PHP：为什么递归需要这么长时间

我有两段代码来计算给定指数的斐波纳契数列.一个使用递归，另一个使用array.它运行这两个函数，并 echo 计算每个函数所需的时间:

<?php
//Calculate the index recursively
function fibonacciRecursiveAtIndex($num){
$num = 0 and $num = 1
    if($num == 0){
        return 0;
    } else if ($num == 1){
        return 1;
    } else {
        return fibonacciRecursiveAtIndex($num-1) + fibonacciRecursiveAtIndex($num-2);
    }
}

//Calculate non-recursively
function fibonacciAtIndex($num){
    $fibonacciArray = [0, 1];

    for($i = 2; $i < $num + 1; $i++){
        array_push($fibonacciArray, $fibonacciArray[$i - 1] + $fibonacciArray[$i - 2]);
    }
    
    return $fibonacciArray[$num];
}

//Recursion becomes noticeably slower for an index value above 15
$indexToCalculate = 40;

//Plug index into the fibonacciRecursiveAtIndex() function and output calculation time. 
$timeStart = microtime(true);
$valueAtIndex = fibonacciRecursiveAtIndex($indexToCalculate);
$timeEnd = microtime(true);
echo "Recursive(" . $indexToCalculate . ") = " . $valueAtIndex . " -- calculated in " . round(($timeEnd - $timeStart),7) . " s";

echo "<br><br>";

//Plug index into the fibonacciAtIndex() function and output calculation time. 
//The calculated time is several orders of magnitudes faster for large indices (index > 15).
$timeStart = microtime(true);
$valueAtIndex = fibonacciAtIndex($indexToCalculate);
$timeEnd = microtime(true);

echo "Fibonacci(" . $indexToCalculate . ") = " . $valueAtIndex . " -- calculated in " . round(($timeEnd - $timeStart),7) . " s";

运行此命令以计算索引为40的fibonaci序列需要大约4秒的递归时间，但数组方法计算索引为40的时间与计算索引为4的时间大致相同(即，在微秒量级上).

这种行为背后的原则是什么？它在这里是如何应用的？