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sum3.c_timeDiff.html
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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<title>criterion report</title>
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xmin=topSentry,ymin=topSentry,xmax=bottomSentry,ymax=bottomSentry;for(j=0;j<points.length;j+=ps){if(points[j]==null)continue;for(m=0;m<ps;++m){val=points[j+m];f=format[m];if(!f||f.autoscale===false||val==fakeInfinity||val==-fakeInfinity)continue;if(f.x){if(val<xmin)xmin=val;if(val>xmax)xmax=val}if(f.y){if(val<ymin)ymin=val;if(val>ymax)ymax=val}}}if(s.bars.show){var delta;switch(s.bars.align){case"left":delta=0;break;case"right":delta=-s.bars.barWidth;break;default:delta=-s.bars.barWidth/2}if(s.bars.horizontal){ymin+=delta;ymax+=delta+s.bars.barWidth}else{xmin+=delta;xmax+=delta+s.bars.barWidth}}updateAxis(s.xaxis,xmin,xmax);updateAxis(s.yaxis,ymin,ymax)}$.each(allAxes(),function(_,axis){if(axis.datamin==topSentry)axis.datamin=null;if(axis.datamax==bottomSentry)axis.datamax=null})}function setupCanvases(){placeholder.css("padding",0).children().filter(function(){return!$(this).hasClass("flot-overlay")&&!$(this).hasClass("flot-base")}).remove();if(placeholder.css("position")=="static")placeholder.css("position","relative");surface=new Canvas("flot-base",placeholder);overlay=new Canvas("flot-overlay",placeholder);ctx=surface.context;octx=overlay.context;eventHolder=$(overlay.element).unbind();var existing=placeholder.data("plot");if(existing){existing.shutdown();overlay.clear()}placeholder.data("plot",plot)}function bindEvents(){if(options.grid.hoverable){eventHolder.mousemove(onMouseMove);eventHolder.bind("mouseleave",onMouseLeave)}if(options.grid.clickable)eventHolder.click(onClick);executeHooks(hooks.bindEvents,[eventHolder])}function shutdown(){if(redrawTimeout)clearTimeout(redrawTimeout);eventHolder.unbind("mousemove",onMouseMove);eventHolder.unbind("mouseleave",onMouseLeave);eventHolder.unbind("click",onClick);executeHooks(hooks.shutdown,[eventHolder])}function setTransformationHelpers(axis){function identity(x){return x}var s,m,t=axis.options.transform||identity,it=axis.options.inverseTransform;if(axis.direction=="x"){s=axis.scale=plotWidth/Math.abs(t(axis.max)-t(axis.min));m=Math.min(t(axis.max),t(axis.min))}else{s=axis.scale=plotHeight/Math.abs(t(axis.max)-t(axis.min));s=-s;m=Math.max(t(axis.max),t(axis.min))}if(t==identity)axis.p2c=function(p){return(p-m)*s};else axis.p2c=function(p){return(t(p)-m)*s};if(!it)axis.c2p=function(c){return m+c/s};else axis.c2p=function(c){return it(m+c/s)}}function measureTickLabels(axis){var opts=axis.options,ticks=axis.ticks||[],labelWidth=opts.labelWidth||0,labelHeight=opts.labelHeight||0,maxWidth=labelWidth||(axis.direction=="x"?Math.floor(surface.width/(ticks.length||1)):null),legacyStyles=axis.direction+"Axis "+axis.direction+axis.n+"Axis",layer="flot-"+axis.direction+"-axis flot-"+axis.direction+axis.n+"-axis "+legacyStyles,font=opts.font||"flot-tick-label tickLabel";for(var i=0;i<ticks.length;++i){var t=ticks[i];if(!t.label)continue;var info=surface.getTextInfo(layer,t.label,font,null,maxWidth);labelWidth=Math.max(labelWidth,info.width);labelHeight=Math.max(labelHeight,info.height)}axis.labelWidth=opts.labelWidth||labelWidth;axis.labelHeight=opts.labelHeight||labelHeight}function allocateAxisBoxFirstPhase(axis){var lw=axis.labelWidth,lh=axis.labelHeight,pos=axis.options.position,isXAxis=axis.direction==="x",tickLength=axis.options.tickLength,axisMargin=options.grid.axisMargin,padding=options.grid.labelMargin,innermost=true,outermost=true,first=true,found=false;$.each(isXAxis?xaxes:yaxes,function(i,a){if(a&&(a.show||a.reserveSpace)){if(a===axis){found=true}else if(a.options.position===pos){if(found){outermost=false}else{innermost=false}}if(!found){first=false}}});if(outermost){axisMargin=0}if(tickLength==null){tickLength=first?"full":5}if(!isNaN(+tickLength))padding+=+tickLength;if(isXAxis){lh+=padding;if(pos=="bottom"){plotOffset.bottom+=lh+axisMargin;axis.box={top:surface.height-plotOffset.bottom,height:lh}}else{axis.box={top:plotOffset.top+axisMargin,height:lh};plotOffset.top+=lh+axisMargin}}else{lw+=padding;if(pos=="left"){axis.box={left:plotOffset.left+axisMargin,width:lw};plotOffset.left+=lw+axisMargin}else{plotOffset.right+=lw+axisMargin;axis.box={left:surface.width-plotOffset.right,width:lw}}}axis.position=pos;axis.tickLength=tickLength;axis.box.padding=padding;axis.innermost=innermost}function allocateAxisBoxSecondPhase(axis){if(axis.direction=="x"){axis.box.left=plotOffset.left-axis.labelWidth/2;axis.box.width=surface.width-plotOffset.left-plotOffset.right+axis.labelWidth}else{axis.box.top=plotOffset.top-axis.labelHeight/2;axis.box.height=surface.height-plotOffset.bottom-plotOffset.top+axis.labelHeight}}function adjustLayoutForThingsStickingOut(){var minMargin=options.grid.minBorderMargin,axis,i;if(minMargin==null){minMargin=0;for(i=0;i<series.length;++i)minMargin=Math.max(minMargin,2*(series[i].points.radius+series[i].points.lineWidth/2))}var margins={left:minMargin,right:minMargin,top:minMargin,bottom:minMargin};$.each(allAxes(),function(_,axis){if(axis.reserveSpace&&axis.ticks&&axis.ticks.length){if(axis.direction==="x"){margins.left=Math.max(margins.left,axis.labelWidth/2);margins.right=Math.max(margins.right,axis.labelWidth/2)}else{margins.bottom=Math.max(margins.bottom,axis.labelHeight/2);margins.top=Math.max(margins.top,axis.labelHeight/2)}}});plotOffset.left=Math.ceil(Math.max(margins.left,plotOffset.left));plotOffset.right=Math.ceil(Math.max(margins.right,plotOffset.right));plotOffset.top=Math.ceil(Math.max(margins.top,plotOffset.top));plotOffset.bottom=Math.ceil(Math.max(margins.bottom,plotOffset.bottom))}function setupGrid(){var i,axes=allAxes(),showGrid=options.grid.show;for(var a in plotOffset){var margin=options.grid.margin||0;plotOffset[a]=typeof margin=="number"?margin:margin[a]||0}executeHooks(hooks.processOffset,[plotOffset]);for(var a in plotOffset){if(typeof options.grid.borderWidth=="object"){plotOffset[a]+=showGrid?options.grid.borderWidth[a]:0}else{plotOffset[a]+=showGrid?options.grid.borderWidth:0}}$.each(axes,function(_,axis){var axisOpts=axis.options;axis.show=axisOpts.show==null?axis.used:axisOpts.show;axis.reserveSpace=axisOpts.reserveSpace==null?axis.show:axisOpts.reserveSpace;setRange(axis)});if(showGrid){var allocatedAxes=$.grep(axes,function(axis){return axis.show||axis.reserveSpace});$.each(allocatedAxes,function(_,axis){setupTickGeneration(axis);setTicks(axis);snapRangeToTicks(axis,axis.ticks);measureTickLabels(axis)});for(i=allocatedAxes.length-1;i>=0;--i)allocateAxisBoxFirstPhase(allocatedAxes[i]);adjustLayoutForThingsStickingOut();$.each(allocatedAxes,function(_,axis){allocateAxisBoxSecondPhase(axis)})}plotWidth=surface.width-plotOffset.left-plotOffset.right;plotHeight=surface.height-plotOffset.bottom-plotOffset.top;$.each(axes,function(_,axis){setTransformationHelpers(axis)});if(showGrid){drawAxisLabels()}insertLegend()}function setRange(axis){var opts=axis.options,min=+(opts.min!=null?opts.min:axis.datamin),max=+(opts.max!=null?opts.max:axis.datamax),delta=max-min;if(delta==0){var widen=max==0?1:.01;if(opts.min==null)min-=widen;if(opts.max==null||opts.min!=null)max+=widen}else{var margin=opts.autoscaleMargin;if(margin!=null){if(opts.min==null){min-=delta*margin;if(min<0&&axis.datamin!=null&&axis.datamin>=0)min=0}if(opts.max==null){max+=delta*margin;if(max>0&&axis.datamax!=null&&axis.datamax<=0)max=0}}}axis.min=min;axis.max=max}function setupTickGeneration(axis){var opts=axis.options;var noTicks;if(typeof opts.ticks=="number"&&opts.ticks>0)noTicks=opts.ticks;else noTicks=.3*Math.sqrt(axis.direction=="x"?surface.width:surface.height);var delta=(axis.max-axis.min)/noTicks,dec=-Math.floor(Math.log(delta)/Math.LN10),maxDec=opts.tickDecimals;if(maxDec!=null&&dec>maxDec){dec=maxDec}var magn=Math.pow(10,-dec),norm=delta/magn,size;if(norm<1.5){size=1}else if(norm<3){size=2;if(norm>2.25&&(maxDec==null||dec+1<=maxDec)){size=2.5;++dec}}else if(norm<7.5){size=5}else{size=10}size*=magn;if(opts.minTickSize!=null&&size<opts.minTickSize){size=opts.minTickSize}axis.delta=delta;axis.tickDecimals=Math.max(0,maxDec!=null?maxDec:dec);axis.tickSize=opts.tickSize||size;if(opts.mode=="time"&&!axis.tickGenerator){throw new Error("Time mode requires the flot.time plugin.")}if(!axis.tickGenerator){axis.tickGenerator=function(axis){var ticks=[],start=floorInBase(axis.min,axis.tickSize),i=0,v=Number.NaN,prev;do{prev=v;v=start+i*axis.tickSize;ticks.push(v);++i}while(v<axis.max&&v!=prev);return ticks};axis.tickFormatter=function(value,axis){var factor=axis.tickDecimals?Math.pow(10,axis.tickDecimals):1;var formatted=""+Math.round(value*factor)/factor;if(axis.tickDecimals!=null){var decimal=formatted.indexOf(".");var precision=decimal==-1?0:formatted.length-decimal-1;if(precision<axis.tickDecimals){return(precision?formatted:formatted+".")+(""+factor).substr(1,axis.tickDecimals-precision)}}return formatted}}if($.isFunction(opts.tickFormatter))axis.tickFormatter=function(v,axis){return""+opts.tickFormatter(v,axis)};if(opts.alignTicksWithAxis!=null){var otherAxis=(axis.direction=="x"?xaxes:yaxes)[opts.alignTicksWithAxis-1];if(otherAxis&&otherAxis.used&&otherAxis!=axis){var niceTicks=axis.tickGenerator(axis);if(niceTicks.length>0){if(opts.min==null)axis.min=Math.min(axis.min,niceTicks[0]);if(opts.max==null&&niceTicks.length>1)axis.max=Math.max(axis.max,niceTicks[niceTicks.length-1])}axis.tickGenerator=function(axis){var ticks=[],v,i;for(i=0;i<otherAxis.ticks.length;++i){v=(otherAxis.ticks[i].v-otherAxis.min)/(otherAxis.max-otherAxis.min);v=axis.min+v*(axis.max-axis.min);ticks.push(v)}return ticks};if(!axis.mode&&opts.tickDecimals==null){var extraDec=Math.max(0,-Math.floor(Math.log(axis.delta)/Math.LN10)+1),ts=axis.tickGenerator(axis);if(!(ts.length>1&&/\..*0$/.test((ts[1]-ts[0]).toFixed(extraDec))))axis.tickDecimals=extraDec}}}}function setTicks(axis){var oticks=axis.options.ticks,ticks=[];if(oticks==null||typeof oticks=="number"&&oticks>0)ticks=axis.tickGenerator(axis);else if(oticks){if($.isFunction(oticks))ticks=oticks(axis);else ticks=oticks}var i,v;axis.ticks=[];for(i=0;i<ticks.length;++i){var label=null;var t=ticks[i];if(typeof t=="object"){v=+t[0];if(t.length>1)label=t[1]}else v=+t;if(label==null)label=axis.tickFormatter(v,axis);if(!isNaN(v))axis.ticks.push({v:v,label:label})}}function snapRangeToTicks(axis,ticks){if(axis.options.autoscaleMargin&&ticks.length>0){if(axis.options.min==null)axis.min=Math.min(axis.min,ticks[0].v);if(axis.options.max==null&&ticks.length>1)axis.max=Math.max(axis.max,ticks[ticks.length-1].v)}}function draw(){surface.clear();executeHooks(hooks.drawBackground,[ctx]);var grid=options.grid;if(grid.show&&grid.backgroundColor)drawBackground();if(grid.show&&!grid.aboveData){drawGrid()}for(var i=0;i<series.length;++i){executeHooks(hooks.drawSeries,[ctx,series[i]]);drawSeries(series[i])}executeHooks(hooks.draw,[ctx]);if(grid.show&&grid.aboveData){drawGrid()}surface.render();triggerRedrawOverlay()}function extractRange(ranges,coord){var axis,from,to,key,axes=allAxes();for(var i=0;i<axes.length;++i){axis=axes[i];if(axis.direction==coord){key=coord+axis.n+"axis";if(!ranges[key]&&axis.n==1)key=coord+"axis";if(ranges[key]){from=ranges[key].from;to=ranges[key].to;break}}}if(!ranges[key]){axis=coord=="x"?xaxes[0]:yaxes[0];from=ranges[coord+"1"];to=ranges[coord+"2"]}if(from!=null&&to!=null&&from>to){var tmp=from;from=to;to=tmp}return{from:from,to:to,axis:axis}}function drawBackground(){ctx.save();ctx.translate(plotOffset.left,plotOffset.top);ctx.fillStyle=getColorOrGradient(options.grid.backgroundColor,plotHeight,0,"rgba(255, 255, 255, 0)");ctx.fillRect(0,0,plotWidth,plotHeight);ctx.restore()}function drawGrid(){var i,axes,bw,bc;ctx.save();ctx.translate(plotOffset.left,plotOffset.top);var markings=options.grid.markings;if(markings){if($.isFunction(markings)){axes=plot.getAxes();axes.xmin=axes.xaxis.min;axes.xmax=axes.xaxis.max;axes.ymin=axes.yaxis.min;axes.ymax=axes.yaxis.max;markings=markings(axes)}for(i=0;i<markings.length;++i){var m=markings[i],xrange=extractRange(m,"x"),yrange=extractRange(m,"y");if(xrange.from==null)xrange.from=xrange.axis.min;if(xrange.to==null)xrange.to=xrange.axis.max;
if(yrange.from==null)yrange.from=yrange.axis.min;if(yrange.to==null)yrange.to=yrange.axis.max;if(xrange.to<xrange.axis.min||xrange.from>xrange.axis.max||yrange.to<yrange.axis.min||yrange.from>yrange.axis.max)continue;xrange.from=Math.max(xrange.from,xrange.axis.min);xrange.to=Math.min(xrange.to,xrange.axis.max);yrange.from=Math.max(yrange.from,yrange.axis.min);yrange.to=Math.min(yrange.to,yrange.axis.max);var xequal=xrange.from===xrange.to,yequal=yrange.from===yrange.to;if(xequal&&yequal){continue}xrange.from=Math.floor(xrange.axis.p2c(xrange.from));xrange.to=Math.floor(xrange.axis.p2c(xrange.to));yrange.from=Math.floor(yrange.axis.p2c(yrange.from));yrange.to=Math.floor(yrange.axis.p2c(yrange.to));if(xequal||yequal){var lineWidth=m.lineWidth||options.grid.markingsLineWidth,subPixel=lineWidth%2?.5:0;ctx.beginPath();ctx.strokeStyle=m.color||options.grid.markingsColor;ctx.lineWidth=lineWidth;if(xequal){ctx.moveTo(xrange.to+subPixel,yrange.from);ctx.lineTo(xrange.to+subPixel,yrange.to)}else{ctx.moveTo(xrange.from,yrange.to+subPixel);ctx.lineTo(xrange.to,yrange.to+subPixel)}ctx.stroke()}else{ctx.fillStyle=m.color||options.grid.markingsColor;ctx.fillRect(xrange.from,yrange.to,xrange.to-xrange.from,yrange.from-yrange.to)}}}axes=allAxes();bw=options.grid.borderWidth;for(var j=0;j<axes.length;++j){var axis=axes[j],box=axis.box,t=axis.tickLength,x,y,xoff,yoff;if(!axis.show||axis.ticks.length==0)continue;ctx.lineWidth=1;if(axis.direction=="x"){x=0;if(t=="full")y=axis.position=="top"?0:plotHeight;else y=box.top-plotOffset.top+(axis.position=="top"?box.height:0)}else{y=0;if(t=="full")x=axis.position=="left"?0:plotWidth;else x=box.left-plotOffset.left+(axis.position=="left"?box.width:0)}if(!axis.innermost){ctx.strokeStyle=axis.options.color;ctx.beginPath();xoff=yoff=0;if(axis.direction=="x")xoff=plotWidth+1;else yoff=plotHeight+1;if(ctx.lineWidth==1){if(axis.direction=="x"){y=Math.floor(y)+.5}else{x=Math.floor(x)+.5}}ctx.moveTo(x,y);ctx.lineTo(x+xoff,y+yoff);ctx.stroke()}ctx.strokeStyle=axis.options.tickColor;ctx.beginPath();for(i=0;i<axis.ticks.length;++i){var v=axis.ticks[i].v;xoff=yoff=0;if(isNaN(v)||v<axis.min||v>axis.max||t=="full"&&(typeof bw=="object"&&bw[axis.position]>0||bw>0)&&(v==axis.min||v==axis.max))continue;if(axis.direction=="x"){x=axis.p2c(v);yoff=t=="full"?-plotHeight:t;if(axis.position=="top")yoff=-yoff}else{y=axis.p2c(v);xoff=t=="full"?-plotWidth:t;if(axis.position=="left")xoff=-xoff}if(ctx.lineWidth==1){if(axis.direction=="x")x=Math.floor(x)+.5;else y=Math.floor(y)+.5}ctx.moveTo(x,y);ctx.lineTo(x+xoff,y+yoff)}ctx.stroke()}if(bw){bc=options.grid.borderColor;if(typeof bw=="object"||typeof bc=="object"){if(typeof bw!=="object"){bw={top:bw,right:bw,bottom:bw,left:bw}}if(typeof bc!=="object"){bc={top:bc,right:bc,bottom:bc,left:bc}}if(bw.top>0){ctx.strokeStyle=bc.top;ctx.lineWidth=bw.top;ctx.beginPath();ctx.moveTo(0-bw.left,0-bw.top/2);ctx.lineTo(plotWidth,0-bw.top/2);ctx.stroke()}if(bw.right>0){ctx.strokeStyle=bc.right;ctx.lineWidth=bw.right;ctx.beginPath();ctx.moveTo(plotWidth+bw.right/2,0-bw.top);ctx.lineTo(plotWidth+bw.right/2,plotHeight);ctx.stroke()}if(bw.bottom>0){ctx.strokeStyle=bc.bottom;ctx.lineWidth=bw.bottom;ctx.beginPath();ctx.moveTo(plotWidth+bw.right,plotHeight+bw.bottom/2);ctx.lineTo(0,plotHeight+bw.bottom/2);ctx.stroke()}if(bw.left>0){ctx.strokeStyle=bc.left;ctx.lineWidth=bw.left;ctx.beginPath();ctx.moveTo(0-bw.left/2,plotHeight+bw.bottom);ctx.lineTo(0-bw.left/2,0);ctx.stroke()}}else{ctx.lineWidth=bw;ctx.strokeStyle=options.grid.borderColor;ctx.strokeRect(-bw/2,-bw/2,plotWidth+bw,plotHeight+bw)}}ctx.restore()}function drawAxisLabels(){$.each(allAxes(),function(_,axis){var box=axis.box,legacyStyles=axis.direction+"Axis "+axis.direction+axis.n+"Axis",layer="flot-"+axis.direction+"-axis flot-"+axis.direction+axis.n+"-axis "+legacyStyles,font=axis.options.font||"flot-tick-label tickLabel",tick,x,y,halign,valign;surface.removeText(layer);if(!axis.show||axis.ticks.length==0)return;for(var i=0;i<axis.ticks.length;++i){tick=axis.ticks[i];if(!tick.label||tick.v<axis.min||tick.v>axis.max)continue;if(axis.direction=="x"){halign="center";x=plotOffset.left+axis.p2c(tick.v);if(axis.position=="bottom"){y=box.top+box.padding}else{y=box.top+box.height-box.padding;valign="bottom"}}else{valign="middle";y=plotOffset.top+axis.p2c(tick.v);if(axis.position=="left"){x=box.left+box.width-box.padding;halign="right"}else{x=box.left+box.padding}}surface.addText(layer,x,y,tick.label,font,null,null,halign,valign)}})}function drawSeries(series){if(series.lines.show)drawSeriesLines(series);if(series.bars.show)drawSeriesBars(series);if(series.points.show)drawSeriesPoints(series)}function drawSeriesLines(series){function plotLine(datapoints,xoffset,yoffset,axisx,axisy){var points=datapoints.points,ps=datapoints.pointsize,prevx=null,prevy=null;ctx.beginPath();for(var i=ps;i<points.length;i+=ps){var x1=points[i-ps],y1=points[i-ps+1],x2=points[i],y2=points[i+1];if(x1==null||x2==null)continue;if(y1<=y2&&y1<axisy.min){if(y2<axisy.min)continue;x1=(axisy.min-y1)/(y2-y1)*(x2-x1)+x1;y1=axisy.min}else if(y2<=y1&&y2<axisy.min){if(y1<axisy.min)continue;x2=(axisy.min-y1)/(y2-y1)*(x2-x1)+x1;y2=axisy.min}if(y1>=y2&&y1>axisy.max){if(y2>axisy.max)continue;x1=(axisy.max-y1)/(y2-y1)*(x2-x1)+x1;y1=axisy.max}else if(y2>=y1&&y2>axisy.max){if(y1>axisy.max)continue;x2=(axisy.max-y1)/(y2-y1)*(x2-x1)+x1;y2=axisy.max}if(x1<=x2&&x1<axisx.min){if(x2<axisx.min)continue;y1=(axisx.min-x1)/(x2-x1)*(y2-y1)+y1;x1=axisx.min}else 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<h1>criterion performance measurements</h1>
<h2>overview</h2>
<p><a href="#grokularation">want to understand this report?</a></p>
<div id="overview" class="ovchart" style="width:900px;height:100px;"></div>
<h2><a name="b0">sum3-Bwd/Symbolic</a></h2>
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<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>OLS regression</td>
<td><span class="confinterval olstimelb0">xxx</span></td>
<td><span class="olstimept0">xxx</span></td>
<td><span class="confinterval olstimeub0">xxx</span></td>
</tr>
<tr>
<td>R² goodness-of-fit</td>
<td><span class="confinterval olsr2lb0">xxx</span></td>
<td><span class="olsr2pt0">xxx</span></td>
<td><span class="confinterval olsr2ub0">xxx</span></td>
</tr>
<tr>
<td>Mean execution time</td>
<td><span class="confinterval citime">6.0905894403662335e-2</span></td>
<td><span class="time">6.1202779837980587e-2</span></td>
<td><span class="confinterval citime">6.236176208563049e-2</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="confinterval citime">1.323497520672195e-3</span></td>
<td><span class="time">2.1281164295710387e-3</span></td>
<td><span class="confinterval citime">2.3808096619622205e-3</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have slight
(<span class="percent">7.638888888888888e-2</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b1">sum3-Bwd/IFDS</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde1" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time1" class="timechart"
style="width:450px;height:278px;"></div></td>
<!--
<td><div id="cycle1" class="cyclechart"
style="width:300px;height:278px;"></div></td>
-->
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>OLS regression</td>
<td><span class="confinterval olstimelb1">xxx</span></td>
<td><span class="olstimept1">xxx</span></td>
<td><span class="confinterval olstimeub1">xxx</span></td>
</tr>
<tr>
<td>R² goodness-of-fit</td>
<td><span class="confinterval olsr2lb1">xxx</span></td>
<td><span class="olsr2pt1">xxx</span></td>
<td><span class="confinterval olsr2ub1">xxx</span></td>
</tr>
<tr>
<td>Mean execution time</td>
<td><span class="confinterval citime">6.494796596367121e-2</span></td>
<td><span class="time">6.658584416142105e-2</span></td>
<td><span class="confinterval citime">6.724456469479898e-2</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="confinterval citime">2.536371904904285e-3</span></td>
<td><span class="time">2.988594417894656e-3</span></td>
<td><span class="confinterval citime">3.7189453988685935e-3</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have slight
(<span class="percent">8.508173117589483e-2</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b2">sum3-Bwd/SDG</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde2" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time2" class="timechart"
style="width:450px;height:278px;"></div></td>
<!--
<td><div id="cycle2" class="cyclechart"
style="width:300px;height:278px;"></div></td>
-->
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>OLS regression</td>
<td><span class="confinterval olstimelb2">xxx</span></td>
<td><span class="olstimept2">xxx</span></td>
<td><span class="confinterval olstimeub2">xxx</span></td>
</tr>
<tr>
<td>R² goodness-of-fit</td>
<td><span class="confinterval olsr2lb2">xxx</span></td>
<td><span class="olsr2pt2">xxx</span></td>
<td><span class="confinterval olsr2ub2">xxx</span></td>
</tr>
<tr>
<td>Mean execution time</td>
<td><span class="confinterval citime">6.775922532016981e-2</span></td>
<td><span class="time">6.775922532016981e-2</span></td>
<td><span class="confinterval citime">6.775922532016981e-2</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="confinterval citime">2.663584331261581e-3</span></td>
<td><span class="time">2.9719132921073098e-3</span></td>
<td><span class="confinterval citime">3.502885123130235e-3</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have slight
(<span class="percent">8.480660808090605e-2</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b3">sum3-Bwd/MWeiser</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde3" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time3" class="timechart"
style="width:450px;height:278px;"></div></td>
<!--
<td><div id="cycle3" class="cyclechart"
style="width:300px;height:278px;"></div></td>
-->
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>OLS regression</td>
<td><span class="confinterval olstimelb3">xxx</span></td>
<td><span class="olstimept3">xxx</span></td>
<td><span class="confinterval olstimeub3">xxx</span></td>
</tr>
<tr>
<td>R² goodness-of-fit</td>
<td><span class="confinterval olsr2lb3">xxx</span></td>
<td><span class="olsr2pt3">xxx</span></td>
<td><span class="confinterval olsr2ub3">xxx</span></td>
</tr>
<tr>
<td>Mean execution time</td>
<td><span class="confinterval citime">8.854530466006207e-2</span></td>
<td><span class="time">8.857706598177756e-2</span></td>
<td><span class="confinterval citime">8.882984762584221e-2</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="confinterval citime">1.1650363787371755e-3</span></td>
<td><span class="time">1.765463395036543e-3</span></td>
<td><span class="confinterval citime">2.0042956750082417e-3</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have slight
(<span class="percent">9.000000000000001e-2</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b4">sum3-Fwd/Symbolic</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde4" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time4" class="timechart"
style="width:450px;height:278px;"></div></td>
<!--
<td><div id="cycle4" class="cyclechart"
style="width:300px;height:278px;"></div></td>
-->
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>OLS regression</td>
<td><span class="confinterval olstimelb4">xxx</span></td>
<td><span class="olstimept4">xxx</span></td>
<td><span class="confinterval olstimeub4">xxx</span></td>
</tr>
<tr>
<td>R² goodness-of-fit</td>
<td><span class="confinterval olsr2lb4">xxx</span></td>
<td><span class="olsr2pt4">xxx</span></td>
<td><span class="confinterval olsr2ub4">xxx</span></td>
</tr>
<tr>
<td>Mean execution time</td>
<td><span class="confinterval citime">6.257940054118638e-2</span></td>
<td><span class="time">6.286533090879917e-2</span></td>
<td><span class="confinterval citime">6.331842878483449e-2</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="confinterval citime">8.638513432790266e-4</span></td>
<td><span class="time">1.0864035843775892e-3</span></td>
<td><span class="confinterval citime">1.191830120027707e-3</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have slight
(<span class="percent">7.638888888888888e-2</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b5">sum3-Fwd/SDG</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde5" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time5" class="timechart"
style="width:450px;height:278px;"></div></td>
<!--
<td><div id="cycle5" class="cyclechart"
style="width:300px;height:278px;"></div></td>
-->
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>OLS regression</td>
<td><span class="confinterval olstimelb5">xxx</span></td>
<td><span class="olstimept5">xxx</span></td>
<td><span class="confinterval olstimeub5">xxx</span></td>
</tr>
<tr>
<td>R² goodness-of-fit</td>
<td><span class="confinterval olsr2lb5">xxx</span></td>
<td><span class="olsr2pt5">xxx</span></td>
<td><span class="confinterval olsr2ub5">xxx</span></td>
</tr>
<tr>
<td>Mean execution time</td>
<td><span class="confinterval citime">7.056559271803152e-2</span></td>
<td><span class="time">7.090128506907076e-2</span></td>
<td><span class="confinterval citime">7.109037598329045e-2</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="confinterval citime">7.920346049700429e-4</span></td>
<td><span class="time">9.600560408117306e-4</span></td>
<td><span class="confinterval citime">1.034486226465883e-3</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have slight
(<span class="percent">8.264462809917338e-2</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b6">sum3-Fwd/IFDS</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde6" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time6" class="timechart"
style="width:450px;height:278px;"></div></td>
<!--
<td><div id="cycle6" class="cyclechart"
style="width:300px;height:278px;"></div></td>
-->
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>OLS regression</td>
<td><span class="confinterval olstimelb6">xxx</span></td>
<td><span class="olstimept6">xxx</span></td>
<td><span class="confinterval olstimeub6">xxx</span></td>
</tr>
<tr>
<td>R² goodness-of-fit</td>
<td><span class="confinterval olsr2lb6">xxx</span></td>
<td><span class="olsr2pt6">xxx</span></td>
<td><span class="confinterval olsr2ub6">xxx</span></td>
</tr>
<tr>
<td>Mean execution time</td>
<td><span class="confinterval citime">6.967672431089451e-2</span></td>
<td><span class="time">7.05090411692357e-2</span></td>
<td><span class="confinterval citime">7.133892463420469e-2</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="confinterval citime">1.6818354860541288e-3</span></td>
<td><span class="time">2.5335910163101862e-3</span></td>
<td><span class="confinterval citime">3.1725031125971258e-3</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have slight
(<span class="percent">8.264462809917346e-2</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b7">sum3-Both/Symbolic</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde7" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time7" class="timechart"
style="width:450px;height:278px;"></div></td>
<!--
<td><div id="cycle7" class="cyclechart"
style="width:300px;height:278px;"></div></td>
-->
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>OLS regression</td>
<td><span class="confinterval olstimelb7">xxx</span></td>
<td><span class="olstimept7">xxx</span></td>
<td><span class="confinterval olstimeub7">xxx</span></td>
</tr>
<tr>
<td>R² goodness-of-fit</td>
<td><span class="confinterval olsr2lb7">xxx</span></td>
<td><span class="olsr2pt7">xxx</span></td>
<td><span class="confinterval olsr2ub7">xxx</span></td>
</tr>
<tr>
<td>Mean execution time</td>
<td><span class="confinterval citime">6.533911742206745e-2</span></td>
<td><span class="time">6.554645668530794e-2</span></td>
<td><span class="confinterval citime">6.570471554894707e-2</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="confinterval citime">1.593103716791475e-3</span></td>
<td><span class="time">1.6751089573916762e-3</span></td>
<td><span class="confinterval citime">1.952716853295596e-3</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have slight
(<span class="percent">8.264462809917356e-2</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b8">sum3-Both/SDG</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde8" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time8" class="timechart"
style="width:450px;height:278px;"></div></td>
<!--
<td><div id="cycle8" class="cyclechart"
style="width:300px;height:278px;"></div></td>
-->
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>OLS regression</td>
<td><span class="confinterval olstimelb8">xxx</span></td>
<td><span class="olstimept8">xxx</span></td>
<td><span class="confinterval olstimeub8">xxx</span></td>
</tr>
<tr>
<td>R² goodness-of-fit</td>
<td><span class="confinterval olsr2lb8">xxx</span></td>
<td><span class="olsr2pt8">xxx</span></td>
<td><span class="confinterval olsr2ub8">xxx</span></td>
</tr>
<tr>
<td>Mean execution time</td>
<td><span class="confinterval citime">7.382753048570763e-2</span></td>
<td><span class="time">7.471861046474516e-2</span></td>
<td><span class="confinterval citime">7.578846778804407e-2</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="confinterval citime">3.396290850100967e-3</span></td>
<td><span class="time">3.5347945003404127e-3</span></td>
<td><span class="confinterval citime">3.950593791620111e-3</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have slight
(<span class="percent">8.566378039511918e-2</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="b9">sum3-Both/IFDS</a></h2>
<table width="100%">
<tbody>
<tr>
<td><div id="kde9" class="kdechart"
style="width:450px;height:278px;"></div></td>
<td><div id="time9" class="timechart"
style="width:450px;height:278px;"></div></td>
<!--
<td><div id="cycle9" class="cyclechart"
style="width:300px;height:278px;"></div></td>
-->
</tr>
</tbody>
</table>
<table>
<thead class="analysis">
<th></th>
<th class="cibound"
title="0.95 confidence level">lower bound</th>
<th>estimate</th>
<th class="cibound"
title="0.95 confidence level">upper bound</th>
</thead>
<tbody>
<tr>
<td>OLS regression</td>
<td><span class="confinterval olstimelb9">xxx</span></td>
<td><span class="olstimept9">xxx</span></td>
<td><span class="confinterval olstimeub9">xxx</span></td>
</tr>
<tr>
<td>R² goodness-of-fit</td>
<td><span class="confinterval olsr2lb9">xxx</span></td>
<td><span class="olsr2pt9">xxx</span></td>
<td><span class="confinterval olsr2ub9">xxx</span></td>
</tr>
<tr>
<td>Mean execution time</td>
<td><span class="confinterval citime">7.045664077838658e-2</span></td>
<td><span class="time">7.22449139040804e-2</span></td>
<td><span class="confinterval citime">7.32111971393167e-2</span></td>
</tr>
<tr>
<td>Standard deviation</td>
<td><span class="confinterval citime">2.347149680733856e-3</span></td>
<td><span class="time">3.6092334915290023e-3</span></td>
<td><span class="confinterval citime">3.917501227966697e-3</span></td>
</tr>
</tbody>
</table>
<span class="outliers">
<p>Outlying measurements have moderate
(<span class="percent">0.16300394699772616</span>%)
effect on estimated standard deviation.</p>
</span>
<h2><a name="grokularation">understanding this report</a></h2>
<p>In this report, each function benchmarked by criterion is assigned
a section of its own. The charts in each section are active; if
you hover your mouse over data points and annotations, you will see
more details.</p>
<ul>
<li>The chart on the left is a
<a href="http://en.wikipedia.org/wiki/Kernel_density_estimation">kernel
density estimate</a> (also known as a KDE) of time
measurements. This graphs the probability of any given time
measurement occurring. A spike indicates that a measurement of a
particular time occurred; its height indicates how often that
measurement was repeated.</li>
<li>The chart on the right is the raw data from which the kernel
density estimate is built. The <i>x</i> axis indicates the
number of loop iterations, while the <i>y</i> axis shows measured
execution time for the given number of loop iterations. The
line behind the values is the linear regression prediction of
execution time for a given number of iterations. Ideally, all
measurements will be on (or very near) this line.</li>
</ul>
<p>Under the charts is a small table.
The first two rows are the results of a linear regression run
on the measurements displayed in the right-hand chart.</p>
<ul>
<li><i>OLS regression</i> indicates the
time estimated for a single loop iteration using an ordinary
least-squares regression model. This number is more accurate
than the <i>mean</i> estimate below it, as it more effectively
eliminates measurement overhead and other constant factors.</li>
<li><i>R² goodness-of-fit</i> is a measure of how
accurately the linear regression model fits the observed
measurements. If the measurements are not too noisy, R²
should lie between 0.99 and 1, indicating an excellent fit. If
the number is below 0.99, something is confounding the accuracy
of the linear model.</li>
<li><i>Mean execution time</i> and <i>standard deviation</i> are
statistics calculated from execution time
divided by number of iterations.</li>
</ul>
<p>We use a statistical technique called
the <a href="http://en.wikipedia.org/wiki/Bootstrapping_(statistics)">bootstrap</a>
to provide confidence intervals on our estimates. The
bootstrap-derived upper and lower bounds on estimates let you see
how accurate we believe those estimates to be. (Hover the mouse
over the table headers to see the confidence levels.)</p>
<p>A noisy benchmarking environment can cause some or many
measurements to fall far from the mean. These outlying
measurements can have a significant inflationary effect on the
estimate of the standard deviation. We calculate and display an
estimate of the extent to which the standard deviation has been
inflated by outliers.</p>
<script type="text/javascript">
$(function () {
function mangulate(rpt) {
var measured = function(key) {
var idx = rpt.reportKeys.indexOf(key);
return rpt.reportMeasured.map(function(r) { return r[idx]; });
};
var number = rpt.reportNumber;
var name = rpt.reportName;
var mean = rpt.reportAnalysis.anMean.estPoint;
var iters = measured("iters");
var times = measured("time");
var kdetimes = rpt.reportKDEs[0].kdeValues;
var kdepdf = rpt.reportKDEs[0].kdePDF;
var meanSecs = mean;
var units = $.timeUnits(mean);
var rgrs = rpt.reportAnalysis.anRegress[0];
var scale = units[0];
var olsTime = rgrs.regCoeffs.iters;
$(".olstimept" + number).text(function() {
return $.renderTime(olsTime.estPoint);
});
$(".olstimelb" + number).text(function() {
return $.renderTime(olsTime.estLowerBound);
});
$(".olstimeub" + number).text(function() {
return $.renderTime(olsTime.estUpperBound);
});
$(".olsr2pt" + number).text(function() {
return rgrs.regRSquare.estPoint.toFixed(3);
});
$(".olsr2lb" + number).text(function() {
return rgrs.regRSquare.estLowerBound.toFixed(3);
});
$(".olsr2ub" + number).text(function() {
return rgrs.regRSquare.estUpperBound.toFixed(3);
});
mean *= scale;
kdetimes = $.scaleBy(scale, kdetimes);
var kq = $("#kde" + number);
var k = $.plot(kq,
[{ label: name + " time densities",
data: $.zip(kdetimes, kdepdf),
}],
{ xaxis: { tickFormatter: $.unitFormatter(scale) },
yaxis: { ticks: false },
grid: { borderColor: "#777",
hoverable: true, markings: [ { color: '#6fd3fb',
lineWidth: 1.5, xaxis: { from: mean, to: mean } } ] },
});
var o = k.pointOffset({ x: mean, y: 0});
kq.append('<div class="meanlegend" title="' + $.renderTime(meanSecs) +
'" style="position:absolute;left:' + (o.left + 4) +
'px;bottom:139px;">mean</div>');
$.addTooltip("#kde" + number,
function(secs) { return $.renderTime(secs / scale); });
var timepairs = new Array(times.length);
var lastiter = iters[iters.length-1];
var olspairs = [[0,0], [lastiter, lastiter * scale * olsTime.estPoint]];
for (var i = 0; i < times.length; i++)
timepairs[i] = [iters[i],times[i]*scale];
iterFormatter = function() {
var denom = 0;
return function(iters) {
if (iters == 0)
return '';
if (denom > 0)
return (iters / denom).toFixed();
var power;
if (iters >= 1e9) {
denom = '1e9'; power = '⁹';
}
if (iters >= 1e6) {
denom = '1e6'; power = '⁶';
}
else if (iters >= 1e3) {
denom = '1e3'; power = '³';
}
else denom = 1;
if (denom > 1) {
iters = (iters / denom).toFixed();
iters += '×10' + power + ' iters';
} else {
iters += ' iters';
}
return iters;
};
};
$.plot($("#time" + number),
[{ label: "regression", data: olspairs,
lines: { show: true } },
{ label: name + " times", data: timepairs,
points: { show: true } }],
{ grid: { borderColor: "#777", hoverable: true },
xaxis: { tickFormatter: iterFormatter() },
yaxis: { tickFormatter: $.unitFormatter(scale) } });
$.addTooltip("#time" + number,
function(iters,secs) {
return ($.renderTime(secs / scale) + ' / ' +
iters.toLocaleString() + ' iters');
});
if (0) {
var cyclepairs = new Array(cycles.length);
for (var i = 0; i < cycles.length; i++)
cyclepairs[i] = [cycles[i],i];