From SymPy

This is the SymPy implementation of the Sage symbolic benchmarks.

Results

Using SymPy 0.6.2-hg.

<source lang="bash"> R1 real(f(f(f(f(f(f(f(f(f(f(i/2))))))))))): 0.171966 R2 Hermite polynomial hermite(15, y): 0.159058 R3 a = [bool(f==f) for _ in range(10)]: 0.000156 R5 blowup(L, 8); L=uniq(L): 0.003254 R6 sum(trim((x+sin(i))/x+(x-sin(i))/x) for i in xrange(100)): 0.107605 R7 [f.subs(x, random()) for _ in xrange(10**4)]: 20.280508 R8 right(x^2,0,5,10^4): 3.463200 R10 v = [-pi,-pi+1/10..,pi]: 0.031427 R11 a = [random() + random()*I for w in [0..1000]]: 0.771343 </source>

Notes

• R4 is missing, we don't have Tuples in SymPy yet.
• R9 is missing, SymPy's factor() cannot do that

Otherwise the benchmarks should be equivalent.

Benchmarks script

Here is the script that produces the above output: <source lang="python">

1. !/usr/bin/env python

from timeit import default_timer as clock from random import random from sympy import Symbol, I, sqrt, Integer, factorial, pi, exp, pprint, \

   simplify, trim, sin, sympify, factor

x = Symbol("x") y = Symbol("y") z = Symbol("z")

def 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
   e = f(f(f(f(f(f(f(f(f(f(I/2)))))))))).as_real_imag()[0]

def 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()

   #def phi(n, y):
   #  return 1/(sqrt(2**n*factorial(n))*pi**(Integer(1)/4))*exp(-y**2/2)* \
   #            hermite(n,y)

   a = hermite(15, y)

def R3():

   "a = [bool(f==f) for _ in range(10)]"
   f = x+y+z
   a = [bool(f==f) for _ in range(10)]

def R4():

   # we don't have Tuples
   pass

def 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 = list(set(x))
       v.sort()
       return v
   L = [x, y, z]
   blowup(L, 8)
   L = uniq(L)

def R6():

   "sum(trim((x+sin(i))/x+(x-sin(i))/x) for i in xrange(100))"
   s = sum(trim((x+sin(i))/x+(x-sin(i))/x) for i in xrange(100))

def R7():

   "[f.subs(x, random()) for _ in xrange(10**4)]"
   f = x**24+34*x**12+45*x**3+9*x**18+34*x**10+32*x**21
   a = [f.subs(x, random()) for _ in xrange(10**4)]

def 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

   a = right(x**2,0,5,10**4)

def R9():

   "factor(x^20 - pi^5*y^20)"
   factor(x**20 - pi**5*y**20)

def 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]
   v = srange(-pi, pi, sympify(1)/10)

def R11():

   "a = [random() + random()*I for w in [0..1000]]"
   a = [random() + random()*I for w in range(1000)]
   a.sort()

def S1():

   "e=(x+y+z+1)**7;f=e*(e+1);f.expand()"
   e = (x+y+z+1)**7
   f = e*(e+1)
   f = f.expand()

benchmarks = [

       R1,
       R2,
       R3,
       R5,
       R6,
       R7,
       R8,
       #R9,
       R10,
       R11,
       #S1,
       ]

report = [] for b in benchmarks:

   t = clock()
   b()
   t = clock()-t
   print "%s%65s: %f" % (b.__name__, b.__doc__, t)

</source>