Sage Symbench

This is the SymPy implementation of the Sage symbolic benchmarks.

Results

Using SymPy 0.6.2-hg.

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

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:

#!/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)