Wolfram Cloud Document

Re: Estimating Euler’s number (e) using probability: a fascinating approach

https://community.wolfram.com/groups/-/m/t/3140700

Implementations

Top-Level code

In[]:=

Clear[estimateE];estimateE[n_] := Module[{count,randomList,m}, randomList = RandomReal[{0, 1}, n]; count = Table[ Module[{prev = randomList[[i]], curr, c = 1}, While[ curr = RandomReal[]; curr < prev , prev = curr; c++ ]; c ], {i, 1, n} ]; m = Mean[N[count]]; 1 + m ]

(Old) Compile

In[]:=

estimateECompiledFunction = Compile{{n, _Integer}}, Module{count=0.,total=0.}, Do[ Module[{prev=RandomReal[],curr=0.,c=1}, While[ curr=RandomReal[]; curr>prev , prev=curr; c++; ]; count+=c; ], {n} ]; total = countn; 1. + total , CompilationTarget -> "C", RuntimeAttributes -> {Listable}, Parallelization -> True, RuntimeOptions->"Speed"

Out[]=

CompiledFunction

Argument count: 1

Argument types:

{_Integer}



FunctionCompile + DownValuesFunction

In[]:=

estimateECompiledCodeFunction1 = FunctionCompile[Typed[DownValuesFunction[estimateE], {"MachineInteger"} -> "MachineReal"]]

Out[]=

CompiledCodeFunction

Signature:

{Integer64}Real64



FunctionCompile + optimizations

In[]:=

estimateECompiledCodeFunction2 = FunctionCompile Function{Typed[n, "MachineInteger"]}, Native`AbortInhibit @ Native`UncheckedBlock @ Module{count = 0., total = 0., randomList}, randomList = RandomReal[{0, 1}, n]; Do[ Module[{prev = randomList[[i]], curr = 0., c = 1}, While[ curr = RandomReal[]; curr > prev , prev = curr; c += 1; ]; count += c; ], {i, n} ]; total = count  n; 1. + total  

Out[]=

CompiledCodeFunction

Signature:

{Integer64}Real64



Timings

In[]:=

Clear[computeEstimations]computeEstimations[estimateFun_] := Module[{res}, res = AbsoluteTiming[<|Table[<|i -> estimateFun[10^i]|>, {i, 4, 8}]|>]; <|"Data" -> res[[2]], "AbsoluteTiming" -> Quantity[res[[1]], "Seconds"]|> ];

In[]:=

res=Association@MapApply[(Print["Computing using ",#1,"..."];#1->computeEstimations[#2])&,{{"Top-Level",estimateE},{"Old Compile",estimateECompiledFunction},{"New Compile",estimateECompiledCodeFunction1},{"New Compile + Optimizations",estimateECompiledCodeFunction2}}];

Computing using Top-Level...

Computing using Old Compile...

Computing using New Compile...

Computing using New Compile + Optimizations...

In[]:=

ListPlot[res[[All,"Data"]],AxesLabel->{"10^","Estimate"},PlotLegends->Keys[res]]

Out[]=

	Top-Level
	Old Compile
	New Compile
	New Compile + Optimizations

In[]:=

Dataset[res[[All,"AbsoluteTiming"]]]

Out[]=

Top-Level	15.7112s
Old Compile	6.14201s
New Compile	5.61131s
New Compile + Optimizations	4.10656s