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I think you need "InlineCompiledFunctions" -> False:

f = With[{bigNastyFunction = 
    Compile[{{y, _Complex}}, Sin[y](*,CompilationTarget\[Rule]C*)]}, 
  Compile[{{x, _Complex}}, 
   bigNastyFunction[x] + bigNastyFunction[x^2]^2 + 3 bigNastyFunction[x^3], 
   CompilationOptions -> {"InlineCompiledFunctions" -> False}]]
……
1 C1 = CompiledFunctionCall[ Hold[CompiledFunction[{y}, Sin[y], -CompiledCode-]][ C0]]
2 C2 = Square[ C0]
……

Related post:

http://mathematica.stackexchange.com/q/31273/1871Is the CompiledFunctionCall WVM opcode efficient?

http://mathematica.stackexchange.com/q/82995/1871CompiledFunctionCall vs. LibraryFunction

I think you need "InlineCompiledFunctions" -> False:

f = With[{bigNastyFunction = 
    Compile[{{y, _Complex}}, Sin[y](*,CompilationTarget\[Rule]C*)]}, 
  Compile[{{x, _Complex}}, 
   bigNastyFunction[x] + bigNastyFunction[x^2]^2 + 3 bigNastyFunction[x^3], 
   CompilationOptions -> {"InlineCompiledFunctions" -> False}]]
……
1 C1 = CompiledFunctionCall[ Hold[CompiledFunction[{y}, Sin[y], -CompiledCode-]][ C0]]
2 C2 = Square[ C0]
……

Related post:

http://mathematica.stackexchange.com/q/31273/1871

http://mathematica.stackexchange.com/q/82995/1871

I think you need "InlineCompiledFunctions" -> False:

f = With[{bigNastyFunction = 
    Compile[{{y, _Complex}}, Sin[y](*,CompilationTarget\[Rule]C*)]}, 
  Compile[{{x, _Complex}}, 
   bigNastyFunction[x] + bigNastyFunction[x^2]^2 + 3 bigNastyFunction[x^3], 
   CompilationOptions -> {"InlineCompiledFunctions" -> False}]]
……
1 C1 = CompiledFunctionCall[ Hold[CompiledFunction[{y}, Sin[y], -CompiledCode-]][ C0]]
2 C2 = Square[ C0]
……

Related post:

Is the CompiledFunctionCall WVM opcode efficient?

CompiledFunctionCall vs. LibraryFunction

1
source | link

I think you need "InlineCompiledFunctions" -> False:

f = With[{bigNastyFunction = 
    Compile[{{y, _Complex}}, Sin[y](*,CompilationTarget\[Rule]C*)]}, 
  Compile[{{x, _Complex}}, 
   bigNastyFunction[x] + bigNastyFunction[x^2]^2 + 3 bigNastyFunction[x^3], 
   CompilationOptions -> {"InlineCompiledFunctions" -> False}]]
……
1 C1 = CompiledFunctionCall[ Hold[CompiledFunction[{y}, Sin[y], -CompiledCode-]][ C0]]
2 C2 = Square[ C0]
……

Related post:

http://mathematica.stackexchange.com/q/31273/1871

http://mathematica.stackexchange.com/q/82995/1871