 0.256 | 0.057 | 0.284 | 9.002 |
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 | 32 | 0 | 34 | 37 | 38 | 37 | 29 | 37 | 35 |
N.S. |
1 | 0.00 | 1.06 | 1.16 | 1.19 | 1.16 | 0.91 | 1.16 | 1.09 |
time (sec) |
N/A | 0.000 | 0.083 | 0.467 | 0.362 | 0.245 | 0.113 | 0.425 | 10.008 |
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 | 20 | 25 | 24 | 18 | 68 | 17 | 14 | 17 | 19 |
N.S. |
1 | 1.25 | 1.20 | 0.90 | 3.40 | 0.85 | 0.70 | 0.85 | 0.95 |
time (sec) |
N/A | 0.242 | 0.061 | 0.040 | 0.186 | 0.246 | 0.047 | 0.263 | 9.395 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 35 | 26 | 34 | 44 | 29 | 34 | 26 | 15 |
N.S. |
1 | 1.59 | 1.18 | 1.55 | 2.00 | 1.32 | 1.55 | 1.18 | 0.68 |
time (sec) |
N/A | 0.197 | 0.040 | 0.125 | 0.196 | 0.254 | 0.110 | 0.276 | 9.169 |
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 | 15 | 15 | 15 | 12 | 19 | 19 | 14 | 20 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 1.27 | 1.27 | 0.93 | 1.33 | 0.73 |
time (sec) |
N/A | 0.133 | 0.002 | 0.025 | 0.192 | 0.240 | 0.026 | 0.264 | 0.085 |
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 | 31 | 47 | 47 | 46 | 61 | 44 | 51 | 45 | 51 |
N.S. |
1 | 1.52 | 1.52 | 1.48 | 1.97 | 1.42 | 1.65 | 1.45 | 1.65 |
time (sec) |
N/A | 0.253 | 0.034 | 0.056 | 0.197 | 0.277 | 0.107 | 0.269 | 9.261 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F(-1) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 36 | 39 | 32 | 42 | 37 | 0 | 133 |
N.S. |
1 | 0.00 | 1.33 | 1.44 | 1.19 | 1.56 | 1.37 | 0.00 | 4.93 |
time (sec) |
N/A | 0.000 | 2.715 | 0.922 | 0.381 | 0.287 | 0.470 | 0.000 | 9.783 |
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 | 21 | 17 | 16 | 15 | 15 | 15 | 15 | 15 |
N.S. |
1 | 0.88 | 0.71 | 0.67 | 0.62 | 0.62 | 0.62 | 0.62 | 0.62 |
time (sec) |
N/A | 0.410 | 0.076 | 0.107 | 0.233 | 0.252 | 0.073 | 0.284 | 9.548 |
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 | 18 | 18 | 19 | 18 | 24 | 19 | 18 | 18 |
N.S. |
1 | 0.90 | 0.90 | 0.95 | 0.90 | 1.20 | 0.95 | 0.90 | 0.90 |
time (sec) |
N/A | 0.291 | 0.009 | 0.039 | 0.217 | 0.250 | 0.056 | 0.274 | 9.402 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 50 | 44 | 24 | 41 | 32 | 31 | 166 | 44 |
N.S. |
1 | 1.79 | 1.57 | 0.86 | 1.46 | 1.14 | 1.11 | 5.93 | 1.57 |
time (sec) |
N/A | 0.371 | 0.851 | 0.077 | 0.202 | 0.258 | 0.084 | 0.304 | 0.432 |
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 | 31 | 29 | 38 | 36 | 37 | 36 | 44 | 37 |
N.S. |
1 | 1.11 | 1.04 | 1.36 | 1.29 | 1.32 | 1.29 | 1.57 | 1.32 |
time (sec) |
N/A | 1.409 | 0.095 | 0.854 | 0.309 | 0.271 | 0.248 | 0.334 | 10.786 |
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 | 25 | 58 | 28 | 35 | 417 | 35 | 31 | 32 | 35 |
N.S. |
1 | 2.32 | 1.12 | 1.40 | 16.68 | 1.40 | 1.24 | 1.28 | 1.40 |
time (sec) |
N/A | 2.357 | 0.290 | 0.055 | 0.199 | 0.247 | 0.055 | 0.273 | 9.318 |
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 | 16 | 14 | 15 | 15 | 15 | 15 | 15 |
N.S. |
1 | 0.95 | 0.84 | 0.74 | 0.79 | 0.79 | 0.79 | 0.79 | 0.79 |
time (sec) |
N/A | 0.280 | 0.520 | 0.093 | 0.284 | 0.253 | 0.096 | 0.279 | 0.132 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 51 | 28 | 34 | 53 | 134 | 51 | 22 | 55 |
N.S. |
1 | 2.04 | 1.12 | 1.36 | 2.12 | 5.36 | 2.04 | 0.88 | 2.20 |
time (sec) |
N/A | 0.760 | 0.028 | 0.062 | 0.186 | 0.264 | 0.089 | 0.287 | 0.112 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 36 | 19 | 35 | 27 | 33 | 34 | 34 | 32 |
N.S. |
1 | 2.00 | 1.06 | 1.94 | 1.50 | 1.83 | 1.89 | 1.89 | 1.78 |
time (sec) |
N/A | 0.552 | 0.149 | 0.162 | 0.632 | 0.252 | 0.105 | 0.280 | 9.402 |
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 | 43 | 21 | 29 | 23 | 24 | 25 | 23 |
N.S. |
1 | 0.00 | 1.79 | 0.88 | 1.21 | 0.96 | 1.00 | 1.04 | 0.96 |
time (sec) |
N/A | 0.000 | 0.765 | 7.809 | 0.249 | 0.269 | 0.440 | 0.369 | 0.452 |
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 | 33 | 37 | 62 | 55 | 34 | 39 | 37 |
N.S. |
1 | 0.00 | 1.14 | 1.28 | 2.14 | 1.90 | 1.17 | 1.34 | 1.28 |
time (sec) |
N/A | 0.000 | 0.059 | 2.053 | 0.207 | 0.270 | 0.056 | 0.466 | 9.709 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 14 | 14 | 13 | 12 | 12 | 10 | 14 | 12 |
N.S. |
1 | 0.54 | 0.54 | 0.50 | 0.46 | 0.46 | 0.38 | 0.54 | 0.46 |
time (sec) |
N/A | 0.177 | 0.005 | 0.102 | 0.194 | 0.264 | 0.040 | 0.268 | 9.126 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 35 | 42 | 37 | 43 | 447 | 47 | 0 |
N.S. |
1 | 0.00 | 1.13 | 1.35 | 1.19 | 1.39 | 14.42 | 1.52 | 0.00 |
time (sec) |
N/A | 0.000 | 0.126 | 0.803 | 0.292 | 0.278 | 0.607 | 0.329 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | F(-1) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 22 | 26 | 56 | 24 | 0 | 30 | 178 |
N.S. |
1 | 0.00 | 0.96 | 1.13 | 2.43 | 1.04 | 0.00 | 1.30 | 7.74 |
time (sec) |
N/A | 0.000 | 5.104 | 0.792 | 0.293 | 0.281 | 0.000 | 0.768 | 9.709 |
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 | 28 | 0 | 34 | 25 | 40 | 34 | 31 | 0 | 56 |
N.S. |
1 | 0.00 | 1.21 | 0.89 | 1.43 | 1.21 | 1.11 | 0.00 | 2.00 |
time (sec) |
N/A | 0.000 | 0.267 | 21.832 | 0.473 | 0.288 | 0.753 | 0.000 | 10.142 |
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 | 32 | 0 | 38 | 30 | 53 | 31 | 31 | 31 | 31 |
N.S. |
1 | 0.00 | 1.19 | 0.94 | 1.66 | 0.97 | 0.97 | 0.97 | 0.97 |
time (sec) |
N/A | 0.000 | 10.437 | 0.053 | 0.204 | 0.275 | 0.107 | 0.277 | 9.125 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | C | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 38 | 32 | 29 | 59 | 28 | 32 | 30 | 30 |
N.S. |
1 | 2.11 | 1.78 | 1.61 | 3.28 | 1.56 | 1.78 | 1.67 | 1.67 |
time (sec) |
N/A | 0.241 | 0.037 | 0.192 | 0.205 | 0.275 | 0.094 | 0.263 | 9.227 |
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 | 4 | 2 | 2 | 3 | 2 | 2 | 2 | 3 | 2 |
N.S. |
1 | 0.50 | 0.50 | 0.75 | 0.50 | 0.50 | 0.50 | 0.75 | 0.50 |
time (sec) |
N/A | 0.117 | 0.000 | 0.018 | 0.180 | 0.262 | 0.017 | 0.259 | 0.009 |
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 | 24 | 24 | 22 | 21 | 21 | 22 | 23 | 21 |
N.S. |
1 | 0.89 | 0.89 | 0.81 | 0.78 | 0.78 | 0.81 | 0.85 | 0.78 |
time (sec) |
N/A | 0.986 | 0.484 | 136.602 | 0.305 | 0.290 | 0.442 | 0.298 | 9.243 |
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 | 22 | 55 | 51 | 40 | 48 | 38 | 48 | 39 | 14 |
N.S. |
1 | 2.50 | 2.32 | 1.82 | 2.18 | 1.73 | 2.18 | 1.77 | 0.64 |
time (sec) |
N/A | 0.217 | 0.014 | 0.027 | 0.185 | 0.281 | 0.070 | 0.270 | 8.810 |
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 | 9 | 8 | 9 | 8 | 8 | 8 | 8 | 8 |
N.S. |
1 | 0.47 | 0.42 | 0.47 | 0.42 | 0.42 | 0.42 | 0.42 | 0.42 |
time (sec) |
N/A | 0.135 | 0.005 | 0.026 | 0.224 | 0.262 | 0.034 | 0.268 | 0.035 |
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 | 23 | 22 | 24 | 34 | 15 | 24 | 21 |
N.S. |
1 | 0.00 | 0.74 | 0.71 | 0.77 | 1.10 | 0.48 | 0.77 | 0.68 |
time (sec) |
N/A | 0.000 | 0.893 | 0.094 | 0.343 | 0.279 | 0.095 | 0.278 | 8.935 |
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 | 28 | 28 | 38 | 22 | 0 | 38 | 19 | 38 | 23 |
N.S. |
1 | 1.00 | 1.36 | 0.79 | 0.00 | 1.36 | 0.68 | 1.36 | 0.82 |
time (sec) |
N/A | 0.398 | 0.173 | 0.149 | 0.000 | 0.283 | 0.067 | 0.273 | 0.161 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 16 | 15 | 15 | 15 | 15 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.88 | 0.88 | 0.88 | 0.88 | 0.88 |
time (sec) |
N/A | 0.261 | 0.020 | 0.200 | 0.221 | 0.262 | 0.080 | 0.272 | 9.502 |
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 | 22 | 21 | 19 | 18 | 25 | 14 | 18 | 18 |
N.S. |
1 | 1.05 | 1.00 | 0.90 | 0.86 | 1.19 | 0.67 | 0.86 | 0.86 |
time (sec) |
N/A | 0.180 | 0.017 | 0.146 | 0.198 | 0.280 | 0.043 | 0.265 | 0.059 |
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 | 10 | 10 | 15 | 15 | 12 | 9 | 9 |
N.S. |
1 | 0.00 | 0.62 | 0.62 | 0.94 | 0.94 | 0.75 | 0.56 | 0.56 |
time (sec) |
N/A | 0.000 | 0.047 | 0.138 | 0.213 | 0.269 | 0.065 | 0.277 | 9.224 |
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 | 21 | 0 | 41 | 48 | 37 | 37 | 31 | 37 | 34 |
N.S. |
1 | 0.00 | 1.95 | 2.29 | 1.76 | 1.76 | 1.48 | 1.76 | 1.62 |
time (sec) |
N/A | 0.000 | 0.211 | 0.341 | 0.221 | 0.268 | 0.081 | 0.286 | 9.765 |
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 | 20 | 62 | 20 | 18 | 17 | 18 | 19 | 0 | 20 |
N.S. |
1 | 3.10 | 1.00 | 0.90 | 0.85 | 0.90 | 0.95 | 0.00 | 1.00 |
time (sec) |
N/A | 0.279 | 0.151 | 0.201 | 0.265 | 0.271 | 0.112 | 0.000 | 9.338 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F | A | A | A | A | B |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 22 | 0 | 25 | 25 | 22 | 24 | 170 |
N.S. |
1 | 0.00 | 0.92 | 0.00 | 1.04 | 1.04 | 0.92 | 1.00 | 7.08 |
time (sec) |
N/A | 0.000 | 0.067 | 0.000 | 0.233 | 0.271 | 0.107 | 0.504 | 10.947 |
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 | 16 | 14 | 17 | 14 | 12 | 17 | 12 |
N.S. |
1 | 1.07 | 1.14 | 1.00 | 1.21 | 1.00 | 0.86 | 1.21 | 0.86 |
time (sec) |
N/A | 0.130 | 0.000 | 0.017 | 0.184 | 0.259 | 0.025 | 0.262 | 0.051 |
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 | 33 | 0 | 24 | 22 | 24 | 48 | 31 | 247 | 54 |
N.S. |
1 | 0.00 | 0.73 | 0.67 | 0.73 | 1.45 | 0.94 | 7.48 | 1.64 |
time (sec) |
N/A | 0.000 | 0.384 | 2.834 | 0.232 | 0.289 | 0.091 | 0.287 | 9.298 |
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 | 36 | 36 | 22 | 108 | 21 | 22 | 19 | 21 |
N.S. |
1 | 1.71 | 1.71 | 1.05 | 5.14 | 1.00 | 1.05 | 0.90 | 1.00 |
time (sec) |
N/A | 0.269 | 0.036 | 0.121 | 0.182 | 0.279 | 0.066 | 0.301 | 9.016 |
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 | 34 | 0 | 33 | 37 | 57 | 53 | 29 | 33 | 57 |
N.S. |
1 | 0.00 | 0.97 | 1.09 | 1.68 | 1.56 | 0.85 | 0.97 | 1.68 |
time (sec) |
N/A | 0.000 | 0.092 | 0.411 | 0.326 | 0.260 | 0.110 | 0.314 | 9.221 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 79 | 67 | 27 | 33 | 34 | 32 | 33 | 33 |
N.S. |
1 | 3.04 | 2.58 | 1.04 | 1.27 | 1.31 | 1.23 | 1.27 | 1.27 |
time (sec) |
N/A | 0.390 | 0.067 | 0.069 | 0.179 | 0.244 | 0.362 | 0.273 | 8.573 |
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 | 25 | 37 | 36 | 28 | 35 | 34 | 32 | 35 | 34 |
N.S. |
1 | 1.48 | 1.44 | 1.12 | 1.40 | 1.36 | 1.28 | 1.40 | 1.36 |
time (sec) |
N/A | 0.206 | 0.019 | 0.178 | 0.187 | 0.246 | 0.101 | 0.271 | 8.893 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 15 | 14 | 14 | 15 | 14 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.82 | 0.82 | 0.88 | 0.82 | 0.88 |
time (sec) |
N/A | 0.287 | 0.045 | 0.146 | 0.188 | 0.240 | 0.148 | 0.265 | 8.485 |
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 | 19 | 19 | 18 | 21 | 23 | 17 | 17 | 17 |
N.S. |
1 | 0.95 | 0.95 | 0.90 | 1.05 | 1.15 | 0.85 | 0.85 | 0.85 |
time (sec) |
N/A | 0.598 | 0.108 | 0.174 | 0.214 | 0.246 | 0.120 | 0.272 | 8.637 |
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 | 14 | 15 | 14 | 14 | 14 | 14 | 14 |
N.S. |
1 | 0.00 | 1.00 | 1.07 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.000 | 0.062 | 0.164 | 0.228 | 0.256 | 0.075 | 0.270 | 8.705 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 63 | 93 | 107 | 107 | 82 | 110 | 314 |
N.S. |
1 | 0.00 | 2.74 | 4.04 | 4.65 | 4.65 | 3.57 | 4.78 | 13.65 |
time (sec) |
N/A | 0.000 | 0.079 | 5.430 | 0.242 | 0.256 | 0.134 | 0.298 | 8.863 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 13 | 13 | 14 | 11 | 11 | 12 | 11 | 11 |
N.S. |
1 | 0.87 | 0.87 | 0.93 | 0.73 | 0.73 | 0.80 | 0.73 | 0.73 |
time (sec) |
N/A | 0.132 | 0.001 | 0.025 | 0.180 | 0.232 | 0.020 | 0.267 | 0.050 |
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 | 21 | 0 | 37 | 18 | 22 | 19 | 14 | 19 | 19 |
N.S. |
1 | 0.00 | 1.76 | 0.86 | 1.05 | 0.90 | 0.67 | 0.90 | 0.90 |
time (sec) |
N/A | 0.000 | 3.647 | 0.111 | 0.219 | 0.244 | 0.073 | 0.287 | 0.328 |
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 | 24 | 23 | 24 | 24 | 27 | 22 | 23 | 24 |
N.S. |
1 | 1.14 | 1.10 | 1.14 | 1.14 | 1.29 | 1.05 | 1.10 | 1.14 |
time (sec) |
N/A | 0.184 | 0.004 | 0.033 | 0.201 | 0.249 | 0.035 | 0.262 | 8.400 |
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 | 14 | 19 | 14 | 13 | 13 | 10 | 14 | 13 |
N.S. |
1 | 0.61 | 0.83 | 0.61 | 0.57 | 0.57 | 0.43 | 0.61 | 0.57 |
time (sec) |
N/A | 0.154 | 0.009 | 0.164 | 0.182 | 0.252 | 0.042 | 0.258 | 0.113 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 39 | 119 | 586 | 178 | 170 | 0 | 83 |
N.S. |
1 | 0.00 | 1.22 | 3.72 | 18.31 | 5.56 | 5.31 | 0.00 | 2.59 |
time (sec) |
N/A | 0.000 | 0.309 | 0.112 | 0.290 | 0.269 | 0.460 | 0.000 | 9.165 |
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 | 28 | 0 | 28 | 27 | 43 | 26 | 26 | 49 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.96 | 1.54 | 0.93 | 0.93 | 1.75 | 0.00 |
time (sec) |
N/A | 0.000 | 0.053 | 2.162 | 0.324 | 0.256 | 0.124 | 0.310 | 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 | 13 | 12 | 8 | 7 | 6 | 6 | 7 | 7 | 6 |
N.S. |
1 | 0.92 | 0.62 | 0.54 | 0.46 | 0.46 | 0.54 | 0.54 | 0.46 |
time (sec) |
N/A | 0.140 | 0.001 | 0.020 | 0.185 | 0.260 | 0.029 | 0.264 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 22 | 22 | 25 | 22 | 26 | 20 | 24 | 19 |
N.S. |
1 | 0.85 | 0.85 | 0.96 | 0.85 | 1.00 | 0.77 | 0.92 | 0.73 |
time (sec) |
N/A | 0.421 | 0.113 | 1.765 | 0.312 | 0.251 | 0.075 | 0.279 | 8.753 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 52 | 30 | 19 | 123 | 0 | 0 | 0 | 0 |
N.S. |
1 | 2.00 | 1.15 | 0.73 | 4.73 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.435 | 0.409 | 1.184 | 0.315 | 0.000 | 0.000 | 0.000 | 0.000 |
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 | 27 | 40 | 23 | 25 | 678 | 37 | 24 | 40 | 0 |
N.S. |
1 | 1.48 | 0.85 | 0.93 | 25.11 | 1.37 | 0.89 | 1.48 | 0.00 |
time (sec) |
N/A | 0.963 | 0.162 | 0.157 | 0.191 | 0.235 | 0.116 | 0.272 | 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 | 28 | 0 | 22 | 22 | 21 | 21 | 20 | 21 | 21 |
N.S. |
1 | 0.00 | 0.79 | 0.79 | 0.75 | 0.75 | 0.71 | 0.75 | 0.75 |
time (sec) |
N/A | 0.000 | 3.842 | 0.125 | 0.211 | 0.237 | 0.106 | 0.285 | 9.135 |
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 | 31 | 0 | 39 | 36 | 35 | 35 | 32 | 35 | 0 |
N.S. |
1 | 0.00 | 1.26 | 1.16 | 1.13 | 1.13 | 1.03 | 1.13 | 0.00 |
time (sec) |
N/A | 0.000 | 3.526 | 0.100 | 0.258 | 0.263 | 0.104 | 0.386 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 20 | 28 | 16 | 35 | 29 | 16 | 17 |
N.S. |
1 | 0.00 | 1.00 | 1.40 | 0.80 | 1.75 | 1.45 | 0.80 | 0.85 |
time (sec) |
N/A | 0.000 | 0.175 | 15.931 | 0.431 | 0.255 | 0.110 | 0.267 | 9.278 |
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 | 38 | 34 | 31 | 33 | 41 | 31 | 32 | 33 | 27 |
N.S. |
1 | 0.89 | 0.82 | 0.87 | 1.08 | 0.82 | 0.84 | 0.87 | 0.71 |
time (sec) |
N/A | 0.274 | 0.059 | 0.055 | 0.221 | 0.239 | 0.102 | 0.263 | 9.047 |
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 | 25 | 35 | 23 | 31 | 0 | 29 | 19 | 43 | 21 |
N.S. |
1 | 1.40 | 0.92 | 1.24 | 0.00 | 1.16 | 0.76 | 1.72 | 0.84 |
time (sec) |
N/A | 0.372 | 0.083 | 0.101 | 0.000 | 0.246 | 0.090 | 0.268 | 9.073 |
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 | 8 | 9 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 1.00 | 1.00 | 0.89 | 1.00 | 1.11 |
time (sec) |
N/A | 0.135 | 0.004 | 0.098 | 0.176 | 0.245 | 0.035 | 0.274 | 8.716 |
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 | 19 | 17 | 15 | 16 | 14 | 12 | 16 | 14 |
N.S. |
1 | 0.90 | 0.81 | 0.71 | 0.76 | 0.67 | 0.57 | 0.76 | 0.67 |
time (sec) |
N/A | 0.135 | 0.000 | 0.030 | 0.176 | 0.252 | 0.017 | 0.262 | 8.854 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 22 | 31 | 42 | 42 | 49 | 57 | 22 |
N.S. |
1 | 0.00 | 0.79 | 1.11 | 1.50 | 1.50 | 1.75 | 2.04 | 0.79 |
time (sec) |
N/A | 0.000 | 0.530 | 13.245 | 0.281 | 0.247 | 0.126 | 0.489 | 9.682 |
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 | 22 | 23 | 22 | 21 | 21 | 17 | 28 | 21 |
N.S. |
1 | 0.73 | 0.77 | 0.73 | 0.70 | 0.70 | 0.57 | 0.93 | 0.70 |
time (sec) |
N/A | 0.184 | 0.011 | 0.080 | 0.185 | 0.245 | 0.045 | 0.278 | 8.608 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 12 | 27 | 11 | 12 | 27 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 1.93 | 0.79 | 0.86 | 1.93 | 0.79 |
time (sec) |
N/A | 0.146 | 0.004 | 0.044 | 0.174 | 0.237 | 0.045 | 0.265 | 8.633 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 66 | 67 | 235 | 71 | 63 | 71 | 113 |
N.S. |
1 | 0.00 | 1.83 | 1.86 | 6.53 | 1.97 | 1.75 | 1.97 | 3.14 |
time (sec) |
N/A | 0.000 | 0.342 | 5.294 | 0.365 | 0.245 | 0.303 | 1.458 | 9.669 |
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 | 12 | 18 | 14 | 19 | 69 | 11 | 20 | 18 | 11 |
N.S. |
1 | 1.50 | 1.17 | 1.58 | 5.75 | 0.92 | 1.67 | 1.50 | 0.92 |
time (sec) |
N/A | 0.308 | 0.018 | 0.108 | 0.186 | 0.235 | 0.065 | 0.267 | 8.564 |
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 | 11 | 9 | 7 | 6 | 6 | 7 | 6 | 7 |
N.S. |
1 | 1.22 | 1.00 | 0.78 | 0.67 | 0.67 | 0.78 | 0.67 | 0.78 |
time (sec) |
N/A | 0.139 | 0.022 | 0.023 | 0.190 | 0.231 | 0.031 | 0.268 | 0.044 |
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 | 37 | 0 | 23 | 41 | 28 | 33 | 31 | 29 | 50 |
N.S. |
1 | 0.00 | 0.62 | 1.11 | 0.76 | 0.89 | 0.84 | 0.78 | 1.35 |
time (sec) |
N/A | 0.000 | 5.131 | 4.222 | 0.312 | 0.252 | 0.454 | 0.428 | 9.080 |
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 | 18 | 15 | 14 | 14 | 14 | 27 | 14 |
N.S. |
1 | 0.00 | 0.82 | 0.68 | 0.64 | 0.64 | 0.64 | 1.23 | 0.64 |
time (sec) |
N/A | 0.000 | 0.021 | 0.054 | 0.217 | 0.246 | 0.079 | 0.263 | 8.460 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | B | A | F | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 0 | 29 | 25 | 87 | 27 | 0 | 30 |
N.S. |
1 | 0.00 | 0.00 | 1.16 | 1.00 | 3.48 | 1.08 | 0.00 | 1.20 |
time (sec) |
N/A | 0.000 | 0.000 | 0.381 | 0.469 | 0.246 | 0.519 | 0.000 | 9.339 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 22 | 22 | 20 | 21 | 21 | 22 | 21 | 20 |
N.S. |
1 | 0.85 | 0.85 | 0.77 | 0.81 | 0.81 | 0.85 | 0.81 | 0.77 |
time (sec) |
N/A | 0.161 | 0.007 | 0.026 | 0.181 | 0.244 | 0.018 | 0.284 | 0.041 |
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 | 10 | 10 | 12 | 11 | 14 | 7 | 11 | 11 |
N.S. |
1 | 0.50 | 0.50 | 0.60 | 0.55 | 0.70 | 0.35 | 0.55 | 0.55 |
time (sec) |
N/A | 0.138 | 0.001 | 0.028 | 0.178 | 0.234 | 0.029 | 0.268 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 43 | 43 | 34 | 37 | 37 | 31 | 37 | 35 |
N.S. |
1 | 1.95 | 1.95 | 1.55 | 1.68 | 1.68 | 1.41 | 1.68 | 1.59 |
time (sec) |
N/A | 0.169 | 0.005 | 0.024 | 0.190 | 0.238 | 0.029 | 0.271 | 8.680 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 36 | 38 | 39 | 39 | 34 | 43 | 32 |
N.S. |
1 | 0.00 | 1.64 | 1.73 | 1.77 | 1.77 | 1.55 | 1.95 | 1.45 |
time (sec) |
N/A | 0.000 | 2.474 | 0.063 | 0.215 | 0.248 | 0.134 | 0.279 | 0.243 |
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 | 28 | 0 | 23 | 29 | 28 | 32 | 32 | 36 | 36 |
N.S. |
1 | 0.00 | 0.82 | 1.04 | 1.00 | 1.14 | 1.14 | 1.29 | 1.29 |
time (sec) |
N/A | 0.000 | 1.211 | 0.095 | 0.233 | 0.257 | 0.149 | 0.371 | 0.303 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | C | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 24 | 24 | 29 | 34 | 17 | 55 | 20 |
N.S. |
1 | 0.00 | 0.92 | 0.92 | 1.12 | 1.31 | 0.65 | 2.12 | 0.77 |
time (sec) |
N/A | 0.000 | 0.205 | 6.608 | 0.340 | 0.253 | 0.085 | 0.282 | 10.095 |
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 | 16 | 15 | 27 | 14 | 15 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.79 | 1.42 | 0.74 | 0.79 | 0.95 |
time (sec) |
N/A | 0.280 | 0.145 | 0.087 | 0.182 | 0.260 | 0.123 | 0.269 | 0.152 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 29 | 57 | 45 | 49 | 42 | 60 | 0 |
N.S. |
1 | 0.00 | 1.16 | 2.28 | 1.80 | 1.96 | 1.68 | 2.40 | 0.00 |
time (sec) |
N/A | 0.000 | 0.557 | 0.439 | 0.314 | 0.260 | 0.198 | 0.290 | 0.000 |