#include <iostream>
#include <cmath>
#include <iomanip>
using namespace std;
 
long double ehoch(long double x){
    long double erg = -1;
    long long counter = 0;
    long double epsilon = 1e-16;
    long double next = 1;
    counter++;
    while(epsilon < abs(next) && counter < 100){
        erg += next;
        next *= x / counter;
        counter++;
    }
    return erg + 1;
}
 
int main() {
    for (double x = 0; x < 10; x++)
	  cout << x << ": " << setprecision(16) << ehoch(x) << " <-> " << exp(x) << endl;
 
	return 0;
}

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