All elementary functions from a single binary operator (arxiv.org)

Article summary

A single binary operator, eml(x,y) = exp(x) - ln(y), can generate all elementary functions, including constants, arithmetic operations, and transcendental functions. This operator, combined with the constant 1, can express any elementary function. The discovery was made through a systematic exhaustive search. The eml operator enables a simple grammar for expressing mathematical functions as binary trees.

Main themes

• elementary functions
• binary operators
• mathematical computation
• hardware implementation
• transcendental functions
• symbolic regression

What commenters say

• The eml operator is not practical for computation due to its limited precision and inability to handle imaginary numbers.
• The discovery of the eml operator is significant because it provides a unified way of expressing elementary functions.
• A hardware implementation of the eml operator could potentially outperform traditional math coprocessors in certain scenarios.
• The eml operator is not suitable for replacing traditional arithmetic operations due to its high computational cost.
• The eml operator could be useful for specific applications such as weather and combustion simulation where transcendental functions are a bottleneck.
• The benefits of the eml operator are limited by the high energy cost of evaluating special functions.
• The eml operator enables gradient-based symbolic regression and can be used to recover exact formulas from numerical data.
• A silicon implementation of an EML machine could potentially achieve high performance and efficiency in evaluating elementary functions.