diff --git a/src/Type/Constant/ConstantFloatType.php b/src/Type/Constant/ConstantFloatType.php
index 008e5cc7468..cdc3b75cda8 100644
--- a/src/Type/Constant/ConstantFloatType.php
+++ b/src/Type/Constant/ConstantFloatType.php
@@ -108,6 +108,10 @@ public function toString(): Type
 			]);
 		}
 
+		if (is_nan($this->value)) {
+			return new ConstantStringType('NAN');
+		}
+
 		return new ConstantStringType((string) $this->value);
 	}
 
diff --git a/tests/PHPStan/Analyser/nsrt/nan-to-string.php b/tests/PHPStan/Analyser/nsrt/nan-to-string.php
new file mode 100644
index 00000000000..a5200bcf489
--- /dev/null
+++ b/tests/PHPStan/Analyser/nsrt/nan-to-string.php
@@ -0,0 +1,14 @@
+<?php // lint >= 8.0
+
+namespace NanToString;
+
+use function PHPStan\Testing\assertType;
+
+function doFoo(): void
+{
+	$nan = NAN;
+	assertType("'NAN'", (string) $nan);
+	assertType("'NAN'", $nan . '');
+	assertType("'INF'", (string) INF);
+	assertType("'-INF'", (string) -INF);
+}
diff --git a/turbo-ext/src/ConstantFloatType.cpp b/turbo-ext/src/ConstantFloatType.cpp
index af15a851b46..5c99caa6fb9 100644
--- a/turbo-ext/src/ConstantFloatType.cpp
+++ b/turbo-ext/src/ConstantFloatType.cpp
@@ -177,8 +177,10 @@ class ConstantFloatType
 	}
 
 	/* new UnionType([new ConstantStringType('0'), new ConstantStringType('-0')])
-	 * for 0.0 (and -0.0, which === 0.0), new ConstantStringType((string) $this->value)
-	 * otherwise — the cast under the current `precision` ini */
+	 * for 0.0 (and -0.0, which === 0.0), new ConstantStringType('NAN') for a
+	 * NAN, which PHP 8.5's zend_double_to_str() would convert with a warning,
+	 * new ConstantStringType((string) $this->value) otherwise — the cast under
+	 * the current `precision` ini */
 	zv::Val toString() const
 	{
 		double v = 0.0;
@@ -193,6 +195,7 @@ class ConstantFloatType
 			types.push(std::move(negativeZero));
 			return pt_type_new_union(std::move(types));
 		}
+		if (std::isnan(v)) return pt_type_new_constant_string("NAN", 3);
 		zend_string *str = zend_double_to_str(v);
 		zv::Val result = pt_type_new_constant_string(ZSTR_VAL(str), ZSTR_LEN(str));
 		zend_string_release(str);