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Amdahl's law in action - 27s to 0.03s by changing a function

Perhaps the most important lesson I've learned while studying computer science is that of Amdahl's law.

Graph Illustrating Amdahl's Law

Amdahl's law

Amdahl's law is generally used to predict the maximum speedup by improving a single component of a system (say, a function or a database). But the implications are simple: Improve the thing that will actually help.

As programmers, however, we would rather contemplate just what is the fastest way to concatenate a string. Or whether PHP is much faster than Ruby. And just how much more traffic you can handle with 5 or 10 fcgi workers. And so on. The internet is riddled with these questions. And let's not forget the age old debate of speed improvements by using raw SQL instead of an ORM.

Once upon a time I even wrote a web framework where I made sure to always use the fastest pattern of doing X in PHP. I knew databases were slow, so I did a lot of the work regarding JOINs and such in PHP.

Yeah.

Optimizing where it matters

The other day I finally assembled all the bits and pieces for an evolutionary algorithm in Haskell.

I'm trying to print Hello World by performing random changes on a population of strings - eventually I want to create an extensible framework for evolutionary algorithms that will let me write poetry programmatically.

It took 27 seconds to go 5 epochs. Just five generations.

INIT time 0.00s ( 0.00s elapsed)
MUT time 26.47s ( 27.00s elapsed)
GC time 0.62s ( 0.62s elapsed)
EXIT time 0.00s ( 0.00s elapsed)
Total time 27.08s ( 27.62s elapsed)
%GC time 2.3% (2.2% elapsed)
Productivity 97.7% of total user, 95.8% of total elapsed

Okay, it's definitely not a problem with memory access. 97.7% of the time is spent in computation, this is good, but slightly worrying. Let's do some profiling!

COST CENTRE MODULE %time %alloc
levenshtein Evaluators.Basic 91.5 100.0
levenshtein.d Evaluators.Basic 8.5 0.0

The levenshtein distance function I implemented costs 100% of computation time!

After replacing my function with the implementation suggested by Reddit life instantly became much easier. It now takes just 0.03 seconds to compute 5 epochs of the algorithm.

27 seconds -> 0.03 seconds by changing a single function.

The problem I have now is anything larger than ~25 epochs makes my computer decide something funny is going and kill the program, which says I'm doing something terrible with memory.

Then again, there are 480195 population members at the 25th epoch ... I probably don't need that many.

By the way, it's still not a memory problem per se (for 20 epochs):

Total time 10.72s ( 10.80s elapsed)
%GC time 23.4% (23.3% elapsed)
Alloc rate 2,736,341,212 bytes per MUT second
Productivity 76.6% of total user, 76.0% of total elapsed
-----
COST CENTRE MODULE %time %alloc
lev'''.lev Evaluators.Basic 61.5 58.8
lev'''.levMemo Evaluators.Basic 17.3 31.4
breedTwo Operators.Basic 2.8 2.4
breedTwo.(...) Operators.Basic 2.0 0.6
breedTwo.(...) Operators.Basic 1.3 0.6
breedTwo.(...) Operators.Basic 1.3 0.6
select.\ Selectors.Basic 1.1 0.3
lev'''.xa Evaluators.Basic 1.1 0.6

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Published on August 17th, 2012 in Amdahl, Amdahl's law, Evolutionary algorithm, Haskell, Hello world program, PHP, Reddit, SQL, Uncategorized

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