Expansion - Common Lisp, Common Lisp

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; Author: Danny Betancourt
; Common Lisp algorithm to calculate 1 - x + (x^2)/(2!) - (x^3)/3! + (x^4)/(4!) - (x^5)/5! + (x^6)/(6!) - (x^7)/7! + (x^8)/(8!) - (x^9)/9! + (x^10)/(10!)
; gnu clisp 2.49

; Function to raise a [b]ase to a [p]ower
(defun power (b p)
    (if (= p 1)
        b
        (* b (power b (- p 1)))
    )
)

; Function to calculate the factorial of a [n]umber
(defun factorial (n)
    (if (= n 1)
        1
        (* n (factorial (- n 1)))
    )
)

; Function to add up only the negative components of the equation
(defun negatives (n p)
    (if (= p 9)
        (/ (power n p) (factorial p)) ; Terminate when we reach the last odd power, 9...
        (-
             0
             (/ (power n p) (factorial p)) ; ...otherwise return the current iteration minus the next odd iteration
             (abs (negatives n (+ p 2))) ; Use absolute value to guard against negative values being returned to ensure proper subtraction
        )
    )
)

; Function to add up only the positive components of the equation
(defun positives (n p)
    (if (= p 10)
        (/ (power n p) (factorial p)) ; Terminate when we reach the last even power, 10...
        (+
             (/ (power n p) (factorial p)) ; ...otherwise return the current iteration plus the next even iteration
             (positives n (+ p 2))
        )
    )
)

(defun expansion (n)
  (+
       1
       (negatives n 1) ; Only negative powers are subtracted, so start at one and increment by 2
       (positives n 2) ; Only positive powers are added, so start at two and increment by 2
  )
)

(print (coerce (expansion 20) 'long-float))

[ + ] Show input
Absolute running time: 0.42 sec, cpu time: 0.17 sec, memory peak: 5 Mb, absolute service time: 0,44 sec