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 | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 48 | 47 | 62 | 46 | 42 | 71 | 42 | 46 |
N.S. |
1 | 0.00 | 1.71 | 1.68 | 2.21 | 1.64 | 1.50 | 2.54 | 1.50 | 1.64 |
time (sec) |
N/A | 0.000 | 0.090 | 2.373 | 0.072 | 0.091 | 0.459 | 0.220 | 0.156 | 3.540 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 55 | 36 | 36 | 34 | 37 | 41 | 42 | 45 | 41 |
N.S. |
1 | 1.83 | 1.20 | 1.20 | 1.13 | 1.23 | 1.37 | 1.40 | 1.50 | 1.37 |
time (sec) |
N/A | 0.313 | 0.013 | 0.234 | 0.029 | 0.092 | 2.423 | 0.114 | 0.156 | 3.369 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 10 | 10 | 9 | 9 | 8 | 9 | 11 | 11 |
N.S. |
1 | 1.00 | 0.83 | 0.83 | 0.75 | 0.75 | 0.67 | 0.75 | 0.92 | 0.92 |
time (sec) |
N/A | 0.131 | 0.001 | 0.064 | 0.033 | 0.088 | 0.037 | 0.112 | 0.155 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 23 | 71 | 36 | 61 | 35 | 32 | 35 | 36 | 35 |
N.S. |
1 | 0.96 | 2.96 | 1.50 | 2.54 | 1.46 | 1.33 | 1.46 | 1.50 | 1.46 |
time (sec) |
N/A | 0.211 | 0.037 | 0.121 | 0.037 | 0.091 | 0.092 | 0.116 | 0.160 | 3.381 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 53 | 34 | 21 | 24 | 18 | 20 | 0 | 17 | 17 |
N.S. |
1 | 1.96 | 1.26 | 0.78 | 0.89 | 0.67 | 0.74 | 0.00 | 0.63 | 0.63 |
time (sec) |
N/A | 1.198 | 0.071 | 0.632 | 0.069 | 0.092 | 0.114 | 0.000 | 0.156 | 3.478 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 14 | 13 | 14 | 16 | 16 | 10 | 16 | 13 | 15 |
N.S. |
1 | 0.58 | 0.54 | 0.58 | 0.67 | 0.67 | 0.42 | 0.67 | 0.54 | 0.62 |
time (sec) |
N/A | 0.211 | 0.001 | 0.024 | 0.028 | 0.088 | 0.021 | 0.108 | 0.153 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 36 | 52 | 75 | 75 | 58 | 78 | 83 | 32 |
N.S. |
1 | 0.00 | 1.44 | 2.08 | 3.00 | 3.00 | 2.32 | 3.12 | 3.32 | 1.28 |
time (sec) |
N/A | 0.000 | 5.940 | 0.554 | 0.076 | 0.094 | 0.105 | 0.127 | 0.157 | 3.522 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 18 | 18 | 20 | 17 | 17 | 15 | 17 | 31 | 18 |
N.S. |
1 | 0.78 | 0.78 | 0.87 | 0.74 | 0.74 | 0.65 | 0.74 | 1.35 | 0.78 |
time (sec) |
N/A | 0.225 | 0.026 | 0.087 | 0.029 | 0.096 | 0.050 | 0.114 | 0.156 | 3.362 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 38 | 28 | 23 | 0 | 37 | 22 | 38 | 35 | 27 |
N.S. |
1 | 1.27 | 0.93 | 0.77 | 0.00 | 1.23 | 0.73 | 1.27 | 1.17 | 0.90 |
time (sec) |
N/A | 0.582 | 0.144 | 0.485 | 0.000 | 0.099 | 0.072 | 0.120 | 0.155 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 15 | 14 | 15 | 28 | 19 | 10 | 14 | 22 | 14 |
N.S. |
1 | 0.62 | 0.58 | 0.62 | 1.17 | 0.79 | 0.42 | 0.58 | 0.92 | 0.58 |
time (sec) |
N/A | 0.346 | 0.033 | 0.119 | 0.030 | 0.097 | 0.063 | 0.108 | 0.156 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | F | A | A | F(-2) | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 0 | 25 | 0 | 29 | 26 | 0 | 45 | 77 |
N.S. |
1 | 0.00 | 0.00 | 1.04 | 0.00 | 1.21 | 1.08 | 0.00 | 1.88 | 3.21 |
time (sec) |
N/A | 0.000 | 0.000 | 0.661 | 0.000 | 0.097 | 0.142 | 0.000 | 0.157 | 3.854 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | B | B | A | B | F | B |
verified | N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 68183 | 21 | 82 | 68 | 32 | 908 | 138 | 38 |
N.S. |
1 | 0.00 | 2525.30 | 0.78 | 3.04 | 2.52 | 1.19 | 33.63 | 5.11 | 1.41 |
time (sec) |
N/A | 0.000 | 81.364 | 1.335 | 0.109 | 0.090 | 0.136 | 0.224 | 200.012 | 0.153 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 69 | 26 | 29 | 87 | 25 | 37 | 27 | 25 | 23 |
N.S. |
1 | 2.30 | 0.87 | 0.97 | 2.90 | 0.83 | 1.23 | 0.90 | 0.83 | 0.77 |
time (sec) |
N/A | 0.412 | 0.032 | 0.270 | 0.031 | 0.091 | 0.167 | 0.114 | 0.168 | 3.412 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | B | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 47 | 37 | 52 | 40 | 39 | 44 | 47 | 34 |
N.S. |
1 | 0.00 | 1.96 | 1.54 | 2.17 | 1.67 | 1.62 | 1.83 | 1.96 | 1.42 |
time (sec) |
N/A | 0.000 | 0.068 | 0.278 | 0.150 | 0.107 | 0.249 | 0.192 | 0.245 | 0.608 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 26 | 21 | 18 | 20 | 19 | 35 | 29 | 24 |
N.S. |
1 | 0.00 | 0.96 | 0.78 | 0.67 | 0.74 | 0.70 | 1.30 | 1.07 | 0.89 |
time (sec) |
N/A | 0.000 | 0.096 | 0.216 | 0.090 | 0.081 | 0.185 | 0.112 | 0.162 | 3.416 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 21 | 25 | 25 | 24 | 17 | 25 | 24 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.19 | 1.19 | 1.14 | 0.81 | 1.19 | 1.14 | 0.00 |
time (sec) |
N/A | 0.000 | 0.069 | 6.258 | 0.080 | 0.092 | 0.502 | 0.229 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 34 | 32 | 34 | 60 | 58 | 34 | 62 | 65 | 34 |
N.S. |
1 | 1.31 | 1.23 | 1.31 | 2.31 | 2.23 | 1.31 | 2.38 | 2.50 | 1.31 |
time (sec) |
N/A | 2.165 | 0.037 | 1.697 | 0.159 | 0.100 | 0.145 | 1.517 | 0.166 | 3.759 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 85 | 106 | 148 | 49 | 51 | 132 | 192 | 35 |
N.S. |
1 | 0.00 | 3.15 | 3.93 | 5.48 | 1.81 | 1.89 | 4.89 | 7.11 | 1.30 |
time (sec) |
N/A | 0.000 | 0.209 | 3.053 | 0.136 | 0.097 | 0.289 | 0.415 | 0.187 | 3.582 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 40 | 38 | 31 | 27 | 0 | 58 | 43 | 0 |
N.S. |
1 | 0.00 | 1.38 | 1.31 | 1.07 | 0.93 | 0.00 | 2.00 | 1.48 | 0.00 |
time (sec) |
N/A | 0.000 | 0.301 | 1.878 | 0.153 | 0.090 | 0.000 | 0.119 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 19 | 16 | 20 | 22 | 14 | 15 | 18 | 15 |
N.S. |
1 | 1.00 | 0.95 | 0.80 | 1.00 | 1.10 | 0.70 | 0.75 | 0.90 | 0.75 |
time (sec) |
N/A | 0.238 | 0.004 | 0.075 | 0.048 | 0.077 | 0.040 | 0.109 | 0.151 | 3.328 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 22 | 21 | 20 | 32 | 20 | 41 | 40 | 20 |
N.S. |
1 | 0.00 | 0.88 | 0.84 | 0.80 | 1.28 | 0.80 | 1.64 | 1.60 | 0.80 |
time (sec) |
N/A | 0.000 | 0.080 | 0.119 | 0.085 | 0.091 | 1.220 | 0.113 | 0.155 | 3.422 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 53 | 0 | 66 | 0 | 0 | 77 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.04 | 0.00 | 2.54 | 0.00 | 0.00 | 2.96 | 0.00 |
time (sec) |
N/A | 1.230 | 0.041 | 0.561 | 0.000 | 0.095 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | A | A | F(-2) | A | F | B |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 24 | 186 | 26 | 35 | 0 | 26 | 747 | 25 |
N.S. |
1 | 0.00 | 0.89 | 6.89 | 0.96 | 1.30 | 0.00 | 0.96 | 27.67 | 0.93 |
time (sec) |
N/A | 0.000 | 0.567 | 0.023 | 0.105 | 0.107 | 0.000 | 0.154 | 0.186 | 3.543 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 14 | 12 | 14 | 13 | 13 | 14 | 13 | 14 | 13 |
N.S. |
1 | 0.88 | 0.75 | 0.88 | 0.81 | 0.81 | 0.88 | 0.81 | 0.88 | 0.81 |
time (sec) |
N/A | 0.221 | 0.002 | 0.056 | 0.024 | 0.094 | 0.058 | 0.113 | 0.153 | 3.424 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 22 | 23 | 16 | 19 | 19 | 19 | 19 | 16 | 15 |
N.S. |
1 | 0.69 | 0.72 | 0.50 | 0.59 | 0.59 | 0.59 | 0.59 | 0.50 | 0.47 |
time (sec) |
N/A | 0.259 | 0.001 | 0.036 | 0.028 | 0.073 | 0.026 | 0.107 | 0.153 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 7 | 9 | 7 | 9 | 9 | 7 | 9 | 7 | 6 |
N.S. |
1 | 0.33 | 0.43 | 0.33 | 0.43 | 0.43 | 0.33 | 0.43 | 0.33 | 0.29 |
time (sec) |
N/A | 0.159 | 0.000 | 0.017 | 0.022 | 0.075 | 0.019 | 0.115 | 0.151 | 0.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 54 | 42 | 33 | 50 | 39 | 34 | 50 | 31 | 30 |
N.S. |
1 | 2.35 | 1.83 | 1.43 | 2.17 | 1.70 | 1.48 | 2.17 | 1.35 | 1.30 |
time (sec) |
N/A | 0.281 | 0.016 | 0.114 | 0.031 | 0.075 | 0.066 | 0.110 | 0.152 | 3.404 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 70 | 61 | 64 | 66 | 66 | 70 | 62 | 1013 | 62 |
N.S. |
1 | 2.12 | 1.85 | 1.94 | 2.00 | 2.00 | 2.12 | 1.88 | 30.70 | 1.88 |
time (sec) |
N/A | 1.054 | 0.257 | 0.638 | 0.073 | 0.094 | 0.306 | 0.185 | 0.173 | 3.693 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | A | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 55 | 27 | 37 | 22 | 22 | 0 | 54 | 22 |
N.S. |
1 | 0.00 | 2.20 | 1.08 | 1.48 | 0.88 | 0.88 | 0.00 | 2.16 | 0.88 |
time (sec) |
N/A | 0.000 | 0.372 | 0.090 | 0.247 | 0.112 | 0.937 | 0.000 | 0.274 | 3.912 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 21 | 21 | 21 | 34 | 36 | 14 | 38 | 36 | 31 |
N.S. |
1 | 0.81 | 0.81 | 0.81 | 1.31 | 1.38 | 0.54 | 1.46 | 1.38 | 1.19 |
time (sec) |
N/A | 1.078 | 2.289 | 0.308 | 0.073 | 0.084 | 0.066 | 0.119 | 0.154 | 3.598 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 30 | 30 | 23 | 28 | 27 | 28 | 40 | 46 |
N.S. |
1 | 0.00 | 1.20 | 1.20 | 0.92 | 1.12 | 1.08 | 1.12 | 1.60 | 1.84 |
time (sec) |
N/A | 0.000 | 0.234 | 0.210 | 0.135 | 0.086 | 0.088 | 0.176 | 0.156 | 3.505 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 45 | 38 | 41 | 41 | 36 | 47 | 42 | 313 |
N.S. |
1 | 0.00 | 1.41 | 1.19 | 1.28 | 1.28 | 1.12 | 1.47 | 1.31 | 9.78 |
time (sec) |
N/A | 0.000 | 0.032 | 1.763 | 0.147 | 0.093 | 0.081 | 0.156 | 0.154 | 3.606 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 27 | 29 | 205 | 29 | 37 | 140 | 34 | 225 |
N.S. |
1 | 0.00 | 0.93 | 1.00 | 7.07 | 1.00 | 1.28 | 4.83 | 1.17 | 7.76 |
time (sec) |
N/A | 0.000 | 1.006 | 0.658 | 0.186 | 0.092 | 0.165 | 0.166 | 0.160 | 4.163 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 37 | 34 | 29 | 32 | 32 | 31 | 32 | 29 | 30 |
N.S. |
1 | 1.85 | 1.70 | 1.45 | 1.60 | 1.60 | 1.55 | 1.60 | 1.45 | 1.50 |
time (sec) |
N/A | 0.173 | 0.006 | 0.089 | 0.027 | 0.088 | 0.026 | 0.112 | 0.153 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 78 | 40 | 43 | 0 | 59 | 42 | 79 | 97 | 52 |
N.S. |
1 | 3.25 | 1.67 | 1.79 | 0.00 | 2.46 | 1.75 | 3.29 | 4.04 | 2.17 |
time (sec) |
N/A | 0.939 | 0.226 | 0.508 | 0.000 | 0.091 | 0.123 | 0.123 | 0.156 | 3.565 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 0 | 36 | 30 | 36 | 31 | 40 | 29 | 37 |
N.S. |
1 | 0.00 | 0.00 | 1.44 | 1.20 | 1.44 | 1.24 | 1.60 | 1.16 | 1.48 |
time (sec) |
N/A | 0.000 | 0.000 | 0.394 | 0.266 | 0.081 | 0.191 | 0.186 | 0.154 | 3.645 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 261 | 25 | 22 | 111 | 32 | 17 | 50 | 29 | 21 |
N.S. |
1 | 12.43 | 1.19 | 1.05 | 5.29 | 1.52 | 0.81 | 2.38 | 1.38 | 1.00 |
time (sec) |
N/A | 1.477 | 0.241 | 0.527 | 0.148 | 0.083 | 0.077 | 0.124 | 0.153 | 3.486 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 23 | 18 | 17 | 33 | 16 | 15 | 21 | 17 | 16 |
N.S. |
1 | 1.35 | 1.06 | 1.00 | 1.94 | 0.94 | 0.88 | 1.24 | 1.00 | 0.94 |
time (sec) |
N/A | 0.480 | 0.120 | 0.093 | 0.052 | 0.085 | 0.045 | 0.115 | 0.152 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 25 | 26 | 56 | 59 | 39 | 56 | 55 | 42 |
N.S. |
1 | 0.00 | 0.74 | 0.76 | 1.65 | 1.74 | 1.15 | 1.65 | 1.62 | 1.24 |
time (sec) |
N/A | 0.000 | 2.501 | 0.449 | 0.079 | 0.100 | 0.085 | 0.128 | 0.154 | 0.146 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 0 | 8 | 9 | 8 | 8 | 8 | 8 | 8 | 8 |
N.S. |
1 | 0.00 | 0.67 | 0.75 | 0.67 | 0.67 | 0.67 | 0.67 | 0.67 | 0.67 |
time (sec) |
N/A | 0.000 | 0.024 | 0.094 | 0.057 | 0.079 | 0.056 | 0.112 | 0.159 | 3.440 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | A | B | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 51 | 72 | 46 | 43 | 60 | 44 | 41 | 60 | 57 |
N.S. |
1 | 2.04 | 2.88 | 1.84 | 1.72 | 2.40 | 1.76 | 1.64 | 2.40 | 2.28 |
time (sec) |
N/A | 0.360 | 0.057 | 0.129 | 0.024 | 0.076 | 0.165 | 0.112 | 0.161 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 10 | 10 | 11 | 12 | 10 | 10 | 12 | 10 | 10 |
N.S. |
1 | 0.67 | 0.67 | 0.73 | 0.80 | 0.67 | 0.67 | 0.80 | 0.67 | 0.67 |
time (sec) |
N/A | 0.151 | 0.001 | 0.024 | 0.022 | 0.069 | 0.028 | 0.113 | 0.156 | 0.013 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 43 | 53 | 82 | 57 | 54 | 142 | 36 | 117 |
N.S. |
1 | 0.00 | 1.26 | 1.56 | 2.41 | 1.68 | 1.59 | 4.18 | 1.06 | 3.44 |
time (sec) |
N/A | 0.000 | 0.271 | 22.984 | 0.219 | 0.116 | 0.574 | 0.334 | 0.163 | 3.644 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 15 | 15 | 12 | 11 | 15 | 8 | 11 | 14 | 11 |
N.S. |
1 | 0.65 | 0.65 | 0.52 | 0.48 | 0.65 | 0.35 | 0.48 | 0.61 | 0.48 |
time (sec) |
N/A | 0.172 | 0.005 | 0.079 | 0.029 | 0.080 | 0.031 | 0.112 | 0.160 | 3.333 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 77 | 133 | 505 | 505 | 238 | 728 | 744 | 0 |
N.S. |
1 | 0.00 | 2.14 | 3.69 | 14.03 | 14.03 | 6.61 | 20.22 | 20.67 | 0.00 |
time (sec) |
N/A | 0.000 | 0.214 | 95.707 | 0.366 | 0.139 | 0.714 | 68.008 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 29 | 27 | 25 | 31 | 45 | 22 | 28 | 52 | 22 |
N.S. |
1 | 0.94 | 0.87 | 0.81 | 1.00 | 1.45 | 0.71 | 0.90 | 1.68 | 0.71 |
time (sec) |
N/A | 0.543 | 0.044 | 0.492 | 0.059 | 0.091 | 4.047 | 0.135 | 0.173 | 3.489 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 19 | 18 | 17 | 16 | 16 | 19 | 0 | 19 | 14 |
N.S. |
1 | 0.86 | 0.82 | 0.77 | 0.73 | 0.73 | 0.86 | 0.00 | 0.86 | 0.64 |
time (sec) |
N/A | 0.169 | 0.014 | 0.093 | 0.025 | 0.085 | 0.423 | 0.000 | 0.172 | 3.461 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 28 | 26 | 25 | 24 | 24 | 26 | 24 | 34 | 24 |
N.S. |
1 | 1.33 | 1.24 | 1.19 | 1.14 | 1.14 | 1.24 | 1.14 | 1.62 | 1.14 |
time (sec) |
N/A | 2.175 | 0.232 | 0.865 | 0.076 | 0.124 | 0.176 | 0.134 | 0.171 | 4.322 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 34 | 27 | 31 | 26 | 26 | 989 | 122 | 0 |
N.S. |
1 | 0.00 | 1.21 | 0.96 | 1.11 | 0.93 | 0.93 | 35.32 | 4.36 | 0.00 |
time (sec) |
N/A | 0.000 | 0.086 | 0.698 | 0.176 | 0.090 | 0.121 | 0.207 | 200.020 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 44 | 39 | 43 | 34 | 41 | 39 | 48 | 52 | 39 |
N.S. |
1 | 1.63 | 1.44 | 1.59 | 1.26 | 1.52 | 1.44 | 1.78 | 1.93 | 1.44 |
time (sec) |
N/A | 1.992 | 0.948 | 0.315 | 0.153 | 0.099 | 0.153 | 0.174 | 1.699 | 3.190 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 30 | 48 | 93 | 46 | 46 | 0 | 88 | 144 |
N.S. |
1 | 0.00 | 1.30 | 2.09 | 4.04 | 2.00 | 2.00 | 0.00 | 3.83 | 6.26 |
time (sec) |
N/A | 0.000 | 0.917 | 0.888 | 0.599 | 0.095 | 0.179 | 0.000 | 0.155 | 3.252 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 10 | 10 | 10 | 9 | 12 | 5 | 9 | 13 | 9 |
N.S. |
1 | 0.59 | 0.59 | 0.59 | 0.53 | 0.71 | 0.29 | 0.53 | 0.76 | 0.53 |
time (sec) |
N/A | 0.147 | 0.001 | 0.035 | 0.031 | 0.072 | 0.029 | 0.111 | 0.151 | 3.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 19 | 19 | 16 | 52 | 17 | 16 | 22 | 17 |
N.S. |
1 | 0.00 | 0.90 | 0.90 | 0.76 | 2.48 | 0.81 | 0.76 | 1.05 | 0.81 |
time (sec) |
N/A | 0.000 | 0.124 | 0.341 | 0.123 | 0.095 | 0.247 | 0.105 | 0.151 | 3.225 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 14 | 14 | 15 | 14 | 19 | 14 | 14 | 19 | 14 |
N.S. |
1 | 0.82 | 0.82 | 0.88 | 0.82 | 1.12 | 0.82 | 0.82 | 1.12 | 0.82 |
time (sec) |
N/A | 0.289 | 0.005 | 0.240 | 0.029 | 0.094 | 0.042 | 0.117 | 0.151 | 3.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 23 | 36 | 20 | 31 | 31 | 60 | 28 | 46 |
N.S. |
1 | 0.00 | 0.88 | 1.38 | 0.77 | 1.19 | 1.19 | 2.31 | 1.08 | 1.77 |
time (sec) |
N/A | 0.000 | 0.358 | 0.411 | 0.249 | 0.098 | 0.223 | 0.118 | 0.155 | 3.185 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 14 | 11 | 10 | 9 | 9 | 8 | 9 | 9 | 9 |
N.S. |
1 | 1.27 | 1.00 | 0.91 | 0.82 | 0.82 | 0.73 | 0.82 | 0.82 | 0.82 |
time (sec) |
N/A | 0.191 | 0.002 | 0.033 | 0.022 | 0.085 | 0.033 | 0.117 | 0.156 | 3.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 16 | 16 | 11 | 10 | 16 | 8 | 11 | 19 | 12 |
N.S. |
1 | 1.23 | 1.23 | 0.85 | 0.77 | 1.23 | 0.62 | 0.85 | 1.46 | 0.92 |
time (sec) |
N/A | 0.307 | 0.005 | 0.031 | 0.029 | 0.089 | 0.036 | 0.114 | 0.154 | 3.133 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | A | A | F | B | F(-1) |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 0 | 34 | 60 | 33 | 36 | 0 | 26 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.26 | 2.22 | 1.22 | 1.33 | 0.00 | 0.96 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 1.261 | 0.338 | 0.111 | 47.769 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 38 | 24 | 36 | 22 | 35 | 36 | 33 | 37 | 36 |
N.S. |
1 | 1.46 | 0.92 | 1.38 | 0.85 | 1.35 | 1.38 | 1.27 | 1.42 | 1.38 |
time (sec) |
N/A | 0.791 | 0.126 | 1.318 | 0.182 | 0.102 | 0.322 | 2.097 | 0.153 | 3.569 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | B | F | B | B | F(-1) | F | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 0 | 252 | 0 | 135 | 168 | 0 | 494 | 178 |
N.S. |
1 | 0.00 | 0.00 | 10.96 | 0.00 | 5.87 | 7.30 | 0.00 | 21.48 | 7.74 |
time (sec) |
N/A | 0.000 | 0.000 | 9.319 | 0.000 | 0.129 | 0.967 | 0.000 | 200.013 | 4.129 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | F(-1) | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 31 | 27 | 67 | 26 | 0 | 0 | 76 | 71 |
N.S. |
1 | 0.00 | 1.03 | 0.90 | 2.23 | 0.87 | 0.00 | 0.00 | 2.53 | 2.37 |
time (sec) |
N/A | 0.000 | 0.174 | 44.508 | 0.787 | 0.110 | 0.000 | 0.000 | 1.390 | 3.478 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 15 | 23 | 17 | 12 | 16 | 19 | 12 | 16 | 15 |
N.S. |
1 | 0.65 | 1.00 | 0.74 | 0.52 | 0.70 | 0.83 | 0.52 | 0.70 | 0.65 |
time (sec) |
N/A | 0.143 | 0.000 | 0.035 | 0.023 | 0.071 | 0.016 | 0.110 | 0.163 | 0.001 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 39 | 27 | 24 | 23 | 26 | 31 | 23 | 28 | 25 |
N.S. |
1 | 1.44 | 1.00 | 0.89 | 0.85 | 0.96 | 1.15 | 0.85 | 1.04 | 0.93 |
time (sec) |
N/A | 0.273 | 0.033 | 0.087 | 0.023 | 0.108 | 0.053 | 0.105 | 0.163 | 0.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 14 | 14 | 15 | 16 | 18 | 17 | 18 | 19 | 13 |
N.S. |
1 | 0.82 | 0.82 | 0.88 | 0.94 | 1.06 | 1.00 | 1.06 | 1.12 | 0.76 |
time (sec) |
N/A | 0.447 | 0.041 | 0.236 | 0.176 | 0.115 | 0.075 | 0.115 | 0.157 | 3.449 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | F | B |
verified | N/A | N/A | N/A | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 0 | 29 | 30 | 26 | 26 | 28 | 46 | 29 |
N.S. |
1 | 0.00 | 0.00 | 0.97 | 1.00 | 0.87 | 0.87 | 0.93 | 1.53 | 0.97 |
time (sec) |
N/A | 0.000 | 0.000 | 0.168 | 0.108 | 0.098 | 115.718 | 0.128 | 200.021 | 3.503 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 22 | 22 | 21 | 22 | 22 | 20 | 22 | 29 | 22 |
N.S. |
1 | 1.05 | 1.05 | 1.00 | 1.05 | 1.05 | 0.95 | 1.05 | 1.38 | 1.05 |
time (sec) |
N/A | 1.324 | 0.155 | 0.719 | 0.072 | 0.100 | 0.139 | 0.143 | 0.176 | 3.468 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | B | F | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 31 | 32 | 52 | 43 | 51 | 0 | 57 | 0 |
N.S. |
1 | 0.00 | 0.86 | 0.89 | 1.44 | 1.19 | 1.42 | 0.00 | 1.58 | 0.00 |
time (sec) |
N/A | 0.000 | 8.348 | 0.312 | 0.123 | 0.102 | 0.142 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | A | B | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 23 | 56 | 267 | 45 | 42 | 0 | 142 | 155 |
N.S. |
1 | 0.00 | 0.88 | 2.15 | 10.27 | 1.73 | 1.62 | 0.00 | 5.46 | 5.96 |
time (sec) |
N/A | 0.000 | 0.931 | 2.452 | 0.455 | 0.092 | 0.466 | 0.000 | 200.028 | 3.555 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 102 | 27 | 26 | 105 | 21 | 14 | 21 | 30 | 22 |
N.S. |
1 | 3.29 | 0.87 | 0.84 | 3.39 | 0.68 | 0.45 | 0.68 | 0.97 | 0.71 |
time (sec) |
N/A | 0.476 | 0.084 | 0.371 | 0.034 | 0.113 | 0.087 | 0.127 | 0.152 | 3.473 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | C | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 23 | 18 | 15 | 14 | 19 | 10 | 4 | 23 | 11 |
N.S. |
1 | 0.96 | 0.75 | 0.62 | 0.58 | 0.79 | 0.42 | 0.17 | 0.96 | 0.46 |
time (sec) |
N/A | 0.207 | 0.010 | 0.049 | 0.031 | 0.084 | 0.068 | 0.112 | 0.161 | 3.451 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 38 | 21 | 21 | 21 | 32 | 14 | 21 | 30 | 21 |
N.S. |
1 | 1.73 | 0.95 | 0.95 | 0.95 | 1.45 | 0.64 | 0.95 | 1.36 | 0.95 |
time (sec) |
N/A | 0.403 | 0.011 | 0.078 | 0.032 | 0.081 | 0.090 | 0.110 | 0.152 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 20 | 18 | 17 | 20 | 20 | 17 | 20 | 17 | 18 |
N.S. |
1 | 1.25 | 1.12 | 1.06 | 1.25 | 1.25 | 1.06 | 1.25 | 1.06 | 1.12 |
time (sec) |
N/A | 0.155 | 0.003 | 0.043 | 0.026 | 0.071 | 0.019 | 0.112 | 0.158 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 14 | 14 | 15 | 40 | 14 | 12 | 14 | 28 | 14 |
N.S. |
1 | 0.88 | 0.88 | 0.94 | 2.50 | 0.88 | 0.75 | 0.88 | 1.75 | 0.88 |
time (sec) |
N/A | 0.272 | 0.022 | 0.189 | 0.032 | 0.102 | 0.055 | 0.119 | 0.162 | 3.482 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 19 | 22 | 40 | 42 | 19 | 42 | 62 | 21 |
N.S. |
1 | 0.00 | 1.00 | 1.16 | 2.11 | 2.21 | 1.00 | 2.21 | 3.26 | 1.11 |
time (sec) |
N/A | 0.000 | 0.034 | 1.312 | 0.079 | 0.110 | 0.086 | 0.210 | 0.161 | 3.968 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 21 | 21 | 20 | 18 | 24 | 12 | 18 | 26 | 19 |
N.S. |
1 | 0.72 | 0.72 | 0.69 | 0.62 | 0.83 | 0.41 | 0.62 | 0.90 | 0.66 |
time (sec) |
N/A | 0.461 | 0.006 | 0.039 | 0.024 | 0.077 | 0.032 | 0.110 | 0.159 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 39 | 25 | 23 | 31 | 22 | 20 | 22 | 30 | 26 |
N.S. |
1 | 1.50 | 0.96 | 0.88 | 1.19 | 0.85 | 0.77 | 0.85 | 1.15 | 1.00 |
time (sec) |
N/A | 0.294 | 0.022 | 0.108 | 0.035 | 0.092 | 0.062 | 0.115 | 0.159 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | C | A | A | F(-1) | B | B | B |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 64 | 569 | 46 | 42 | 0 | 61 | 39 | 62 |
N.S. |
1 | 0.00 | 2.06 | 18.35 | 1.48 | 1.35 | 0.00 | 1.97 | 1.26 | 2.00 |
time (sec) |
N/A | 0.000 | 0.206 | 0.128 | 0.260 | 0.105 | 0.000 | 0.314 | 0.411 | 3.674 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 153 | 184 | 109 | 265 | 98 | 124 | 108 | 111 | 107 |
N.S. |
1 | 6.65 | 8.00 | 4.74 | 11.52 | 4.26 | 5.39 | 4.70 | 4.83 | 4.65 |
time (sec) |
N/A | 0.655 | 0.041 | 11.910 | 0.040 | 0.109 | 1.603 | 0.116 | 0.159 | 3.529 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 19 | 18 | 23 | 17 | 15 | 34 | 20 | 19 |
N.S. |
1 | 0.00 | 0.83 | 0.78 | 1.00 | 0.74 | 0.65 | 1.48 | 0.87 | 0.83 |
time (sec) |
N/A | 0.000 | 0.311 | 0.650 | 0.129 | 0.105 | 0.416 | 0.462 | 0.165 | 3.595 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 55 | 19 | 15 | 43 | 15 | 14 | 17 | 15 | 46 |
N.S. |
1 | 2.50 | 0.86 | 0.68 | 1.95 | 0.68 | 0.64 | 0.77 | 0.68 | 2.09 |
time (sec) |
N/A | 0.408 | 0.031 | 0.188 | 0.147 | 0.097 | 0.160 | 0.119 | 0.163 | 3.484 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | A | F(-2) | B | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 74 | 56 | 66 | 56 | 0 | 82 | 0 | 0 |
N.S. |
1 | 0.00 | 2.11 | 1.60 | 1.89 | 1.60 | 0.00 | 2.34 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.148 | 0.050 | 0.412 | 0.104 | 0.000 | 1.142 | 0.545 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 18 | 18 | 19 | 18 | 18 | 15 | 18 | 18 | 18 |
N.S. |
1 | 0.95 | 0.95 | 1.00 | 0.95 | 0.95 | 0.79 | 0.95 | 0.95 | 0.95 |
time (sec) |
N/A | 0.688 | 0.083 | 0.237 | 0.097 | 0.095 | 0.130 | 0.119 | 0.164 | 3.555 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 22 | 22 | 21 | 26 | 20 | 22 | 20 | 36 | 20 |
N.S. |
1 | 0.92 | 0.92 | 0.88 | 1.08 | 0.83 | 0.92 | 0.83 | 1.50 | 0.83 |
time (sec) |
N/A | 0.178 | 0.022 | 0.122 | 0.026 | 0.085 | 0.287 | 0.111 | 0.160 | 0.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 43 | 30 | 29 | 28 | 24 | 31 | 29 | 34 | 29 |
N.S. |
1 | 1.39 | 0.97 | 0.94 | 0.90 | 0.77 | 1.00 | 0.94 | 1.10 | 0.94 |
time (sec) |
N/A | 0.227 | 0.026 | 0.152 | 0.026 | 0.083 | 0.193 | 0.108 | 0.158 | 3.495 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 18 | 18 | 17 | 16 | 32 | 14 | 43 | 28 | 16 |
N.S. |
1 | 0.60 | 0.60 | 0.57 | 0.53 | 1.07 | 0.47 | 1.43 | 0.93 | 0.53 |
time (sec) |
N/A | 0.429 | 0.036 | 0.149 | 0.076 | 0.095 | 0.223 | 0.109 | 0.159 | 0.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 33 | 18 | 16 | 52 | 15 | 17 | 15 | 28 | 18 |
N.S. |
1 | 1.83 | 1.00 | 0.89 | 2.89 | 0.83 | 0.94 | 0.83 | 1.56 | 1.00 |
time (sec) |
N/A | 0.539 | 0.092 | 0.185 | 0.142 | 0.089 | 0.145 | 0.126 | 0.157 | 3.516 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 26 | 26 | 25 | 24 | 24 | 20 | 24 | 26 | 24 |
N.S. |
1 | 0.96 | 0.96 | 0.93 | 0.89 | 0.89 | 0.74 | 0.89 | 0.96 | 0.89 |
time (sec) |
N/A | 0.522 | 0.013 | 0.735 | 0.027 | 0.109 | 0.211 | 0.119 | 0.160 | 3.592 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 74 | 60 | 58 | 91 | 61 | 56 | 76 | 83 | 63 |
N.S. |
1 | 2.18 | 1.76 | 1.71 | 2.68 | 1.79 | 1.65 | 2.24 | 2.44 | 1.85 |
time (sec) |
N/A | 0.368 | 0.080 | 0.588 | 0.034 | 0.090 | 0.221 | 0.119 | 0.161 | 3.546 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 23 | 24 | 27 | 23 | 22 | 181 | 40 | 41 |
N.S. |
1 | 0.00 | 0.85 | 0.89 | 1.00 | 0.85 | 0.81 | 6.70 | 1.48 | 1.52 |
time (sec) |
N/A | 0.000 | 5.050 | 0.577 | 0.169 | 0.135 | 0.217 | 0.133 | 0.712 | 0.319 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | F(-1) | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 21 | 21 | 89 | 20 | 0 | 20 | 21 | 20 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 4.24 | 0.95 | 0.00 | 0.95 | 1.00 | 0.95 |
time (sec) |
N/A | 0.000 | 0.974 | 101.902 | 0.173 | 0.099 | 0.000 | 2.885 | 0.169 | 3.576 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 36 | 42 | 49 | 49 | 36 | 39 | 50 | 39 |
N.S. |
1 | 0.00 | 1.50 | 1.75 | 2.04 | 2.04 | 1.50 | 1.62 | 2.08 | 1.62 |
time (sec) |
N/A | 0.000 | 0.153 | 0.370 | 0.075 | 0.106 | 0.149 | 0.129 | 0.168 | 3.575 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 60 | 41 | 33 | 65 | 31 | 37 | 37 | 26 | 18 |
N.S. |
1 | 3.16 | 2.16 | 1.74 | 3.42 | 1.63 | 1.95 | 1.95 | 1.37 | 0.95 |
time (sec) |
N/A | 0.245 | 0.010 | 0.660 | 0.036 | 0.094 | 0.067 | 0.119 | 0.167 | 3.473 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 22 | 24 | 26 | 0 | 21 | 20 | 33 | 23 | 20 |
N.S. |
1 | 0.92 | 1.00 | 1.08 | 0.00 | 0.88 | 0.83 | 1.38 | 0.96 | 0.83 |
time (sec) |
N/A | 0.539 | 0.068 | 0.226 | 0.000 | 0.098 | 0.168 | 0.118 | 0.168 | 3.877 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | F(-1) | B | B | B | F | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 0 | 56 | 0 | 81 | 85 | 302 | 289 | 223 |
N.S. |
1 | 0.00 | 0.00 | 1.75 | 0.00 | 2.53 | 2.66 | 9.44 | 9.03 | 6.97 |
time (sec) |
N/A | 0.000 | 0.000 | 0.066 | 0.000 | 0.121 | 1.258 | 0.589 | 200.025 | 4.220 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 21 | 21 | 188 | 20 | 15 | 20 | 21 | 20 |
N.S. |
1 | 0.00 | 0.95 | 0.95 | 8.55 | 0.91 | 0.68 | 0.91 | 0.95 | 0.91 |
time (sec) |
N/A | 0.000 | 0.227 | 3.222 | 0.166 | 0.100 | 0.085 | 0.120 | 0.167 | 0.139 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 18 | 15 | 16 | 15 | 16 | 15 | 16 | 18 | 63 |
N.S. |
1 | 1.20 | 1.00 | 1.07 | 1.00 | 1.07 | 1.00 | 1.07 | 1.20 | 4.20 |
time (sec) |
N/A | 0.595 | 0.166 | 0.195 | 0.134 | 0.094 | 0.056 | 0.114 | 0.169 | 0.147 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 21 | 22 | 15 | 16 | 14 | 14 | 15 | 15 | 13 |
N.S. |
1 | 1.11 | 1.16 | 0.79 | 0.84 | 0.74 | 0.74 | 0.79 | 0.79 | 0.68 |
time (sec) |
N/A | 0.162 | 0.005 | 0.089 | 0.025 | 0.083 | 0.045 | 0.110 | 0.168 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F(-1) | F | A | A | F | F | F(-1) |
verified | N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 29 | 0 | 0 | 57 | 29 | 0 | 135 | 0 |
N.S. |
1 | 0.00 | 0.91 | 0.00 | 0.00 | 1.78 | 0.91 | 0.00 | 4.22 | 0.00 |
time (sec) |
N/A | 0.000 | 0.088 | 0.000 | 0.000 | 0.094 | 75.890 | 0.000 | 36.558 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F(-1) | F | B | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 0 | 19 | 15 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 1.00 | 0.79 | 0.00 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 2.190 | 0.167 | 0.000 | 0.140 | 0.103 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 95 | 45 | 32 | 58 | 34 | 29 | 77 | 64 | 77 |
N.S. |
1 | 2.79 | 1.32 | 0.94 | 1.71 | 1.00 | 0.85 | 2.26 | 1.88 | 2.26 |
time (sec) |
N/A | 1.326 | 0.524 | 32.841 | 0.148 | 0.099 | 2.356 | 0.161 | 0.174 | 4.229 |