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 | 30 | 30 | 24 | 19 | 17 | 23 | 15 | 18 | 32 | 19 |
N.S. |
1 | 1.00 | 0.80 | 0.63 | 0.57 | 0.77 | 0.50 | 0.60 | 1.07 | 0.63 |
time (sec) |
N/A | 0.266 | 0.008 | 0.046 | 0.034 | 0.091 | 0.058 | 0.112 | 0.180 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F(-1) | B | B | B | B | B | B |
verified | N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 46 | 0 | 697 | 104 | 100 | 160 | 440 | 358 |
N.S. |
1 | 0.00 | 1.35 | 0.00 | 20.50 | 3.06 | 2.94 | 4.71 | 12.94 | 10.53 |
time (sec) |
N/A | 0.000 | 0.338 | 0.000 | 1.253 | 0.109 | 0.533 | 2.125 | 0.773 | 5.453 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 45 | 55 | 55 | 55 | 53 | 71 | 55 | 46 |
N.S. |
1 | 0.00 | 1.61 | 1.96 | 1.96 | 1.96 | 1.89 | 2.54 | 1.96 | 1.64 |
time (sec) |
N/A | 0.000 | 0.043 | 2.148 | 0.089 | 0.097 | 0.114 | 0.143 | 0.202 | 2.973 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 18 | 18 | 16 | 15 | 17 | 10 | 17 | 18 | 15 |
N.S. |
1 | 0.95 | 0.95 | 0.84 | 0.79 | 0.89 | 0.53 | 0.89 | 0.95 | 0.79 |
time (sec) |
N/A | 0.183 | 0.005 | 0.099 | 0.031 | 0.078 | 0.043 | 0.115 | 0.190 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 12 | 31 | 11 | 10 | 11 | 32 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 2.38 | 0.85 | 0.77 | 0.85 | 2.46 | 0.85 |
time (sec) |
N/A | 0.333 | 0.014 | 0.144 | 0.161 | 0.081 | 0.051 | 0.118 | 0.184 | 0.082 |
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 | 24 | 21 | 22 | 21 | 21 | 17 | 21 | 34 | 21 |
N.S. |
1 | 0.96 | 0.84 | 0.88 | 0.84 | 0.84 | 0.68 | 0.84 | 1.36 | 0.84 |
time (sec) |
N/A | 0.660 | 0.318 | 7.604 | 0.081 | 0.087 | 0.279 | 0.297 | 0.190 | 3.661 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | F(-1) | F(-1) | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 24 | 22 | 65 | 21 | 0 | 0 | 30 | 26 |
N.S. |
1 | 0.00 | 0.92 | 0.85 | 2.50 | 0.81 | 0.00 | 0.00 | 1.15 | 1.00 |
time (sec) |
N/A | 0.000 | 0.113 | 0.040 | 0.211 | 0.083 | 0.000 | 0.000 | 0.264 | 3.032 |
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 | 20 | 12 | 8 | 8 | 12 | 7 | 7 | 7 | 8 | 7 |
N.S. |
1 | 0.60 | 0.40 | 0.40 | 0.60 | 0.35 | 0.35 | 0.35 | 0.40 | 0.35 |
time (sec) |
N/A | 0.171 | 0.002 | 0.024 | 0.034 | 0.086 | 0.033 | 0.187 | 0.189 | 2.991 |
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 | 12 | 12 | 11 | 10 | 10 | 10 | 10 | 17 | 14 |
N.S. |
1 | 0.50 | 0.50 | 0.46 | 0.42 | 0.42 | 0.42 | 0.42 | 0.71 | 0.58 |
time (sec) |
N/A | 0.152 | 0.003 | 0.039 | 0.029 | 0.068 | 0.057 | 0.159 | 0.179 | 0.025 |
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 | 22 | 0 | 20 | 19 | 26 | 40 | 19 | 0 | 37 | 31 |
N.S. |
1 | 0.00 | 0.91 | 0.86 | 1.18 | 1.82 | 0.86 | 0.00 | 1.68 | 1.41 |
time (sec) |
N/A | 0.000 | 1.131 | 1.046 | 0.159 | 0.094 | 0.236 | 0.000 | 0.189 | 3.159 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 41 | 25 | 0 | 35 | 31 | 49 | 54 | 56 |
N.S. |
1 | 0.00 | 1.24 | 0.76 | 0.00 | 1.06 | 0.94 | 1.48 | 1.64 | 1.70 |
time (sec) |
N/A | 0.000 | 0.125 | 6.738 | 0.000 | 0.088 | 0.428 | 0.217 | 187.487 | 3.149 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | A | A | F(-1) | A | B | B |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 29 | 136 | 29 | 28 | 0 | 29 | 28 | 28 |
N.S. |
1 | 0.00 | 1.16 | 5.44 | 1.16 | 1.12 | 0.00 | 1.16 | 1.12 | 1.12 |
time (sec) |
N/A | 0.000 | 0.174 | 0.017 | 0.237 | 0.096 | 0.000 | 5.676 | 0.240 | 6.411 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | C | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 30 | 56 | 28 | 200 | 24 | 20 | 19 | 76 | 23 |
N.S. |
1 | 1.11 | 2.07 | 1.04 | 7.41 | 0.89 | 0.74 | 0.70 | 2.81 | 0.85 |
time (sec) |
N/A | 0.593 | 0.174 | 0.422 | 0.189 | 0.099 | 0.217 | 0.162 | 31.583 | 3.264 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | A | F(-1) | B | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 0 | 34 | 87 | 34 | 0 | 58 | 31 | 57 |
N.S. |
1 | 0.00 | 0.00 | 1.13 | 2.90 | 1.13 | 0.00 | 1.93 | 1.03 | 1.90 |
time (sec) |
N/A | 0.000 | 0.000 | 33.606 | 0.362 | 0.085 | 0.000 | 0.239 | 0.175 | 3.226 |
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 | 32 | 0 | 46 | 35 | 132 | 35 | 29 | 52 | 77 | 87 |
N.S. |
1 | 0.00 | 1.44 | 1.09 | 4.12 | 1.09 | 0.91 | 1.62 | 2.41 | 2.72 |
time (sec) |
N/A | 0.000 | 5.074 | 1.401 | 0.273 | 0.089 | 0.274 | 0.268 | 0.176 | 3.312 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 29 | 24 | 28 | 27 | 32 | 0 | 105 | 28 | 51 |
N.S. |
1 | 1.21 | 1.00 | 1.17 | 1.12 | 1.33 | 0.00 | 4.38 | 1.17 | 2.12 |
time (sec) |
N/A | 0.315 | 0.043 | 0.423 | 0.037 | 0.106 | 0.000 | 0.128 | 0.154 | 3.212 |
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 | 19 | 24 | 24 | 24 | 31 | 34 | 29 | 34 | 61 | 32 |
N.S. |
1 | 1.26 | 1.26 | 1.26 | 1.63 | 1.79 | 1.53 | 1.79 | 3.21 | 1.68 |
time (sec) |
N/A | 1.051 | 0.257 | 0.216 | 0.166 | 0.097 | 0.158 | 0.137 | 33.134 | 3.120 |
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 | 20 | 22 | 40 | 38 | 14 | 38 | 51 | 24 |
N.S. |
1 | 0.00 | 0.87 | 0.96 | 1.74 | 1.65 | 0.61 | 1.65 | 2.22 | 1.04 |
time (sec) |
N/A | 0.000 | 1.112 | 0.151 | 0.075 | 0.087 | 0.057 | 0.116 | 0.166 | 3.103 |
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 | 23 | 0 | 19 | 27 | 19 | 26 | 20 | 24 | 24 | 0 |
N.S. |
1 | 0.00 | 0.83 | 1.17 | 0.83 | 1.13 | 0.87 | 1.04 | 1.04 | 0.00 |
time (sec) |
N/A | 0.000 | 0.110 | 7.352 | 0.150 | 0.087 | 0.143 | 0.270 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 22 | 20 | 22 | 60 | 26 | 36 | 30 | 32 | 37 |
N.S. |
1 | 1.05 | 0.95 | 1.05 | 2.86 | 1.24 | 1.71 | 1.43 | 1.52 | 1.76 |
time (sec) |
N/A | 0.248 | 0.029 | 0.320 | 0.039 | 0.090 | 0.155 | 0.119 | 0.153 | 3.148 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | A | B | F | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 0 | 28 | 85 | 51 | 58 | 0 | 182 | 101 |
N.S. |
1 | 0.00 | 0.00 | 0.90 | 2.74 | 1.65 | 1.87 | 0.00 | 5.87 | 3.26 |
time (sec) |
N/A | 0.000 | 0.000 | 2.201 | 0.373 | 0.112 | 0.415 | 0.000 | 0.798 | 3.453 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F(-2) | A | F(-2) | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 24 | 22 | 0 | 21 | 0 | 27 | 28 | 28 |
N.S. |
1 | 0.00 | 0.86 | 0.79 | 0.00 | 0.75 | 0.00 | 0.96 | 1.00 | 1.00 |
time (sec) |
N/A | 0.000 | 0.172 | 0.570 | 0.000 | 0.092 | 0.000 | 0.121 | 0.153 | 3.265 |
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 | 28 | 30 | 29 | 28 | 28 | 26 | 29 | 28 | 28 |
N.S. |
1 | 1.04 | 1.11 | 1.07 | 1.04 | 1.04 | 0.96 | 1.07 | 1.04 | 1.04 |
time (sec) |
N/A | 0.212 | 0.003 | 0.051 | 0.028 | 0.073 | 0.049 | 0.114 | 0.148 | 0.025 |
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 | 26 | 0 | 39 | 17 | 0 | 16 | 20 | 16 | 33 | 18 |
N.S. |
1 | 0.00 | 1.50 | 0.65 | 0.00 | 0.62 | 0.77 | 0.62 | 1.27 | 0.69 |
time (sec) |
N/A | 0.000 | 3.187 | 0.162 | 0.000 | 0.085 | 0.075 | 0.147 | 0.156 | 2.984 |
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 | 28 | 0 | 26 | 31 | 91 | 34 | 19 | 69 | 53 | 25 |
N.S. |
1 | 0.00 | 0.93 | 1.11 | 3.25 | 1.21 | 0.68 | 2.46 | 1.89 | 0.89 |
time (sec) |
N/A | 0.000 | 0.536 | 2.393 | 0.225 | 0.090 | 12.892 | 0.136 | 0.155 | 3.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | A | F(-1) | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 25 | 60 | 51 | 120 | 45 | 0 | 40 | 34 | 59 |
N.S. |
1 | 1.39 | 3.33 | 2.83 | 6.67 | 2.50 | 0.00 | 2.22 | 1.89 | 3.28 |
time (sec) |
N/A | 0.464 | 1.424 | 0.233 | 0.307 | 0.085 | 0.000 | 0.237 | 0.158 | 3.034 |
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 | 26 | 36 | 25 | 29 | 31 | 31 | 29 | 31 | 29 | 29 |
N.S. |
1 | 1.38 | 0.96 | 1.12 | 1.19 | 1.19 | 1.12 | 1.19 | 1.12 | 1.12 |
time (sec) |
N/A | 0.179 | 0.009 | 0.107 | 0.029 | 0.081 | 0.066 | 0.111 | 0.152 | 2.927 |
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 | 35 | 0 | 0 | 42 | 120 | 41 | 41 | 90 | 49 | 41 |
N.S. |
1 | 0.00 | 0.00 | 1.20 | 3.43 | 1.17 | 1.17 | 2.57 | 1.40 | 1.17 |
time (sec) |
N/A | 0.000 | 0.000 | 2.762 | 0.179 | 0.108 | 0.442 | 5.093 | 0.159 | 3.876 |
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 | 46 | 44 | 38 | 24 | 41 | 39 | 47 | 45 | 28 |
N.S. |
1 | 1.53 | 1.47 | 1.27 | 0.80 | 1.37 | 1.30 | 1.57 | 1.50 | 0.93 |
time (sec) |
N/A | 0.250 | 0.013 | 0.326 | 0.030 | 0.082 | 0.122 | 0.114 | 0.157 | 2.979 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 116 | 22 | 18 | 158 | 26 | 32 | 55 | 25 | 20 |
N.S. |
1 | 5.27 | 1.00 | 0.82 | 7.18 | 1.18 | 1.45 | 2.50 | 1.14 | 0.91 |
time (sec) |
N/A | 0.842 | 0.113 | 0.364 | 0.159 | 0.078 | 0.156 | 0.118 | 0.154 | 2.973 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 47 | 24 | 57 | 149 | 58 | 0 | 0 | 60 |
N.S. |
1 | 0.00 | 1.68 | 0.86 | 2.04 | 5.32 | 2.07 | 0.00 | 0.00 | 2.14 |
time (sec) |
N/A | 0.000 | 0.407 | 34.784 | 1.407 | 0.106 | 12.546 | 0.000 | 1.932 | 3.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 27 | 28 | 26 | 70 | 26 | 22 | 26 | 283 | 26 |
N.S. |
1 | 1.04 | 1.08 | 1.00 | 2.69 | 1.00 | 0.85 | 1.00 | 10.88 | 1.00 |
time (sec) |
N/A | 0.778 | 0.156 | 0.338 | 0.536 | 0.102 | 0.132 | 0.114 | 0.187 | 3.050 |
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 | 12 | 26 | 12 | 12 | 14 | 21 | 10 | 26 | 23 | 11 |
N.S. |
1 | 2.17 | 1.00 | 1.00 | 1.17 | 1.75 | 0.83 | 2.17 | 1.92 | 0.92 |
time (sec) |
N/A | 0.198 | 0.010 | 0.071 | 0.039 | 0.095 | 0.055 | 0.112 | 0.156 | 0.039 |
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 | 9 | 8 | 8 | 8 | 8 | 10 | 9 |
N.S. |
1 | 0.92 | 0.92 | 0.75 | 0.67 | 0.67 | 0.67 | 0.67 | 0.83 | 0.75 |
time (sec) |
N/A | 0.158 | 0.013 | 0.045 | 0.029 | 0.079 | 0.050 | 0.113 | 0.154 | 0.037 |
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 | 29 | 31 | 31 | 29 | 29 | 32 | 42 | 30 | 2977 |
N.S. |
1 | 1.45 | 1.55 | 1.55 | 1.45 | 1.45 | 1.60 | 2.10 | 1.50 | 148.85 |
time (sec) |
N/A | 0.310 | 0.021 | 0.164 | 0.040 | 0.076 | 0.764 | 0.116 | 0.156 | 3.371 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 132 | 28 | 25 | 281 | 38 | 27 | 43 | 44 | 31 |
N.S. |
1 | 4.71 | 1.00 | 0.89 | 10.04 | 1.36 | 0.96 | 1.54 | 1.57 | 1.11 |
time (sec) |
N/A | 0.692 | 0.166 | 12.799 | 0.097 | 0.082 | 0.213 | 0.133 | 0.158 | 3.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 15 | 0 | 17 | 14 | 0 | 23 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.00 | 1.00 | 0.82 | 0.00 | 1.35 | 0.94 |
time (sec) |
N/A | 0.175 | 0.052 | 0.125 | 0.000 | 0.078 | 0.079 | 0.000 | 0.155 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 23 | 23 | 31 | 53 | 21 | 29 | 35 | 37 | 17 |
N.S. |
1 | 1.05 | 1.05 | 1.41 | 2.41 | 0.95 | 1.32 | 1.59 | 1.68 | 0.77 |
time (sec) |
N/A | 0.566 | 0.022 | 0.246 | 0.082 | 0.095 | 3.187 | 0.120 | 0.157 | 3.193 |
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 | 24 | 21 | 20 | 27 | 26 | 0 | 29 | 23 |
N.S. |
1 | 0.00 | 1.04 | 0.91 | 0.87 | 1.17 | 1.13 | 0.00 | 1.26 | 1.00 |
time (sec) |
N/A | 0.000 | 0.077 | 7.359 | 0.206 | 0.097 | 0.309 | 0.000 | 0.155 | 3.210 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | F(-2) | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 22 | 26 | 33 | 28 | 0 | 0 | 1324 | 31 |
N.S. |
1 | 0.00 | 0.96 | 1.13 | 1.43 | 1.22 | 0.00 | 0.00 | 57.57 | 1.35 |
time (sec) |
N/A | 0.000 | 0.173 | 55.035 | 0.224 | 0.083 | 0.000 | 0.000 | 0.825 | 3.596 |
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 | 16 | 82 | 53 | 48 | 78 | 53 | 53 | 66 | 40 | 18 |
N.S. |
1 | 5.12 | 3.31 | 3.00 | 4.88 | 3.31 | 3.31 | 4.12 | 2.50 | 1.12 |
time (sec) |
N/A | 0.225 | 0.009 | 0.120 | 0.026 | 0.081 | 0.108 | 0.116 | 0.163 | 3.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | A | A | F(-1) | F | F | B |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 35 | 754 | 43 | 38 | 0 | 0 | 188 | 44 |
N.S. |
1 | 0.00 | 1.25 | 26.93 | 1.54 | 1.36 | 0.00 | 0.00 | 6.71 | 1.57 |
time (sec) |
N/A | 0.000 | 0.101 | 0.089 | 0.216 | 0.086 | 0.000 | 0.000 | 200.012 | 3.324 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 321 | 224 | 197 | 197 | 230 | 383 | 408 | 225 |
N.S. |
1 | 0.00 | 8.92 | 6.22 | 5.47 | 5.47 | 6.39 | 10.64 | 11.33 | 6.25 |
time (sec) |
N/A | 0.000 | 14.839 | 1.234 | 0.066 | 0.100 | 2.762 | 0.161 | 200.022 | 0.510 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 36 | 23 | 19 | 32 | 32 | 31 | 0 | 43 | 40 |
N.S. |
1 | 1.89 | 1.21 | 1.00 | 1.68 | 1.68 | 1.63 | 0.00 | 2.26 | 2.11 |
time (sec) |
N/A | 0.407 | 0.433 | 0.146 | 0.029 | 0.084 | 0.080 | 0.000 | 0.289 | 0.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 24 | 23 | 39 | 39 | 19 | 22 | 36 | 24 |
N.S. |
1 | 0.00 | 1.09 | 1.05 | 1.77 | 1.77 | 0.86 | 1.00 | 1.64 | 1.09 |
time (sec) |
N/A | 0.000 | 0.113 | 0.454 | 0.067 | 0.090 | 0.065 | 0.116 | 0.175 | 3.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 35 | 41 | 89 | 78 | 102 | 212 | 105 | 98 |
N.S. |
1 | 0.00 | 1.09 | 1.28 | 2.78 | 2.44 | 3.19 | 6.62 | 3.28 | 3.06 |
time (sec) |
N/A | 0.000 | 3.557 | 0.554 | 0.189 | 0.087 | 0.150 | 0.201 | 0.163 | 3.212 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 44 | 28 | 31 | 0 | 25 | 34 | 40 | 36 | 34 |
N.S. |
1 | 1.63 | 1.04 | 1.15 | 0.00 | 0.93 | 1.26 | 1.48 | 1.33 | 1.26 |
time (sec) |
N/A | 0.212 | 0.089 | 0.157 | 0.000 | 0.075 | 0.178 | 0.116 | 0.161 | 2.994 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 52 | 41 | 40 | 0 | 47 | 49 | 114 | 45 | 40 |
N.S. |
1 | 2.26 | 1.78 | 1.74 | 0.00 | 2.04 | 2.13 | 4.96 | 1.96 | 1.74 |
time (sec) |
N/A | 0.330 | 0.064 | 2.139 | 0.000 | 0.091 | 0.147 | 0.119 | 0.169 | 3.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 51 | 22 | 46 | 45 | 36 | 34 | 29 | 62 | 36 |
N.S. |
1 | 2.22 | 0.96 | 2.00 | 1.96 | 1.57 | 1.48 | 1.26 | 2.70 | 1.57 |
time (sec) |
N/A | 0.259 | 0.021 | 0.069 | 0.036 | 0.101 | 0.114 | 0.114 | 0.162 | 3.002 |
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 | 55 | 22 | 24 | 26 | 35 | 24 | 24 | 31 | 24 |
N.S. |
1 | 1.77 | 0.71 | 0.77 | 0.84 | 1.13 | 0.77 | 0.77 | 1.00 | 0.77 |
time (sec) |
N/A | 0.412 | 0.048 | 0.285 | 0.112 | 0.087 | 0.080 | 0.116 | 0.160 | 3.029 |
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 | 24 | 0 | 41 | 26 | 0 | 24 | 29 | 50 | 29 | 26 |
N.S. |
1 | 0.00 | 1.71 | 1.08 | 0.00 | 1.00 | 1.21 | 2.08 | 1.21 | 1.08 |
time (sec) |
N/A | 0.000 | 0.317 | 0.161 | 0.000 | 0.079 | 0.210 | 0.116 | 0.159 | 3.015 |
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 | 21 | 21 | 20 | 19 | 18 | 18 | 17 | 18 | 16 | 18 |
N.S. |
1 | 1.00 | 0.95 | 0.90 | 0.86 | 0.86 | 0.81 | 0.86 | 0.76 | 0.86 |
time (sec) |
N/A | 0.167 | 0.003 | 0.073 | 0.033 | 0.082 | 0.067 | 0.116 | 0.163 | 2.968 |
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 | 35 | 55 | 45 | 26 | 51 | 34 | 49 | 27 | 48 | 48 |
N.S. |
1 | 1.57 | 1.29 | 0.74 | 1.46 | 0.97 | 1.40 | 0.77 | 1.37 | 1.37 |
time (sec) |
N/A | 0.718 | 0.093 | 0.276 | 0.155 | 0.103 | 0.108 | 0.128 | 0.161 | 3.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 30 | 20 | 19 | 18 | 18 | 15 | 0 | 19 | 0 |
N.S. |
1 | 1.36 | 0.91 | 0.86 | 0.82 | 0.82 | 0.68 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.741 | 0.069 | 4.214 | 0.164 | 0.082 | 0.137 | 0.000 | 0.166 | 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 | 35 | 0 | 37 | 36 | 41 | 38 | 29 | 52 | 35 | 0 |
N.S. |
1 | 0.00 | 1.06 | 1.03 | 1.17 | 1.09 | 0.83 | 1.49 | 1.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.095 | 23.878 | 0.420 | 0.106 | 0.437 | 0.471 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | B | A | F(-1) | B | B | B |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 36 | 124 | 50 | 37 | 0 | 53 | 43 | 36 |
N.S. |
1 | 0.00 | 1.33 | 4.59 | 1.85 | 1.37 | 0.00 | 1.96 | 1.59 | 1.33 |
time (sec) |
N/A | 0.000 | 0.122 | 1.456 | 0.186 | 0.109 | 0.000 | 3.837 | 0.391 | 3.450 |
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 | 15 | 12 | 12 | 12 | 39 | 11 | 8 | 11 | 12 | 11 |
N.S. |
1 | 0.80 | 0.80 | 0.80 | 2.60 | 0.73 | 0.53 | 0.73 | 0.80 | 0.73 |
time (sec) |
N/A | 0.184 | 0.039 | 0.056 | 0.057 | 0.082 | 0.052 | 0.116 | 0.155 | 0.029 |
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 | 23 | 0 | 27 | 62 | 54 | 55 | 60 | 82 | 58 | 26 |
N.S. |
1 | 0.00 | 1.17 | 2.70 | 2.35 | 2.39 | 2.61 | 3.57 | 2.52 | 1.13 |
time (sec) |
N/A | 0.000 | 0.185 | 250.497 | 0.066 | 0.086 | 0.180 | 0.120 | 0.155 | 3.008 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | F | F | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 0 | 25 | 28 | 28 | 31 | 0 | 493 | 34 |
N.S. |
1 | 0.00 | 0.00 | 1.04 | 1.17 | 1.17 | 1.29 | 0.00 | 20.54 | 1.42 |
time (sec) |
N/A | 0.000 | 0.000 | 1.067 | 0.710 | 0.083 | 0.753 | 0.000 | 1.453 | 3.134 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 35 | 23 | 36 | 38 | 28 | 34 | 38 | 27 | 0 |
N.S. |
1 | 1.30 | 0.85 | 1.33 | 1.41 | 1.04 | 1.26 | 1.41 | 1.00 | 0.00 |
time (sec) |
N/A | 0.763 | 0.132 | 163.855 | 0.268 | 0.107 | 0.289 | 0.137 | 0.171 | 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 | 27 | 0 | 24 | 25 | 28 | 28 | 20 | 28 | 26 | 0 |
N.S. |
1 | 0.00 | 0.89 | 0.93 | 1.04 | 1.04 | 0.74 | 1.04 | 0.96 | 0.00 |
time (sec) |
N/A | 0.000 | 0.137 | 0.284 | 0.069 | 0.079 | 0.139 | 0.125 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 149 | 42 | 41 | 49 | 43 | 46 | 0 | 63 | 54 |
N.S. |
1 | 5.14 | 1.45 | 1.41 | 1.69 | 1.48 | 1.59 | 0.00 | 2.17 | 1.86 |
time (sec) |
N/A | 1.888 | 0.071 | 0.331 | 0.306 | 0.085 | 3.219 | 0.000 | 0.774 | 3.073 |
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 | 18 | 18 | 17 | 17 | 19 | 17 | 18 | 19 |
N.S. |
1 | 0.00 | 0.72 | 0.72 | 0.68 | 0.68 | 0.76 | 0.68 | 0.72 | 0.76 |
time (sec) |
N/A | 0.000 | 0.187 | 4.550 | 0.078 | 0.090 | 0.123 | 0.117 | 0.175 | 3.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 21 | 25 | 30 | 24 | 32 | 30 | 24 | 21 |
N.S. |
1 | 0.00 | 1.00 | 1.19 | 1.43 | 1.14 | 1.52 | 1.43 | 1.14 | 1.00 |
time (sec) |
N/A | 0.000 | 0.246 | 1.379 | 0.093 | 0.088 | 0.081 | 0.120 | 0.172 | 3.194 |
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 | 21 | 0 | 35 | 26 | 34 | 35 | 19 | 42 | 489 | 31 |
N.S. |
1 | 0.00 | 1.67 | 1.24 | 1.62 | 1.67 | 0.90 | 2.00 | 23.29 | 1.48 |
time (sec) |
N/A | 0.000 | 3.351 | 0.188 | 0.088 | 0.096 | 0.108 | 0.119 | 0.179 | 0.089 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 22 | 20 | 21 | 26 | 20 | 15 | 20 | 20 | 20 |
N.S. |
1 | 0.85 | 0.77 | 0.81 | 1.00 | 0.77 | 0.58 | 0.77 | 0.77 | 0.77 |
time (sec) |
N/A | 0.339 | 0.013 | 0.086 | 0.160 | 0.076 | 0.087 | 0.114 | 0.172 | 3.089 |
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 | 24 | 0 | 22 | 21 | 44 | 24 | 31 | 0 | 834 | 47 |
N.S. |
1 | 0.00 | 0.92 | 0.88 | 1.83 | 1.00 | 1.29 | 0.00 | 34.75 | 1.96 |
time (sec) |
N/A | 0.000 | 5.085 | 0.362 | 0.345 | 0.105 | 0.276 | 0.000 | 0.404 | 3.173 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 35 | 13 | 15 | 12 | 12 | 14 | 14 | 35 | 10 |
N.S. |
1 | 2.33 | 0.87 | 1.00 | 0.80 | 0.80 | 0.93 | 0.93 | 2.33 | 0.67 |
time (sec) |
N/A | 0.166 | 0.017 | 0.098 | 0.033 | 0.093 | 0.133 | 0.109 | 0.166 | 3.023 |
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 | 24 | 24 | 30 | 25 | 22 | 0 | 55 | 29 |
N.S. |
1 | 0.00 | 0.92 | 0.92 | 1.15 | 0.96 | 0.85 | 0.00 | 2.12 | 1.12 |
time (sec) |
N/A | 0.000 | 1.204 | 3.701 | 0.125 | 0.091 | 13.878 | 0.000 | 0.170 | 3.088 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 65 | 24 | 21 | 25 | 21 | 19 | 179 | 29 | 111 |
N.S. |
1 | 2.41 | 0.89 | 0.78 | 0.93 | 0.78 | 0.70 | 6.63 | 1.07 | 4.11 |
time (sec) |
N/A | 0.379 | 0.087 | 0.234 | 0.203 | 0.082 | 0.108 | 0.542 | 0.172 | 3.492 |
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 | 18 | 19 | 24 | 24 | 27 | 31 | 18 | 19 |
N.S. |
1 | 0.00 | 0.95 | 1.00 | 1.26 | 1.26 | 1.42 | 1.63 | 0.95 | 1.00 |
time (sec) |
N/A | 0.000 | 1.391 | 0.290 | 0.145 | 0.083 | 0.078 | 0.117 | 0.174 | 3.333 |
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 | 30 | 23 | 26 | 26 | 32 | 26 | 27 | 19 |
N.S. |
1 | 1.08 | 1.15 | 0.88 | 1.00 | 1.00 | 1.23 | 1.00 | 1.04 | 0.73 |
time (sec) |
N/A | 0.171 | 0.010 | 0.042 | 0.034 | 0.095 | 0.039 | 0.115 | 0.164 | 3.082 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | F | B | B | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 71 | 76 | 0 | 71 | 70 | 124 | 151 | 161 |
N.S. |
1 | 0.00 | 2.37 | 2.53 | 0.00 | 2.37 | 2.33 | 4.13 | 5.03 | 5.37 |
time (sec) |
N/A | 0.000 | 0.073 | 2.080 | 0.000 | 0.091 | 0.161 | 0.180 | 0.175 | 3.144 |
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 | 21 | 78 | 18 | 20 | 22 | 22 | 19 | 22 | 19 | 16 |
N.S. |
1 | 3.71 | 0.86 | 0.95 | 1.05 | 1.05 | 0.90 | 1.05 | 0.90 | 0.76 |
time (sec) |
N/A | 1.414 | 0.124 | 0.148 | 0.070 | 0.089 | 0.045 | 0.107 | 0.167 | 3.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | F | B | F(-1) |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 0 | 42 | 36 | 31 | 29 | 0 | 31 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.35 | 1.16 | 1.00 | 0.94 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 2.302 | 0.166 | 0.110 | 0.187 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 12 | 12 | 9 | 0 | 8 | 8 | 8 | 11 | 8 |
N.S. |
1 | 0.86 | 0.86 | 0.64 | 0.00 | 0.57 | 0.57 | 0.57 | 0.79 | 0.57 |
time (sec) |
N/A | 0.174 | 0.009 | 0.059 | 0.000 | 0.082 | 0.063 | 0.112 | 0.164 | 3.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 39 | 37 | 64 | 47 | 32 | 36 | 42 | 33 |
N.S. |
1 | 0.00 | 1.86 | 1.76 | 3.05 | 2.24 | 1.52 | 1.71 | 2.00 | 1.57 |
time (sec) |
N/A | 0.000 | 3.886 | 0.161 | 0.066 | 0.117 | 0.192 | 0.122 | 0.159 | 0.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 13 | 13 | 11 | 10 | 10 | 8 | 10 | 14 | 10 |
N.S. |
1 | 0.87 | 0.87 | 0.73 | 0.67 | 0.67 | 0.53 | 0.67 | 0.93 | 0.67 |
time (sec) |
N/A | 0.265 | 0.011 | 0.029 | 0.032 | 0.107 | 0.032 | 0.108 | 0.159 | 0.022 |
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 | 24 | 92 | 29 | 35 | 37 | 31 | 34 | 35 | 30 | 28 |
N.S. |
1 | 3.83 | 1.21 | 1.46 | 1.54 | 1.29 | 1.42 | 1.46 | 1.25 | 1.17 |
time (sec) |
N/A | 0.619 | 0.015 | 0.256 | 0.027 | 0.099 | 0.347 | 0.118 | 0.158 | 0.095 |
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 | 24 | 22 | 21 | 17 | 19 | 23 | 21 | 16 |
N.S. |
1 | 1.14 | 1.14 | 1.05 | 1.00 | 0.81 | 0.90 | 1.10 | 1.00 | 0.76 |
time (sec) |
N/A | 0.476 | 0.016 | 0.050 | 0.028 | 0.085 | 0.086 | 0.114 | 0.155 | 3.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 21 | 21 | 30 | 0 | 23 | 17 | 25 | 25 | 0 |
N.S. |
1 | 0.95 | 0.95 | 1.36 | 0.00 | 1.05 | 0.77 | 1.14 | 1.14 | 0.00 |
time (sec) |
N/A | 1.008 | 0.068 | 0.639 | 0.000 | 0.111 | 0.137 | 0.124 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B | B |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 49 | 24 | 22 | 21 | 21 | 17 | 0 | 31 | 25 |
N.S. |
1 | 2.04 | 1.00 | 0.92 | 0.88 | 0.88 | 0.71 | 0.00 | 1.29 | 1.04 |
time (sec) |
N/A | 0.591 | 0.072 | 0.152 | 0.161 | 0.108 | 0.139 | 0.000 | 0.165 | 3.105 |
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 | 42 | 0 | 53 | 50 | 53 | 53 | 44 | 708 | 83 | 49 |
N.S. |
1 | 0.00 | 1.26 | 1.19 | 1.26 | 1.26 | 1.05 | 16.86 | 1.98 | 1.17 |
time (sec) |
N/A | 0.000 | 0.101 | 2.415 | 0.150 | 0.104 | 0.198 | 0.338 | 0.170 | 3.137 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 25 | 23 | 0 | 22 | 22 | 0 | 268 | 22 |
N.S. |
1 | 0.00 | 1.00 | 0.92 | 0.00 | 0.88 | 0.88 | 0.00 | 10.72 | 0.88 |
time (sec) |
N/A | 0.000 | 0.340 | 0.246 | 0.000 | 0.086 | 0.193 | 0.000 | 0.167 | 3.299 |
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 | 35 | 17 | 17 | 12 | 11 | 17 | 10 | 11 | 14 | 13 |
N.S. |
1 | 0.49 | 0.49 | 0.34 | 0.31 | 0.49 | 0.29 | 0.31 | 0.40 | 0.37 |
time (sec) |
N/A | 0.186 | 0.006 | 0.096 | 0.025 | 0.086 | 0.036 | 0.112 | 0.156 | 2.969 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 21 | 21 | 20 | 0 | 37 | 15 | 39 | 41 | 18 |
N.S. |
1 | 0.66 | 0.66 | 0.62 | 0.00 | 1.16 | 0.47 | 1.22 | 1.28 | 0.56 |
time (sec) |
N/A | 0.319 | 0.015 | 0.244 | 0.000 | 0.088 | 0.079 | 0.114 | 0.158 | 0.062 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 12 | 12 | 11 | 10 | 24 | 10 | 24 | 16 | 10 |
N.S. |
1 | 0.63 | 0.63 | 0.58 | 0.53 | 1.26 | 0.53 | 1.26 | 0.84 | 0.53 |
time (sec) |
N/A | 0.413 | 0.011 | 0.113 | 0.032 | 0.103 | 0.097 | 0.124 | 0.153 | 2.964 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 61 | 31 | 32 | 37 | 39 | 32 | 32 | 40 | 52 |
N.S. |
1 | 2.10 | 1.07 | 1.10 | 1.28 | 1.34 | 1.10 | 1.10 | 1.38 | 1.79 |
time (sec) |
N/A | 1.819 | 1.554 | 0.710 | 0.092 | 0.088 | 0.131 | 0.116 | 0.171 | 0.119 |
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 | 33 | 0 | 24 | 17 | 16 | 60 | 19 | 60 | 20 | 16 |
N.S. |
1 | 0.00 | 0.73 | 0.52 | 0.48 | 1.82 | 0.58 | 1.82 | 0.61 | 0.48 |
time (sec) |
N/A | 0.000 | 0.140 | 0.187 | 0.164 | 0.099 | 0.267 | 0.150 | 0.158 | 3.165 |
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 | 33 | 34 | 28 | 33 | 24 | 26 | 50 | 30 |
N.S. |
1 | 0.00 | 1.00 | 1.03 | 0.85 | 1.00 | 0.73 | 0.79 | 1.52 | 0.91 |
time (sec) |
N/A | 0.000 | 0.041 | 10.346 | 0.202 | 0.088 | 0.209 | 0.158 | 0.172 | 3.467 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 34 | 18 | 29 | 36 | 70 | 62 | 37 | 20 |
N.S. |
1 | 0.00 | 1.62 | 0.86 | 1.38 | 1.71 | 3.33 | 2.95 | 1.76 | 0.95 |
time (sec) |
N/A | 0.000 | 1.892 | 0.244 | 0.079 | 0.097 | 0.122 | 0.121 | 0.158 | 3.108 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 24 | 21 | 25 | 0 | 22 | 20 | 34 | 21 | 30 |
N.S. |
1 | 1.04 | 0.91 | 1.09 | 0.00 | 0.96 | 0.87 | 1.48 | 0.91 | 1.30 |
time (sec) |
N/A | 0.194 | 0.052 | 0.115 | 0.000 | 0.094 | 0.237 | 0.116 | 0.155 | 0.158 |
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 | 4 | 4 | 5 | 4 | 4 | 3 | 5 | 4 | 4 |
N.S. |
1 | 0.27 | 0.27 | 0.33 | 0.27 | 0.27 | 0.20 | 0.33 | 0.27 | 0.27 |
time (sec) |
N/A | 0.129 | 0.000 | 0.016 | 0.030 | 0.083 | 0.020 | 0.111 | 0.157 | 0.004 |
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 | 28 | 0 | 22 | 25 | 22 | 27 | 24 | 23 | 61 | 26 |
N.S. |
1 | 0.00 | 0.79 | 0.89 | 0.79 | 0.96 | 0.86 | 0.82 | 2.18 | 0.93 |
time (sec) |
N/A | 0.000 | 0.094 | 0.256 | 0.057 | 0.088 | 0.157 | 0.131 | 0.158 | 3.236 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 61 | 37 | 279 | 45 | 39 | 0 | 40 | 80 |
N.S. |
1 | 0.00 | 2.03 | 1.23 | 9.30 | 1.50 | 1.30 | 0.00 | 1.33 | 2.67 |
time (sec) |
N/A | 0.000 | 0.441 | 0.821 | 0.162 | 0.097 | 0.211 | 0.000 | 0.166 | 3.313 |
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 | 27 | 0 | 29 | 47 | 29 | 29 | 22 | 36 | 99 | 171 |
N.S. |
1 | 0.00 | 1.07 | 1.74 | 1.07 | 1.07 | 0.81 | 1.33 | 3.67 | 6.33 |
time (sec) |
N/A | 0.000 | 0.139 | 18.582 | 0.110 | 0.100 | 0.881 | 0.234 | 200.019 | 3.274 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 25 | 23 | 22 | 22 | 19 | 22 | 23 | 22 |
N.S. |
1 | 0.00 | 1.00 | 0.92 | 0.88 | 0.88 | 0.76 | 0.88 | 0.92 | 0.88 |
time (sec) |
N/A | 0.000 | 1.109 | 0.076 | 0.076 | 0.099 | 0.235 | 0.144 | 0.155 | 3.313 |
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 | 30 | 0 | 39 | 42 | 44 | 44 | 39 | 46 | 49 | 0 |
N.S. |
1 | 0.00 | 1.30 | 1.40 | 1.47 | 1.47 | 1.30 | 1.53 | 1.63 | 0.00 |
time (sec) |
N/A | 0.000 | 3.879 | 0.359 | 0.133 | 0.083 | 0.152 | 0.129 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | F | B | C | C | F(-1) | B | B | B |
verified | N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 98 | 0 | 98 | 281 | 255 | 0 | 14865 | 129 | 168 |
N.S. |
1 | 4.67 | 0.00 | 4.67 | 13.38 | 12.14 | 0.00 | 707.86 | 6.14 | 8.00 |
time (sec) |
N/A | 1.511 | 0.000 | 7.430 | 0.367 | 0.094 | 0.000 | 0.782 | 4.298 | 3.379 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 25 | 45 | 45 | 72 | 44 | 37 | 52 | 650 | 181 |
N.S. |
1 | 0.93 | 1.67 | 1.67 | 2.67 | 1.63 | 1.37 | 1.93 | 24.07 | 6.70 |
time (sec) |
N/A | 2.537 | 1.614 | 0.325 | 0.191 | 0.091 | 0.261 | 0.328 | 0.394 | 3.254 |