Highlighting a common subexpression using sympy
I am trying to learn how to use sympy to optimize the numerical evaluation of mathematical expressions in C. On the one hand, I know that sympy can generate C code to evaluate a single expression like this:
from mpmath import *
from sympy.utilities.codegen import codegen
from sympy import *
x,y,z = symbols('x y z')
[(c_name, c_code), (h_name, c_header)] = codegen([('x', sin(x))], 'C')
and then you can print c_code to destination file. On the other hand, I know that cse can be used to simplify expressions like this:
from mpmath import *
from sympy.utilities.codegen import codegen
from sympy import *
x,y,z, B1, B2, B3, B4 = symbols('x y z B1 B2 B3 B4 ')
cse([3.0*B2 + 8.0*B3*x**2 + 3.0*B3*x*y + 4.0*B3*x*z + B3*y**2 + B3*z**2 + B4*x**4 + B4*x**3*y + B4*x**3*z + B4*x**2*y**2 + B4*x**2*y*z + B4*x**2*z**2, 7.0*B3*x*y + 2*B3*x*z + B3*(x**2 + y**2) + B4*x**3*y + B4*x**2*y**2 + B4*x**2*y*z + B4*x*y**3 + B4*x*y**2*z + B4*x*y*z**2, B3*x*y + 8.0*B3*x*z + B3*(x**2 + z**2) + B4*x**3*z + B4*x**2*y*z + B4*x**2*z**2 + B4*x*y**2*z + B4*x*y*z**2 + B4*x*z**3, 3.0*B2 + B3*x**2 + 3.0*B3*x*y + B3*x*z + 8.0*B3*y**2 + 3.0*B3*y*z + B3*z**2 + B4*x**2*y**2 + B4*x*y**3 + B4*x*y**2*z + B4*y**4 + B4*y**3*z + B4*y**2*z**2, B3*x*y + 2*B3*x*z + 6.0*B3*y*z + B3*(y**2 + z**2) + B4*x**2*y*z + B4*x*y**2*z + B4*x*y*z**2 + B4*y**3*z + B4*y**2*z**2 + B4*y*z**3, 3.0*B2 + B3*x**2 + B3*x*y + 3.0*B3*x*z + B3*y**2 + 3.0*B3*y*z + 8.0*B3*z**2 + B4*x**2*z**2 + B4*x*y*z**2 + B4*x*z**3 + B4*y**2*z**2 + B4*y*z**3 + B4*z**4])
as a conclusion:
([(x0, z**2),
(x1, B3*x0),
(x2, B3*x),
(x3, x2*y),
(x4, 3.0*x3),
(x5, 3.0*B2),
(x6, y**2),
(x7, B3*x6),
(x8, x2*z),
(x9, x**2),
(x10, B3*x9),
(x11, B4*x**3),
(x12, x11*y),
(x13, x11*z),
(x14, B4*y),
(x15, x14*x9*z),
(x16, B4*x9),
(x17, x16*x6),
(x18, x0*x16),
(x19, 2*x8),
(x20, y**3),
(x21, B4*x),
(x22, x20*x21),
(x23, x0*x21*y),
(x24, x21*x6*z),
(x25, z**3),
(x26, x21*x25),
(x27, B3*y*z),
(x28, x10 + 3.0*x27),
(x29, B4*x20*z),
(x30, B4*x0*x6),
(x31, x14*x25)],
[B4*x**4 + x1 + 8.0*x10 + x12 + x13 + x15 + x17 + x18 + x4 + x5 + x7 + 4.0*x8,
B3*(x6 + x9) + x12 + x15 + x17 + x19 + x22 + x23 + x24 + 7.0*x3,
B3*(x0 + x9) + x13 + x15 + x18 + x23 + x24 + x26 + x3 + 8.0*x8,
B4*y**4 + x1 + x17 + x22 + x24 + x28 + x29 + x30 + x4 + x5 + 8.0*x7 + x8,
B3*(x0 + x6) + x15 + x19 + x23 + x24 + 6.0*x27 + x29 + x3 + x30 + x31,
B4*z**4 + 8.0*x1 + x18 + x23 + x26 + x28 + x3 + x30 + x31 + x5 + x7 + 3.0*x8])
My question is, how do I correctly convert the former result to C code? sometimes it can be useful to convert the given expressions to strings and work with such strings, how can this be done? The goal is to automate the post-CSE code generation process so that it can be applied in many expressions.
EDIT:
Building on the answer below, thanks to Wrzlprmft, the code to generate the corresponding C code snippet is:
from sympy.printing import ccode
from sympy import symbols, cse, numbered_symbols
x,y,z, B1, B2, B3, B4 = symbols('x y z B1 B2 B3 B4 ')
results = [3.0*B2 + 8.0*B3*x**2 + 3.0*B3*x*y + 4.0*B3*x*z + B3*y**2 + B3*z**2 + B4*x**4 + B4*x**3*y + B4*x**3*z + B4*x**2*y**2 + B4*x**2*y*z + B4*x**2*z**2, 7.0*B3*x*y + 2*B3*x*z + B3*(x**2 + y**2) + B4*x**3*y + B4*x**2*y**2 + B4*x**2*y*z + B4*x*y**3 + B4*x*y**2*z + B4*x*y*z**2, B3*x*y + 8.0*B3*x*z + B3*(x**2 + z**2) + B4*x**3*z + B4*x**2*y*z + B4*x**2*z**2 + B4*x*y**2*z + B4*x*y*z**2 + B4*x*z**3, 3.0*B2 + B3*x**2 + 3.0*B3*x*y + B3*x*z + 8.0*B3*y**2 + 3.0*B3*y*z + B3*z**2 + B4*x**2*y**2 + B4*x*y**3 + B4*x*y**2*z + B4*y**4 + B4*y**3*z + B4*y**2*z**2, B3*x*y + 2*B3*x*z + 6.0*B3*y*z + B3*(y**2 + z**2) + B4*x**2*y*z + B4*x*y**2*z + B4*x*y*z**2 + B4*y**3*z + B4*y**2*z**2 + B4*y*z**3, 3.0*B2 + B3*x**2 + B3*x*y + 3.0*B3*x*z + B3*y**2 + 3.0*B3*y*z + 8.0*B3*z**2 + B4*x**2*z**2 + B4*x*y*z**2 + B4*x*z**3 + B4*y**2*z**2 + B4*y*z**3 + B4*z**4]
CSE_results = cse(results,numbered_symbols("helper_"))
with open("snippet.c", "w") as output:
for helper in CSE_results[0]:
output.write("double ")
output.write(ccode(helper[1],helper[0]))
output.write("\n")
for i,result in enumerate(CSE_results[1]):
output.write(ccode(result,"result_%d"%i))
output.write("\n")
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The least painful way, perhaps, is to use a ccode
lower-level subroutine (and then, if desired, create a surrounding C template):
from sympy.printing import ccode
from sympy import symbols, cse, numbered_symbols
x,y,z, B1, B2, B3, B4 = symbols('x y z B1 B2 B3 B4 ')
results = [3.0*B2 + 8.0*B3*x**2 + 3.0*B3*x*y + 4.0*B3*x*z + B3*y**2 + B3*z**2 + B4*x**4 + B4*x**3*y + B4*x**3*z + B4*x**2*y**2 + B4*x**2*y*z + B4*x**2*z**2, 7.0*B3*x*y + 2*B3*x*z + B3*(x**2 + y**2) + B4*x**3*y + B4*x**2*y**2 + B4*x**2*y*z + B4*x*y**3 + B4*x*y**2*z + B4*x*y*z**2, B3*x*y + 8.0*B3*x*z + B3*(x**2 + z**2) + B4*x**3*z + B4*x**2*y*z + B4*x**2*z**2 + B4*x*y**2*z + B4*x*y*z**2 + B4*x*z**3, 3.0*B2 + B3*x**2 + 3.0*B3*x*y + B3*x*z + 8.0*B3*y**2 + 3.0*B3*y*z + B3*z**2 + B4*x**2*y**2 + B4*x*y**3 + B4*x*y**2*z + B4*y**4 + B4*y**3*z + B4*y**2*z**2, B3*x*y + 2*B3*x*z + 6.0*B3*y*z + B3*(y**2 + z**2) + B4*x**2*y*z + B4*x*y**2*z + B4*x*y*z**2 + B4*y**3*z + B4*y**2*z**2 + B4*y*z**3, 3.0*B2 + B3*x**2 + B3*x*y + 3.0*B3*x*z + B3*y**2 + 3.0*B3*y*z + 8.0*B3*z**2 + B4*x**2*z**2 + B4*x*y*z**2 + B4*x*z**3 + B4*y**2*z**2 + B4*y*z**3 + B4*z**4]
CSE_results = cse(results,numbered_symbols("helper_"))
with open("snippet.c", "w") as output:
for helper in CSE_results[0]:
output.write("double ")
output.write(ccode(helper[1],helper[0]))
output.write("\n")
for i,result in enumerate(CSE_results[1]):
output.write(ccode(result,"result_%i"%i))
output.write("\n")
This will create a file snippet.c
that looks like this:
double helper_0 = pow(z, 2);
double helper_1 = B3*helper_0;
[β¦]
double helper_31 = helper_14*helper_25;
result_0 = B4*pow(x, 4) + helper_1 + 8.0*helper_10 + [β¦];
[β¦]
result_5 = B4*pow(z, 4) + 8.0*helper_1 + helper_18 + [β¦];
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