diff --git a/src/levenberg.jl b/src/levenberg.jl
index c71c9016c..d4eb23a3f 100644
--- a/src/levenberg.jl
+++ b/src/levenberg.jl
@@ -274,18 +274,19 @@ function perform_step!(cache::LevenbergMarquardtCache{false})
     end
     @unpack u, p, λ, JᵀJ, DᵀD, J = cache
 
+    cache.mat_tmp = JᵀJ + λ * DᵀD
     # Usual Levenberg-Marquardt step ("velocity").
-    cache.v = -(JᵀJ + λ * DᵀD) \ (J' * fu1)
+    cache.v = -cache.mat_tmp \ (J' * fu1)
 
     @unpack v, h, α_geodesic = cache
     # Geodesic acceleration (step_size = v + a / 2).
-    cache.a = -J \ ((2 / h) .* ((f(u .+ h .* v, p) .- fu1) ./ h .- J * v))
+    cache.a = -cache.mat_tmp \ ((2 / h) .* ((f(u .+ h .* v, p) .- fu1) ./ h .- J * v))
     cache.stats.nsolve += 1
     cache.stats.nfactors += 1
 
     # Require acceptable steps to satisfy the following condition.
     norm_v = norm(v)
-    if (2 * norm(cache.a) / norm_v) < α_geodesic
+    if @fastmath((1 + log2(norm(cache.a)) - log2(norm_v))≤log2(α_geodesic))
         cache.δ = v .+ cache.a ./ 2
         @unpack δ, loss_old, norm_v_old, v_old, b_uphill = cache
         fu_new = f(u .+ δ, p)