# ex:=A + B \cos(x);
# nevaluate(ex, {$A$: 1, $B$: 3, $x$: np.linspace(0, 10, 10)});

import time
# import matplotlib.pyplot as plt
import numpy as np

def test01():
   start = time.time()
   ex:= \cos(x) \sin(y).
   xv = np.linspace(0, 3.14, 100);
   yv = np.linspace(0, 3.14, 100);
   z = np.array( nevaluate(ex, {$x$: xv, $y$: yv} ) )
   end = time.time()
   # print("that took", end-start, "seconds")
   assert( abs( z[10, 20] - 0.563 ) < 0.001)
   print("Test 01 passed")
   # XV, YV=np.meshgrid(xv, yv)
   # plt.figure(figsize=(20, 10))
   # ax = plt.axes(projection='3d')
   # ax.plot_surface(XV, YV, z, rstride=1, cstride=1, cmap='terrain', edgecolor=None)                   

test01()



def test02():
   res = np.array(nevaluate( $3\cos(x)$, {$x$: [0]}))
   assert(abs(res[0] - 3.0) < 0.001)
   print("Test 02a passed")
   res = np.array(nevaluate( $3\cos(3 x + \pi/4)$, {$x$: [0]}))
   assert(abs(res[0] - 2.1213) < 0.001)
   print("Test 02b passed")

test02()

def test03():
   res = np.array(nevaluate( $\pi x$, {$x$: [0,1,2]}))
   assert(np.max(res - np.array([0, 3.14, 6.28])) < 0.01)
   print("Test 03a passed")
   res = np.array(nevaluate( $x \pi$, {$x$: [0,1,2]}))
   assert(np.max(res - np.array([0, 3.14, 6.28])) < 0.01)
   print("Test 03b passed")
   res = np.array(nevaluate( $\pi + x$, {$x$: [0,1,2]}))
   assert(np.max(res - np.array([3.14, 4.14, 5.14])) < 0.01)
   print("Test 03c passed")
   res = np.array(nevaluate( $x + \pi$, {$x$: [0,1,2]}))
   assert(np.max(res - np.array([3.14, 4.14, 5.14])) < 0.01)
   print("Test 03d passed")

test03()

def test04():
   res = np.array( nevaluate($3 \cos(5 x)$, {$x$: [0.1, 0.3]}) )
   assert(np.max(res - np.array([2.6327, 0.2112])) < 0.01)
   print("Test 04a passed")
   xv = np.array([2.0, 5.0])
   res = np.array( nevaluate($\sin(3.0*x)*\cos(-1/2 x)*\exp(-x**(2/5))$, {$x$: xv} ))
   assert(np.max(res - np.sin(3.0*xv)*np.cos(-1/2*xv)*np.exp(-xv**(2/5))) < 0.01)
   print("Test 04b passed")

test04()

ex:=\cos(v x);
vv=0.2
substitute(ex, $v -> @(vv)$);