diff --git a/pkg/sql/analyze.go b/pkg/sql/analyze.go
index 62d247a8b8c5..cc1c17c8e9ea 100644
--- a/pkg/sql/analyze.go
+++ b/pkg/sql/analyze.go
@@ -207,8 +207,20 @@ func simplifyNotExpr(evalCtx *parser.EvalContext, n *parser.NotExpr) (parser.Typ
 			op = parser.SimilarTo
 		case parser.RegMatch:
 			op = parser.NotRegMatch
+		case parser.NotRegMatch:
+			op = parser.RegMatch
 		case parser.RegIMatch:
 			op = parser.NotRegIMatch
+		case parser.NotRegIMatch:
+			op = parser.RegIMatch
+		case parser.IsDistinctFrom:
+			op = parser.IsNotDistinctFrom
+		case parser.IsNotDistinctFrom:
+			op = parser.IsDistinctFrom
+		case parser.Is:
+			op = parser.IsNot
+		case parser.IsNot:
+			op = parser.Is
 		default:
 			return parser.MakeDBool(true), false
 		}
diff --git a/pkg/sql/analyze_test.go b/pkg/sql/analyze_test.go
index 13838b5723c0..cf4ca0c1e661 100644
--- a/pkg/sql/analyze_test.go
+++ b/pkg/sql/analyze_test.go
@@ -330,6 +330,14 @@ func TestSimplifyNotExpr(t *testing.T) {
 		{`NOT i NOT LIKE 'foo'`, `i = 'foo'`, false, false},
 		{`NOT i SIMILAR TO 'foo'`, `true`, false, false},
 		{`NOT i NOT SIMILAR TO 'foo'`, `i = 'foo'`, false, false},
+		{`NOT i ~ 'foo'`, `true`, false, false},
+		{`NOT i !~ 'foo'`, `true`, false, false},
+		{`NOT i ~* 'foo'`, `true`, false, false},
+		{`NOT i !~* 'foo'`, `true`, false, false},
+		{`NOT a IS DISTINCT FROM 1`, `true`, false, false},
+		{`NOT a IS NOT DISTINCT FROM 1`, `true`, false, false},
+		{`NOT a IS NULL`, `a IS NOT NULL`, true, true},
+		{`NOT a IS NOT NULL`, `a IS NULL`, true, true},
 		{`NOT (a != 1 AND b != 1)`, `(a = 1) OR (b = 1)`, true, true},
 		{`NOT (a != 1 OR a < 1)`, `a = 1`, true, true},
 		{`NOT NOT a = 1`, `a = 1`, true, true},