# (Program) Profiling

Premature optimization is the root of all evil…
– Donald Knuth

A profiler is a program that analyzes another program's execution to measure performance. Profilers sit among debuggers and compilers as a powerful tool in a programmer's arsenal.

## Use Case

Profilers help programmers optimize their programs. They answer an essential question, "where is my program spending its time?" Profiling establishes bottlenecks and helps prevent blind, premature optimization.

## Methods

Profilers fall into two major categories: deterministic and nondeterministic. Deterministic profilers instrument the program to collect timings. In contrast, nondeterministic profilers generally appear outside the program being analyzed. Nondeterministic profilers sample the instruction pointer and statistically deduce performance.

## Output

Profilers can collect a significant amount of information. CPU (time) and memory (space) are common metrics. Profilers also provide a trace of the program. A trace is a history of events (usually function calls) annotated with performance metrics.

## Example

```from random import random
import math

def estimate_pi(iterations):
"""Discover pi with Monte Carlo simulation."""
points = [(random(), random()) for _ in range(iterations)]
points_in_circle = 0
for point in points:
if is_in_circle(*point):
points_in_circle += 1
return 4 * (points_in_circle / iterations)

"""Where does the point appear in a circle superimposed on a square?"""
return measure(x, y, 0, 0) < radius

def measure(x1, y1, x2, y2):
"""Find the distance between two points."""
return math.sqrt((x2 - x1)**2 + (y2 - y1)**2)
```

`cProfile` is Python's built-in, deterministic profiler. Let's try running the profiler on the code above.

```> import cProfile
> cProfile.run('estimate_pi(10000000)', sort='cumulative')

50000005 function calls in 15.574 seconds

Ordered by: cumulative time

ncalls  tottime  percall  cumtime  percall filename:lineno(function)
1    0.000    0.000   15.574   15.574 {built-in method builtins.exec}
1    0.398    0.398   15.574   15.574 <string>:1(<module>)
1    2.229    2.229   15.175   15.175 pi.py:4(estimate_pi)
10000000    2.657    0.000    7.951    0.000 pi.py:13(is_in_circle)
10000000    4.551    0.000    5.293    0.000 pi.py:17(measure)
1    3.134    3.134    4.996    4.996 pi.py:6(<listcomp>)
20000000    1.862    0.000    1.862    0.000 {method 'random' of '_random.Random' objects}
10000000    0.743    0.000    0.743    0.000 {built-in method math.sqrt}
1    0.000    0.000    0.000    0.000 {method 'disable' of '_lsprof.Profiler' objects}
```

We can optimize this program in many ways. Most notably, we probably don't need to manually calculate Pi! We could simply use Python's `math.pi` constant. This is something that profiling won't tell you.