expm1() function in PHP

The expm1() function returns e raised to the power x minus 1, which is mathematically represented as e^x - 1. This function is particularly useful for calculating values close to zero with higher precision than using exp(x) - 1.

Syntax

expm1(number)

Parameters

• number − A floating point value representing the exponent

Return Value

Returns a float representing e^x - 1, where e is Euler's number (approximately 2.718281828).

Example 1

Basic usage of expm1() with different values −

<?php
    echo "expm1(0) = " . expm1(0) . "<br>";
    echo "expm1(1) = " . expm1(1) . "<br>";
    echo "expm1(2) = " . expm1(2) . "<br>";
?>

expm1(0) = 0
expm1(1) = 1.718281828459
expm1(2) = 6.3890560989307

Example 2

Demonstrating the mathematical formula e^x - 1 −

<?php
    $val = 1.5;
    echo "For x = " . $val . "<br>";
    echo "expm1(" . $val . ") = " . expm1($val) . "<br>";
    echo "exp(" . $val . ") - 1 = " . (exp($val) - 1) . "<br>";
?>

For x = 1.5
expm1(1.5) = 3.4816890703382
exp(1.5) - 1 = 3.4816890703382

Conclusion

The expm1() function provides an accurate way to calculate e^x - 1, especially for small values of x where precision matters. It's equivalent to exp(x) - 1 but offers better numerical stability.