diff --git a/app-proto/src/engine.rs b/app-proto/src/engine.rs
index 7e6e5ba..3d4ef8c 100644
--- a/app-proto/src/engine.rs
+++ b/app-proto/src/engine.rs
@@ -335,8 +335,7 @@ mod tests {
     //   "Japan's 'Wasan' Mathematical Tradition", by Abe Haruki
     //   https://www.nippon.com/en/japan-topics/c12801/
     //
-    #[test]
-    fn irisawa_hexlet_test() {
+    fn realize_irisawa_hexlet(scaled_tol: f64) -> (DMatrix<f64>, bool, DescentHistory) {
         let gram = {
             let mut gram_to_be = PartialMatrix::new();
             for s in 0..9 {
@@ -364,6 +363,7 @@ mod tests {
             }
             gram_to_be
         };
+        
         let guess = DMatrix::from_columns(
             [
                 sphere(0.0, 0.0, 0.0, 15.0),
@@ -378,17 +378,31 @@ mod tests {
                 )
             ).collect::<Vec<_>>().as_slice()
         );
+        
+        // the frozen entries fix the radii of the circumscribing sphere, the
+        // "sun" and "moon" spheres, and one of the chain spheres
         let frozen: [(usize, usize); 4] = array::from_fn(|k| (3, k));
-        const SCALED_TOL: f64 = 1.0e-12;
-        let (config, success, history) = realize_gram(
+        
+        realize_gram(
             &gram, guess, &frozen,
-            SCALED_TOL, 0.5, 0.9, 1.1, 200, 110
-        );
+            scaled_tol, 0.5, 0.9, 1.1, 200, 110
+        )
+    }
+    
+    #[test]
+    fn irisawa_hexlet_test() {
+        // solve Irisawa's problem
+        const SCALED_TOL: f64 = 1.0e-12;
+        let (config, success, history) = realize_irisawa_hexlet(SCALED_TOL);
+        
+        // check against Irisawa's solution
         let entry_tol = SCALED_TOL.sqrt();
         let solution_diams = [30.0, 10.0, 6.0, 5.0, 15.0, 10.0, 3.75, 2.5, 2.0 + 8.0/11.0];
         for (k, diam) in solution_diams.into_iter().enumerate() {
             assert!((config[(3, k)] - 1.0 / diam).abs() < entry_tol);
         }
+        
+        // print info
         print!("\nCompleted Gram matrix:{}", config.tr_mul(&*Q) * &config);
         if success {
             println!("Target accuracy achieved!");