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copied!<p>Using your F# version I got:</p> <pre><code>> e28(100000L);; Real: 00:00:00.061, CPU: 00:00:00.062, GC gen0: 2, gen1: 0, gen2: 0 val it : int64 = 666691667100001L </code></pre> <p>Using:</p> <pre><code>let e28d N = seq {2L..2L..N} |> Seq.collect(fun x->seq{yield x;yield x; yield x; yield x}) |> Seq.scan (+) 1L |> Seq.sum </code></pre> <p>I got:</p> <pre><code>> e28d(100000L);; Real: 00:00:00.040, CPU: 00:00:00.031, GC gen0: 2, gen1: 0, gen2: 0 val it : int64 = 666691667100001L </code></pre> <p>You will probably have a difficult time getting the python to perform quite as well as the F# simply since F# is compiled and Python is interpreted. That being said, the above improvement will work for the python as well:</p> <pre><code>>>> def e28a(N = 100000): diagNumber = 1; sum = diagNumber; for width in range(2, N+1, 2): for j in range(4): diagNumber += width; sum += diagNumber; return sum; >>> if __name__ == '__main__': import timeit print(timeit.timeit("e28a()", setup="from __main__ import e28a", number=10)) 0.5249497228663813 >>> def e28a(N = 100000): diagNumber = 1; sum = diagNumber; for width in range(2, N+1, 2): diagNumber += width; sum += diagNumber; diagNumber += width; sum += diagNumber; diagNumber += width; sum += diagNumber; diagNumber += width; sum += diagNumber; return sum; >>> if __name__ == '__main__': import timeit print(timeit.timeit("e28a()", setup="from __main__ import e28a", number=10)) 0.2585966329330063 >>> </code></pre> <p>Part of this improvement comes from fewer function calls, i.e.:</p> <pre><code>>>> def e28a(N = 100000): diagNumber = 1; sum = diagNumber; temp_range = range(4) #Change here for width in range(2, N+1, 2): for j in temp_range: #Change here diagNumber += width; sum += diagNumber; return sum; >>> if __name__ == '__main__': import timeit print(timeit.timeit("e28a()", setup="from __main__ import e28a", number=10)) 0.40251470339956086 >>> </code></pre> <p>And I think the other part comes from removing the loop. Both of these can be fairly expensive in Python.</p>

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