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 | 22 | 27 | 27 | 20 | 21 | 23 | 20 | 21 | 27 | 21 |
N.S. |
1 | 1.23 | 1.23 | 0.91 | 0.95 | 1.05 | 0.91 | 0.95 | 1.23 | 0.95 |
time (sec) |
N/A | 0.155 | 0.004 | 0.171 | 0.034 | 0.100 | 0.059 | 0.126 | 0.175 | 0.085 |
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 | 18 | 18 | 17 | 17 | 15 | 17 | 24 | 18 |
N.S. |
1 | 0.00 | 0.75 | 0.75 | 0.71 | 0.71 | 0.62 | 0.71 | 1.00 | 0.75 |
time (sec) |
N/A | 0.000 | 0.078 | 0.287 | 0.061 | 0.081 | 0.107 | 0.113 | 0.176 | 3.003 |
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 | 27 | 0 | 29 | 29 | 27 | 26 | 27 | 0 | 42 | 29 |
N.S. |
1 | 0.00 | 1.07 | 1.07 | 1.00 | 0.96 | 1.00 | 0.00 | 1.56 | 1.07 |
time (sec) |
N/A | 0.000 | 5.080 | 0.795 | 0.142 | 0.091 | 11.515 | 0.000 | 0.176 | 3.339 |
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 | 23 | 51 | 22 | 22 | 28 | 21 | 20 | 21 | 23 | 0 |
N.S. |
1 | 2.22 | 0.96 | 0.96 | 1.22 | 0.91 | 0.87 | 0.91 | 1.00 | 0.00 |
time (sec) |
N/A | 1.833 | 0.717 | 0.518 | 0.215 | 0.093 | 0.383 | 0.140 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 25 | 23 | 22 | 23 | 31 | 17 | 23 | 38 | 22 |
N.S. |
1 | 1.09 | 1.00 | 0.96 | 1.00 | 1.35 | 0.74 | 1.00 | 1.65 | 0.96 |
time (sec) |
N/A | 0.383 | 0.017 | 0.737 | 0.042 | 0.082 | 0.505 | 0.126 | 0.175 | 0.221 |
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 | 24 | 19 | 19 | 19 | 101 | 26 | 17 | 26 | 27 | 18 |
N.S. |
1 | 0.79 | 0.79 | 0.79 | 4.21 | 1.08 | 0.71 | 1.08 | 1.12 | 0.75 |
time (sec) |
N/A | 0.921 | 0.209 | 1.084 | 0.094 | 0.091 | 0.156 | 0.126 | 0.174 | 3.008 |
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 | 18 | 18 | 16 | 19 | 15 | 15 | 17 | 18 | 15 |
N.S. |
1 | 0.90 | 0.90 | 0.80 | 0.95 | 0.75 | 0.75 | 0.85 | 0.90 | 0.75 |
time (sec) |
N/A | 0.389 | 97.086 | 0.152 | 0.156 | 0.102 | 0.121 | 0.128 | 0.176 | 2.981 |
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 | 23 | 24 | 26 | 22 | 88 | 28 | 32 | 45 | 24 | 19 |
N.S. |
1 | 1.04 | 1.13 | 0.96 | 3.83 | 1.22 | 1.39 | 1.96 | 1.04 | 0.83 |
time (sec) |
N/A | 0.247 | 0.035 | 0.089 | 0.112 | 0.103 | 0.130 | 0.125 | 0.179 | 2.948 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 38 | 87 | 103 | 91 | 85 | 115 | 178 | 117 |
N.S. |
1 | 0.00 | 1.23 | 2.81 | 3.32 | 2.94 | 2.74 | 3.71 | 5.74 | 3.77 |
time (sec) |
N/A | 0.000 | 0.134 | 0.852 | 1.152 | 0.103 | 0.556 | 0.588 | 200.034 | 3.228 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | F(-1) | A | A | F(-1) | F(-1) | F | F(-1) |
verified | N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 0 | 143 | 0 | 54 | 46 | 0 | 0 | 316 | 0 |
N.S. |
1 | 0.00 | 3.76 | 0.00 | 1.42 | 1.21 | 0.00 | 0.00 | 8.32 | 0.00 |
time (sec) |
N/A | 0.000 | 0.243 | 0.000 | 18.788 | 0.104 | 0.000 | 0.000 | 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 | 10 | 10 | 10 | 9 | 8 | 8 | 7 | 9 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.80 | 0.80 | 0.70 | 0.90 | 0.80 | 0.80 |
time (sec) |
N/A | 0.207 | 0.002 | 0.083 | 0.033 | 0.079 | 0.036 | 0.110 | 0.176 | 4.091 |
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 | 31 | 32 | 51 | 49 | 29 | 34 | 121 | 66 |
N.S. |
1 | 0.00 | 1.07 | 1.10 | 1.76 | 1.69 | 1.00 | 1.17 | 4.17 | 2.28 |
time (sec) |
N/A | 0.000 | 0.056 | 34.115 | 0.164 | 0.109 | 0.137 | 0.145 | 0.193 | 4.153 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 0 | 12 | 11 | 10 | 10 | 24 | 10 | 10 | 10 |
N.S. |
1 | 0.00 | 1.00 | 0.92 | 0.83 | 0.83 | 2.00 | 0.83 | 0.83 | 0.83 |
time (sec) |
N/A | 0.000 | 0.085 | 0.207 | 0.062 | 0.090 | 0.240 | 0.114 | 0.183 | 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 | 11 | 16 | 11 | 9 | 11 | 11 | 12 | 11 | 13 | 13 |
N.S. |
1 | 1.45 | 1.00 | 0.82 | 1.00 | 1.00 | 1.09 | 1.00 | 1.18 | 1.18 |
time (sec) |
N/A | 0.206 | 0.012 | 0.127 | 0.027 | 0.093 | 0.039 | 0.110 | 0.183 | 3.761 |
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 | 31 | 0 | 113 | 82 | 99 | 100 | 116 | 100 | 123 | 101 |
N.S. |
1 | 0.00 | 3.65 | 2.65 | 3.19 | 3.23 | 3.74 | 3.23 | 3.97 | 3.26 |
time (sec) |
N/A | 0.000 | 2.759 | 1.134 | 0.119 | 0.100 | 0.218 | 0.217 | 0.198 | 3.969 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 10 | 10 | 11 | 10 | 10 | 8 | 10 | 13 | 10 |
N.S. |
1 | 0.59 | 0.59 | 0.65 | 0.59 | 0.59 | 0.47 | 0.59 | 0.76 | 0.59 |
time (sec) |
N/A | 0.172 | 0.004 | 0.053 | 0.031 | 0.083 | 0.038 | 0.123 | 0.180 | 3.314 |
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 | 25 | 19 | 20 | 22 | 17 | 17 | 22 | 15 | 15 |
N.S. |
1 | 1.67 | 1.27 | 1.33 | 1.47 | 1.13 | 1.13 | 1.47 | 1.00 | 1.00 |
time (sec) |
N/A | 0.166 | 0.001 | 0.069 | 0.046 | 0.087 | 0.019 | 0.122 | 0.184 | 3.423 |
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 | 22 | 21 | 21 | 20 | 21 | 24 | 101 |
N.S. |
1 | 0.00 | 0.92 | 0.88 | 0.84 | 0.84 | 0.80 | 0.84 | 0.96 | 4.04 |
time (sec) |
N/A | 0.000 | 0.403 | 5.252 | 0.119 | 0.095 | 0.130 | 0.139 | 0.289 | 3.595 |
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 | 20 | 19 | 22 | 22 | 24 | 20 | 20 | 18 |
N.S. |
1 | 0.00 | 0.83 | 0.79 | 0.92 | 0.92 | 1.00 | 0.83 | 0.83 | 0.75 |
time (sec) |
N/A | 0.000 | 0.157 | 0.223 | 0.080 | 0.093 | 0.086 | 0.128 | 0.183 | 3.501 |
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 | 30 | 18 | 17 | 29 | 22 | 27 | 29 | 29 | 18 |
N.S. |
1 | 1.03 | 0.62 | 0.59 | 1.00 | 0.76 | 0.93 | 1.00 | 1.00 | 0.62 |
time (sec) |
N/A | 0.223 | 0.011 | 0.122 | 0.032 | 0.103 | 0.056 | 0.122 | 0.186 | 3.297 |
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 | 22 | 0 | 19 | 20 | 54 | 20 | 17 | 0 | 719 | 21 |
N.S. |
1 | 0.00 | 0.86 | 0.91 | 2.45 | 0.91 | 0.77 | 0.00 | 32.68 | 0.95 |
time (sec) |
N/A | 0.000 | 0.293 | 0.734 | 0.214 | 0.102 | 0.270 | 0.000 | 0.251 | 3.780 |
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 | 22 | 22 | 22 | 77 | 21 | 20 | 21 | 38 | 22 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 3.50 | 0.95 | 0.91 | 0.95 | 1.73 | 1.00 |
time (sec) |
N/A | 0.356 | 0.046 | 0.256 | 0.066 | 0.110 | 0.103 | 0.321 | 0.193 | 3.386 |
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 | 7 | 7 | 7 | 6 | 6 | 7 | 6 | 9 | 6 |
N.S. |
1 | 0.54 | 0.54 | 0.54 | 0.46 | 0.46 | 0.54 | 0.46 | 0.69 | 0.46 |
time (sec) |
N/A | 0.244 | 0.001 | 0.047 | 0.029 | 0.080 | 0.030 | 0.121 | 0.184 | 0.016 |
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 | 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 | 0.229 | 0.000 | 0.036 | 0.024 | 0.073 | 0.028 | 0.112 | 0.189 | 0.005 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | F | B |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 20 | 24 | 21 | 37 | 60 | 40 | 74 | 74 |
N.S. |
1 | 0.00 | 0.91 | 1.09 | 0.95 | 1.68 | 2.73 | 1.82 | 3.36 | 3.36 |
time (sec) |
N/A | 0.000 | 0.034 | 0.480 | 0.036 | 0.093 | 0.188 | 0.133 | 0.182 | 3.724 |
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 | 6 | 6 | 5 | 4 | 4 | 5 | 5 | 4 | 4 |
N.S. |
1 | 0.46 | 0.46 | 0.38 | 0.31 | 0.31 | 0.38 | 0.38 | 0.31 | 0.31 |
time (sec) |
N/A | 0.209 | 0.000 | 0.020 | 0.028 | 0.086 | 0.025 | 0.114 | 0.188 | 3.286 |
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 | 14 | 12 | 12 | 10 | 19 | 9 | 12 | 9 | 11 | 9 |
N.S. |
1 | 0.86 | 0.86 | 0.71 | 1.36 | 0.64 | 0.86 | 0.64 | 0.79 | 0.64 |
time (sec) |
N/A | 0.281 | 0.024 | 0.150 | 0.065 | 0.080 | 0.042 | 0.119 | 0.184 | 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 | 21 | 24 | 21 | 19 | 19 | 19 | 14 | 19 | 21 | 16 |
N.S. |
1 | 1.14 | 1.00 | 0.90 | 0.90 | 0.90 | 0.67 | 0.90 | 1.00 | 0.76 |
time (sec) |
N/A | 0.295 | 0.002 | 0.117 | 0.030 | 0.090 | 0.081 | 0.127 | 0.184 | 3.262 |
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 | 8 | 8 | 13 | 10 | 12 | 12 | 10 | 12 | 10 | 9 |
N.S. |
1 | 1.00 | 1.62 | 1.25 | 1.50 | 1.50 | 1.25 | 1.50 | 1.25 | 1.12 |
time (sec) |
N/A | 0.220 | 0.000 | 0.046 | 0.025 | 0.071 | 0.019 | 0.119 | 0.178 | 3.271 |
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 | 27 | 0 | 19 | 19 | 29 | 20 | 26 | 19 | 21 | 0 |
N.S. |
1 | 0.00 | 0.70 | 0.70 | 1.07 | 0.74 | 0.96 | 0.70 | 0.78 | 0.00 |
time (sec) |
N/A | 0.000 | 0.827 | 0.125 | 0.151 | 0.105 | 0.151 | 0.130 | 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 | 31 | 51 | 33 | 44 | 34 | 28 | 29 | 43 | 80 | 32 |
N.S. |
1 | 1.65 | 1.06 | 1.42 | 1.10 | 0.90 | 0.94 | 1.39 | 2.58 | 1.03 |
time (sec) |
N/A | 1.890 | 0.278 | 0.303 | 0.068 | 0.111 | 0.196 | 0.166 | 7.825 | 3.715 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 25 | 25 | 23 | 67 | 39 | 24 | 23 | 56 | 20 |
N.S. |
1 | 1.04 | 1.04 | 0.96 | 2.79 | 1.62 | 1.00 | 0.96 | 2.33 | 0.83 |
time (sec) |
N/A | 0.658 | 0.022 | 0.776 | 0.081 | 0.087 | 0.109 | 0.134 | 0.195 | 3.439 |
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 | 22 | 38 | 33 | 33 | 37 | 18 | 27 | 32 | 47 | 33 |
N.S. |
1 | 1.73 | 1.50 | 1.50 | 1.68 | 0.82 | 1.23 | 1.45 | 2.14 | 1.50 |
time (sec) |
N/A | 0.522 | 0.038 | 0.399 | 0.234 | 0.082 | 0.093 | 0.135 | 0.194 | 3.426 |
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 | 18 | 16 | 16 | 15 | 15 | 19 | 29 | 20 | 16 |
N.S. |
1 | 0.86 | 0.76 | 0.76 | 0.71 | 0.71 | 0.90 | 1.38 | 0.95 | 0.76 |
time (sec) |
N/A | 0.398 | 0.064 | 0.344 | 0.086 | 0.087 | 0.092 | 0.132 | 0.200 | 3.370 |
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 | 9 | 6 | 6 | 7 | 6 | 6 | 3 | 7 | 6 | 6 |
N.S. |
1 | 0.67 | 0.67 | 0.78 | 0.67 | 0.67 | 0.33 | 0.78 | 0.67 | 0.67 |
time (sec) |
N/A | 0.142 | 0.000 | 0.032 | 0.024 | 0.070 | 0.027 | 0.120 | 0.202 | 0.015 |
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 | 2 | 2 | 3 | 2 | 2 | 2 | 3 | 2 | 2 |
N.S. |
1 | 0.22 | 0.22 | 0.33 | 0.22 | 0.22 | 0.22 | 0.33 | 0.22 | 0.22 |
time (sec) |
N/A | 0.126 | 0.000 | 0.017 | 0.026 | 0.092 | 0.016 | 0.118 | 0.204 | 0.002 |
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 | 29 | 157 | 28 | 54 | 63 | 53 | 70 | 53 | 54 | 23 |
N.S. |
1 | 5.41 | 0.97 | 1.86 | 2.17 | 1.83 | 2.41 | 1.83 | 1.86 | 0.79 |
time (sec) |
N/A | 0.314 | 0.409 | 2.776 | 0.040 | 0.091 | 0.104 | 0.131 | 0.213 | 3.349 |
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 | 21 | 79 | 24 | 128 | 155 | 119 | 78 | 187 | 63 | 75 |
N.S. |
1 | 3.76 | 1.14 | 6.10 | 7.38 | 5.67 | 3.71 | 8.90 | 3.00 | 3.57 |
time (sec) |
N/A | 0.513 | 0.281 | 0.115 | 0.204 | 0.115 | 0.255 | 0.139 | 0.197 | 4.347 |
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 | 17 | 18 | 30 | 30 | 15 | 20 | 26 | 17 |
N.S. |
1 | 0.00 | 0.81 | 0.86 | 1.43 | 1.43 | 0.71 | 0.95 | 1.24 | 0.81 |
time (sec) |
N/A | 0.000 | 0.133 | 0.500 | 0.069 | 0.091 | 0.048 | 0.126 | 0.193 | 3.540 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 17 | 17 | 18 | 17 | 15 | 17 | 17 | 17 | 19 |
N.S. |
1 | 0.89 | 0.89 | 0.95 | 0.89 | 0.79 | 0.89 | 0.89 | 0.89 | 1.00 |
time (sec) |
N/A | 0.251 | 0.002 | 0.111 | 0.037 | 0.085 | 0.052 | 0.117 | 0.201 | 3.286 |
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 | 24 | 18 | 23 | 20 | 23 | 24 | 23 |
N.S. |
1 | 1.00 | 1.00 | 1.04 | 0.78 | 1.00 | 0.87 | 1.00 | 1.04 | 1.00 |
time (sec) |
N/A | 1.179 | 0.195 | 0.314 | 0.071 | 0.083 | 0.169 | 0.151 | 0.194 | 0.304 |
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 | 31 | 0 | 32 | 26 | 27 | 25 | 24 | 41 | 67 | 44 |
N.S. |
1 | 0.00 | 1.03 | 0.84 | 0.87 | 0.81 | 0.77 | 1.32 | 2.16 | 1.42 |
time (sec) |
N/A | 0.000 | 0.137 | 0.746 | 0.242 | 0.097 | 0.459 | 0.317 | 0.198 | 3.435 |
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 | 25 | 0 | 22 | 21 | 87 | 32 | 19 | 28 | 35 | 20 |
N.S. |
1 | 0.00 | 0.88 | 0.84 | 3.48 | 1.28 | 0.76 | 1.12 | 1.40 | 0.80 |
time (sec) |
N/A | 0.000 | 2.165 | 3.132 | 0.161 | 0.097 | 0.081 | 0.128 | 0.194 | 3.388 |
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 | 19 | 22 | 21 | 15 | 21 | 21 | 16488 |
N.S. |
1 | 0.81 | 0.81 | 0.90 | 1.05 | 1.00 | 0.71 | 1.00 | 1.00 | 785.14 |
time (sec) |
N/A | 0.260 | 0.016 | 0.240 | 0.035 | 0.097 | 0.431 | 0.122 | 0.193 | 16.085 |
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 | 7 | 7 | 8 | 13 | 7 | 5 | 7 | 7 | 7 |
N.S. |
1 | 0.35 | 0.35 | 0.40 | 0.65 | 0.35 | 0.25 | 0.35 | 0.35 | 0.35 |
time (sec) |
N/A | 0.151 | 0.001 | 0.035 | 0.028 | 0.094 | 0.041 | 0.114 | 0.188 | 3.369 |
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 | 23 | 28 | 25 | 27 | 19 | 21 | 29 | 21 |
N.S. |
1 | 0.00 | 1.00 | 1.22 | 1.09 | 1.17 | 0.83 | 0.91 | 1.26 | 0.91 |
time (sec) |
N/A | 0.000 | 6.374 | 0.928 | 0.148 | 0.104 | 0.067 | 0.163 | 0.187 | 3.535 |
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 | 14 | 14 | 13 | 13 | 12 | 13 | 14 | 13 |
N.S. |
1 | 1.08 | 1.08 | 1.08 | 1.00 | 1.00 | 0.92 | 1.00 | 1.08 | 1.00 |
time (sec) |
N/A | 0.251 | 0.002 | 0.082 | 0.033 | 0.083 | 0.035 | 0.130 | 0.182 | 3.375 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | C | A | A | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 23 | 23 | 30 | 23 | 19 | 24 | 26 | 0 |
N.S. |
1 | 0.00 | 0.96 | 0.96 | 1.25 | 0.96 | 0.79 | 1.00 | 1.08 | 0.00 |
time (sec) |
N/A | 0.000 | 0.056 | 18.883 | 0.178 | 0.089 | 0.272 | 0.322 | 0.214 | 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 | 22 | 20 | 20 | 20 | 19 | 19 | 15 | 27 | 37 | 18 |
N.S. |
1 | 0.91 | 0.91 | 0.91 | 0.86 | 0.86 | 0.68 | 1.23 | 1.68 | 0.82 |
time (sec) |
N/A | 0.332 | 0.008 | 0.189 | 0.036 | 0.095 | 0.080 | 0.130 | 0.191 | 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 | 28 | 0 | 31 | 35 | 32 | 46 | 26 | 58 | 980 | 60 |
N.S. |
1 | 0.00 | 1.11 | 1.25 | 1.14 | 1.64 | 0.93 | 2.07 | 35.00 | 2.14 |
time (sec) |
N/A | 0.000 | 0.055 | 0.428 | 0.109 | 0.099 | 0.123 | 0.150 | 0.218 | 3.557 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | F(-2) | A | F(-2) | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 48 | 19 | 0 | 23 | 0 | 30 | 24 | 23 |
N.S. |
1 | 0.00 | 2.29 | 0.90 | 0.00 | 1.10 | 0.00 | 1.43 | 1.14 | 1.10 |
time (sec) |
N/A | 0.000 | 0.436 | 0.852 | 0.000 | 0.114 | 0.000 | 0.129 | 0.197 | 4.041 |
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 | 17 | 33 | 17 | 14 | 129 | 18 | 14 | 88 | 28 | 19 |
N.S. |
1 | 1.94 | 1.00 | 0.82 | 7.59 | 1.06 | 0.82 | 5.18 | 1.65 | 1.12 |
time (sec) |
N/A | 0.673 | 0.281 | 1.618 | 0.127 | 0.097 | 0.156 | 0.138 | 0.189 | 0.641 |
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 | 17 | 33 | 19 | 24 | 74 | 28 | 27 | 30 | 25 | 24 |
N.S. |
1 | 1.94 | 1.12 | 1.41 | 4.35 | 1.65 | 1.59 | 1.76 | 1.47 | 1.41 |
time (sec) |
N/A | 0.361 | 0.019 | 0.132 | 0.045 | 0.105 | 0.088 | 0.121 | 0.194 | 3.441 |
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 | 28 | 62 | 48 | 28 | 57 | 56 | 61 | 122 | 59 | 55 |
N.S. |
1 | 2.21 | 1.71 | 1.00 | 2.04 | 2.00 | 2.18 | 4.36 | 2.11 | 1.96 |
time (sec) |
N/A | 0.981 | 0.587 | 0.270 | 0.084 | 0.120 | 0.124 | 0.125 | 0.183 | 3.436 |
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 | 28 | 31 | 29 | 26 | 34 | 29 | 31 | 27 |
N.S. |
1 | 0.00 | 1.17 | 1.29 | 1.21 | 1.08 | 1.42 | 1.21 | 1.29 | 1.12 |
time (sec) |
N/A | 0.000 | 0.629 | 0.265 | 0.132 | 0.113 | 0.142 | 0.157 | 0.200 | 3.550 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | F(-2) | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 0 | 58 | 49 | 49 | 159 | 0 | 0 | 34 | 90 |
N.S. |
1 | 0.00 | 1.53 | 1.29 | 1.29 | 4.18 | 0.00 | 0.00 | 0.89 | 2.37 |
time (sec) |
N/A | 0.000 | 0.613 | 69.415 | 0.699 | 0.133 | 0.000 | 0.000 | 0.252 | 3.942 |
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 | 26 | 0 | 33 | 55 | 63 | 59 | 68 | 349 | 77 | 79 |
N.S. |
1 | 0.00 | 1.27 | 2.12 | 2.42 | 2.27 | 2.62 | 13.42 | 2.96 | 3.04 |
time (sec) |
N/A | 0.000 | 0.104 | 0.122 | 0.083 | 0.113 | 0.172 | 0.181 | 0.196 | 4.395 |
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 | 28 | 24 | 41 | 22 | 31 | 27 | 39 | 37 |
N.S. |
1 | 0.00 | 1.08 | 0.92 | 1.58 | 0.85 | 1.19 | 1.04 | 1.50 | 1.42 |
time (sec) |
N/A | 0.000 | 1.715 | 0.218 | 0.115 | 0.121 | 0.218 | 0.120 | 0.195 | 0.226 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | F(-1) | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 23 | 21 | 31 | 25 | 0 | 31 | 90 | 25 |
N.S. |
1 | 0.00 | 1.28 | 1.17 | 1.72 | 1.39 | 0.00 | 1.72 | 5.00 | 1.39 |
time (sec) |
N/A | 0.000 | 0.096 | 1.213 | 0.191 | 0.092 | 0.000 | 0.206 | 200.030 | 3.411 |
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 | 15 | 23 | 16 |
N.S. |
1 | 0.76 | 0.76 | 0.76 | 0.71 | 0.71 | 0.67 | 0.71 | 1.10 | 0.76 |
time (sec) |
N/A | 0.292 | 0.005 | 0.049 | 0.024 | 0.076 | 0.090 | 0.120 | 0.440 | 0.080 |
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 | 20 | 0 | 31 | 20 | 23 | 22 | 20 | 23 | 23 | 23 |
N.S. |
1 | 0.00 | 1.55 | 1.00 | 1.15 | 1.10 | 1.00 | 1.15 | 1.15 | 1.15 |
time (sec) |
N/A | 0.000 | 0.066 | 0.161 | 0.067 | 0.107 | 0.115 | 0.123 | 0.448 | 3.381 |
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 | 22 | 0 | 22 | 19 | 18 | 102 | 0 | 0 | 22 | 18 |
N.S. |
1 | 0.00 | 1.00 | 0.86 | 0.82 | 4.64 | 0.00 | 0.00 | 1.00 | 0.82 |
time (sec) |
N/A | 0.000 | 0.069 | 0.043 | 0.498 | 0.108 | 0.000 | 0.000 | 0.499 | 3.645 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | F | B | B | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 83 | 45 | 0 | 57 | 60 | 0 | 65 | 74 |
N.S. |
1 | 0.00 | 2.86 | 1.55 | 0.00 | 1.97 | 2.07 | 0.00 | 2.24 | 2.55 |
time (sec) |
N/A | 0.000 | 8.942 | 1.761 | 0.000 | 0.132 | 81.617 | 0.000 | 0.497 | 3.530 |
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 | 37 | 27 | 26 | 26 | 29 | 28 | 29 | 60 |
N.S. |
1 | 0.00 | 1.16 | 0.84 | 0.81 | 0.81 | 0.91 | 0.88 | 0.91 | 1.88 |
time (sec) |
N/A | 0.000 | 0.063 | 21.907 | 0.080 | 0.125 | 0.171 | 0.235 | 0.480 | 3.604 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 10 | 10 | 9 | 8 | 8 | 12 | 9 | 8 | 8 |
N.S. |
1 | 0.59 | 0.59 | 0.53 | 0.47 | 0.47 | 0.71 | 0.53 | 0.47 | 0.47 |
time (sec) |
N/A | 0.226 | 0.001 | 0.165 | 0.027 | 0.081 | 0.024 | 0.121 | 0.480 | 3.339 |
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 | 20 | 16 | 15 | 17 | 17 | 17 | 17 | 12 | 17 |
N.S. |
1 | 1.54 | 1.23 | 1.15 | 1.31 | 1.31 | 1.31 | 1.31 | 0.92 | 1.31 |
time (sec) |
N/A | 0.263 | 0.002 | 0.049 | 0.026 | 0.092 | 0.021 | 0.124 | 0.423 | 0.064 |
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 | 31 | 48 | 31 | 68 | 79 | 85 | 60 | 83 | 123 | 50 |
N.S. |
1 | 1.55 | 1.00 | 2.19 | 2.55 | 2.74 | 1.94 | 2.68 | 3.97 | 1.61 |
time (sec) |
N/A | 0.443 | 0.025 | 0.706 | 0.048 | 0.096 | 0.134 | 0.127 | 0.508 | 3.461 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 28 | 21 | 27 | 26 | 26 | 26 | 26 | 21 | 18 |
N.S. |
1 | 1.12 | 0.84 | 1.08 | 1.04 | 1.04 | 1.04 | 1.04 | 0.84 | 0.72 |
time (sec) |
N/A | 0.211 | 0.021 | 0.102 | 0.041 | 0.100 | 0.108 | 0.122 | 0.478 | 3.406 |
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 | 20 | 0 | 28 | 24 | 29 | 29 | 20 | 24 | 30 | 31 |
N.S. |
1 | 0.00 | 1.40 | 1.20 | 1.45 | 1.45 | 1.00 | 1.20 | 1.50 | 1.55 |
time (sec) |
N/A | 0.000 | 0.081 | 0.339 | 0.076 | 0.121 | 0.055 | 0.121 | 0.428 | 3.359 |
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 | 24 | 25 | 20 | 24 | 19 | 24 | 26 | 22 |
N.S. |
1 | 1.08 | 1.00 | 1.04 | 0.83 | 1.00 | 0.79 | 1.00 | 1.08 | 0.92 |
time (sec) |
N/A | 0.861 | 0.053 | 2.297 | 0.168 | 0.091 | 0.200 | 0.243 | 0.518 | 3.508 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 10 | 10 | 9 | 10 | 12 | 8 | 12 | 10 | 10 |
N.S. |
1 | 0.67 | 0.67 | 0.60 | 0.67 | 0.80 | 0.53 | 0.80 | 0.67 | 0.67 |
time (sec) |
N/A | 0.190 | 0.005 | 0.112 | 0.031 | 0.100 | 0.041 | 0.120 | 0.476 | 3.257 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 78 | 44 | 30 | 189 | 30 | 26 | 30 | 78 | 27 |
N.S. |
1 | 4.11 | 2.32 | 1.58 | 9.95 | 1.58 | 1.37 | 1.58 | 4.11 | 1.42 |
time (sec) |
N/A | 0.471 | 0.077 | 1.067 | 0.180 | 0.095 | 0.105 | 0.129 | 0.486 | 3.607 |
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 | 35 | 0 | 33 | 34 | 34 | 36 | 37 | 43 | 1018 | 106 |
N.S. |
1 | 0.00 | 0.94 | 0.97 | 0.97 | 1.03 | 1.06 | 1.23 | 29.09 | 3.03 |
time (sec) |
N/A | 0.000 | 0.502 | 1.087 | 0.087 | 0.105 | 0.101 | 0.438 | 0.603 | 3.490 |
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 | 7 | 10 | 9 | 9 | 10 | 9 | 9 | 7 |
N.S. |
1 | 0.00 | 0.47 | 0.67 | 0.60 | 0.60 | 0.67 | 0.60 | 0.60 | 0.47 |
time (sec) |
N/A | 0.000 | 0.021 | 0.096 | 0.079 | 0.104 | 0.076 | 0.135 | 0.460 | 3.389 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | C | C | C | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 1463 | 123 | 315 | 136 | 114 | 70 | 317 | 105 |
N.S. |
1 | 0.00 | 54.19 | 4.56 | 11.67 | 5.04 | 4.22 | 2.59 | 11.74 | 3.89 |
time (sec) |
N/A | 0.000 | 5.535 | 19.493 | 0.193 | 0.098 | 5.055 | 0.145 | 0.512 | 4.086 |
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 | 26 | 0 | 51 | 51 | 46 | 43 | 53 | 62 | 59 | 0 |
N.S. |
1 | 0.00 | 1.96 | 1.96 | 1.77 | 1.65 | 2.04 | 2.38 | 2.27 | 0.00 |
time (sec) |
N/A | 0.000 | 0.166 | 6.397 | 0.085 | 0.100 | 0.892 | 0.172 | 0.566 | 0.000 |
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 | 33 | 0 | 27 | 60 | 63 | 48 | 63 | 93 | 43 | 25 |
N.S. |
1 | 0.00 | 0.82 | 1.82 | 1.91 | 1.45 | 1.91 | 2.82 | 1.30 | 0.76 |
time (sec) |
N/A | 0.000 | 0.221 | 0.648 | 0.031 | 0.100 | 0.404 | 0.124 | 0.469 | 3.495 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 58 | 16 | 15 | 21 | 17 | 20 | 0 | 27 | 0 |
N.S. |
1 | 3.22 | 0.89 | 0.83 | 1.17 | 0.94 | 1.11 | 0.00 | 1.50 | 0.00 |
time (sec) |
N/A | 0.596 | 0.297 | 46.774 | 0.210 | 0.087 | 41.509 | 0.000 | 0.418 | 0.000 |
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 | 28 | 0 | 25 | 34 | 34 | 33 | 36 | 32 | 32 | 0 |
N.S. |
1 | 0.00 | 0.89 | 1.21 | 1.21 | 1.18 | 1.29 | 1.14 | 1.14 | 0.00 |
time (sec) |
N/A | 0.000 | 5.046 | 13.127 | 0.205 | 0.103 | 0.176 | 0.140 | 0.413 | 0.000 |
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 | 19 | 19 | 20 | 46 | 29 | 20 | 87 | 28 | 19 |
N.S. |
1 | 0.95 | 0.95 | 1.00 | 2.30 | 1.45 | 1.00 | 4.35 | 1.40 | 0.95 |
time (sec) |
N/A | 0.340 | 0.042 | 0.283 | 0.076 | 0.101 | 0.046 | 0.134 | 0.437 | 3.281 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | A | A | F | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 47 | 136 | 141 | 43 | 39 | 0 | 98 | 0 |
N.S. |
1 | 0.00 | 1.38 | 4.00 | 4.15 | 1.26 | 1.15 | 0.00 | 2.88 | 0.00 |
time (sec) |
N/A | 0.000 | 0.139 | 0.339 | 0.329 | 0.107 | 0.827 | 0.000 | 0.451 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 31 | 42 | 84 | 66 | 36 | 130 | 138 | 165 |
N.S. |
1 | 0.00 | 1.00 | 1.35 | 2.71 | 2.13 | 1.16 | 4.19 | 4.45 | 5.32 |
time (sec) |
N/A | 0.000 | 0.071 | 2.191 | 0.086 | 0.102 | 0.295 | 0.604 | 0.460 | 4.178 |
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 | 33 | 54 | 50 | 38 | 53 | 41 | 37 | 54 | 56 | 46 |
N.S. |
1 | 1.64 | 1.52 | 1.15 | 1.61 | 1.24 | 1.12 | 1.64 | 1.70 | 1.39 |
time (sec) |
N/A | 0.412 | 0.054 | 0.517 | 0.063 | 0.085 | 0.088 | 0.123 | 0.447 | 3.362 |
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 | 18 | 0 | 17 | 29 | 1148 | 26 | 26 | 27 | 28 | 27 |
N.S. |
1 | 0.00 | 0.94 | 1.61 | 63.78 | 1.44 | 1.44 | 1.50 | 1.56 | 1.50 |
time (sec) |
N/A | 0.000 | 0.320 | 245.654 | 0.383 | 0.107 | 0.233 | 0.125 | 0.478 | 4.156 |
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 | 11 | 11 | 11 | 10 | 10 | 8 | 10 | 11 | 10 |
N.S. |
1 | 0.92 | 0.92 | 0.92 | 0.83 | 0.83 | 0.67 | 0.83 | 0.92 | 0.83 |
time (sec) |
N/A | 0.223 | 0.000 | 0.038 | 0.024 | 0.088 | 0.019 | 0.123 | 0.475 | 0.020 |
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 | 8 | 8 | 9 | 8 | 8 | 7 | 9 | 8 | 8 |
N.S. |
1 | 0.44 | 0.44 | 0.50 | 0.44 | 0.44 | 0.39 | 0.50 | 0.44 | 0.44 |
time (sec) |
N/A | 0.199 | 0.001 | 0.033 | 0.041 | 0.080 | 0.028 | 0.123 | 0.503 | 0.018 |
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 | 12 | 19 | 15 | 18 | 44 | 17 | 17 | 19 | 13 | 54 |
N.S. |
1 | 1.58 | 1.25 | 1.50 | 3.67 | 1.42 | 1.42 | 1.58 | 1.08 | 4.50 |
time (sec) |
N/A | 0.773 | 0.020 | 0.194 | 0.164 | 0.108 | 0.074 | 0.125 | 0.455 | 0.144 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | F(-2) | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 52 | 85 | 70 | 53 | 0 | 84 | 76 | 49 |
N.S. |
1 | 0.00 | 1.93 | 3.15 | 2.59 | 1.96 | 0.00 | 3.11 | 2.81 | 1.81 |
time (sec) |
N/A | 0.000 | 0.162 | 35.756 | 0.106 | 0.124 | 0.000 | 0.422 | 0.499 | 4.015 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | A | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 42 | 37 | 38 | 0 | 72 | 37 | 0 | 104 | 42 |
N.S. |
1 | 1.45 | 1.28 | 1.31 | 0.00 | 2.48 | 1.28 | 0.00 | 3.59 | 1.45 |
time (sec) |
N/A | 0.655 | 0.064 | 1.043 | 0.000 | 0.131 | 0.488 | 0.000 | 200.024 | 3.639 |
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 | 23 | 47 | 47 | 45 | 48 | 42 | 42 | 44 | 43 | 36 |
N.S. |
1 | 2.04 | 2.04 | 1.96 | 2.09 | 1.83 | 1.83 | 1.91 | 1.87 | 1.57 |
time (sec) |
N/A | 0.208 | 0.006 | 0.458 | 0.039 | 0.117 | 0.076 | 0.121 | 0.209 | 3.471 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 29 | 25 | 51 | 59 | 26 | 68 | 75 | 26 |
N.S. |
1 | 0.00 | 1.00 | 0.86 | 1.76 | 2.03 | 0.90 | 2.34 | 2.59 | 0.90 |
time (sec) |
N/A | 0.000 | 0.318 | 3.232 | 0.234 | 0.112 | 0.558 | 0.136 | 0.207 | 3.730 |
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 | 29 | 18 | 18 | 17 | 17 | 17 | 17 | 15 | 14 |
N.S. |
1 | 1.38 | 0.86 | 0.86 | 0.81 | 0.81 | 0.81 | 0.81 | 0.71 | 0.67 |
time (sec) |
N/A | 0.175 | 0.007 | 0.095 | 0.032 | 0.098 | 0.045 | 0.116 | 0.219 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 26 | 84 | 23 | 22 | 97 | 141 | 79 | 168 | 122 |
N.S. |
1 | 1.18 | 3.82 | 1.05 | 1.00 | 4.41 | 6.41 | 3.59 | 7.64 | 5.55 |
time (sec) |
N/A | 0.289 | 0.029 | 0.439 | 0.035 | 0.108 | 0.038 | 0.127 | 0.198 | 3.399 |
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 | 26 | 26 | 23 | 31 | 28 | 22 | 26 | 22 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 1.19 | 1.08 | 0.85 | 1.00 | 0.85 | 1.00 |
time (sec) |
N/A | 0.628 | 0.138 | 0.490 | 0.177 | 0.092 | 0.109 | 0.134 | 0.190 | 3.503 |
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 | 30 | 36 | 35 | 32 | 31 | 31 | 37 | 74 | 32 | 29 |
N.S. |
1 | 1.20 | 1.17 | 1.07 | 1.03 | 1.03 | 1.23 | 2.47 | 1.07 | 0.97 |
time (sec) |
N/A | 0.189 | 0.005 | 0.204 | 0.033 | 0.095 | 0.059 | 0.121 | 0.189 | 3.405 |
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 | 28 | 32 | 21 | 21 | 27 | 17 | 21 | 29 | 20 |
N.S. |
1 | 1.17 | 1.33 | 0.88 | 0.88 | 1.12 | 0.71 | 0.88 | 1.21 | 0.83 |
time (sec) |
N/A | 0.292 | 0.009 | 0.102 | 0.032 | 0.078 | 0.064 | 0.121 | 0.219 | 3.423 |
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 | 14 | 0 | 17 | 12 | 11 | 11 | 14 | 11 | 11 | 11 |
N.S. |
1 | 0.00 | 1.21 | 0.86 | 0.79 | 0.79 | 1.00 | 0.79 | 0.79 | 0.79 |
time (sec) |
N/A | 0.000 | 0.133 | 0.299 | 0.081 | 0.104 | 0.371 | 1.169 | 0.235 | 3.761 |
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 | 12 | 12 | 10 | 9 | 9 | 12 | 9 | 10 | 9 |
N.S. |
1 | 0.86 | 0.86 | 0.71 | 0.64 | 0.64 | 0.86 | 0.64 | 0.71 | 0.64 |
time (sec) |
N/A | 0.137 | 0.001 | 0.030 | 0.032 | 0.104 | 0.021 | 0.117 | 0.198 | 0.032 |
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 | 47 | 30 | 19 | 40 | 25 | 26 | 40 | 52 | 33 |
N.S. |
1 | 1.74 | 1.11 | 0.70 | 1.48 | 0.93 | 0.96 | 1.48 | 1.93 | 1.22 |
time (sec) |
N/A | 0.267 | 0.045 | 0.513 | 0.216 | 0.101 | 0.093 | 0.119 | 0.210 | 0.173 |
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 | 24 | 37 | 30 | 35 | 27 | 34 | 34 | 34 | 36 | 31 |
N.S. |
1 | 1.54 | 1.25 | 1.46 | 1.12 | 1.42 | 1.42 | 1.42 | 1.50 | 1.29 |
time (sec) |
N/A | 0.780 | 0.415 | 0.212 | 0.232 | 0.108 | 0.136 | 0.169 | 0.239 | 3.487 |