(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 239420, 5215]*) (*NotebookOutlinePosition[ 269170, 6316]*) (* CellTagsIndexPosition[ 269126, 6312]*) (*WindowFrame->Normal*) Notebook[{ Cell["The SinSurface application example", "Title"], Cell[TextData[StyleBox[ "Copyright \[Copyright] MathCore AB 1998"]], "Copyright"], Cell[CellGroupData[{ Cell["Introduction", "Section"], Cell[TextData[{ StyleBox[ "Below we describe the SinSurface program example. The actual computation \ is performed by the functions "], StyleBox["calcPlot", FontFamily->"Courier"], StyleBox[", "], StyleBox["sinFun2", FontFamily->"Courier"], StyleBox[" and their help functions."] }], "Text"], Cell[TextData[{ StyleBox["The two functions "], StyleBox["calcPlot", FontFamily->"Courier"], StyleBox[" and "], StyleBox["sinFun2", FontFamily->"Courier"], StyleBox[ " in the SinSurface package will be translated to C++ together with the \ declaration of the global array "], StyleBox["xyMatrix", FontFamily->"Courier"], StyleBox["."] }], "Text"], Cell[TextData[{ StyleBox["The array "], StyleBox["xyMatrix", FontFamily->"Courier"], StyleBox[" represents a 21x21 grid on which which the numeric function "], StyleBox["sinFun2", FontFamily->"Courier"], StyleBox[" will be computed."] }], "Text"], Cell[TextData[{ "The function ", StyleBox["calcPlot", FontFamily->"Courier"], " accepts four arguments which are coordinates that describe a square in \ the x-y plane, and one counter (", StyleBox["iter", FontFamily->"Courier"], ") to make the function repeat the computation as many times as necessary \ for measuring execution time. For each point on a 21x21 grid in that square, \ the numeric function ", StyleBox["sinFun2", FontFamily->"Courier"], " is called to compute a value that is stored as a matrix element in the \ matrix representing the grid." }], "Text"], Cell[TextData[{ "The function ", StyleBox["sinFun2", FontFamily->"Courier"], " computes essentially the same values as ", Cell[BoxData[ FormBox[ RowBox[{ StyleBox["Sin", FontFamily->"Courier"], "(", \(x + y\), ")"}], TraditionalForm]]], ", but in a more complicated way using a rather large expression obtained \ through conversion of the arguments into polar coordinates (through ", StyleBox["arcTan", FontFamily->"Courier"], ") and then using series expansion of both ", StyleBox["Sin", FontFamily->"Courier"], " and ", StyleBox["Cos", FontFamily->"Courier"], " in 10 terms. The resulting large symbolic expression (more than a page) \ becomes the body of ", StyleBox["sinFun2", FontFamily->"Courier"], ", and is then used as input to ", StyleBox["CompileEvaluateFunction", FontFamily->"Courier"], " (see Section 7.5 and Section 7.6.3 in the manual) to generate efficient \ C++ code." }], "Text"], Cell[TextData[{ "The SinSurface example application computes a function (here ", StyleBox["sinFun2", FontFamily->"Courier"], ") over a 2-D grid. The function values are first stored in the matrix ", StyleBox["xyMatrix", FontFamily->"Courier"], " before being plotted. The execution of compiled C++ code for the function \ ", StyleBox["sinFun2", FontFamily->"Courier"], " is approximately 500-1000 times faster than evaluating the same function \ interpretively within Mathematica." }], "Text"], Cell["\<\ To run this example, evaluate this notebook cell by cell or the whole at \ once.\ \>", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Initialization", "Section", InitializationCell->True], Cell[CellGroupData[{ Cell["Load the MathCode package", "Subsection", InitializationCell->True], Cell["\<\ First put a Needs statement, to make sure that the MathCode application is \ loaded:\ \>", "Text", InitializationCell->True], Cell[CellGroupData[{ Cell[BoxData[ \(Needs["\"]\)], "Input", InitializationCell->True], Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"MathCode C++ ver \"\>", "\[InvisibleSpace]", TagBox[ InterpretationBox["\<\" 1.01\"\>", 1.01, AutoDelete->True], (PaddedForm[ #, {3, 2}]&)], "\[InvisibleSpace]", "\<\" loaded.\"\>"}], SequenceForm[ "MathCode C++ ver ", PaddedForm[ 1.01, {3, 2}], " loaded."], Editable->False]], "Print"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Check current directory", "Subsection", InitializationCell->True], Cell["\<\ Check the current directory, since a number of files will be placed there \ during the code generation process.\ \>", "Text", InitializationCell->True], Cell[CellGroupData[{ Cell[BoxData[ \(Directory[]\)], "Input", InitializationCell->True], Cell[BoxData[ \("/home/pontus"\)], "Output"] }, Open ]], Cell["\<\ You might want to set the directory to some place where all generated files \ are put, e.g. the one below, or some other directory.\ \>", "Text", InitializationCell->True], Cell["\<\ SetDirectory[$MCRoot<>$PathnameSeparator<>\"Demos\"<>$\ PathnameSeparator<>\"SinSurface\"];\ \>", "Input", InitializationCell->True], Cell["Check whether this file is in the current directory.", "Text", InitializationCell->True], Cell["ExistFileQ[\"SinSurface.nb\"]", "Input", InitializationCell->True] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Start of the SinSurface package", "Section", InitializationCell->True], Cell["\<\ The SinSurface package starts in the usual way by a BeginPackage declaration \ which references other packages.The MathCodeContexts are needed in order to \ call the code generation related functions. \ \>", "Text", InitializationCell->True], Cell[BoxData[ \(\(BeginPackage["\", \ {MathCodeContexts}]; \ \n Off[General::spell]; \nClear["\"]; \ \)\)], "Input", InitializationCell->True], Cell[CellGroupData[{ Cell["Exported symbols", "Subsection", InitializationCell->True], Cell[TextData[{ "Define possibly exported symbols. Even though it is not necessary here, we \ enclose these names within a ", StyleBox["Begin[\"SinSurface\[OpenCurlyQuote]\"] ... End[]", FontFamily->"Courier"], " kind of \[OpenCurlyDoubleQuote]context bracket\[CloseCurlyDoubleQuote], \ since this can be put into a cell in the notebook, and conveniently \ re-evaluated (only this cell!) when a new name is added to the list below." }], "Text", InitializationCell->True], Cell[CellGroupData[{ Cell[BoxData[{ \(Begin["\"]\), \(\ xyMatrix; \ \n\ calcPlot; \n\ sinFun1; \n\ sinFun2; \ \n\ arcTan; \ \n \ sin; \ \n\ cos; \n\ plot; \ \n\ cplus; \ \n\ plotfile; \nEnd[]\)}], "Input", InitializationCell->True], Cell[BoxData[ \("SinSurface`"\)], "Output"], Cell[BoxData[ \("SinSurface`"\)], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Setting compilation options", "Subsection", InitializationCell->True], Cell[TextData[{ "This defines how the functions and variables in the package should be \ compiled to C++. By default, all typed variables and functions are compiled. \ However, the compilation process can be controlled in a more detailed manner \ by setting compilation options via ", StyleBox["SetCompilationOptions", FontFamily->"Courier"], ". For example, in this package the function ", StyleBox["sinFun2", FontFamily->"Courier"], " should be symbolically evaluated before being translated to code since it \ contains symbolic operations; the functions ", StyleBox["sin", FontFamily->"Courier"], ", ", StyleBox["cos", FontFamily->"Courier"], ", and ", StyleBox["arcTan", FontFamily->"Courier"], " should not be compiled at all since they are expanded within the body of \ ", StyleBox["sinFun2.", FontFamily->"Courier"], " The remaining typed function, ", StyleBox["calcPlot", FontFamily->"Courier"], ", will be compiled in the normal way." }], "Text", InitializationCell->True], Cell[BoxData[ \(\(SetCompilationOptions[\n\ \ EvaluateFunctions -> {sinFun2}, \n\ \ UnCompiledFunctions -> {sin, cos, arcTan}, \n\ \ MainFileAndFunction -> "\"\n]; \)\)], "Input", InitializationCell->True] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["The body of the SinSurface package", "Section", InitializationCell->True], Cell["\<\ Begin the implementation section of the SinSurface package, where functions \ are defined. This is usually private, to avoid accidental name shadowing due \ to identical local variables in several packages.\ \>", "Text", InitializationCell->True], Cell[BoxData[ \(\(Begin["\"]; \)\)], "Input", InitializationCell->True], Cell[CellGroupData[{ Cell["Global variables", "Subsection", InitializationCell->True], Cell["Declare global variables.", "Text", InitializationCell->True], Cell[TextData[{ StyleBox["Declare", FontColor->RGBColor[0, 0, 1]], "[\n ", StyleBox["Real[21,21]@", FontColor->RGBColor[0, 0, 1]], " xyMatrix \n];" }], "Input", InitializationCell->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["sin, cos"]], "Subsection", InitializationCell->True], Cell[TextData[StyleBox["Taylor-expanded sin and cos functions."]], "Text", InitializationCell->True], Cell[TextData[{ StyleBox["sin", FontColor->RGBColor[1, 0, 0]], "[Real@ x_ ]->Real := Normal[Series[Sin[z], {z,0,10}]] /. z -> x ;\n", StyleBox["cos", FontColor->RGBColor[1, 0, 0]], "[Real@ x_ ]->Real := Normal[Series[Cos[z], {z,0,10}]] /. z -> x ;" }], "Input", InitializationCell->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["arcTan"]], "Subsection", InitializationCell->True], Cell[TextData[{ StyleBox["Conversion of grid point to an angle, called by "], StyleBox["sinFun2.", FontFamily->"Courier"] }], "Text", InitializationCell->True], Cell[TextData[{ StyleBox["arcTan", FontColor->RGBColor[1, 0, 0]], "[Real@ x_,Real@ y_]->Real := (\n If[x < 0, Pi, 0] + If[ x == 0, \ Sign[y]*Pi/2, ArcTan[y/x] ]\n );" }], "Input", InitializationCell->True] }, Open ]], Cell[CellGroupData[{ Cell["sinFun2", "Subsection", InitializationCell->True], Cell[TextData[{ "The function ", StyleBox["sinFun2", FontFamily->"Courier"], " is the function to be computed and plotted, called by ", StyleBox["calcPlot", FontFamily->"Courier"], ". It provides a more complicated and computationally heavier way (series \ expansion) to calculate approximately the same as ", StyleBox["Sin[x+y]", FontFamily->"Courier"], ". This gives an example of a combination of symbolic and numeric \ operations as well as a rather standard mix of arithmetic operations. The \ expanded symbolic expression which comprises the body of ", StyleBox["SinFun2", FontFamily->"Courier"], " is between 1 and 2 pages long when printed." }], "Text", InitializationCell->True], Cell[TextData[{ "Note that the types of local variables to ", StyleBox["sinFun2", FontFamily->"Courier"], " need not necessarily be declared since ", StyleBox["CompileEvaluateFunction", FontFamily->"Courier"], " will symbolically expand the whole body before translating it to C++ \ code. " }], "Text", InitializationCell->True], Cell["\<\ Note also that a function to be symbolically expanded before final code \ generation should be without side effects, e.g. assignment to global \ variables or input/output, since otherwise these actions will be performed \ during the symbolic evaluation, which would be problematic.\ \>", "Text", InitializationCell->True], Cell[TextData[{ StyleBox["sinFun2", FontColor->RGBColor[1, 0, 0]], "[Real@ x_,Real@ y_]->Real := Block[\n {\n \tReal@ {r,xx,yy}\n },\n \ r = Sqrt[x^2+y^2];\n xx = r*cos[arcTan[x,y]];\n yy = \ r*sin[arcTan[x,y]]; \n sin[xx+yy]\n ];" }], "Input", InitializationCell->True] }, Open ]], Cell[CellGroupData[{ Cell["calcPlot ", "Subsection", InitializationCell->True], Cell[TextData[{ "The function ", StyleBox["calcPlot", FontFamily->"Courier"], " calculates data for a plot of sinFun2 over a 21x21 grid, which is \ returned as a 21x21 array." }], "Text", InitializationCell->True], Cell[TextData[{ StyleBox["calcPlot", FontColor->RGBColor[1, 0, 0]], "[Real@ xmin_, Real@ xmax_, Real@ ymin_,\n Real@ ymax_, Integer@ \ iter_]->Real[_,_] := \n Module[{ \n Integer@ n = 20,\n Real@ {x,y}, \n\ Integer@ {i, j, count}\n },\n For[count=1,count<=iter,count=count+1,\n \ \tFor[i=1, i<=(n+1), i=i+1, \n For[j=1, j<=(n+1), j=j+1,\n\t x = \ xmin+(xmax-xmin)*(i-1)/n; \n\t y = ymin+(ymax-ymin)*(j-1)/n;\n\t \ xyMatrix[[i,j]] = sinFun2[x,y]\n ]\n ]\n ];\n xyMatrix\n ];" }], "Input", InitializationCell->True] }, Open ]], Cell[CellGroupData[{ Cell["End of the SinSurface package", "Subsection", InitializationCell->True], Cell[CellGroupData[{ Cell["\<\ End[] EndPackage[]; \ \>", "Input", InitializationCell->True], Cell[BoxData[ \("SinSurface`Private`"\)], "Output"] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Execution", "Section"], Cell[TextData[{ "We first execute the application interpretively within ", StyleBox["Mathematica", FontSlant->"Italic"], ", and then compile the key function and execute the 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Metetra .747 .981 .742 r .83553 .57676 .8466 .57251 .87591 .54279 .86537 .54694 Metetra .742 .977 .73 r .86537 .54694 .87591 .54279 .90524 .51373 .89512 .51677 Metetra .75 .983 .751 r .89512 .51677 .90524 .51373 .93475 .48642 .9249 .48728 Metetra .77 .995 .803 r .9249 .48728 .93475 .48642 .96465 .46198 .95487 .45954 Metetra .439 .485 .81 r .35617 .60275 .37152 .63474 .39725 .64609 .38192 .61225 Metetra .423 .466 .8 r .38192 .61225 .39725 .64609 .42351 .6585 .40813 .62352 Metetra .415 .456 .795 r .40813 .62352 .42351 .6585 .45035 .67118 .43489 .63586 Metetra .415 .456 .795 r .43489 .63586 .45035 .67118 .47779 .6833 .46225 .64848 Metetra .423 .466 .8 r .46225 .64848 .47779 .6833 .50585 .69403 .49024 .66053 Metetra .437 .484 .81 r .49024 .66053 .50585 .69403 .5345 .70255 .51885 .67118 Metetra .46 .512 .825 r .51885 .67118 .5345 .70255 .56369 .7081 .54806 .67959 Metetra .49 .551 .846 r .54806 .67959 .56369 .7081 .59334 .71005 .57782 .68502 Metetra .528 .601 .87 r .57782 .68502 .59334 .71005 .62337 .70789 .60805 .6868 Metetra .574 .663 .898 r .60805 .6868 .62337 .70789 .65367 .70131 .63866 .68445 Metetra .626 .735 .925 r .63866 .68445 .65367 .70131 .68412 .6902 .66951 .67763 Metetra .681 .814 .946 r .66951 .67763 .68412 .6902 .71461 .67464 .70052 .66622 Metetra .732 .89 .952 r .70052 .66622 .71461 .67464 .74506 .65495 .73155 .65034 Metetra .768 .952 .935 r .73155 .65034 .74506 .65495 .77539 .63161 .76252 .63028 Metetra .782 .988 .894 r .76252 .63028 .77539 .63161 .80555 .60528 .79334 .60654 Metetra .777 .998 .837 r .79334 .60654 .80555 .60528 .83553 .57676 .82399 .57979 Metetra .762 .991 .782 r .82399 .57979 .83553 .57676 .86537 .54694 .85444 .55083 Metetra .747 .981 .742 r .85444 .55083 .86537 .54694 .89512 .51677 .88473 .52055 Metetra .742 .977 .73 r .88473 .52055 .89512 .51677 .9249 .48728 .91493 .48993 Metetra .75 .983 .751 r .91493 .48993 .9249 .48728 .95487 .45954 .94517 .45999 Metetra .464 .514 .825 r .34059 .57273 .35617 .60275 .38192 .61225 .3664 .57971 Metetra .439 .485 .81 r .3664 .57971 .38192 .61225 .40813 .62352 .39262 .58911 Metetra .423 .466 .8 r .39262 .58911 .40813 .62352 .43489 .63586 .41933 .6003 Metetra .415 .456 .795 r .41933 .6003 .43489 .63586 .46225 .64848 .44661 .61256 Metetra .415 .456 .795 r .44661 .61256 .46225 .64848 .49024 .66053 .47451 .6251 Metetra .423 .466 .8 r .47451 .6251 .49024 .66053 .51885 .67118 .50306 .63707 Metetra .437 .484 .81 r .50306 .63707 .51885 .67118 .54806 .67959 .53224 .64763 Metetra .46 .512 .825 r .53224 .64763 .54806 .67959 .57782 .68502 .56204 .65593 Metetra .49 .551 .846 r .56204 .65593 .57782 .68502 .60805 .6868 .5924 .66122 Metetra .528 .601 .87 r .5924 .66122 .60805 .6868 .63866 .68445 .62323 .66283 Metetra .574 .663 .898 r .62323 .66283 .63866 .68445 .66951 .67763 .65442 .66026 Metetra .626 .735 .925 r .65442 .66026 .66951 .67763 .70052 .66622 .68586 .65319 Metetra .681 .814 .946 r .68586 .65319 .70052 .66622 .73155 .65034 .71744 .64149 Metetra .732 .89 .952 r .71744 .64149 .73155 .65034 .76252 .63028 .74903 .62526 Metetra .768 .952 .935 r .74903 .62526 .76252 .63028 .79334 .60654 .78053 .60482 Metetra .782 .988 .894 r .78053 .60482 .79334 .60654 .82399 .57979 .81187 .58067 Metetra .777 .998 .837 r .81187 .58067 .82399 .57979 .85444 .55083 .84302 .55348 Metetra .762 .991 .782 r .84302 .55348 .85444 .55083 .88473 .52055 .87395 .52406 Metetra .747 .981 .742 r .87395 .52406 .88473 .52055 .91493 .48993 .90472 .49332 Metetra .742 .977 .73 r .90472 .49332 .91493 .48993 .94517 .45999 .93539 .46223 Metetra .497 .553 .843 r .32469 .54523 .34059 .57273 .3664 .57971 .35064 .54915 Metetra .464 .514 .825 r .35064 .54915 .3664 .57971 .39262 .58911 .37692 .55601 Metetra .439 .485 .81 r .37692 .55601 .39262 .58911 .41933 .6003 .40364 .5653 Metetra .423 .466 .8 r .40364 .5653 .41933 .6003 .44661 .61256 .43087 .5764 Metetra .415 .456 .795 r .43087 .5764 .44661 .61256 .47451 .6251 .45868 .58857 Metetra .415 .456 .795 r .45868 .58857 .47451 .6251 .50306 .63707 .48714 .60102 Metetra .423 .466 .8 r .48714 .60102 .50306 .63707 .53224 .64763 .51627 .6129 Metetra .437 .484 .81 r .51627 .6129 .53224 .64763 .56204 .65593 .54605 .62335 Metetra .46 .512 .825 r .54605 .62335 .56204 .65593 .5924 .66122 .57646 .63153 Metetra .49 .551 .846 r .57646 .63153 .5924 .66122 .62323 .66283 .60743 .63667 Metetra .528 .601 .87 r .60743 .63667 .62323 .66283 .65442 .66026 .63888 .6381 Metetra .574 .663 .898 r .63888 .6381 .65442 .66026 .68586 .65319 .67069 .6353 Metetra .626 .735 .925 r .67069 .6353 .68586 .65319 .71744 .64149 .70274 .62796 Metetra .681 .814 .946 r .70274 .62796 .71744 .64149 .74903 .62526 .73491 .61595 Metetra .732 .89 .952 r .73491 .61595 .74903 .62526 .78053 .60482 .76707 .59937 Metetra .768 .952 .935 r .76707 .59937 .78053 .60482 .81187 .58067 .79913 .57854 Metetra .782 .988 .894 r .79913 .57854 .81187 .58067 .84302 .55348 .83101 .55396 Metetra .777 .998 .837 r .83101 .55396 .84302 .55348 .87395 .52406 .86267 .52632 Metetra .762 .991 .782 r .86267 .52632 .87395 .52406 .90472 .49332 .8941 .49642 Metetra .747 .981 .742 r .8941 .49642 .90472 .49332 .93539 .46223 .92535 .4652 Metetra .54 .602 .864 r .30839 .52073 .32469 .54523 .35064 .54915 .33457 .52113 Metetra .497 .553 .843 r .33457 .52113 .35064 .54915 .37692 .55601 .36099 .52489 Metetra .464 .514 .825 r .36099 .52489 .37692 .55601 .40364 .5653 .38775 .53161 Metetra .439 .485 .81 r .38775 .53161 .40364 .5653 .43087 .5764 .41498 .54078 Metetra .423 .466 .8 r .41498 .54078 .43087 .5764 .45868 .58857 .44274 .55177 Metetra .415 .456 .795 r .44274 .55177 .45868 .58857 .48714 .60102 .47112 .56384 Metetra .415 .456 .795 r .47112 .56384 .48714 .60102 .51627 .6129 .50016 .57619 Metetra .423 .466 .8 r .50016 .57619 .51627 .6129 .54605 .62335 .52989 .58797 Metetra .437 .484 .81 r .52989 .58797 .54605 .62335 .57646 .63153 .56029 .59831 Metetra .46 .512 .825 r .56029 .59831 .57646 .63153 .60743 .63667 .59134 .60636 Metetra .49 .551 .846 r .59134 .60636 .60743 .63667 .63888 .6381 .62295 .61133 Metetra .528 .601 .87 r .62295 .61133 .63888 .6381 .67069 .6353 .65504 .61256 Metetra .574 .663 .898 r .65504 .61256 .67069 .6353 .70274 .62796 .68749 .60953 Metetra .626 .735 .925 r .68749 .60953 .70274 .62796 .73491 .61595 .72017 .60191 Metetra .681 .814 .946 r .72017 .60191 .73491 .61595 .76707 .59937 .75295 .58957 Metetra .732 .89 .952 r .75295 .58957 .76707 .59937 .79913 .57854 .78571 .57263 Metetra .768 .952 .935 r .78571 .57263 .79913 .57854 .83101 .55396 .81835 .55138 Metetra .782 .988 .894 r .81835 .55138 .83101 .55396 .86267 .52632 .85078 .52636 Metetra .777 .998 .837 r .85078 .52636 .86267 .52632 .8941 .49642 .88297 .49825 Metetra .762 .991 .782 r .88297 .49825 .8941 .49642 .92535 .4652 .91492 .46787 Metetra .59 .658 .885 r .29163 .49956 .30839 .52073 .33457 .52113 .3181 .49611 Metetra .54 .602 .864 r .3181 .49611 .33457 .52113 .36099 .52489 .34474 .49632 Metetra .497 .553 .843 r .34474 .49632 .36099 .52489 .38775 .53161 .37163 .49991 Metetra .464 .514 .825 r .37163 .49991 .38775 .53161 .41498 .54078 .39891 .50649 Metetra .439 .485 .81 r .39891 .50649 .41498 .54078 .44274 .55177 .42666 .51553 Metetra .423 .466 .8 r .42666 .51553 .44274 .55177 .47112 .56384 .45498 .52639 Metetra .415 .456 .795 r .45498 .52639 .47112 .56384 .50016 .57619 .48394 .53835 Metetra .415 .456 .795 r .48394 .53835 .50016 .57619 .52989 .58797 .51359 .5506 Metetra .423 .466 .8 r .51359 .5506 .52989 .58797 .56029 .59831 .54394 .56226 Metetra .437 .484 .81 r .54394 .56226 .56029 .59831 .59134 .60636 .57499 .57247 Metetra .46 .512 .825 r .57499 .57247 .59134 .60636 .62295 .61133 .60669 .58037 Metetra .49 .551 .846 r .60669 .58037 .62295 .61133 .65504 .61256 .63897 .58517 Metetra .528 .601 .87 r .63897 .58517 .65504 .61256 .68749 .60953 .67173 .58619 Metetra .574 .663 .898 r .67173 .58619 .68749 .60953 .72017 .60191 .70484 .58291 Metetra .626 .735 .925 r .70484 .58291 .72017 .60191 .75295 .58957 .73818 .57499 Metetra .681 .814 .946 r .73818 .57499 .75295 .58957 .78571 .57263 .7716 .56231 Metetra .732 .89 .952 r .7716 .56231 .78571 .57263 .81835 .55138 .80498 .54498 Metetra .768 .952 .935 r .80498 .54498 .81835 .55138 .85078 .52636 .83821 .52331 Metetra .782 .988 .894 r .83821 .52331 .85078 .52636 .88297 .49825 .87122 .49783 Metetra .777 .998 .837 r .87122 .49783 .88297 .49825 .91492 .46787 .90396 .46923 Metetra .644 .719 .903 r .2743 .48195 .29163 .49956 .3181 .49611 .30117 .47444 Metetra .59 .658 .885 r .30117 .47444 .3181 .49611 .34474 .49632 .3281 .47076 Metetra .54 .602 .864 r .3281 .47076 .34474 .49632 .37163 .49991 .35521 .47077 Metetra .497 .553 .843 r .35521 .47077 .37163 .49991 .39891 .50649 .3826 .47418 Metetra .464 .514 .825 r .3826 .47418 .39891 .50649 .42666 .51553 .4104 .4806 Metetra .439 .485 .81 r .4104 .4806 .42666 .51553 .45498 .52639 .4387 .4895 Metetra .423 .466 .8 r .4387 .4895 .45498 .52639 .48394 .53835 .4676 .50023 Metetra .415 .456 .795 r .4676 .50023 .48394 .53835 .51359 .5506 .49716 .51207 Metetra .415 .456 .795 r .49716 .51207 .51359 .5506 .54394 .56226 .52744 .52419 Metetra .423 .466 .8 r .52744 .52419 .54394 .56226 .57499 .57247 .55844 .53573 Metetra .437 .484 .81 r .55844 .53573 .57499 .57247 .60669 .58037 .59016 .5458 Metetra .46 .512 .825 r .59016 .5458 .60669 .58037 .63897 .58517 .62255 .55353 Metetra .49 .551 .846 r .62255 .55353 .63897 .58517 .67173 .58619 .65552 .55814 Metetra .528 .601 .87 r .65552 .55814 .67173 .58619 .70484 .58291 .68898 .55894 Metetra .574 .663 .898 r .68898 .55894 .70484 .58291 .73818 .57499 .72278 .55539 Metetra .626 .735 .925 r .72278 .55539 .73818 .57499 .7716 .56231 .7568 .54716 Metetra .681 .814 .946 r .7568 .54716 .7716 .56231 .80498 .54498 .79088 .53412 Metetra .732 .89 .952 r .79088 .53412 .80498 .54498 .83821 .52331 .8249 .51639 Metetra .768 .952 .935 r .8249 .51639 .83821 .52331 .87122 .49783 .85875 .49428 Metetra .782 .988 .894 r .85875 .49428 .87122 .49783 .90396 .46923 .89235 .46832 Metetra .699 .78 .915 r .25634 .46798 .2743 .48195 .30117 .47444 .28368 .45633 Metetra .644 .719 .903 r .28368 .45633 .30117 .47444 .3281 .47076 .31099 .44857 Metetra .59 .658 .885 r .31099 .44857 .3281 .47076 .35521 .47077 .33839 .44465 Metetra .54 .602 .864 r .33839 .44465 .35521 .47077 .3826 .47418 .36599 .44445 Metetra .497 .553 .843 r .36599 .44445 .3826 .47418 .4104 .4806 .39391 .44768 Metetra .464 .514 .825 r .39391 .44768 .4104 .4806 .4387 .4895 .42225 .45392 Metetra .439 .485 .81 r .42225 .45392 .4387 .4895 .4676 .50023 .45112 .46266 Metetra .423 .466 .8 r .45112 .46266 .4676 .50023 .49716 .51207 .48061 .47325 Metetra .415 .456 .795 r .48061 .47325 .49716 .51207 .52744 .52419 .5108 .48495 Metetra .415 .456 .795 r .5108 .48495 .52744 .52419 .55844 .53573 .54173 .49693 Metetra .423 .466 .8 r .54173 .49693 .55844 .53573 .59016 .5458 .57342 .50833 Metetra .437 .484 .81 r .57342 .50833 .59016 .5458 .62255 .55353 .60583 .51824 Metetra .46 .512 .825 r .60583 .51824 .62255 .55353 .65552 .55814 .63893 .5258 Metetra .49 .551 .846 r .63893 .5258 .65552 .55814 .68898 .55894 .67263 .5302 Metetra .528 .601 .87 r .67263 .5302 .68898 .55894 .72278 .55539 .70681 .53076 Metetra .574 .663 .898 r .70681 .53076 .72278 .55539 .7568 .54716 .74133 .52692 Metetra .626 .735 .925 r .74133 .52692 .7568 .54716 .79088 .53412 .77606 .51836 Metetra .681 .814 .946 r .77606 .51836 .79088 .53412 .8249 .51639 .81083 .50496 Metetra .732 .89 .952 r .81083 .50496 .8249 .51639 .85875 .49428 .84552 .4868 Metetra .768 .952 .935 r .84552 .4868 .85875 .49428 .89235 .46832 .88001 .46423 Metetra .749 .836 .918 r .23766 .45761 .25634 .46798 .28368 .45633 .26554 .44189 Metetra .699 .78 .915 r .26554 .44189 .28368 .45633 .31099 .44857 .29333 .42995 Metetra .644 .719 .903 r .29333 .42995 .31099 .44857 .33839 .44465 .32111 .42191 Metetra .59 .658 .885 r .32111 .42191 .33839 .44465 .36599 .44445 .349 .41776 Metetra .54 .602 .864 r .349 .41776 .36599 .44445 .39391 .44768 .37711 .41733 Metetra .497 .553 .843 r .37711 .41733 .39391 .44768 .42225 .45392 .40556 .42035 Metetra .464 .514 .825 r .40556 .42035 .42225 .45392 .45112 .46266 .43446 .42641 Metetra .439 .485 .81 r .43446 .42641 .45112 .46266 .48061 .47325 .46392 .43498 Metetra .423 .466 .8 r .46392 .43498 .48061 .47325 .5108 .48495 .49404 .44541 Metetra .415 .456 .795 r .49404 .44541 .5108 .48495 .54173 .49693 .52489 .45695 Metetra .415 .456 .795 r .52489 .45695 .54173 .49693 .57342 .50833 .5565 .46878 Metetra .423 .466 .8 r .5565 .46878 .57342 .50833 .60583 .51824 .58889 .48002 Metetra .437 .484 .81 r .58889 .48002 .60583 .51824 .63893 .5258 .62203 .48976 Metetra .46 .512 .825 r .62203 .48976 .63893 .5258 .67263 .5302 .65588 .49713 Metetra .49 .551 .846 r .65588 .49713 .67263 .5302 .70681 .53076 .69033 .50131 Metetra .528 .601 .87 r .69033 .50131 .70681 .53076 .74133 .52692 .72526 .5016 Metetra .574 .663 .898 r .72526 .5016 .74133 .52692 .77606 .51836 .76053 .49747 Metetra .626 .735 .925 r .76053 .49747 .77606 .51836 .81083 .50496 .79599 .48856 Metetra .681 .814 .946 r .79599 .48856 .81083 .50496 .84552 .4868 .83149 .47476 Metetra .732 .89 .952 r .83149 .47476 .84552 .4868 .88001 .46423 .86687 .45617 Metetra .657 .656 .837 r .21997 .43175 .23766 .45761 .26554 .44189 .24746 .42202 Metetra .642 .707 .894 r .24746 .42202 .26554 .44189 .29333 .42995 .2751 .41402 Metetra .608 .746 .942 r .2751 .41402 .29333 .42995 .32111 .42191 .30293 .40777 Metetra .562 .757 .969 r .30293 .40777 .32111 .42191 .349 .41776 .33101 .40325 Metetra .521 .739 .974 r .33101 .40325 .349 .41776 .37711 .41733 .3594 .40046 Metetra .498 .698 .959 r .3594 .40046 .37711 .41733 .40556 .42035 .38815 .39937 Metetra .489 .644 .926 r .38815 .39937 .40556 .42035 .43446 .42641 .41731 .40003 Metetra .482 .586 .882 r .41731 .40003 .43446 .42641 .46392 .43498 .44695 .40264 Metetra .466 .531 .84 r .44695 .40264 .46392 .43498 .49404 .44541 .47712 .40786 Metetra .435 .481 .809 r .47712 .40786 .49404 .44541 .52489 .45695 .50791 .41677 Metetra .416 .458 .795 r .50791 .41677 .52489 .45695 .5565 .46878 .53943 .42804 Metetra .415 .457 .795 r .53943 .42804 .5565 .46878 .58889 .48002 .57175 .4397 Metetra .423 .466 .8 r .57175 .4397 .58889 .48002 .62203 .48976 .60488 .45076 Metetra .437 .484 .81 r .60488 .45076 .62203 .48976 .65588 .49713 .63878 .46031 Metetra .46 .512 .825 r .63878 .46031 .65588 .49713 .69033 .50131 .6734 .46747 Metetra .49 .551 .846 r .6734 .46747 .69033 .50131 .72526 .5016 .70864 .47141 Metetra .528 .601 .87 r .70864 .47141 .72526 .5016 .76053 .49747 .74436 .47142 Metetra .574 .663 .898 r .74436 .47142 .76053 .49747 .79599 .48856 .78041 .46697 Metetra .626 .735 .925 r .78041 .46697 .79599 .48856 .83149 .47476 .81664 .4577 Metetra .681 .814 .946 r .81664 .4577 .83149 .47476 .86687 .45617 .85288 .44348 Metetra .724 .84 .936 r .20045 .42133 .21997 .43175 .24746 .42202 .22855 .40732 Metetra .698 .785 .918 r .22855 .40732 .24746 .42202 .2751 .41402 .25672 .39507 Metetra .67 .731 .896 r .25672 .39507 .2751 .41402 .30293 .40777 .28499 .3847 Metetra .641 .682 .873 r .28499 .3847 .30293 .40777 .33101 .40325 .31343 .37629 Metetra .613 .639 .853 r .31343 .37629 .33101 .40325 .3594 .40046 .34208 .36995 Metetra .586 .602 .835 r .34208 .36995 .3594 .40046 .38815 .39937 .371 .36584 Metetra .558 .57 .822 r .371 .36584 .38815 .39937 .41731 .40003 .40025 .36416 Metetra .526 .541 .813 r .40025 .36416 .41731 .40003 .44695 .40264 .42991 .36526 Metetra .489 .513 .809 r .42991 .36526 .44695 .40264 .47712 .40786 .46005 .36957 Metetra .45 .488 .806 r .46005 .36957 .47712 .40786 .50791 .41677 .49079 .37711 Metetra .425 .467 .8 r .49079 .37711 .50791 .41677 .53943 .42804 .52223 .38701 Metetra .415 .457 .795 r .52223 .38701 .53943 .42804 .57175 .4397 .55446 .39817 Metetra .415 .457 .795 r .55446 .39817 .57175 .4397 .60488 .45076 .58752 .40964 Metetra .423 .466 .8 r .58752 .40964 .60488 .45076 .63878 .46031 .62142 .4205 Metetra .437 .484 .81 r .62142 .4205 .63878 .46031 .6734 .46747 .65611 .42984 Metetra .46 .512 .825 r .65611 .42984 .6734 .46747 .70864 .47141 .69154 .43677 Metetra .49 .551 .846 r .69154 .43677 .70864 .47141 .74436 .47142 .7276 .44045 Metetra .528 .601 .87 r .7276 .44045 .74436 .47142 .78041 .46697 .76414 .44016 Metetra .574 .663 .898 r .76414 .44016 .78041 .46697 .81664 .4577 .80101 .43537 Metetra .626 .735 .925 r .80101 .43537 .81664 .4577 .85288 .44348 .83804 .42571 Metetra .763 .927 .941 r .17972 .41761 .20045 .42133 .22855 .40732 .20851 .3996 Metetra .748 .882 .941 r .20851 .3996 .22855 .40732 .25672 .39507 .2373 .38325 Metetra .724 .831 .931 r .2373 .38325 .25672 .39507 .28499 .3847 .26614 .36876 Metetra .695 .778 .915 r .26614 .36876 .28499 .3847 .31343 .37629 .29505 .35632 Metetra .662 .726 .897 r .29505 .35632 .31343 .37629 .34208 .36995 .32409 .34615 Metetra .627 .678 .879 r .32409 .34615 .34208 .36995 .371 .36584 .3533 .33851 Metetra .589 .633 .863 r .3533 .33851 .371 .36584 .40025 .36416 .38276 .33368 Metetra .55 .592 .849 r .38276 .33368 .40025 .36416 .42991 .36526 .41255 .33201 Metetra .508 .552 .836 r .41255 .33201 .42991 .36526 .46005 .36957 .44276 .33372 Metetra .47 .516 .823 r .44276 .33372 .46005 .36957 .49079 .37711 .4735 .33874 Metetra .441 .486 .81 r .4735 .33874 .49079 .37711 .52223 .38701 .50489 .34653 Metetra .423 .466 .8 r .50489 .34653 .52223 .38701 .55446 .39817 .53703 .35632 Metetra .415 .457 .795 r .53703 .35632 .55446 .39817 .58752 .40964 .57 .36728 Metetra .415 .457 .795 r .57 .36728 .58752 .40964 .62142 .4205 .60384 .37854 Metetra .423 .466 .8 r .60384 .37854 .62142 .4205 .65611 .42984 .63853 .38919 Metetra .437 .484 .81 r .63853 .38919 .65611 .42984 .69154 .43677 .67406 .3983 Metetra .46 .512 .826 r .67406 .3983 .69154 .43677 .7276 .44045 .71033 .40497 Metetra .49 .551 .846 r .71033 .40497 .7276 .44045 .76414 .44016 .74724 .40837 Metetra .528 .601 .87 r .74724 .40837 .76414 .44016 .80101 .43537 .78465 .40776 Metetra .574 .663 .898 r .78465 .40776 .80101 .43537 .83804 .42571 .82237 .40261 Metetra .786 .97 .917 r .15785 .41851 .17972 .41761 .20851 .3996 .18738 .39692 Metetra .782 .941 .93 r .18738 .39692 .20851 .3996 .2373 .38325 .21688 .37674 Metetra 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.50173 .27501 .53454 .28242 .51657 .24156 Metetra .439 .485 .81 r .51657 .24156 .53454 .28242 .56818 .29175 .55014 .2487 Metetra .423 .466 .8 r .55014 .2487 .56818 .29175 .60273 .30224 .58458 .25776 Metetra .415 .457 .795 r .58458 .25776 .60273 .30224 .63821 .31302 .61997 .26798 Metetra .415 .457 .795 r .61997 .26798 .63821 .31302 .67462 .32317 .65633 .27848 Metetra .423 .466 .8 r .65633 .27848 .67462 .32317 .71191 .33175 .69366 .28834 Metetra .437 .484 .81 r .69366 .28834 .71191 .33175 .75 .33785 .7319 .29662 Metetra .46 .512 .826 r .7319 .29662 .75 .33785 .78874 .34061 .77095 .30239 Metetra .825 .988 .873 r .08626 .43287 .11101 .42755 .14203 .40075 .11793 .40478 Metetra .832 .983 .876 r .11793 .40478 .14203 .40075 .17303 .37442 .14964 .3765 Metetra .835 .974 .883 r .14964 .3765 .17303 .37442 .20398 .34904 .18133 .34857 Metetra .833 .96 .892 r .18133 .34857 .20398 .34904 .23485 .32508 .21295 .32158 Metetra .824 .94 .903 r .21295 .32158 .23485 .32508 .26565 .30305 .24447 .29611 Metetra 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"Subsection"], Cell[TextData[{ "Redefine ", StyleBox["sinFun2", FontFamily->"Courier"], " to become a compiled version, using ", StyleBox["Mathematica", FontSlant->"Italic"], " standard ", StyleBox["Compile[]", FontFamily->"Courier"], "." }], "Text"], Cell["sinFun2 = Compile[{x, y}, Evaluate[sinFun2[x, y]]]; ", "Input"], Cell[CellGroupData[{ Cell["Timing[plot = calcPlot[-2., 2., -2., 2., 1]; ]", "Input"], Cell[BoxData[ \({0.52999999999999936`\ Second, Null}\)], "Output"] }, Open ]], Cell["compeval = %[[1]]; ", "Input"], Cell["sinFun2 =. ", "Input"] }, Open ]], Cell[CellGroupData[{ Cell["Fully Expanded Symbolic expression to be compiled to C++", "Subsection"], Cell[TextData[{ "This shows the size of ", StyleBox["sinFun2", FontFamily->"Courier"], " fully expanded. Be prepared for a big output." }], "Text"], Cell[CellGroupData[{ Cell["sinFun2[a, b]", "Input"], Cell[BoxData[ \(\@\(a\^2 + b\^2\)\ \((If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0] - 1\/6\ \(( If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^3 + 1\/120\ \(( If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^5 - \((If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^7\/5040 + \((If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^9\/362880)\) + \@\(a\^2 + b\^2\)\ \((1 - 1\/2\ \((If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^2 + 1\/24\ \(( If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^4 - 1\/720\ \(( If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^6 + \((If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^8\/40320 - \((If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^10\/3628800)\) - 1\/6\ \((\@\(a\^2 + b\^2\)\ \((If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0] - 1\/6\ \(( If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^3 + 1\/120\ \(( If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^5 - \((If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^7\/5040 + \((If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^9\/362880)\) + \@\(a\^2 + b\^2\)\ \((1 - 1\/2\ \((If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^2 + 1\/24\ \(( If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^4 - 1\/720\ \(( If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^6 + \((If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^8\/40320 - \((If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^10\/3628800)\))\)^3 + 1\/120\ \((\@\(a\^2 + b\^2\)\ \((If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0] - 1\/6\ \(( If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^3 + 1\/120\ \(( If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^5 - \((If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^7\/5040 + \((If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^9\/362880)\) + \@\(a\^2 + b\^2\)\ \((1 - 1\/2\ \((If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^2 + 1\/24\ \(( If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^4 - 1\/720\ \(( If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^6 + \((If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^8\/40320 - \((If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^10\/3628800)\))\)^5 - \(1\/5040\(( \((\@\(a\^2 + b\^2\)\ \((If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0] - 1\/6\ \(( If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^3 + 1\/120\ \(( If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^5 - \((If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^7\/5040 + \((If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^9\/362880)\) + \@\(a\^2 + b\^2\)\ \((1 - 1\/2\ \((If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^2 + 1\/24\ \(( If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^4 - 1\/720\ \(( If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^6 + \((If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^8\/40320 - \((If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^10\/3628800)\))\)^7) \)\) + \(1\/362880\(( \((\@\(a\^2 + b\^2\)\ \((If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0] - 1\/6\ \(( If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^3 + 1\/120\ \(( If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^5 - \((If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^7\/5040 + \((If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^9\/362880)\) + \@\(a\^2 + b\^2\)\ \((1 - 1\/2\ \((If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^2 + 1\/24\ \(( If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^4 - 1\/720\ \(( If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^6 + \((If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^8\/40320 - \((If[a == 0, 1\/2\ Sign[b]\ \[Pi], ArcTan[b\/a]] + If[a < 0, \[Pi], 0])\)\^10\/3628800)\))\)^9) \)\)\)], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Using the MathCode code generator", "Subsection"], Cell["Compile the SinSurface package:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(CompilePackage["\"]\)], "Input", InitializationCell->True], Cell[BoxData[ \("Successful compilation to C++: 3 function(s)"\)], "Print"] }, Open ]], Cell[TextData[{ "The warnings produced by ", StyleBox["CompilePackage", FontFamily->"Courier"], " is due to the lack of type information for the local variables of ", StyleBox["SinFun2.", FontFamily->"Courier"], " Since we have chosen to perform symbolic expansion ", StyleBox["SinFun2", FontFamily->"Courier"], " will be evaluated and the local variables therefore disappear." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["The generated C++ code", "Subsection"], Cell[TextData[{ "Below follows the generated C++ code from the SinSurface program. Notice \ that the package name becomes a prefix of the name of the generated C++ \ function. Thus the Mathematica function ", StyleBox["SinSurface\[OpenCurlyQuote]sinFun2", FontFamily->"Courier"], " becomes ", StyleBox["SinSurface_TsinFun2", FontFamily->"Courier"], " in C++." }], "Text"], Cell[TextData[{ "The generated code from ", StyleBox["SinSurface\[OpenCurlyQuote]sinFun2", FontFamily->"Courier"], " is produced from a large expression by ", StyleBox["CompileEvaluateFunction", FontFamily->"Courier"], ". Common subexpression elimination is performed by the code generator, \ producing many temporary variables and subexpressions which can be seen in \ the body of the C++ function ", StyleBox["SinSurface_TsinFun2.", FontFamily->"Courier"] }], "Text"], Cell[TextData[{ "By contrast, the C++ code in the body of function ", StyleBox["SinSurface_TcalcPlot", FontFamily->"Courier"], " produced by ", StyleBox["CompileFunction", FontFamily->"Courier"], " from the ", StyleBox["Mathematica", FontSlant->"Italic"], " function ", StyleBox["SinSurface\[OpenCurlyQuote]calcPlot", FontFamily->"Courier"], ", follows the structure of the original code quite closely." }], "Text"], Cell["\<\ We give a command to type out the text of the generated C++ file:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(!! SinSurface.cc\)\)], "Input"], Cell["\<\ #include \"SinSurface.h\" #include \"SinSurface.icc\" #include #include doubleNN SinSurface_TcalcPlot ( const double &xmin, const double &xmax, const \ double &ymin, const double &ymax, const int &iter) { int n = 20; double x; double y; int i; int j; int count; count = 1; while (count <= iter) { i = 1; while (i <= n+1) { j = 1; while (j <= n+1) { x = xmin+(((xmax+-xmin)*(i+-1))/n); y = ymin+(((ymax+-ymin)*(j+-1))/n); SinSurface_TxyMatrix(i, j) = SinSurface_TsinFun2 (x, y); j = j+1; } i = i+1; } count = count+1; } return SinSurface_TxyMatrix; } void SinSurface_TSinSurfaceInit () { ; } double SinSurface_TsinFun2 ( const double &x, const double &y) { int mc_T1; double mc_T2; double mc_T3; double mc_T4; int mc_T5; double mc_T6; double mc_T7; int mc_T8; double mc_T9; double mc_T10; double mc_T11; double mc_T12; double mc_T13; double mc_T14; double mc_T15; double mc_T16; double mc_T17; double mc_T18; double mc_T19; double mc_T20; double mc_T21; double mc_T22; double mc_T23; double mc_T24; double mc_T25; double mc_T26; double mc_T27; double mc_T28; double mc_T29; double mc_T30; double mc_T31; double mc_T32; double mc_T33; double mc_T34; double mc_T35; double mc_T36; double mc_T37; double mc_T38; double mc_T39; double mc_T40; double mc_T41; double mc_T42; double mc_T43; double mc_T44; double mc_T45; double mc_T46; double mc_T47; double mc_T48; double mc_T49; double mc_T50; double mc_T51; double mc_T52; mc_T1 = x < 0; if (mc_T1) { mc_T2 = 3.14159265358979323846; } else { mc_T2 = 0; } mc_T3 = y/x; mc_T4 = atan(mc_T3); mc_T5 = sign (y); mc_T6 = 3.14159265358979323846*mc_T5; mc_T7 = mc_T6/2; mc_T8 = x == 0; if (mc_T8) { mc_T9 = mc_T7; } else { mc_T9 = mc_T4; } mc_T10 = mc_T9+mc_T2; mc_T11 = pow(mc_T10, 10); mc_T12 = -2.755731922398589e-07; mc_T13 = mc_T12*mc_T11; mc_T14 = pow(mc_T10, 8); mc_T15 = mc_T14/40320; mc_T16 = pow(mc_T10, 6); mc_T17 = -0.001388888888888889; mc_T18 = mc_T17*mc_T16; mc_T19 = (mc_T10*mc_T10*mc_T10*mc_T10); mc_T20 = mc_T19/24; mc_T21 = (mc_T10*mc_T10); mc_T22 = -0.5; mc_T23 = mc_T22*mc_T21; mc_T24 = 1+mc_T23+mc_T20+mc_T18+mc_T15+mc_T13; mc_T25 = 0.5; mc_T26 = (y*y); mc_T27 = (x*x); mc_T28 = mc_T27+mc_T26; mc_T29 = pow(mc_T28, mc_T25); mc_T30 = mc_T29*mc_T24; mc_T31 = pow(mc_T10, 9); mc_T32 = mc_T31/362880; mc_T33 = pow(mc_T10, 7); mc_T34 = -0.0001984126984126984; mc_T35 = mc_T34*mc_T33; mc_T36 = pow(mc_T10, 5); mc_T37 = mc_T36/120; mc_T38 = (mc_T10*mc_T10*mc_T10); mc_T39 = -0.1666666666666667; mc_T40 = mc_T39*mc_T38; mc_T41 = mc_T9+mc_T2+mc_T40+mc_T37+mc_T35+mc_T32; mc_T42 = mc_T29*mc_T41; mc_T43 = mc_T42+mc_T30; mc_T44 = pow(mc_T43, 9); mc_T45 = mc_T44/362880; mc_T46 = pow(mc_T43, 7); mc_T47 = mc_T34*mc_T46; mc_T48 = pow(mc_T43, 5); mc_T49 = mc_T48/120; mc_T50 = (mc_T43*mc_T43*mc_T43); mc_T51 = mc_T39*mc_T50; mc_T52 = mc_T42+mc_T30+mc_T51+mc_T49+mc_T47+mc_T45; return mc_T52; } doubleNN SinSurface_TxyMatrix(21, 21);\ \>", "Print"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Compiling and linking the C++ code", "Subsection"], Cell[TextData[{ "The command ", StyleBox["MakeBinary", FontFamily->"Courier"], " compiles the generated C++ code using some C++ compiler (in this \ particular case the MicroSoft Visual C++, version 4.0, for Windows95). The \ object code is by default linked into two executables: ", StyleBox["SinSurfaceml.exe", FontFamily->"Courier"], " for calling the compiled code via ", StyleBox["MathLink", FontSlant->"Italic"], ", and ", StyleBox["SinSurfacemain.exe", FontFamily->"Courier"], " as a stand-alone executable." }], "Text"], Cell[BoxData[ \(\(MakeBinary[]; \)\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["Installing and connecting to Mathematica", "Subsection"], Cell[TextData[{ "The command ", StyleBox["InstallCode", FontFamily->"Courier"], " installs and connects the external process containing the compiled and \ linked SinSurface code." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(installedLink = InstallCode["\"]\)], "Input"], Cell[BoxData[ InterpretationBox[\("SinSurface"\[InvisibleSpace]" is installed."\), SequenceForm[ "SinSurface", " is installed."], Editable->False]], "Print"], Cell[BoxData[ \(LinkObject["'./SinSurfaceml.exe'", 3, 2]\)], "Output"] }, Open ]], Cell["Define a time measurement function called AbsTime:", "Text"], Cell[BoxData[ \(SetAttributes[AbsTime, HoldFirst]; \n\n AbsTime[x_]\ := \ Module[{\n\ \ start, res\n\ }, \n\ \ \ start\ = \ AbsoluteTime[]; \n \ \ \ res = x; \n \ \ \ {\((AbsoluteTime[] - start)\)\ Second, res}\n]; \)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["Execution of generated C++ code", "Subsection"], Cell["Perform the computation and the plot:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\((plot\ = \ calcPlot[\(-2.0\), 2.0, \(-2.0\), 2.0, 500]; )\)\ // \ AbsTime\)], "Input"], Cell[BoxData[ \({4.`6.3216\ Second, Null}\)], "Output"] }, Open ]], Cell["\<\ Since the external computation was performed 500 times, the time needed for \ one external computation is:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(externaleval\ = \ %[\([1]\)]/500\)], "Input"], Cell[BoxData[ \(0.008`6.3216\ Second\)], "Output"] }, Open ]], Cell["Just check that we get the right result", "Text"], Cell[CellGroupData[{ Cell[BoxData[ 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.59895 L s .40529 .59895 m .03716 .25514 L s .68874 0 m .96935 .42924 L s .96935 .42924 m 1 .6535 L s 1 .6535 m .70298 .24544 L s .70298 .24544 m .68874 0 L s .03716 .25514 m 0 .48963 L s 0 .48963 m .70298 .24544 L s .70298 .24544 m .68874 0 L s .68874 0 m .03716 .25514 L s .40529 .59895 m .96935 .42924 L s .96935 .42924 m 1 .6535 L s 1 .6535 m .39787 .81114 L s .39787 .81114 m .40529 .59895 L s 0 0 m 1 0 L 1 .81114 L 0 .81114 L closepath clip newpath .5 Mabswid .415 .456 .795 r .38667 .66802 .40169 .70187 .42754 .71466 .41245 .68049 Metetra .415 .456 .795 r .41245 .68049 .42754 .71466 .45396 .7269 .43878 .69323 Metetra .423 .466 .8 r .43878 .69323 .45396 .7269 .48097 .73777 .46571 .70541 Metetra .437 .484 .81 r .46571 .70541 .48097 .73777 .50855 .74646 .49323 .71622 Metetra .46 .512 .825 r .49323 .71622 .50855 .74646 .53666 .75224 .52134 .72483 Metetra .49 .551 .846 r .52134 .72483 .53666 .75224 .56523 .75448 .54997 .7305 Metetra .528 .601 .87 r .54997 .7305 .56523 .75448 .59417 .75269 .57907 .7326 Metetra .574 .663 .898 r .57907 .7326 .59417 .75269 .6234 .74656 .60855 .73063 Metetra .626 .735 .925 r .60855 .73063 .6234 .74656 .6528 .73598 .6383 .72428 Metetra .681 .814 .946 r .6383 .72428 .6528 .73598 .68227 .72104 .66822 .71344 Metetra .732 .89 .952 r .66822 .71344 .68227 .72104 .71174 .70204 .6982 .6982 Metetra .768 .952 .935 r .6982 .6982 .71174 .70204 .74111 .67946 .72814 .67886 Metetra .782 .988 .894 r .72814 .67886 .74111 .67946 .77035 .65395 .75799 .6559 Metetra .777 .998 .837 r .75799 .6559 .77035 .65395 .79943 .62628 .78768 .62999 Metetra .762 .991 .782 r .78768 .62999 .79943 .62628 .82839 .59732 .81721 .6019 Metetra .747 .981 .742 r .81721 .6019 .82839 .59732 .85727 .56802 .8466 .57251 Metetra .742 .977 .73 r .8466 .57251 .85727 .56802 .88618 .53939 .87591 .54279 Metetra .75 .983 .751 r .87591 .54279 .88618 .53939 .91525 .51248 .90524 .51373 Metetra .77 .995 .803 r .90524 .51373 .91525 .51248 .94467 .48843 .93475 .48642 Metetra .788 .994 .874 r .93475 .48642 .94467 .48843 .97471 .4685 .96465 .46198 Metetra .423 .466 .8 r .37152 .63474 .38667 .66802 .41245 .68049 .39725 .64609 Metetra .415 .456 .795 r .39725 .64609 .41245 .68049 .43878 .69323 .42351 .6585 Metetra .415 .456 .795 r .42351 .6585 .43878 .69323 .46571 .70541 .45035 .67118 Metetra .423 .466 .8 r .45035 .67118 .46571 .70541 .49323 .71622 .47779 .6833 Metetra .437 .484 .81 r .47779 .6833 .49323 .71622 .52134 .72483 .50585 .69403 Metetra .46 .512 .825 r .50585 .69403 .52134 .72483 .54997 .7305 .5345 .70255 Metetra .49 .551 .846 r .5345 .70255 .54997 .7305 .57907 .7326 .56369 .7081 Metetra .528 .601 .87 r .56369 .7081 .57907 .7326 .60855 .73063 .59334 .71005 Metetra .574 .663 .898 r .59334 .71005 .60855 .73063 .6383 .72428 .62337 .70789 Metetra .626 .735 .925 r .62337 .70789 .6383 .72428 .66822 .71344 .65367 .70131 Metetra .681 .814 .946 r .65367 .70131 .66822 .71344 .6982 .6982 .68412 .6902 Metetra .732 .89 .952 r .68412 .6902 .6982 .6982 .72814 .67886 .71461 .67464 Metetra .768 .952 .935 r .71461 .67464 .72814 .67886 .75799 .6559 .74506 .65495 Metetra .782 .988 .894 r .74506 .65495 .75799 .6559 .78768 .62999 .77539 .63161 Metetra .777 .998 .837 r .77539 .63161 .78768 .62999 .81721 .6019 .80555 .60528 Metetra .762 .991 .782 r .80555 .60528 .81721 .6019 .8466 .57251 .83553 .57676 Metetra .747 .981 .742 r .83553 .57676 .8466 .57251 .87591 .54279 .86537 .54694 Metetra .742 .977 .73 r .86537 .54694 .87591 .54279 .90524 .51373 .89512 .51677 Metetra .75 .983 .751 r .89512 .51677 .90524 .51373 .93475 .48642 .9249 .48728 Metetra .77 .995 .803 r .9249 .48728 .93475 .48642 .96465 .46198 .95487 .45954 Metetra .439 .485 .81 r .35617 .60275 .37152 .63474 .39725 .64609 .38192 .61225 Metetra .423 .466 .8 r .38192 .61225 .39725 .64609 .42351 .6585 .40813 .62352 Metetra .415 .456 .795 r .40813 .62352 .42351 .6585 .45035 .67118 .43489 .63586 Metetra .415 .456 .795 r .43489 .63586 .45035 .67118 .47779 .6833 .46225 .64848 Metetra .423 .466 .8 r .46225 .64848 .47779 .6833 .50585 .69403 .49024 .66053 Metetra .437 .484 .81 r .49024 .66053 .50585 .69403 .5345 .70255 .51885 .67118 Metetra .46 .512 .825 r .51885 .67118 .5345 .70255 .56369 .7081 .54806 .67959 Metetra .49 .551 .846 r .54806 .67959 .56369 .7081 .59334 .71005 .57782 .68502 Metetra .528 .601 .87 r .57782 .68502 .59334 .71005 .62337 .70789 .60805 .6868 Metetra .574 .663 .898 r .60805 .6868 .62337 .70789 .65367 .70131 .63866 .68445 Metetra .626 .735 .925 r .63866 .68445 .65367 .70131 .68412 .6902 .66951 .67763 Metetra .681 .814 .946 r .66951 .67763 .68412 .6902 .71461 .67464 .70052 .66622 Metetra .732 .89 .952 r .70052 .66622 .71461 .67464 .74506 .65495 .73155 .65034 Metetra .768 .952 .935 r .73155 .65034 .74506 .65495 .77539 .63161 .76252 .63028 Metetra .782 .988 .894 r .76252 .63028 .77539 .63161 .80555 .60528 .79334 .60654 Metetra .777 .998 .837 r .79334 .60654 .80555 .60528 .83553 .57676 .82399 .57979 Metetra .762 .991 .782 r .82399 .57979 .83553 .57676 .86537 .54694 .85444 .55083 Metetra .747 .981 .742 r .85444 .55083 .86537 .54694 .89512 .51677 .88473 .52055 Metetra .742 .977 .73 r .88473 .52055 .89512 .51677 .9249 .48728 .91493 .48993 Metetra .75 .983 .751 r .91493 .48993 .9249 .48728 .95487 .45954 .94517 .45999 Metetra .464 .514 .825 r .34059 .57273 .35617 .60275 .38192 .61225 .3664 .57971 Metetra .439 .485 .81 r .3664 .57971 .38192 .61225 .40813 .62352 .39262 .58911 Metetra .423 .466 .8 r .39262 .58911 .40813 .62352 .43489 .63586 .41933 .6003 Metetra .415 .456 .795 r .41933 .6003 .43489 .63586 .46225 .64848 .44661 .61256 Metetra .415 .456 .795 r .44661 .61256 .46225 .64848 .49024 .66053 .47451 .6251 Metetra .423 .466 .8 r .47451 .6251 .49024 .66053 .51885 .67118 .50306 .63707 Metetra .437 .484 .81 r .50306 .63707 .51885 .67118 .54806 .67959 .53224 .64763 Metetra .46 .512 .825 r .53224 .64763 .54806 .67959 .57782 .68502 .56204 .65593 Metetra .49 .551 .846 r .56204 .65593 .57782 .68502 .60805 .6868 .5924 .66122 Metetra .528 .601 .87 r .5924 .66122 .60805 .6868 .63866 .68445 .62323 .66283 Metetra .574 .663 .898 r .62323 .66283 .63866 .68445 .66951 .67763 .65442 .66026 Metetra .626 .735 .925 r .65442 .66026 .66951 .67763 .70052 .66622 .68586 .65319 Metetra .681 .814 .946 r .68586 .65319 .70052 .66622 .73155 .65034 .71744 .64149 Metetra .732 .89 .952 r .71744 .64149 .73155 .65034 .76252 .63028 .74903 .62526 Metetra .768 .952 .935 r .74903 .62526 .76252 .63028 .79334 .60654 .78053 .60482 Metetra .782 .988 .894 r .78053 .60482 .79334 .60654 .82399 .57979 .81187 .58067 Metetra .777 .998 .837 r .81187 .58067 .82399 .57979 .85444 .55083 .84302 .55348 Metetra .762 .991 .782 r .84302 .55348 .85444 .55083 .88473 .52055 .87395 .52406 Metetra .747 .981 .742 r .87395 .52406 .88473 .52055 .91493 .48993 .90472 .49332 Metetra .742 .977 .73 r .90472 .49332 .91493 .48993 .94517 .45999 .93539 .46223 Metetra .497 .553 .843 r .32469 .54523 .34059 .57273 .3664 .57971 .35064 .54915 Metetra .464 .514 .825 r .35064 .54915 .3664 .57971 .39262 .58911 .37692 .55601 Metetra .439 .485 .81 r .37692 .55601 .39262 .58911 .41933 .6003 .40364 .5653 Metetra .423 .466 .8 r .40364 .5653 .41933 .6003 .44661 .61256 .43087 .5764 Metetra .415 .456 .795 r .43087 .5764 .44661 .61256 .47451 .6251 .45868 .58857 Metetra .415 .456 .795 r .45868 .58857 .47451 .6251 .50306 .63707 .48714 .60102 Metetra .423 .466 .8 r .48714 .60102 .50306 .63707 .53224 .64763 .51627 .6129 Metetra .437 .484 .81 r .51627 .6129 .53224 .64763 .56204 .65593 .54605 .62335 Metetra .46 .512 .825 r .54605 .62335 .56204 .65593 .5924 .66122 .57646 .63153 Metetra .49 .551 .846 r .57646 .63153 .5924 .66122 .62323 .66283 .60743 .63667 Metetra .528 .601 .87 r .60743 .63667 .62323 .66283 .65442 .66026 .63888 .6381 Metetra .574 .663 .898 r .63888 .6381 .65442 .66026 .68586 .65319 .67069 .6353 Metetra .626 .735 .925 r .67069 .6353 .68586 .65319 .71744 .64149 .70274 .62796 Metetra .681 .814 .946 r .70274 .62796 .71744 .64149 .74903 .62526 .73491 .61595 Metetra .732 .89 .952 r .73491 .61595 .74903 .62526 .78053 .60482 .76707 .59937 Metetra .768 .952 .935 r .76707 .59937 .78053 .60482 .81187 .58067 .79913 .57854 Metetra .782 .988 .894 r .79913 .57854 .81187 .58067 .84302 .55348 .83101 .55396 Metetra .777 .998 .837 r .83101 .55396 .84302 .55348 .87395 .52406 .86267 .52632 Metetra .762 .991 .782 r .86267 .52632 .87395 .52406 .90472 .49332 .8941 .49642 Metetra .747 .981 .742 r .8941 .49642 .90472 .49332 .93539 .46223 .92535 .4652 Metetra .54 .602 .864 r .30839 .52073 .32469 .54523 .35064 .54915 .33457 .52113 Metetra .497 .553 .843 r .33457 .52113 .35064 .54915 .37692 .55601 .36099 .52489 Metetra .464 .514 .825 r .36099 .52489 .37692 .55601 .40364 .5653 .38775 .53161 Metetra .439 .485 .81 r .38775 .53161 .40364 .5653 .43087 .5764 .41498 .54078 Metetra .423 .466 .8 r .41498 .54078 .43087 .5764 .45868 .58857 .44274 .55177 Metetra .415 .456 .795 r .44274 .55177 .45868 .58857 .48714 .60102 .47112 .56384 Metetra .415 .456 .795 r .47112 .56384 .48714 .60102 .51627 .6129 .50016 .57619 Metetra .423 .466 .8 r .50016 .57619 .51627 .6129 .54605 .62335 .52989 .58797 Metetra .437 .484 .81 r .52989 .58797 .54605 .62335 .57646 .63153 .56029 .59831 Metetra .46 .512 .825 r .56029 .59831 .57646 .63153 .60743 .63667 .59134 .60636 Metetra .49 .551 .846 r .59134 .60636 .60743 .63667 .63888 .6381 .62295 .61133 Metetra .528 .601 .87 r .62295 .61133 .63888 .6381 .67069 .6353 .65504 .61256 Metetra .574 .663 .898 r .65504 .61256 .67069 .6353 .70274 .62796 .68749 .60953 Metetra .626 .735 .925 r .68749 .60953 .70274 .62796 .73491 .61595 .72017 .60191 Metetra .681 .814 .946 r .72017 .60191 .73491 .61595 .76707 .59937 .75295 .58957 Metetra .732 .89 .952 r .75295 .58957 .76707 .59937 .79913 .57854 .78571 .57263 Metetra .768 .952 .935 r .78571 .57263 .79913 .57854 .83101 .55396 .81835 .55138 Metetra .782 .988 .894 r .81835 .55138 .83101 .55396 .86267 .52632 .85078 .52636 Metetra .777 .998 .837 r .85078 .52636 .86267 .52632 .8941 .49642 .88297 .49825 Metetra .762 .991 .782 r .88297 .49825 .8941 .49642 .92535 .4652 .91492 .46787 Metetra .59 .658 .885 r .29163 .49956 .30839 .52073 .33457 .52113 .3181 .49611 Metetra .54 .602 .864 r .3181 .49611 .33457 .52113 .36099 .52489 .34474 .49632 Metetra .497 .553 .843 r .34474 .49632 .36099 .52489 .38775 .53161 .37163 .49991 Metetra .464 .514 .825 r .37163 .49991 .38775 .53161 .41498 .54078 .39891 .50649 Metetra .439 .485 .81 r .39891 .50649 .41498 .54078 .44274 .55177 .42666 .51553 Metetra .423 .466 .8 r .42666 .51553 .44274 .55177 .47112 .56384 .45498 .52639 Metetra .415 .456 .795 r .45498 .52639 .47112 .56384 .50016 .57619 .48394 .53835 Metetra .415 .456 .795 r .48394 .53835 .50016 .57619 .52989 .58797 .51359 .5506 Metetra .423 .466 .8 r .51359 .5506 .52989 .58797 .56029 .59831 .54394 .56226 Metetra .437 .484 .81 r .54394 .56226 .56029 .59831 .59134 .60636 .57499 .57247 Metetra .46 .512 .825 r .57499 .57247 .59134 .60636 .62295 .61133 .60669 .58037 Metetra .49 .551 .846 r .60669 .58037 .62295 .61133 .65504 .61256 .63897 .58517 Metetra .528 .601 .87 r .63897 .58517 .65504 .61256 .68749 .60953 .67173 .58619 Metetra .574 .663 .898 r .67173 .58619 .68749 .60953 .72017 .60191 .70484 .58291 Metetra .626 .735 .925 r .70484 .58291 .72017 .60191 .75295 .58957 .73818 .57499 Metetra .681 .814 .946 r .73818 .57499 .75295 .58957 .78571 .57263 .7716 .56231 Metetra .732 .89 .952 r .7716 .56231 .78571 .57263 .81835 .55138 .80498 .54498 Metetra .768 .952 .935 r .80498 .54498 .81835 .55138 .85078 .52636 .83821 .52331 Metetra .782 .988 .894 r .83821 .52331 .85078 .52636 .88297 .49825 .87122 .49783 Metetra .777 .998 .837 r .87122 .49783 .88297 .49825 .91492 .46787 .90396 .46923 Metetra .644 .719 .903 r .2743 .48195 .29163 .49956 .3181 .49611 .30117 .47444 Metetra .59 .658 .885 r .30117 .47444 .3181 .49611 .34474 .49632 .3281 .47076 Metetra .54 .602 .864 r .3281 .47076 .34474 .49632 .37163 .49991 .35521 .47077 Metetra .497 .553 .843 r .35521 .47077 .37163 .49991 .39891 .50649 .3826 .47418 Metetra .464 .514 .825 r .3826 .47418 .39891 .50649 .42666 .51553 .4104 .4806 Metetra .439 .485 .81 r .4104 .4806 .42666 .51553 .45498 .52639 .4387 .4895 Metetra .423 .466 .8 r .4387 .4895 .45498 .52639 .48394 .53835 .4676 .50023 Metetra .415 .456 .795 r .4676 .50023 .48394 .53835 .51359 .5506 .49716 .51207 Metetra .415 .456 .795 r .49716 .51207 .51359 .5506 .54394 .56226 .52744 .52419 Metetra .423 .466 .8 r .52744 .52419 .54394 .56226 .57499 .57247 .55844 .53573 Metetra .437 .484 .81 r .55844 .53573 .57499 .57247 .60669 .58037 .59016 .5458 Metetra .46 .512 .825 r .59016 .5458 .60669 .58037 .63897 .58517 .62255 .55353 Metetra .49 .551 .846 r .62255 .55353 .63897 .58517 .67173 .58619 .65552 .55814 Metetra .528 .601 .87 r .65552 .55814 .67173 .58619 .70484 .58291 .68898 .55894 Metetra .574 .663 .898 r .68898 .55894 .70484 .58291 .73818 .57499 .72278 .55539 Metetra .626 .735 .925 r .72278 .55539 .73818 .57499 .7716 .56231 .7568 .54716 Metetra .681 .814 .946 r .7568 .54716 .7716 .56231 .80498 .54498 .79088 .53412 Metetra .732 .89 .952 r .79088 .53412 .80498 .54498 .83821 .52331 .8249 .51639 Metetra .768 .952 .935 r .8249 .51639 .83821 .52331 .87122 .49783 .85875 .49428 Metetra .782 .988 .894 r .85875 .49428 .87122 .49783 .90396 .46923 .89235 .46832 Metetra .699 .78 .915 r .25634 .46798 .2743 .48195 .30117 .47444 .28368 .45633 Metetra .644 .719 .903 r .28368 .45633 .30117 .47444 .3281 .47076 .31099 .44857 Metetra .59 .658 .885 r .31099 .44857 .3281 .47076 .35521 .47077 .33839 .44465 Metetra .54 .602 .864 r .33839 .44465 .35521 .47077 .3826 .47418 .36599 .44445 Metetra .497 .553 .843 r .36599 .44445 .3826 .47418 .4104 .4806 .39391 .44768 Metetra .464 .514 .825 r .39391 .44768 .4104 .4806 .4387 .4895 .42225 .45392 Metetra .439 .485 .81 r .42225 .45392 .4387 .4895 .4676 .50023 .45112 .46266 Metetra .423 .466 .8 r .45112 .46266 .4676 .50023 .49716 .51207 .48061 .47325 Metetra .415 .456 .795 r .48061 .47325 .49716 .51207 .52744 .52419 .5108 .48495 Metetra .415 .456 .795 r .5108 .48495 .52744 .52419 .55844 .53573 .54173 .49693 Metetra .423 .466 .8 r .54173 .49693 .55844 .53573 .59016 .5458 .57342 .50833 Metetra .437 .484 .81 r .57342 .50833 .59016 .5458 .62255 .55353 .60583 .51824 Metetra .46 .512 .825 r .60583 .51824 .62255 .55353 .65552 .55814 .63893 .5258 Metetra .49 .551 .846 r .63893 .5258 .65552 .55814 .68898 .55894 .67263 .5302 Metetra .528 .601 .87 r .67263 .5302 .68898 .55894 .72278 .55539 .70681 .53076 Metetra .574 .663 .898 r .70681 .53076 .72278 .55539 .7568 .54716 .74133 .52692 Metetra .626 .735 .925 r .74133 .52692 .7568 .54716 .79088 .53412 .77606 .51836 Metetra .681 .814 .946 r .77606 .51836 .79088 .53412 .8249 .51639 .81083 .50496 Metetra .732 .89 .952 r .81083 .50496 .8249 .51639 .85875 .49428 .84552 .4868 Metetra .768 .952 .935 r .84552 .4868 .85875 .49428 .89235 .46832 .88001 .46423 Metetra .749 .836 .918 r .23766 .45761 .25634 .46798 .28368 .45633 .26554 .44189 Metetra .699 .78 .915 r .26554 .44189 .28368 .45633 .31099 .44857 .29333 .42995 Metetra .644 .719 .903 r .29333 .42995 .31099 .44857 .33839 .44465 .32111 .42191 Metetra .59 .658 .885 r .32111 .42191 .33839 .44465 .36599 .44445 .349 .41776 Metetra .54 .602 .864 r .349 .41776 .36599 .44445 .39391 .44768 .37711 .41733 Metetra .497 .553 .843 r .37711 .41733 .39391 .44768 .42225 .45392 .40556 .42035 Metetra .464 .514 .825 r .40556 .42035 .42225 .45392 .45112 .46266 .43446 .42641 Metetra .439 .485 .81 r .43446 .42641 .45112 .46266 .48061 .47325 .46392 .43498 Metetra .423 .466 .8 r .46392 .43498 .48061 .47325 .5108 .48495 .49404 .44541 Metetra .415 .456 .795 r .49404 .44541 .5108 .48495 .54173 .49693 .52489 .45695 Metetra .415 .456 .795 r .52489 .45695 .54173 .49693 .57342 .50833 .5565 .46878 Metetra .423 .466 .8 r .5565 .46878 .57342 .50833 .60583 .51824 .58889 .48002 Metetra .437 .484 .81 r .58889 .48002 .60583 .51824 .63893 .5258 .62203 .48976 Metetra .46 .512 .825 r .62203 .48976 .63893 .5258 .67263 .5302 .65588 .49713 Metetra .49 .551 .846 r .65588 .49713 .67263 .5302 .70681 .53076 .69033 .50131 Metetra .528 .601 .87 r .69033 .50131 .70681 .53076 .74133 .52692 .72526 .5016 Metetra .574 .663 .898 r .72526 .5016 .74133 .52692 .77606 .51836 .76053 .49747 Metetra .626 .735 .925 r .76053 .49747 .77606 .51836 .81083 .50496 .79599 .48856 Metetra .681 .814 .946 r .79599 .48856 .81083 .50496 .84552 .4868 .83149 .47476 Metetra .732 .89 .952 r .83149 .47476 .84552 .4868 .88001 .46423 .86687 .45617 Metetra .657 .656 .837 r .21997 .43175 .23766 .45761 .26554 .44189 .24746 .42202 Metetra .642 .707 .894 r .24746 .42202 .26554 .44189 .29333 .42995 .2751 .41402 Metetra .608 .746 .942 r .2751 .41402 .29333 .42995 .32111 .42191 .30293 .40777 Metetra .562 .757 .969 r .30293 .40777 .32111 .42191 .349 .41776 .33101 .40325 Metetra .521 .739 .974 r .33101 .40325 .349 .41776 .37711 .41733 .3594 .40046 Metetra .498 .698 .959 r .3594 .40046 .37711 .41733 .40556 .42035 .38815 .39937 Metetra .489 .644 .926 r .38815 .39937 .40556 .42035 .43446 .42641 .41731 .40003 Metetra .482 .586 .882 r .41731 .40003 .43446 .42641 .46392 .43498 .44695 .40264 Metetra .466 .531 .84 r .44695 .40264 .46392 .43498 .49404 .44541 .47712 .40786 Metetra .435 .481 .809 r .47712 .40786 .49404 .44541 .52489 .45695 .50791 .41677 Metetra .416 .458 .795 r .50791 .41677 .52489 .45695 .5565 .46878 .53943 .42804 Metetra .415 .457 .795 r .53943 .42804 .5565 .46878 .58889 .48002 .57175 .4397 Metetra .423 .466 .8 r .57175 .4397 .58889 .48002 .62203 .48976 .60488 .45076 Metetra .437 .484 .81 r .60488 .45076 .62203 .48976 .65588 .49713 .63878 .46031 Metetra .46 .512 .825 r .63878 .46031 .65588 .49713 .69033 .50131 .6734 .46747 Metetra .49 .551 .846 r .6734 .46747 .69033 .50131 .72526 .5016 .70864 .47141 Metetra .528 .601 .87 r .70864 .47141 .72526 .5016 .76053 .49747 .74436 .47142 Metetra .574 .663 .898 r .74436 .47142 .76053 .49747 .79599 .48856 .78041 .46697 Metetra .626 .735 .925 r .78041 .46697 .79599 .48856 .83149 .47476 .81664 .4577 Metetra .681 .814 .946 r .81664 .4577 .83149 .47476 .86687 .45617 .85288 .44348 Metetra .724 .84 .936 r .20045 .42133 .21997 .43175 .24746 .42202 .22855 .40732 Metetra .698 .785 .918 r .22855 .40732 .24746 .42202 .2751 .41402 .25672 .39507 Metetra .67 .731 .896 r .25672 .39507 .2751 .41402 .30293 .40777 .28499 .3847 Metetra .641 .682 .873 r .28499 .3847 .30293 .40777 .33101 .40325 .31343 .37629 Metetra .613 .639 .853 r .31343 .37629 .33101 .40325 .3594 .40046 .34208 .36995 Metetra .586 .602 .835 r .34208 .36995 .3594 .40046 .38815 .39937 .371 .36584 Metetra .558 .57 .822 r .371 .36584 .38815 .39937 .41731 .40003 .40025 .36416 Metetra .526 .541 .813 r .40025 .36416 .41731 .40003 .44695 .40264 .42991 .36526 Metetra .489 .513 .809 r .42991 .36526 .44695 .40264 .47712 .40786 .46005 .36957 Metetra .45 .488 .806 r .46005 .36957 .47712 .40786 .50791 .41677 .49079 .37711 Metetra .425 .467 .8 r .49079 .37711 .50791 .41677 .53943 .42804 .52223 .38701 Metetra .415 .457 .795 r .52223 .38701 .53943 .42804 .57175 .4397 .55446 .39817 Metetra .415 .457 .795 r .55446 .39817 .57175 .4397 .60488 .45076 .58752 .40964 Metetra .423 .466 .8 r .58752 .40964 .60488 .45076 .63878 .46031 .62142 .4205 Metetra .437 .484 .81 r .62142 .4205 .63878 .46031 .6734 .46747 .65611 .42984 Metetra .46 .512 .825 r .65611 .42984 .6734 .46747 .70864 .47141 .69154 .43677 Metetra .49 .551 .846 r .69154 .43677 .70864 .47141 .74436 .47142 .7276 .44045 Metetra .528 .601 .87 r .7276 .44045 .74436 .47142 .78041 .46697 .76414 .44016 Metetra .574 .663 .898 r .76414 .44016 .78041 .46697 .81664 .4577 .80101 .43537 Metetra .626 .735 .925 r .80101 .43537 .81664 .4577 .85288 .44348 .83804 .42571 Metetra .763 .927 .941 r .17972 .41761 .20045 .42133 .22855 .40732 .20851 .3996 Metetra .748 .882 .941 r .20851 .3996 .22855 .40732 .25672 .39507 .2373 .38325 Metetra .724 .831 .931 r .2373 .38325 .25672 .39507 .28499 .3847 .26614 .36876 Metetra .695 .778 .915 r .26614 .36876 .28499 .3847 .31343 .37629 .29505 .35632 Metetra .662 .726 .897 r .29505 .35632 .31343 .37629 .34208 .36995 .32409 .34615 Metetra .627 .678 .879 r .32409 .34615 .34208 .36995 .371 .36584 .3533 .33851 Metetra .589 .633 .863 r .3533 .33851 .371 .36584 .40025 .36416 .38276 .33368 Metetra .55 .592 .849 r .38276 .33368 .40025 .36416 .42991 .36526 .41255 .33201 Metetra .508 .552 .836 r .41255 .33201 .42991 .36526 .46005 .36957 .44276 .33372 Metetra .47 .516 .823 r .44276 .33372 .46005 .36957 .49079 .37711 .4735 .33874 Metetra .441 .486 .81 r .4735 .33874 .49079 .37711 .52223 .38701 .50489 .34653 Metetra .423 .466 .8 r .50489 .34653 .52223 .38701 .55446 .39817 .53703 .35632 Metetra .415 .457 .795 r .53703 .35632 .55446 .39817 .58752 .40964 .57 .36728 Metetra .415 .457 .795 r .57 .36728 .58752 .40964 .62142 .4205 .60384 .37854 Metetra .423 .466 .8 r .60384 .37854 .62142 .4205 .65611 .42984 .63853 .38919 Metetra .437 .484 .81 r .63853 .38919 .65611 .42984 .69154 .43677 .67406 .3983 Metetra .46 .512 .826 r .67406 .3983 .69154 .43677 .7276 .44045 .71033 .40497 Metetra .49 .551 .846 r .71033 .40497 .7276 .44045 .76414 .44016 .74724 .40837 Metetra .528 .601 .87 r .74724 .40837 .76414 .44016 .80101 .43537 .78465 .40776 Metetra .574 .663 .898 r .78465 .40776 .80101 .43537 .83804 .42571 .82237 .40261 Metetra .786 .97 .917 r .15785 .41851 .17972 .41761 .20851 .3996 .18738 .39692 Metetra .782 .941 .93 r .18738 .39692 .20851 .3996 .2373 .38325 .21688 .37674 Metetra .768 .902 .935 r .21688 .37674 .2373 .38325 .26614 .36876 .24636 .35825 Metetra .745 .856 .931 r .24636 .35825 .26614 .36876 .29505 .35632 .27585 .34176 Metetra .713 .805 .922 r .27585 .34176 .29505 .35632 .32409 .34615 .30539 .32756 Metetra .676 .752 .908 r .30539 .32756 .32409 .34615 .3533 .33851 .33502 .31601 Metetra .635 .7 .893 r .33502 .31601 .3533 .33851 .38276 .33368 .3648 .30745 Metetra .59 .649 .877 r .3648 .30745 .38276 .33368 .41255 .33201 .39482 .30222 Metetra .544 .599 .86 r .39482 .30222 .41255 .33201 .44276 .33372 .42518 .30053 Metetra .501 .554 .842 r .42518 .30053 .44276 .33372 .4735 .33874 .45599 .30235 Metetra .466 .515 .825 r .45599 .30235 .4735 .33874 .50489 .34653 .48738 .30736 Metetra .44 .486 .81 r .48738 .30736 .50489 .34653 .53703 .35632 .51946 .315 Metetra .423 .466 .8 r .51946 .315 .53703 .35632 .57 .36728 .55234 .32459 Metetra .415 .457 .795 r .55234 .32459 .57 .36728 .60384 .37854 .58608 .33532 Metetra .415 .457 .795 r .58608 .33532 .60384 .37854 .63853 .38919 .62072 .34635 Metetra .423 .466 .8 r .62072 .34635 .63853 .38919 .67406 .3983 .65626 .35676 Metetra .437 .484 .81 r .65626 .35676 .67406 .3983 .71033 .40497 .69265 .36562 Metetra .46 .512 .826 r .69265 .36562 .71033 .40497 .74724 .40837 .7298 .37202 Metetra .49 .551 .846 r .7298 .37202 .74724 .40837 .78465 .40776 .76761 .37511 Metetra .528 .601 .87 r .76761 .37511 .78465 .40776 .82237 .40261 .80591 .37416 Metetra .802 .986 .891 r .13491 .42231 .15785 .41851 .18738 .39692 .1652 .39773 Metetra .805 .97 .907 r .1652 .39773 .18738 .39692 .21688 .37674 .19545 .37417 Metetra .8 .944 .919 r .19545 .37417 .21688 .37674 .24636 .35825 .22565 .35199 Metetra .785 .909 .926 r .22565 .35199 .24636 .35825 .27585 .34176 .2558 .33159 Metetra .76 .867 .927 r .2558 .33159 .27585 .34176 .30539 .32756 .28593 .31338 Metetra .727 .818 .922 r .28593 .31338 .30539 .32756 .33502 .31601 .31608 .29777 Metetra .686 .765 .912 r .31608 .29777 .33502 .31601 .3648 .30745 .34629 .28517 Metetra .639 .71 .899 r .34629 .28517 .3648 .30745 .39482 .30222 .37664 .27597 Metetra .589 .655 .882 r .37664 .27597 .39482 .30222 .42518 .30053 .40724 .2704 Metetra .541 .601 .863 r .40724 .2704 .42518 .30053 .45599 .30235 .4382 .26853 Metetra .499 .554 .843 r .4382 .26853 .45599 .30235 .48738 .30736 .46966 .2702 Metetra .465 .514 .825 r .46966 .2702 .48738 .30736 .51946 .315 .50173 .27501 Metetra .439 .485 .81 r .50173 .27501 .51946 .315 .55234 .32459 .53454 .28242 Metetra .423 .466 .8 r .53454 .28242 .55234 .32459 .58608 .33532 .56818 .29175 Metetra .415 .457 .795 r .56818 .29175 .58608 .33532 .62072 .34635 .60273 .30224 Metetra .415 .457 .795 r .60273 .30224 .62072 .34635 .65626 .35676 .63821 .31302 Metetra .423 .466 .8 r .63821 .31302 .65626 .35676 .69265 .36562 .67462 .32317 Metetra .437 .484 .81 r .67462 .32317 .69265 .36562 .7298 .37202 .71191 .33175 Metetra .46 .512 .826 r .71191 .33175 .7298 .37202 .76761 .37511 .75 .33785 Metetra .49 .551 .846 r .75 .33785 .76761 .37511 .80591 .37416 .78874 .34061 Metetra .815 .99 .875 r .11101 .42755 .13491 .42231 .1652 .39773 .14203 .40075 Metetra .821 .981 .887 r .14203 .40075 .1652 .39773 .19545 .37417 .17303 .37442 Metetra .821 .965 .899 r .17303 .37442 .19545 .37417 .22565 .35199 .20398 .34904 Metetra .814 .942 .91 r .20398 .34904 .22565 .35199 .2558 .33159 .23485 .32508 Metetra .797 .911 .918 r .23485 .32508 .2558 .33159 .28593 .31338 .26565 .30305 Metetra .771 .872 .922 r .26565 .30305 .28593 .31338 .31608 .29777 .29639 .28345 Metetra .735 .825 .92 r .29639 .28345 .31608 .29777 .34629 .28517 .32713 .26674 Metetra .691 .772 .913 r .32713 .26674 .34629 .28517 .37664 .27597 .35792 .25337 Metetra .641 .715 .901 r .35792 .25337 .37664 .27597 .40724 .2704 .38886 .24366 Metetra .589 .656 .884 r .38886 .24366 .40724 .2704 .4382 .26853 .42007 .23775 Metetra .54 .601 .864 r .42007 .23775 .4382 .26853 .46966 .2702 .45166 .23562 Metetra .498 .553 .843 r .45166 .23562 .46966 .2702 .50173 .27501 .48379 .23702 Metetra .464 .514 .825 r .48379 .23702 .50173 .27501 .53454 .28242 .51657 .24156 Metetra .439 .485 .81 r .51657 .24156 .53454 .28242 .56818 .29175 .55014 .2487 Metetra .423 .466 .8 r .55014 .2487 .56818 .29175 .60273 .30224 .58458 .25776 Metetra .415 .457 .795 r .58458 .25776 .60273 .30224 .63821 .31302 .61997 .26798 Metetra .415 .457 .795 r .61997 .26798 .63821 .31302 .67462 .32317 .65633 .27848 Metetra .423 .466 .8 r .65633 .27848 .67462 .32317 .71191 .33175 .69366 .28834 Metetra .437 .484 .81 r .69366 .28834 .71191 .33175 .75 .33785 .7319 .29662 Metetra .46 .512 .826 r .7319 .29662 .75 .33785 .78874 .34061 .77095 .30239 Metetra .825 .988 .873 r .08626 .43287 .11101 .42755 .14203 .40075 .11793 .40478 Metetra .832 .983 .876 r .11793 .40478 .14203 .40075 .17303 .37442 .14964 .3765 Metetra .835 .974 .883 r .14964 .3765 .17303 .37442 .20398 .34904 .18133 .34857 Metetra .833 .96 .892 r .18133 .34857 .20398 .34904 .23485 .32508 .21295 .32158 Metetra .824 .94 .903 r .21295 .32158 .23485 .32508 .26565 .30305 .24447 .29611 Metetra .806 .911 .912 r .24447 .29611 .26565 .30305 .29639 .28345 .27589 .27274 Metetra .778 .874 .918 r .27589 .27274 .29639 .28345 .32713 .26674 .30724 .25204 Metetra .74 .828 .919 r .30724 .25204 .32713 .26674 .35792 .25337 .33857 .2345 Metetra .694 .775 .914 r .33857 .2345 .35792 .25337 .38886 .24366 .36995 .22051 Metetra .642 .716 .902 r .36995 .22051 .38886 .24366 .42007 .23775 .40149 .21035 Metetra .589 .657 .884 r .40149 .21035 .42007 .23775 .45166 .23562 .43332 .20408 Metetra .54 .602 .864 r .43332 .20408 .45166 .23562 .48379 .23702 .46558 .20162 Metetra .498 .553 .843 r .46558 .20162 .48379 .23702 .51657 .24156 .49841 .20271 Metetra .464 .514 .825 r .49841 .20271 .51657 .24156 .55014 .2487 .53194 .20695 Metetra .439 .485 .81 r .53194 .20695 .55014 .2487 .58458 .25776 .56629 .21379 Metetra .423 .466 .8 r .56629 .21379 .58458 .25776 .61997 .26798 .60157 .22255 Metetra .415 .457 .795 r .60157 .22255 .61997 .26798 .65633 .27848 .63783 .23246 Metetra .415 .457 .795 r .63783 .23246 .65633 .27848 .69366 .28834 .67512 .24266 Metetra .423 .466 .8 r .67512 .24266 .69366 .28834 .7319 .29662 .71341 .25221 Metetra .437 .484 .81 r .71341 .25221 .7319 .29662 .77095 .30239 .75264 .26016 Metetra .83 .981 .881 r .06079 .4369 .08626 .43287 .11793 .40478 .09298 .40866 Metetra .839 .98 .874 r .09298 .40866 .11793 .40478 .14964 .3765 .12532 .37938 Metetra .844 .976 .874 r .12532 .37938 .14964 .3765 .18133 .34857 .15772 .34973 Metetra .845 .969 .879 r .15772 .34973 .18133 .34857 .21295 .32158 .19008 .32038 Metetra .842 .956 .887 r .19008 .32038 .21295 .32158 .24447 .29611 .22235 .29201 Metetra .831 .937 .897 r .22235 .29201 .24447 .29611 .27589 .27274 .2545 .26528 Metetra .811 .911 .908 r .2545 .26528 .27589 .27274 .30724 .25204 .28654 .24085 Metetra .782 .876 .916 r .28654 .24085 .30724 .25204 .33857 .2345 .31848 .21927 Metetra .743 .83 .918 r .31848 .21927 .33857 .2345 .36995 .22051 .3504 .20105 Metetra .695 .777 .914 r .3504 .20105 .36995 .22051 .40149 .21035 .38238 .18653 Metetra .642 .717 .902 r .38238 .18653 .40149 .21035 .43332 .20408 .41455 .17593 Metetra .589 .657 .885 r .41455 .17593 .43332 .20408 .46558 .20162 .44704 .16928 Metetra .54 .601 .864 r .44704 .16928 .46558 .20162 .49841 .20271 .47998 .16646 Metetra .498 .553 .843 r .47998 .16646 .49841 .20271 .53194 .20695 .51354 .16721 Metetra .464 .514 .825 r .51354 .16721 .53194 .20695 .56629 .21379 .54785 .17111 Metetra .439 .485 .81 r .54785 .17111 .56629 .21379 .60157 .22255 .58303 .17762 Metetra .423 .466 .8 r .58303 .17762 .60157 .22255 .63783 .23246 .61918 .18605 Metetra .415 .457 .795 r .61918 .18605 .63783 .23246 .67512 .24266 .65636 .19563 Metetra .415 .457 .795 r .65636 .19563 .67512 .24266 .71341 .25221 .69462 .20549 Metetra .423 .466 .8 r .69462 .20549 .71341 .25221 .75264 .26016 .73392 .21469 Metetra .825 .965 .896 r .03483 .43822 .06079 .4369 .09298 .40866 .06733 .41112 Metetra .838 .972 .882 r .06733 .41112 .09298 .40866 .12532 .37938 .10017 .38199 Metetra .847 .973 .874 r .10017 .38199 .12532 .37938 .15772 .34973 .13317 .35159 Metetra .852 .971 .872 r .13317 .35159 .15772 .34973 .19008 .32038 .16623 .32072 Metetra .852 .964 .875 r .16623 .32072 .19008 .32038 .22235 .29201 .19925 .29013 Metetra .847 .953 .883 r .19925 .29013 .22235 .29201 .2545 .26528 .23216 .26059 Metetra .835 .936 .894 r .23216 .26059 .2545 .26528 .28654 .24085 .26494 .23283 Metetra .815 .911 .905 r .26494 .23283 .28654 .24085 .31848 .21927 .29758 .20751 Metetra .785 .877 .914 r .29758 .20751 .31848 .21927 .3504 .20105 .33012 .18521 Metetra .745 .832 .918 r .33012 .18521 .3504 .20105 .38238 .18653 .36264 .16639 Metetra .696 .778 .914 r .36264 .16639 .38238 .18653 .41455 .17593 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The generated C++ code for this example is roughly 500-1000 \ times faster than standard interpreted ", StyleBox["Mathematica", FontSlant->"Italic"], " code, and almost 50-100 times faster than expression code compiled by the \ internal ", StyleBox["Mathematica", FontSlant->"Italic"], " ", StyleBox["Compile[]", FontFamily->"Courier"], " command." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"TableForm", "[", RowBox[{ RowBox[{"(", GridBox[{ {"meval", \(meval/externaleval\)}, {"compeval", \(compeval/externaleval\)}, {"externaleval", "1"} }], ")"}], " ", ",", \(TableHeadings -> {{"\", "\", "\"}, {"\