diff --git a/bindings/node/index.js b/bindings/node/index.js
index b68f1e1..ba74a12 100644
--- a/bindings/node/index.js
+++ b/bindings/node/index.js
@@ -35,14 +35,6 @@ async function transformer (root, path, ruleset, trails, originalSchema, from) {
           }
 
           return false
-        },
-
-        // TODO: Use standard JSON-e operators instead
-        omit: (object, keys) => {
-          return _.omit(object, _.castArray(keys))
-        },
-        replace: (value, regex, replacement) => {
-          return value.replace(new RegExp(regex, 'g'), replacement)
         }
       })
 
diff --git a/rules/jsonschema-2019-09-to-2019-09.json b/rules/jsonschema-2019-09-to-2019-09.json
index dd59c0c..21fa0b1 100644
--- a/rules/jsonschema-2019-09-to-2019-09.json
+++ b/rules/jsonschema-2019-09-to-2019-09.json
@@ -15,7 +15,17 @@
         }
       },
       "transform": {
-        "$eval": "omit(schema, 'dependentSchemas')"
+        "$map": {
+          "$eval": "schema"
+        },
+        "each(v,k)": {
+          "${k}": {
+            "$if": "k!='dependentSchemas'",
+            "then": {
+              "$eval": "v"
+            }
+          }
+        }
       }
     },
     {
@@ -32,7 +42,17 @@
         }
       },
       "transform": {
-        "$eval": "omit(schema, 'dependentRequired')"
+        "$map": {
+          "$eval": "schema"
+        },
+        "each(v,k)": {
+          "${k}": {
+            "$if": "k!='dependentRequired'",
+            "then": {
+              "$eval": "v"
+            }
+          }
+        }
       }
     }
   ]
diff --git a/rules/jsonschema-2019-09-to-2020-12.json b/rules/jsonschema-2019-09-to-2020-12.json
index 3728567..7e94865 100644
--- a/rules/jsonschema-2019-09-to-2020-12.json
+++ b/rules/jsonschema-2019-09-to-2020-12.json
@@ -38,7 +38,17 @@
       },
       "transform": {
         "$merge": [
-          { "$eval": "omit(schema, 'items')" },
+          { "$map": {
+            "$eval": "schema"
+          },
+          "each(v,k)": {
+            "${k}": {
+              "$if": "k!='items'",
+              "then": {
+                "$eval": "v"
+              }
+            }
+          } },
           {
             "prefixItems": {
               "$eval": "schema.items"
@@ -64,10 +74,23 @@
       },
       "transform": {
         "$merge": [
-          { "$eval": "omit(schema, '$ref')" },
+          { "$map": {
+            "$eval": "schema"
+          },
+          "each(v,k)": {
+            "${k}": {
+              "$if": "k!='$ref'",
+              "then": {
+                "$eval": "v"
+              }
+            }
+          } },
           {
             "$$ref": {
-              "$eval": "replace(schema['$ref'], '/items/(\\d+)', '/prefixItems/$1')"
+              "$if": "split(schema['$ref'], 'items')[1][1] in '1234567890'",
+              "then":{
+                "$eval": "join(split(schema['$ref'], 'items'), 'prefixItems')"
+              }
             }
           }
         ]
@@ -90,10 +113,20 @@
       },
       "transform": {
         "$merge": [
-          { "$eval": "omit(schema, '$ref')" },
+          { "$map": {
+            "$eval": "schema"
+          },
+          "each(v,k)": {
+            "${k}": {
+              "$if": "k!='$ref'",
+              "then": {
+                "$eval": "v"
+              }
+            }
+          } },
           {
             "$$ref": {
-              "$eval": "replace(schema['$ref'], '/additionalItems', '/items')"
+                "$eval": "join(split(schema['$ref'], 'additionalItems'), 'items')"
             }
           }
         ]
@@ -116,7 +149,17 @@
       },
       "transform": {
         "$merge": [
-          { "$eval": "omit(schema, 'additionalItems')" },
+          { "$map": {
+            "$eval": "schema"
+          },
+          "each(v,k)": {
+            "${k}": {
+              "$if": "k!='additionalItems'",
+              "then": {
+                "$eval": "v"
+              }
+            }
+          } },
           {
             "items": {
               "$eval": "schema.additionalItems"
@@ -167,7 +210,17 @@
       },
       "transform": {
         "$merge": [
-          { "$eval": "omit(schema, 'enum')" },
+          { "$map": {
+            "$eval": "schema"
+          },
+          "each(v,k)": {
+            "${k}": {
+              "$if": "k!='enum'",
+              "then": {
+                "$eval": "v"
+              }
+            }
+          } },
           {
             "const": {
               "$eval": "schema.enum[0]"
@@ -190,7 +243,17 @@
         }
       },
       "transform": {
-        "$eval": "omit(schema, '$recursiveAnchor')"
+        "$map": {
+          "$eval": "schema"
+        },
+        "each(v,k)": {
+          "${k}": {
+            "$if": "k!='$recursiveAnchor'",
+            "then": {
+              "$eval": "v"
+            }
+          }
+        }
       }
     },
     {
@@ -208,7 +271,17 @@
       },
       "transform": {
         "$merge": [
-          { "$eval": "omit(schema, '$recursiveAnchor')" },
+          { "$map": {
+            "$eval": "schema"
+          },
+          "each(v,k)": {
+            "${k}": {
+              "$if": "k!='$recursiveAnchor'",
+              "then": {
+                "$eval": "v"
+              }
+            }
+          } },
           {
             "$$dynamicAnchor": {
               "$eval": "'anchor-' + jsonHash(original)"
@@ -232,7 +305,17 @@
       },
       "transform": {
         "$merge": [
-          { "$eval": "omit(schema, '$recursiveRef')" },
+          { "$map": {
+            "$eval": "schema"
+          },
+          "each(v,k)": {
+            "${k}": {
+              "$if": "k!='$recursiveRef'",
+              "then": {
+                "$eval": "v"
+              }
+            }
+          } },
           {
             "$$dynamicRef": {
               "$if": "hasContext('$recursiveAnchor', true)",
diff --git a/rules/jsonschema-draft3-to-draft4.json b/rules/jsonschema-draft3-to-draft4.json
index bbb41aa..281247e 100644
--- a/rules/jsonschema-draft3-to-draft4.json
+++ b/rules/jsonschema-draft3-to-draft4.json
@@ -35,7 +35,17 @@
         }
       },
       "transform": {
-        "$eval": "omit(schema, 'type')"
+        "$map": {
+          "$eval": "schema"
+        },
+        "each(v,k)": {
+          "${k}": {
+            "$if": "k!='type'",
+            "then": {
+              "$eval": "v"
+            }
+          }
+        }
       }
     },
     {
@@ -55,7 +65,17 @@
         }
       },
       "transform": {
-        "$eval": "omit(schema, 'type')"
+        "$map": {
+          "$eval": "schema"
+        },
+        "each(v,k)": {
+          "${k}": {
+            "$if": "k!='type'",
+            "then": {
+              "$eval": "v"
+            }
+          }
+        }
       }
     },
     {
@@ -73,7 +93,17 @@
       },
       "transform": {
         "$merge": [
-          { "$eval": "omit(schema, 'divisibleBy')" },
+          { "$map": {
+            "$eval": "schema"
+          },
+          "each(v,k)": {
+            "${k}": {
+              "$if": "k!='divisibleBy'",
+              "then": {
+                "$eval": "v"
+              }
+            }
+          } },
           {
             "multipleOf": {
               "$eval": "schema.divisibleBy"
diff --git a/rules/jsonschema-draft4-to-draft6.json b/rules/jsonschema-draft4-to-draft6.json
index c3f4127..9f76891 100644
--- a/rules/jsonschema-draft4-to-draft6.json
+++ b/rules/jsonschema-draft4-to-draft6.json
@@ -36,7 +36,17 @@
       },
       "transform": {
         "$merge": [
-          { "$eval": "omit(schema, 'id')" },
+          { "$map": {
+            "$eval": "schema"
+          },
+          "each(v,k)": {
+            "${k}": {
+              "$if": "k!='id'",
+              "then": {
+                "$eval": "v"
+              }
+            }
+          } },
           {
             "$$id": {
               "$eval": "schema.id"
@@ -63,7 +73,17 @@
       },
       "transform": {
         "$merge": [
-          { "$eval": "omit(schema, 'minimum')" },
+          { "$map": {
+            "$eval": "schema"
+          },
+          "each(v,k)": {
+            "${k}": {
+              "$if": "k!='minimum'",
+              "then": {
+                "$eval": "v"
+              }
+            }
+          } },
           {
             "exclusiveMinimum": {
               "$eval": "schema.minimum"
@@ -90,7 +110,17 @@
       },
       "transform": {
         "$merge": [
-          { "$eval": "omit(schema, 'maximum')" },
+          { "$map": {
+            "$eval": "schema"
+          },
+          "each(v,k)": {
+            "${k}": {
+              "$if": "k!='maximum'",
+              "then": {
+                "$eval": "v"
+              }
+            }
+          } },
           {
             "exclusiveMaximum": {
               "$eval": "schema.maximum"
@@ -117,7 +147,17 @@
       },
       "transform": {
         "$merge": [
-          { "$eval": "omit(schema, 'exclusiveMinimum')" }
+          { "$map": {
+            "$eval": "schema"
+          },
+          "each(v,k)": {
+            "${k}": {
+              "$if": "k!='exclusiveMinimum'",
+              "then": {
+                "$eval": "v"
+              }
+            }
+          } }
         ]
       }
     },
@@ -139,7 +179,17 @@
       },
       "transform": {
         "$merge": [
-          { "$eval": "omit(schema, 'exclusiveMaximum')" }
+          { "$map": {
+            "$eval": "schema"
+          },
+          "each(v,k)": {
+            "${k}": {
+              "$if": "k!='exclusiveMaximum'",
+              "then": {
+                "$eval": "v"
+              }
+            }
+          } }
         ]
       }
     },
@@ -182,7 +232,17 @@
       },
       "transform": {
         "$merge": [
-          { "$eval": "omit(schema, 'enum')" },
+          { "$map": {
+            "$eval": "schema"
+          },
+          "each(v,k)": {
+            "${k}": {
+              "$if": "k!='enum'",
+              "then": {
+                "$eval": "v"
+              }
+            }
+          } },
           {
             "const": {
               "$eval": "schema.enum[0]"
diff --git a/rules/jsonschema-draft6-to-draft7.json b/rules/jsonschema-draft6-to-draft7.json
index 7557e41..63d7fd8 100644
--- a/rules/jsonschema-draft6-to-draft7.json
+++ b/rules/jsonschema-draft6-to-draft7.json
@@ -60,7 +60,17 @@
       },
       "transform": {
         "$merge": [
-          { "$eval": "omit(schema, 'enum')" },
+          { "$map": {
+            "$eval": "schema"
+          },
+          "each(v,k)": {
+            "${k}": {
+              "$if": "k!='enum'",
+              "then": {
+                "$eval": "v"
+              }
+            }
+          }},
           {
             "const": {
               "$eval": "schema.enum[0]"
diff --git a/rules/jsonschema-draft7-to-2019-09.json b/rules/jsonschema-draft7-to-2019-09.json
index 6a0621f..81f7bd9 100644
--- a/rules/jsonschema-draft7-to-2019-09.json
+++ b/rules/jsonschema-draft7-to-2019-09.json
@@ -37,7 +37,17 @@
       },
       "transform": {
         "$merge": [
-          { "$eval": "omit(schema, '$id')" },
+          { "$map": {
+            "$eval": "schema"
+          },
+          "each(v,k)": {
+            "${k}": {
+              "$if": "k!='$id'",
+              "then": {
+                "$eval": "v"
+              }
+            }
+          } },
           {
             "$$anchor": {
               "$eval": "schema['$id'][1:]"
@@ -61,7 +71,17 @@
       },
       "transform": {
         "$merge": [
-          { "$eval": "omit(schema, 'definitions')" },
+          { "$map": {
+            "$eval": "schema"
+          },
+          "each(v,k)": {
+            "${k}": {
+              "$if": "k!='definitions'",
+              "then": {
+                "$eval": "v"
+              }
+            }
+          }},
           {
             "$$defs": {
               "$eval": "schema.definitions"
@@ -86,10 +106,20 @@
       },
       "transform": {
         "$merge": [
-          { "$eval": "omit(schema, '$ref')" },
+          { "$map": {
+            "$eval": "schema"
+          },
+          "each(v,k)": {
+            "${k}": {
+              "$if": "k!='$ref'",
+              "then": {
+                "$eval": "v"
+              }
+            }
+          } },
           {
             "$$ref": {
-              "$eval": "replace(schema['$ref'], '/definitions/', '/$defs/')"
+                "$eval": "join(split(schema['$ref'], 'definitions'), '$defs')"
             }
           }
         ]
@@ -134,7 +164,17 @@
       },
       "transform": {
         "$merge": [
-          { "$eval": "omit(schema, 'enum')" },
+          { "$map": {
+            "$eval": "schema"
+          },
+          "each(v,k)": {
+            "${k}": {
+              "$if": "k!='enum'",
+              "then": {
+                "$eval": "v"
+              }
+            }
+          } },
           {
             "const": {
               "$eval": "schema.enum[0]"
@@ -158,7 +198,17 @@
       },
       "transform": {
         "$merge": [
-          { "$eval": "omit(schema, 'dependencies')" },
+          { "$map": {
+            "$eval": "schema"
+          },
+          "each(v,k)": {
+            "${k}": {
+              "$if": "k!='dependencies'",
+              "then": {
+                "$eval": "v"
+              }
+            }
+          } },
           {
             "dependentRequired": {
               "$map": {