diff --git a/make/compiler_flags b/make/compiler_flags
index 0be4905ccee..5a3a703f07f 100644
--- a/make/compiler_flags
+++ b/make/compiler_flags
@@ -17,16 +17,18 @@ endif
 
 ## Set OS specific library filename extensions
 ifeq ($(OS),Windows_NT)
-  WINARM64 := $(shell echo | $(CXX) -E -dM -  | findstr __aarch64__)
   LIBRARY_SUFFIX ?= .dll
+  STR_SEARCH ?= findstr
 endif
 
 ifeq ($(OS),Darwin)
   LIBRARY_SUFFIX ?= .dylib
+  STR_SEARCH ?= grep
 endif
 
 ifeq ($(OS),Linux)
   LIBRARY_SUFFIX ?= .so
+  STR_SEARCH ?= grep
 endif
 
 ## Set default compiler
@@ -42,6 +44,11 @@ ifeq (default,$(origin CXX))
   endif
 endif
 
+ARM64_CHECK := $(shell echo | $(CXX) -E -dM -  | $(STR_SEARCH) __aarch64__)
+ifneq ($(ARM64_CHECK),)
+  ARM64 = true
+endif
+
 # Detect compiler type
 # - CXX_TYPE: {gcc, clang, mingw32-gcc, other}
 # - CXX_MAJOR: major version of CXX
@@ -164,7 +171,7 @@ ifeq ($(OS),Windows_NT)
 
   make/ucrt:
     pound := \#
-    UCRT_STRING := $(shell echo '$(pound)include <windows.h>' | $(CXX) -E -dM -  | findstr _UCRT)
+    UCRT_STRING := $(shell echo '$(pound)include <windows.h>' | $(CXX) -E -dM -  | $(STR_SEARCH) _UCRT)
     ifneq (,$(UCRT_STRING))
       IS_UCRT ?= true
     else
@@ -211,6 +218,10 @@ endif
 ## makes reentrant version lgamma_r available from cmath
 CXXFLAGS_OS += -D_REENTRANT
 
+ifeq ($(ARM64), true)
+  CXXFLAGS_OS += -ffp-contract=off
+endif
+
 ## silence warnings occuring due to the TBB and Eigen libraries
 CXXFLAGS_WARNINGS += -Wno-ignored-attributes
 
@@ -275,7 +286,7 @@ endif
 LDFLAGS_TBB ?= -Wl,-L,"$(TBB_LIB)" -Wl,--disable-new-dtags
 
 # Windows LLVM/Clang does not support -rpath, but is not needed on Windows anyway
-ifeq ($(WINARM64),)
+ifneq ($(OS), Windows_NT)
   LDFLAGS_TBB += -Wl,-rpath,"$(TBB_LIB)"
 endif
 
@@ -299,7 +310,7 @@ CXXFLAGS_TBB ?= -I $(TBB)/include
 LDFLAGS_TBB ?= -Wl,-L,"$(TBB_BIN_ABSOLUTE_PATH)" $(LDFLAGS_FLTO_FLTO) $(LDFLAGS_OPTIM_TBB)
 
 # Windows LLVM/Clang does not support -rpath, but is not needed on Windows anyway
-ifeq ($(WINARM64),)
+ifneq ($(OS), Windows_NT)
   LDFLAGS_TBB += -Wl,-rpath,"$(TBB_BIN_ABSOLUTE_PATH)"
 endif
 LDLIBS_TBB ?= -ltbb
diff --git a/make/libraries b/make/libraries
index 10460c6c75b..f6beafcda46 100644
--- a/make/libraries
+++ b/make/libraries
@@ -141,10 +141,11 @@ ifeq (Windows_NT, $(OS))
     TBB_CXXFLAGS += -D_UCRT
   endif
   # TBB does not have assembly code for Windows ARM64, so we need to use GCC builtins
-  ifneq ($(WINARM64),)
-	TBB_CXXFLAGS += -DTBB_USE_GCC_BUILTINS
-	CXXFLAGS_TBB += -DTBB_USE_GCC_BUILTINS
-  endif
+	ifeq ($(ARM64),true)
+		TBB_CXXFLAGS += -DTBB_USE_GCC_BUILTINS
+		CXXFLAGS_TBB += -DTBB_USE_GCC_BUILTINS
+		WINARM64 = true
+	endif
 	SH_CHECK := $(shell command -v sh 2>/dev/null)
 	ifdef SH_CHECK
 		WINDOWS_HAS_SH ?= true
diff --git a/stan/math/prim/fun/inv_sqrt.hpp b/stan/math/prim/fun/inv_sqrt.hpp
index f0fc82eafe5..c4e58fcbedb 100644
--- a/stan/math/prim/fun/inv_sqrt.hpp
+++ b/stan/math/prim/fun/inv_sqrt.hpp
@@ -60,8 +60,14 @@ inline auto inv_sqrt(const Container& x) {
 template <typename Container, require_not_var_matrix_t<Container>* = nullptr,
           require_container_st<std::is_arithmetic, Container>* = nullptr>
 inline auto inv_sqrt(const Container& x) {
+// Eigen 3.4.0 has precision issues on ARM64 with vectorised rsqrt
+// Resolved in current master branch, below can be removed on next release
+#ifdef __aarch64__
+  return apply_scalar_unary<inv_sqrt_fun, Container>::apply(x);
+#else
   return apply_vector_unary<Container>::apply(
       x, [](const auto& v) { return v.array().rsqrt(); });
+#endif
 }
 
 }  // namespace math
diff --git a/test/unit/math/fwd/core/std_numeric_limits_test.cpp b/test/unit/math/fwd/core/std_numeric_limits_test.cpp
index 798736eb571..5ce4200e55f 100644
--- a/test/unit/math/fwd/core/std_numeric_limits_test.cpp
+++ b/test/unit/math/fwd/core/std_numeric_limits_test.cpp
@@ -103,8 +103,10 @@ TEST(AgradFwdNumericLimits, All_Fvar) {
   EXPECT_FALSE(std::numeric_limits<fvar<double> >::traps);
   EXPECT_FALSE(std::numeric_limits<fvar<fvar<double> > >::traps);
 
-  EXPECT_FALSE(std::numeric_limits<fvar<double> >::tinyness_before);
-  EXPECT_FALSE(std::numeric_limits<fvar<fvar<double> > >::tinyness_before);
+  EXPECT_EQ(std::numeric_limits<fvar<double> >::tinyness_before,
+            std::numeric_limits<double>::tinyness_before);
+  EXPECT_EQ(std::numeric_limits<fvar<fvar<double> > >::tinyness_before,
+            std::numeric_limits<double>::tinyness_before);
 
   EXPECT_TRUE(std::numeric_limits<fvar<double> >::round_style);
   EXPECT_TRUE(std::numeric_limits<fvar<fvar<double> > >::round_style);
diff --git a/test/unit/math/mix/core/std_numeric_limits_test.cpp b/test/unit/math/mix/core/std_numeric_limits_test.cpp
index 9dde1d79f78..8d4455dc5e8 100644
--- a/test/unit/math/mix/core/std_numeric_limits_test.cpp
+++ b/test/unit/math/mix/core/std_numeric_limits_test.cpp
@@ -108,8 +108,10 @@ TEST(AgradMixNumericLimits, All_Fvar) {
   EXPECT_FALSE(std::numeric_limits<fvar<var> >::traps);
   EXPECT_FALSE(std::numeric_limits<fvar<fvar<var> > >::traps);
 
-  EXPECT_FALSE(std::numeric_limits<fvar<var> >::tinyness_before);
-  EXPECT_FALSE(std::numeric_limits<fvar<fvar<var> > >::tinyness_before);
+  EXPECT_EQ(std::numeric_limits<fvar<var> >::tinyness_before,
+            std::numeric_limits<double>::tinyness_before);
+  EXPECT_EQ(std::numeric_limits<fvar<fvar<var> > >::tinyness_before,
+            std::numeric_limits<double>::tinyness_before);
 
   EXPECT_TRUE(std::numeric_limits<fvar<var> >::round_style);
   EXPECT_TRUE(std::numeric_limits<fvar<fvar<var> > >::round_style);
diff --git a/test/unit/math/prim/fun/offset_multiplier_transform_test.cpp b/test/unit/math/prim/fun/offset_multiplier_transform_test.cpp
index a17b98b9023..1139d77ac34 100644
--- a/test/unit/math/prim/fun/offset_multiplier_transform_test.cpp
+++ b/test/unit/math/prim/fun/offset_multiplier_transform_test.cpp
@@ -193,7 +193,7 @@ TEST(prob_transform, offset_multiplier_constrain_matrix) {
       EXPECT_FLOAT_EQ(result(i), stan::math::offset_multiplier_constrain(
                                      x(i), offsetd, sigma(i), lp1));
     }
-    EXPECT_EQ(lp0, lp1);
+    EXPECT_FLOAT_EQ(lp0, lp1);
     auto x_free = stan::math::offset_multiplier_free(result, offsetd, sigma);
     for (size_t i = 0; i < x.size(); ++i) {
       EXPECT_FLOAT_EQ(x.coeff(i), x_free.coeff(i));
@@ -211,7 +211,7 @@ TEST(prob_transform, offset_multiplier_constrain_matrix) {
       EXPECT_FLOAT_EQ(result(i), stan::math::offset_multiplier_constrain(
                                      x(i), offset(i), sigma(i), lp1));
     }
-    EXPECT_EQ(lp0, lp1);
+    EXPECT_FLOAT_EQ(lp0, lp1);
     auto x_free = stan::math::offset_multiplier_free(result, offset, sigma);
     for (size_t i = 0; i < x.size(); ++i) {
       EXPECT_FLOAT_EQ(x.coeff(i), x_free.coeff(i));
diff --git a/test/unit/math/prim/prob/neg_binomial_test.cpp b/test/unit/math/prim/prob/neg_binomial_test.cpp
index ac5b0f611cb..addc39f5d40 100644
--- a/test/unit/math/prim/prob/neg_binomial_test.cpp
+++ b/test/unit/math/prim/prob/neg_binomial_test.cpp
@@ -189,8 +189,11 @@ TEST(ProbDistributionsNegBinomial, chiSquareGoodnessFitTest3) {
 
   double chi = 0;
 
-  for (int j = 0; j < K; j++)
-    chi += ((bin[j] - expect[j]) * (bin[j] - expect[j]) / expect[j]);
+  for (int j = 0; j < K; j++) {
+    if (expect[j] != 0) {
+      chi += ((bin[j] - expect[j]) * (bin[j] - expect[j]) / expect[j]);
+    }
+  }
 
   EXPECT_LT(chi, boost::math::quantile(boost::math::complement(mydist, 1e-6)));
 }
diff --git a/test/unit/math/test_ad.hpp b/test/unit/math/test_ad.hpp
index 7d7547bdbd9..d596f6b2e0c 100644
--- a/test/unit/math/test_ad.hpp
+++ b/test/unit/math/test_ad.hpp
@@ -1991,7 +1991,7 @@ void expect_common_unary_vectorized(const F& f) {
   for (double x1 : args)
     stan::test::expect_ad_vectorized<ComplexSupport>(tols, f, x1);
   auto int_args = internal::common_int_args();
-  for (int x1 : args)
+  for (int x1 : int_args)
     stan::test::expect_ad_vectorized<ComplexSupport>(tols, f, x1);
 }
 
@@ -2022,7 +2022,7 @@ void expect_common_unary_vectorized(const F& f) {
   for (double x1 : args)
     stan::test::expect_ad_vectorized<ComplexSupport>(tols, f, x1);
   auto int_args = internal::common_int_args();
-  for (int x1 : args)
+  for (int x1 : int_args)
     stan::test::expect_ad_vectorized<ComplexSupport>(tols, f, x1);
   for (auto x1 : common_complex())
     stan::test::expect_ad_vectorized<ComplexSupport>(tols, f, x1);