auto deduction fails with message "inconsistent deduction for auto return type"

I have written the following test :

#include <cassert>
#include <iostream>
#include <string>
#include <cmath>
#include <functional>

// Works with std::function !
//std::function<double(double)> set_unary_operation(const std::string& unary)
auto set_unary_operation(const std::string& unary)
{
    if(unary == "EXP")
      return [](const double& x){ return std::exp(x);};
    if(unary == "LOG")
      return [](const double& x){ return std::log10(x);};
    if(unary == "_LN")
      return [](const double& x){ return std::log(x);};
    if(unary == "ABS")
      return [](const double& x){ return std::abs(x);};

    return [](const double& x){return x;};

}
  
bool is_equal(double&& value, double&& test)
{
    double epsilon = 0.0000001;
    return (value-epsilon < test) && (value+epsilon > test);
}

int main()
{
  // TEST OPERATOR --------------------------------------------------------------------------
  {
    std::string in = "EXP";

    auto f = set_unary_operation(in);

    std::cout << "f = EXP ; f(1) = "<< f(1) << "; f(2.5) = " << f(2.5) << std::endl;

    assert(is_equal(f(1)  , 2.71828182));
    assert(is_equal(f(2.5), 12.1824939607));
  }

  return 0;
}

The code works fine if I define the return type of set_unary_operation as std::function<double(double)>, but failed when I use auto with the following message :

error: inconsistent deduction for auto return type: ‘moteur_de_calcul::set_unary_operation(const string&)::<lambda(const double&)>’ and then ‘moteur_de_calcul::set_unary_operation(const string&)::<lambda(const double&)>’

I try to understand why the deduction failed (example can be found here : https://onlinegdb.com/Sk7bitBxD).