import math
import random
import numpy as np
from numba import jit, vectorize, float64
import matplotlib.pyplot as plt
import seaborn
%matplotlib inline

def step():
    return 1. if random.random() > .5 else -1.

def walk(n):
    x = np.zeros(n)
    dx = 1. / n
    for i in range(n - 1):
        x_new = x[i] + dx * step()
        if x_new > 5e-3:
            x[i + 1] = 0.
        else:
            x[i + 1] = x_new
    return x

n = 100000
x = walk(n)

plt.plot(x)

%%timeit
walk(n)

@jit(nopython=True)
def step_numba():
    return 1. if random.random() > .5 else -1.

@jit(nopython=True)
def walk_numba(n):
    x = np.zeros(n)
    dx = 1. / n
    for i in range(n - 1):
        x_new = x[i] + dx * step_numba()
        if x_new > 5e-3:
            x[i + 1] = 0.
        else:
            x[i + 1] = x_new
    return x

%%timeit
walk_numba(n)

x = np.random.rand(10000000)
%timeit np.cos(2*x**2 + 3*x + 4*np.exp(x**3))

@vectorize
def kernel(x):
    return np.cos(2*x**2 + 3*x + 4*np.exp(x**3))

kernel(1.)

%timeit kernel(x)

import numexpr
%timeit numexpr.evaluate('cos(2*x**2 + 3*x + 4*exp(x**3))')

numexpr.detect_number_of_cores()