Edit Distance Cost Symmetry Pair Tool

Description

Return symmetric when insertion equals deletion cost and the supplied forward/backward substitution costs are exactly equal.

A similarity term depends on the comparison universe, missing-value policy, treatment of repeated features, and normalization. A score can also have a caller-selected value when its mathematical denominator vanishes. Those conventions matter before interpreting a threshold or comparing methods.

Return symmetric when insertion equals deletion cost and the supplied forward/backward substitution costs are exactly equal.

When to use this tool

Use Edit Distance Cost Symmetry Pair when you need this particular comparison term, normalization, domain condition, or empty-result policy in a larger matching workflow.

How to use the tool and how it works

Enter insertion, deletion, substitutionForward, substitutionBackward. Use the units and conventions below.
Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
Read symmetric, insertionDeletionGap, substitutionGap. Inspect symmetric before interpreting the associated values.

Return symmetric when insertion equals deletion cost and the supplied forward/backward substitution costs are exactly equal. Also return both signed cost gaps, requiring nonnegative costs.^[1]

Input field	Meaning and units	Accepted input
insertion	Insertion	Required. Finite number.
deletion	Deletion	Required. Finite number.
substitutionForward	Substitution Forward	Required. Finite number.
substitutionBackward	Substitution Backward	Required. Finite number.

Output field	Interpretation	Returned shape
symmetric	Symmetric	Required. Boolean.
insertionDeletionGap	Insertion Deletion Gap	Required. Finite number.
substitutionGap	Substitution Gap	Required. Finite number.

json

{
  "input": {
    "insertion": 1,
    "deletion": 2,
    "substitutionForward": 3,
    "substitutionBackward": 3
  },
  "output": {
    "symmetric": false,
    "insertionDeletionGap": -1,
    "substitutionGap": 0
  }
}

Limitations and assumptions

This checks the supplied local cost pair only. It does not establish symmetry for an entire alphabet matrix or guarantee other distance-metric properties.
The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.

Alternative or Complementary methods

Compare methods only after aligning feature definitions, missingness, empty policies, multiplicities, and normalizers. Use a complete comparison when the tool returns only one contribution or count check.

References

Calculation and input contract: similarity/edit-distance-cost-symmetry-pair — tool.io

Similar or alternative tools

Edit Distance Insert Delete Reversal Cost
Calculate forward=insertions*insertionCost+deletions*deletionCost and reverse with the counts exchanged, then gap=reverse-forward.
Edit Gap Extension Term
Evaluate one affine gap cost using opening+(length−1)*extension and zero cost for an empty gap.