🏆 ยอดนิยม: web//https://www.geeksforgeeks.org/program to efficiently calculate ex

The value of Exponential Function e^x can be expressed using following Taylor Series.

e^x = 1 + x/1! + x^2/2! + x^3/3! + ......

How to efficiently calculate the sum of above series?
The series can be re-written as

e^x = 1 + (x/1) (1 + (x/2) (1 + (x/3) (........) ) )

Let the sum needs to be calculated for n terms, we can calculate sum using following loop.

for (i = n - 1, sum = 1; i > 0; --i )
    sum = 1 + x * sum / i;

Following is implementation of the above idea.

C++

// C++ Efficient program to calculate  
// e raise to the power x  
#include <bits/stdc++.h> 
using namespace std; 
  
// Returns approximate value of e^x  
// using sum of first n terms of Taylor Series  
float exponential(int n, float x)  
{  
    float sum = 1.0f; // initialize sum of series  
  
    for (int i = n - 1; i > 0; --i )  
        sum = 1 + x * sum / i;  
  
    return sum;  
}  
  
// Driver code  
int main()  
{  
    int n = 10;  
    float x = 1.0f;  
    cout << "e^x = " << fixed << setprecision(5) << exponential(n, x);  
    return 0;  
}  
  
// This code is contributed by rathbhupendra 

C

// C Efficient program to calculate 
// e raise to the power x 
#include <stdio.h> 
  
// Returns approximate value of e^x  
// using sum of first n terms of Taylor Series 
float exponential(int n, float x) 
{ 
    float sum = 1.0f; // initialize sum of series 
  
    for (int i = n - 1; i > 0; --i ) 
        sum = 1 + x * sum / i; 
  
    return sum; 
} 
  
// Driver program to test above function 
int main() 
{ 
    int n = 10; 
    float x = 1.0f; 
    printf("e^x = %f", exponential(n, x)); 
    return 0; 
} 

Java

// Java efficient program to calculate  
// e raise to the power x 
import java.io.*; 
  
class GFG  
{ 
    // Function returns approximate value of e^x  
    // using sum of first n terms of Taylor Series 
    static float exponential(int n, float x) 
    { 
        // initialize sum of series 
        float sum = 1;  
   
        for (int i = n - 1; i > 0; --i ) 
            sum = 1 + x * sum / i; 
   
        return sum; 
    } 
      
    // driver program 
    public static void main (String[] args)  
    { 
        int n = 10; 
        float x = 1; 
        System.out.println("e^x = "+exponential(n,x)); 
    } 
} 
  
// Contributed by Pramod Kumar 

Python3

# Python program to calculate 
# e raise to the power x 
  
# Function to calculate value 
# using sum of first n terms of  
# Taylor Series 
def exponential(n, x): 
  
    # initialize sum of series 
    sum = 1.0 
    for i in range(n, 0, -1): 
        sum = 1 + x * sum / i 
    print ("e^x =", sum) 
  
# Driver program to test above function 
n = 10
x = 1.0
exponential(n, x) 
  
# This code is contributed by Danish Raza 

C#

// C# efficient program to calculate  
// e raise to the power x 
using System; 
  
class GFG  
{ 
    // Function returns approximate value of e^x  
    // using sum of first n terms of Taylor Series 
    static float exponential(int n, float x) 
    { 
        // initialize sum of series 
        float sum = 1;  
  
        for (int i = n - 1; i > 0; --i ) 
            sum = 1 + x * sum / i; 
  
        return sum; 
    } 
      
    // driver program 
    public static void Main ()  
    { 
        int n = 10; 
        float x = 1; 
        Console.Write("e^x = " + exponential(n, x)); 
    } 
} 
  
// This code is contributed by nitin mittal. 

PHP

<?php 
// PHP Efficient program to calculate 
// e raise to the power x 
  
// Returns approximate value of e^x  
// using sum of first n terms  
// of Taylor Series 
function exponential($n, $x) 
{ 
    // initialize sum of series 
    $sum = 1.0;  
  
    for ($i = $n - 1; $i > 0; --$i ) 
        $sum = 1 + $x * $sum / $i; 
  
    return $sum; 
} 
  
// Driver Code 
$n = 10; 
$x = 1.0; 
echo("e^x = " . exponential($n, $x)); 
  
// This code is contributed by Ajit. 
?> 

Output:

e^x = 2.718282

This article is compiled by Rahul and reviewed by GeeksforGeeks team. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above

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Efficient program to calculate e^x

C++

C

Java

Python3

C#

PHP

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