Simplified Input \(F(a, b, c)\):
\[\frac{1}{a + \frac{2}{b + \frac{3}{c + 4}}}\]
Error Function \(\sigma_{F}(a, b, c)\):
\[\sqrt{\frac{\sigma_{a}^{2} \left(b \left(c + 4\right) + 3\right)^{4} + 4 \sigma_{b}^{2} \left(c + 4\right)^{4} + 36 \sigma_{c}^{2}}{\left(a \left(b \left(c + 4\right) + 3\right) + 2 c + 8\right)^{4}}}\]
Numerical Value \(F(a, b, c)\pm \sigma_{F}(a, b, c)\):
\[0.4333333333 \pm 0.03859380108\]