diff --git a/bigframes/core/compile/sqlglot/expressions/numeric_ops.py b/bigframes/core/compile/sqlglot/expressions/numeric_ops.py
index f7c763e207..28d3532b8b 100644
--- a/bigframes/core/compile/sqlglot/expressions/numeric_ops.py
+++ b/bigframes/core/compile/sqlglot/expressions/numeric_ops.py
@@ -93,12 +93,19 @@ def _(expr: TypedExpr) -> sge.Expression:
 def _(expr: TypedExpr) -> sge.Expression:
     return sge.Case(
         ifs=[
+            # |x| < 1: The standard formula
+            sge.If(
+                this=sge.func("ABS", expr.expr) < sge.convert(1),
+                true=sge.func("ATANH", expr.expr),
+            ),
+            # |x| > 1: Returns NaN
             sge.If(
                 this=sge.func("ABS", expr.expr) > sge.convert(1),
                 true=constants._NAN,
-            )
+            ),
         ],
-        default=sge.func("ATANH", expr.expr),
+        # |x| = 1: Returns Infinity or -Infinity
+        default=sge.Mul(this=constants._INF, expression=expr.expr),
     )
 
 
@@ -145,15 +152,11 @@ def _(expr: TypedExpr) -> sge.Expression:
 
 @register_unary_op(ops.expm1_op)
 def _(expr: TypedExpr) -> sge.Expression:
-    return sge.Case(
-        ifs=[
-            sge.If(
-                this=expr.expr > constants._FLOAT64_EXP_BOUND,
-                true=constants._INF,
-            )
-        ],
-        default=sge.func("EXP", expr.expr),
-    ) - sge.convert(1)
+    return sge.If(
+        this=expr.expr > constants._FLOAT64_EXP_BOUND,
+        true=constants._INF,
+        false=sge.func("EXP", expr.expr) - sge.convert(1),
+    )
 
 
 @register_unary_op(ops.floor_op)
@@ -166,11 +169,22 @@ def _(expr: TypedExpr) -> sge.Expression:
     return sge.Case(
         ifs=[
             sge.If(
-                this=expr.expr <= sge.convert(0),
+                this=sge.Is(this=expr.expr, expression=sge.Null()),
+                true=sge.null(),
+            ),
+            # |x| > 0: The standard formula
+            sge.If(
+                this=expr.expr > sge.convert(0),
+                true=sge.Ln(this=expr.expr),
+            ),
+            # |x| < 0: Returns NaN
+            sge.If(
+                this=expr.expr < sge.convert(0),
                 true=constants._NAN,
-            )
+            ),
         ],
-        default=sge.Ln(this=expr.expr),
+        # |x| == 0: Returns -Infinity
+        default=constants._NEG_INF,
     )
 
 
@@ -179,11 +193,22 @@ def _(expr: TypedExpr) -> sge.Expression:
     return sge.Case(
         ifs=[
             sge.If(
-                this=expr.expr <= sge.convert(0),
+                this=sge.Is(this=expr.expr, expression=sge.Null()),
+                true=sge.null(),
+            ),
+            # |x| > 0: The standard formula
+            sge.If(
+                this=expr.expr > sge.convert(0),
+                true=sge.Log(this=sge.convert(10), expression=expr.expr),
+            ),
+            # |x| < 0: Returns NaN
+            sge.If(
+                this=expr.expr < sge.convert(0),
                 true=constants._NAN,
-            )
+            ),
         ],
-        default=sge.Log(this=expr.expr, expression=sge.convert(10)),
+        # |x| == 0: Returns -Infinity
+        default=constants._NEG_INF,
     )
 
 
@@ -192,11 +217,22 @@ def _(expr: TypedExpr) -> sge.Expression:
     return sge.Case(
         ifs=[
             sge.If(
-                this=expr.expr <= sge.convert(-1),
+                this=sge.Is(this=expr.expr, expression=sge.Null()),
+                true=sge.null(),
+            ),
+            # Domain: |x| > -1 (The standard formula)
+            sge.If(
+                this=expr.expr > sge.convert(-1),
+                true=sge.Ln(this=sge.convert(1) + expr.expr),
+            ),
+            # Out of Domain: |x| < -1 (Returns NaN)
+            sge.If(
+                this=expr.expr < sge.convert(-1),
                 true=constants._NAN,
-            )
+            ),
         ],
-        default=sge.Ln(this=sge.convert(1) + expr.expr),
+        # Boundary: |x| == -1 (Returns -Infinity)
+        default=constants._NEG_INF,
     )
 
 
@@ -608,7 +644,7 @@ def isfinite(arg: TypedExpr) -> sge.Expression:
     return sge.Not(
         this=sge.Or(
             this=sge.IsInf(this=arg.expr),
-            right=sge.IsNan(this=arg.expr),
+            expression=sge.IsNan(this=arg.expr),
         ),
     )
 
diff --git a/bigframes/core/compile/sqlglot/sqlglot_ir.py b/bigframes/core/compile/sqlglot/sqlglot_ir.py
index cefe983e24..d4dc4ecc06 100644
--- a/bigframes/core/compile/sqlglot/sqlglot_ir.py
+++ b/bigframes/core/compile/sqlglot/sqlglot_ir.py
@@ -674,7 +674,7 @@ def _literal(value: typing.Any, dtype: dtypes.Dtype) -> sge.Expression:
             expressions=[_literal(value=v, dtype=value_type) for v in value]
         )
         return values if len(value) > 0 else _cast(values, sqlglot_type)
-    elif pd.isna(value):
+    elif pd.isna(value) or (isinstance(value, pa.Scalar) and not value.is_valid):
         return _cast(sge.Null(), sqlglot_type)
     elif dtype == dtypes.JSON_DTYPE:
         return sge.ParseJSON(this=sge.convert(str(value)))
diff --git a/tests/unit/core/compile/sqlglot/expressions/snapshots/test_numeric_ops/test_arctanh/out.sql b/tests/unit/core/compile/sqlglot/expressions/snapshots/test_numeric_ops/test_arctanh/out.sql
index 197bf59306..dc6de62e7b 100644
--- a/tests/unit/core/compile/sqlglot/expressions/snapshots/test_numeric_ops/test_arctanh/out.sql
+++ b/tests/unit/core/compile/sqlglot/expressions/snapshots/test_numeric_ops/test_arctanh/out.sql
@@ -6,9 +6,11 @@ WITH `bfcte_0` AS (
   SELECT
     *,
     CASE
+      WHEN ABS(`float64_col`) < 1
+      THEN ATANH(`float64_col`)
       WHEN ABS(`float64_col`) > 1
       THEN CAST('NaN' AS FLOAT64)
-      ELSE ATANH(`float64_col`)
+      ELSE CAST('Infinity' AS FLOAT64) * `float64_col`
     END AS `bfcol_1`
   FROM `bfcte_0`
 )
diff --git a/tests/unit/core/compile/sqlglot/expressions/snapshots/test_numeric_ops/test_expm1/out.sql b/tests/unit/core/compile/sqlglot/expressions/snapshots/test_numeric_ops/test_expm1/out.sql
index 076ad584c2..13038bf8e8 100644
--- a/tests/unit/core/compile/sqlglot/expressions/snapshots/test_numeric_ops/test_expm1/out.sql
+++ b/tests/unit/core/compile/sqlglot/expressions/snapshots/test_numeric_ops/test_expm1/out.sql
@@ -5,11 +5,7 @@ WITH `bfcte_0` AS (
 ), `bfcte_1` AS (
   SELECT
     *,
-    CASE
-      WHEN `float64_col` > 709.78
-      THEN CAST('Infinity' AS FLOAT64)
-      ELSE EXP(`float64_col`)
-    END - 1 AS `bfcol_1`
+    IF(`float64_col` > 709.78, CAST('Infinity' AS FLOAT64), EXP(`float64_col`) - 1) AS `bfcol_1`
   FROM `bfcte_0`
 )
 SELECT
diff --git a/tests/unit/core/compile/sqlglot/expressions/snapshots/test_numeric_ops/test_ln/out.sql b/tests/unit/core/compile/sqlglot/expressions/snapshots/test_numeric_ops/test_ln/out.sql
index 776cc33e0f..bd4cfa7c9a 100644
--- a/tests/unit/core/compile/sqlglot/expressions/snapshots/test_numeric_ops/test_ln/out.sql
+++ b/tests/unit/core/compile/sqlglot/expressions/snapshots/test_numeric_ops/test_ln/out.sql
@@ -5,7 +5,15 @@ WITH `bfcte_0` AS (
 ), `bfcte_1` AS (
   SELECT
     *,
-    CASE WHEN `float64_col` <= 0 THEN CAST('NaN' AS FLOAT64) ELSE LN(`float64_col`) END AS `bfcol_1`
+    CASE
+      WHEN `float64_col` IS NULL
+      THEN NULL
+      WHEN `float64_col` > 0
+      THEN LN(`float64_col`)
+      WHEN `float64_col` < 0
+      THEN CAST('NaN' AS FLOAT64)
+      ELSE CAST('-Infinity' AS FLOAT64)
+    END AS `bfcol_1`
   FROM `bfcte_0`
 )
 SELECT
diff --git a/tests/unit/core/compile/sqlglot/expressions/snapshots/test_numeric_ops/test_log10/out.sql b/tests/unit/core/compile/sqlglot/expressions/snapshots/test_numeric_ops/test_log10/out.sql
index 11a318c22d..c5bbff0e62 100644
--- a/tests/unit/core/compile/sqlglot/expressions/snapshots/test_numeric_ops/test_log10/out.sql
+++ b/tests/unit/core/compile/sqlglot/expressions/snapshots/test_numeric_ops/test_log10/out.sql
@@ -6,9 +6,13 @@ WITH `bfcte_0` AS (
   SELECT
     *,
     CASE
-      WHEN `float64_col` <= 0
+      WHEN `float64_col` IS NULL
+      THEN NULL
+      WHEN `float64_col` > 0
+      THEN LOG(`float64_col`, 10)
+      WHEN `float64_col` < 0
       THEN CAST('NaN' AS FLOAT64)
-      ELSE LOG(10, `float64_col`)
+      ELSE CAST('-Infinity' AS FLOAT64)
     END AS `bfcol_1`
   FROM `bfcte_0`
 )
diff --git a/tests/unit/core/compile/sqlglot/expressions/snapshots/test_numeric_ops/test_log1p/out.sql b/tests/unit/core/compile/sqlglot/expressions/snapshots/test_numeric_ops/test_log1p/out.sql
index 4297fff227..22e67e24ee 100644
--- a/tests/unit/core/compile/sqlglot/expressions/snapshots/test_numeric_ops/test_log1p/out.sql
+++ b/tests/unit/core/compile/sqlglot/expressions/snapshots/test_numeric_ops/test_log1p/out.sql
@@ -6,9 +6,13 @@ WITH `bfcte_0` AS (
   SELECT
     *,
     CASE
-      WHEN `float64_col` <= -1
+      WHEN `float64_col` IS NULL
+      THEN NULL
+      WHEN `float64_col` > -1
+      THEN LN(1 + `float64_col`)
+      WHEN `float64_col` < -1
       THEN CAST('NaN' AS FLOAT64)
-      ELSE LN(1 + `float64_col`)
+      ELSE CAST('-Infinity' AS FLOAT64)
     END AS `bfcol_1`
   FROM `bfcte_0`
 )