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Decay docs changes using math directive #137369

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7fef424
Decay docs changes
ioanatia Oct 22, 2025
77fa96f
Change math directive
ioanatia Oct 30, 2025
cf33702
fix examples
ioanatia Nov 3, 2025
92474bf
Maybe don't use \Big ?
ioanatia Nov 3, 2025
5a94027
Use \left( and right\)
ioanatia Nov 3, 2025
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33 changes: 24 additions & 9 deletions docs/reference/query-languages/query-dsl/query-dsl-function-score-query.md
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Expand Up @@ -369,35 +369,50 @@ The `DECAY_FUNCTION` determines the shape of the decay:
`gauss`
: Normal decay, computed as:

![Gaussian](../images/Gaussian.png "")

where ![sigma](../images/sigma.png "") is computed to assure that the score takes the value `decay` at distance `scale` from `origin`+-`offset`
:::{math}
S(doc) = exp \left( - \dfrac{max(0, | fieldvalue_{doc} - origin| - offset)^2)}{ 2\sigma^2 } \right)
:::

where $\sigma$ is computed to assure that the score takes the value `decay` at distance `scale` from `origin ± offset`

![sigma calc](../images/sigma_calc.png "")
:::{math}
\sigma^2 = -scale^2 / (2 \cdot ln(decay))
:::

See [Normal decay, keyword `gauss`](#gauss-decay) for graphs demonstrating the curve generated by the `gauss` function.


`exp`
: Exponential decay, computed as:

![Exponential](../images/Exponential.png "")

where again the parameter ![lambda](../images/lambda.png "") is computed to assure that the score takes the value `decay` at distance `scale` from `origin`+-`offset`
:::{math}
S(doc) = exp(\lambda \cdot max(0, |fieldvalue_{doc} - origin| - offset))
:::

![lambda calc](../images/lambda_calc.png "")
where again the parameter $\lambda$ is computed to assure that the score takes the value `decay` at distance `scale` from `origin ± offset`

:::{math}
\lambda = ln(decay)/scale
:::

See [Exponential decay, keyword `exp`](#exp-decay) for graphs demonstrating the curve generated by the `exp` function.


`linear`
: Linear decay, computed as:

![Linear](../images/Linear.png "").

where again the parameter `s` is computed to assure that the score takes the value `decay` at distance `scale` from `origin`+-`offset`
:::{math}
S(doc) = max \left( \dfrac{s - max(0, | fieldvalue_{doc} - origin| - offset)^2)}{ s }, 0 \right)
:::

where again the parameter `s` is computed to assure that the score takes the value `decay` at distance `scale` from `origin ± offset`

![s calc](../images/s_calc.png "")
:::{math}
s = scale / (1.0 - decay)
:::

In contrast to the normal and exponential decay, this function actually sets the score to 0 if the field value exceeds twice the user given scale value.

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