diff --git a/engine-proto/gram-test/Engine.jl b/engine-proto/gram-test/Engine.jl
index 1eb72f5..6dfb6e9 100644
--- a/engine-proto/gram-test/Engine.jl
+++ b/engine-proto/gram-test/Engine.jl
@@ -324,7 +324,6 @@ function realize_gram_alt_proj(
   frozen = CartesianIndex[];
   scaled_tol = 1e-30,
   min_efficiency = 0.5,
-  init_rate = 1.0,
   backoff = 0.9,
   reg_scale = 1.1,
   max_descent_steps = 200,
@@ -349,13 +348,12 @@ function realize_gram_alt_proj(
   # convert the frozen indices to stacked format
   frozen_stacked = [(index[2]-1)*element_dim + index[1] for index in frozen]
   
-  # initialize variables
-  grad_rate = init_rate
+  # initialize search state
   L = copy(guess)
-  
-  # use Newton's method with backtracking and gradient descent backup
   Δ_proj = proj_diff(gram, L'*Q*L)
   loss = dot(Δ_proj, Δ_proj)
+  
+  # use Newton's method with backtracking and gradient descent backup
   for step in 1:max_descent_steps
     # stop if the loss is tolerably low
     if loss < tol
@@ -411,6 +409,7 @@ function realize_gram_alt_proj(
     empty!(history.last_line_loss)
     rate = one(T)
     step_success = false
+    base_target_improvement = dot(neg_grad, base_step)
     for backoff_steps in 0:max_backoff_steps
       history.stepsize[end] = rate
       L = L_last + rate * base_step
@@ -419,7 +418,7 @@ function realize_gram_alt_proj(
       improvement = loss_last - loss
       push!(history.last_line_L, L)
       push!(history.last_line_loss, loss / scale_adjustment)
-      if improvement >= min_efficiency * rate * dot(neg_grad, base_step)
+      if improvement >= min_efficiency * rate * base_target_improvement
         history.backoff_steps[end] = backoff_steps
         step_success = true
         break
@@ -446,7 +445,6 @@ function realize_gram(
   frozen = nothing;
   scaled_tol = 1e-30,
   min_efficiency = 0.5,
-  init_rate = 1.0,
   backoff = 0.9,
   reg_scale = 1.1,
   max_descent_steps = 200,
@@ -477,13 +475,12 @@ function realize_gram(
     unfrozen_stacked = reshape(is_unfrozen, total_dim)
   end
   
-  # initialize variables
-  grad_rate = init_rate
+  # initialize search state
   L = copy(guess)
-  
-  # use Newton's method with backtracking and gradient descent backup
   Δ_proj = proj_diff(gram, L'*Q*L)
   loss = dot(Δ_proj, Δ_proj)
+  
+  # use Newton's method with backtracking and gradient descent backup
   for step in 1:max_descent_steps
     # stop if the loss is tolerably low
     if loss < tol
@@ -545,6 +542,7 @@ function realize_gram(
     empty!(history.last_line_loss)
     rate = one(T)
     step_success = false
+    base_target_improvement = dot(neg_grad, base_step)
     for backoff_steps in 0:max_backoff_steps
       history.stepsize[end] = rate
       L = L_last + rate * base_step
@@ -553,7 +551,7 @@ function realize_gram(
       improvement = loss_last - loss
       push!(history.last_line_L, L)
       push!(history.last_line_loss, loss / scale_adjustment)
-      if improvement >= min_efficiency * rate * dot(neg_grad, base_step)
+      if improvement >= min_efficiency * rate * base_target_improvement
         history.backoff_steps[end] = backoff_steps
         step_success = true
         break