text: #!/usr/bin/env python
  from random import random
  from sympy.core.numbers import (I, Integer, pi)
  from sympy.core.symbol import Symbol
  from sympy.core.sympify import sympify
  from sympy.functions.elementary.miscellaneous import sqrt
  from sympy.functions.elementary.trigonometric import sin
  from sympy.polys.polytools import factor
  from sympy.simplify.simplify import simplify
  from sympy.abc import x, y, z
  from timeit import default_timer as clock
  
  
  def bench_R1():
      "real(f(f(f(f(f(f(f(f(f(f(i/2)))))))))))"
      def f(z):
          return sqrt(Integer(1)/3)*z**2 + I/3
      f(f(f(f(f(f(f(f(f(f(I/2)))))))))).as_real_imag()[0]
  
  
  def bench_R2():
      "Hermite polynomial hermite(15, y)"
      def hermite(n, y):
          if n == 1:
              return 2*y
          if n == 0:
              return 1
          return (2*y*hermite(n - 1, y) - 2*(n - 1)*hermite(n - 2, y)).expand()
  
      hermite(15, y)
  
  
  def bench_R3():
      "a = [bool(f==f) for _ in range(10)]"
      f = x + y + z
      [bool(f == f) for _ in range(10)]
  
  
  def bench_R4():
      # we don't have Tuples
      pass
  
  
  def bench_R5():
      "blowup(L, 8); L=uniq(L)"
      def blowup(L, n):
          for i in range(n):
              L.append( (L[i] + L[i + 1]) * L[i + 2] )
  
      def uniq(x):
          v = set(x)
          return v
      L = [x, y, z]
      blowup(L, 8)
      L = uniq(L)
  
  
  def bench_R6():
      "sum(simplify((x+sin(i))/x+(x-sin(i))/x) for i in range(100))"
      sum(simplify((x + sin(i))/x + (x - sin(i))/x) for i in range(100))
  
  
  def bench_R7():
      "[f.subs(x, random()) for _ in range(10**4)]"
      f = x**24 + 34*x**12 + 45*x**3 + 9*x**18 + 34*x**10 + 32*x**21
      [f.subs(x, random()) for _ in range(10**4)]
  
  
  def bench_R8():
      "right(x^2,0,5,10^4)"
      def right(f, a, b, n):
          a = sympify(a)
          b = sympify(b)
          n = sympify(n)
          x = f.atoms(Symbol).pop()
          Deltax = (b - a)/n
          c = a
          est = 0
          for i in range(n):
              c += Deltax
              est += f.subs(x, c)
          return est*Deltax
  
      right(x**2, 0, 5, 10**4)
  
  
  def _bench_R9():
      "factor(x^20 - pi^5*y^20)"
      factor(x**20 - pi**5*y**20)
  
  
  def bench_R10():
      "v = [-pi,-pi+1/10..,pi]"
      def srange(min, max, step):
          v = [min]
          while (max - v[-1]).evalf() > 0:
              v.append(v[-1] + step)
          return v[:-1]
      srange(-pi, pi, sympify(1)/10)
  
  
  def bench_R11():
      "a = [random() + random()*I for w in [0..1000]]"
      [random() + random()*I for w in range(1000)]
  
  
  def bench_S1():
      "e=(x+y+z+1)**7;f=e*(e+1);f.expand()"
      e = (x + y + z + 1)**7
      f = e*(e + 1)
      f.expand()
  
  
  if __name__ == '__main__':
      benchmarks = [
          bench_R1,
          bench_R2,
          bench_R3,
          bench_R5,
          bench_R6,
          bench_R7,
          bench_R8,
          #_bench_R9,
          bench_R10,
          bench_R11,
          #bench_S1,
      ]
  
      report = []
      for b in benchmarks:
          t = clock()
          b()
          t = clock() - t
          print("%s%65s: %f" % (b.__name__, b.__doc__, t))
  