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import math
 
 
def f(x):
    return x**3 - 3
 
 
def df(x):
    return 3 * x**2
 
 
def g(x):
    return 5*x + math.log(x, math.e) - 10000
 
 
def dg(x):
    return 5 + 1/x
 
 
def h(x):
    return 2 - x**2 - math.sin(x)
 
 
def dh(x):
    return -2*x - math.cos(x)
 
 
def j(x):
    return x**2 - 10
 
 
def dj(x):
    return 2*x
 
 
def k(x):
    return math.log((x**2 + 1), math.e) - math.e**(0.4*x)*math.cos(math.pi * x)
 
 
def dk(x):
    return math.pi * math.e**((2 * x) / 5) * math.sin(math.pi * x) - (((2 * math.e**((2 * x) / 5)) * math.cos(math.pi * x)) / 5) + ((2 * x) / (x**2 + 1))
 
 
def calc_relative_error(current_error, last_error):
    return abs((current_error - last_error) / current_error)
 
 
def newton_rhapson_f(x, n, tol):
    for i in range(n):
        if f(x) == 0:
            return x
        if df(x) == 0:
            break
 
        last_estimate = x
        x = x - (f(x) / df(x))
        current_estimate = x
        relative_error = calc_relative_error(current_estimate, last_estimate)
 
        if relative_error <= tol:
            return current_estimate
 
    return -1
 
 
def newton_rhapson_g(x, n, tol):
    for i in range(n):
        if g(x) == 0:
            return x
        if dg(x) == 0:
            break
 
        last_estimate = x
        x = x - (g(x) / dg(x))
        current_estimate = x
 
        relative_error = calc_relative_error(current_estimate, last_estimate)
 
        if relative_error <= tol:
            return current_estimate
 
    return -1
 
 
def newton_rhapson_h(x, n, tol):
    for i in range(n):
        if h(x) == 0:
            return x
        if dh(x) == 0:
            break
 
        last_estimate = x
        x = x - (h(x) / dh(x))
        current_estimate = x
 
        relative_error = calc_relative_error(current_estimate, last_estimate)
 
        if relative_error <= tol:
            return current_estimate
 
    return -1
 
 
def newton_rhapson_j(x, n, tol):
    for i in range(n):
        if j(x) == 0:
            return x
        if dj(x) == 0:
            break
 
        last_estimate = x
        x = (x - (j(x) / dj(x)))
        current_estimate = x
 
        relative_error = calc_relative_error(current_estimate, last_estimate)
 
        if relative_error <= tol:
            return current_estimate
 
    return -1
 
 
def newton_rhapson_k(x, n, tol):
    for i in range(n):
        if k(x) == 0:
            return x
        if dk(x) == 0:
            break
 
        last_estimate = x
        x = (x - (k(x) / dk(x)))
        current_estimate = x
 
        relative_error = calc_relative_error(current_estimate, last_estimate)
 
        if relative_error <= tol:
            return current_estimate
 
    return -1
 
 
# Shared variables
max_iter = 100
 
# Function specific variables
f_x_start = 2.5
g_x_start = 3
h_x_start = -2
h_x2_start = 3
j_x_start = 3
k_x_start = -2
 
root_f = newton_rhapson_f(f_x_start, 100, 1.E-9)
root_g = newton_rhapson_g(g_x_start, 100, 1.E-9)
root_h = newton_rhapson_h(h_x_start, 100, 1.E-9)
root_h2 = newton_rhapson_h(h_x2_start, 100, 1.E-9)
root_j = newton_rhapson_j(j_x_start, 100, 1.E-9)
root_k = newton_rhapson_k(k_x_start, 100, 1.E-9)
 
print(root_f)
print(root_g)
print(root_h)
print(root_h2)
print(root_j)
print(root_k)