diff --git a/src/erf.jl b/src/erf.jl
index 79f6afe5..95943890 100644
--- a/src/erf.jl
+++ b/src/erf.jl
@@ -555,7 +555,7 @@ function _erfinv(y::BigFloat)
         isfinite(x) || return x
     end
     sqrtπhalf = sqrtπ * big(0.5)
-    tol = 2eps(abs(x))
+    tol = 2max(eps(abs(y)),eps(abs(x)))
     while true # Newton iterations
         Δx = sqrtπhalf * (erf(x) - y) * exp(x^2)
         x -= Δx
@@ -695,7 +695,7 @@ function _erfcinv(y::BigFloat)
         isfinite(x) || return x
     end
     sqrtπhalf = sqrtπ * big(0.5)
-    tol = 2eps(abs(x))
+    tol = 2max(eps(abs(y)),eps(abs(x)))
     while true # Newton iterations
         Δx = sqrtπhalf * (erfc(x) - y) * exp(x^2)
         x += Δx
diff --git a/test/erf.jl b/test/erf.jl
index d402989b..62e5c18d 100644
--- a/test/erf.jl
+++ b/test/erf.jl
@@ -145,6 +145,10 @@
             @test_throws DomainError erfinv(x)
             @test_throws DomainError erfcinv(1-x)
         end
+
+        # Those two values were hanging before, see issue #557
+        @test erfcinv(2big"0.8") ≈ erfcinv(2big(0.8)) rtol= 2eps()
+        @test erfcinv(2big"0.41") ≈ erfcinv(2big(0.41)) rtol= 2eps()
     end
 
     @testset "Other float types" begin