I am expecting achieve function composition. The output for laplace defined as composition is different to symmetric
This is my tried.

from sympy import Function, Symbol
from sympy.printing import pprint

x = Symbol(name="x", real=True)
h = Symbol(name="h", positive=True)
u = Function("u")


def forward(x):
    return (u(x + h) - u(x)) / h


def backward(x):
    return (u(x) - u(x - h)) / h


def centered(x):
    return (u(x + h) - u(x - h)) / (2 * h)


def symmetric(x):
    return (u(x - h) - 2 * u(x) + u(x + h)) / h**2


def compose(f, g):
    return lambda x: f(g(x))


laplace = compose(backward, forward)

pprint(forward(x))
pprint(backward(x))
pprint(centered(x))
pprint(symmetric(x))
pprint(laplace(x))
# assert symmetric.equals(laplace().simplify())

-u(x) + u(h + x)
────────────────
       h        
u(x) - u(-h + x)
────────────────
       h        
-u(-h + x) + u(h + x)
─────────────────────
         2⋅h         
-2⋅u(x) + u(-h + x) + u(h + x)
──────────────────────────────
               2              
              h               
 ⎛-u(x) + u(h + x)⎞    ⎛     -u(x) + u(h + x)⎞
u⎜────────────────⎟ - u⎜-h + ────────────────⎟
 ⎝       h        ⎠    ⎝            h        ⎠
──────────────────────────────────────────────
                      h                       

I asked a while ago something related to composition, since composition is about replacing expressions, but I would like if we can do it in a naive way.