diff --git a/src/AL_alg.jl b/src/AL_alg.jl
index c4cc8ec5..62dfe933 100644
--- a/src/AL_alg.jl
+++ b/src/AL_alg.jl
@@ -209,7 +209,7 @@ function SolverCore.solve!(
   callback = (args...) -> nothing,
   x::V = reg_nlp.model.meta.x0,
   y::V = reg_nlp.model.meta.y0,
-  atol::T = √eps(T),
+  atol::T = eps(T)^(1 / 3),
   verbose::Int = 0,
   max_iter::Int = 10000,
   max_time::Float64 = 30.0,
diff --git a/src/LMTR_alg.jl b/src/LMTR_alg.jl
index 26187432..dd063cb0 100644
--- a/src/LMTR_alg.jl
+++ b/src/LMTR_alg.jl
@@ -190,9 +190,9 @@ function SolverCore.solve!(
   stats::GenericExecutionStats{T, V};
   callback = (args...) -> nothing,
   x::V = reg_nls.model.meta.x0,
-  atol::T = √eps(T),
+  atol::T = eps(T)^(1 / 3),
   sub_atol::T = atol,
-  rtol::T = √eps(T),
+  rtol::T = eps(T)^(1 / 3),
   neg_tol::T = zero(T),
   verbose::Int = 0,
   max_iter::Int = 10000,
diff --git a/src/LM_alg.jl b/src/LM_alg.jl
index ef514b44..1163f566 100644
--- a/src/LM_alg.jl
+++ b/src/LM_alg.jl
@@ -190,8 +190,8 @@ function SolverCore.solve!(
   callback = (args...) -> nothing,
   x::V = reg_nls.model.meta.x0,
   nonlinear::Bool = true,
-  atol::T = √eps(T),
-  rtol::T = √eps(T),
+  atol::T = eps(T)^(1 / 3),
+  rtol::T = eps(T)^(1 / 3),
   neg_tol::T = zero(T),
   verbose::Int = 0,
   max_iter::Int = 10000,
diff --git a/src/R2DH.jl b/src/R2DH.jl
index de93ffcb..4a0861fe 100644
--- a/src/R2DH.jl
+++ b/src/R2DH.jl
@@ -223,8 +223,8 @@ function SolverCore.solve!(
   stats::GenericExecutionStats{T, V};
   callback = (args...) -> nothing,
   x::V = reg_nlp.model.meta.x0,
-  atol::T = √eps(T),
-  rtol::T = √eps(T),
+  atol::T = eps(T)^(1 / 3),
+  rtol::T = eps(T)^(1 / 3),
   neg_tol::T = eps(T)^(1 / 4),
   verbose::Int = 0,
   max_iter::Int = 10000,
diff --git a/src/R2N.jl b/src/R2N.jl
index acb05d94..59f07009 100644
--- a/src/R2N.jl
+++ b/src/R2N.jl
@@ -216,8 +216,8 @@ function SolverCore.solve!(
   qn_update_y!::Function = _qn_grad_update_y!,
   qn_copy!::Function = _qn_grad_copy!,
   x::V = reg_nlp.model.meta.x0,
-  atol::T = √eps(T),
-  rtol::T = √eps(T),
+  atol::T = eps(T)^(1 / 3),
+  rtol::T = eps(T)^(1 / 3),
   neg_tol::T = eps(T)^(1 / 4),
   verbose::Int = 0,
   max_iter::Int = 10000,
diff --git a/src/R2_alg.jl b/src/R2_alg.jl
index 08b058d5..96b99f34 100644
--- a/src/R2_alg.jl
+++ b/src/R2_alg.jl
@@ -313,8 +313,8 @@ function SolverCore.solve!(
   stats::GenericExecutionStats{T, V};
   callback = (args...) -> nothing,
   x::V = reg_nlp.model.meta.x0,
-  atol::T = √eps(T),
-  rtol::T = √eps(T),
+  atol::T = eps(T)^(1 / 3),
+  rtol::T = eps(T)^(1 / 3),
   neg_tol::T = eps(T)^(1 / 4),
   verbose::Int = 0,
   max_iter::Int = 10000,
diff --git a/src/TRDH_alg.jl b/src/TRDH_alg.jl
index 6a76ce0c..5b116ad4 100644
--- a/src/TRDH_alg.jl
+++ b/src/TRDH_alg.jl
@@ -237,8 +237,8 @@ function SolverCore.solve!(
   stats::GenericExecutionStats{T, V};
   callback = (args...) -> nothing,
   x::V = reg_nlp.model.meta.x0,
-  atol::T = √eps(T),
-  rtol::T = √eps(T),
+  atol::T = eps(T)^(1 / 3),
+  rtol::T = eps(T)^(1 / 3),
   neg_tol::T = eps(T)^(1 / 4),
   verbose::Int = 0,
   max_iter::Int = 10000,
diff --git a/src/TR_alg.jl b/src/TR_alg.jl
index 7ebec003..d92dca9a 100644
--- a/src/TR_alg.jl
+++ b/src/TR_alg.jl
@@ -211,9 +211,9 @@ function SolverCore.solve!(
   stats::GenericExecutionStats{T, V};
   callback = (args...) -> nothing,
   x::V = reg_nlp.model.meta.x0,
-  atol::T = √eps(T),
-  sub_atol::T = √eps(T),
-  rtol::T = √eps(T),
+  atol::T = eps(T)^(1 / 3),
+  sub_atol::T = atol,
+  rtol::T = eps(T)^(1 / 3),
   neg_tol::T = eps(T)^(1 / 4),
   verbose::Int = 0,
   subsolver_logger::Logging.AbstractLogger = Logging.SimpleLogger(),