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 | B | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 48 | 47 | 62 | 46 | 42 | 71 | 46 |
N.S. |
1 | 0.00 | 1.71 | 1.68 | 2.21 | 1.64 | 1.50 | 2.54 | 1.64 |
time (sec) |
N/A | 0.000 | 0.148 | 2.435 | 0.270 | 0.257 | 0.402 | 0.388 | 13.592 |
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 | 55 | 36 | 36 | 34 | 37 | 41 | 42 | 41 |
N.S. |
1 | 1.83 | 1.20 | 1.20 | 1.13 | 1.23 | 1.37 | 1.40 | 1.37 |
time (sec) |
N/A | 0.292 | 0.022 | 0.216 | 0.222 | 0.267 | 1.784 | 0.287 | 12.929 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 10 | 10 | 9 | 9 | 8 | 9 | 11 |
N.S. |
1 | 1.00 | 0.83 | 0.83 | 0.75 | 0.75 | 0.67 | 0.75 | 0.92 |
time (sec) |
N/A | 0.123 | 0.002 | 0.494 | 0.204 | 0.245 | 0.034 | 0.257 | 0.071 |
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 | 24 | 23 | 71 | 36 | 61 | 35 | 32 | 35 | 35 |
N.S. |
1 | 0.96 | 2.96 | 1.50 | 2.54 | 1.46 | 1.33 | 1.46 | 1.46 |
time (sec) |
N/A | 0.200 | 0.061 | 0.198 | 0.210 | 0.257 | 0.074 | 0.274 | 12.594 |
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 | 27 | 53 | 34 | 21 | 24 | 18 | 20 | 0 | 17 |
N.S. |
1 | 1.96 | 1.26 | 0.78 | 0.89 | 0.67 | 0.74 | 0.00 | 0.63 |
time (sec) |
N/A | 0.717 | 0.118 | 0.153 | 0.238 | 0.241 | 0.099 | 0.000 | 12.272 |
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 | 14 | 13 | 14 | 16 | 16 | 10 | 16 | 15 |
N.S. |
1 | 0.58 | 0.54 | 0.58 | 0.67 | 0.67 | 0.42 | 0.67 | 0.62 |
time (sec) |
N/A | 0.127 | 0.002 | 0.047 | 0.194 | 0.241 | 0.018 | 0.302 | 0.078 |
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 | 25 | 0 | 36 | 52 | 75 | 75 | 58 | 78 | 32 |
N.S. |
1 | 0.00 | 1.44 | 2.08 | 3.00 | 3.00 | 2.32 | 3.12 | 1.28 |
time (sec) |
N/A | 0.000 | 6.680 | 0.095 | 0.270 | 0.258 | 0.080 | 0.292 | 12.682 |
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 | 23 | 18 | 18 | 20 | 17 | 17 | 15 | 17 | 18 |
N.S. |
1 | 0.78 | 0.78 | 0.87 | 0.74 | 0.74 | 0.65 | 0.74 | 0.78 |
time (sec) |
N/A | 0.181 | 0.043 | 0.040 | 0.193 | 0.257 | 0.043 | 0.267 | 12.901 |
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 | 30 | 38 | 28 | 23 | 0 | 37 | 22 | 38 | 27 |
N.S. |
1 | 1.27 | 0.93 | 0.77 | 0.00 | 1.23 | 0.73 | 1.27 | 0.90 |
time (sec) |
N/A | 0.566 | 0.232 | 0.494 | 0.000 | 0.258 | 0.067 | 0.298 | 0.134 |
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 | 15 | 14 | 15 | 28 | 19 | 10 | 14 | 14 |
N.S. |
1 | 0.62 | 0.58 | 0.62 | 1.17 | 0.79 | 0.42 | 0.58 | 0.58 |
time (sec) |
N/A | 0.322 | 0.054 | 0.037 | 0.191 | 0.240 | 0.050 | 0.274 | 12.147 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F(-1) | A | F | A | A | F(-2) | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 0 | 25 | 0 | 29 | 26 | 0 | 77 |
N.S. |
1 | 0.00 | 0.00 | 1.04 | 0.00 | 1.21 | 1.08 | 0.00 | 3.21 |
time (sec) |
N/A | 0.000 | 0.000 | 0.520 | 0.000 | 0.256 | 0.124 | 0.000 | 14.007 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F(-1) | A | B | B | A | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 0 | 21 | 82 | 68 | 32 | 908 | 38 |
N.S. |
1 | 0.00 | 0.00 | 0.78 | 3.04 | 2.52 | 1.19 | 33.63 | 1.41 |
time (sec) |
N/A | 0.000 | 0.000 | 0.463 | 0.321 | 0.264 | 0.124 | 0.399 | 0.415 |
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 | 30 | 69 | 26 | 29 | 87 | 25 | 37 | 27 | 23 |
N.S. |
1 | 2.30 | 0.87 | 0.97 | 2.90 | 0.83 | 1.23 | 0.90 | 0.77 |
time (sec) |
N/A | 0.400 | 0.055 | 0.623 | 0.204 | 0.257 | 0.142 | 0.271 | 13.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | B | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 47 | 37 | 52 | 40 | 39 | 44 | 34 |
N.S. |
1 | 0.00 | 1.96 | 1.54 | 2.17 | 1.67 | 1.62 | 1.83 | 1.42 |
time (sec) |
N/A | 0.000 | 0.114 | 0.240 | 0.360 | 0.275 | 0.212 | 0.388 | 1.144 |
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 | 27 | 0 | 26 | 21 | 18 | 20 | 19 | 35 | 24 |
N.S. |
1 | 0.00 | 0.96 | 0.78 | 0.67 | 0.74 | 0.70 | 1.30 | 0.89 |
time (sec) |
N/A | 0.000 | 0.165 | 0.594 | 0.278 | 0.259 | 0.153 | 0.272 | 12.430 |
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 | 21 | 0 | 21 | 25 | 25 | 24 | 17 | 25 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.19 | 1.19 | 1.14 | 0.81 | 1.19 | 0.00 |
time (sec) |
N/A | 0.000 | 0.108 | 11.985 | 0.260 | 0.245 | 0.441 | 0.407 | 0.000 |
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 | 26 | 34 | 32 | 34 | 60 | 58 | 34 | 62 | 34 |
N.S. |
1 | 1.31 | 1.23 | 1.31 | 2.31 | 2.23 | 1.31 | 2.38 | 1.31 |
time (sec) |
N/A | 1.278 | 0.062 | 2.944 | 0.339 | 0.256 | 0.134 | 1.740 | 13.435 |
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 | 27 | 0 | 85 | 106 | 148 | 49 | 51 | 132 | 35 |
N.S. |
1 | 0.00 | 3.15 | 3.93 | 5.48 | 1.81 | 1.89 | 4.89 | 1.30 |
time (sec) |
N/A | 0.000 | 0.346 | 4.932 | 0.309 | 0.251 | 0.277 | 0.561 | 12.804 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 40 | 38 | 31 | 27 | 0 | 58 | 0 |
N.S. |
1 | 0.00 | 1.38 | 1.31 | 1.07 | 0.93 | 0.00 | 2.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.512 | 1.825 | 0.314 | 0.251 | 0.000 | 0.287 | 0.000 |
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 | 20 | 19 | 16 | 20 | 22 | 14 | 15 | 15 |
N.S. |
1 | 1.00 | 0.95 | 0.80 | 1.00 | 1.10 | 0.70 | 0.75 | 0.75 |
time (sec) |
N/A | 0.228 | 0.007 | 0.021 | 0.222 | 0.245 | 0.038 | 0.272 | 12.517 |
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 | 22 | 21 | 20 | 32 | 20 | 41 | 20 |
N.S. |
1 | 0.00 | 0.88 | 0.84 | 0.80 | 1.28 | 0.80 | 1.64 | 0.80 |
time (sec) |
N/A | 0.000 | 0.132 | 0.164 | 0.282 | 0.257 | 1.177 | 0.275 | 12.871 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 53 | 0 | 66 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.04 | 0.00 | 2.54 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.171 | 0.070 | 0.372 | 0.000 | 0.251 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | A | A | F(-2) | A | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 24 | 186 | 26 | 35 | 0 | 26 | 25 |
N.S. |
1 | 0.00 | 0.89 | 6.89 | 0.96 | 1.30 | 0.00 | 0.96 | 0.93 |
time (sec) |
N/A | 0.000 | 0.946 | 0.071 | 0.289 | 0.261 | 0.000 | 0.315 | 13.370 |
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 | 14 | 12 | 14 | 13 | 13 | 14 | 13 | 13 |
N.S. |
1 | 0.88 | 0.75 | 0.88 | 0.81 | 0.81 | 0.88 | 0.81 | 0.81 |
time (sec) |
N/A | 0.142 | 0.003 | 0.063 | 0.195 | 0.268 | 0.053 | 0.288 | 12.918 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 22 | 23 | 16 | 19 | 19 | 19 | 19 | 15 |
N.S. |
1 | 0.69 | 0.72 | 0.50 | 0.59 | 0.59 | 0.59 | 0.59 | 0.47 |
time (sec) |
N/A | 0.153 | 0.002 | 0.088 | 0.196 | 0.231 | 0.025 | 0.276 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 7 | 9 | 7 | 9 | 9 | 7 | 9 | 6 |
N.S. |
1 | 0.33 | 0.43 | 0.33 | 0.43 | 0.43 | 0.33 | 0.43 | 0.29 |
time (sec) |
N/A | 0.120 | 0.000 | 0.006 | 0.194 | 0.239 | 0.016 | 0.287 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 54 | 42 | 33 | 50 | 39 | 34 | 50 | 30 |
N.S. |
1 | 2.35 | 1.83 | 1.43 | 2.17 | 1.70 | 1.48 | 2.17 | 1.30 |
time (sec) |
N/A | 0.176 | 0.028 | 0.095 | 0.195 | 0.263 | 0.060 | 0.263 | 12.497 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | F | B | B | B | B | B | B |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 70 | 0 | 64 | 66 | 66 | 70 | 62 | 62 |
N.S. |
1 | 2.12 | 0.00 | 1.94 | 2.00 | 2.00 | 2.12 | 1.88 | 1.88 |
time (sec) |
N/A | 0.977 | 0.000 | 0.350 | 0.230 | 0.262 | 0.254 | 0.332 | 13.760 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 55 | 27 | 37 | 22 | 22 | 0 | 22 |
N.S. |
1 | 0.00 | 2.20 | 1.08 | 1.48 | 0.88 | 0.88 | 0.00 | 0.88 |
time (sec) |
N/A | 0.000 | 0.595 | 0.146 | 0.393 | 0.255 | 0.874 | 0.000 | 13.578 |
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 | 21 | 21 | 21 | 34 | 36 | 14 | 38 | 31 |
N.S. |
1 | 0.81 | 0.81 | 0.81 | 1.31 | 1.38 | 0.54 | 1.46 | 1.19 |
time (sec) |
N/A | 0.968 | 3.144 | 0.113 | 0.241 | 0.259 | 0.071 | 0.283 | 0.190 |
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 | 30 | 23 | 28 | 27 | 28 | 46 |
N.S. |
1 | 0.00 | 1.20 | 1.20 | 0.92 | 1.12 | 1.08 | 1.12 | 1.84 |
time (sec) |
N/A | 0.000 | 0.386 | 0.744 | 0.303 | 0.257 | 0.091 | 0.323 | 12.467 |
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 | 45 | 38 | 41 | 41 | 36 | 47 | 313 |
N.S. |
1 | 0.00 | 1.41 | 1.19 | 1.28 | 1.28 | 1.12 | 1.47 | 9.78 |
time (sec) |
N/A | 0.000 | 0.051 | 4.698 | 0.331 | 0.246 | 0.082 | 0.305 | 13.702 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 27 | 29 | 205 | 29 | 37 | 140 | 225 |
N.S. |
1 | 0.00 | 0.93 | 1.00 | 7.07 | 1.00 | 1.28 | 4.83 | 7.76 |
time (sec) |
N/A | 0.000 | 1.710 | 0.525 | 0.390 | 0.281 | 0.161 | 0.347 | 15.668 |
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 | 37 | 34 | 29 | 32 | 32 | 31 | 32 | 30 |
N.S. |
1 | 1.85 | 1.70 | 1.45 | 1.60 | 1.60 | 1.55 | 1.60 | 1.50 |
time (sec) |
N/A | 0.157 | 0.012 | 0.040 | 0.196 | 0.238 | 0.024 | 0.275 | 0.055 |
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 | 24 | 78 | 40 | 43 | 0 | 59 | 42 | 79 | 52 |
N.S. |
1 | 3.25 | 1.67 | 1.79 | 0.00 | 2.46 | 1.75 | 3.29 | 2.17 |
time (sec) |
N/A | 0.864 | 0.373 | 0.256 | 0.000 | 0.253 | 0.129 | 0.275 | 13.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 0 | 36 | 30 | 36 | 31 | 40 | 37 |
N.S. |
1 | 0.00 | 0.00 | 1.44 | 1.20 | 1.44 | 1.24 | 1.60 | 1.48 |
time (sec) |
N/A | 0.000 | 0.000 | 0.715 | 0.430 | 0.278 | 0.201 | 0.341 | 13.602 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 261 | 25 | 22 | 111 | 32 | 17 | 50 | 21 |
N.S. |
1 | 12.43 | 1.19 | 1.05 | 5.29 | 1.52 | 0.81 | 2.38 | 1.00 |
time (sec) |
N/A | 0.850 | 0.409 | 0.561 | 0.330 | 0.258 | 0.076 | 0.311 | 12.850 |
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 | 17 | 23 | 18 | 17 | 33 | 16 | 15 | 21 | 16 |
N.S. |
1 | 1.35 | 1.06 | 1.00 | 1.94 | 0.94 | 0.88 | 1.24 | 0.94 |
time (sec) |
N/A | 0.273 | 0.196 | 0.262 | 0.218 | 0.264 | 0.057 | 0.268 | 0.103 |
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 | 34 | 0 | 25 | 26 | 56 | 59 | 39 | 56 | 42 |
N.S. |
1 | 0.00 | 0.74 | 0.76 | 1.65 | 1.74 | 1.15 | 1.65 | 1.24 |
time (sec) |
N/A | 0.000 | 3.080 | 0.375 | 0.263 | 0.251 | 0.104 | 0.319 | 0.293 |
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 | 12 | 0 | 8 | 9 | 8 | 8 | 8 | 8 | 8 |
N.S. |
1 | 0.00 | 0.67 | 0.75 | 0.67 | 0.67 | 0.67 | 0.67 | 0.67 |
time (sec) |
N/A | 0.000 | 0.046 | 0.804 | 0.207 | 0.258 | 0.061 | 0.275 | 12.550 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 51 | 72 | 46 | 43 | 60 | 44 | 41 | 57 |
N.S. |
1 | 2.04 | 2.88 | 1.84 | 1.72 | 2.40 | 1.76 | 1.64 | 2.28 |
time (sec) |
N/A | 0.316 | 0.096 | 0.113 | 0.184 | 0.250 | 0.162 | 0.267 | 13.208 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 10 | 10 | 11 | 12 | 10 | 10 | 12 | 10 |
N.S. |
1 | 0.67 | 0.67 | 0.73 | 0.80 | 0.67 | 0.67 | 0.80 | 0.67 |
time (sec) |
N/A | 0.139 | 0.002 | 0.056 | 0.203 | 0.260 | 0.028 | 0.271 | 0.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 43 | 53 | 82 | 57 | 54 | 142 | 117 |
N.S. |
1 | 0.00 | 1.26 | 1.56 | 2.41 | 1.68 | 1.59 | 4.18 | 3.44 |
time (sec) |
N/A | 0.000 | 0.450 | 18.672 | 0.377 | 0.267 | 0.579 | 0.568 | 13.735 |
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 | 15 | 15 | 12 | 11 | 15 | 8 | 11 | 11 |
N.S. |
1 | 0.65 | 0.65 | 0.52 | 0.48 | 0.65 | 0.35 | 0.48 | 0.48 |
time (sec) |
N/A | 0.161 | 0.009 | 0.796 | 0.206 | 0.245 | 0.031 | 0.265 | 13.265 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 77 | 133 | 505 | 505 | 238 | 728 | 0 |
N.S. |
1 | 0.00 | 2.14 | 3.69 | 14.03 | 14.03 | 6.61 | 20.22 | 0.00 |
time (sec) |
N/A | 0.000 | 0.381 | 4.354 | 0.530 | 0.309 | 0.704 | 67.576 | 0.000 |
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 | 31 | 29 | 27 | 25 | 31 | 45 | 22 | 28 | 22 |
N.S. |
1 | 0.94 | 0.87 | 0.81 | 1.00 | 1.45 | 0.71 | 0.90 | 0.71 |
time (sec) |
N/A | 0.482 | 0.072 | 0.608 | 0.232 | 0.266 | 3.972 | 0.296 | 13.170 |
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 | 22 | 19 | 18 | 17 | 16 | 16 | 19 | 0 | 14 |
N.S. |
1 | 0.86 | 0.82 | 0.77 | 0.73 | 0.73 | 0.86 | 0.00 | 0.64 |
time (sec) |
N/A | 0.156 | 0.023 | 0.136 | 0.212 | 0.264 | 0.437 | 0.000 | 13.654 |
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 | 28 | 26 | 25 | 24 | 24 | 26 | 24 | 24 |
N.S. |
1 | 1.33 | 1.24 | 1.19 | 1.14 | 1.14 | 1.24 | 1.14 | 1.14 |
time (sec) |
N/A | 2.064 | 0.379 | 1.238 | 0.263 | 0.272 | 0.173 | 0.286 | 15.134 |
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 | 28 | 0 | 34 | 27 | 31 | 26 | 26 | 989 | 0 |
N.S. |
1 | 0.00 | 1.21 | 0.96 | 1.11 | 0.93 | 0.93 | 35.32 | 0.00 |
time (sec) |
N/A | 0.000 | 0.151 | 0.646 | 0.377 | 0.263 | 0.121 | 0.357 | 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 | 44 | 39 | 43 | 34 | 41 | 39 | 48 | 39 |
N.S. |
1 | 1.63 | 1.44 | 1.59 | 1.26 | 1.52 | 1.44 | 1.78 | 1.44 |
time (sec) |
N/A | 1.160 | 1.568 | 0.219 | 0.347 | 0.281 | 0.156 | 0.337 | 13.828 |
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 | 23 | 0 | 30 | 48 | 93 | 46 | 46 | 0 | 144 |
N.S. |
1 | 0.00 | 1.30 | 2.09 | 4.04 | 2.00 | 2.00 | 0.00 | 6.26 |
time (sec) |
N/A | 0.000 | 1.569 | 0.536 | 0.817 | 0.261 | 0.188 | 0.000 | 12.756 |
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 | 10 | 10 | 10 | 9 | 12 | 5 | 9 | 9 |
N.S. |
1 | 0.59 | 0.59 | 0.59 | 0.53 | 0.71 | 0.29 | 0.53 | 0.53 |
time (sec) |
N/A | 0.137 | 0.001 | 0.078 | 0.207 | 0.272 | 0.032 | 0.280 | 12.714 |
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 | 21 | 0 | 19 | 19 | 16 | 52 | 17 | 16 | 17 |
N.S. |
1 | 0.00 | 0.90 | 0.90 | 0.76 | 2.48 | 0.81 | 0.76 | 0.81 |
time (sec) |
N/A | 0.000 | 0.213 | 0.425 | 0.308 | 0.272 | 0.249 | 0.258 | 13.213 |
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 | 14 | 14 | 15 | 14 | 19 | 14 | 14 | 14 |
N.S. |
1 | 0.82 | 0.82 | 0.88 | 0.82 | 1.12 | 0.82 | 0.82 | 0.82 |
time (sec) |
N/A | 0.264 | 0.008 | 0.046 | 0.192 | 0.271 | 0.047 | 0.264 | 12.759 |
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 | 26 | 0 | 23 | 36 | 20 | 31 | 31 | 60 | 46 |
N.S. |
1 | 0.00 | 0.88 | 1.38 | 0.77 | 1.19 | 1.19 | 2.31 | 1.77 |
time (sec) |
N/A | 0.000 | 0.601 | 0.382 | 0.449 | 0.266 | 0.226 | 0.294 | 13.855 |
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 | 14 | 11 | 10 | 9 | 9 | 8 | 9 | 9 |
N.S. |
1 | 1.27 | 1.00 | 0.91 | 0.82 | 0.82 | 0.73 | 0.82 | 0.82 |
time (sec) |
N/A | 0.139 | 0.004 | 0.034 | 0.204 | 0.244 | 0.039 | 0.272 | 13.258 |
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 | 16 | 16 | 11 | 10 | 16 | 8 | 11 | 12 |
N.S. |
1 | 1.23 | 1.23 | 0.85 | 0.77 | 1.23 | 0.62 | 0.85 | 0.92 |
time (sec) |
N/A | 0.200 | 0.010 | 0.046 | 0.208 | 0.247 | 0.038 | 0.267 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | B | A | A | F | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 0 | 34 | 60 | 33 | 36 | 0 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.26 | 2.22 | 1.22 | 1.33 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 1.191 | 0.500 | 0.271 | 48.404 | 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 | 26 | 38 | 24 | 36 | 22 | 35 | 36 | 33 | 36 |
N.S. |
1 | 1.46 | 0.92 | 1.38 | 0.85 | 1.35 | 1.38 | 1.27 | 1.38 |
time (sec) |
N/A | 0.724 | 0.198 | 2.063 | 0.409 | 0.253 | 0.330 | 1.437 | 14.333 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | B | F | B | B | F(-1) | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 0 | 252 | 0 | 135 | 168 | 0 | 178 |
N.S. |
1 | 0.00 | 0.00 | 10.96 | 0.00 | 5.87 | 7.30 | 0.00 | 7.74 |
time (sec) |
N/A | 0.000 | 0.000 | 11.447 | 0.000 | 0.268 | 0.972 | 0.000 | 15.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | F(-1) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 31 | 27 | 67 | 26 | 0 | 0 | 71 |
N.S. |
1 | 0.00 | 1.03 | 0.90 | 2.23 | 0.87 | 0.00 | 0.00 | 2.37 |
time (sec) |
N/A | 0.000 | 0.286 | 62.063 | 1.015 | 0.258 | 0.000 | 0.000 | 14.480 |
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 | 15 | 23 | 17 | 12 | 16 | 19 | 12 | 15 |
N.S. |
1 | 0.65 | 1.00 | 0.74 | 0.52 | 0.70 | 0.83 | 0.52 | 0.65 |
time (sec) |
N/A | 0.131 | 0.000 | 0.030 | 0.192 | 0.261 | 0.017 | 0.270 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 39 | 27 | 24 | 23 | 26 | 31 | 23 | 25 |
N.S. |
1 | 1.44 | 1.00 | 0.89 | 0.85 | 0.96 | 1.15 | 0.85 | 0.93 |
time (sec) |
N/A | 0.253 | 0.055 | 0.071 | 0.206 | 0.260 | 0.051 | 0.285 | 0.104 |
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 | 14 | 14 | 15 | 16 | 18 | 17 | 18 | 13 |
N.S. |
1 | 0.82 | 0.82 | 0.88 | 0.94 | 1.06 | 1.00 | 1.06 | 0.76 |
time (sec) |
N/A | 0.396 | 0.067 | 0.274 | 0.355 | 0.256 | 0.072 | 0.272 | 14.282 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 0 | 29 | 30 | 26 | 26 | 28 | 29 |
N.S. |
1 | 0.00 | 0.00 | 0.97 | 1.00 | 0.87 | 0.87 | 0.93 | 0.97 |
time (sec) |
N/A | 0.000 | 0.000 | 0.168 | 0.288 | 0.278 | 111.828 | 0.267 | 14.383 |
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 | 22 | 21 | 22 | 22 | 20 | 22 | 22 |
N.S. |
1 | 1.05 | 1.05 | 1.00 | 1.05 | 1.05 | 0.95 | 1.05 | 1.05 |
time (sec) |
N/A | 1.226 | 0.265 | 1.411 | 0.247 | 0.275 | 0.115 | 0.280 | 14.355 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | B | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 31 | 32 | 52 | 43 | 51 | 0 | 0 |
N.S. |
1 | 0.00 | 0.86 | 0.89 | 1.44 | 1.19 | 1.42 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 8.922 | 0.253 | 0.291 | 0.263 | 0.136 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | A | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 23 | 56 | 267 | 45 | 42 | 0 | 155 |
N.S. |
1 | 0.00 | 0.88 | 2.15 | 10.27 | 1.73 | 1.62 | 0.00 | 5.96 |
time (sec) |
N/A | 0.000 | 1.561 | 2.278 | 0.711 | 0.271 | 0.416 | 0.000 | 14.469 |
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 | 31 | 102 | 27 | 26 | 105 | 21 | 14 | 21 | 22 |
N.S. |
1 | 3.29 | 0.87 | 0.84 | 3.39 | 0.68 | 0.45 | 0.68 | 0.71 |
time (sec) |
N/A | 0.410 | 0.141 | 0.624 | 0.222 | 0.264 | 0.083 | 0.276 | 14.176 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | C | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 23 | 18 | 15 | 14 | 19 | 10 | 4 | 11 |
N.S. |
1 | 0.96 | 0.75 | 0.62 | 0.58 | 0.79 | 0.42 | 0.17 | 0.46 |
time (sec) |
N/A | 0.185 | 0.019 | 0.108 | 0.209 | 0.266 | 0.062 | 0.273 | 14.175 |
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 | 38 | 21 | 21 | 21 | 32 | 14 | 21 | 21 |
N.S. |
1 | 1.73 | 0.95 | 0.95 | 0.95 | 1.45 | 0.64 | 0.95 | 0.95 |
time (sec) |
N/A | 0.333 | 0.020 | 0.108 | 0.189 | 0.252 | 0.083 | 0.266 | 0.079 |
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 | 20 | 18 | 17 | 20 | 20 | 17 | 20 | 18 |
N.S. |
1 | 1.25 | 1.12 | 1.06 | 1.25 | 1.25 | 1.06 | 1.25 | 1.12 |
time (sec) |
N/A | 0.146 | 0.005 | 0.055 | 0.188 | 0.239 | 0.020 | 0.255 | 0.039 |
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 | 16 | 14 | 14 | 15 | 40 | 14 | 12 | 14 | 14 |
N.S. |
1 | 0.88 | 0.88 | 0.94 | 2.50 | 0.88 | 0.75 | 0.88 | 0.88 |
time (sec) |
N/A | 0.245 | 0.038 | 0.529 | 0.201 | 0.263 | 0.051 | 0.266 | 13.890 |
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 | 19 | 0 | 19 | 22 | 40 | 42 | 19 | 42 | 21 |
N.S. |
1 | 0.00 | 1.00 | 1.16 | 2.11 | 2.21 | 1.00 | 2.21 | 1.11 |
time (sec) |
N/A | 0.000 | 0.055 | 1.815 | 0.273 | 0.258 | 0.083 | 0.366 | 15.629 |
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 | 21 | 21 | 20 | 18 | 24 | 12 | 18 | 19 |
N.S. |
1 | 0.72 | 0.72 | 0.69 | 0.62 | 0.83 | 0.41 | 0.62 | 0.66 |
time (sec) |
N/A | 0.260 | 0.011 | 0.048 | 0.206 | 0.259 | 0.031 | 0.275 | 0.055 |
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 | 39 | 25 | 23 | 31 | 22 | 20 | 22 | 26 |
N.S. |
1 | 1.50 | 0.96 | 0.88 | 1.19 | 0.85 | 0.77 | 0.85 | 1.00 |
time (sec) |
N/A | 0.169 | 0.035 | 0.052 | 0.199 | 0.253 | 0.054 | 0.299 | 0.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | C | A | A | F(-1) | B | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 64 | 569 | 46 | 42 | 0 | 61 | 62 |
N.S. |
1 | 0.00 | 2.06 | 18.35 | 1.48 | 1.35 | 0.00 | 1.97 | 2.00 |
time (sec) |
N/A | 0.000 | 0.345 | 0.195 | 0.457 | 0.265 | 0.000 | 0.661 | 14.024 |
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 | 23 | 153 | 184 | 109 | 265 | 98 | 124 | 108 | 107 |
N.S. |
1 | 6.65 | 8.00 | 4.74 | 11.52 | 4.26 | 5.39 | 4.70 | 4.65 |
time (sec) |
N/A | 0.607 | 0.066 | 0.140 | 0.228 | 0.259 | 0.634 | 0.275 | 13.777 |
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 | 19 | 18 | 23 | 17 | 15 | 34 | 19 |
N.S. |
1 | 0.00 | 0.83 | 0.78 | 1.00 | 0.74 | 0.65 | 1.48 | 0.83 |
time (sec) |
N/A | 0.000 | 0.516 | 0.541 | 0.297 | 0.257 | 0.164 | 0.691 | 14.704 |
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 | 22 | 55 | 19 | 15 | 43 | 15 | 14 | 17 | 46 |
N.S. |
1 | 2.50 | 0.86 | 0.68 | 1.95 | 0.68 | 0.64 | 0.77 | 2.09 |
time (sec) |
N/A | 0.378 | 0.056 | 0.439 | 0.337 | 0.266 | 0.071 | 0.269 | 0.155 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | B | A | F(-2) | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 74 | 56 | 66 | 56 | 0 | 82 | 0 |
N.S. |
1 | 0.00 | 2.11 | 1.60 | 1.89 | 1.60 | 0.00 | 2.34 | 0.00 |
time (sec) |
N/A | 0.000 | 0.240 | 0.125 | 0.564 | 0.280 | 0.000 | 1.046 | 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 | 18 | 18 | 19 | 18 | 18 | 15 | 18 | 18 |
N.S. |
1 | 0.95 | 0.95 | 1.00 | 0.95 | 0.95 | 0.79 | 0.95 | 0.95 |
time (sec) |
N/A | 0.650 | 0.136 | 0.597 | 0.266 | 0.265 | 0.113 | 0.269 | 15.045 |
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 | 22 | 22 | 21 | 26 | 20 | 22 | 20 | 20 |
N.S. |
1 | 0.92 | 0.92 | 0.88 | 1.08 | 0.83 | 0.92 | 0.83 | 0.83 |
time (sec) |
N/A | 0.167 | 0.041 | 0.098 | 0.192 | 0.254 | 0.089 | 0.258 | 0.125 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 43 | 30 | 29 | 28 | 24 | 31 | 29 | 29 |
N.S. |
1 | 1.39 | 0.97 | 0.94 | 0.90 | 0.77 | 1.00 | 0.94 | 0.94 |
time (sec) |
N/A | 0.215 | 0.048 | 0.102 | 0.216 | 0.248 | 0.086 | 0.262 | 14.534 |
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 | 18 | 18 | 17 | 16 | 32 | 14 | 43 | 16 |
N.S. |
1 | 0.60 | 0.60 | 0.57 | 0.53 | 1.07 | 0.47 | 1.43 | 0.53 |
time (sec) |
N/A | 0.403 | 0.060 | 0.515 | 0.257 | 0.265 | 0.098 | 0.273 | 14.613 |
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 | 18 | 33 | 18 | 16 | 52 | 15 | 17 | 15 | 18 |
N.S. |
1 | 1.83 | 1.00 | 0.89 | 2.89 | 0.83 | 0.94 | 0.83 | 1.00 |
time (sec) |
N/A | 0.502 | 0.154 | 0.688 | 0.331 | 0.260 | 0.061 | 0.266 | 15.194 |
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 | 26 | 25 | 24 | 24 | 20 | 24 | 24 |
N.S. |
1 | 0.96 | 0.96 | 0.93 | 0.89 | 0.89 | 0.74 | 0.89 | 0.89 |
time (sec) |
N/A | 0.484 | 0.022 | 0.059 | 0.211 | 0.270 | 0.087 | 0.260 | 13.888 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 74 | 60 | 58 | 91 | 61 | 56 | 76 | 63 |
N.S. |
1 | 2.18 | 1.76 | 1.71 | 2.68 | 1.79 | 1.65 | 2.24 | 1.85 |
time (sec) |
N/A | 0.335 | 0.132 | 0.185 | 0.212 | 0.268 | 0.092 | 0.278 | 14.132 |
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 | 27 | 0 | 23 | 24 | 27 | 23 | 22 | 181 | 41 |
N.S. |
1 | 0.00 | 0.85 | 0.89 | 1.00 | 0.85 | 0.81 | 6.70 | 1.52 |
time (sec) |
N/A | 0.000 | 5.085 | 0.627 | 0.350 | 0.256 | 0.093 | 0.293 | 0.694 |
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 | 21 | 0 | 21 | 21 | 89 | 20 | 0 | 20 | 20 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 4.24 | 0.95 | 0.00 | 0.95 | 0.95 |
time (sec) |
N/A | 0.000 | 1.631 | 2.515 | 0.371 | 0.267 | 0.000 | 3.088 | 13.768 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 36 | 42 | 49 | 49 | 36 | 39 | 39 |
N.S. |
1 | 0.00 | 1.50 | 1.75 | 2.04 | 2.04 | 1.50 | 1.62 | 1.62 |
time (sec) |
N/A | 0.000 | 0.260 | 1.132 | 0.240 | 0.260 | 0.139 | 0.274 | 13.900 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 60 | 41 | 33 | 65 | 31 | 37 | 37 | 18 |
N.S. |
1 | 3.16 | 2.16 | 1.74 | 3.42 | 1.63 | 1.95 | 1.95 | 0.95 |
time (sec) |
N/A | 0.239 | 0.018 | 0.546 | 0.205 | 0.272 | 0.067 | 0.272 | 13.545 |
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 | 24 | 22 | 24 | 26 | 0 | 21 | 20 | 33 | 20 |
N.S. |
1 | 0.92 | 1.00 | 1.08 | 0.00 | 0.88 | 0.83 | 1.38 | 0.83 |
time (sec) |
N/A | 0.507 | 0.115 | 0.233 | 0.000 | 0.261 | 0.166 | 0.266 | 14.204 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | F(-1) | B | B | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 0 | 56 | 0 | 81 | 85 | 302 | 223 |
N.S. |
1 | 0.00 | 0.00 | 1.75 | 0.00 | 2.53 | 2.66 | 9.44 | 6.97 |
time (sec) |
N/A | 0.000 | 0.000 | 117.568 | 0.000 | 0.281 | 1.259 | 1.066 | 15.054 |
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 | 22 | 0 | 21 | 21 | 188 | 20 | 15 | 20 | 20 |
N.S. |
1 | 0.00 | 0.95 | 0.95 | 8.55 | 0.91 | 0.68 | 0.91 | 0.91 |
time (sec) |
N/A | 0.000 | 0.389 | 0.386 | 0.326 | 0.261 | 0.096 | 0.267 | 0.308 |
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 | 18 | 15 | 16 | 15 | 16 | 15 | 16 | 63 |
N.S. |
1 | 1.20 | 1.00 | 1.07 | 1.00 | 1.07 | 1.00 | 1.07 | 4.20 |
time (sec) |
N/A | 0.348 | 0.299 | 0.709 | 0.311 | 0.267 | 0.058 | 0.266 | 0.274 |
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 | 21 | 22 | 15 | 16 | 14 | 14 | 15 | 13 |
N.S. |
1 | 1.11 | 1.16 | 0.79 | 0.84 | 0.74 | 0.74 | 0.79 | 0.68 |
time (sec) |
N/A | 0.152 | 0.009 | 0.491 | 0.194 | 0.254 | 0.049 | 0.260 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 29 | 37 | 0 | 57 | 29 | 0 | 0 |
N.S. |
1 | 0.00 | 0.91 | 1.16 | 0.00 | 1.78 | 0.91 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.147 | 44.371 | 0.000 | 0.269 | 76.464 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 0 | 19 | 15 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 1.00 | 0.79 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.558 | 0.294 | 0.000 | 0.299 | 0.246 | 0.000 | 0.000 | 0.000 |
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 | 34 | 95 | 45 | 32 | 58 | 34 | 29 | 77 | 77 |
N.S. |
1 | 2.79 | 1.32 | 0.94 | 1.71 | 1.00 | 0.85 | 2.26 | 2.26 |
time (sec) |
N/A | 0.822 | 0.516 | 44.715 | 0.315 | 0.243 | 2.291 | 0.325 | 14.449 |