# Removing singularities from callable functions built from symbolic expressions

**URL:** <https://discourse.julialang.org/t/removing-singularities-from-callable-functions-built-from-symbolic-expressions/83505>\
**Category:** Numerics\
**Tags:** question, symbolics\
**Created:** [June 29, 2022, 7:49am UTC](https://discourse.julialang.org/t/removing-singularities-from-callable-functions-built-from-symbolic-expressions/83505 "2022-06-29T07:49:31Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![mrhardman](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mrhardman/32/37517_2.png) [@mrhardman](https://discourse.julialang.org/u/mrhardman)\
**Post date:** [June 29, 2022, 7:49am UTC](https://discourse.julialang.org/t/removing-singularities-from-callable-functions-built-from-symbolic-expressions/83505/1 "2022-06-29T07:49:32Z")

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I have a basic question regarding building functions from symbolic expressions for which I cannot find the answer on the documentation ([Symbolic Calculations and Building Callable Functions · Symbolics.jl](https://symbolics.juliasymbolics.org/dev/tutorials/symbolic_functions/))

Suppose that I want to build a callable function from a reasonable symbolic expression that happens to have a singularity at a particular point. In ordinary non-symbolic programming I would be able to put a special exception to remove the singularity artificially, so that NaNs did not propagate through the code. I would like to do something similar to the callable function built from a symbolic expression.

For example, let us consider the function f = x/sqrt(x^2 + y^2). There is an undefined point at x = y = 0, and the value of the function there depends on how you approach x = y = 0. If one takes y-\>0 first, then x-\>0, the result is f =1, whereas if one takes x-\>0 then y-\> 0 the result is f= 0. I would like to force a choice of limit on this point rather than evaluating 0/0 = NaN.

Output from the Julia REPL below. I would like the final call f(0.0,0.0) = 0.0 rather than NaN. Is there an easy way to build special exceptions into the build\_function call? I can wrap if statements around calls to f\_callable, but this seems like a dumb solution.

using Symbolics  
julia\> @variables x y  
2-element Vector{Num}:  
x  
y

julia\> f = x/sqrt(x^2 + y^2)  
x / sqrt(x^2 + y^2)

julia\> f\_callable = build\_function(f, x, y, expression=Val{false})

julia\> f\_callable(1.0,1.0)  
0.7071067811865475

julia\> f\_callable(0.0,1.0)  
0.0

julia\> f\_callable(0.0,0.0)  
NaN

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**Author:** ![contradict](https://avatars.discourse-cdn.com/v4/letter/c/ac91a4/32.png) [@contradict](https://discourse.julialang.org/u/contradict)\
**Post date:** [June 29, 2022, 5:04pm UTC](https://discourse.julialang.org/t/removing-singularities-from-callable-functions-built-from-symbolic-expressions/83505/2 "2022-06-29T17:04:57Z")

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I don’t know of an automatic way to do this, but you can write your expression using `ifelse`.

```julia
julia> using IfElse

julia> same_type_zero(x) = zero(x)
same_type_zero (generic function with 1 method)

julia> @register_symbolic same_type_zero(x)

julia> f = IfElse.ifelse(x==0.0, same_type_zero(x), x/sqrt(x^2+y^2))
IfElse.ifelse(x == 0.0, same_type_zero(x), x / sqrt(x^2 + y^2))

julia> f_callable = build_function(f, x, y, expression=Val{false});

julia> f_callable(0.0,0.0)
0.0

```

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<div class="post-metadata">

**Author:** ![YingboMa](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/yingboma/32/2181_2.png) [@YingboMa](https://discourse.julialang.org/u/YingboMa)\
**Post date:** [June 29, 2022, 5:11pm UTC](https://discourse.julialang.org/t/removing-singularities-from-callable-functions-built-from-symbolic-expressions/83505/3 "2022-06-29T17:11:09Z")

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I think you are asking for `limit(f, x=>xval, y=>yval)`. We currently don’t have limit computation in Symbolics yet, unfortunately.