diff --git a/Project.toml b/Project.toml
index 83b5223b8..b409c12a9 100644
--- a/Project.toml
+++ b/Project.toml
@@ -16,6 +16,7 @@ julia = "1"
 
 [extras]
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["Test"]
+test = ["Test", "Zygote"]
diff --git a/src/activation.jl b/src/activation.jl
index 9dffa5b18..b40a42403 100644
--- a/src/activation.jl
+++ b/src/activation.jl
@@ -72,7 +72,8 @@ elu(x, α = one(x)) = ifelse(x ≥ 0, x/one(x), α * (exp(x) - one(x)))
 activation function.
 """
 function gelu(x::Real)
-    λ = oftype(x/1, √(2/π))
+    p = oftype(x/1, π)
+    λ = oftype(x/1, √(2/p))
     α = oftype(x/1, 0.044715)
     h = oftype(x/1, 0.5)
     h * x * (one(x) + tanh(λ * (x + α * x^3)))
@@ -126,12 +127,6 @@ Return `log(cosh(x))` which is computed in a numerically stable way.
 """
 logcosh(x::T) where T = x + softplus(-2x) - log(convert(T, 2))
 
-# Provide an informative error message if activation functions are called with an array
-for f in (:σ, :σ_stable, :logσ, :relu, :leakyrelu, :elu, :gelu, :swish, :selu, :softsign, :softplus, :logcosh)
-  @eval $(f)(x::AbstractArray, args...) =
-    error("Use broadcasting (`", $(string(f)), ".(x)`) to apply activation functions to arrays.")
-end
-
 
 """
     mish(x) = x * tanh(softplus(x))
@@ -140,3 +135,10 @@ Self Regularized Non-Monotonic Neural Activation Function
 See [Mish: A Self Regularized Non-Monotonic Neural Activation Function](https://arxiv.org/abs/1908.08681).
 """
 mish(x::Real) = x * tanh(softplus(x))
+
+
+# Provide an informative error message if activation functions are called with an array
+for f in (:σ, :σ_stable, :logσ, :relu, :leakyrelu, :elu, :gelu, :swish, :selu, :softsign, :softplus, :logcosh, :mish)
+    @eval $(f)(x::AbstractArray, args...) =
+      error("Use broadcasting (`", $(string(f)), ".(x)`) to apply activation functions to arrays.")
+end
\ No newline at end of file
diff --git a/test/activation.jl b/test/activation.jl
index 1c53e17e3..68da3cde7 100644
--- a/test/activation.jl
+++ b/test/activation.jl
@@ -1,6 +1,6 @@
-using NNlib, Test
+using NNlib, Test, Zygote
 
-ACTIVATION_FUNCTIONS = [σ, relu, leakyrelu, elu, gelu, swish, selu, softplus, softsign, logcosh];
+ACTIVATION_FUNCTIONS = [σ, relu, leakyrelu, elu, gelu, swish, selu, softplus, softsign, logcosh, mish];
 
 function test_value_float_precision_preserving(a)
     @testset "$(a): " begin
@@ -24,6 +24,17 @@ function test_value_int_input_forces_float64(a)
     end
 end
 
+function test_gradient_float_precision_preserving(a)
+    @testset "$(a): " begin
+        for T in [Float32, Float64]
+            for val in [-10, -1, 0, 1, 10]
+                val = @inferred a'(T(val))
+                @test typeof(val) == T
+            end
+        end
+    end
+end
+
 @testset "Activation Functions" begin
     @test σ(0.0) == 0.5
     @test relu(0.0) == 0.0
@@ -83,6 +94,10 @@ end
             @test typeof(relu(Int32(1))) == Int32
         end
     end
+    
+    @testset "Float gradient inference" begin
+        test_gradient_float_precision_preserving.(ACTIVATION_FUNCTIONS)
+    end
 
     @testset "softmax" begin
         xs = rand(5,5)