Structured Random Generator
This uses your function
y = ((sin(x^(1/n))+err1)/(sin(x^(1/(n+1)))+err2+δ))
+ ((cos(x^(1/n))+err3)/(cos(x^(1/(n-1)))+err4+δ))
with small random perturbations, integer mapping, prime analysis, and feedback mode where the previous output can become the next x.
Lower values soften the jump in x between iterations.
Model
y(x,n)=
((sin(x^(1/n))+err1)/(sin(x^(1/(n+1)))+err2+δ))
+
((cos(x^(1/n))+err3)/(cos(x^(1/(n-1)))+err4+δ))