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jasnell/render.svg

Created September 5, 2026 06:44
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gistfile1.txt
'use strict';
const fs = require('node:fs');
const { createHistogram } = require('node:perf_hooks');
const outputSvg = '/tmp/opencode/qrde-latency-plot.svg';
const outputJson = '/tmp/opencode/qrde-latency-data.json';
const sampleCount = 250_000;
function mulberry32(seed) {
return function random() {
let value = seed += 0x6D2B79F5;
value = Math.imul(value ^ value >>> 15, value | 1);
value ^= value + Math.imul(value ^ value >>> 7, value | 61);
return ((value ^ value >>> 14) >>> 0) / 4294967296;
};
}
function normalGenerator(random) {
let spare;
return function normal() {
if (spare !== undefined) {
const value = spare;
spare = undefined;
return value;
}
const radius = Math.sqrt(-2 * Math.log(Math.max(random(), Number.EPSILON)));
const angle = 2 * Math.PI * random();
spare = radius * Math.sin(angle);
return radius * Math.cos(angle);
};
}
function quantile(sorted, probability) {
const rank = probability * (sorted.length - 1);
const lower = Math.floor(rank);
const fraction = rank - lower;
const upper = Math.min(lower + 1, sorted.length - 1);
return sorted[lower] + fraction * (sorted[upper] - sorted[lower]);
}
function formatLatency(value) {
if (value < 1) return `${(value * 1000).toFixed(0)} us`;
if (value < 10) return `${value.toFixed(2)} ms`;
if (value < 100) return `${value.toFixed(1)} ms`;
return `${value.toFixed(0)} ms`;
}
function formatPercentile(probability) {
if (probability === 0.5) return 'p50';
const decimals = Math.max(0, Math.round(-Math.log10(1 - probability)) - 2);
return `p${(100 * probability).toFixed(decimals)}`;
}
function escapeXml(value) {
return String(value)
.replaceAll('&', '&amp;')
.replaceAll('<', '&lt;')
.replaceAll('>', '&gt;')
.replaceAll('"', '&quot;');
}
function niceMaximum(value) {
const exponent = 10 ** Math.floor(Math.log10(value));
const scaled = value / exponent;
const nice = scaled <= 1 ? 1 : scaled <= 2 ? 2 : scaled <= 5 ? 5 : 10;
return nice * exponent;
}
function pathFromPoints(points) {
return points.map(([x, y], index) =>
`${index === 0 ? 'M' : 'L'}${x.toFixed(2)},${y.toFixed(2)}`).join(' ');
}
function logarithmicDomain(quantiles) {
const positive = quantiles.filter((value) => value > 0);
return [
10 ** Math.floor(Math.log10(Math.min(...positive))),
10 ** Math.ceil(Math.log10(Math.max(...positive))),
];
}
function buildLogHistogram(samples, minimumMs, maximumMs, binCount) {
const minimumLog = Math.log10(minimumMs);
const logWidth = (Math.log10(maximumMs) - minimumLog) / binCount;
const counts = new BigUint64Array(binCount);
for (const sampleUs of samples) {
const index = Math.max(0, Math.min(binCount - 1,
Math.floor((Math.log10(sampleUs / 1000) - minimumLog) / logWidth)));
counts[index]++;
}
return Array.from(counts, (count, index) => ({
lowerMs: 10 ** (minimumLog + index * logWidth),
upperMs: 10 ** (minimumLog + (index + 1) * logWidth),
count: Number(count),
probabilityPerLog10Latency: Number(count) / samples.length / logWidth,
}));
}
function renderPlot(result, markers, logDensities, fixedHistogram, integral) {
const width = 1400;
const height = 900;
const plotX = 76;
const plotWidth = 936;
const densityY = 148;
const densityHeight = 384;
const tailY = 638;
const tailHeight = 174;
const sideX = 1060;
const sideWidth = 276;
const quantilesMs = Array.from(result.quantiles, (value) => value / 1000);
const xMinimum = fixedHistogram[0].lowerMs;
const xMaximum = fixedHistogram.at(-1).upperMs;
const xLogMinimum = Math.log10(xMinimum);
const xLogMaximum = Math.log10(xMaximum);
const xScale = (value) => plotX +
(Math.log10(value) - xLogMinimum) /
(xLogMaximum - xLogMinimum) * plotWidth;
const finiteLogDensities = logDensities.filter(Number.isFinite);
const densityMaximum = niceMaximum(Math.max(
...finiteLogDensities,
...fixedHistogram.map(({ probabilityPerLog10Latency }) =>
probabilityPerLog10Latency),
));
const densityScale = (value) => densityY + densityHeight -
value / densityMaximum * densityHeight;
const tailScale = (survival) => tailY +
Math.log10(1 / survival) / 5 * tailHeight;
const densitySteps = [];
for (let i = 0; i < logDensities.length; i++) {
if (!Number.isFinite(logDensities[i])) continue;
densitySteps.push([xScale(quantilesMs[i]), densityScale(logDensities[i])]);
densitySteps.push([xScale(quantilesMs[i + 1]), densityScale(logDensities[i])]);
}
const densityArea = [
[densitySteps[0][0], densityY + densityHeight],
...densitySteps,
[densitySteps.at(-1)[0], densityY + densityHeight],
];
const tailPoints = [];
for (let i = 0; i < result.probabilities.length - 1; i++) {
const survival = 1 - result.probabilities[i];
if (survival < 1e-5 || quantilesMs[i] <= 0) continue;
tailPoints.push([xScale(quantilesMs[i]), tailScale(survival)]);
}
const xTicks = [];
for (let exponent = Math.floor(xLogMinimum);
exponent <= Math.ceil(xLogMaximum); exponent++) {
for (const multiplier of [1, 2, 5]) {
const value = multiplier * 10 ** exponent;
if (value >= xMinimum && value <= xMaximum) xTicks.push(value);
}
}
const svg = [];
const add = (value) => svg.push(value);
add(`<svg xmlns="http://www.w3.org/2000/svg" width="${width}" height="${height}" viewBox="0 0 ${width} ${height}" fill="#16212b">`);
add('<defs>');
add('<linearGradient id="densityFill" x1="0" y1="0" x2="0" y2="1"><stop offset="0" stop-color="#087e8b" stop-opacity="0.75"/><stop offset="1" stop-color="#087e8b" stop-opacity="0.08"/></linearGradient>');
add('<filter id="shadow" x="-20%" y="-20%" width="140%" height="140%"><feDropShadow dx="0" dy="3" stdDeviation="8" flood-color="#16212b" flood-opacity="0.09"/></filter>');
add('<style>text{font-family:Inter,ui-sans-serif,system-ui,sans-serif}.muted{fill:#63717b}.axis{font-size:12px}.small{font-size:11px;letter-spacing:.02em}.label{font-size:13px;font-weight:650}.metric{font-size:20px;font-weight:720}.rule{stroke:#d9d5ca;stroke-width:1}.grid{stroke:#dedbd2;stroke-width:1;stroke-dasharray:2 5}</style>');
add('</defs>');
add(`<rect width="${width}" height="${height}" fill="#f7f4ec"/>`);
add('<rect x="0" y="0" width="18" height="900" fill="#ff6b4a"/>');
add('<text x="76" y="61" font-size="31" font-weight="760" letter-spacing="-.6">Request latency, reconstructed from QRDE</text>');
add(`<text x="76" y="91" font-size="14" class="muted">Synthetic service workload | ${sampleCount.toLocaleString('en-US')} observations | fixed-bin histogram compared with adaptive QRDE</text>`);
add(`<rect x="${plotX - 18}" y="${densityY - 36}" width="${plotWidth + 36}" height="${densityHeight + 72}" rx="12" fill="#fffdf8" filter="url(#shadow)"/>`);
add(`<text x="${plotX}" y="${densityY - 12}" class="label">HISTOGRAM VS QRDE</text>`);
add(`<rect x="${plotX + plotWidth - 300}" y="${densityY - 24}" width="12" height="12" rx="2" fill="#ff6b4a" fill-opacity=".32" stroke="#c9452a" stroke-width=".7"/>`);
add(`<text x="${plotX + plotWidth - 281}" y="${densityY - 13}" class="small muted">48 fixed bins</text>`);
add(`<line x1="${plotX + plotWidth - 158}" y1="${densityY - 18}" x2="${plotX + plotWidth - 136}" y2="${densityY - 18}" stroke="#076b76" stroke-width="2.4"/>`);
add(`<text x="${plotX + plotWidth - 128}" y="${densityY - 13}" class="small muted">QRDE (${result.densities.length} intervals)</text>`);
for (const tick of xTicks) {
const x = xScale(tick);
add(`<line x1="${x}" y1="${densityY}" x2="${x}" y2="${densityY + densityHeight}" class="grid"/>`);
add(`<line x1="${x}" y1="${tailY}" x2="${x}" y2="${tailY + tailHeight}" class="grid"/>`);
}
for (let i = 0; i <= 4; i++) {
const value = densityMaximum * i / 4;
const y = densityScale(value);
add(`<line x1="${plotX}" y1="${y}" x2="${plotX + plotWidth}" y2="${y}" class="grid"/>`);
add(`<text x="${plotX - 11}" y="${y + 4}" text-anchor="end" class="axis muted">${(value * 100).toFixed(0)}%</text>`);
}
for (const bin of fixedHistogram) {
const x = xScale(bin.lowerMs);
const right = xScale(bin.upperMs);
const y = densityScale(bin.probabilityPerLog10Latency);
add(`<rect x="${(x + 0.6).toFixed(2)}" y="${y.toFixed(2)}" width="${Math.max(0, right - x - 1.2).toFixed(2)}" height="${(densityY + densityHeight - y).toFixed(2)}" fill="#ff6b4a" fill-opacity=".25" stroke="#c9452a" stroke-opacity=".55" stroke-width=".65"/>`);
}
add(`<path d="${pathFromPoints(densityArea)} Z" fill="url(#densityFill)"/>`);
add(`<path d="${pathFromPoints(densitySteps)}" fill="none" stroke="#076b76" stroke-width="1.65" stroke-linejoin="round"/>`);
add(`<line x1="${plotX}" y1="${densityY + densityHeight}" x2="${plotX + plotWidth}" y2="${densityY + densityHeight}" stroke="#16212b" stroke-width="1.2"/>`);
add(`<text transform="translate(29 ${densityY + densityHeight / 2}) rotate(-90)" text-anchor="middle" class="axis muted">Probability density (% per decade)</text>`);
const modeLabels = [
[1.15, 'FAST PATH'],
[4.8, 'REMOTE CACHE'],
[24, 'DATABASE'],
[180, 'RETRY / STALL'],
];
for (const [latency, label] of modeLabels) {
if (latency < xMinimum || latency > xMaximum) continue;
const x = xScale(latency);
add(`<line x1="${x}" y1="${densityY + 18}" x2="${x}" y2="${densityY + 48}" stroke="#ff6b4a" stroke-width="1.5"/>`);
add(`<text x="${x}" y="${densityY + 12}" text-anchor="middle" font-size="10" font-weight="700" fill="#c9452a">${label}</text>`);
}
add(`<rect x="${plotX - 18}" y="${tailY - 43}" width="${plotWidth + 36}" height="${tailHeight + 86}" rx="12" fill="#fffdf8" filter="url(#shadow)"/>`);
add(`<text x="${plotX}" y="${tailY - 17}" class="label">TAIL PROFILE</text>`);
add(`<text x="${plotX + plotWidth}" y="${tailY - 17}" text-anchor="end" class="small muted">QRDE curve; dots are exact quantiles from the original observations</text>`);
for (let exponent = 0; exponent <= 5; exponent++) {
const survival = 10 ** -exponent;
const y = tailScale(survival);
add(`<line x1="${plotX}" y1="${y}" x2="${plotX + plotWidth}" y2="${y}" class="grid"/>`);
const label = exponent === 0 ? '100%' : `${10 ** (2 - exponent)}%`;
add(`<text x="${plotX - 11}" y="${y + 4}" text-anchor="end" class="axis muted">${label}</text>`);
}
add(`<path d="${pathFromPoints(tailPoints)}" fill="none" stroke="#ff6b4a" stroke-width="2.4" stroke-linecap="round" stroke-linejoin="round"/>`);
for (const marker of markers.slice(1)) {
const y = tailScale(1 - marker.probability);
const x = xScale(marker.exactMs);
add(`<circle cx="${x}" cy="${y}" r="4.2" fill="#fffdf8" stroke="#16212b" stroke-width="1.7"/>`);
}
add(`<line x1="${plotX}" y1="${tailY + tailHeight}" x2="${plotX + plotWidth}" y2="${tailY + tailHeight}" stroke="#16212b" stroke-width="1.2"/>`);
for (const tick of xTicks) {
const x = xScale(tick);
add(`<text x="${x}" y="${tailY + tailHeight + 21}" text-anchor="middle" class="axis muted">${formatLatency(tick)}</text>`);
}
add(`<text x="${plotX + plotWidth / 2}" y="${tailY + tailHeight + 48}" text-anchor="middle" class="axis muted">Latency (log scale)</text>`);
add(`<text transform="translate(29 ${tailY + tailHeight / 2}) rotate(-90)" text-anchor="middle" class="axis muted">Probability above latency</text>`);
add(`<rect x="${sideX}" y="112" width="${sideWidth}" height="700" rx="12" fill="#16212b"/>`);
add(`<text x="${sideX + 24}" y="151" font-size="12" font-weight="700" letter-spacing="1.4" fill="#8fd3d8">LATENCY LANDMARKS</text>`);
let markerY = 188;
for (const marker of markers) {
add(`<text x="${sideX + 24}" y="${markerY}" font-size="13" fill="#b9c3c8">${escapeXml(marker.label)}</text>`);
add(`<text x="${sideX + sideWidth - 24}" y="${markerY}" text-anchor="end" font-size="19" font-weight="720" fill="#fffdf8">${escapeXml(formatLatency(marker.qrdeMs))}</text>`);
add(`<text x="${sideX + sideWidth - 24}" y="${markerY + 18}" text-anchor="end" font-size="10" fill="#7f929c">exact ${escapeXml(formatLatency(marker.exactMs))}</text>`);
markerY += 64;
}
add(`<line x1="${sideX + 24}" y1="${markerY - 25}" x2="${sideX + sideWidth - 24}" y2="${markerY - 25}" stroke="#34454f"/>`);
add(`<text x="${sideX + 24}" y="${markerY + 7}" font-size="12" font-weight="700" letter-spacing="1.4" fill="#8fd3d8">ESTIMATE CHECK</text>`);
const checks = [
['Integrated mass', integral.toFixed(12)],
['Histogram bins', fixedHistogram.length.toLocaleString('en-US')],
['QRDE intervals', result.densities.length.toLocaleString('en-US')],
['HDR buckets', result.bucketCount.toLocaleString('en-US')],
['Monotonic fixes', String(result.corrections)],
];
let checkY = markerY + 39;
for (const [name, value] of checks) {
add(`<text x="${sideX + 24}" y="${checkY}" font-size="11" fill="#8fa0a8">${escapeXml(name)}</text>`);
add(`<text x="${sideX + sideWidth - 24}" y="${checkY}" text-anchor="end" font-size="12" font-weight="650" fill="#fffdf8">${escapeXml(value)}</text>`);
checkY += 27;
}
add(`<text x="${sideX + 24}" y="${checkY + 18}" font-size="10" fill="#71838c">Both views integrate to the same mass.</text>`);
add(`<text x="${sideX + 24}" y="${checkY + 35}" font-size="10" fill="#71838c">QRDE is independent of fixed value bins.</text>`);
add('</svg>');
return svg.join('\n');
}
async function main() {
const random = mulberry32(0x5eed1234);
const normal = normalGenerator(random);
const histogram = createHistogram({
lowest: 1,
highest: 1_000_000_000,
figures: 3,
});
const samples = new Float64Array(sampleCount);
const components = [
{ cumulative: 0.82, medianMs: 1.15, sigma: 0.20 },
{ cumulative: 0.95, medianMs: 4.8, sigma: 0.25 },
{ cumulative: 0.995, medianMs: 24, sigma: 0.30 },
{ cumulative: 1, medianMs: 180, sigma: 0.35 },
];
for (let i = 0; i < sampleCount; i++) {
const selection = random();
const component = components.find(({ cumulative }) => selection < cumulative);
const latencyMs = component.medianMs * Math.exp(component.sigma * normal());
const latencyUs = Math.max(1, Math.round(latencyMs * 1000));
histogram.record(latencyUs);
samples[i] = latencyUs;
}
samples.sort();
const probabilitySet = new Set([0, 0.5, 0.9, 0.99, 0.999, 0.9999, 1]);
for (let i = 1; i <= 400; i++) probabilitySet.add(0.98 * i / 400);
for (let i = 1; i <= 240; i++) {
const survival = 0.02 * (0.00001 / 0.02) ** (i / 240);
probabilitySet.add(1 - survival);
}
const probabilities = Array.from(probabilitySet).sort((a, b) => a - b);
const result = await histogram.qrde({ probabilities, dequantize: 'hdr' });
let integral = 0;
const logDensities = new Array(result.densities.length);
for (let i = 0; i < result.densities.length; i++) {
const lower = result.quantiles[i];
const upper = result.quantiles[i + 1];
const mass = result.densities[i] * (upper - lower);
integral += mass;
logDensities[i] = mass / Math.log10(upper / lower);
}
const markerProbabilities = [0.5, 0.9, 0.99, 0.999, 0.9999];
const markers = markerProbabilities.map((probability) => {
const index = result.probabilities.indexOf(probability);
if (index === -1) throw new Error(`Missing marker probability ${probability}`);
const qrdeMs = result.quantiles[index] / 1000;
const exactMs = quantile(samples, probability) / 1000;
return {
probability,
label: formatPercentile(probability),
qrdeMs,
exactMs,
relativeError: (qrdeMs - exactMs) / exactMs,
};
});
const quantilesMs = Array.from(result.quantiles, (value) => value / 1000);
const [plotMinimumMs, plotMaximumMs] = logarithmicDomain(quantilesMs);
const fixedHistogram = buildLogHistogram(
samples, plotMinimumMs, plotMaximumMs, 48);
const monotonic = result.quantiles.every((value, index, values) =>
index === 0 || value >= values[index - 1]);
const data = {
scenario: {
sampleCount,
unit: 'milliseconds',
mixture: components,
},
diagnostics: {
integratedMass: integral,
monotonic,
count: result.count.toString(),
occupiedHdrBuckets: result.bucketCount,
corrections: result.corrections,
dequantize: result.dequantize,
},
markers,
histogram: {
type: 'fixed-width in log10 latency',
bins: fixedHistogram,
},
qrde: {
probabilities: Array.from(result.probabilities),
quantilesMs,
densitiesPerMs: Array.from(result.densities, (value) => value * 1000),
probabilityPerLog10Latency: logDensities,
},
};
fs.writeFileSync(outputJson, `${JSON.stringify(data, null, 2)}\n`);
fs.writeFileSync(outputSvg,
renderPlot(result, markers, logDensities,
fixedHistogram, integral));
console.log(JSON.stringify({
outputSvg,
outputJson,
probabilities: result.probabilities.length,
count: result.count.toString(),
bucketCount: result.bucketCount,
corrections: result.corrections,
integratedMass: integral,
monotonic,
markers,
}, null, 2));
}
main().catch((error) => {
console.error(error);
process.exitCode = 1;
});
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sample data
{
"scenario": {
"sampleCount": 250000,
"unit": "milliseconds",
"mixture": [
{
"cumulative": 0.82,
"medianMs": 1.15,
"sigma": 0.2
},
{
"cumulative": 0.95,
"medianMs": 4.8,
"sigma": 0.25
},
{
"cumulative": 0.995,
"medianMs": 24,
"sigma": 0.3
},
{
"cumulative": 1,
"medianMs": 180,
"sigma": 0.35
}
]
},
"diagnostics": {
"integratedMass": 1,
"monotonic": true,
"count": "250000",
"occupiedHdrBuckets": 6596,
"corrections": 0,
"dequantize": "hdr"
},
"markers": [
{
"probability": 0.5,
"label": "p50",
"qrdeMs": 1.2150886168442836,
"exactMs": 1.215,
"relativeError": 0.00007293567430742205
},
{
"probability": 0.9,
"label": "p90",
"qrdeMs": 5.152479793518291,
"exactMs": 5.152,
"relativeError": 0.00009312762389179497
},
{
"probability": 0.99,
"label": "p99",
"qrdeMs": 33.795300915888404,
"exactMs": 33.78002000000002,
"relativeError": 0.00045236550743257825
},
{
"probability": 0.999,
"label": "p99.9",
"qrdeMs": 241.12324653077832,
"exactMs": 240.98068999999262,
"relativeError": 0.0005915682737305692
},
{
"probability": 0.9999,
"label": "p99.99",
"qrdeMs": 372.41040262565843,
"exactMs": 374.1740825000039,
"relativeError": -0.004713527624793377
}
],
"histogram": {
"type": "fixed-width in log10 latency",
"bins": [
{
"lowerMs": 0.1,
"upperMs": 0.12115276586285885,
"count": 0,
"probabilityPerLog10Latency": 0
},
{
"lowerMs": 0.12115276586285885,
"upperMs": 0.14677992676220694,
"count": 0,
"probabilityPerLog10Latency": 0
},
{
"lowerMs": 0.14677992676220694,
"upperMs": 0.1778279410038923,
"count": 0,
"probabilityPerLog10Latency": 0
},
{
"lowerMs": 0.1778279410038923,
"upperMs": 0.21544346900318834,
"count": 0,
"probabilityPerLog10Latency": 0
},
{
"lowerMs": 0.21544346900318834,
"upperMs": 0.26101572156825364,
"count": 0,
"probabilityPerLog10Latency": 0
},
{
"lowerMs": 0.26101572156825364,
"upperMs": 0.31622776601683794,
"count": 0,
"probabilityPerLog10Latency": 0
},
{
"lowerMs": 0.31622776601683794,
"upperMs": 0.3831186849557287,
"count": 0,
"probabilityPerLog10Latency": 0
},
{
"lowerMs": 0.3831186849557287,
"upperMs": 0.46415888336127786,
"count": 0,
"probabilityPerLog10Latency": 0
},
{
"lowerMs": 0.46415888336127786,
"upperMs": 0.5623413251903491,
"count": 33,
"probabilityPerLog10Latency": 0.0015840000000000001
},
{
"lowerMs": 0.5623413251903491,
"upperMs": 0.6812920690579611,
"count": 833,
"probabilityPerLog10Latency": 0.039984
},
{
"lowerMs": 0.6812920690579611,
"upperMs": 0.8254041852680184,
"count": 9058,
"probabilityPerLog10Latency": 0.434784
},
{
"lowerMs": 0.8254041852680184,
"upperMs": 1,
"count": 39527,
"probabilityPerLog10Latency": 1.897296
},
{
"lowerMs": 1,
"upperMs": 1.2115276586285881,
"count": 74382,
"probabilityPerLog10Latency": 3.570336
},
{
"lowerMs": 1.2115276586285881,
"upperMs": 1.467799267622069,
"count": 58431,
"probabilityPerLog10Latency": 2.804688
},
{
"lowerMs": 1.467799267622069,
"upperMs": 1.7782794100389228,
"count": 19807,
"probabilityPerLog10Latency": 0.9507360000000001
},
{
"lowerMs": 1.7782794100389228,
"upperMs": 2.1544346900318834,
"count": 2865,
"probabilityPerLog10Latency": 0.13752
},
{
"lowerMs": 2.1544346900318834,
"upperMs": 2.610157215682536,
"count": 373,
"probabilityPerLog10Latency": 0.017904000000000003
},
{
"lowerMs": 2.610157215682536,
"upperMs": 3.1622776601683795,
"count": 1286,
"probabilityPerLog10Latency": 0.061728000000000005
},
{
"lowerMs": 3.1622776601683795,
"upperMs": 3.831186849557287,
"count": 4401,
"probabilityPerLog10Latency": 0.21124800000000002
},
{
"lowerMs": 3.831186849557287,
"upperMs": 4.6415888336127775,
"count": 8514,
"probabilityPerLog10Latency": 0.40867200000000004
},
{
"lowerMs": 4.6415888336127775,
"upperMs": 5.623413251903491,
"count": 9635,
"probabilityPerLog10Latency": 0.46248
},
{
"lowerMs": 5.623413251903491,
"upperMs": 6.812920690579611,
"count": 5860,
"probabilityPerLog10Latency": 0.28128000000000003
},
{
"lowerMs": 6.812920690579611,
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