Evaluating a mathematical [removed]function) for a large number of input values fast

Question

The following questions

• Evaluating a mathematical expression in a string
  
• Equation parsing in Python
  
• Safe way to parse user-supplied

Answer 1

I have used the C++ ExprTK library in the past with great success. Here is a benchmark speed test amongst other C++ parsers (e.g. Muparser, MathExpr, ATMSP etc...) and ExprTK comes out on top.

There is a Python wrapper to ExprTK called cexprtk which I have used and have found to be very fast. You are able to compile the mathematical expression just once and then evaluate this serialised expression as many times as required. Here is a simple example code using cexprtk with the userinput_function:

import cexprtk
import time

userinput_function = '5*(1-(x*0.1))' # String - numbers should be handled as floats
demo_len = 20000 # Parameter for benchmark (20k to 30k in real life)

time_start = time.time()
x = 1

st = cexprtk.Symbol_Table({"x":x}, add_constants = True) # Setup the symbol table
Expr = cexprtk.Expression(userinput_function, st) # Apply the symbol table to the userinput_function

for x in range(0,demo_len,1):
    st.variables['x'] = x # Update the symbol table with the new x value
    Expr() # evaluate expression
time_end = time.time()

print('1 cexprtk: ' + str(round(time_end - time_start, 4)) + ' seconds')

On my machine (Linux, dual core, 2.5GHz), for a demo length of 20000 this completes in 0.0202 seconds.

For a demo length of 2,000,000 cexprtk finishes in 1.23 seconds.