﻿<?xml version="1.0" encoding="utf-8" standalone="yes"?>
<?application progid="SMath Studio Desktop" version="0.99.7921.69"?>
<worksheet xmlns="http://smath.info/schemas/worksheet/1.0">
  <settings ppi="144">
    <identity>
      <id>9a11cfaf-b87f-4d6b-9321-84972669fce9</id>
      <revision>56</revision>
    </identity>
    <metadata lang="ger">
      <author>Johannes Piel</author>
    </metadata>
    <metadata lang="eng">
      <author>Johannes Piel</author>
    </metadata>
    <calculation>
      <precision>4</precision>
      <exponentialThreshold>5</exponentialThreshold>
      <trailingZeros>false</trailingZeros>
      <significantDigitsMode>false</significantDigitsMode>
      <roundingMode>0</roundingMode>
      <fractions>decimal</fractions>
    </calculation>
    <pageModel active="false" viewMode="1" printGrid="false" printAreas="true" simpleEqualsOnly="false" printBackgroundImages="true">
      <paper id="9" orientation="Portrait" width="827" height="1169" />
      <margins left="39" right="39" top="49" bottom="49" />
      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
      <footer alignment="Center" color="#a9a9a9">&amp;[PAGENUM] / &amp;[COUNT]</footer>
      <backgrounds />
    </pageModel>
    <dependencies>
      <assembly name="SMath Studio Desktop" version="0.99.7921.69" guid="a37cba83-b69c-4c71-9992-55ff666763bd" />
      <assembly name="MathRegion" version="1.11.7921.69" guid="02f1ab51-215b-466e-a74d-5d8b1cf85e8d" />
      <assembly name="Custom Functions" version="1.1.7840.30466" guid="18dadffd-79a3-4cf9-aee1-d66deb0ea720" />
      <assembly name="SpecialFunctions" version="1.12.7921.69" guid="2814e667-4e12-48b1-8d51-194e480eabc5" />
      <assembly name="TextRegion" version="1.11.7921.69" guid="485d28c5-349a-48b6-93be-12a35a1c1e39" />
      <assembly name="Statistical Tools" version="1.0.6824.32561" guid="76f6e9f5-ac86-4ffb-9e4d-284c8daecaf9" />
    </dependencies>
  </settings>
  <regions type="content">
    <region left="18" top="90" width="354" height="57" color="#000000" fontSize="10">
      <math optimize="2" decimalPlaces="3" exponentialThreshold="15" trailingZeros="true">
        <input>
          <e type="operand">N</e>
          <e type="operand">μ</e>
          <e type="operand">σ</e>
          <e type="function" args="3">rnorm1</e>
          <e type="operand">R</e>
          <e type="operand">N</e>
          <e type="function" args="1">Random</e>
          <e type="operator" args="2">:</e>
          <e type="operand">μ</e>
          <e type="operand">σ</e>
          <e type="operand">2</e>
          <e type="function" args="1">sqrt</e>
          <e type="operand">2</e>
          <e type="operand">R</e>
          <e type="operator" args="2">*</e>
          <e type="operand">1</e>
          <e type="operator" args="2">-</e>
          <e type="function" args="1">erfinv</e>
          <e type="function" args="1">vectorize</e>
          <e type="operator" args="2">*</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="operand">2</e>
          <e type="operand">1</e>
          <e type="function" args="4">line</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="468" top="90" width="356" height="95" color="#000000" fontSize="10" showInputData="false">
      <math optimize="2" decimalPlaces="3" exponentialThreshold="15" trailingZeros="true">
        <input>
          <e type="operand">N</e>
          <e type="operand">μ</e>
          <e type="operand">σ</e>
          <e type="function" args="3">rnorm2</e>
          <e type="operand">R</e>
          <e type="operand">N</e>
          <e type="function" args="1">Random</e>
          <e type="operator" args="2">:</e>
          <e type="operand">i</e>
          <e type="operand">1</e>
          <e type="operand">N</e>
          <e type="function" args="2">range</e>
          <e type="operand">R</e>
          <e type="operand">i</e>
          <e type="function" args="2">el</e>
          <e type="operand">R</e>
          <e type="operand">i</e>
          <e type="function" args="2">el</e>
          <e type="operand">μ</e>
          <e type="operand">σ</e>
          <e type="function" args="3">ICDF.Normal</e>
          <e type="operator" args="2">:</e>
          <e type="function" args="3">for</e>
          <e type="operand">R</e>
          <e type="operand">3</e>
          <e type="operand">1</e>
          <e type="function" args="5">line</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="864" top="90" width="335" height="133" color="#000000" fontSize="10" showInputData="false">
      <math optimize="2" decimalPlaces="3" exponentialThreshold="15" trailingZeros="true">
        <input>
          <e type="operand">N</e>
          <e type="operand">μ</e>
          <e type="operand">σ</e>
          <e type="function" args="3">rnorm3</e>
          <e type="operand">N'</e>
          <e type="operand">N</e>
          <e type="operand">20</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">:</e>
          <e type="operand">R</e>
          <e type="operand">N'</e>
          <e type="operand">1</e>
          <e type="function" args="2">matrix</e>
          <e type="operator" args="2">:</e>
          <e type="operand">i</e>
          <e type="operand">1</e>
          <e type="operand">N'</e>
          <e type="function" args="2">range</e>
          <e type="operand">R</e>
          <e type="operand">i</e>
          <e type="function" args="2">el</e>
          <e type="operand">20</e>
          <e type="operand">μ</e>
          <e type="operand">σ</e>
          <e type="function" args="3">rnorm1</e>
          <e type="operator" args="2">:</e>
          <e type="function" args="3">for</e>
          <e type="operand">R</e>
          <e type="operand">R</e>
          <e type="function" args="1">mat2sys</e>
          <e type="function" args="1">sys2mat</e>
          <e type="operator" args="2">:</e>
          <e type="operand">4</e>
          <e type="operand">1</e>
          <e type="function" args="6">line</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="180" top="234" width="50" height="41" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ</e>
          <e type="operand">1</e>
          <e type="operand">3</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="81" top="243" width="54" height="24" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">μ</e>
          <e type="operand">10</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="657" top="243" width="70" height="24" color="#000000" fontSize="10">
      <math evaluate="false" optimize="2">
        <input>
          <e type="operand">N</e>
          <e type="operand">1000</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="846" top="243" width="70" height="24" color="#000000" fontSize="10">
      <math evaluate="false" optimize="2">
        <input>
          <e type="operand">N</e>
          <e type="operand">5000</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="1035" top="243" width="78" height="24" color="#000000" fontSize="10">
      <math optimize="2">
        <input>
          <e type="operand">N</e>
          <e type="operand">10000</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="1206" top="243" width="84" height="24" color="#000000" fontSize="10">
      <math evaluate="false" optimize="2">
        <input>
          <e type="operand">N</e>
          <e type="operand">100000</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="36" top="288" width="100" height="31" color="#000000" fontSize="10">
      <math optimize="2" decimalPlaces="3" exponentialThreshold="15" trailingZeros="true">
        <input>
          <e type="operand">t.0</e>
          <e type="operand">0</e>
          <e type="function" args="1">time</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="252" top="288" width="221" height="28" color="#000000" fontSize="10">
      <math optimize="2">
        <input>
          <e type="operand">r1a</e>
          <e type="operand">N</e>
          <e type="operand">μ</e>
          <e type="operand">σ</e>
          <e type="function" args="3">rnorm1</e>
          <e type="function" args="1">eval</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="621" top="288" width="149" height="31" color="#000000" fontSize="10">
      <math evaluate="false" decimalPlaces="1" exponentialThreshold="15" trailingZeros="true">
        <input>
          <e type="operand">0</e>
          <e type="function" args="1">time</e>
          <e type="operand">t.0</e>
          <e type="operator" args="2">-</e>
        </input>
        <result action="numeric">
          <e type="operand">0.6</e>
          <e type="operand" style="unit">s</e>
          <e type="operator" args="2">*</e>
        </result>
      </math>
    </region>
    <region left="810" top="288" width="157" height="31" color="#000000" fontSize="10">
      <math evaluate="false" decimalPlaces="1" exponentialThreshold="15" trailingZeros="true">
        <input>
          <e type="operand">0</e>
          <e type="function" args="1">time</e>
          <e type="operand">t.0</e>
          <e type="operator" args="2">-</e>
        </input>
        <result action="numeric">
          <e type="operand">13.4</e>
          <e type="operand" style="unit">s</e>
          <e type="operator" args="2">*</e>
        </result>
      </math>
    </region>
    <region left="999" top="288" width="149" height="31" color="#000000" fontSize="10">
      <math decimalPlaces="1" exponentialThreshold="15" trailingZeros="true">
        <input>
          <e type="operand">0</e>
          <e type="function" args="1">time</e>
          <e type="operand">t.0</e>
          <e type="operator" args="2">-</e>
        </input>
        <result action="numeric">
          <e type="operand">0.6</e>
          <e type="operand" style="unit">s</e>
          <e type="operator" args="2">*</e>
        </result>
      </math>
    </region>
    <region left="36" top="324" width="100" height="31" color="#000000" fontSize="10">
      <math optimize="2" decimalPlaces="3" exponentialThreshold="15" trailingZeros="true">
        <input>
          <e type="operand">t.0</e>
          <e type="operand">0</e>
          <e type="function" args="1">time</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="252" top="324" width="221" height="28" color="#000000" fontSize="10">
      <math optimize="2" matrixOptions="0,0,1,1">
        <input>
          <e type="operand">r2a</e>
          <e type="operand">N</e>
          <e type="operand">μ</e>
          <e type="operand">σ</e>
          <e type="function" args="3">rnorm2</e>
          <e type="function" args="1">eval</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="621" top="324" width="149" height="31" color="#000000" fontSize="10">
      <math evaluate="false" decimalPlaces="1" exponentialThreshold="15" trailingZeros="true">
        <input>
          <e type="operand">0</e>
          <e type="function" args="1">time</e>
          <e type="operand">t.0</e>
          <e type="operator" args="2">-</e>
        </input>
        <result action="numeric">
          <e type="operand">0.2</e>
          <e type="operand" style="unit">s</e>
          <e type="operator" args="2">*</e>
        </result>
      </math>
    </region>
    <region left="810" top="324" width="149" height="31" color="#000000" fontSize="10">
      <math evaluate="false" decimalPlaces="1" exponentialThreshold="15" trailingZeros="true">
        <input>
          <e type="operand">0</e>
          <e type="function" args="1">time</e>
          <e type="operand">t.0</e>
          <e type="operator" args="2">-</e>
        </input>
        <result action="numeric">
          <e type="operand">0.8</e>
          <e type="operand" style="unit">s</e>
          <e type="operator" args="2">*</e>
        </result>
      </math>
    </region>
    <region left="999" top="324" width="149" height="31" color="#000000" fontSize="10">
      <math decimalPlaces="1" exponentialThreshold="15" trailingZeros="true">
        <input>
          <e type="operand">0</e>
          <e type="function" args="1">time</e>
          <e type="operand">t.0</e>
          <e type="operator" args="2">-</e>
        </input>
        <result action="numeric">
          <e type="operand">1.6</e>
          <e type="operand" style="unit">s</e>
          <e type="operator" args="2">*</e>
        </result>
      </math>
    </region>
    <region left="1170" top="324" width="155" height="31" color="#000000" fontSize="10">
      <math evaluate="false" decimalPlaces="1" exponentialThreshold="15" trailingZeros="true">
        <input>
          <e type="operand">0</e>
          <e type="function" args="1">time</e>
          <e type="operand">t.0</e>
          <e type="operator" args="2">-</e>
        </input>
        <result action="numeric">
          <e type="operand">70.3</e>
          <e type="operand" style="unit">s</e>
          <e type="operator" args="2">*</e>
        </result>
      </math>
    </region>
    <region left="36" top="360" width="100" height="31" color="#000000" fontSize="10">
      <math optimize="2" decimalPlaces="3" exponentialThreshold="15" trailingZeros="true">
        <input>
          <e type="operand">t.0</e>
          <e type="operand">0</e>
          <e type="function" args="1">time</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="252" top="360" width="221" height="28" color="#000000" fontSize="10">
      <math optimize="2">
        <input>
          <e type="operand">r3a</e>
          <e type="operand">N</e>
          <e type="operand">μ</e>
          <e type="operand">σ</e>
          <e type="function" args="3">rnorm3</e>
          <e type="function" args="1">eval</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="621" top="360" width="149" height="31" color="#000000" fontSize="10">
      <math evaluate="false" decimalPlaces="1" exponentialThreshold="15" trailingZeros="true">
        <input>
          <e type="operand">0</e>
          <e type="function" args="1">time</e>
          <e type="operand">t.0</e>
          <e type="operator" args="2">-</e>
        </input>
        <result action="numeric">
          <e type="operand">0.1</e>
          <e type="operand" style="unit">s</e>
          <e type="operator" args="2">*</e>
        </result>
      </math>
    </region>
    <region left="810" top="360" width="149" height="31" color="#000000" fontSize="10">
      <math evaluate="false" decimalPlaces="1" exponentialThreshold="15" trailingZeros="true">
        <input>
          <e type="operand">0</e>
          <e type="function" args="1">time</e>
          <e type="operand">t.0</e>
          <e type="operator" args="2">-</e>
        </input>
        <result action="numeric">
          <e type="operand">0.6</e>
          <e type="operand" style="unit">s</e>
          <e type="operator" args="2">*</e>
        </result>
      </math>
    </region>
    <region left="999" top="360" width="149" height="31" color="#000000" fontSize="10">
      <math decimalPlaces="1" exponentialThreshold="15" trailingZeros="true">
        <input>
          <e type="operand">0</e>
          <e type="function" args="1">time</e>
          <e type="operand">t.0</e>
          <e type="operator" args="2">-</e>
        </input>
        <result action="numeric">
          <e type="operand">1.0</e>
          <e type="operand" style="unit">s</e>
          <e type="operator" args="2">*</e>
        </result>
      </math>
    </region>
    <region left="1170" top="360" width="155" height="31" color="#000000" fontSize="10">
      <math evaluate="false" decimalPlaces="1" exponentialThreshold="15" trailingZeros="true">
        <input>
          <e type="operand">0</e>
          <e type="function" args="1">time</e>
          <e type="operand">t.0</e>
          <e type="operator" args="2">-</e>
        </input>
        <result action="numeric">
          <e type="operand">12.9</e>
          <e type="operand" style="unit">s</e>
          <e type="operator" args="2">*</e>
        </result>
      </math>
    </region>
    <region left="630" top="432" width="494" height="38" color="#000000" fontSize="10">
      <text lang="eng" width="494" fontFamily="Arial" fontSize="10">
        <content>
          <p>I have no idea why this different definitions of rnorm execute with this different speeds. And even the fastest solution here is still slow...</p>
        </content>
      </text>
    </region>
  </regions>
</worksheet>