Expression Generation
Generate candidate expressions across permitted numerical terms and operator patterns, including addition, subtraction, multiplication, division, and exponentiation.
01 / SOFTWARE
Equation Matcher
A symbolic formula discovery engine built in Java.
Equation Matcher works backward from numerical sequences: it searches candidate expressions, identifies those that match the target values, tracks how their terms change across successive inputs, and uses those substitution patterns to reconstruct a symbolic formula in terms of n.
LANGUAGEJava
DOMAINSymbolic computation
METHODExhaustive search
OUTPUTFormula candidates
01
OVERVIEW
Given the values, can a formula be discovered?
Rather than starting with a known formula and calculating its values, Equation Matcher approaches the problem in reverse. A target sequence becomes the evidence; the engine searches for numerical expressions that reproduce it and then looks for a consistent symbolic relationship behind those matches.
The result is not simply a list of expressions that happen to evaluate correctly. The program preserves the substitution path across inputs so that repeated numerical structure can be interpreted as a candidate formula in n.
02
HOW IT WORKS
A four-phase search.
Sequence Matching
Evaluate generated expressions against the selected sequence and retain candidates whose values match the required inputs.
Substitution Tracking
Compare surviving expressions across successive inputs and record which positions vary and which remain constant.
Formula Reconstruction
Use those repeated substitution patterns to infer a symbolic expression in terms of n and surface verified formula candidates.
03
EXAMPLE
From a sequence to a symbolic rule.
136101521…
⟶
n(n + 1)2
For the Summandial sequence, the search identifies numerical expressions that continue to match as the input changes. The changing positions resolve to n, while the stable positions remain constants, producing the familiar Gaussian sum.
04
TECHNICAL NOTES
Search first. Symbolic interpretation second.
The engine systematically explores combinations of numerical terms and operators rather than relying on a preloaded catalog of formulas. Candidate expressions are evaluated left-to-right, filtered by the target sequence, and carried forward only when they continue to satisfy the verification range.
This separation between expression search and symbolic reconstruction is central to the project: numerical matches establish the path, while substitution behavior across inputs supplies the information needed to generalize that path into a formula.
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