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      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
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          <p style="font-weight: bold; font-style: normal; text-decoration: underline;">LETS MAKE SOME SIMPLIFICATIONS</p>
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                <e type="operator" args="2">^</e>
                <e type="function" args="1">log10</e>
                <e type="operand">σ'.vf_ctr</e>
                <e type="operand">j</e>
                <e type="function" args="2">el</e>
                <e type="bracket">(</e>
                <e type="operand">C.c</e>
                <e type="operand">j</e>
                <e type="function" args="2">el</e>
                <e type="operator" args="2">^</e>
                <e type="operand">σ'.v</e>
                <e type="operand">j</e>
                <e type="function" args="2">el</e>
                <e type="bracket">(</e>
                <e type="operand">C.r</e>
                <e type="operand">j</e>
                <e type="function" args="2">el</e>
                <e type="operator" args="2">^</e>
                <e type="operator" args="2">/</e>
                <e type="function" args="1">log10</e>
                <e type="operator" args="2">+</e>
              </input>
            </math>
          </region>
          <region id="15b0866bd83141a2b4c71b5e95cc2dae" left="34" top="328" width="496" height="67" color="#000000" fontSize="10">
            <math>
              <input>
                <e type="operand">C.r</e>
                <e type="operand">j</e>
                <e type="function" args="2">el</e>
                <e type="operand">C.c</e>
                <e type="operand">j</e>
                <e type="function" args="2">el</e>
                <e type="operator" args="2">-</e>
                <e type="bracket">(</e>
                <e type="operand">p.c</e>
                <e type="operand">j</e>
                <e type="function" args="2">el</e>
                <e type="function" args="1">log10</e>
                <e type="operator" args="2">*</e>
                <e type="operand">σ'.vf_ctr</e>
                <e type="operand">j</e>
                <e type="function" args="2">el</e>
                <e type="bracket">(</e>
                <e type="operand">C.c</e>
                <e type="operand">j</e>
                <e type="function" args="2">el</e>
                <e type="operator" args="2">^</e>
                <e type="function" args="1">log10</e>
                <e type="operator" args="2">+</e>
                <e type="operand">σ'.v</e>
                <e type="operand">j</e>
                <e type="function" args="2">el</e>
                <e type="bracket">(</e>
                <e type="operand">C.r</e>
                <e type="operand">j</e>
                <e type="function" args="2">el</e>
                <e type="operator" args="2">^</e>
                <e type="function" args="1">log10</e>
                <e type="operator" args="2">-</e>
              </input>
            </math>
          </region>
          <region id="d2d0bd7e60fe42a9966e6990e096c650" left="34" top="388" width="486" height="41" color="#000000" fontSize="10">
            <math>
              <input>
                <e type="operand">C.r</e>
                <e type="operand">j</e>
                <e type="function" args="2">el</e>
                <e type="operand">C.c</e>
                <e type="operand">j</e>
                <e type="function" args="2">el</e>
                <e type="operator" args="2">-</e>
                <e type="bracket">(</e>
                <e type="operand">p.c</e>
                <e type="operand">j</e>
                <e type="function" args="2">el</e>
                <e type="function" args="1">log10</e>
                <e type="operator" args="2">*</e>
                <e type="operand">C.c</e>
                <e type="operand">j</e>
                <e type="function" args="2">el</e>
                <e type="operand">σ'.vf_ctr</e>
                <e type="operand">j</e>
                <e type="function" args="2">el</e>
                <e type="function" args="1">log10</e>
                <e type="operator" args="2">*</e>
                <e type="operator" args="2">+</e>
                <e type="operand">C.r</e>
                <e type="operand">j</e>
                <e type="function" args="2">el</e>
                <e type="operand">σ'.v</e>
                <e type="operand">j</e>
                <e type="function" args="2">el</e>
                <e type="function" args="1">log10</e>
                <e type="operator" args="2">*</e>
                <e type="operator" args="2">-</e>
              </input>
            </math>
          </region>
        </regions>
      </text>
    </region>
    <region left="9" top="1080" width="158" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p style="font-weight: bold; text-decoration: underline;">SIMPLIFIED RESULTS</p>
        </content>
      </text>
    </region>
    <region left="36" top="1107" width="314" height="43" color="#000000" fontSize="10">
      <math>
        <description active="true" position="Top" lang="eng">
          <content>
            <p>OCR[j]≤1</p>
          </content>
        </description>
        <input>
          <e type="operand">C.c</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="operand">σ'.vf_ctr</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="function" args="1">log10</e>
          <e type="operator" args="2">*</e>
          <e type="operand">C.c</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="operand">σ'.v</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="function" args="1">log10</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">-</e>
          <e type="bracket">(</e>
        </input>
      </math>
    </region>
    <region left="36" top="1188" width="314" height="43" color="#000000" fontSize="10">
      <math>
        <description active="true" position="Top" lang="eng">
          <content>
            <p>σ'.vf_ctr[j]≤p.c[j]</p>
          </content>
        </description>
        <input>
          <e type="operand">C.r</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="operand">σ'.vf_ctr</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="function" args="1">log10</e>
          <e type="operator" args="2">*</e>
          <e type="operand">C.r</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="operand">σ'.v</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="function" args="1">log10</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">-</e>
          <e type="bracket">(</e>
        </input>
      </math>
    </region>
    <region left="36" top="1260" width="486" height="41" color="#000000" fontSize="10">
      <math>
        <description active="true" position="Top" lang="eng">
          <content>
            <p>σ'.vf_ctr[j]&gt;p.c[j]</p>
          </content>
        </description>
        <input>
          <e type="operand">C.r</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="operand">C.c</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="operator" args="2">-</e>
          <e type="bracket">(</e>
          <e type="operand">p.c</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="function" args="1">log10</e>
          <e type="operator" args="2">*</e>
          <e type="operand">C.c</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="operand">σ'.vf_ctr</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="function" args="1">log10</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="operand">C.r</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="operand">σ'.v</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="function" args="1">log10</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">-</e>
        </input>
      </math>
    </region>
    <region left="36" top="1359" width="416" height="41" color="#000000" fontSize="10">
      <math>
        <description active="true" position="Top" lang="eng">
          <content>
            <p>Single function for all cases</p>
          </content>
        </description>
        <input>
          <e type="operand">b</e>
          <e type="operand">a</e>
          <e type="operator" args="2">-</e>
          <e type="bracket">(</e>
          <e type="operand">p.c</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="function" args="1">log10</e>
          <e type="operator" args="2">*</e>
          <e type="operand">a</e>
          <e type="operand">σ'.vf_ctr</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="function" args="1">log10</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="operand">b</e>
          <e type="operand">σ'.v</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="function" args="1">log10</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">-</e>
        </input>
      </math>
    </region>
    <region left="54" top="1458" width="579" height="218" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">j</e>
          <e type="operand">1</e>
          <e type="operand">h</e>
          <e type="function" args="1">length</e>
          <e type="function" args="2">range</e>
          <e type="operand">a</e>
          <e type="operand">b</e>
          <e type="operand">1</e>
          <e type="operand">2</e>
          <e type="function" args="4">mat</e>
          <e type="operand">C.c</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="operand">C.c</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="operand">1</e>
          <e type="operand">2</e>
          <e type="function" args="4">mat</e>
          <e type="operand">OCR</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="operand">1</e>
          <e type="operator" args="2">≤</e>
          <e type="operand">C.r</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="operand">C.r</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="operand">1</e>
          <e type="operand">2</e>
          <e type="function" args="4">mat</e>
          <e type="operand">σ'.vf_ctr</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="operand">p.c</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="operator" args="2">≤</e>
          <e type="bracket">(</e>
          <e type="operand">C.c</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="operand">C.r</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="operand">1</e>
          <e type="operand">2</e>
          <e type="function" args="4">mat</e>
          <e type="operand">σ'.vf_ctr</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="operand">p.c</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="operator" args="2">&gt;</e>
          <e type="bracket">(</e>
          <e type="operand">0</e>
          <e type="function" args="7">cases</e>
          <e type="operator" args="2">:</e>
          <e type="operand">s.c_ctr</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="operand">h</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="operand">1</e>
          <e type="operand">e.0</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="operator" args="2">+</e>
          <e type="operator" args="2">/</e>
          <e type="operand">b</e>
          <e type="operand">a</e>
          <e type="operator" args="2">-</e>
          <e type="bracket">(</e>
          <e type="operand">p.c</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="function" args="1">log10</e>
          <e type="operator" args="2">*</e>
          <e type="operand">a</e>
          <e type="operand">σ'.vf_ctr</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="function" args="1">log10</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="operand">b</e>
          <e type="operand">σ'.v</e>
          <e type="operand">j</e>
          <e type="function" args="2">el</e>
          <e type="function" args="1">log10</e>
          <e type="operator" args="2">*</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="function" args="3">for</e>
        </input>
      </math>
    </region>
  </regions>
</worksheet>