Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F(-2) | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 27 | 36 | 24 | 35 | 32 | 0 | 42 | 69 |
N.S. |
1 | 0.00 | 0.84 | 1.12 | 0.75 | 1.09 | 1.00 | 0.00 | 1.31 | 2.16 |
time (sec) |
N/A | 0.000 | 0.121 | 0.437 | 0.086 | 0.069 | 0.193 | 0.000 | 0.196 | 2.174 |
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 | 22 | 22 | 22 | 20 | 21 | 43 | 19 | 21 | 43 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.95 | 1.95 | 0.86 | 0.95 | 1.95 | 0.95 |
time (sec) |
N/A | 2.193 | 0.231 | 0.685 | 0.133 | 0.063 | 0.108 | 0.121 | 0.735 | 0.280 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | A | A | A | A | B | F(-1) |
verified | N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 29 | 0 | 32 | 35 | 39 | 39 | 27 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.00 | 1.10 | 1.21 | 1.34 | 1.34 | 0.93 | 0.00 |
time (sec) |
N/A | 0.000 | 0.070 | 0.000 | 0.183 | 0.069 | 0.160 | 0.178 | 0.215 | 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 | 16 | 17 | 17 | 16 | 15 | 17 | 14 | 17 | 15 | 15 |
N.S. |
1 | 1.06 | 1.06 | 1.00 | 0.94 | 1.06 | 0.88 | 1.06 | 0.94 | 0.94 |
time (sec) |
N/A | 0.214 | 0.005 | 0.145 | 0.036 | 0.057 | 0.040 | 0.111 | 0.187 | 1.900 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 22 | 20 | 19 | 18 | 18 | 19 | 19 | 18 | 18 |
N.S. |
1 | 0.88 | 0.80 | 0.76 | 0.72 | 0.72 | 0.76 | 0.76 | 0.72 | 0.72 |
time (sec) |
N/A | 0.178 | 0.001 | 0.049 | 0.045 | 0.059 | 0.037 | 0.115 | 0.188 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | C | A | B | F(-1) | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 71 | 59 | 111 | 64 | 100 | 0 | 82 | 67 |
N.S. |
1 | 0.00 | 2.03 | 1.69 | 3.17 | 1.83 | 2.86 | 0.00 | 2.34 | 1.91 |
time (sec) |
N/A | 0.000 | 0.098 | 0.467 | 0.192 | 0.069 | 0.195 | 0.000 | 0.198 | 0.165 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 22 | 20 | 17 | 16 | 16 | 17 | 16 | 25 | 17 |
N.S. |
1 | 1.10 | 1.00 | 0.85 | 0.80 | 0.80 | 0.85 | 0.80 | 1.25 | 0.85 |
time (sec) |
N/A | 0.164 | 0.016 | 0.084 | 0.026 | 0.069 | 0.047 | 0.114 | 0.187 | 0.095 |
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 | 29 | 0 | 47 | 2156 | 61 | 58 | 70 | 259 | 77 | 59 |
N.S. |
1 | 0.00 | 1.62 | 74.34 | 2.10 | 2.00 | 2.41 | 8.93 | 2.66 | 2.03 |
time (sec) |
N/A | 0.000 | 1.362 | 0.223 | 0.076 | 0.079 | 0.272 | 0.466 | 0.197 | 2.004 |
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 | 26 | 27 | 30 | 30 | 22 | 26 | 27 | 26 |
N.S. |
1 | 0.00 | 1.08 | 1.12 | 1.25 | 1.25 | 0.92 | 1.08 | 1.12 | 1.08 |
time (sec) |
N/A | 0.000 | 0.041 | 1.432 | 0.241 | 0.064 | 0.306 | 0.133 | 0.198 | 2.235 |
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 | 48 | 43 | 44 | 44 | 42 | 44 | 50 | 44 |
N.S. |
1 | 0.00 | 1.66 | 1.48 | 1.52 | 1.52 | 1.45 | 1.52 | 1.72 | 1.52 |
time (sec) |
N/A | 0.000 | 0.510 | 2.588 | 0.082 | 0.077 | 0.410 | 0.428 | 0.202 | 2.668 |
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 | 32 | 89 | 111 | 89 | 92 | 97 | 105 | 107 | 121 | 90 |
N.S. |
1 | 2.78 | 3.47 | 2.78 | 2.88 | 3.03 | 3.28 | 3.34 | 3.78 | 2.81 |
time (sec) |
N/A | 0.344 | 0.024 | 0.318 | 0.032 | 0.065 | 2.619 | 0.117 | 0.186 | 2.138 |
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 | 34 | 25 | 30 | 24 | 30 | 26 | 22 | 32 | 26 |
N.S. |
1 | 1.36 | 1.00 | 1.20 | 0.96 | 1.20 | 1.04 | 0.88 | 1.28 | 1.04 |
time (sec) |
N/A | 0.804 | 0.140 | 1.776 | 0.122 | 0.069 | 0.471 | 0.181 | 0.196 | 2.095 |
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 | 19 | 0 | 15 | 14 | 33 | 30 | 27 | 14 | 15 | 14 |
N.S. |
1 | 0.00 | 0.79 | 0.74 | 1.74 | 1.58 | 1.42 | 0.74 | 0.79 | 0.74 |
time (sec) |
N/A | 0.000 | 0.135 | 0.119 | 0.074 | 0.071 | 0.185 | 0.115 | 0.192 | 2.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | B | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 223 | 42 | 62 | 41 | 39 | 79 | 41 | 39 |
N.S. |
1 | 0.00 | 8.26 | 1.56 | 2.30 | 1.52 | 1.44 | 2.93 | 1.52 | 1.44 |
time (sec) |
N/A | 0.000 | 1.149 | 1.869 | 0.115 | 0.064 | 0.124 | 0.708 | 0.191 | 2.199 |
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 | 24 | 18 | 17 | 17 | 15 | 17 | 21 | 18 |
N.S. |
1 | 0.79 | 0.86 | 0.64 | 0.61 | 0.61 | 0.54 | 0.61 | 0.75 | 0.64 |
time (sec) |
N/A | 0.169 | 0.003 | 0.116 | 0.036 | 0.062 | 0.043 | 0.115 | 0.200 | 1.861 |
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 | 7 | 6 | 6 | 5 | 6 | 11 | 7 |
N.S. |
1 | 0.50 | 0.50 | 0.50 | 0.43 | 0.43 | 0.36 | 0.43 | 0.79 | 0.50 |
time (sec) |
N/A | 0.149 | 0.013 | 0.061 | 0.034 | 0.058 | 0.034 | 0.124 | 0.191 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | C | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 0 | 21 | 17 | 30 | 20 | 12 | 16 | 20 | 16 |
N.S. |
1 | 0.00 | 1.31 | 1.06 | 1.88 | 1.25 | 0.75 | 1.00 | 1.25 | 1.00 |
time (sec) |
N/A | 0.000 | 0.056 | 0.155 | 0.061 | 0.063 | 0.039 | 0.114 | 0.188 | 1.913 |
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 | 23 | 0 | 31 | 45 | 76 | 101 | 94 | 107 | 84 | 0 |
N.S. |
1 | 0.00 | 1.35 | 1.96 | 3.30 | 4.39 | 4.09 | 4.65 | 3.65 | 0.00 |
time (sec) |
N/A | 0.000 | 5.104 | 0.214 | 0.280 | 0.076 | 0.385 | 1.384 | 0.208 | 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 | 22 | 22 | 20 | 37 | 19 | 17 | 28 | 20 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 1.68 | 0.86 | 0.77 | 1.27 | 0.91 | 0.86 |
time (sec) |
N/A | 1.298 | 0.240 | 0.994 | 0.152 | 0.073 | 4.944 | 0.151 | 0.207 | 2.191 |
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 | 31 | 18 | 29 | 28 | 28 | 26 | 28 | 33 | 33 |
N.S. |
1 | 1.72 | 1.00 | 1.61 | 1.56 | 1.56 | 1.44 | 1.56 | 1.83 | 1.83 |
time (sec) |
N/A | 0.281 | 0.021 | 0.166 | 0.047 | 0.063 | 0.056 | 0.122 | 0.201 | 0.142 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 12 | 12 | 13 | 12 | 10 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.09 | 1.09 | 1.18 | 1.09 | 0.91 | 0.91 | 1.09 | 1.09 | 1.09 |
time (sec) |
N/A | 0.161 | 0.001 | 0.073 | 0.026 | 0.063 | 0.049 | 0.116 | 0.200 | 1.910 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 28 | 29 | 26 | 80 | 52 | 27 | 60 | 73 | 69 |
N.S. |
1 | 1.17 | 1.21 | 1.08 | 3.33 | 2.17 | 1.12 | 2.50 | 3.04 | 2.88 |
time (sec) |
N/A | 0.830 | 0.073 | 0.727 | 0.163 | 0.065 | 0.122 | 0.127 | 0.229 | 2.441 |
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 | 23 | 0 | 26 | 25 | 24 | 24 | 24 | 0 | 54 | 24 |
N.S. |
1 | 0.00 | 1.13 | 1.09 | 1.04 | 1.04 | 1.04 | 0.00 | 2.35 | 1.04 |
time (sec) |
N/A | 0.000 | 2.377 | 0.655 | 0.074 | 0.077 | 0.525 | 0.000 | 0.193 | 2.157 |
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 | 19 | 23 | 22 | 22 | 29 | 22 | 28 | 22 |
N.S. |
1 | 0.00 | 0.86 | 1.05 | 1.00 | 1.00 | 1.32 | 1.00 | 1.27 | 1.00 |
time (sec) |
N/A | 0.000 | 0.066 | 0.835 | 0.149 | 0.062 | 0.104 | 0.127 | 0.189 | 2.842 |
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 | 30 | 39 | 28 | 46 | 34 | 34 | 29 | 49 | 147 | 31 |
N.S. |
1 | 1.30 | 0.93 | 1.53 | 1.13 | 1.13 | 0.97 | 1.63 | 4.90 | 1.03 |
time (sec) |
N/A | 1.514 | 0.120 | 1.158 | 0.106 | 0.069 | 0.186 | 0.233 | 200.033 | 2.261 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 55 | 22 | 39 | 19 | 22 | 34 | 78 |
N.S. |
1 | 0.00 | 1.00 | 2.39 | 0.96 | 1.70 | 0.83 | 0.96 | 1.48 | 3.39 |
time (sec) |
N/A | 0.000 | 0.080 | 0.386 | 0.141 | 0.067 | 0.113 | 0.247 | 0.176 | 2.256 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 49 | 24 | 42 | 26 | 29 | 501 | 41 | 40 |
N.S. |
1 | 0.00 | 1.96 | 0.96 | 1.68 | 1.04 | 1.16 | 20.04 | 1.64 | 1.60 |
time (sec) |
N/A | 0.000 | 7.554 | 0.418 | 0.092 | 0.065 | 0.080 | 0.128 | 0.182 | 3.368 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 38 | 53 | 39 | 35 | 46 | 51 | 55 | 46 | 54 |
N.S. |
1 | 1.65 | 2.30 | 1.70 | 1.52 | 2.00 | 2.22 | 2.39 | 2.00 | 2.35 |
time (sec) |
N/A | 0.750 | 0.030 | 155.041 | 0.159 | 0.070 | 0.154 | 0.132 | 0.170 | 2.178 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 47 | 31 | 35 | 30 | 50 | 27 | 54 | 46 | 56 |
N.S. |
1 | 1.88 | 1.24 | 1.40 | 1.20 | 2.00 | 1.08 | 2.16 | 1.84 | 2.24 |
time (sec) |
N/A | 1.926 | 6.526 | 0.390 | 0.077 | 0.069 | 0.087 | 0.117 | 0.168 | 2.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 182 | 163 | 154 | 149 | 240 | 168 | 93 | 192 | 640 |
N.S. |
1 | 6.28 | 5.62 | 5.31 | 5.14 | 8.28 | 5.79 | 3.21 | 6.62 | 22.07 |
time (sec) |
N/A | 0.965 | 0.129 | 3.747 | 0.055 | 0.071 | 18.261 | 0.140 | 200.026 | 20.964 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 64 | 96 | 34 | 317 | 31 | 27 | 45 | 176 | 32 |
N.S. |
1 | 1.94 | 2.91 | 1.03 | 9.61 | 0.94 | 0.82 | 1.36 | 5.33 | 0.97 |
time (sec) |
N/A | 1.026 | 0.110 | 1.109 | 0.171 | 0.068 | 0.130 | 0.186 | 0.198 | 2.579 |
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 | 21 | 15 | 15 | 15 | 15 | 15 | 17 | 14 |
N.S. |
1 | 1.00 | 0.84 | 0.60 | 0.60 | 0.60 | 0.60 | 0.60 | 0.68 | 0.56 |
time (sec) |
N/A | 0.163 | 0.005 | 0.091 | 0.045 | 0.065 | 0.040 | 0.116 | 0.196 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | A | B | B | F(-2) | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 64 | 97 | 104 | 52 | 82 | 58 | 0 | 117 | 48 |
N.S. |
1 | 2.13 | 3.23 | 3.47 | 1.73 | 2.73 | 1.93 | 0.00 | 3.90 | 1.60 |
time (sec) |
N/A | 0.702 | 0.089 | 1.145 | 0.042 | 0.075 | 0.901 | 0.000 | 0.186 | 0.402 |
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 | 26 | 0 | 23 | 27 | 37 | 21 | 27 | 0 | 35 | 34 |
N.S. |
1 | 0.00 | 0.88 | 1.04 | 1.42 | 0.81 | 1.04 | 0.00 | 1.35 | 1.31 |
time (sec) |
N/A | 0.000 | 0.108 | 0.173 | 0.149 | 0.075 | 0.091 | 0.000 | 0.182 | 0.173 |
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 | 13 | 31 | 14 | 12 | 25 | 11 | 10 | 11 | 16 | 9 |
N.S. |
1 | 2.38 | 1.08 | 0.92 | 1.92 | 0.85 | 0.77 | 0.85 | 1.23 | 0.69 |
time (sec) |
N/A | 0.174 | 0.028 | 0.099 | 0.034 | 0.062 | 0.045 | 0.121 | 0.188 | 0.046 |
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 | 17 | 20 | 24 | 17 | 17 | 24 | 18 | 27 | 35 |
N.S. |
1 | 1.00 | 1.18 | 1.41 | 1.00 | 1.00 | 1.41 | 1.06 | 1.59 | 2.06 |
time (sec) |
N/A | 0.147 | 0.010 | 0.241 | 0.033 | 0.060 | 0.046 | 0.120 | 0.191 | 2.176 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | B | B | B | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 0 | 33 | 174 | 85 | 87 | 174 | 192 | 155 |
N.S. |
1 | 0.00 | 0.00 | 1.06 | 5.61 | 2.74 | 2.81 | 5.61 | 6.19 | 5.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.077 | 0.641 | 0.072 | 1.044 | 0.510 | 5.586 | 2.848 |
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 | 26 | 20 | 15 | 14 | 22 | 14 | 59 | 22 | 14 |
N.S. |
1 | 1.30 | 1.00 | 0.75 | 0.70 | 1.10 | 0.70 | 2.95 | 1.10 | 0.70 |
time (sec) |
N/A | 0.204 | 0.027 | 0.219 | 0.045 | 0.066 | 0.057 | 0.124 | 0.176 | 1.973 |
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 | 24 | 28 | 26 | 27 | 47 | 46 | 27 | 47 | 52 | 0 |
N.S. |
1 | 1.17 | 1.08 | 1.12 | 1.96 | 1.92 | 1.12 | 1.96 | 2.17 | 0.00 |
time (sec) |
N/A | 0.922 | 0.731 | 1.188 | 0.154 | 0.072 | 0.063 | 0.126 | 0.184 | 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 | 14 | 12 | 10 | 9 | 9 | 10 | 9 | 13 | 11 |
N.S. |
1 | 0.64 | 0.55 | 0.45 | 0.41 | 0.41 | 0.45 | 0.41 | 0.59 | 0.50 |
time (sec) |
N/A | 0.143 | 0.001 | 0.286 | 0.034 | 0.057 | 0.035 | 0.117 | 0.178 | 0.038 |
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 | 37 | 27 | 47 | 28 | 22 | 26 | 38 | 26 |
N.S. |
1 | 0.00 | 1.48 | 1.08 | 1.88 | 1.12 | 0.88 | 1.04 | 1.52 | 1.04 |
time (sec) |
N/A | 0.000 | 10.118 | 0.227 | 0.097 | 0.068 | 0.113 | 0.118 | 0.188 | 0.259 |
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 | 7 | 7 | 7 | 6 | 5 | 5 | 7 | 5 | 5 | 5 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.71 | 0.71 | 1.00 | 0.71 | 0.71 | 0.71 |
time (sec) |
N/A | 0.126 | 0.000 | 0.040 | 0.028 | 0.050 | 0.015 | 0.112 | 0.189 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 57 | 30 | 32 | 57 | 30 | 29 | 0 | 32 | 34 |
N.S. |
1 | 2.19 | 1.15 | 1.23 | 2.19 | 1.15 | 1.12 | 0.00 | 1.23 | 1.31 |
time (sec) |
N/A | 0.608 | 0.240 | 0.926 | 0.156 | 0.074 | 0.121 | 0.000 | 0.198 | 2.155 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 23 | 34 | 86 | 26 | 20 | 36 | 410 | 0 |
N.S. |
1 | 0.00 | 0.96 | 1.42 | 3.58 | 1.08 | 0.83 | 1.50 | 17.08 | 0.00 |
time (sec) |
N/A | 0.000 | 0.240 | 0.943 | 0.168 | 0.059 | 0.139 | 0.279 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 22 | 22 | 20 | 25 | 19 | 19 | 19 | 20 | 19 |
N.S. |
1 | 1.10 | 1.10 | 1.00 | 1.25 | 0.95 | 0.95 | 0.95 | 1.00 | 0.95 |
time (sec) |
N/A | 0.783 | 0.126 | 0.276 | 0.156 | 0.068 | 0.146 | 0.132 | 0.180 | 2.233 |
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 | 25 | 23 | 26 | 23 | 36 | 62 | 24 | 22 |
N.S. |
1 | 0.00 | 0.89 | 0.82 | 0.93 | 0.82 | 1.29 | 2.21 | 0.86 | 0.79 |
time (sec) |
N/A | 0.000 | 0.456 | 19.243 | 0.201 | 0.065 | 0.128 | 0.133 | 0.193 | 2.478 |
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 | 28 | 152 | 26 | 93 | 120 | 120 | 153 | 120 | 146 | 96 |
N.S. |
1 | 5.43 | 0.93 | 3.32 | 4.29 | 4.29 | 5.46 | 4.29 | 5.21 | 3.43 |
time (sec) |
N/A | 0.278 | 0.020 | 0.289 | 0.025 | 0.075 | 0.041 | 0.112 | 0.174 | 2.038 |
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 | 22 | 25 | 19 | 18 | 26 | 17 | 18 | 24 | 17 |
N.S. |
1 | 1.22 | 1.39 | 1.06 | 1.00 | 1.44 | 0.94 | 1.00 | 1.33 | 0.94 |
time (sec) |
N/A | 0.274 | 0.027 | 0.243 | 0.184 | 0.074 | 1.255 | 0.110 | 0.181 | 2.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | C | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 88 | 198 | 51 | 1477 | 193 | 291 | 415 | 57 | 586 |
N.S. |
1 | 2.75 | 6.19 | 1.59 | 46.16 | 6.03 | 9.09 | 12.97 | 1.78 | 18.31 |
time (sec) |
N/A | 1.840 | 0.368 | 0.976 | 0.159 | 0.076 | 1.310 | 0.135 | 0.195 | 2.236 |
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 | 27 | 23 | 24 | 28 | 22 | 28 | 38 | 22 |
N.S. |
1 | 0.00 | 0.87 | 0.74 | 0.77 | 0.90 | 0.71 | 0.90 | 1.23 | 0.71 |
time (sec) |
N/A | 0.000 | 0.156 | 0.113 | 0.034 | 0.066 | 0.099 | 0.118 | 0.183 | 2.082 |
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 | 25 | 31 | 31 | 26 | 32 | 29 | 26 | 30 | 32 | 26 |
N.S. |
1 | 1.24 | 1.24 | 1.04 | 1.28 | 1.16 | 1.04 | 1.20 | 1.28 | 1.04 |
time (sec) |
N/A | 0.268 | 0.032 | 0.358 | 0.066 | 0.065 | 0.056 | 0.113 | 0.184 | 0.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 20 | 23 | 23 | 0 | 51 | 22 | 77 | 79 | 22 |
N.S. |
1 | 0.95 | 1.10 | 1.10 | 0.00 | 2.43 | 1.05 | 3.67 | 3.76 | 1.05 |
time (sec) |
N/A | 0.604 | 0.018 | 0.493 | 0.000 | 0.068 | 0.082 | 0.117 | 0.192 | 0.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 120 | 23 | 23 | 51 | 39 | 20 | 47 | 55 | 22 |
N.S. |
1 | 3.87 | 0.74 | 0.74 | 1.65 | 1.26 | 0.65 | 1.52 | 1.77 | 0.71 |
time (sec) |
N/A | 1.640 | 1.107 | 0.516 | 0.154 | 0.068 | 0.086 | 0.117 | 0.173 | 2.140 |
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 | 32 | 21 | 22 | 16 | 21 | 27 | 16 | 26 | 18 |
N.S. |
1 | 1.52 | 1.00 | 1.05 | 0.76 | 1.00 | 1.29 | 0.76 | 1.24 | 0.86 |
time (sec) |
N/A | 0.311 | 0.127 | 0.238 | 0.136 | 0.063 | 0.119 | 0.136 | 0.183 | 0.068 |
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 | 26 | 0 | 38 | 48 | 43 | 43 | 41 | 38 | 49 | 60 |
N.S. |
1 | 0.00 | 1.46 | 1.85 | 1.65 | 1.65 | 1.58 | 1.46 | 1.88 | 2.31 |
time (sec) |
N/A | 0.000 | 0.854 | 9.938 | 0.083 | 0.067 | 0.220 | 0.124 | 0.189 | 2.150 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 26 | 31 | 0 | 50 | 31 | 70 | 77 | 27 |
N.S. |
1 | 0.00 | 0.96 | 1.15 | 0.00 | 1.85 | 1.15 | 2.59 | 2.85 | 1.00 |
time (sec) |
N/A | 0.000 | 0.108 | 0.032 | 0.000 | 0.070 | 0.261 | 0.119 | 0.196 | 2.152 |
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 | 28 | 26 | 37 | 55 | 20 | 37 | 46 | 31 |
N.S. |
1 | 0.00 | 0.85 | 0.79 | 1.12 | 1.67 | 0.61 | 1.12 | 1.39 | 0.94 |
time (sec) |
N/A | 0.000 | 3.681 | 0.655 | 0.070 | 0.070 | 0.077 | 0.130 | 0.186 | 2.183 |
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 | 24 | 0 | 46 | 20 | 26 | 22 | 48 | 26 | 30 | 19 |
N.S. |
1 | 0.00 | 1.92 | 0.83 | 1.08 | 0.92 | 2.00 | 1.08 | 1.25 | 0.79 |
time (sec) |
N/A | 0.000 | 2.409 | 0.352 | 0.168 | 0.072 | 0.106 | 0.113 | 0.179 | 2.224 |
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 | 13 | 13 | 12 | 12 | 14 | 12 | 13 | 12 |
N.S. |
1 | 0.00 | 0.93 | 0.93 | 0.86 | 0.86 | 1.00 | 0.86 | 0.93 | 0.86 |
time (sec) |
N/A | 0.000 | 0.105 | 0.313 | 0.089 | 0.066 | 0.153 | 0.146 | 0.177 | 0.277 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | C | F | A | B | F | B | F(-1) |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 77 | 266 | 0 | 66 | 100 | 0 | 89 | 0 |
N.S. |
1 | 0.00 | 2.20 | 7.60 | 0.00 | 1.89 | 2.86 | 0.00 | 2.54 | 0.00 |
time (sec) |
N/A | 0.000 | 0.238 | 0.043 | 0.000 | 0.081 | 0.684 | 0.000 | 0.188 | 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 | 29 | 25 | 23 | 22 | 21 | 21 | 22 | 21 | 20 | 21 |
N.S. |
1 | 0.86 | 0.79 | 0.76 | 0.72 | 0.72 | 0.76 | 0.72 | 0.69 | 0.72 |
time (sec) |
N/A | 0.158 | 0.003 | 0.117 | 0.024 | 0.062 | 0.055 | 0.106 | 0.188 | 1.974 |
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 | 25 | 0 | 24 | 67 | 98 | 43 | 22 | 1320 | 65 | 118 |
N.S. |
1 | 0.00 | 0.96 | 2.68 | 3.92 | 1.72 | 0.88 | 52.80 | 2.60 | 4.72 |
time (sec) |
N/A | 0.000 | 0.090 | 39.142 | 0.162 | 0.071 | 0.273 | 3.062 | 0.186 | 2.940 |
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 | 28 | 30 | 33 | 33 | 27 | 34 | 28 | 402 |
N.S. |
1 | 0.00 | 1.27 | 1.36 | 1.50 | 1.50 | 1.23 | 1.55 | 1.27 | 18.27 |
time (sec) |
N/A | 0.000 | 0.059 | 10.474 | 0.095 | 0.067 | 0.119 | 0.135 | 0.197 | 2.864 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 32 | 30 | 29 | 77 | 31 | 0 | 250 | 32 |
N.S. |
1 | 0.00 | 1.10 | 1.03 | 1.00 | 2.66 | 1.07 | 0.00 | 8.62 | 1.10 |
time (sec) |
N/A | 0.000 | 1.855 | 1.057 | 0.369 | 0.067 | 0.168 | 0.000 | 0.304 | 2.304 |
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 | 30 | 0 | 40 | 41 | 41 | 40 | 37 | 38 | 41 | 39 |
N.S. |
1 | 0.00 | 1.33 | 1.37 | 1.37 | 1.33 | 1.23 | 1.27 | 1.37 | 1.30 |
time (sec) |
N/A | 0.000 | 0.112 | 6.984 | 0.194 | 0.071 | 0.170 | 0.243 | 0.171 | 2.066 |
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 | 582 | 31 | 28 | 308 | 34 | 27 | 38 | 95 | 27 |
N.S. |
1 | 18.19 | 0.97 | 0.88 | 9.62 | 1.06 | 0.84 | 1.19 | 2.97 | 0.84 |
time (sec) |
N/A | 2.521 | 0.143 | 1.167 | 0.189 | 0.079 | 0.134 | 0.130 | 0.184 | 2.271 |
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 | 27 | 25 | 17 | 18 | 19 | 14 | 18 | 19 | 18 |
N.S. |
1 | 1.08 | 1.00 | 0.68 | 0.72 | 0.76 | 0.56 | 0.72 | 0.76 | 0.72 |
time (sec) |
N/A | 0.388 | 0.050 | 0.272 | 0.065 | 0.064 | 0.116 | 0.113 | 0.182 | 2.028 |
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 | 18 | 0 | 15 | 16 | 25 | 20 | 20 | 0 | 165 | 20 |
N.S. |
1 | 0.00 | 0.83 | 0.89 | 1.39 | 1.11 | 1.11 | 0.00 | 9.17 | 1.11 |
time (sec) |
N/A | 0.000 | 0.060 | 0.310 | 0.114 | 0.063 | 0.151 | 0.000 | 0.203 | 2.086 |
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 | 45 | 25 | 32 | 39 | 33 | 32 | 33 | 43 | 37 |
N.S. |
1 | 1.80 | 1.00 | 1.28 | 1.56 | 1.32 | 1.28 | 1.32 | 1.72 | 1.48 |
time (sec) |
N/A | 0.190 | 0.103 | 0.365 | 0.040 | 0.066 | 0.091 | 0.117 | 0.184 | 2.023 |
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 | 28 | 17 | 15 | 15 | 15 | 19 | 15 | 20 | 15 |
N.S. |
1 | 1.40 | 0.85 | 0.75 | 0.75 | 0.75 | 0.95 | 0.75 | 1.00 | 0.75 |
time (sec) |
N/A | 0.195 | 0.019 | 0.089 | 0.028 | 0.065 | 0.047 | 0.110 | 0.169 | 1.980 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 40 | 35 | 47 | 39 | 48 | 48 | 39 | 440 | 0 |
N.S. |
1 | 1.05 | 0.92 | 1.24 | 1.03 | 1.26 | 1.26 | 1.03 | 11.58 | 0.00 |
time (sec) |
N/A | 3.560 | 0.165 | 0.679 | 0.100 | 0.069 | 0.483 | 0.149 | 0.328 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 24 | 19 | 19 | 20 | 19 | 19 | 25 | 18 |
N.S. |
1 | 0.00 | 1.00 | 0.79 | 0.79 | 0.83 | 0.79 | 0.79 | 1.04 | 0.75 |
time (sec) |
N/A | 0.000 | 0.097 | 0.426 | 0.113 | 0.066 | 0.292 | 0.142 | 0.177 | 2.217 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 24 | 14 | 14 | 22 | 21 | 20 | 22 | 21 | 16 |
N.S. |
1 | 1.20 | 0.70 | 0.70 | 1.10 | 1.05 | 1.00 | 1.10 | 1.05 | 0.80 |
time (sec) |
N/A | 0.165 | 0.006 | 0.115 | 0.030 | 0.057 | 0.054 | 0.124 | 0.189 | 0.043 |
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 | 19 | 24 | 19 | 18 | 18 | 15 | 18 | 19 | 18 |
N.S. |
1 | 1.06 | 1.33 | 1.06 | 1.00 | 1.00 | 0.83 | 1.00 | 1.06 | 1.00 |
time (sec) |
N/A | 0.718 | 0.431 | 0.105 | 0.076 | 0.068 | 0.087 | 0.115 | 0.201 | 0.149 |
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 | 19 | 17 | 21 | 21 | 14 | 21 | 18 | 16 |
N.S. |
1 | 1.33 | 1.06 | 0.94 | 1.17 | 1.17 | 0.78 | 1.17 | 1.00 | 0.89 |
time (sec) |
N/A | 0.153 | 0.004 | 0.083 | 0.028 | 0.068 | 0.023 | 0.110 | 0.174 | 0.064 |
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 | 13 | 20 | 11 | 10 | 71 | 9 | 10 | 9 | 9 | 9 |
N.S. |
1 | 1.54 | 0.85 | 0.77 | 5.46 | 0.69 | 0.77 | 0.69 | 0.69 | 0.69 |
time (sec) |
N/A | 0.392 | 0.049 | 0.160 | 0.166 | 0.069 | 0.059 | 0.115 | 0.175 | 0.185 |
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 | 12 | 21 | 21 | 20 | 19 | 19 | 17 | 21 | 19 | 19 |
N.S. |
1 | 1.75 | 1.75 | 1.67 | 1.58 | 1.58 | 1.42 | 1.75 | 1.58 | 1.58 |
time (sec) |
N/A | 0.328 | 0.006 | 0.049 | 0.045 | 0.060 | 0.055 | 0.113 | 0.178 | 0.088 |
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 | 20 | 87 | 20 | 88 | 87 | 70 | 85 | 107 | 35 | 21 |
N.S. |
1 | 4.35 | 1.00 | 4.40 | 4.35 | 3.50 | 4.25 | 5.35 | 1.75 | 1.05 |
time (sec) |
N/A | 1.099 | 0.194 | 0.043 | 0.148 | 0.070 | 0.219 | 0.117 | 0.176 | 2.071 |
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 | 23 | 23 | 24 | 23 | 34 | 19 | 24 | 33 | 23 |
N.S. |
1 | 0.82 | 0.82 | 0.86 | 0.82 | 1.21 | 0.68 | 0.86 | 1.18 | 0.82 |
time (sec) |
N/A | 0.268 | 0.008 | 0.062 | 0.028 | 0.056 | 0.045 | 0.118 | 0.198 | 0.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | A | A | B | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 0 | 45 | 64 | 47 | 48 | 65 | 48 | 44688 |
N.S. |
1 | 0.00 | 0.00 | 1.32 | 1.88 | 1.38 | 1.41 | 1.91 | 1.41 | 1314.35 |
time (sec) |
N/A | 0.000 | 0.000 | 8.829 | 0.188 | 0.074 | 0.143 | 0.149 | 0.188 | 5.825 |
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 | 29 | 0 | 29 | 38 | 96 | 41 | 24 | 40 | 48 | 54 |
N.S. |
1 | 0.00 | 1.00 | 1.31 | 3.31 | 1.41 | 0.83 | 1.38 | 1.66 | 1.86 |
time (sec) |
N/A | 0.000 | 0.055 | 1.881 | 0.146 | 0.072 | 0.161 | 0.144 | 0.189 | 2.442 |
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 | 29 | 31 | 30 | 27 | 26 | 26 | 27 | 0 | 31 | 28 |
N.S. |
1 | 1.07 | 1.03 | 0.93 | 0.90 | 0.90 | 0.93 | 0.00 | 1.07 | 0.97 |
time (sec) |
N/A | 0.343 | 0.649 | 0.346 | 0.145 | 0.064 | 0.129 | 0.000 | 0.186 | 2.110 |
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 | 12 | 11 | 10 | 10 | 8 | 11 | 10 | 10 |
N.S. |
1 | 1.00 | 1.20 | 1.10 | 1.00 | 1.00 | 0.80 | 1.10 | 1.00 | 1.00 |
time (sec) |
N/A | 0.154 | 0.003 | 0.156 | 0.032 | 0.058 | 0.038 | 0.109 | 0.182 | 0.034 |
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 | 33 | 24 | 26 | 19 | 20 | 26 | 17 | 20 | 25 | 20 |
N.S. |
1 | 0.73 | 0.79 | 0.58 | 0.61 | 0.79 | 0.52 | 0.61 | 0.76 | 0.61 |
time (sec) |
N/A | 0.254 | 0.008 | 0.083 | 0.024 | 0.055 | 0.038 | 0.118 | 0.176 | 1.969 |
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 | 26 | 52 | 24 | 27 | 37 | 26 | 24 | 54 | 24 | 29 |
N.S. |
1 | 2.00 | 0.92 | 1.04 | 1.42 | 1.00 | 0.92 | 2.08 | 0.92 | 1.12 |
time (sec) |
N/A | 0.199 | 0.054 | 0.405 | 0.031 | 0.064 | 0.058 | 0.113 | 0.178 | 0.070 |
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 | 25 | 86 | 101 | 74 | 78 | 80 | 117 | 81 | 105 | 73 |
N.S. |
1 | 3.44 | 4.04 | 2.96 | 3.12 | 3.20 | 4.68 | 3.24 | 4.20 | 2.92 |
time (sec) |
N/A | 0.268 | 0.160 | 0.933 | 0.033 | 0.083 | 0.157 | 0.112 | 0.192 | 2.083 |
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 | 28 | 135 | 31 | 27 | 89 | 37 | 24 | 41 | 45 | 26 |
N.S. |
1 | 4.82 | 1.11 | 0.96 | 3.18 | 1.32 | 0.86 | 1.46 | 1.61 | 0.93 |
time (sec) |
N/A | 1.169 | 0.027 | 0.421 | 0.072 | 0.066 | 0.085 | 0.117 | 0.198 | 0.182 |
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 | 27 | 25 | 27 | 26 | 27 | 35 | 40 | 25 |
N.S. |
1 | 1.15 | 1.00 | 0.93 | 1.00 | 0.96 | 1.00 | 1.30 | 1.48 | 0.93 |
time (sec) |
N/A | 0.570 | 0.058 | 8.511 | 0.241 | 0.068 | 107.034 | 0.686 | 0.195 | 2.506 |
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 | 25 | 0 | 20 | 23 | 18 | 22 | 19 | 18 | 58 | 19 |
N.S. |
1 | 0.00 | 0.80 | 0.92 | 0.72 | 0.88 | 0.76 | 0.72 | 2.32 | 0.76 |
time (sec) |
N/A | 0.000 | 0.268 | 0.396 | 0.177 | 0.069 | 0.131 | 0.187 | 32.415 | 2.058 |
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 | 12 | 12 | 13 | 12 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 0.67 | 0.67 | 0.72 | 0.67 | 0.67 | 0.56 | 0.67 | 0.67 | 0.67 |
time (sec) |
N/A | 0.151 | 0.000 | 0.066 | 0.042 | 0.053 | 0.017 | 0.110 | 0.191 | 0.022 |
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 | 32 | 29 | 29 | 27 | 39 | 33 | 26 | 33 | 34 | 26 |
N.S. |
1 | 0.91 | 0.91 | 0.84 | 1.22 | 1.03 | 0.81 | 1.03 | 1.06 | 0.81 |
time (sec) |
N/A | 0.533 | 0.120 | 2.351 | 0.061 | 0.066 | 0.080 | 0.120 | 0.183 | 2.041 |
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 | 17 | 21 | 15 | 15 | 14 | 18 | 15 | 18 | 19 | 14 |
N.S. |
1 | 1.24 | 0.88 | 0.88 | 0.82 | 1.06 | 0.88 | 1.06 | 1.12 | 0.82 |
time (sec) |
N/A | 0.244 | 0.009 | 0.303 | 0.126 | 0.062 | 0.068 | 0.111 | 0.194 | 2.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 32 | 32 | 301 | 41 | 39 | 76 | 45 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 9.41 | 1.28 | 1.22 | 2.38 | 1.41 | 0.00 |
time (sec) |
N/A | 0.000 | 0.058 | 3.618 | 1.925 | 0.074 | 4.101 | 0.128 | 0.205 | 0.000 |
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 | 21 | 79 | 19 | 18 | 21 | 35 | 29 | 27 | 15 | 17 |
N.S. |
1 | 3.76 | 0.90 | 0.86 | 1.00 | 1.67 | 1.38 | 1.29 | 0.71 | 0.81 |
time (sec) |
N/A | 0.492 | 0.111 | 0.806 | 0.148 | 0.071 | 0.068 | 0.109 | 0.225 | 2.268 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 128 | 23 | 23 | 141 | 33 | 29 | 0 | 34 | 0 |
N.S. |
1 | 4.92 | 0.88 | 0.88 | 5.42 | 1.27 | 1.12 | 0.00 | 1.31 | 0.00 |
time (sec) |
N/A | 13.753 | 0.124 | 40.199 | 1.016 | 0.072 | 0.369 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 26 | 22 | 75 | 21 | 15 | 0 | 28 | 21 |
N.S. |
1 | 0.00 | 1.08 | 0.92 | 3.12 | 0.88 | 0.62 | 0.00 | 1.17 | 0.88 |
time (sec) |
N/A | 0.000 | 0.361 | 0.842 | 0.303 | 0.073 | 0.175 | 0.000 | 0.182 | 2.599 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F(-2) | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 34 | 32 | 0 | 31 | 42 | 35 | 32 | 29 |
N.S. |
1 | 0.00 | 1.10 | 1.03 | 0.00 | 1.00 | 1.35 | 1.13 | 1.03 | 0.94 |
time (sec) |
N/A | 0.000 | 0.520 | 10.903 | 0.000 | 0.069 | 0.250 | 0.138 | 0.215 | 3.181 |
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 | 21 | 21 | 17 | 21 | 36 | 18 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 0.95 | 0.95 | 0.77 | 0.95 | 1.64 | 0.82 |
time (sec) |
N/A | 0.000 | 0.143 | 0.792 | 0.144 | 0.063 | 0.068 | 0.121 | 0.224 | 2.713 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 40 | 38 | 38 | 47 | 48 | 37 | 77 | 71 | 0 |
N.S. |
1 | 1.38 | 1.31 | 1.31 | 1.62 | 1.66 | 1.28 | 2.66 | 2.45 | 0.00 |
time (sec) |
N/A | 1.321 | 0.070 | 6.490 | 0.088 | 0.076 | 0.250 | 0.178 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | B | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 45 | 35 | 33 | 109 | 39 | 37 | 37 | 41 | 23 |
N.S. |
1 | 2.05 | 1.59 | 1.50 | 4.95 | 1.77 | 1.68 | 1.68 | 1.86 | 1.05 |
time (sec) |
N/A | 0.704 | 0.040 | 0.295 | 0.033 | 0.066 | 0.095 | 0.125 | 0.184 | 2.147 |