Python code using cse from sympy:
from sympy import *
x=Symbol('x')
y=Symbol('y')
eq1 = 5*x**3*y**2 + y**3
eq2 = 4*x**2*y**3 + y**2
eq = [eq1,eq2]
print eq
(red,rep) = cse(eq)
print red
print rep
eq = [eq2,eq1]
print eq
(red,rep) = cse(eq)
print red
print rep
***********************************************
Output from the code:
[5*x**3*y**2 + y**3, 4*x**2*y**3 + y**2]
[(x0, y**3), (x1, x0**(2/3))]
[5*x**3*x1 + x0, 4*x**2*x0 + x1]
[4*x**2*y**3 + y**2, 5*x**3*y**2 + y**3]
[(x0, y**2), (x1, x0**(3/2))]
[4*x**2*x1 + x0, 5*x**3*x0 + x1]
**********************************************
The introduction of the powers 2/3 and 3/2 is not acceptable.
For one thing in Fortran 2/3 will beocme 0 and 3/2 will become 1.
Even if we make 2 and 3 floating point numbers this is not efficient.
Also if we take x0=y**2 and then try to compute y**3 using x0**(1.5)
we get the wrong answer in the case y is negative.
************************************************************
Is there some way to run cse to avoid this undesirable behavior?
Can cse be modified to avoid this undesirable behavior?
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