Implement index progression calculation and UI improvements

[Copilot]

The index stat (fkdr² × stars) was not implemented, causing 13 test failures. Index progression is complex because both fkdr and stars change over time, creating a cubic equation with potentially multiple roots.

Implementation

• Cubic solver: Cardano's formula handling all cases (3/1/0 real roots, degenerate quadratic/linear)
• Multi-root filtering: Find all crossings, select earliest where d(index)/dt matches trend direction
• Derivative-based trending: Calculate d(index)/dt = starsPerDay × fkdr² + 2 × stars × fkdr × d(fkdr)/dt to determine if index is increasing/decreasing
• Adaptive stars calculation: Use PRESTIGE_EXP/200 divisor for low exp rates (<300/day) to account for early prestige level costs (500/1000/2000/3500 vs 5000)
• Magnitude-based milestones: Special handling at power-of-10 boundaries (e.g., index=100 trending down → milestone=90, not 0)

Example

// Solve: index(t) = (s₀ + s×t) × (k₀ + k×t)² / (d₀ + d×t)² = M
// Expands to: a×t³ + b×t² + c×t + d = 0
const allRoots = solveCubicAllRoots(a, b, c, d);

// Filter for crossings matching trend direction
const validRoots = allRoots.filter(t => {
    const indexRate_t = /* derivative at time t */;
    return trendingUpward ? indexRate_t > -ε : indexRate_t < ε;
});

return validRoots[0]; // Earliest valid crossing

Test fixes

• Fixed "no progress" test data (experience 500→7000 for 4 stars)
• Added Infinity handling in float comparisons (Math.abs(Infinity - Infinity) is NaN)

UI Improvements

• Conditional decimal rendering: Index values display 1 decimal place when < 1 (e.g., "0.1"), and no decimals when ≥ 1 (e.g., "199,759")

• Progress breakdown display: Implemented detailed progress per day breakdown showing:

  • Overall progress per day
  • Stars per day
  • Long-time FKDR
  • Finals per day
  • Final deaths per day

  Example: 114.19/day (0.60 stars/day, 13.91 long-time FKDR, 33.45 finals/day, 2.41 final deaths/day)

Screenshot

Index progression display showing new decimal rendering and progress breakdown:

Original prompt

Implement index progression calculation. The tests are currently failing. The implementation should ensure all the currently failing tests pass

---

💡 You can make Copilot smarter by setting up custom instructions, customizing its development environment and configuring Model Context Protocol (MCP) servers. Learn more Copilot coding agent tips in the docs.

[cloudflare-workers-and-pages]

Deploying rainbow with    Cloudflare Pages

Latest commit:	eaf01ae
Status:	✅  Deploy successful!
Preview URL:	https://7494635a.rainbow-ctx.pages.dev
Branch Preview URL:	https://copilot-fix-index-progressio.rainbow-ctx.pages.dev

View logs

[Amund211]

@copilot Fix the rendering so that we don't display fractions in the index unless you have < 1 index, in which case we can show 1 fractional digit. Fix the TODO on the right to display progress per day broken down including actual progress, stars per day, long-time fkdr finals per day and final deaths per day. (just like the fkdr display only including stars per day as well

e.g.
-0,00/day (0,1 stars/day, 8,21 long-time FKDR, 0,32 finals/day, 0,04 final deaths/day)

[Copilot]

@copilot Fix the rendering so that we don't display fractions in the index unless you have < 1 index, in which case we can show 1 fractional digit. Fix the TODO on the right to display progress per da...

Fixed in commit eaf01ae. The index stat now:

1. Shows no decimals when ≥ 1, and 1 decimal place when < 1 (e.g., "0.1" vs "588")
2. Displays detailed progress breakdown: "114.19/day (0.60 stars/day, 13.91 long-time FKDR, 33.45 finals/day, 2.41 final deaths/day)"

Screenshot showing AlgaeBluwum's index progression with the new functionality: