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 | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 0 | 17 | 19 | 18 | 18 | 12 | 18 | 17 | 18 |
N.S. |
1 | 0.00 | 1.00 | 1.12 | 1.06 | 1.06 | 0.71 | 1.06 | 1.00 | 1.06 |
time (sec) |
N/A | 0.000 | 0.150 | 0.505 | 0.062 | 0.087 | 0.067 | 0.126 | 0.166 | 3.983 |
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 | 29 | 0 | 19 | 18 | 51 | 35 | 32 | 20 | 35 | 20 |
N.S. |
1 | 0.00 | 0.66 | 0.62 | 1.76 | 1.21 | 1.10 | 0.69 | 1.21 | 0.69 |
time (sec) |
N/A | 0.000 | 0.012 | 0.350 | 0.112 | 0.095 | 0.065 | 0.116 | 0.164 | 4.016 |
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 | 13 | 17 | 14 | 13 | 20 | 10 | 13 | 19 | 13 |
N.S. |
1 | 0.62 | 0.81 | 0.67 | 0.62 | 0.95 | 0.48 | 0.62 | 0.90 | 0.62 |
time (sec) |
N/A | 0.214 | 0.008 | 0.339 | 0.053 | 0.083 | 0.042 | 0.110 | 0.160 | 3.667 |
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 | 22 | 0 | 24 | 25 | 25 | 25 | 20 | 25 | 24 | 23 |
N.S. |
1 | 0.00 | 1.09 | 1.14 | 1.14 | 1.14 | 0.91 | 1.14 | 1.09 | 1.05 |
time (sec) |
N/A | 0.000 | 0.323 | 0.147 | 0.076 | 0.095 | 0.057 | 0.110 | 0.163 | 0.056 |
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 | 5 | 3 | 3 | 3 | 2 | 2 | 2 | 2 | 3 | 2 |
N.S. |
1 | 0.60 | 0.60 | 0.60 | 0.40 | 0.40 | 0.40 | 0.40 | 0.60 | 0.40 |
time (sec) |
N/A | 0.137 | 0.000 | 0.068 | 0.034 | 0.083 | 0.026 | 0.109 | 0.166 | 0.005 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | B | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 339 | 35 | 22 | 120 | 49 | 20 | 55 | 55 | 23 |
N.S. |
1 | 12.56 | 1.30 | 0.81 | 4.44 | 1.81 | 0.74 | 2.04 | 2.04 | 0.85 |
time (sec) |
N/A | 1.338 | 0.825 | 0.895 | 0.153 | 0.097 | 0.092 | 0.119 | 0.164 | 3.695 |
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 | 29 | 30 | 25 | 25 | 39 | 24 | 31 | 28 | 26 | 29 |
N.S. |
1 | 1.03 | 0.86 | 0.86 | 1.34 | 0.83 | 1.07 | 0.97 | 0.90 | 1.00 |
time (sec) |
N/A | 0.921 | 0.051 | 0.143 | 0.062 | 0.100 | 0.045 | 0.110 | 0.163 | 3.649 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | A | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 303 | 72 | 48 | 856 | 41 | 44 | 366 | 66 | 47 |
N.S. |
1 | 11.22 | 2.67 | 1.78 | 31.70 | 1.52 | 1.63 | 13.56 | 2.44 | 1.74 |
time (sec) |
N/A | 1.233 | 0.106 | 1.568 | 0.051 | 0.100 | 0.165 | 0.121 | 0.164 | 0.224 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | A | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 48 | 90 | 87 | 52 | 87 | 271 | 176 | 94 |
N.S. |
1 | 0.00 | 1.66 | 3.10 | 3.00 | 1.79 | 3.00 | 9.34 | 6.07 | 3.24 |
time (sec) |
N/A | 0.000 | 0.061 | 9.150 | 0.193 | 0.103 | 0.323 | 0.438 | 0.183 | 7.281 |
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 | 14 | 75 | 63 | 15 | 27 | 14 | 12 | 14 | 14 | 11 |
N.S. |
1 | 5.36 | 4.50 | 1.07 | 1.93 | 1.00 | 0.86 | 1.00 | 1.00 | 0.79 |
time (sec) |
N/A | 0.478 | 0.012 | 0.281 | 0.036 | 0.115 | 0.054 | 0.114 | 0.174 | 3.992 |
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 | 28 | 28 | 24 | 21 | 30 | 20 | 29 | 20 | 20 | 18 |
N.S. |
1 | 1.00 | 0.86 | 0.75 | 1.07 | 0.71 | 1.04 | 0.71 | 0.71 | 0.64 |
time (sec) |
N/A | 0.211 | 0.036 | 0.273 | 0.063 | 0.116 | 0.059 | 0.118 | 0.164 | 3.659 |
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 | 19 | 20 | 19 | 24 | 19 | 26 | 27 | 19 |
N.S. |
1 | 1.73 | 0.86 | 0.91 | 0.86 | 1.09 | 0.86 | 1.18 | 1.23 | 0.86 |
time (sec) |
N/A | 0.976 | 0.142 | 0.371 | 0.149 | 0.108 | 0.079 | 0.107 | 0.167 | 0.070 |
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 | 26 | 21 | 26 | 25 | 25 | 27 | 25 | 22 | 20 |
N.S. |
1 | 1.24 | 1.00 | 1.24 | 1.19 | 1.19 | 1.29 | 1.19 | 1.05 | 0.95 |
time (sec) |
N/A | 0.206 | 0.060 | 0.258 | 0.031 | 0.090 | 0.050 | 0.108 | 0.161 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 28 | 24 | 24 | 47 | 31 | 0 | 41 | 62 |
N.S. |
1 | 0.00 | 0.97 | 0.83 | 0.83 | 1.62 | 1.07 | 0.00 | 1.41 | 2.14 |
time (sec) |
N/A | 0.000 | 0.063 | 2.273 | 0.267 | 0.093 | 0.209 | 0.000 | 0.168 | 4.573 |
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 | 24 | 22 | 19 | 18 | 21 | 15 | 21 | 23 | 18 |
N.S. |
1 | 1.09 | 1.00 | 0.86 | 0.82 | 0.95 | 0.68 | 0.95 | 1.05 | 0.82 |
time (sec) |
N/A | 0.184 | 0.010 | 0.259 | 0.045 | 0.086 | 0.046 | 0.113 | 0.170 | 0.043 |
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 | 25 | 34 | 385 | 28 | 705 | 23 | 26 | 38 | 283 | 27 |
N.S. |
1 | 1.36 | 15.40 | 1.12 | 28.20 | 0.92 | 1.04 | 1.52 | 11.32 | 1.08 |
time (sec) |
N/A | 1.216 | 0.577 | 10.535 | 1.519 | 0.090 | 0.100 | 0.154 | 0.171 | 4.604 |
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 | 25 | 21 | 25 | 19 | 68 | 18 | 19 | 18 | 57 | 18 |
N.S. |
1 | 0.84 | 1.00 | 0.76 | 2.72 | 0.72 | 0.76 | 0.72 | 2.28 | 0.72 |
time (sec) |
N/A | 0.447 | 0.047 | 0.737 | 0.167 | 0.098 | 0.075 | 0.117 | 0.165 | 3.656 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | A | B | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 57 | 38 | 55 | 44 | 49 | 44 | 38 | 46 |
N.S. |
1 | 0.00 | 2.11 | 1.41 | 2.04 | 1.63 | 1.81 | 1.63 | 1.41 | 1.70 |
time (sec) |
N/A | 0.000 | 5.123 | 0.311 | 0.091 | 0.118 | 0.132 | 0.148 | 0.234 | 3.749 |
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 | 25 | 22 | 24 | 19 | 18 | 18 | 17 | 18 | 20 | 18 |
N.S. |
1 | 0.88 | 0.96 | 0.76 | 0.72 | 0.72 | 0.68 | 0.72 | 0.80 | 0.72 |
time (sec) |
N/A | 0.323 | 0.010 | 0.253 | 0.026 | 0.084 | 0.093 | 0.112 | 0.165 | 3.625 |
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 | 18 | 18 | 18 | 17 | 16 | 16 | 15 | 19 | 16 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.89 | 0.89 | 0.83 | 1.06 | 0.89 | 1.22 |
time (sec) |
N/A | 0.285 | 0.006 | 0.203 | 0.025 | 0.109 | 0.057 | 0.112 | 0.171 | 3.863 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 8 | 8 | 9 | 8 | 8 | 7 | 27 | 8 | 8 |
N.S. |
1 | 0.62 | 0.62 | 0.69 | 0.62 | 0.62 | 0.54 | 2.08 | 0.62 | 0.62 |
time (sec) |
N/A | 0.212 | 0.024 | 0.177 | 0.031 | 0.079 | 0.054 | 0.114 | 0.161 | 3.838 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | B | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 41 | 46 | 34 | 50 | 40 | 41 | 31 | 40 | 16 |
N.S. |
1 | 2.05 | 2.30 | 1.70 | 2.50 | 2.00 | 2.05 | 1.55 | 2.00 | 0.80 |
time (sec) |
N/A | 0.278 | 0.010 | 0.355 | 0.028 | 0.095 | 0.075 | 0.107 | 0.176 | 3.821 |
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 | 15 | 50 | 16 | 17 | 41 | 20 | 76 | 43 | 60 | 18 |
N.S. |
1 | 3.33 | 1.07 | 1.13 | 2.73 | 1.33 | 5.07 | 2.87 | 4.00 | 1.20 |
time (sec) |
N/A | 0.195 | 0.011 | 0.312 | 0.035 | 0.104 | 0.462 | 0.108 | 0.169 | 3.835 |
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 | 30 | 56 | 50 | 40 | 24 | 37 | 40 | 183 |
N.S. |
1 | 0.00 | 0.94 | 1.75 | 1.56 | 1.25 | 0.75 | 1.16 | 1.25 | 5.72 |
time (sec) |
N/A | 0.000 | 0.086 | 11.425 | 0.191 | 0.105 | 0.212 | 0.191 | 0.166 | 4.277 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 192 | 35 | 33 | 157 | 72 | 131 | 89 | 125 | 109 |
N.S. |
1 | 7.38 | 1.35 | 1.27 | 6.04 | 2.77 | 5.04 | 3.42 | 4.81 | 4.19 |
time (sec) |
N/A | 0.902 | 5.318 | 0.375 | 0.038 | 0.088 | 0.107 | 0.122 | 0.165 | 3.904 |
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 | 33 | 0 | 39 | 42 | 46 | 40 | 34 | 46 | 57 | 40 |
N.S. |
1 | 0.00 | 1.18 | 1.27 | 1.39 | 1.21 | 1.03 | 1.39 | 1.73 | 1.21 |
time (sec) |
N/A | 0.000 | 0.137 | 1.599 | 0.314 | 0.103 | 0.539 | 0.344 | 0.175 | 4.370 |
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 | 34 | 22 | 34 | 34 | 26 | 34 | 34 | 34 | 22 |
N.S. |
1 | 1.31 | 0.85 | 1.31 | 1.31 | 1.00 | 1.31 | 1.31 | 1.31 | 0.85 |
time (sec) |
N/A | 0.209 | 0.003 | 0.161 | 0.025 | 0.070 | 0.057 | 0.108 | 0.167 | 0.029 |
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 | 40 | 36 | 29 | 31 | 34 | 31 | 30 | 31 | 34 |
N.S. |
1 | 1.82 | 1.64 | 1.32 | 1.41 | 1.55 | 1.41 | 1.36 | 1.41 | 1.55 |
time (sec) |
N/A | 0.328 | 0.020 | 0.160 | 0.034 | 0.082 | 0.365 | 0.112 | 0.165 | 0.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 21 | 53 | 74 | 52 | 71 | 73 | 77 | 0 |
N.S. |
1 | 0.00 | 0.91 | 2.30 | 3.22 | 2.26 | 3.09 | 3.17 | 3.35 | 0.00 |
time (sec) |
N/A | 0.000 | 3.950 | 1.294 | 0.099 | 0.091 | 3.953 | 0.159 | 0.182 | 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 | 53 | 36 | 52 | 44 | 47 | 42 | 54 | 59 | 49 |
N.S. |
1 | 1.96 | 1.33 | 1.93 | 1.63 | 1.74 | 1.56 | 2.00 | 2.19 | 1.81 |
time (sec) |
N/A | 1.027 | 0.151 | 10.568 | 0.099 | 0.103 | 0.185 | 0.129 | 0.166 | 3.822 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 34 | 37 | 22 | 41 | 26 | 49 | 0 | 60 | 50 |
N.S. |
1 | 1.42 | 1.54 | 0.92 | 1.71 | 1.08 | 2.04 | 0.00 | 2.50 | 2.08 |
time (sec) |
N/A | 0.827 | 0.344 | 4.266 | 0.147 | 0.086 | 4.103 | 0.000 | 54.379 | 4.430 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 20 | 18 | 24 | 48 | 14 | 0 | 31 | 17 |
N.S. |
1 | 0.00 | 1.00 | 0.90 | 1.20 | 2.40 | 0.70 | 0.00 | 1.55 | 0.85 |
time (sec) |
N/A | 0.000 | 1.199 | 1.192 | 0.271 | 0.088 | 0.238 | 0.000 | 0.177 | 4.311 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 69 | 30 | 38 | 181 | 43 | 44 | 44 | 40 | 20 |
N.S. |
1 | 3.29 | 1.43 | 1.81 | 8.62 | 2.05 | 2.10 | 2.10 | 1.90 | 0.95 |
time (sec) |
N/A | 0.912 | 0.484 | 0.129 | 0.042 | 0.085 | 0.065 | 0.115 | 0.153 | 0.050 |
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 | 22 | 20 | 22 | 20 | 30 | 20 | 20 | 21 | 26 |
N.S. |
1 | 1.10 | 1.00 | 1.10 | 1.00 | 1.50 | 1.00 | 1.00 | 1.05 | 1.30 |
time (sec) |
N/A | 0.388 | 0.014 | 0.355 | 0.029 | 0.074 | 0.063 | 0.102 | 0.150 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 49 | 49 | 65 | 43 | 75 | 60 | 0 | 174 | 47 |
N.S. |
1 | 1.63 | 1.63 | 2.17 | 1.43 | 2.50 | 2.00 | 0.00 | 5.80 | 1.57 |
time (sec) |
N/A | 19.975 | 0.190 | 0.079 | 0.297 | 0.108 | 1.857 | 0.000 | 200.025 | 4.140 |
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 | 21 | 17 | 20 | 17 | 20 | 22 | 18 | 17 |
N.S. |
1 | 0.00 | 0.91 | 0.74 | 0.87 | 0.74 | 0.87 | 0.96 | 0.78 | 0.74 |
time (sec) |
N/A | 0.000 | 0.228 | 0.286 | 0.160 | 0.085 | 0.128 | 0.120 | 0.165 | 4.207 |
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 | 28 | 0 | 79 | 80 | 131 | 145 | 119 | 155 | 0 | 0 |
N.S. |
1 | 0.00 | 2.82 | 2.86 | 4.68 | 5.18 | 4.25 | 5.54 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.154 | 1.468 | 0.357 | 0.133 | 0.305 | 3.496 | 0.209 | 0.000 |
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 | 25 | 0 | 31 | 21 | 26 | 32 | 26 | 55 | 29 | 28 |
N.S. |
1 | 0.00 | 1.24 | 0.84 | 1.04 | 1.28 | 1.04 | 2.20 | 1.16 | 1.12 |
time (sec) |
N/A | 0.000 | 0.768 | 5.505 | 0.154 | 0.115 | 1.834 | 0.139 | 0.192 | 3.854 |
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 | 32 | 0 | 26 | 30 | 42 | 42 | 37 | 31 | 32 | 0 |
N.S. |
1 | 0.00 | 0.81 | 0.94 | 1.31 | 1.31 | 1.16 | 0.97 | 1.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.331 | 1.886 | 0.073 | 0.103 | 0.309 | 0.120 | 0.160 | 0.000 |
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 | 32 | 0 | 49 | 36 | 56 | 38 | 37 | 89 | 90 | 63 |
N.S. |
1 | 0.00 | 1.53 | 1.12 | 1.75 | 1.19 | 1.16 | 2.78 | 2.81 | 1.97 |
time (sec) |
N/A | 0.000 | 3.175 | 1.533 | 0.098 | 0.086 | 0.098 | 0.985 | 0.168 | 3.804 |
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 | 10 | 10 | 8 | 7 | 7 | 8 | 7 | 8 | 7 |
N.S. |
1 | 0.83 | 0.83 | 0.67 | 0.58 | 0.58 | 0.67 | 0.58 | 0.67 | 0.58 |
time (sec) |
N/A | 0.148 | 0.000 | 0.052 | 0.031 | 0.073 | 0.015 | 0.114 | 0.163 | 0.023 |
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 | 22 | 23 | 23 | 20 | 24 | 19 | 19 | 21 | 24 | 20 |
N.S. |
1 | 1.05 | 1.05 | 0.91 | 1.09 | 0.86 | 0.86 | 0.95 | 1.09 | 0.91 |
time (sec) |
N/A | 0.236 | 0.061 | 0.221 | 0.059 | 0.093 | 0.057 | 0.104 | 0.166 | 3.610 |
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 | 15 | 15 | 14 | 13 | 27 | 12 | 13 | 28 | 13 |
N.S. |
1 | 0.94 | 0.94 | 0.88 | 0.81 | 1.69 | 0.75 | 0.81 | 1.75 | 0.81 |
time (sec) |
N/A | 0.166 | 0.013 | 0.151 | 0.030 | 0.087 | 0.053 | 0.113 | 0.165 | 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 | 16 | 15 | 18 | 21 | 14 | 21 | 21 | 14 |
N.S. |
1 | 1.25 | 1.00 | 0.94 | 1.12 | 1.31 | 0.88 | 1.31 | 1.31 | 0.88 |
time (sec) |
N/A | 0.184 | 0.005 | 0.153 | 0.030 | 0.087 | 0.053 | 0.110 | 0.164 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | F(-1) | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 27 | 35 | 0 | 34 | 0 | 0 | 43 | 72 |
N.S. |
1 | 0.00 | 0.93 | 1.21 | 0.00 | 1.17 | 0.00 | 0.00 | 1.48 | 2.48 |
time (sec) |
N/A | 0.000 | 0.246 | 9.507 | 0.000 | 0.111 | 0.000 | 0.000 | 0.324 | 3.795 |
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 | 25 | 23 | 18 | 16 | 15 | 23 | 14 | 16 | 28 | 17 |
N.S. |
1 | 0.92 | 0.72 | 0.64 | 0.60 | 0.92 | 0.56 | 0.64 | 1.12 | 0.68 |
time (sec) |
N/A | 0.260 | 0.012 | 0.108 | 0.034 | 0.079 | 0.122 | 0.110 | 0.173 | 0.048 |
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 | 26 | 0 | 30 | 34 | 57 | 31 | 31 | 57 | 32 | 443 |
N.S. |
1 | 0.00 | 1.15 | 1.31 | 2.19 | 1.19 | 1.19 | 2.19 | 1.23 | 17.04 |
time (sec) |
N/A | 0.000 | 0.027 | 22.611 | 0.083 | 0.087 | 0.089 | 0.162 | 0.178 | 4.009 |
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 | 38 | 27 | 26 | 25 | 26 | 34 |
N.S. |
1 | 0.96 | 0.96 | 0.93 | 1.41 | 1.00 | 0.96 | 0.93 | 0.96 | 1.26 |
time (sec) |
N/A | 0.355 | 0.061 | 0.212 | 0.075 | 0.103 | 0.130 | 0.117 | 0.167 | 3.753 |
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 | 26 | 26 | 24 | 25 | 39 | 22 | 25 | 34 | 23 |
N.S. |
1 | 0.84 | 0.84 | 0.77 | 0.81 | 1.26 | 0.71 | 0.81 | 1.10 | 0.74 |
time (sec) |
N/A | 0.487 | 0.014 | 0.354 | 0.031 | 0.086 | 0.080 | 0.115 | 0.169 | 0.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 0 | 16 | 12 | 14 | 14 | 15 | 0 | 136 | 15 |
N.S. |
1 | 0.00 | 0.94 | 0.71 | 0.82 | 0.82 | 0.88 | 0.00 | 8.00 | 0.88 |
time (sec) |
N/A | 0.000 | 0.358 | 0.536 | 0.235 | 0.097 | 0.209 | 0.000 | 0.183 | 4.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 21 | 18 | 37 | 43 | 24 | 25 | 41 | 28 |
N.S. |
1 | 1.00 | 0.91 | 0.78 | 1.61 | 1.87 | 1.04 | 1.09 | 1.78 | 1.22 |
time (sec) |
N/A | 0.539 | 0.069 | 0.533 | 0.054 | 0.081 | 0.058 | 0.128 | 0.170 | 4.251 |
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 | 21 | 0 | 21 | 23 | 21 | 21 | 19 | 21 | 34 | 23 |
N.S. |
1 | 0.00 | 1.00 | 1.10 | 1.00 | 1.00 | 0.90 | 1.00 | 1.62 | 1.10 |
time (sec) |
N/A | 0.000 | 0.512 | 4.193 | 0.125 | 0.102 | 0.214 | 0.118 | 0.190 | 4.291 |
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 | 14 | 11 | 10 | 11 | 9 | 10 | 10 | 11 | 9 |
N.S. |
1 | 1.08 | 0.85 | 0.77 | 0.85 | 0.69 | 0.77 | 0.77 | 0.85 | 0.69 |
time (sec) |
N/A | 0.170 | 0.012 | 0.130 | 0.033 | 0.085 | 0.048 | 0.104 | 0.169 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 29 | 104 | 26 | 24 | 20 | 36 | 36 | 24 |
N.S. |
1 | 0.00 | 1.16 | 4.16 | 1.04 | 0.96 | 0.80 | 1.44 | 1.44 | 0.96 |
time (sec) |
N/A | 0.000 | 0.102 | 3.192 | 0.073 | 0.089 | 0.922 | 0.338 | 0.197 | 4.030 |
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 | 21 | 0 | 21 | 22 | 25 | 25 | 22 | 26 | 21 | 513 |
N.S. |
1 | 0.00 | 1.00 | 1.05 | 1.19 | 1.19 | 1.05 | 1.24 | 1.00 | 24.43 |
time (sec) |
N/A | 0.000 | 0.167 | 1.506 | 0.148 | 0.093 | 0.087 | 0.122 | 0.168 | 4.257 |
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 | 28 | 0 | 27 | 20 | 19 | 30 | 20 | 38 | 47 | 42 |
N.S. |
1 | 0.00 | 0.96 | 0.71 | 0.68 | 1.07 | 0.71 | 1.36 | 1.68 | 1.50 |
time (sec) |
N/A | 0.000 | 2.788 | 0.627 | 0.079 | 0.102 | 0.066 | 0.131 | 0.172 | 4.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 28 | 27 | 32 | 44 | 20 | 0 | 37 | 139 |
N.S. |
1 | 0.00 | 1.00 | 0.96 | 1.14 | 1.57 | 0.71 | 0.00 | 1.32 | 4.96 |
time (sec) |
N/A | 0.000 | 0.067 | 55.047 | 0.169 | 0.104 | 0.145 | 0.000 | 0.176 | 4.459 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 43 | 28 | 21 | 38 | 25 | 19 | 95 | 37 | 21 |
N.S. |
1 | 1.59 | 1.04 | 0.78 | 1.41 | 0.93 | 0.70 | 3.52 | 1.37 | 0.78 |
time (sec) |
N/A | 0.489 | 0.063 | 0.370 | 0.037 | 0.084 | 0.066 | 0.116 | 0.186 | 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 | 23 | 39 | 39 | 34 | 38 | 38 | 34 | 38 | 33 | 32 |
N.S. |
1 | 1.70 | 1.70 | 1.48 | 1.65 | 1.65 | 1.48 | 1.65 | 1.43 | 1.39 |
time (sec) |
N/A | 0.180 | 0.005 | 0.133 | 0.033 | 0.088 | 0.024 | 0.114 | 0.170 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | B | B | F(-1) | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 79 | 25 | 40 | 43 | 43 | 44 | 0 | 44 | 0 |
N.S. |
1 | 3.29 | 1.04 | 1.67 | 1.79 | 1.79 | 1.83 | 0.00 | 1.83 | 0.00 |
time (sec) |
N/A | 1.895 | 0.139 | 22.593 | 0.168 | 0.100 | 0.384 | 0.000 | 0.175 | 0.000 |
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 | 26 | 0 | 31 | 31 | 30 | 30 | 29 | 30 | 31 | 30 |
N.S. |
1 | 0.00 | 1.19 | 1.19 | 1.15 | 1.15 | 1.12 | 1.15 | 1.19 | 1.15 |
time (sec) |
N/A | 0.000 | 2.567 | 0.227 | 0.064 | 0.098 | 0.069 | 0.111 | 0.175 | 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 | 9 | 9 | 9 | 9 | 8 | 8 | 8 | 8 | 10 | 8 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.89 | 0.89 | 0.89 | 0.89 | 1.11 | 0.89 |
time (sec) |
N/A | 0.236 | 0.014 | 0.093 | 0.034 | 0.088 | 0.039 | 0.111 | 0.170 | 0.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 40 | 45 | 91 | 65 | 49 | 52 | 0 | 0 |
N.S. |
1 | 0.00 | 1.67 | 1.88 | 3.79 | 2.71 | 2.04 | 2.17 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 1.514 | 9.941 | 0.164 | 0.086 | 0.171 | 0.202 | 0.198 | 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 | 9 | 9 | 9 | 9 | 8 | 8 | 5 | 8 | 9 | 8 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.89 | 0.89 | 0.56 | 0.89 | 1.00 | 0.89 |
time (sec) |
N/A | 0.134 | 0.000 | 0.056 | 0.025 | 0.066 | 0.014 | 0.103 | 0.174 | 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 | 38 | 32 | 32 | 32 | 53 | 48 | 31 | 59 | 41 | 50 |
N.S. |
1 | 0.84 | 0.84 | 0.84 | 1.39 | 1.26 | 0.82 | 1.55 | 1.08 | 1.32 |
time (sec) |
N/A | 2.066 | 5.054 | 3.123 | 0.232 | 0.090 | 0.131 | 0.128 | 0.171 | 4.270 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F(-2) | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 0 | 48 | 27 | 41 | 41 | 26 | 0 | 49 | 30 |
N.S. |
1 | 0.00 | 1.30 | 0.73 | 1.11 | 1.11 | 0.70 | 0.00 | 1.32 | 0.81 |
time (sec) |
N/A | 0.000 | 0.068 | 23.031 | 0.095 | 0.105 | 0.101 | 0.000 | 1.777 | 4.103 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 28 | 21 | 0 | 22 | 27 | 0 | 24 | 21 |
N.S. |
1 | 0.00 | 0.93 | 0.70 | 0.00 | 0.73 | 0.90 | 0.00 | 0.80 | 0.70 |
time (sec) |
N/A | 0.000 | 0.075 | 0.737 | 0.000 | 0.093 | 31.939 | 0.000 | 0.173 | 4.480 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 33 | 25 | 26 | 48 | 24 | 0 | 80 | 48 |
N.S. |
1 | 0.00 | 1.10 | 0.83 | 0.87 | 1.60 | 0.80 | 0.00 | 2.67 | 1.60 |
time (sec) |
N/A | 0.000 | 0.196 | 0.515 | 0.192 | 0.089 | 0.160 | 0.000 | 0.173 | 0.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 32 | 25 | 31 | 27 | 31 | 0 | 48 | 35 |
N.S. |
1 | 0.00 | 1.10 | 0.86 | 1.07 | 0.93 | 1.07 | 0.00 | 1.66 | 1.21 |
time (sec) |
N/A | 0.000 | 1.001 | 0.289 | 0.126 | 0.108 | 0.189 | 0.000 | 0.177 | 4.132 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 28 | 26 | 26 | 31 | 28 | 27 | 28 | 29 | 0 |
N.S. |
1 | 0.93 | 0.87 | 0.87 | 1.03 | 0.93 | 0.90 | 0.93 | 0.97 | 0.00 |
time (sec) |
N/A | 1.555 | 0.059 | 1.645 | 0.099 | 0.096 | 0.166 | 0.240 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 0 | 144 | 117 | 148 | 94 | 177 | 0 | 136 | 125 |
N.S. |
1 | 0.00 | 3.89 | 3.16 | 4.00 | 2.54 | 4.78 | 0.00 | 3.68 | 3.38 |
time (sec) |
N/A | 0.000 | 0.149 | 3.257 | 0.091 | 0.091 | 0.309 | 0.000 | 0.339 | 0.430 |
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 | 17 | 27 | 17 | 34 | 35 | 35 | 34 | 40 | 39 | 27 |
N.S. |
1 | 1.59 | 1.00 | 2.00 | 2.06 | 2.06 | 2.00 | 2.35 | 2.29 | 1.59 |
time (sec) |
N/A | 0.196 | 0.011 | 0.122 | 0.036 | 0.093 | 0.051 | 0.111 | 0.185 | 0.045 |
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 | 13 | 13 | 16 | 12 | 11 | 14 | 12 | 13 | 11 |
N.S. |
1 | 0.87 | 0.87 | 1.07 | 0.80 | 0.73 | 0.93 | 0.80 | 0.87 | 0.73 |
time (sec) |
N/A | 0.136 | 0.001 | 0.085 | 0.026 | 0.087 | 0.020 | 0.110 | 0.176 | 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 | 30 | 16 | 16 | 13 | 12 | 12 | 12 | 15 | 18 | 12 |
N.S. |
1 | 0.53 | 0.53 | 0.43 | 0.40 | 0.40 | 0.40 | 0.50 | 0.60 | 0.40 |
time (sec) |
N/A | 0.214 | 0.033 | 0.208 | 0.060 | 0.087 | 0.079 | 0.117 | 0.171 | 3.931 |
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 | 22 | 0 | 22 | 20 | 24 | 19 | 17 | 19 | 21 | 19 |
N.S. |
1 | 0.00 | 1.00 | 0.91 | 1.09 | 0.86 | 0.77 | 0.86 | 0.95 | 0.86 |
time (sec) |
N/A | 0.000 | 0.098 | 0.302 | 0.162 | 0.077 | 0.080 | 0.123 | 0.169 | 4.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 33 | 39 | 49 | 43 | 37 | 0 | 31 | 30 |
N.S. |
1 | 0.00 | 1.38 | 1.62 | 2.04 | 1.79 | 1.54 | 0.00 | 1.29 | 1.25 |
time (sec) |
N/A | 0.000 | 5.438 | 0.760 | 0.150 | 0.086 | 0.227 | 0.000 | 0.174 | 4.099 |
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 | 18 | 0 | 18 | 18 | 17 | 17 | 17 | 17 | 20 | 17 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 0.94 | 0.94 | 0.94 | 0.94 | 1.11 | 0.94 |
time (sec) |
N/A | 0.000 | 0.080 | 0.239 | 0.104 | 0.085 | 0.079 | 0.110 | 0.190 | 0.127 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 32 | 34 | 31 | 28 | 28 | 31 | 28 | 29 | 30 |
N.S. |
1 | 2.13 | 2.27 | 2.07 | 1.87 | 1.87 | 2.07 | 1.87 | 1.93 | 2.00 |
time (sec) |
N/A | 0.253 | 0.003 | 0.132 | 0.034 | 0.082 | 0.021 | 0.114 | 0.173 | 0.025 |
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 | 26 | 0 | 33 | 34 | 53 | 33 | 0 | 0 | 26 | 25 |
N.S. |
1 | 0.00 | 1.27 | 1.31 | 2.04 | 1.27 | 0.00 | 0.00 | 1.00 | 0.96 |
time (sec) |
N/A | 0.000 | 0.218 | 27.654 | 0.211 | 0.088 | 0.000 | 0.000 | 0.187 | 4.139 |
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 | 23 | 27 | 24 | 29 | 27 | 38 | 37 | 24 |
N.S. |
1 | 0.00 | 0.92 | 1.08 | 0.96 | 1.16 | 1.08 | 1.52 | 1.48 | 0.96 |
time (sec) |
N/A | 0.000 | 0.295 | 0.760 | 0.080 | 0.094 | 0.084 | 0.197 | 0.175 | 3.883 |
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 | 28 | 27 | 22 | 22 | 26 | 26 | 24 | 26 | 46 | 27 |
N.S. |
1 | 0.96 | 0.79 | 0.79 | 0.93 | 0.93 | 0.86 | 0.93 | 1.64 | 0.96 |
time (sec) |
N/A | 0.202 | 0.041 | 0.183 | 0.033 | 0.094 | 0.050 | 0.104 | 0.192 | 3.939 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | B | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 48 | 44 | 45 | 178 | 85 | 63 | 41 | 44 | 47 |
N.S. |
1 | 1.85 | 1.69 | 1.73 | 6.85 | 3.27 | 2.42 | 1.58 | 1.69 | 1.81 |
time (sec) |
N/A | 0.755 | 0.297 | 1.420 | 0.166 | 0.081 | 0.150 | 0.109 | 0.176 | 4.444 |
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 | 36 | 36 | 30 | 29 | 33 | 27 | 33 | 36 | 29 |
N.S. |
1 | 1.12 | 1.12 | 0.94 | 0.91 | 1.03 | 0.84 | 1.03 | 1.12 | 0.91 |
time (sec) |
N/A | 2.688 | 0.123 | 1.296 | 0.080 | 0.104 | 0.540 | 0.168 | 0.181 | 3.832 |
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 | 25 | 74 | 29 | 40 | 152 | 33 | 37 | 34 | 57 | 29 |
N.S. |
1 | 2.96 | 1.16 | 1.60 | 6.08 | 1.32 | 1.48 | 1.36 | 2.28 | 1.16 |
time (sec) |
N/A | 0.661 | 0.059 | 0.905 | 0.087 | 0.086 | 0.116 | 0.113 | 0.172 | 3.622 |
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 | 34 | 37 | 23 | 22 | 0 | 20 | 24 | 22 | 29 | 27 |
N.S. |
1 | 1.09 | 0.68 | 0.65 | 0.00 | 0.59 | 0.71 | 0.65 | 0.85 | 0.79 |
time (sec) |
N/A | 0.717 | 0.129 | 0.613 | 0.000 | 0.083 | 0.082 | 0.112 | 0.169 | 0.055 |
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 | 28 | 0 | 49 | 64 | 123 | 123 | 131 | 167 | 189 | 121 |
N.S. |
1 | 0.00 | 1.75 | 2.29 | 4.39 | 4.39 | 4.68 | 5.96 | 6.75 | 4.32 |
time (sec) |
N/A | 0.000 | 0.140 | 13.367 | 0.222 | 0.102 | 0.240 | 0.414 | 0.193 | 4.033 |
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 | 26 | 27 | 27 | 26 | 24 | 27 | 26 | 27 |
N.S. |
1 | 0.00 | 0.81 | 0.84 | 0.84 | 0.81 | 0.75 | 0.84 | 0.81 | 0.84 |
time (sec) |
N/A | 0.000 | 0.037 | 0.530 | 0.078 | 0.110 | 0.220 | 0.144 | 0.176 | 4.267 |
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 | 24 | 19 | 20 | 25 | 30 | 22 | 32 | 31 | 19 |
N.S. |
1 | 1.20 | 0.95 | 1.00 | 1.25 | 1.50 | 1.10 | 1.60 | 1.55 | 0.95 |
time (sec) |
N/A | 0.213 | 0.010 | 0.387 | 0.027 | 0.094 | 0.068 | 0.119 | 0.177 | 0.054 |
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 | 24 | 18 | 20 | 17 | 17 | 17 | 20 | 18 |
N.S. |
1 | 0.92 | 1.00 | 0.75 | 0.83 | 0.71 | 0.71 | 0.71 | 0.83 | 0.75 |
time (sec) |
N/A | 0.555 | 0.096 | 0.701 | 0.056 | 0.094 | 0.059 | 0.112 | 0.177 | 0.046 |
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 | 35 | 0 | 36 | 36 | 35 | 45 | 27 | 47 | 53 | 29 |
N.S. |
1 | 0.00 | 1.03 | 1.03 | 1.00 | 1.29 | 0.77 | 1.34 | 1.51 | 0.83 |
time (sec) |
N/A | 0.000 | 16.662 | 10.798 | 0.157 | 0.125 | 0.235 | 0.118 | 0.176 | 3.841 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 18 | 18 | 103 | 29 | 15 | 108 | 33 | 16 |
N.S. |
1 | 1.00 | 0.90 | 0.90 | 5.15 | 1.45 | 0.75 | 5.40 | 1.65 | 0.80 |
time (sec) |
N/A | 0.698 | 0.025 | 0.433 | 0.120 | 0.095 | 0.121 | 0.108 | 0.174 | 4.057 |
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 | 19 | 17 | 15 | 20 | 14 | 12 | 14 | 18 | 14 |
N.S. |
1 | 1.19 | 1.06 | 0.94 | 1.25 | 0.88 | 0.75 | 0.88 | 1.12 | 0.88 |
time (sec) |
N/A | 0.678 | 0.211 | 0.538 | 0.140 | 0.080 | 0.053 | 0.111 | 0.185 | 0.160 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 54 | 24 | 22 | 19 | 21 | 19 | 21 | 20 | 21 |
N.S. |
1 | 2.45 | 1.09 | 1.00 | 0.86 | 0.95 | 0.86 | 0.95 | 0.91 | 0.95 |
time (sec) |
N/A | 0.368 | 2.149 | 0.263 | 0.098 | 0.108 | 0.106 | 0.113 | 0.198 | 3.817 |
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 | 15 | 15 | 15 | 14 | 18 | 12 | 15 | 18 | 14 |
N.S. |
1 | 0.88 | 0.88 | 0.88 | 0.82 | 1.06 | 0.71 | 0.88 | 1.06 | 0.82 |
time (sec) |
N/A | 0.246 | 0.004 | 0.092 | 0.032 | 0.089 | 0.040 | 0.111 | 0.183 | 3.619 |
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 | 30 | 30 | 26 | 25 | 26 | 26 | 25 | 28 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.83 | 0.87 | 0.87 | 0.83 | 0.93 | 0.87 |
time (sec) |
N/A | 0.354 | 0.020 | 0.364 | 0.029 | 0.072 | 0.111 | 0.110 | 0.177 | 3.639 |
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 | 10 | 10 | 11 | 10 | 10 | 10 | 11 | 10 | 10 |
N.S. |
1 | 0.83 | 0.83 | 0.92 | 0.83 | 0.83 | 0.83 | 0.92 | 0.83 | 0.83 |
time (sec) |
N/A | 0.269 | 0.001 | 0.099 | 0.024 | 0.101 | 0.041 | 0.111 | 0.173 | 3.577 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 31 | 27 | 26 | 39 | 32 | 0 | 46 | 26 |
N.S. |
1 | 0.00 | 0.91 | 0.79 | 0.76 | 1.15 | 0.94 | 0.00 | 1.35 | 0.76 |
time (sec) |
N/A | 0.000 | 0.067 | 0.287 | 0.092 | 0.105 | 0.120 | 0.000 | 0.173 | 3.777 |
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 | 21 | 18 | 16 | 15 | 17 | 15 | 17 | 23 | 16 |
N.S. |
1 | 0.78 | 0.67 | 0.59 | 0.56 | 0.63 | 0.56 | 0.63 | 0.85 | 0.59 |
time (sec) |
N/A | 0.167 | 0.016 | 0.155 | 0.030 | 0.087 | 0.032 | 0.109 | 0.175 | 3.646 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 23 | 15 | 38 | 0 | 15 | 26 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.28 | 0.83 | 2.11 | 0.00 | 0.83 | 1.44 | 1.00 |
time (sec) |
N/A | 0.502 | 0.115 | 3.206 | 0.137 | 0.094 | 0.000 | 0.119 | 0.187 | 3.796 |
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 | 26 | 26 | 23 | 34 | 22 | 22 | 23 | 24 | 33 |
N.S. |
1 | 1.08 | 1.08 | 0.96 | 1.42 | 0.92 | 0.92 | 0.96 | 1.00 | 1.38 |
time (sec) |
N/A | 0.800 | 0.123 | 0.945 | 0.150 | 0.107 | 0.135 | 0.126 | 0.175 | 3.853 |