Description
Calculate log((exp(left)+exp(right))/2) using the larger input as a shift before exponentiation.
A statistical term depends on its data summaries, weighting convention, centering, denominator, and boundary rules. A contribution, derivative, domain check, or converted summary answers a narrower question than a complete estimator. Those conventions must match before terms are combined or compared.
Calculate log((exp(left)+exp(right))/2) using the larger input as a shift before exponentiation.
When to use this tool
Use Log Mean Exp Two Value Stability when you need this specific summary conversion, contribution, domain rule, or sensitivity term with matching statistical conventions.
How to use the tool and how it works
- Enter left, right. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read value. Use the output convention below.
Calculate log((exp(left)+exp(right))/2) using the larger input as a shift before exponentiation.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| left | Left | Required. Finite number. |
| right | Right | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| value | Value | Required. Finite number. |
{
"input": {
"left": 1000,
"right": 1000
},
"output": {
"value": 1000
}
}Limitations and assumptions
- Inputs are natural-log quantities and output is log of their mean exponential, not their arithmetic mean or mean logarithm. The stable shift reduces overflow without defining probability or data conventions.
- 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
Use a complete estimator or model when a contribution, sensitivity, or domain check is insufficient. Verify the weight semantics, centering, denominator, and sampling assumptions before combining summaries.
References
Similar or alternative tools
- Arithmetic Harmonic Mean Two Value Gap
Return arithmetic=first/2+second/2, harmonic=2*first*second/(first+second), and gap=arithmetic-harmonic for positive inputs.
- Arithmetic Geometric Mean Gap Two Values
Return arithmetic=(left+right)/2, geometric=sqrt(left)*sqrt(right), and gap=arithmetic-geometric for nonnegative inputs.