Update operators.md

docs/operators.md

@@ -2,46 +2,60 @@
 
 ## Pre-defined
 
-All Base julia operators that take 1 or 2 scalars as input,
-and output a scalar as output, are available. A selection
-of these and other valid operators are stated below.
+First, note that pretty much any valid Julia function which
+takes one or two scalars as input, and returns on scalar as output,
+is likely to be a valid operator[^1].
+A selection of these and other valid operators are stated below.
 
 **Binary**
 
-`+`, `-`, `*`, `/`, `^`, `greater`, `mod`, `logical_or`,
-`logical_and`
+- `+`
+- `-`
+- `*`
+- `/`
+- `^`
+- `cond`
+    - Equal to `(x, y) -> x > 0 ? y : 0`
+- `greater`
+    - Equal to `(x, y) -> x > y ? 1 : 0`
+- `logical_or`
+    - Equal to `(x, y) -> (x > 0 || y > 0) ? 1 : 0`
+- `logical_and`
+    - Equal to `(x, y) -> (x > 0 && y > 0) ? 1 : 0`
+- `mod`
 
 **Unary**
 
-`neg`,
-`square`,
-`cube`,
-`exp`,
-`abs`,
-`log`,
-`log10`,
-`log2`,
-`log1p`,
-`sqrt`,
-`sin`,
-`cos`,
-`tan`,
-`sinh`,
-`cosh`,
-`tanh`,
-`atan`,
-`asinh`,
-`acosh`,
-`atanh_clip` (=atanh((x+1)%2 - 1)),
-`erf`,
-`erfc`,
-`gamma`,
-`relu`,
-`round`,
-`floor`,
-`ceil`,
-`round`,
-`sign`.
+- `neg`
+- `square`
+- `cube`
+- `exp`
+- `abs`
+- `log`
+- `log10`
+- `log2`
+- `log1p`
+- `sqrt`
+- `sin`
+- `cos`
+- `tan`
+- `sinh`
+- `cosh`
+- `tanh`
+- `atan`
+- `asinh`
+- `acosh`
+- `atanh_clip`
+    - Equal to `atanh(mod(x + 1, 2) - 1)`
+- `erf`
+- `erfc`
+- `gamma`
+- `relu`
+- `round`
+- `floor`
+- `ceil`
+- `round`
+- `sign`
 
 ## Custom
 
@@ -52,7 +66,11 @@ you can define with by passing it to the `pysr` function, with, e.g.,
     PySRRegressor(
         ...,
         unary_operators=["myfunction(x) = x^2"],
-        binary_operators=["myotherfunction(x, y) = x^2*y"]
+        binary_operators=["myotherfunction(x, y) = x^2*y"],
+        extra_sympy_mappings={
+            "myfunction": lambda x: x**2,
+            "myotherfunction": lambda x, y: x**2 * y,
+        },
     )
 ```
 
@@ -62,7 +80,7 @@ Make sure that it works with
 instead of `1.5e3`, if you write any constant numbers, or simply convert a result to `Float64(...)`.
 
 PySR expects that operators not throw an error for any input value over the entire real line from `-3.4e38` to `+3.4e38`.
-Thus, for "invalid" inputs, such as negative numbers to a `sqrt` function, you may simply return a `NaN` of the same type as the input. For example,
+Thus, for invalid inputs, such as negative numbers to a `sqrt` function, you may simply return a `NaN` of the same type as the input. For example,
 
 ```julia
 my_sqrt(x) = x >= 0 ? sqrt(x) : convert(typeof(x), NaN)
@@ -71,3 +89,9 @@ my_sqrt(x) = x >= 0 ? sqrt(x) : convert(typeof(x), NaN)
 would be a valid operator. The genetic algorithm
 will preferentially selection expressions which avoid
 any invalid values over the training dataset.
+
+
+<!-- Footnote for 1: -->
+<!-- (Will say "However, you may need to define a `extra_sympy_mapping`":) -->
+
+[^1]: However, you will need to define a sympy equivalent in `extra_sympy_mapping` if you want to use a function not in the above list.