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 | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 18 | 17 | 19 | 17 | 16 | 15 | 17 | 17 | 19 |
N.S. |
1 | 0.95 | 0.89 | 1.00 | 0.89 | 0.84 | 0.79 | 0.89 | 0.89 | 1.00 |
time (sec) |
N/A | 0.156 | 0.005 | 0.137 | 0.043 | 0.089 | 0.055 | 0.114 | 0.153 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 37 | 51 | 37 | 33 | 112 | 62 | 61 | 285 |
N.S. |
1 | 0.00 | 1.23 | 1.70 | 1.23 | 1.10 | 3.73 | 2.07 | 2.03 | 9.50 |
time (sec) |
N/A | 0.000 | 0.088 | 4.554 | 0.245 | 0.125 | 0.494 | 0.322 | 0.161 | 3.096 |
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 | 32 | 30 | 28 | 61 | 53 | 24 | 28 | 36 | 29 |
N.S. |
1 | 1.28 | 1.20 | 1.12 | 2.44 | 2.12 | 0.96 | 1.12 | 1.44 | 1.16 |
time (sec) |
N/A | 0.260 | 0.187 | 1.444 | 0.062 | 0.160 | 0.066 | 0.116 | 0.158 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 27 | 23 | 32 | 14 | 47 | 26 | 0 | 27 | 0 |
N.S. |
1 | 1.50 | 1.28 | 1.78 | 0.78 | 2.61 | 1.44 | 0.00 | 1.50 | 0.00 |
time (sec) |
N/A | 0.686 | 0.038 | 0.877 | 0.192 | 0.105 | 0.183 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 57 | 41 | 46 | 49 | 49 | 48 | 49 | 53 | 46 |
N.S. |
1 | 2.38 | 1.71 | 1.92 | 2.04 | 2.04 | 2.00 | 2.04 | 2.21 | 1.92 |
time (sec) |
N/A | 0.213 | 0.011 | 0.221 | 0.037 | 0.101 | 0.027 | 0.108 | 0.153 | 2.714 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 30 | 118 | 65 | 48 | 48 | 98 | 86 | 96 |
N.S. |
1 | 0.00 | 1.07 | 4.21 | 2.32 | 1.71 | 1.71 | 3.50 | 3.07 | 3.43 |
time (sec) |
N/A | 0.000 | 0.378 | 0.275 | 0.199 | 0.114 | 0.205 | 0.195 | 0.155 | 0.189 |
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 | 12 | 12 | 14 | 14 | 10 | 14 | 14 | 12 |
N.S. |
1 | 1.23 | 0.92 | 0.92 | 1.08 | 1.08 | 0.77 | 1.08 | 1.08 | 0.92 |
time (sec) |
N/A | 0.139 | 0.001 | 0.089 | 0.044 | 0.064 | 0.018 | 0.109 | 0.152 | 2.738 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 57 | 57 | 50 | 66 | 41 | 60 | 41 | 52 | 22 |
N.S. |
1 | 2.38 | 2.38 | 2.08 | 2.75 | 1.71 | 2.50 | 1.71 | 2.17 | 0.92 |
time (sec) |
N/A | 0.293 | 0.020 | 1.050 | 0.052 | 0.100 | 0.119 | 0.124 | 0.157 | 2.852 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 40 | 31 | 0 | 34 | 29 | 42 | 67 | 48 |
N.S. |
1 | 0.00 | 1.33 | 1.03 | 0.00 | 1.13 | 0.97 | 1.40 | 2.23 | 1.60 |
time (sec) |
N/A | 0.000 | 10.059 | 1.740 | 0.000 | 0.113 | 4.515 | 0.152 | 0.153 | 2.901 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 24 | 24 | 23 | 23 | 22 | 0 | 0 | 36 | 23 |
N.S. |
1 | 0.86 | 0.86 | 0.82 | 0.82 | 0.79 | 0.00 | 0.00 | 1.29 | 0.82 |
time (sec) |
N/A | 0.264 | 0.048 | 1.257 | 0.331 | 0.097 | 0.000 | 0.000 | 0.153 | 2.868 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 28 | 30 | 29 | 31 | 24 | 62 | 517 | 54 |
N.S. |
1 | 0.00 | 1.22 | 1.30 | 1.26 | 1.35 | 1.04 | 2.70 | 22.48 | 2.35 |
time (sec) |
N/A | 0.000 | 1.369 | 0.483 | 0.100 | 0.123 | 0.133 | 0.119 | 0.160 | 0.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 21 | 25 | 33 | 33 | 29 | 71 | 286 | 21 |
N.S. |
1 | 0.00 | 0.95 | 1.14 | 1.50 | 1.50 | 1.32 | 3.23 | 13.00 | 0.95 |
time (sec) |
N/A | 0.000 | 0.199 | 0.697 | 0.081 | 0.129 | 0.070 | 0.127 | 0.267 | 2.883 |
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 | 21 | 34 | 19 | 17 | 28 | 29 | 31 | 29 | 34 | 16 |
N.S. |
1 | 1.62 | 0.90 | 0.81 | 1.33 | 1.38 | 1.48 | 1.38 | 1.62 | 0.76 |
time (sec) |
N/A | 0.207 | 0.003 | 0.142 | 0.036 | 0.093 | 0.058 | 0.112 | 0.154 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 83 | 259 | 390 | 390 | 291 | 548 | 577 | 0 |
N.S. |
1 | 0.00 | 2.77 | 8.63 | 13.00 | 13.00 | 9.70 | 18.27 | 19.23 | 0.00 |
time (sec) |
N/A | 0.000 | 10.157 | 181.668 | 0.259 | 0.130 | 0.396 | 0.436 | 0.245 | 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 | 20 | 16 | 14 | 15 | 16 | 16 | 15 | 18 | 16 | 12 |
N.S. |
1 | 0.80 | 0.70 | 0.75 | 0.80 | 0.80 | 0.75 | 0.90 | 0.80 | 0.60 |
time (sec) |
N/A | 0.188 | 0.004 | 0.144 | 0.036 | 0.093 | 0.042 | 0.109 | 0.152 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F(-2) | A | B | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 29 | 56 | 0 | 56 | 53 | 35 | 39 | 36 |
N.S. |
1 | 0.00 | 0.94 | 1.81 | 0.00 | 1.81 | 1.71 | 1.13 | 1.26 | 1.16 |
time (sec) |
N/A | 0.000 | 0.101 | 238.764 | 0.000 | 0.094 | 0.576 | 5.738 | 18.378 | 2.965 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | F | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 1053 | 82 | 299 | 0 | 23 | 37 | 263 | 188 | 23 |
N.S. |
1 | 40.50 | 3.15 | 11.50 | 0.00 | 0.88 | 1.42 | 10.12 | 7.23 | 0.88 |
time (sec) |
N/A | 2.613 | 0.294 | 0.104 | 0.000 | 0.093 | 0.210 | 0.152 | 0.163 | 2.885 |
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 | 25 | 25 | 23 | 23 | 19 | 23 | 52 | 113 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 0.92 | 0.92 | 0.76 | 0.92 | 2.08 | 4.52 |
time (sec) |
N/A | 0.000 | 0.608 | 1.216 | 0.179 | 0.099 | 0.108 | 0.191 | 0.246 | 2.854 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | A | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 39 | 72 | 56 | 51 | 53 | 74 | 296 | 0 |
N.S. |
1 | 0.00 | 1.22 | 2.25 | 1.75 | 1.59 | 1.66 | 2.31 | 9.25 | 0.00 |
time (sec) |
N/A | 0.000 | 0.251 | 1.367 | 0.103 | 0.095 | 0.179 | 0.379 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | B | A | A | B | B | B |
verified | N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 28 | 0 | 124 | 31 | 27 | 92 | 31 | 33 |
N.S. |
1 | 0.00 | 1.47 | 0.00 | 6.53 | 1.63 | 1.42 | 4.84 | 1.63 | 1.74 |
time (sec) |
N/A | 0.000 | 0.046 | 0.000 | 0.114 | 0.133 | 0.238 | 0.558 | 0.159 | 3.691 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 21 | 24 | 21 | 21 | 37 | 37 | 25 | 19 |
N.S. |
1 | 0.00 | 0.95 | 1.09 | 0.95 | 0.95 | 1.68 | 1.68 | 1.14 | 0.86 |
time (sec) |
N/A | 0.000 | 0.115 | 1.852 | 0.163 | 0.088 | 0.092 | 0.119 | 0.188 | 2.752 |
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 | 29 | 68 | 23 | 20 | 17 | 19 | 15 | 19 | 20 | 17 |
N.S. |
1 | 2.34 | 0.79 | 0.69 | 0.59 | 0.66 | 0.52 | 0.66 | 0.69 | 0.59 |
time (sec) |
N/A | 0.248 | 0.015 | 0.208 | 0.116 | 0.119 | 0.087 | 0.120 | 0.174 | 2.668 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F(-1) | A | A | A | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 22 | 22 | 0 | 21 | 19 | 21 | 71 | 22 |
N.S. |
1 | 0.00 | 1.16 | 1.16 | 0.00 | 1.11 | 1.00 | 1.11 | 3.74 | 1.16 |
time (sec) |
N/A | 0.000 | 0.205 | 0.265 | 0.000 | 0.095 | 0.089 | 0.124 | 0.176 | 2.751 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 55 | 39 | 20 | 18 | 19 | 24 | 0 | 21 | 20 |
N.S. |
1 | 2.39 | 1.70 | 0.87 | 0.78 | 0.83 | 1.04 | 0.00 | 0.91 | 0.87 |
time (sec) |
N/A | 0.450 | 0.032 | 0.917 | 0.166 | 0.096 | 0.104 | 0.000 | 0.163 | 0.189 |
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 | 26 | 20 | 15 | 14 | 14 | 14 | 14 | 28 | 15 |
N.S. |
1 | 1.13 | 0.87 | 0.65 | 0.61 | 0.61 | 0.61 | 0.61 | 1.22 | 0.65 |
time (sec) |
N/A | 0.158 | 0.019 | 0.100 | 0.030 | 0.114 | 0.037 | 0.111 | 0.175 | 0.048 |
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 | 32 | 81 | 35 | 34 | 134 | 45 | 32 | 56 | 69 | 25 |
N.S. |
1 | 2.53 | 1.09 | 1.06 | 4.19 | 1.41 | 1.00 | 1.75 | 2.16 | 0.78 |
time (sec) |
N/A | 1.617 | 5.653 | 0.721 | 0.088 | 0.095 | 0.093 | 0.117 | 0.176 | 2.746 |
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 | 16 | 89 | 26 | 20 | 81 | 142 | 131 | 85 | 98 | 81 |
N.S. |
1 | 5.56 | 1.62 | 1.25 | 5.06 | 8.88 | 8.19 | 5.31 | 6.12 | 5.06 |
time (sec) |
N/A | 0.374 | 0.073 | 1.280 | 0.036 | 0.109 | 0.123 | 0.124 | 0.172 | 2.925 |
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 | 31 | 21 | 19 | 18 | 18 | 24 | 18 | 45 | 18 |
N.S. |
1 | 1.07 | 0.72 | 0.66 | 0.62 | 0.62 | 0.83 | 0.62 | 1.55 | 0.62 |
time (sec) |
N/A | 0.213 | 0.931 | 0.230 | 0.025 | 0.133 | 0.054 | 0.115 | 0.296 | 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 | 19 | 17 | 17 | 18 | 18 | 23 | 19 | 18 | 20 | 28 |
N.S. |
1 | 0.89 | 0.89 | 0.95 | 0.95 | 1.21 | 1.00 | 0.95 | 1.05 | 1.47 |
time (sec) |
N/A | 0.154 | 0.005 | 0.160 | 0.031 | 0.136 | 0.048 | 0.112 | 0.169 | 2.684 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 51 | 55 | 71 | 47 | 44 | 0 | 156 | 50 |
N.S. |
1 | 0.00 | 1.65 | 1.77 | 2.29 | 1.52 | 1.42 | 0.00 | 5.03 | 1.61 |
time (sec) |
N/A | 0.000 | 0.184 | 20.710 | 0.203 | 0.096 | 0.752 | 0.000 | 200.022 | 2.867 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | B | B | B | B | B |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 30 | 27 | 1472 | 141 | 88 | 202 | 149 | 151 | 97 |
N.S. |
1 | 1.15 | 1.04 | 56.62 | 5.42 | 3.38 | 7.77 | 5.73 | 5.81 | 3.73 |
time (sec) |
N/A | 0.980 | 0.029 | 0.918 | 0.086 | 0.105 | 0.435 | 0.144 | 0.156 | 3.508 |
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 | 21 | 21 | 15 | 33 | 20 | 15 | 25 | 15 |
N.S. |
1 | 0.00 | 0.78 | 0.78 | 0.56 | 1.22 | 0.74 | 0.56 | 0.93 | 0.56 |
time (sec) |
N/A | 0.000 | 0.127 | 0.220 | 0.074 | 0.156 | 0.119 | 0.141 | 0.174 | 2.798 |
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 | 22 | 21 | 20 | 20 | 20 | 20 | 24 | 24 |
N.S. |
1 | 0.00 | 0.76 | 0.72 | 0.69 | 0.69 | 0.69 | 0.69 | 0.83 | 0.83 |
time (sec) |
N/A | 0.000 | 0.008 | 0.089 | 0.026 | 0.086 | 0.052 | 0.115 | 0.148 | 0.031 |
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 | 14 | 13 | 13 | 15 | 13 | 14 | 13 |
N.S. |
1 | 0.60 | 0.60 | 0.47 | 0.43 | 0.43 | 0.50 | 0.43 | 0.47 | 0.43 |
time (sec) |
N/A | 0.155 | 0.005 | 0.089 | 0.032 | 0.074 | 0.037 | 0.104 | 0.151 | 0.024 |
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 | 10 | 8 | 11 | 9 | 8 | 8 | 8 | 8 | 9 | 8 |
N.S. |
1 | 0.80 | 1.10 | 0.90 | 0.80 | 0.80 | 0.80 | 0.80 | 0.90 | 0.80 |
time (sec) |
N/A | 0.148 | 0.001 | 0.098 | 0.027 | 0.124 | 0.037 | 0.111 | 0.158 | 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 | 18 | 24 | 22 | 17 | 17 | 24 | 12 | 17 | 23 | 16 |
N.S. |
1 | 1.33 | 1.22 | 0.94 | 0.94 | 1.33 | 0.67 | 0.94 | 1.28 | 0.89 |
time (sec) |
N/A | 0.247 | 0.009 | 0.115 | 0.032 | 0.085 | 0.065 | 0.115 | 0.153 | 0.037 |
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 | 20 | 19 | 18 | 18 | 15 | 36 | 20 | 18 |
N.S. |
1 | 0.00 | 0.62 | 0.59 | 0.56 | 0.56 | 0.47 | 1.12 | 0.62 | 0.56 |
time (sec) |
N/A | 0.000 | 0.143 | 0.229 | 0.075 | 0.141 | 0.081 | 0.121 | 0.165 | 0.067 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 69 | 60 | 49 | 112 | 37 | 51 | 67 | 62 | 46 |
N.S. |
1 | 2.76 | 2.40 | 1.96 | 4.48 | 1.48 | 2.04 | 2.68 | 2.48 | 1.84 |
time (sec) |
N/A | 0.377 | 0.042 | 0.754 | 0.033 | 0.172 | 0.123 | 0.114 | 0.155 | 2.819 |
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 | 22 | 20 | 76 | 22 | 19 | 19 | 32 | 2169 |
N.S. |
1 | 0.00 | 1.00 | 0.91 | 3.45 | 1.00 | 0.86 | 0.86 | 1.45 | 98.59 |
time (sec) |
N/A | 0.000 | 0.334 | 0.264 | 0.137 | 0.113 | 0.126 | 0.261 | 0.338 | 3.713 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 39 | 39 | 36 | 0 | 38 | 39 | 0 | 541 | 39 |
N.S. |
1 | 1.39 | 1.39 | 1.29 | 0.00 | 1.36 | 1.39 | 0.00 | 19.32 | 1.39 |
time (sec) |
N/A | 1.834 | 0.114 | 1.160 | 0.000 | 0.108 | 0.425 | 0.000 | 0.555 | 3.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-1) | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 30 | 30 | 27 | 31 | 28 | 27 | 0 | 38 | 26 |
N.S. |
1 | 0.94 | 0.94 | 0.84 | 0.97 | 0.88 | 0.84 | 0.00 | 1.19 | 0.81 |
time (sec) |
N/A | 3.075 | 0.072 | 233.939 | 0.207 | 0.181 | 0.492 | 0.000 | 0.164 | 5.682 |
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 | 24 | 0 | 23 | 41 | 22 | 31 | 31 | 35 | 29 | 0 |
N.S. |
1 | 0.00 | 0.96 | 1.71 | 0.92 | 1.29 | 1.29 | 1.46 | 1.21 | 0.00 |
time (sec) |
N/A | 0.000 | 5.075 | 0.984 | 0.099 | 0.184 | 0.139 | 0.171 | 0.185 | 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 | 23 | 24 | 22 | 20 | 39 | 19 | 20 | 39 | 22 | 19 |
N.S. |
1 | 1.04 | 0.96 | 0.87 | 1.70 | 0.83 | 0.87 | 1.70 | 0.96 | 0.83 |
time (sec) |
N/A | 0.169 | 0.004 | 0.210 | 0.025 | 0.149 | 0.061 | 0.108 | 0.166 | 3.183 |
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 | 26 | 31 | 29 | 27 | 32 | 26 | 28 | 31 | 22 |
N.S. |
1 | 0.90 | 1.07 | 1.00 | 0.93 | 1.10 | 0.90 | 0.97 | 1.07 | 0.76 |
time (sec) |
N/A | 0.223 | 0.006 | 0.154 | 0.037 | 0.110 | 0.047 | 0.113 | 0.160 | 0.044 |
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 | 19 | 46 | 24 | 18 | 17 | 17 | 17 | 17 | 17 | 17 |
N.S. |
1 | 2.42 | 1.26 | 0.95 | 0.89 | 0.89 | 0.89 | 0.89 | 0.89 | 0.89 |
time (sec) |
N/A | 0.182 | 0.027 | 0.177 | 0.030 | 0.116 | 0.047 | 0.111 | 0.164 | 0.032 |
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 | 18 | 28 | 19 | 19 | 20 | 26 | 24 | 27 | 32 | 24 |
N.S. |
1 | 1.56 | 1.06 | 1.06 | 1.11 | 1.44 | 1.33 | 1.50 | 1.78 | 1.33 |
time (sec) |
N/A | 0.525 | 0.088 | 0.483 | 0.206 | 0.112 | 0.087 | 0.120 | 1.694 | 2.803 |
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 | 22 | 26 | 32 | 27 | 29 | 32 | 23 | 26 |
N.S. |
1 | 1.10 | 1.10 | 1.30 | 1.60 | 1.35 | 1.45 | 1.60 | 1.15 | 1.30 |
time (sec) |
N/A | 0.183 | 0.005 | 0.207 | 0.030 | 0.111 | 0.085 | 0.111 | 0.170 | 2.746 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 22 | 23 | 43 | 43 | 0 | 24 | 24 | 22 |
N.S. |
1 | 0.00 | 0.81 | 0.85 | 1.59 | 1.59 | 0.00 | 0.89 | 0.89 | 0.81 |
time (sec) |
N/A | 0.000 | 0.622 | 0.727 | 0.144 | 0.162 | 0.000 | 0.116 | 0.168 | 2.808 |
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 | 19 | 19 | 20 | 26 | 20 | 19 | 20 | 20 | 19 |
N.S. |
1 | 1.00 | 1.00 | 1.05 | 1.37 | 1.05 | 1.00 | 1.05 | 1.05 | 1.00 |
time (sec) |
N/A | 0.666 | 0.011 | 0.745 | 0.138 | 0.099 | 0.059 | 0.118 | 0.170 | 2.854 |
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 | 14 | 7 | 7 | 8 | 7 | 7 | 7 | 7 | 8 | 8 |
N.S. |
1 | 0.50 | 0.50 | 0.57 | 0.50 | 0.50 | 0.50 | 0.50 | 0.57 | 0.57 |
time (sec) |
N/A | 0.230 | 0.000 | 0.069 | 0.029 | 0.108 | 0.035 | 0.110 | 0.172 | 2.788 |
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 | 27 | 39 | 39 | 24 | 30 | 37 | 31 |
N.S. |
1 | 0.00 | 0.96 | 1.00 | 1.44 | 1.44 | 0.89 | 1.11 | 1.37 | 1.15 |
time (sec) |
N/A | 0.000 | 0.931 | 13.618 | 0.140 | 0.112 | 0.069 | 0.122 | 0.171 | 2.858 |
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 | 19 | 19 | 19 | 23 | 68 | 18 | 17 | 18 | 19 | 51 |
N.S. |
1 | 1.00 | 1.00 | 1.21 | 3.58 | 0.95 | 0.89 | 0.95 | 1.00 | 2.68 |
time (sec) |
N/A | 1.310 | 0.082 | 1.131 | 0.301 | 0.110 | 0.215 | 0.170 | 0.178 | 2.913 |
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 | 23 | 49 | 27 | 26 | 44 | 38 | 27 | 32 | 47 | 25 |
N.S. |
1 | 2.13 | 1.17 | 1.13 | 1.91 | 1.65 | 1.17 | 1.39 | 2.04 | 1.09 |
time (sec) |
N/A | 0.396 | 0.024 | 0.717 | 0.032 | 0.091 | 0.071 | 0.115 | 0.172 | 0.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | A | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 79 | 54 | 26 | 53 | 51 | 181 | 51 | 184 |
N.S. |
1 | 0.00 | 3.29 | 2.25 | 1.08 | 2.21 | 2.12 | 7.54 | 2.12 | 7.67 |
time (sec) |
N/A | 0.000 | 0.118 | 1.690 | 0.358 | 0.106 | 1.086 | 0.140 | 0.186 | 3.449 |
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 | 24 | 73 | 73 | 72 | 73 | 67 | 68 | 70 | 73 | 73 |
N.S. |
1 | 3.04 | 3.04 | 3.00 | 3.04 | 2.79 | 2.83 | 2.92 | 3.04 | 3.04 |
time (sec) |
N/A | 0.334 | 0.011 | 3.993 | 0.035 | 0.110 | 0.080 | 0.108 | 0.169 | 2.939 |
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 | 27 | 27 | 24 | 27 | 28 | 24 |
N.S. |
1 | 0.00 | 1.09 | 1.14 | 1.23 | 1.23 | 1.09 | 1.23 | 1.27 | 1.09 |
time (sec) |
N/A | 0.000 | 0.120 | 0.516 | 0.056 | 0.083 | 0.049 | 0.112 | 0.176 | 2.972 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 28 | 27 | 30 | 30 | 29 | 26 | 211 | 26 |
N.S. |
1 | 0.00 | 0.97 | 0.93 | 1.03 | 1.03 | 1.00 | 0.90 | 7.28 | 0.90 |
time (sec) |
N/A | 0.000 | 3.644 | 0.340 | 0.090 | 0.122 | 0.211 | 0.155 | 0.182 | 0.093 |
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 | 37 | 22 | 36 | 38 | 28 | 31 | 28 | 25 | 33 |
N.S. |
1 | 1.68 | 1.00 | 1.64 | 1.73 | 1.27 | 1.41 | 1.27 | 1.14 | 1.50 |
time (sec) |
N/A | 0.200 | 0.067 | 0.222 | 0.027 | 0.166 | 0.274 | 0.125 | 0.173 | 0.069 |
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 | 22 | 22 | 19 | 18 | 18 | 15 | 18 | 24 | 20 |
N.S. |
1 | 0.79 | 0.79 | 0.68 | 0.64 | 0.64 | 0.54 | 0.64 | 0.86 | 0.71 |
time (sec) |
N/A | 0.297 | 0.188 | 0.218 | 0.098 | 0.170 | 0.105 | 0.123 | 0.183 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | F | B |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 68 | 25 | 21 | 19 | 19 | 22 | 34 | 222 | 20 |
N.S. |
1 | 2.27 | 0.83 | 0.70 | 0.63 | 0.63 | 0.73 | 1.13 | 7.40 | 0.67 |
time (sec) |
N/A | 0.245 | 0.043 | 0.288 | 0.325 | 0.093 | 2.178 | 0.161 | 0.201 | 3.389 |
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 | 23 | 23 | 19 | 18 | 22 | 22 | 22 | 26 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.78 | 0.96 | 0.96 | 0.96 | 1.13 | 0.78 |
time (sec) |
N/A | 0.187 | 0.018 | 0.244 | 0.026 | 0.135 | 0.064 | 0.114 | 0.170 | 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 | 18 | 9 | 9 | 8 | 7 | 7 | 7 | 7 | 7 | 7 |
N.S. |
1 | 0.50 | 0.50 | 0.44 | 0.39 | 0.39 | 0.39 | 0.39 | 0.39 | 0.39 |
time (sec) |
N/A | 0.132 | 0.000 | 0.065 | 0.025 | 0.107 | 0.022 | 0.106 | 0.175 | 0.014 |
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 | 29 | 35 | 35 | 31 | 32 | 38 | 32 | 49 |
N.S. |
1 | 0.00 | 1.00 | 1.21 | 1.21 | 1.07 | 1.10 | 1.31 | 1.10 | 1.69 |
time (sec) |
N/A | 0.000 | 0.114 | 171.899 | 0.176 | 0.150 | 1.156 | 0.640 | 0.229 | 3.504 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | A | F(-2) | B | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 0 | 30 | 63 | 29 | 0 | 67 | 39 | 31 |
N.S. |
1 | 0.00 | 0.00 | 1.20 | 2.52 | 1.16 | 0.00 | 2.68 | 1.56 | 1.24 |
time (sec) |
N/A | 0.000 | 0.000 | 41.302 | 0.134 | 0.122 | 0.000 | 0.625 | 0.185 | 2.878 |
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 | 15 | 0 | 15 | 19 | 14 | 18 | 15 | 20 | 20 | 15 |
N.S. |
1 | 0.00 | 1.00 | 1.27 | 0.93 | 1.20 | 1.00 | 1.33 | 1.33 | 1.00 |
time (sec) |
N/A | 0.000 | 0.075 | 0.263 | 0.104 | 0.157 | 0.089 | 0.119 | 0.171 | 2.818 |
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 | 31 | 24 | 23 | 23 | 26 | 33 | 29 | 23 |
N.S. |
1 | 0.00 | 0.94 | 0.73 | 0.70 | 0.70 | 0.79 | 1.00 | 0.88 | 0.70 |
time (sec) |
N/A | 0.000 | 0.325 | 13.008 | 0.067 | 0.153 | 0.106 | 0.124 | 0.178 | 2.882 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 39 | 38 | 44 | 44 | 39 | 44 | 195 | 0 |
N.S. |
1 | 0.00 | 1.08 | 1.06 | 1.22 | 1.22 | 1.08 | 1.22 | 5.42 | 0.00 |
time (sec) |
N/A | 0.000 | 0.290 | 4.462 | 0.198 | 0.178 | 0.165 | 0.659 | 200.027 | 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 | 17 | 20 | 25 | 21 | 22 | 25 | 37 | 5106 |
N.S. |
1 | 1.63 | 0.63 | 0.74 | 0.93 | 0.78 | 0.81 | 0.93 | 1.37 | 189.11 |
time (sec) |
N/A | 0.322 | 0.013 | 0.180 | 0.030 | 0.126 | 0.301 | 0.111 | 0.168 | 3.270 |
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 | 32 | 19 | 42 | 38 | 37 | 35 | 43 | 18 |
N.S. |
1 | 0.00 | 1.45 | 0.86 | 1.91 | 1.73 | 1.68 | 1.59 | 1.95 | 0.82 |
time (sec) |
N/A | 0.000 | 0.573 | 0.615 | 0.147 | 0.126 | 0.152 | 0.128 | 0.187 | 2.964 |
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 | 22 | 22 | 21 | 20 | 22 | 15 | 20 | 22 | 20 |
N.S. |
1 | 0.85 | 0.85 | 0.81 | 0.77 | 0.85 | 0.58 | 0.77 | 0.85 | 0.77 |
time (sec) |
N/A | 0.266 | 0.006 | 0.328 | 0.024 | 0.107 | 0.053 | 0.121 | 0.169 | 2.792 |
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 | 15 | 18 | 13 | 10 | 10 | 19 | 10 | 11 | 15 |
N.S. |
1 | 1.15 | 1.38 | 1.00 | 0.77 | 0.77 | 1.46 | 0.77 | 0.85 | 1.15 |
time (sec) |
N/A | 0.188 | 0.002 | 0.078 | 0.033 | 0.125 | 0.057 | 0.115 | 0.170 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F(-2) | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 26 | 25 | 44 | 44 | 44 | 0 | 104 | 108 |
N.S. |
1 | 0.00 | 1.04 | 1.00 | 1.76 | 1.76 | 1.76 | 0.00 | 4.16 | 4.32 |
time (sec) |
N/A | 0.000 | 2.170 | 29.931 | 0.175 | 0.089 | 0.466 | 0.000 | 200.019 | 2.898 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 36 | 24 | 22 | 35 | 21 | 19 | 38 | 23 | 21 |
N.S. |
1 | 1.80 | 1.20 | 1.10 | 1.75 | 1.05 | 0.95 | 1.90 | 1.15 | 1.05 |
time (sec) |
N/A | 0.270 | 0.104 | 0.176 | 0.071 | 0.111 | 0.058 | 0.110 | 0.207 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 71 | 32 | 35 | 50 | 30 | 42 | 30 | 45 | 40 |
N.S. |
1 | 2.73 | 1.23 | 1.35 | 1.92 | 1.15 | 1.62 | 1.15 | 1.73 | 1.54 |
time (sec) |
N/A | 0.918 | 1.460 | 0.751 | 0.088 | 0.095 | 0.222 | 0.130 | 0.209 | 2.802 |
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 | 17 | 17 | 17 | 16 | 16 | 15 | 16 | 18 | 16 |
N.S. |
1 | 0.81 | 0.81 | 0.81 | 0.76 | 0.76 | 0.71 | 0.76 | 0.86 | 0.76 |
time (sec) |
N/A | 0.192 | 0.009 | 0.158 | 0.098 | 0.095 | 0.080 | 0.112 | 0.213 | 2.753 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | F | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 57 | 59 | 53 | 52 | 58 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 2.04 | 2.11 | 1.89 | 1.86 | 2.07 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.155 | 2.754 | 0.469 | 0.102 | 0.302 | 0.000 | 0.378 | 0.000 |
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 | 20 | 24 | 20 | 18 | 24 | 17 | 20 | 58 | 18 | 17 |
N.S. |
1 | 1.20 | 1.00 | 0.90 | 1.20 | 0.85 | 1.00 | 2.90 | 0.90 | 0.85 |
time (sec) |
N/A | 0.734 | 0.389 | 107.470 | 0.179 | 0.119 | 0.128 | 0.150 | 0.207 | 4.291 |
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 | 16 | 34 | 15 | 33 | 35 | 35 | 27 | 35 | 35 | 15 |
N.S. |
1 | 2.12 | 0.94 | 2.06 | 2.19 | 2.19 | 1.69 | 2.19 | 2.19 | 0.94 |
time (sec) |
N/A | 0.176 | 0.006 | 0.261 | 0.024 | 0.088 | 0.021 | 0.111 | 0.204 | 2.757 |
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 | 22 | 0 | 23 | 21 | 24 | 24 | 20 | 0 | 28 | 23 |
N.S. |
1 | 0.00 | 1.05 | 0.95 | 1.09 | 1.09 | 0.91 | 0.00 | 1.27 | 1.05 |
time (sec) |
N/A | 0.000 | 0.752 | 3.243 | 0.077 | 0.132 | 0.230 | 0.000 | 0.208 | 2.904 |
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 | 19 | 0 | 17 | 19 | 27 | 27 | 17 | 27 | 29 | 0 |
N.S. |
1 | 0.00 | 0.89 | 1.00 | 1.42 | 1.42 | 0.89 | 1.42 | 1.53 | 0.00 |
time (sec) |
N/A | 0.000 | 0.144 | 0.322 | 0.151 | 0.152 | 0.079 | 0.178 | 0.210 | 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 | 35 | 27 | 35 | 34 | 34 | 37 | 34 | 37 | 36 |
N.S. |
1 | 1.84 | 1.42 | 1.84 | 1.79 | 1.79 | 1.95 | 1.79 | 1.95 | 1.89 |
time (sec) |
N/A | 0.226 | 0.010 | 0.278 | 0.107 | 0.109 | 0.056 | 0.115 | 0.209 | 2.702 |
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 | 12 | 11 | 11 | 15 | 10 | 8 | 10 | 12 | 10 |
N.S. |
1 | 0.63 | 0.58 | 0.58 | 0.79 | 0.53 | 0.42 | 0.53 | 0.63 | 0.53 |
time (sec) |
N/A | 0.178 | 0.001 | 0.107 | 0.039 | 0.096 | 0.046 | 0.117 | 0.206 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 23 | 25 | 19 | 21 | 22 | 20 | 22 | 343 | 18 |
N.S. |
1 | 1.10 | 1.19 | 0.90 | 1.00 | 1.05 | 0.95 | 1.05 | 16.33 | 0.86 |
time (sec) |
N/A | 0.605 | 0.269 | 0.398 | 0.146 | 0.103 | 0.187 | 0.131 | 0.209 | 0.329 |
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 | 15 | 28 | 28 | 25 | 34 | 22 | 24 | 28 | 24 | 22 |
N.S. |
1 | 1.87 | 1.87 | 1.67 | 2.27 | 1.47 | 1.60 | 1.87 | 1.60 | 1.47 |
time (sec) |
N/A | 0.352 | 0.004 | 0.302 | 0.031 | 0.103 | 0.076 | 0.115 | 0.197 | 2.700 |
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 | 26 | 17 | 14 | 13 | 20 | 12 | 13 | 21 | 14 |
N.S. |
1 | 1.44 | 0.94 | 0.78 | 0.72 | 1.11 | 0.67 | 0.72 | 1.17 | 0.78 |
time (sec) |
N/A | 1.025 | 0.029 | 0.329 | 0.026 | 0.147 | 0.070 | 0.123 | 0.206 | 2.716 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | A | A | F | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 0 | 23 | 94 | 40 | 22 | 0 | 43 | 24 |
N.S. |
1 | 0.00 | 0.00 | 0.68 | 2.76 | 1.18 | 0.65 | 0.00 | 1.26 | 0.71 |
time (sec) |
N/A | 0.000 | 0.000 | 5.204 | 0.191 | 0.101 | 0.241 | 0.000 | 0.221 | 2.960 |
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 | 35 | 16 | 18 | 16 | 28 | 24 | 23 | 20 | 15 |
N.S. |
1 | 1.84 | 0.84 | 0.95 | 0.84 | 1.47 | 1.26 | 1.21 | 1.05 | 0.79 |
time (sec) |
N/A | 0.505 | 0.018 | 0.533 | 0.181 | 0.122 | 0.135 | 0.119 | 0.215 | 2.864 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 74 | 73 | 73 | 76 | 75 | 69 | 73 |
N.S. |
1 | 1.00 | 1.00 | 4.35 | 4.29 | 4.29 | 4.47 | 4.41 | 4.06 | 4.29 |
time (sec) |
N/A | 0.617 | 0.020 | 18.201 | 0.097 | 0.147 | 0.580 | 0.155 | 0.203 | 2.986 |
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 | 27 | 0 | 38 | 32 | 51 | 38 | 39 | 63 | 49 | 68 |
N.S. |
1 | 0.00 | 1.41 | 1.19 | 1.89 | 1.41 | 1.44 | 2.33 | 1.81 | 2.52 |
time (sec) |
N/A | 0.000 | 5.075 | 2.413 | 0.181 | 0.108 | 36.442 | 0.142 | 0.369 | 2.879 |
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 | 15 | 15 | 15 | 13 | 0 | 13 | 14 | 12 | 17 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.00 | 0.87 | 0.93 | 0.80 | 1.13 | 0.87 |
time (sec) |
N/A | 0.173 | 0.009 | 0.399 | 0.000 | 0.116 | 0.075 | 0.114 | 0.189 | 0.034 |
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 | 21 | 30 | 19 | 21 | 45 | 21 | 14 | 21 | 33 | 20 |
N.S. |
1 | 1.43 | 0.90 | 1.00 | 2.14 | 1.00 | 0.67 | 1.00 | 1.57 | 0.95 |
time (sec) |
N/A | 0.203 | 0.050 | 0.186 | 0.032 | 0.095 | 0.063 | 0.108 | 0.201 | 0.044 |
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 | 15 | 33 | 22 | 22 | 21 | 21 | 26 | 24 | 31 | 21 |
N.S. |
1 | 2.20 | 1.47 | 1.47 | 1.40 | 1.40 | 1.73 | 1.60 | 2.07 | 1.40 |
time (sec) |
N/A | 0.257 | 0.006 | 0.109 | 0.026 | 0.128 | 0.153 | 0.107 | 0.207 | 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 | 20 | 20 | 23 | 20 | 21 | 21 | 19 | 21 | 21 | 22 |
N.S. |
1 | 1.00 | 1.15 | 1.00 | 1.05 | 1.05 | 0.95 | 1.05 | 1.05 | 1.10 |
time (sec) |
N/A | 0.139 | 0.000 | 0.130 | 0.028 | 0.102 | 0.030 | 0.112 | 0.221 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | B | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 48 | 50 | 55 | 49 | 53 | 69 | 703 | 49 |
N.S. |
1 | 0.00 | 1.85 | 1.92 | 2.12 | 1.88 | 2.04 | 2.65 | 27.04 | 1.88 |
time (sec) |
N/A | 0.000 | 0.068 | 1.473 | 0.167 | 0.102 | 0.707 | 0.223 | 0.265 | 2.832 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | C | B | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 28 | 145 | 215 | 88 | 39 | 31752 | 92 | 27 |
N.S. |
1 | 0.00 | 1.00 | 5.18 | 7.68 | 3.14 | 1.39 | 1134.00 | 3.29 | 0.96 |
time (sec) |
N/A | 0.000 | 0.112 | 67.808 | 0.387 | 0.102 | 0.390 | 15.848 | 0.223 | 3.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | A | A | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 33 | 154 | 41 | 41 | 36 | 39 | 34 | 0 |
N.S. |
1 | 0.00 | 1.27 | 5.92 | 1.58 | 1.58 | 1.38 | 1.50 | 1.31 | 0.00 |
time (sec) |
N/A | 0.000 | 0.050 | 72.529 | 0.095 | 0.143 | 0.200 | 0.204 | 0.200 | 0.000 |
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 | 20 | 26 | 21 | 25 | 24 | 24 | 20 | 0 | 20 | 18 |
N.S. |
1 | 1.30 | 1.05 | 1.25 | 1.20 | 1.20 | 1.00 | 0.00 | 1.00 | 0.90 |
time (sec) |
N/A | 0.176 | 0.023 | 0.187 | 0.027 | 0.145 | 0.087 | 0.000 | 0.215 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | C | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 98 | 32 | 174 | 728 | 137 | 240 | 180 | 188 | 216 |
N.S. |
1 | 3.27 | 1.07 | 5.80 | 24.27 | 4.57 | 8.00 | 6.00 | 6.27 | 7.20 |
time (sec) |
N/A | 0.593 | 0.060 | 395.451 | 0.169 | 0.106 | 0.463 | 0.137 | 0.241 | 3.524 |
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 | 23 | 27 | 19 | 21 | 25 | 17 | 21 | 19 | 21 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 0.91 | 1.09 | 0.74 | 0.91 | 0.83 | 0.91 |
time (sec) |
N/A | 0.241 | 0.007 | 0.321 | 0.026 | 0.073 | 0.031 | 0.109 | 0.231 | 0.028 |
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 | 13 | 13 | 13 | 12 | 12 | 10 | 14 | 13 | 12 |
N.S. |
1 | 0.48 | 0.48 | 0.48 | 0.44 | 0.44 | 0.37 | 0.52 | 0.48 | 0.44 |
time (sec) |
N/A | 0.162 | 0.003 | 0.221 | 0.025 | 0.115 | 0.093 | 0.113 | 0.225 | 0.051 |