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 | 21 | 16 | 16 | 16 | 15 | 15 | 14 | 17 | 16 | 13 |
N.S. |
1 | 0.76 | 0.76 | 0.76 | 0.71 | 0.71 | 0.67 | 0.81 | 0.76 | 0.62 |
time (sec) |
N/A | 0.239 | 0.005 | 0.156 | 0.031 | 0.099 | 0.060 | 0.105 | 0.156 | 0.060 |
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 | 21 | 0 | 20 | 20 | 127 | 32 | 56 | 61 | 33 | 33 |
N.S. |
1 | 0.00 | 0.95 | 0.95 | 6.05 | 1.52 | 2.67 | 2.90 | 1.57 | 1.57 |
time (sec) |
N/A | 0.000 | 0.649 | 0.394 | 0.164 | 0.094 | 0.078 | 0.112 | 0.160 | 0.119 |
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 | 19 | 0 | 22 | 22 | 33 | 23 | 22 | 46 | 22 | 46 |
N.S. |
1 | 0.00 | 1.16 | 1.16 | 1.74 | 1.21 | 1.16 | 2.42 | 1.16 | 2.42 |
time (sec) |
N/A | 0.000 | 0.088 | 0.663 | 0.155 | 0.134 | 0.145 | 0.128 | 0.154 | 4.447 |
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 | 28 | 0 | 31 | 37 | 36 | 52 | 29 | 65 | 67 | 78 |
N.S. |
1 | 0.00 | 1.11 | 1.32 | 1.29 | 1.86 | 1.04 | 2.32 | 2.39 | 2.79 |
time (sec) |
N/A | 0.000 | 0.058 | 8.192 | 0.107 | 0.125 | 0.146 | 0.127 | 0.156 | 3.585 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 19 | 17 | 16 | 50 | 15 | 17 | 37 | 15 | 0 |
N.S. |
1 | 0.90 | 0.81 | 0.76 | 2.38 | 0.71 | 0.81 | 1.76 | 0.71 | 0.00 |
time (sec) |
N/A | 0.886 | 0.117 | 180.236 | 0.115 | 0.090 | 2.168 | 0.113 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 98 | 346 | 63 | 103 | 79 | 102 | 82 | 54 | 0 |
N.S. |
1 | 2.97 | 10.48 | 1.91 | 3.12 | 2.39 | 3.09 | 2.48 | 1.64 | 0.00 |
time (sec) |
N/A | 0.630 | 0.147 | 0.369 | 0.035 | 0.102 | 2.366 | 0.113 | 0.154 | 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 | 10 | 10 | 10 | 10 | 11 | 12 | 5 | 12 | 13 | 9 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 1.10 | 1.20 | 0.50 | 1.20 | 1.30 | 0.90 |
time (sec) |
N/A | 0.185 | 0.005 | 0.135 | 0.052 | 0.095 | 0.035 | 0.108 | 0.164 | 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 | 32 | 32 | 26 | 24 | 25 | 25 | 20 | 26 | 29 | 23 |
N.S. |
1 | 1.00 | 0.81 | 0.75 | 0.78 | 0.78 | 0.62 | 0.81 | 0.91 | 0.72 |
time (sec) |
N/A | 0.363 | 0.070 | 0.175 | 0.027 | 0.088 | 0.061 | 0.105 | 0.146 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | B | B | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 46 | 106 | 126 | 66 | 32 | 91 | 66 | 54 |
N.S. |
1 | 0.00 | 1.64 | 3.79 | 4.50 | 2.36 | 1.14 | 3.25 | 2.36 | 1.93 |
time (sec) |
N/A | 0.000 | 0.225 | 0.030 | 0.183 | 0.090 | 0.119 | 0.531 | 0.155 | 3.795 |
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 | 31 | 62 | 82 | 76 | 83 | 71 | 65 | 73 |
N.S. |
1 | 0.00 | 1.24 | 2.48 | 3.28 | 3.04 | 3.32 | 2.84 | 2.60 | 2.92 |
time (sec) |
N/A | 0.000 | 0.073 | 1.204 | 0.170 | 0.145 | 0.111 | 0.180 | 0.151 | 3.565 |
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 | 22 | 0 | 33 | 36 | 109 | 35 | 27 | 69 | 31 | 57 |
N.S. |
1 | 0.00 | 1.50 | 1.64 | 4.95 | 1.59 | 1.23 | 3.14 | 1.41 | 2.59 |
time (sec) |
N/A | 0.000 | 0.158 | 1.905 | 0.289 | 0.110 | 0.258 | 0.412 | 0.166 | 3.456 |
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 | 37 | 26 | 42 | 25 | 24 | 25 | 38 | 25 |
N.S. |
1 | 0.00 | 1.42 | 1.00 | 1.62 | 0.96 | 0.92 | 0.96 | 1.46 | 0.96 |
time (sec) |
N/A | 0.000 | 0.227 | 276.029 | 0.130 | 0.128 | 2.767 | 0.546 | 0.168 | 3.613 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 99 | 115 | 112 | 93 | 109 | 114 | 175 | 102 |
N.S. |
1 | 0.00 | 2.75 | 3.19 | 3.11 | 2.58 | 3.03 | 3.17 | 4.86 | 2.83 |
time (sec) |
N/A | 0.000 | 0.254 | 0.811 | 0.056 | 0.115 | 25.296 | 0.529 | 0.165 | 0.611 |
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 | 18 | 14 | 14 | 17 | 17 | 15 | 17 | 23 | 19 |
N.S. |
1 | 1.12 | 0.88 | 0.88 | 1.06 | 1.06 | 0.94 | 1.06 | 1.44 | 1.19 |
time (sec) |
N/A | 0.329 | 0.031 | 0.095 | 0.026 | 0.090 | 0.045 | 0.111 | 0.204 | 3.253 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | F(-1) | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 152 | 33 | 42 | 70 | 41 | 0 | 41 | 1518 | 42 |
N.S. |
1 | 5.24 | 1.14 | 1.45 | 2.41 | 1.41 | 0.00 | 1.41 | 52.34 | 1.45 |
time (sec) |
N/A | 0.678 | 0.081 | 100.704 | 26.558 | 0.119 | 0.000 | 0.443 | 0.927 | 3.511 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 26 | 31 | 31 | 33 | 0 | 23 | 39 | 32 |
N.S. |
1 | 0.00 | 1.04 | 1.24 | 1.24 | 1.32 | 0.00 | 0.92 | 1.56 | 1.28 |
time (sec) |
N/A | 0.000 | 0.099 | 2.966 | 0.154 | 0.108 | 0.000 | 0.118 | 0.166 | 3.424 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | F | A | A | A | F | F | B |
verified | N/A | N/A | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 123 | 0 | 24 | 24 | 24 | 0 | 139 | 26 |
N.S. |
1 | 0.00 | 5.35 | 0.00 | 1.04 | 1.04 | 1.04 | 0.00 | 6.04 | 1.13 |
time (sec) |
N/A | 0.000 | 0.246 | 0.000 | 0.191 | 0.086 | 0.829 | 0.000 | 200.015 | 3.613 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | B | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 0 | 19 | 21 | 21 | 17 | 44 | 18 | 20 |
N.S. |
1 | 0.00 | 0.00 | 0.95 | 1.05 | 1.05 | 0.85 | 2.20 | 0.90 | 1.00 |
time (sec) |
N/A | 0.000 | 0.000 | 6.930 | 0.139 | 0.115 | 0.168 | 0.120 | 0.173 | 3.609 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 50 | 23 | 23 | 0 | 27 | 22 | 32 | 22 | 21 |
N.S. |
1 | 1.85 | 0.85 | 0.85 | 0.00 | 1.00 | 0.81 | 1.19 | 0.81 | 0.78 |
time (sec) |
N/A | 1.176 | 0.111 | 1.712 | 0.000 | 0.102 | 0.162 | 0.152 | 0.185 | 3.582 |
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 | 25 | 23 | 30 | 32 | 39 | 32 | 27 | 45 | 28 |
N.S. |
1 | 1.00 | 0.92 | 1.20 | 1.28 | 1.56 | 1.28 | 1.08 | 1.80 | 1.12 |
time (sec) |
N/A | 0.302 | 0.011 | 0.208 | 0.030 | 0.087 | 0.155 | 0.113 | 0.173 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F(-2) | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 31 | 27 | 0 | 26 | 26 | 0 | 30 | 26 |
N.S. |
1 | 0.00 | 0.94 | 0.82 | 0.00 | 0.79 | 0.79 | 0.00 | 0.91 | 0.79 |
time (sec) |
N/A | 0.000 | 0.070 | 0.101 | 0.000 | 0.116 | 0.581 | 0.000 | 0.170 | 3.574 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | B | B | B | B | B | B |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 43 | 1812 | 185 | 85 | 133 | 149 | 110 | 39 |
N.S. |
1 | 0.00 | 1.39 | 58.45 | 5.97 | 2.74 | 4.29 | 4.81 | 3.55 | 1.26 |
time (sec) |
N/A | 0.000 | 0.113 | 0.214 | 0.201 | 0.118 | 0.312 | 0.260 | 0.196 | 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 | 27 | 31 | 29 | 26 | 26 | 30 | 24 | 25 | 30 | 24 |
N.S. |
1 | 1.15 | 1.07 | 0.96 | 0.96 | 1.11 | 0.89 | 0.93 | 1.11 | 0.89 |
time (sec) |
N/A | 0.217 | 0.009 | 0.132 | 0.031 | 0.104 | 0.053 | 0.116 | 0.177 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | A | A | A | A | A | B | B |
verified | N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 29 | 0 | 26 | 25 | 34 | 26 | 32 | 29 | 25 |
N.S. |
1 | 0.97 | 0.00 | 0.87 | 0.83 | 1.13 | 0.87 | 1.07 | 0.97 | 0.83 |
time (sec) |
N/A | 0.308 | 0.000 | 0.266 | 0.030 | 0.093 | 0.126 | 0.114 | 0.176 | 3.410 |
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 | 21 | 21 | 21 | 18 | 49 | 17 | 15 | 17 | 23 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 2.33 | 0.81 | 0.71 | 0.81 | 1.10 | 0.90 |
time (sec) |
N/A | 0.216 | 0.169 | 0.077 | 0.062 | 0.095 | 0.047 | 0.109 | 0.161 | 3.255 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 101 | 19960 | 157 | 136 | 115 | 139 | 120 | 156 | 0 |
N.S. |
1 | 4.59 | 907.27 | 7.14 | 6.18 | 5.23 | 6.32 | 5.45 | 7.09 | 0.00 |
time (sec) |
N/A | 1.405 | 30.614 | 1.724 | 0.048 | 0.119 | 11.744 | 0.291 | 0.176 | 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 | 24 | 40 | 22 | 27 | 44 | 26 | 27 | 35 | 27 | 19 |
N.S. |
1 | 1.67 | 0.92 | 1.12 | 1.83 | 1.08 | 1.12 | 1.46 | 1.12 | 0.79 |
time (sec) |
N/A | 0.262 | 0.173 | 0.212 | 0.065 | 0.122 | 0.069 | 0.110 | 0.160 | 0.044 |
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 | 21 | 90 | 99 | 97 | 99 | 127 | 95 | 104 | 180 | 124 |
N.S. |
1 | 4.29 | 4.71 | 4.62 | 4.71 | 6.05 | 4.52 | 4.95 | 8.57 | 5.90 |
time (sec) |
N/A | 0.541 | 0.101 | 0.437 | 0.035 | 0.090 | 0.420 | 0.111 | 0.161 | 0.213 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | F | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 34 | 28 | 34 | 574 | 29 | 24 | 0 | 96 | 0 |
N.S. |
1 | 1.17 | 0.97 | 1.17 | 19.79 | 1.00 | 0.83 | 0.00 | 3.31 | 0.00 |
time (sec) |
N/A | 0.692 | 0.066 | 3.290 | 0.334 | 0.106 | 0.243 | 0.000 | 64.950 | 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 | 27 | 1216 | 40 | 535 | 1389 | 123 | 141 | 614 | 235 | 39 |
N.S. |
1 | 45.04 | 1.48 | 19.81 | 51.44 | 4.56 | 5.22 | 22.74 | 8.70 | 1.44 |
time (sec) |
N/A | 6.144 | 0.057 | 0.022 | 0.079 | 0.115 | 0.176 | 0.142 | 0.177 | 3.736 |
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 | 34 | 69 | 33 | 34 | 41 | 37 | 36 | 37 | 93 | 43 |
N.S. |
1 | 2.03 | 0.97 | 1.00 | 1.21 | 1.09 | 1.06 | 1.09 | 2.74 | 1.26 |
time (sec) |
N/A | 1.257 | 0.662 | 0.566 | 0.170 | 0.102 | 0.103 | 0.123 | 1.477 | 3.667 |
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 | 22 | 21 | 21 | 22 | 21 | 22 | 21 |
N.S. |
1 | 0.92 | 0.92 | 0.92 | 0.88 | 0.88 | 0.92 | 0.88 | 0.92 | 0.88 |
time (sec) |
N/A | 0.190 | 0.005 | 0.146 | 0.026 | 0.088 | 0.071 | 0.104 | 0.163 | 3.418 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | F | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 23 | 29 | 84 | 85 | 78 | 0 | 76 | 0 |
N.S. |
1 | 0.00 | 0.82 | 1.04 | 3.00 | 3.04 | 2.79 | 0.00 | 2.71 | 0.00 |
time (sec) |
N/A | 0.000 | 0.047 | 4.736 | 0.137 | 0.100 | 0.162 | 0.000 | 0.164 | 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 | 28 | 29 | 25 | 25 | 25 | 37 | 25 | 30 | 25 |
N.S. |
1 | 1.08 | 1.12 | 0.96 | 0.96 | 0.96 | 1.42 | 0.96 | 1.15 | 0.96 |
time (sec) |
N/A | 0.730 | 0.065 | 0.177 | 0.025 | 0.116 | 0.073 | 0.117 | 0.187 | 3.595 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 15 | 15 | 14 | 13 | 13 | 12 | 13 | 98 | 13 |
N.S. |
1 | 0.88 | 0.88 | 0.82 | 0.76 | 0.76 | 0.71 | 0.76 | 5.76 | 0.76 |
time (sec) |
N/A | 0.677 | 0.030 | 0.350 | 0.070 | 0.084 | 0.046 | 0.116 | 0.179 | 3.645 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | F | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 91 | 196 | 0 | 145 | 233 | 294 | 280 | 233 |
N.S. |
1 | 0.00 | 2.84 | 6.12 | 0.00 | 4.53 | 7.28 | 9.19 | 8.75 | 7.28 |
time (sec) |
N/A | 0.000 | 0.095 | 0.044 | 0.000 | 0.112 | 0.246 | 0.186 | 0.197 | 4.354 |
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 | 18 | 42 | 27 | 26 | 44 | 25 | 27 | 25 | 24 | 25 |
N.S. |
1 | 2.33 | 1.50 | 1.44 | 2.44 | 1.39 | 1.50 | 1.39 | 1.33 | 1.39 |
time (sec) |
N/A | 0.215 | 0.008 | 0.300 | 0.029 | 0.096 | 0.058 | 0.108 | 0.171 | 3.668 |
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 | 12 | 31 | 22 | 13 | 54 | 12 | 12 | 12 | 28 | 10 |
N.S. |
1 | 2.58 | 1.83 | 1.08 | 4.50 | 1.00 | 1.00 | 1.00 | 2.33 | 0.83 |
time (sec) |
N/A | 0.267 | 0.023 | 0.208 | 0.106 | 0.096 | 0.048 | 0.112 | 0.158 | 0.069 |
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 | 20 | 0 | 15 | 19 | 14 | 23 | 17 | 0 | 22 | 16 |
N.S. |
1 | 0.00 | 0.75 | 0.95 | 0.70 | 1.15 | 0.85 | 0.00 | 1.10 | 0.80 |
time (sec) |
N/A | 0.000 | 0.087 | 0.183 | 0.094 | 0.097 | 0.105 | 0.000 | 0.178 | 3.708 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 63 | 95 | 94 | 63 | 70 | 63 | 94 | 67 |
N.S. |
1 | 0.00 | 2.74 | 4.13 | 4.09 | 2.74 | 3.04 | 2.74 | 4.09 | 2.91 |
time (sec) |
N/A | 0.000 | 0.063 | 1.193 | 0.082 | 0.097 | 0.218 | 0.200 | 0.169 | 3.817 |
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 | 42 | 37 | 37 | 46 | 36 | 34 | 38 | 41 | 36 |
N.S. |
1 | 1.50 | 1.32 | 1.32 | 1.64 | 1.29 | 1.21 | 1.36 | 1.46 | 1.29 |
time (sec) |
N/A | 0.336 | 0.604 | 0.366 | 0.056 | 0.081 | 0.067 | 0.109 | 0.168 | 3.661 |
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 | 16 | 16 | 16 | 12 | 15 | 12 | 13 | 11 | 15 |
N.S. |
1 | 0.89 | 0.89 | 0.89 | 0.67 | 0.83 | 0.67 | 0.72 | 0.61 | 0.83 |
time (sec) |
N/A | 0.191 | 0.005 | 0.138 | 0.024 | 0.094 | 0.048 | 0.110 | 0.164 | 3.661 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 33 | 46 | 91 | 39 | 0 | 50 | 119 | 121 |
N.S. |
1 | 1.00 | 0.94 | 1.31 | 2.60 | 1.11 | 0.00 | 1.43 | 3.40 | 3.46 |
time (sec) |
N/A | 0.577 | 0.492 | 0.581 | 0.076 | 0.106 | 0.000 | 0.111 | 0.168 | 3.978 |
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 | 36 | 36 | 25 | 50 | 25 | 22 | 25 | 24 | 24 |
N.S. |
1 | 1.80 | 1.80 | 1.25 | 2.50 | 1.25 | 1.10 | 1.25 | 1.20 | 1.20 |
time (sec) |
N/A | 0.472 | 0.051 | 0.217 | 0.064 | 0.081 | 0.041 | 0.112 | 0.163 | 3.547 |
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 | 16 | 19 | 15 | 15 | 15 | 15 | 21 | 15 |
N.S. |
1 | 0.00 | 0.94 | 1.12 | 0.88 | 0.88 | 0.88 | 0.88 | 1.24 | 0.88 |
time (sec) |
N/A | 0.000 | 0.166 | 0.192 | 0.061 | 0.104 | 0.062 | 0.116 | 0.164 | 3.732 |
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 | 10 | 10 | 10 | 9 | 9 | 8 | 9 | 10 | 9 |
N.S. |
1 | 0.53 | 0.53 | 0.53 | 0.47 | 0.47 | 0.42 | 0.47 | 0.53 | 0.47 |
time (sec) |
N/A | 0.210 | 0.021 | 0.065 | 0.029 | 0.104 | 0.037 | 0.117 | 0.156 | 3.651 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | F(-1) | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 21 | 35 | 0 | 32 | 0 | 64 | 32 | 55 |
N.S. |
1 | 0.00 | 0.78 | 1.30 | 0.00 | 1.19 | 0.00 | 2.37 | 1.19 | 2.04 |
time (sec) |
N/A | 0.000 | 0.364 | 0.280 | 0.000 | 0.102 | 0.000 | 0.114 | 0.173 | 4.031 |
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 | 23 | 23 | 24 | 23 | 31 | 22 | 19 | 27 | 19 | 18 |
N.S. |
1 | 1.00 | 1.04 | 1.00 | 1.35 | 0.96 | 0.83 | 1.17 | 0.83 | 0.78 |
time (sec) |
N/A | 0.214 | 0.007 | 0.337 | 0.053 | 0.093 | 0.062 | 0.122 | 0.158 | 3.605 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 36 | 28 | 30 | 29 | 33 | 39 | 29 | 40 | 29 |
N.S. |
1 | 1.64 | 1.27 | 1.36 | 1.32 | 1.50 | 1.77 | 1.32 | 1.82 | 1.32 |
time (sec) |
N/A | 0.813 | 0.082 | 0.157 | 0.029 | 0.100 | 0.157 | 0.106 | 0.163 | 3.585 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 64 | 51 | 45 | 78 | 44 | 49 | 44 | 59 | 87 |
N.S. |
1 | 2.56 | 2.04 | 1.80 | 3.12 | 1.76 | 1.96 | 1.76 | 2.36 | 3.48 |
time (sec) |
N/A | 1.423 | 0.104 | 0.569 | 0.321 | 0.088 | 0.195 | 0.259 | 0.166 | 3.836 |
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 | 13 | 13 | 12 | 11 | 23 | 8 | 16 | 13 | 11 |
N.S. |
1 | 0.57 | 0.57 | 0.52 | 0.48 | 1.00 | 0.35 | 0.70 | 0.57 | 0.48 |
time (sec) |
N/A | 0.164 | 0.016 | 0.144 | 0.030 | 0.085 | 0.042 | 0.106 | 0.168 | 3.680 |
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 | 32 | 0 | 30 | 35 | 24 | 55 | 31 | 0 | 40 | 24 |
N.S. |
1 | 0.00 | 0.94 | 1.09 | 0.75 | 1.72 | 0.97 | 0.00 | 1.25 | 0.75 |
time (sec) |
N/A | 0.000 | 5.084 | 1.071 | 0.186 | 0.107 | 0.300 | 0.000 | 0.178 | 3.875 |
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 | 6 | 6 | 6 | 6 | 5 | 5 | 5 | 5 | 6 | 5 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.83 | 0.83 | 0.83 | 0.83 | 1.00 | 0.83 |
time (sec) |
N/A | 0.178 | 0.000 | 0.036 | 0.026 | 0.065 | 0.036 | 0.116 | 0.175 | 0.001 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | F(-1) | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 37 | 33 | 34 | 119 | 0 | 0 | 37 | 36 |
N.S. |
1 | 0.00 | 1.32 | 1.18 | 1.21 | 4.25 | 0.00 | 0.00 | 1.32 | 1.29 |
time (sec) |
N/A | 0.000 | 0.167 | 229.395 | 0.240 | 0.092 | 0.000 | 0.000 | 0.932 | 3.942 |
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 | 13 | 14 | 17 | 17 | 12 | 17 | 16 | 14 |
N.S. |
1 | 1.08 | 1.00 | 1.08 | 1.31 | 1.31 | 0.92 | 1.31 | 1.23 | 1.08 |
time (sec) |
N/A | 0.136 | 0.001 | 0.075 | 0.026 | 0.096 | 0.017 | 0.110 | 0.168 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 0 | 67 | 63 | 142 | 142 | 119 | 176 | 186 | 0 |
N.S. |
1 | 0.00 | 1.81 | 1.70 | 3.84 | 3.84 | 3.22 | 4.76 | 5.03 | 0.00 |
time (sec) |
N/A | 0.000 | 6.310 | 2.179 | 0.181 | 0.119 | 0.212 | 0.168 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 29 | 12 | 14 | 120 | 15 | 12 | 15 | 24 | 13 |
N.S. |
1 | 2.23 | 0.92 | 1.08 | 9.23 | 1.15 | 0.92 | 1.15 | 1.85 | 1.00 |
time (sec) |
N/A | 0.179 | 0.040 | 0.117 | 0.076 | 0.096 | 0.044 | 0.106 | 0.164 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-2) | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 27 | 19 | 21 | 22 | 21 | 0 | 16 | 43 | 15 |
N.S. |
1 | 1.42 | 1.00 | 1.11 | 1.16 | 1.11 | 0.00 | 0.84 | 2.26 | 0.79 |
time (sec) |
N/A | 0.621 | 0.034 | 0.627 | 0.171 | 0.102 | 0.000 | 0.114 | 63.621 | 3.723 |
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 | 15 | 16 | 15 | 15 | 14 | 15 | 15 | 15 |
N.S. |
1 | 0.00 | 0.83 | 0.89 | 0.83 | 0.83 | 0.78 | 0.83 | 0.83 | 0.83 |
time (sec) |
N/A | 0.000 | 0.101 | 0.713 | 0.061 | 0.100 | 0.145 | 0.123 | 0.160 | 4.168 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 482 | 19 | 19 | 18 | 18 | 14 | 18 | 19 | 18 |
N.S. |
1 | 21.91 | 0.86 | 0.86 | 0.82 | 0.82 | 0.64 | 0.82 | 0.86 | 0.82 |
time (sec) |
N/A | 1.214 | 0.381 | 0.136 | 0.069 | 0.080 | 0.053 | 0.112 | 0.156 | 0.136 |
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 | 25 | 25 | 24 | 39 | 19 | 39 | 46 | 24 |
N.S. |
1 | 0.00 | 0.96 | 0.96 | 0.92 | 1.50 | 0.73 | 1.50 | 1.77 | 0.92 |
time (sec) |
N/A | 0.000 | 1.301 | 0.253 | 0.059 | 0.096 | 0.054 | 0.122 | 0.160 | 0.103 |
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 | 36 | 23 | 22 | 27 | 25 | 24 | 25 | 22 | 24 |
N.S. |
1 | 1.64 | 1.05 | 1.00 | 1.23 | 1.14 | 1.09 | 1.14 | 1.00 | 1.09 |
time (sec) |
N/A | 0.334 | 0.014 | 0.131 | 0.026 | 0.086 | 0.273 | 0.104 | 0.157 | 3.811 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 441 | 112 | 103 | 71 | 192 | 146 | 114 | 49 | 0 |
N.S. |
1 | 17.64 | 4.48 | 4.12 | 2.84 | 7.68 | 5.84 | 4.56 | 1.96 | 0.00 |
time (sec) |
N/A | 0.972 | 0.187 | 12.637 | 0.111 | 0.094 | 0.163 | 0.143 | 0.160 | 0.000 |
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 | 29 | 0 | 30 | 23 | 28 | 82 | 22 | 0 | 35 | 31 |
N.S. |
1 | 0.00 | 1.03 | 0.79 | 0.97 | 2.83 | 0.76 | 0.00 | 1.21 | 1.07 |
time (sec) |
N/A | 0.000 | 2.036 | 0.296 | 0.331 | 0.102 | 0.348 | 0.000 | 1.688 | 3.650 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 20 | 20 | 21 | 22 | 22 | 22 | 19 | 115 | 20 |
N.S. |
1 | 0.77 | 0.77 | 0.81 | 0.85 | 0.85 | 0.85 | 0.73 | 4.42 | 0.77 |
time (sec) |
N/A | 0.337 | 0.242 | 0.137 | 0.025 | 0.112 | 0.086 | 0.158 | 0.401 | 3.528 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | F | B | B | A | B | F(-1) |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 0 | 42 | 0 | 57 | 53 | 50 | 76 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.40 | 0.00 | 1.90 | 1.77 | 1.67 | 2.53 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 2.171 | 0.000 | 0.099 | 1.616 | 0.814 | 0.163 | 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 | 30 | 59 | 45 | 23 | 50 | 25 | 29 | 25 | 55 | 29 |
N.S. |
1 | 1.97 | 1.50 | 0.77 | 1.67 | 0.83 | 0.97 | 0.83 | 1.83 | 0.97 |
time (sec) |
N/A | 0.834 | 0.083 | 0.813 | 0.142 | 0.095 | 0.132 | 0.122 | 0.163 | 3.745 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 93 | 19 | 27 | 18 | 18 | 26 | 26 | 27 | 0 |
N.S. |
1 | 4.89 | 1.00 | 1.42 | 0.95 | 0.95 | 1.37 | 1.37 | 1.42 | 0.00 |
time (sec) |
N/A | 3.653 | 0.240 | 45.753 | 0.071 | 0.101 | 6.970 | 0.163 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-2) | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 24 | 25 | 23 | 0 | 24 | 0 | 26 | 26 | 25 |
N.S. |
1 | 1.09 | 1.14 | 1.05 | 0.00 | 1.09 | 0.00 | 1.18 | 1.18 | 1.14 |
time (sec) |
N/A | 1.199 | 0.465 | 14.978 | 0.000 | 0.091 | 0.000 | 0.118 | 0.161 | 3.864 |
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 | 16 | 46 | 16 | 19 | 51 | 29 | 39 | 38 | 19 | 16 |
N.S. |
1 | 2.88 | 1.00 | 1.19 | 3.19 | 1.81 | 2.44 | 2.38 | 1.19 | 1.00 |
time (sec) |
N/A | 0.190 | 0.008 | 0.821 | 0.028 | 0.083 | 0.311 | 0.116 | 0.159 | 3.569 |
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 | 23 | 14 | 15 | 21 | 21 | 12 | 21 | 18 | 17 |
N.S. |
1 | 1.53 | 0.93 | 1.00 | 1.40 | 1.40 | 0.80 | 1.40 | 1.20 | 1.13 |
time (sec) |
N/A | 0.141 | 0.005 | 0.089 | 0.028 | 0.081 | 0.019 | 0.108 | 0.156 | 3.678 |
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 | 29 | 0 | 32 | 37 | 36 | 32 | 32 | 0 | 89 | 111 |
N.S. |
1 | 0.00 | 1.10 | 1.28 | 1.24 | 1.10 | 1.10 | 0.00 | 3.07 | 3.83 |
time (sec) |
N/A | 0.000 | 0.057 | 0.579 | 31.721 | 0.095 | 0.162 | 0.000 | 200.016 | 0.098 |
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 | 24 | 27 | 32 | 24 | 29 | 50 | 26 | 29 | 49 | 32 |
N.S. |
1 | 1.12 | 1.33 | 1.00 | 1.21 | 2.08 | 1.08 | 1.21 | 2.04 | 1.33 |
time (sec) |
N/A | 0.323 | 0.013 | 0.086 | 0.029 | 0.085 | 0.047 | 0.111 | 0.176 | 0.043 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | F | A | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 43 | 20 | 75 | 0 | 34 | 65 | 58 | 19 | 20 |
N.S. |
1 | 2.15 | 1.00 | 3.75 | 0.00 | 1.70 | 3.25 | 2.90 | 0.95 | 1.00 |
time (sec) |
N/A | 1.036 | 0.168 | 0.075 | 0.000 | 0.096 | 0.117 | 0.119 | 0.174 | 3.910 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 16 | 14 | 14 | 12 | 26 | 14 | 37 | 14 | 13 |
N.S. |
1 | 0.67 | 0.58 | 0.58 | 0.50 | 1.08 | 0.58 | 1.54 | 0.58 | 0.54 |
time (sec) |
N/A | 0.344 | 0.043 | 0.125 | 0.129 | 0.092 | 0.072 | 0.132 | 0.191 | 3.545 |
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 | 38 | 38 | 27 | 35 | 26 | 27 | 26 | 27 | 26 |
N.S. |
1 | 1.65 | 1.65 | 1.17 | 1.52 | 1.13 | 1.17 | 1.13 | 1.17 | 1.13 |
time (sec) |
N/A | 0.221 | 0.009 | 0.264 | 0.030 | 0.091 | 0.074 | 0.109 | 0.182 | 3.603 |
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 | 16 | 18 | 22 | 22 | 19 | 22 | 16 | 15 |
N.S. |
1 | 0.00 | 0.89 | 1.00 | 1.22 | 1.22 | 1.06 | 1.22 | 0.89 | 0.83 |
time (sec) |
N/A | 0.000 | 0.183 | 0.220 | 0.065 | 0.090 | 0.061 | 0.129 | 0.185 | 3.662 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 37 | 34 | 31 | 34 | 30 | 29 | 30 | 416 | 25 |
N.S. |
1 | 1.12 | 1.03 | 0.94 | 1.03 | 0.91 | 0.88 | 0.91 | 12.61 | 0.76 |
time (sec) |
N/A | 1.478 | 0.032 | 0.852 | 0.134 | 0.105 | 0.192 | 0.157 | 0.199 | 3.983 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | F(-1) | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 28 | 93 | 487 | 630 | 195 | 201 | 0 | 483 | 132776 |
N.S. |
1 | 1.08 | 3.58 | 18.73 | 24.23 | 7.50 | 7.73 | 0.00 | 18.58 | 5106.77 |
time (sec) |
N/A | 4.569 | 0.168 | 16.160 | 0.743 | 0.117 | 2.163 | 0.000 | 0.202 | 39.057 |
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 | 15 | 11 | 11 | 12 | 27 | 11 | 14 | 27 | 12 | 11 |
N.S. |
1 | 0.73 | 0.73 | 0.80 | 1.80 | 0.73 | 0.93 | 1.80 | 0.80 | 0.73 |
time (sec) |
N/A | 0.147 | 0.003 | 0.088 | 0.030 | 0.083 | 0.045 | 0.110 | 0.188 | 3.583 |
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 | 24 | 0 | 24 | 26 | 32 | 22 | 19 | 22 | 30 | 22 |
N.S. |
1 | 0.00 | 1.00 | 1.08 | 1.33 | 0.92 | 0.79 | 0.92 | 1.25 | 0.92 |
time (sec) |
N/A | 0.000 | 0.175 | 2.495 | 0.144 | 0.089 | 0.062 | 0.101 | 0.187 | 3.601 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 31 | 29 | 26 | 36 | 0 | 127 | 34 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.94 | 0.84 | 1.16 | 0.00 | 4.10 | 1.10 | 0.00 |
time (sec) |
N/A | 0.000 | 0.121 | 223.813 | 0.140 | 0.081 | 0.000 | 0.257 | 0.187 | 0.000 |
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 | 19 | 69 | 48 | 49 | 53 | 50 | 54 | 54 | 63 | 50 |
N.S. |
1 | 3.63 | 2.53 | 2.58 | 2.79 | 2.63 | 2.84 | 2.84 | 3.32 | 2.63 |
time (sec) |
N/A | 0.272 | 0.012 | 0.174 | 0.024 | 0.072 | 0.285 | 0.109 | 0.185 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 26 | 33 | 97 | 127 | 162 | 154 | 1028 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.27 | 3.73 | 4.88 | 6.23 | 5.92 | 39.54 | 0.00 |
time (sec) |
N/A | 0.000 | 5.044 | 9.648 | 0.249 | 0.109 | 0.333 | 0.281 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | A | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 78 | 59 | 55 | 51 | 51 | 88 | 51 | 75 | 62 |
N.S. |
1 | 2.79 | 2.11 | 1.96 | 1.82 | 1.82 | 3.14 | 1.82 | 2.68 | 2.21 |
time (sec) |
N/A | 0.398 | 0.021 | 0.152 | 0.027 | 0.067 | 0.028 | 0.110 | 0.181 | 0.041 |
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 | 36 | 36 | 26 | 32 | 35 | 24 | 33 | 69 | 23 |
N.S. |
1 | 1.50 | 1.50 | 1.08 | 1.33 | 1.46 | 1.00 | 1.38 | 2.88 | 0.96 |
time (sec) |
N/A | 0.533 | 0.011 | 0.257 | 0.029 | 0.082 | 0.126 | 0.116 | 0.180 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | F | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 77 | 66 | 83 | 0 | 59 | 71 | 80 | 86 | 70 |
N.S. |
1 | 2.75 | 2.36 | 2.96 | 0.00 | 2.11 | 2.54 | 2.86 | 3.07 | 2.50 |
time (sec) |
N/A | 0.692 | 0.058 | 0.046 | 0.000 | 0.092 | 0.176 | 0.126 | 0.170 | 4.091 |
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 | 34 | 75 | 26 | 26 | 26 | 26 | 26 | 39 | 50 | 23 |
N.S. |
1 | 2.21 | 0.76 | 0.76 | 0.76 | 0.76 | 0.76 | 1.15 | 1.47 | 0.68 |
time (sec) |
N/A | 0.401 | 0.080 | 0.216 | 0.091 | 0.092 | 1.303 | 0.113 | 0.182 | 4.267 |
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 | 23 | 0 | 20 | 20 | 28 | 28 | 24 | 20 | 120 | 19 |
N.S. |
1 | 0.00 | 0.87 | 0.87 | 1.22 | 1.22 | 1.04 | 0.87 | 5.22 | 0.83 |
time (sec) |
N/A | 0.000 | 0.437 | 0.159 | 0.054 | 0.101 | 0.114 | 0.116 | 0.176 | 3.752 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 35 | 44 | 37 | 36 | 87 | 47 | 46 | 0 |
N.S. |
1 | 0.00 | 1.13 | 1.42 | 1.19 | 1.16 | 2.81 | 1.52 | 1.48 | 0.00 |
time (sec) |
N/A | 0.000 | 10.986 | 0.402 | 0.093 | 0.085 | 0.359 | 0.127 | 0.191 | 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 | 35 | 25 | 27 | 26 | 26 | 22 | 26 | 42 | 28 |
N.S. |
1 | 1.30 | 0.93 | 1.00 | 0.96 | 0.96 | 0.81 | 0.96 | 1.56 | 1.04 |
time (sec) |
N/A | 0.185 | 0.034 | 0.391 | 0.032 | 0.090 | 0.066 | 0.115 | 0.190 | 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 | 29 | 33 | 29 | 28 | 28 | 41 | 26 | 29 | 91 | 28 |
N.S. |
1 | 1.14 | 1.00 | 0.97 | 0.97 | 1.41 | 0.90 | 1.00 | 3.14 | 0.97 |
time (sec) |
N/A | 0.338 | 0.040 | 0.691 | 0.027 | 0.094 | 1.362 | 0.149 | 0.197 | 0.159 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F(-2) | B | F(-2) | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 150 | 40 | 54 | 0 | 60 | 0 | 0 | 60 | 34 |
N.S. |
1 | 4.69 | 1.25 | 1.69 | 0.00 | 1.88 | 0.00 | 0.00 | 1.88 | 1.06 |
time (sec) |
N/A | 1.098 | 0.088 | 3.930 | 0.000 | 0.100 | 0.000 | 0.000 | 0.187 | 4.318 |
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 | 23 | 26 | 25 | 76 | 69 | 72 | 70 | 85 | 75 | 104 |
N.S. |
1 | 1.13 | 1.09 | 3.30 | 3.00 | 3.13 | 3.04 | 3.70 | 3.26 | 4.52 |
time (sec) |
N/A | 0.781 | 0.075 | 4.276 | 0.105 | 0.100 | 0.148 | 0.136 | 0.187 | 0.211 |
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 | 26 | 26 | 24 | 23 | 23 | 20 | 23 | 48 | 28 |
N.S. |
1 | 1.04 | 1.04 | 0.96 | 0.92 | 0.92 | 0.80 | 0.92 | 1.92 | 1.12 |
time (sec) |
N/A | 0.369 | 1.035 | 0.196 | 0.257 | 0.122 | 0.194 | 0.129 | 0.201 | 0.096 |
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 | 22 | 25 | 21 | 24 | 29 | 23 | 28 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 1.14 | 0.95 | 1.09 | 1.32 | 1.05 | 1.27 |
time (sec) |
N/A | 0.000 | 0.500 | 0.222 | 0.089 | 0.097 | 0.098 | 0.120 | 0.165 | 4.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | F(-1) | B | B | F(-1) |
verified | N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 109 | 232 | 933 | 180 | 0 | 209 | 212 | 0 |
N.S. |
1 | 0.00 | 3.52 | 7.48 | 30.10 | 5.81 | 0.00 | 6.74 | 6.84 | 0.00 |
time (sec) |
N/A | 0.000 | 0.273 | 0.034 | 6.913 | 0.139 | 0.000 | 13.250 | 0.221 | 0.000 |
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 | 28 | 235 | 216 | 226 | 179 | 171 | 226 | 239 | 250 | 241 |
N.S. |
1 | 8.39 | 7.71 | 8.07 | 6.39 | 6.11 | 8.07 | 8.54 | 8.93 | 8.61 |
time (sec) |
N/A | 0.650 | 0.034 | 0.324 | 0.028 | 0.099 | 8.687 | 0.105 | 0.168 | 0.163 |
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 | 26 | 29 | 20 | 23 | 32 | 28 | 24 | 31 | 27 | 23 |
N.S. |
1 | 1.12 | 0.77 | 0.88 | 1.23 | 1.08 | 0.92 | 1.19 | 1.04 | 0.88 |
time (sec) |
N/A | 0.384 | 0.032 | 0.305 | 0.025 | 0.112 | 0.084 | 0.109 | 0.166 | 3.899 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-2) | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 16 | 16 | 22 | 0 | 21 | 0 | 21 | 22 | 17 |
N.S. |
1 | 0.70 | 0.70 | 0.96 | 0.00 | 0.91 | 0.00 | 0.91 | 0.96 | 0.74 |
time (sec) |
N/A | 0.956 | 0.345 | 1.058 | 0.000 | 0.095 | 0.000 | 0.261 | 0.176 | 0.458 |