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. Single binaryoperator can replace all elementary functions

"exp(x)=eml(x,1), ln(x)=eml(1,eml(eml(1,x),1)), and likewise for all other operations" – simplesighman

2. The result is mainly of theoretical interest; practical use is unclear > "I don't think anyone has found a practical application for their result yet, but that's not the point of the work." – tgtweak

3. Implementation depends on extended‑real conventions (e.g., ln 0 = ‑∞) > "EML-compiled formulas work flawlessly in symbolic Mathematica and IEEE754 floating-point… This is because some formulas internally might rely on the following properties of extended reals: ln 0 = −∞, e^(−∞) = 0." – Rubicund

4. Analogous to functional‑completeness ideas such as NAND gates

"This too is universal." – SideQuark

🚀 Project Ideas

[EML Expression Builder]

Summary

  • Visual drag‑and‑drop editor for constructing EML expression trees using only the constant 1 and the eml operator.
  • Generates full elementary functions (addition, multiplication, trig, etc.) as finite trees.
  • Exports trees to source code or HDL for embedding in calculators or research projects.

Details

Key Value
Target Audience Math educators, symbolic‑regression hobbyists, hardware hobbyists
Core Feature Tree construction with live preview of numeric result and symbolic form
Tech Stack React + TypeScript front‑end, Graphviz rendering, Node.js validation backend
Difficulty Medium
Monetization Revenue-ready: Tiered SaaS (Free tier, $9/mo Pro)

Notes

  • Directly answers the “how do you actually add/compose expressions?” pain point from the HN thread.
  • Visual feedback clarifies the exponential blow‑up described in Table 4 of the paper.
  • Monetization via subscription for advanced export options (HDL templates, API access) keeps it sustainable.

[Web‑based EML Calculator]

Summary

  • Browser calculator that only accepts inputs 1 and the eml operator, yet can compute any elementary function.
  • Internally maps EML trees to standard functions for display, handling NaN, infinities, and complex numbers.
  • Provides step‑by‑step walkthroughs of each transformation, reinforcing the “two‑button calculator” idea.

Details

Key Value
Target Audience Students, hobbyist programmers, math enthusiasts
Core Feature Interactive “type‑only‑1‑and‑eml” UI that resolves to real‑world functions
Tech Stack Vue.js front‑end, Math.js for numeric evaluation, WebAssembly fallback for exp/ln
Difficulty Low
Monetization Hobby

Notes

  • Implements the exact scenario discussed by several commenters (e.g., lioeters, DoctorOetker).
  • Low friction encourages sharing and experimentation on forums.
  • Keeps monetization minimal to remain a community tool, but could later offer premium function packs.

[EML Circuit Compiler (FPGA/Verilog)]

Summary- Toolchain that compiles EML expression trees into synthesizable HDL (Verilog/VHDL) for FPGA implementation.

  • Optimizes tree depth and resource usage (LUTs, DSP slices) to evaluate elementary functions in a single pipeline pass.
  • Generates timing reports and testbenches comparing against traditional FPU primitives.

Details

Key Value
Target Audience Hardware engineers, FPGA designers, research labs
Core Feature Automatic conversion of EML trees to hardware pipelines with depth‑aware resource allocation
Tech Stack Python front‑end, Yosys/nextpnr synthesis, JSON schema for tree input
Difficulty High
Monetization Revenue-ready: License per design (e.g., $199 perpetual)

Notes

  • Addresses the hardware‑efficiency concerns raised by tgtweak and tripletao in the discussion.
  • Demonstrates concrete silicon benefits when the tree can be fixed‑function.
  • Potential to sell as an IP core or SaaS for rapid prototyping of EML‑based math coprocessors.

[EML Symbolic Regression Engine]

Summary- Automated search engine that finds minimal EML trees approximating arbitrary target functions via gradient‑based optimization and sparsity regularization.

  • Supports both exact recovery (when possible) and numerical approximation with error metrics.
  • Outputs human‑readable tree diagrams and intermediate constants.

Details| Key | Value |

|-----|-------| | Target Audience | Data scientists, symbolic‑regression researchers, ML engineers | | Core Feature | Gradient descent on discrete tree structure using Gumbel‑Softmax tricks; supports constraints (max depth, max leaves) | | Tech Stack | Python, PyTorch, JAX for autodiff, NumPy for numerics, Plotly for visualization | | Difficulty | High | | Monetization | Revenue-ready: Subscription $15/mo for API access + custom consulting |

Notes

  • Directly responds to the curiosity about “symbolic regression with EML trees” expressed in several comments.
  • Enables users to discover compact EML representations without manually expanding Table 4 formulas.
  • Can be packaged as a cloud API for integration into ML pipelines or sold as a hosted service.

[Continuous Math Playground]

Summary

  • Interactive web platform that visualizes the construction of elementary functions using a single binary eml operator and constant 1.
  • Includes guided tutorials, “build‑your‑own‑function” sandbox, and community challenges to craft target expressions.
  • Provides step‑by‑step breakdowns of operation depth, complexity metrics, and error analysis.

Details

Key Value
Target Audience Teachers, university students, math hobbyists
Core Feature Playground where users compose EML trees, see numeric output, and compare with standard calculator functions
Tech Stack React, D3.js for diagrams, MathJax for rendering formulas, Node.js backend evaluation
Difficulty Low
Monetization Hobby

Notes

  • Tackles the “why would anyone use this?” question by offering educational value and community engagement.
  • Can host contests (e.g., minimal depth addition) to surface practical insights.
  • Potential to monetize through premium lesson packs or institutional licenses.

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