Update app.py

app.py

@@ -115,17 +115,18 @@ def compute_low_y_curve(betas, z_a, y):
 
 @st.cache_data
 def compute_high_y_curve(betas, z_a, y):
-   """
-   Compute the expression: ((4y + 12)(4 - a) + 16y*β*(a - 1))/(3(4 - a))
-   """
-   betas = np.array(betas)
-   denominator = 3*(4 - z_a)
-   
-   if denominator == 0:
-       return np.full_like(betas, np.nan)
-       
-   numerator = (4*y + 12)*(4 - z_a) + 16*y*betas*(z_a - 1)
-   return numerator/denominator
+    """
+    Compute the expression: (-4a(a-1)yβ - 2ay + 2a(2a-1))/(1-2a)
+    """
+    a = z_a  # for clarity in the formula
+    betas = np.array(betas)
+    denominator = 1 - 2*a
+    
+    if denominator == 0:
+        return np.full_like(betas, np.nan)
+        
+    numerator = -4*a*(a-1)*y*betas - 2*a*y + 2*a*(2*a-1)
+    return numerator/denominator
 
 def generate_z_vs_beta_plot(z_a, y, z_min, z_max, beta_steps, z_steps):
    if z_a <= 0 or y <= 0 or z_min >= z_max: