bernoullicharts/log_1_x_flajolet__bound.svg

<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<!-- Created with matplotlib (https://matplotlib.org/) -->
<svg height="345.6pt" version="1.1" viewBox="0 0 460.8 345.6" width="460.8pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
 <defs>
  <style type="text/css">
*{stroke-linecap:butt;stroke-linejoin:round;}
  </style>
 </defs>
 <g id="figure_1">
  <g id="patch_1">
   <path d="M 0 345.6 
L 460.8 345.6 
L 460.8 0 
L 0 0 
z
" style="fill:#ffffff;"/>
  </g>
  <g id="axes_1">
   <g id="patch_2">
    <path d="M 57.6 307.584 
L 414.72 307.584 
L 414.72 41.472 
L 57.6 41.472 
z
" style="fill:#ffffff;"/>
   </g>
   <g id="matplotlib.axis_1">
    <g id="xtick_1">
     <g id="line2d_1">
      <defs>
       <path d="M 0 0 
L 0 3.5 
" id="m2c50ffa4b6" style="stroke:#000000;stroke-width:0.8;"/>
      </defs>
      <g>
       <use style="stroke:#000000;stroke-width:0.8;" x="73.800255" xlink:href="#m2c50ffa4b6" y="307.584"/>
      </g>
     </g>
     <g id="text_1">
      <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:middle;" transform="rotate(-0, 73.800255, 322.182437)" x="73.800255" y="322.182437">0.0</text>
     </g>
    </g>
    <g id="xtick_2">
     <g id="line2d_2">
      <g>
       <use style="stroke:#000000;stroke-width:0.8;" x="138.744153" xlink:href="#m2c50ffa4b6" y="307.584"/>
      </g>
     </g>
     <g id="text_2">
      <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:middle;" transform="rotate(-0, 138.744153, 322.182437)" x="138.744153" y="322.182437">0.2</text>
     </g>
    </g>
    <g id="xtick_3">
     <g id="line2d_3">
      <g>
       <use style="stroke:#000000;stroke-width:0.8;" x="203.688051" xlink:href="#m2c50ffa4b6" y="307.584"/>
      </g>
     </g>
     <g id="text_3">
      <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:middle;" transform="rotate(-0, 203.688051, 322.182437)" x="203.688051" y="322.182437">0.4</text>
     </g>
    </g>
    <g id="xtick_4">
     <g id="line2d_4">
      <g>
       <use style="stroke:#000000;stroke-width:0.8;" x="268.631949" xlink:href="#m2c50ffa4b6" y="307.584"/>
      </g>
     </g>
     <g id="text_4">
      <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:middle;" transform="rotate(-0, 268.631949, 322.182437)" x="268.631949" y="322.182437">0.6</text>
     </g>
    </g>
    <g id="xtick_5">
     <g id="line2d_5">
      <g>
       <use style="stroke:#000000;stroke-width:0.8;" x="333.575847" xlink:href="#m2c50ffa4b6" y="307.584"/>
      </g>
     </g>
     <g id="text_5">
      <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:middle;" transform="rotate(-0, 333.575847, 322.182437)" x="333.575847" y="322.182437">0.8</text>
     </g>
    </g>
    <g id="xtick_6">
     <g id="line2d_6">
      <g>
       <use style="stroke:#000000;stroke-width:0.8;" x="398.519745" xlink:href="#m2c50ffa4b6" y="307.584"/>
      </g>
     </g>
     <g id="text_6">
      <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:middle;" transform="rotate(-0, 398.519745, 322.182437)" x="398.519745" y="322.182437">1.0</text>
     </g>
    </g>
    <g id="text_7">
     <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:middle;" transform="rotate(-0, 236.16, 335.860562)" x="236.16" y="335.860562">Input Coin's Heads Probability (λ)</text>
    </g>
   </g>
   <g id="matplotlib.axis_2">
    <g id="ytick_1">
     <g id="line2d_7">
      <defs>
       <path d="M 0 0 
L -3.5 0 
" id="maadecf192a" style="stroke:#000000;stroke-width:0.8;"/>
      </defs>
      <g>
       <use style="stroke:#000000;stroke-width:0.8;" x="57.6" xlink:href="#maadecf192a" y="295.489795"/>
      </g>
     </g>
     <g id="text_8">
      <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:end;" transform="rotate(-0, 50.6, 299.289014)" x="50.6" y="299.289014">0</text>
     </g>
    </g>
    <g id="ytick_2">
     <g id="line2d_8">
      <g>
       <use style="stroke:#000000;stroke-width:0.8;" x="57.6" xlink:href="#maadecf192a" y="264.940257"/>
      </g>
     </g>
     <g id="text_9">
      <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:end;" transform="rotate(-0, 50.6, 268.739475)" x="50.6" y="268.739475">2</text>
     </g>
    </g>
    <g id="ytick_3">
     <g id="line2d_9">
      <g>
       <use style="stroke:#000000;stroke-width:0.8;" x="57.6" xlink:href="#maadecf192a" y="234.390718"/>
      </g>
     </g>
     <g id="text_10">
      <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:end;" transform="rotate(-0, 50.6, 238.189937)" x="50.6" y="238.189937">4</text>
     </g>
    </g>
    <g id="ytick_4">
     <g id="line2d_10">
      <g>
       <use style="stroke:#000000;stroke-width:0.8;" x="57.6" xlink:href="#maadecf192a" y="203.84118"/>
      </g>
     </g>
     <g id="text_11">
      <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:end;" transform="rotate(-0, 50.6, 207.640399)" x="50.6" y="207.640399">6</text>
     </g>
    </g>
    <g id="ytick_5">
     <g id="line2d_11">
      <g>
       <use style="stroke:#000000;stroke-width:0.8;" x="57.6" xlink:href="#maadecf192a" y="173.291641"/>
      </g>
     </g>
     <g id="text_12">
      <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:end;" transform="rotate(-0, 50.6, 177.09086)" x="50.6" y="177.09086">8</text>
     </g>
    </g>
    <g id="ytick_6">
     <g id="line2d_12">
      <g>
       <use style="stroke:#000000;stroke-width:0.8;" x="57.6" xlink:href="#maadecf192a" y="142.742103"/>
      </g>
     </g>
     <g id="text_13">
      <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:end;" transform="rotate(-0, 50.6, 146.541322)" x="50.6" y="146.541322">10</text>
     </g>
    </g>
    <g id="ytick_7">
     <g id="line2d_13">
      <g>
       <use style="stroke:#000000;stroke-width:0.8;" x="57.6" xlink:href="#maadecf192a" y="112.192564"/>
      </g>
     </g>
     <g id="text_14">
      <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:end;" transform="rotate(-0, 50.6, 115.991783)" x="50.6" y="115.991783">12</text>
     </g>
    </g>
    <g id="ytick_8">
     <g id="line2d_14">
      <g>
       <use style="stroke:#000000;stroke-width:0.8;" x="57.6" xlink:href="#maadecf192a" y="81.643026"/>
      </g>
     </g>
     <g id="text_15">
      <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:end;" transform="rotate(-0, 50.6, 85.442245)" x="50.6" y="85.442245">14</text>
     </g>
    </g>
    <g id="ytick_9">
     <g id="line2d_15">
      <g>
       <use style="stroke:#000000;stroke-width:0.8;" x="57.6" xlink:href="#maadecf192a" y="51.093487"/>
      </g>
     </g>
     <g id="text_16">
      <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:end;" transform="rotate(-0, 50.6, 54.892706)" x="50.6" y="54.892706">16</text>
     </g>
    </g>
    <g id="text_17">
     <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:middle;" transform="rotate(-90, 31.795312, 174.528)" x="31.795312" y="174.528">Coin Flips Needed</text>
    </g>
   </g>
   <g id="line2d_16">
    <path clip-path="url(#pffc8727ee5)" d="M 73.832727 280.217317 
L 77.112066 280.446483 
L 80.391405 280.671395 
L 83.670744 280.892202 
L 86.950083 281.109052 
L 90.229421 281.322084 
L 93.50876 281.531432 
L 96.788099 281.737226 
L 100.067438 281.93959 
L 103.346777 282.138644 
L 106.626116 282.334503 
L 109.905455 282.527278 
L 113.184793 282.717078 
L 116.464132 282.904005 
L 119.743471 283.08816 
L 123.02281 283.269639 
L 126.302149 283.448537 
L 129.581488 283.624943 
L 132.860826 283.798945 
L 136.140165 283.970628 
L 139.419504 284.140075 
L 142.698843 284.307365 
L 145.978182 284.472575 
L 149.257521 284.635782 
L 152.53686 284.797057 
L 155.816198 284.956473 
L 159.095537 285.114098 
L 162.374876 285.270001 
L 165.654215 285.424246 
L 168.933554 285.576898 
L 172.212893 285.72802 
L 175.492231 285.877673 
L 178.77157 286.025916 
L 182.050909 286.172808 
L 185.330248 286.318407 
L 188.609587 286.462768 
L 191.888926 286.605948 
L 195.168264 286.747999 
L 198.447603 286.888976 
L 201.726942 287.028931 
L 205.006281 287.167914 
L 208.28562 287.305978 
L 211.564959 287.443173 
L 214.844298 287.579547 
L 218.123636 287.71515 
L 221.402975 287.85003 
L 224.682314 287.984236 
L 227.961653 288.117816 
L 231.240992 288.250815 
L 234.520331 288.383282 
L 237.799669 288.515264 
L 241.079008 288.646806 
L 244.358347 288.777956 
L 247.637686 288.908761 
L 250.917025 289.039265 
L 254.196364 289.169517 
L 257.475702 289.299563 
L 260.755041 289.42945 
L 264.03438 289.559224 
L 267.313719 289.688933 
L 270.593058 289.818625 
L 273.872397 289.948348 
L 277.151736 290.07815 
L 280.431074 290.208081 
L 283.710413 290.33819 
L 286.989752 290.468528 
L 290.269091 290.599145 
L 293.54843 290.730094 
L 296.827769 290.861427 
L 300.107107 290.993199 
L 303.386446 291.125464 
L 306.665785 291.258278 
L 309.945124 291.391699 
L 313.224463 291.525785 
L 316.503802 291.660596 
L 319.78314 291.796193 
L 323.062479 291.932641 
L 326.341818 292.070004 
L 329.621157 292.208349 
L 332.900496 292.347745 
L 336.179835 292.488263 
L 339.459174 292.629977 
L 342.738512 292.772962 
L 346.017851 292.917297 
L 349.29719 293.063064 
L 352.576529 293.210347 
L 355.855868 293.359234 
L 359.135207 293.509815 
L 362.414545 293.662186 
L 365.693884 293.816446 
L 368.973223 293.972696 
L 372.252562 294.131045 
L 375.531901 294.291605 
L 378.81124 294.454492 
L 382.090579 294.619829 
L 385.369917 294.787746 
L 388.649256 294.958376 
L 391.928595 295.131862 
L 395.207934 295.308351 
L 398.487273 295.488 
" style="fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:1.5;"/>
   </g>
   <g id="line2d_17">
    <path clip-path="url(#pffc8727ee5)" d="M 73.832727 272.852587 
L 77.112066 272.058299 
L 80.391405 272.088849 
L 83.670744 272.272146 
L 86.950083 272.058299 
L 90.229421 272.394344 
L 93.50876 273.249731 
L 96.788099 272.69984 
L 100.067438 272.822038 
L 103.346777 273.402479 
L 106.626116 272.333245 
L 109.905455 272.272146 
L 113.184793 272.883137 
L 116.464132 272.211047 
L 119.743471 273.371929 
L 123.02281 272.424894 
L 126.302149 272.485993 
L 129.581488 272.394344 
L 132.860826 273.066434 
L 136.140165 273.005335 
L 139.419504 273.249731 
L 142.698843 272.211047 
L 145.978182 272.577641 
L 149.257521 272.63874 
L 152.53686 272.180497 
L 155.816198 272.883137 
L 159.095537 271.936101 
L 162.374876 272.974785 
L 165.654215 272.69984 
L 168.933554 272.333245 
L 172.212893 272.119398 
L 175.492231 272.485993 
L 178.77157 272.66929 
L 182.050909 271.752804 
L 185.330248 271.569507 
L 188.609587 272.66929 
L 191.888926 273.219182 
L 195.168264 272.119398 
L 198.447603 271.936101 
L 201.726942 271.752804 
L 205.006281 272.02775 
L 208.28562 272.516542 
L 211.564959 271.9972 
L 214.844298 272.730389 
L 218.123636 271.752804 
L 221.402975 271.477858 
L 224.682314 271.508408 
L 227.961653 271.905552 
L 231.240992 271.32511 
L 234.520331 272.180497 
L 237.799669 270.469723 
L 241.079008 270.775219 
L 244.358347 271.691705 
L 247.637686 271.386209 
L 250.917025 270.927966 
L 254.196364 269.828183 
L 257.475702 270.836318 
L 260.755041 269.767084 
L 264.03438 270.255876 
L 267.313719 270.286426 
L 270.593058 272.119398 
L 273.872397 270.164228 
L 277.151736 268.69785 
L 280.431074 271.661155 
L 283.710413 268.881147 
L 286.989752 268.636751 
L 290.269091 270.836318 
L 293.54843 268.178508 
L 296.827769 267.964661 
L 300.107107 268.086859 
L 303.386446 268.514553 
L 306.665785 267.628616 
L 309.945124 267.720265 
L 313.224463 266.620481 
L 316.503802 265.917842 
L 319.78314 266.009491 
L 323.062479 268.178508 
L 326.341818 266.68158 
L 329.621157 265.795644 
L 332.900496 265.123554 
L 336.179835 264.268167 
L 339.459174 262.893438 
L 342.738512 263.748825 
L 346.017851 263.932122 
L 349.29719 260.907718 
L 352.576529 263.015636 
L 355.855868 259.716286 
L 359.135207 255.989242 
L 362.414545 257.272323 
L 365.693884 257.852764 
L 368.973223 258.280457 
L 372.252562 258.616502 
L 375.531901 258.09716 
L 378.81124 252.476045 
L 382.090579 245.755147 
L 385.369917 249.696037 
L 388.649256 246.18284 
L 391.928595 241.814256 
L 395.207934 237.231825 
L 398.487273 53.568 
" style="fill:none;stroke:#ff7f0e;stroke-linecap:square;stroke-width:1.5;"/>
   </g>
   <g id="patch_3">
    <path d="M 57.6 307.584 
L 57.6 41.472 
" style="fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;"/>
   </g>
   <g id="patch_4">
    <path d="M 414.72 307.584 
L 414.72 41.472 
" style="fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;"/>
   </g>
   <g id="patch_5">
    <path d="M 57.6 307.584 
L 414.72 307.584 
" style="fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;"/>
   </g>
   <g id="patch_6">
    <path d="M 57.6 41.472 
L 414.72 41.472 
" style="fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;"/>
   </g>
   <g id="text_18">
    <text style="font-family:DejaVu Sans;font-size:12px;font-style:normal;font-weight:normal;text-anchor:middle;" transform="rotate(-0, 236.16, 35.472)" x="236.16" y="35.472">Coin Flips for log(1+x)</text>
   </g>
   <g id="legend_1">
    <g id="patch_7">
     <path d="M 64.6 78.82825 
L 282.8625 78.82825 
Q 284.8625 78.82825 284.8625 76.82825 
L 284.8625 48.472 
Q 284.8625 46.472 282.8625 46.472 
L 64.6 46.472 
Q 62.6 46.472 62.6 48.472 
L 62.6 76.82825 
Q 62.6 78.82825 64.6 78.82825 
z
" style="fill:#ffffff;opacity:0.8;stroke:#cccccc;stroke-linejoin:miter;"/>
    </g>
    <g id="line2d_18">
     <path d="M 66.6 54.570437 
L 86.6 54.570437 
" style="fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:1.5;"/>
    </g>
    <g id="line2d_19"/>
    <g id="text_19">
     <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:start;" transform="rotate(-0, 94.6, 58.070437)" x="94.6" y="58.070437">Coin Flip Lower Bound (Mendo)</text>
    </g>
    <g id="line2d_20">
     <path d="M 66.6 69.248562 
L 86.6 69.248562 
" style="fill:none;stroke:#ff7f0e;stroke-linecap:square;stroke-width:1.5;"/>
    </g>
    <g id="line2d_21"/>
    <g id="text_20">
     <text style="font-family:DejaVu Sans;font-size:10px;font-style:normal;font-weight:normal;text-anchor:start;" transform="rotate(-0, 94.6, 72.748562)" x="94.6" y="72.748562">Avg. Coins Flipped log(1+x) (Flajolet)</text>
    </g>
   </g>
  </g>
 </g>
 <defs>
  <clipPath id="pffc8727ee5">
   <rect height="266.112" width="357.12" x="57.6" y="41.472"/>
  </clipPath>
 </defs>
</svg>