IdeaWell

Project ideas from Hacker News discussions.

All elementary functions from a single binary operator

Original Article

Hacker News Discussion

📝 Discussion Summary (Click to expand)

1. A single binary operator can generate all elementary functions

“A calculator with just two buttons, EML and the digit 1, can compute everything a full scientific calculator does.” — DoctorOetker

2. Practical hurdles and numerical limits

“For larger or negative inputs you get a NaN because ECMAScript has limited precision and doesn’t handle imaginary numbers.” — simplesighman

3. Community reaction and analogies

“But even tighter. With eml and 1 you could encode a function in RPN as bits.” — Lerc

These three themes capture the core of the discussion: the mathematical breakthrough, the real‑world constraints that surface when trying to implement it, and how commentators situate the work alongside familiar computational primitives.

🚀 Project Ideas

Generating project ideas…

EML Calculator Web App

Summary

  • A browser‑based calculator that lets users perform any elementary math operation using only the binary EML operator and the constant 1, eliminating the need for multiple function buttons.
  • Solves the frustration of traditional calculators that require separate keys for exp, ln, sqrt, etc., by offering a minimalist UI that reuses a single “EML” key.

Details

Key Value
Target Audience Math hobbyists, educators, and developers interested in functional minimalism
Core Feature One‑click EML entry with optional 1‑button input, automatic conversion to exp/ln‑based expressions
Tech Stack React frontend, TypeScript, Web Workers for heavy math, Math.js library for fallback
Difficulty Low
Monetization Revenue-ready: Subscription ($4.99/mo) for premium custom operators

Notes

  • HN commenters highlighted the elegance of a single binary operator; this app makes that tangible.
  • Potential for educational demos showing how addition/multiplication emerge from repeated EML usage.

EML Symbolic Regression SaaS

Summary

  • A cloud API that takes a set of numeric samples and returns a compact expression built from the EML operator and constant 1, enabling exact symbolic regression without manual formula hunting.
  • Addresses the pain point of noisy regression tools that produce bloated polynomial fits by delivering minimal, human‑readable formulas.

Details

Key Value
Target Audience Data scientists, researchers, and engineers needing interpretable models
Core Feature REST endpoint that performs gradient‑descent tree search over EML expressions, returning AST and confidence score
Tech Stack Python backend (FastAPI), JAX for automatic differentiation, PostgreSQL for storage
Difficulty Medium
Monetization Revenue-ready: Pay‑per‑query ($0.01 per call) with volume discounts

Notes

  • Users in the thread asked “How would you actually add?” – this service directly answers that by providing ready‑made addition via EML trees.
  • Could be integrated into Jupyter notebooks, offering instant symbolic derivation from data.

EML Gate Simulator for Embedded Systems

Summary

  • An open‑source RTL design kit that models EML gates (exp‑ln subtraction) in Verilog/VHDL, allowing hardware designers to experiment with a single‑operation continuous‑math primitive.
  • Captures the niche interest of engineers wanting to evaluate analog‑style computation on digital FPGAs.

Details

Key Value
Target Audience FPGA developers, hobbyist hardware hackers, and academic researchers in low‑power computing
Core Feature Parameterizable EML module that computes exp(x)-ln(y) using lookup‑table blocks and DSP slices, with optional pipelining
Tech Stack Verilog‑2001, Xilinx Vivado, Python testbench with NumPy, GitHub Actions CI
Difficulty Medium
Monetization Hobby

Notes

  • Discussion referenced physical implementations (“op‑amps”, “transistor gates”) – this simulator provides a safe sandbox to explore those ideas.
  • Could inspire a teaching module on “universal continuous primitives” analogous to NAND for discrete logic.

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