docs: DOC-888: Refactor auto-imported functions (deephaven#7708)

Refactors the page to reduce load time

Author: margaretkennedy

docs/groovy/conceptual/time-in-deephaven.md

@@ -28,7 +28,7 @@ There are four important tools provided by DQL that are relevant to the discussi
 
 ### 1. Built-in Java functions
 
-Deephaven has a collection of [built-in functions](../reference/query-language/query-library/auto-imported-functions.md) that are useful for working with date-time types. For the sake of performance, these functions are implemented in Java. DQL supports calling these functions directly in query strings, opening up all of Deephaven's [built-in Java functions](../reference/query-language/query-library/auto-imported-functions.md) to the Groovy interface. The following example uses the built-in Deephaven function [`now`](https://deephaven.io/core/javadoc/io/deephaven/time/DateTimeUtils.html#now()) to get the current system time as a Java [`Instant`](https://docs.oracle.com/en/java/javase/17/docs/api/java.base/java/time/Instant.html):
+Deephaven has a collection of [built-in functions](../reference/query-language/formulas/auto-imported-functions.md) that are useful for working with date-time types. For the sake of performance, these functions are implemented in Java. DQL supports calling these functions directly in query strings, opening up all of Deephaven's [built-in Java functions](../reference/query-language/formulas/auto-imported-functions.md) to the Groovy interface. The following example uses the built-in Deephaven function [`now`](https://deephaven.io/core/javadoc/io/deephaven/time/DateTimeUtils.html#now()) to get the current system time as a Java [`Instant`](https://docs.oracle.com/en/java/javase/17/docs/api/java.base/java/time/Instant.html):
 
 ```groovy test-set=2
 t = emptyTable(5).update("CurrentTime = now()")
@@ -37,7 +37,7 @@ t = emptyTable(5).update("CurrentTime = now()")
 > [!NOTE]
 > [`now`](https://deephaven.io/core/javadoc/io/deephaven/time/DateTimeUtils.html#now()) uses the [current clock](https://deephaven.io/core/javadoc/io/deephaven/time/DateTimeUtils.html#currentClock()) of the Deephaven engine. This clock is typically the system clock, but it may be set to a simulated clock when replaying tables.
 
-These [functions](../reference/query-language/query-library/auto-imported-functions.md) can also be applied to columns, constants, and variables. This slightly more complex example uses the built-in Deephaven function [`epochDaysToLocalDate`](https://deephaven.io/core/javadoc/io/deephaven/time/DateTimeUtils.html#epochDaysToLocalDate(long)) to create a [`LocalDate`](https://docs.oracle.com/en/java/javase/17/docs//api/java.base/java/time/LocalDate.html) from a long that represents the number of days since the [Unix epoch](https://en.wikipedia.org/wiki/Unix_time):
+These [functions](../reference/query-language/formulas/auto-imported-functions.md) can also be applied to columns, constants, and variables. This slightly more complex example uses the built-in Deephaven function [`epochDaysToLocalDate`](https://deephaven.io/core/javadoc/io/deephaven/time/DateTimeUtils.html#epochDaysToLocalDate(long)) to create a [`LocalDate`](https://docs.oracle.com/en/java/javase/17/docs//api/java.base/java/time/LocalDate.html) from a long that represents the number of days since the [Unix epoch](https://en.wikipedia.org/wiki/Unix_time):
 
 ```groovy test-set=3
 t = emptyTable(5).update("DaysSinceEpoch = ii", "LocalDateColumn = epochDaysToLocalDate(DaysSinceEpoch)")
@@ -72,7 +72,7 @@ To be clear:
 
 - `DaysSinceEpoch` is a 64-bit integer.
 - `LocalDateColumn` is a Java [`LocalDate`](https://docs.oracle.com/en/java/javase/17/docs//api/java.base/java/time/LocalDate.html) object.
-- [`epochDaysToLocalDate`](https://deephaven.io/core/javadoc/io/deephaven/time/DateTimeUtils.html#epochDaysToLocalDate(long)) is a Java function from the [built-in Deephaven library](../reference/query-language/query-library/auto-imported-functions.md).
+- [`epochDaysToLocalDate`](https://deephaven.io/core/javadoc/io/deephaven/time/DateTimeUtils.html#epochDaysToLocalDate(long)) is a Java function from the [built-in Deephaven library](../reference/query-language/formulas/auto-imported-functions.md).
 - `DayOfWeek` is the return value of [`getDayOfWeek`](https://docs.oracle.com/en/java/javase/11/docs/api/java.base/java/time/LocalDate.html#getDayOfWeek()), a Java method bound to the [`LocalDate`](https://docs.oracle.com/en/java/javase/17/docs//api/java.base/java/time/LocalDate.html) class.
 
 ### 3. Arithmetic and inequality operators
@@ -95,7 +95,7 @@ t = emptyTable(5).update(
 
 ### 4. Date-times using DQL
 
-In Deephaven, date-time values can be expressed using very simple [literal](https://en.wikipedia.org/wiki/Literal_(computer_programming)) syntax. These literal values can be used directly in query strings or as string inputs to [built-in functions](../reference/query-language/query-library/auto-imported-functions.md).
+In Deephaven, date-time values can be expressed using very simple [literal](https://en.wikipedia.org/wiki/Literal_(computer_programming)) syntax. These literal values can be used directly in query strings or as string inputs to [built-in functions](../reference/query-language/formulas/auto-imported-functions.md).
 
 > [!TIP]
 > In query strings, time literals are denoted with _single quotes_.

docs/groovy/getting-started/crash-course/query-strings.md

@@ -163,7 +163,7 @@ There are many more such operators supported in Deephaven. See the [guide on ope
 
 ## Built-in functions
 
-Aside from the common operations, Deephaven hosts a large library of functions known as [built-in or auto-imported functions](../../reference/query-language/query-library/auto-imported-functions.md) that can be used in query strings.
+Aside from the common operations, Deephaven hosts a large library of functions known as [built-in or auto-imported functions](../../reference/query-language/formulas/auto-imported-functions.md) that can be used in query strings.
 
 The [numeric subset of this library](/core/javadoc/io/deephaven/function/package-summary.html) is full of functions that perform common mathematical operations on numeric types. These include exponentials, trigonometric functions, random number generators, and more.
 
@@ -251,7 +251,7 @@ lastByBin = binnedTimestamps.lastBy("Last5Mins")
 
 The [time user guide](../../conceptual/time-in-deephaven.md) provides a comprehensive overview of working with date-time data in Deephaven.
 
-These functions provide only a glimpse of what the built-in library offers. There are modules for [sorting](/core/javadoc/io/deephaven/function/Sort.html), [searching](/core/javadoc/io/deephaven/function/BinSearch.html), [string parsing](/core/javadoc/io/deephaven/function/Parse.html), [null handling](https://deephaven.io/core/javadoc/io/deephaven/function/Basic.html#isNull(byte)), and much more. See the document on [auto-imported functions](../../reference/query-language/query-library/auto-imported-functions.md) for a comprehensive list of what's available or the [module summary page](/core/javadoc/io/deephaven/function/package-summary.html) for a high-level overview of what's offered.
+These functions provide only a glimpse of what the built-in library offers. There are modules for [sorting](/core/javadoc/io/deephaven/function/Sort.html), [searching](/core/javadoc/io/deephaven/function/BinSearch.html), [string parsing](/core/javadoc/io/deephaven/function/Parse.html), [null handling](https://deephaven.io/core/javadoc/io/deephaven/function/Basic.html#isNull(byte)), and much more. See the document on [auto-imported functions](../../reference/query-language/formulas/auto-imported-functions.md) for a comprehensive list of what's available or the [module summary page](/core/javadoc/io/deephaven/function/package-summary.html) for a high-level overview of what's offered.
 
 ## Java methods
 

docs/groovy/how-to-guides/built-in-constants.md

@@ -124,6 +124,6 @@ Deephaven has only two built-in math constants:
 - [Built-in functions](./built-in-functions.md)
 - [Handle nulls, infinities, and NaNs](./null-inf-nan.md)
 - [Work with date-times](../conceptual/time-in-deephaven.md)
-- [Auto-imported functions](../reference/query-language/query-library/auto-imported-functions.md)
+- [Auto-imported functions](../reference/query-language/formulas/auto-imported-functions.md)
 - [`emptyTable`](../reference/table-operations/create/emptyTable.md)
 - [`update`](../reference/table-operations/select/update.md)

docs/groovy/how-to-guides/built-in-functions.md

@@ -44,10 +44,10 @@ source = emptyTable(40).update(
 )
 ```
 
-This page does not provide a comprehensive list of all built-ins. For the complete list of functions built into the query language, see [Auto-imported functions](../reference/query-language/query-library/auto-imported-functions.md).
+This page does not provide a comprehensive list of all built-ins. For the complete list of functions built into the query language, see [Auto-imported functions](../reference/query-language/formulas/auto-imported-functions.md).
 
 ## Related documentation
 
 - [Built-in constants](./built-in-constants.md)
 - [Built-in variables](./built-in-variables.md)
-- [Auto-imported functions](../reference/query-language/query-library/auto-imported-functions.md)
+- [Auto-imported functions](../reference/query-language/formulas/auto-imported-functions.md)

docs/groovy/how-to-guides/groovy-closures.md

@@ -56,7 +56,7 @@ Deephaven has a built-in [`sin`](https://deephaven.io/core/javadoc/io/deephaven/
 source = emptyTable(100).update("X = 0.1 * ii", "Y = sin(X)")
 ```
 
-Familiarity with Deephaven's built-in methods can speed up your workflow. Deephaven has a large number of built-in methods that can be called from query strings without any imports or classpaths. For more information and a complete list of what's available, see [auto-imported functions in Deephaven](../reference/query-language/query-library/auto-imported-functions.md).
+Familiarity with Deephaven's built-in methods can speed up your workflow. Deephaven has a large number of built-in methods that can be called from query strings without any imports or classpaths. For more information and a complete list of what's available, see [auto-imported functions in Deephaven](../reference/query-language/formulas/auto-imported-functions.md).
 
 ## Passing tables to functions
 
@@ -142,12 +142,12 @@ import com.example.MyClass
 
 ## Related documentation
 
-- [Auto-imported functions](../reference/query-language/query-library/auto-imported-functions.md)
+- [Auto-imported functions](../reference/query-language/formulas/auto-imported-functions.md)
 - [Create a new table](../how-to-guides/new-and-empty-table.md#newtable)
 - [Docker volumes](../conceptual/docker-data-volumes.md)
 - [How to use variables and functions in query strings](../how-to-guides/query-scope.md)
 - [How to install Java packages](../how-to-guides/install-and-use-java-packages.md)
 - [How to use Deephaven's built-in query language functions](../how-to-guides/built-in-functions.md)
-- [Query language functions](../reference/query-language/query-library/auto-imported-functions.md)
+- [Query language functions](../reference/query-language/formulas/auto-imported-functions.md)
 - [update](../reference/table-operations/select/update.md)
 - [view](../reference/table-operations/select/view.md)

docs/groovy/how-to-guides/null-inf-nan.md

@@ -204,4 +204,4 @@ result = source.update(
 - [Operators in query strings](./operators.md)
 - [Groovy variables in query strings](./groovy-variables.md)
 - [Groovy closures in query strings](./groovy-closures.md)
-- [Auto-imported functions](../reference/query-language/query-library/auto-imported-functions.md)
+- [Auto-imported functions](../reference/query-language/formulas/auto-imported-functions.md)

docs/groovy/how-to-guides/rolling-aggregations.md

@@ -597,7 +597,7 @@ fXyz = plotBollinger(result, "XYZ")
 
 The [`updateBy`](/core/javadoc/io/deephaven/engine/table/impl/updateby/UpdateBy.html) module enables users to create custom rolling aggregations with the [`RollingFormula`](../reference/table-operations/update-by-operations/rolling-formula.md) function.
 
-The user-defined formula can utilize any of Deephaven's [built-in functions](../reference/query-language/query-library/auto-imported-functions.md), [arithmetic operators](../how-to-guides/operators.md), or even [user-defined Groovy functions](../how-to-guides/groovy-closures.md).
+The user-defined formula can utilize any of Deephaven's [built-in functions](../reference/query-language/formulas/auto-imported-functions.md), [arithmetic operators](../how-to-guides/operators.md), or even [user-defined Groovy functions](../how-to-guides/groovy-closures.md).
 
 #### Tick-based rolling formulas
 

docs/groovy/sidebar.json

@@ -826,15 +826,6 @@
                   }
                 ]
               },
-              {
-                "label": "Imports",
-                "items": [
-                  {
-                    "label": "Auto-imported functions",
-                    "path": "reference/query-language/query-library/auto-imported-functions.md"
-                  }
-                ]
-              },
               {
                 "label": "Errors and troubleshooting",
                 "items": [

docs/python/conceptual/time-in-deephaven.md

@@ -62,7 +62,7 @@ There are four important tools provided by DQL that are relevant to the discussi
 
 ### 1. Built-in Java functions
 
-Deephaven has a collection of [built-in functions](../reference/query-language/query-library/auto-imported-functions.md) that are useful for working with date-time types. For the sake of performance, these functions are implemented in Java. DQL supports calling these functions directly in query strings, opening up all of Deephaven's [built-in Java functions](../reference/query-language/query-library/auto-imported-functions.md) to the Python interface. The following example uses the built-in Deephaven function [`now`](https://deephaven.io/core/javadoc/io/deephaven/time/DateTimeUtils.html#now()) to get the current system time as a Java [`Instant`](https://docs.oracle.com/en/java/javase/17/docs/api/java.base/java/time/Instant.html):
+Deephaven has a collection of [built-in functions](../reference/query-language/query-library/auto-imported/index.md) that are useful for working with date-time types. For the sake of performance, these functions are implemented in Java. DQL supports calling these functions directly in query strings, opening up all of Deephaven's [built-in Java functions](../reference/query-language/query-library/auto-imported/index.md) to the Python interface. The following example uses the built-in Deephaven function [`now`](https://deephaven.io/core/javadoc/io/deephaven/time/DateTimeUtils.html#now()) to get the current system time as a Java [`Instant`](https://docs.oracle.com/en/java/javase/17/docs/api/java.base/java/time/Instant.html):
 
 ```python test-set=2
 from deephaven import empty_table
@@ -73,7 +73,7 @@ t = empty_table(5).update("CurrentTime = now()")
 > [!NOTE]
 > The [`now`](https://deephaven.io/core/javadoc/io/deephaven/time/DateTimeUtils.html#now()) function uses the [current clock](https://deephaven.io/core/javadoc/io/deephaven/time/DateTimeUtils.html#currentClock()) of the Deephaven engine. This clock is typically the system clock, but it may be set to a simulated clock when replaying tables.
 
-These [functions](../reference/query-language/query-library/auto-imported-functions.md) can also be applied to columns, constants, and variables. This slightly more complex example uses the built-in Deephaven function [`epochDaysToLocalDate`](https://deephaven.io/core/javadoc/io/deephaven/time/DateTimeUtils.html#epochDaysToLocalDate(long)) to create a [`LocalDate`](https://docs.oracle.com/en/java/javase/17/docs//api/java.base/java/time/LocalDate.html) from a long that represents the number of days since the [Unix epoch](https://en.wikipedia.org/wiki/Unix_time):
+These [functions](../reference/query-language/query-library/auto-imported/index.md) can also be applied to columns, constants, and variables. This slightly more complex example uses the built-in Deephaven function [`epochDaysToLocalDate`](https://deephaven.io/core/javadoc/io/deephaven/time/DateTimeUtils.html#epochDaysToLocalDate(long)) to create a [`LocalDate`](https://docs.oracle.com/en/java/javase/17/docs//api/java.base/java/time/LocalDate.html) from a long that represents the number of days since the [Unix epoch](https://en.wikipedia.org/wiki/Unix_time):
 
 ```python test-set=3
 from deephaven import empty_table
@@ -120,7 +120,7 @@ To be clear:
 
 - `DaysSinceEpoch` is a 64-bit integer.
 - `LocalDateColumn` is a Java [`LocalDate`](https://docs.oracle.com/en/java/javase/17/docs//api/java.base/java/time/LocalDate.html) object.
-- [`epochDaysToLocalDate`](https://deephaven.io/core/javadoc/io/deephaven/time/DateTimeUtils.html#epochDaysToLocalDate(long)) is a Java function from the [built-in Deephaven library](../reference/query-language/query-library/auto-imported-functions.md).
+- [`epochDaysToLocalDate`](https://deephaven.io/core/javadoc/io/deephaven/time/DateTimeUtils.html#epochDaysToLocalDate(long)) is a Java function from the [built-in Deephaven library](../reference/query-language/query-library/auto-imported/index.md).
 - `DayOfWeek` is the return value of [`getDayOfWeek`](https://docs.oracle.com/en/java/javase/11/docs/api/java.base/java/time/LocalDate.html#getDayOfWeek()), a Java method bound to the [`LocalDate`](https://docs.oracle.com/en/java/javase/17/docs//api/java.base/java/time/LocalDate.html) class.
 
 DQL enables them all to be used seamlessly from the Python API!
@@ -149,7 +149,7 @@ t = empty_table(5).update(
 
 ### 4. Date-times using DQL
 
-In Deephaven, date-time values can be expressed using very simple [literal](https://en.wikipedia.org/wiki/Literal_(computer_programming)) syntax. These literal values can be used directly in query strings or as string inputs to [built-in functions](../reference/query-language/query-library/auto-imported-functions.md).
+In Deephaven, date-time values can be expressed using very simple [literal](https://en.wikipedia.org/wiki/Literal_(computer_programming)) syntax. These literal values can be used directly in query strings or as string inputs to [built-in functions](../reference/query-language/query-library/auto-imported/index.md).
 
 > [!TIP]
 > In query strings, time literals are denoted with _single quotes_.
@@ -708,7 +708,7 @@ reformat_gsod_local_date = format_gsod_local_date.update(
 Because Deephaven queries can contain Python and the Deephaven query engine is implemented in Java, performance-conscious users should be aware of [Python-Java boundary crossings](../conceptual/python-java-boundary.md). Every time a query's execution passes between Python and Java, there is a performance penalty. Fast queries must be written to minimize such [boundary crossings](../conceptual/python-java-boundary.md).
 
 > [!WARNING]
-> Avoid [`deephaven.time`](/core/pydoc/code/deephaven.time.html#module-deephaven.time) functions in query strings. Because [`deephaven.time`](/core/pydoc/code/deephaven.time.html#module-deephaven.time) provides functions that convert between Python and Java types, every call crosses the [Python-Java boundary](../conceptual/python-java-boundary.md). Thus, each call incurs a tiny overhead. This overhead can add up when applied millions or billions of times during a query. Instead, use the [built-in functions](../reference/query-language/query-library/auto-imported-functions.md) that provide the same functionality and do not cross the [Python-Java boundary](../conceptual/python-java-boundary.md).
+> Avoid [`deephaven.time`](/core/pydoc/code/deephaven.time.html#module-deephaven.time) functions in query strings. Because [`deephaven.time`](/core/pydoc/code/deephaven.time.html#module-deephaven.time) provides functions that convert between Python and Java types, every call crosses the [Python-Java boundary](../conceptual/python-java-boundary.md). Thus, each call incurs a tiny overhead. This overhead can add up when applied millions or billions of times during a query. Instead, use the [built-in functions](../reference/query-language/query-library/auto-imported/index.md) that provide the same functionality and do not cross the [Python-Java boundary](../conceptual/python-java-boundary.md).
 
 Here is an example that demonstrates the effects that excess boundary crossings can have on performance: