diff --git a/source/rk/tautodiff/aux/tape.d b/source/rk/tautodiff/aux/tape.d
index 374cd12..3ee5ca7 100644
--- a/source/rk/tautodiff/aux/tape.d
+++ b/source/rk/tautodiff/aux/tape.d
@@ -30,7 +30,7 @@ class Tape
 
     /// Update tape elements values starting from the begining of the tape
     void update() {
-        foreach (v; values) v.update();
+        foreach (ref v; values) v.update();
     }
 
     /// Locks the tape. Tape can only be unlocked with `reset()` afterwards.
@@ -42,5 +42,61 @@ class Tape
     bool isLocked() {
         return this.locked;
     }
+
+    // Push back a single value
+    void pushBack(Value v) 
+    {
+        this.values ~= v;
+    }
+
+    /// Push back values
+    void pushBack(Value[] vs) 
+    {
+        this.values ~= vs;
+    }
+
+    /// Append a single value
+    void opOpAssign(string op: "~")(Value v)
+    {
+        this.pushBack(v);
+    }
+
+    /// Append values
+    void opOpAssign(string op: "~")(Value[] vs)
+    {
+        this.pushBack(vs);
+    }
 }
 
+unittest
+{
+    // init
+    auto tape = new Tape();
+    assert(tape.values == []);
+    assert(tape.values.length == 0);
+    assert(tape.locked == false);
+    assert(!tape.isLocked);
+
+    // d = a * b - c
+    auto a = 5.value;
+    auto b = 10.value;
+    auto c = 25.value;
+    auto d = a * b;
+    auto e = d - c;
+    assert(e.data == 25);
+
+    // push
+    tape.pushBack(a);
+    tape ~= b;
+    tape ~= [c, d, e];
+    assert(tape.values == [a, b, c, d, e]);
+    assert(tape.values.length == 5);
+    assert(tape.lastValue.data == 25);
+
+    // modify value
+    a.data = 6;
+    
+    // update tape
+    tape.update();
+    assert(tape.lastValue.data == 35);
+}
diff --git a/source/rk/tautodiff/core/value.d b/source/rk/tautodiff/core/value.d
index 2f463bd..6e76066 100644
--- a/source/rk/tautodiff/core/value.d
+++ b/source/rk/tautodiff/core/value.d
@@ -88,7 +88,7 @@ class Value : INeuron
 
     /// Update variable value from cached `op` and `parents` information
     void update() {
-        if (this.parents[0] && this.parents[1])
+        if (this.parents.length == 2 && this.parents[0] && this.parents[1])
         {
             auto lhs = this.parents[0];
             auto rhs = this.parents[1];
@@ -171,11 +171,11 @@ class Value : INeuron
     {
         static if (op == "+" || op == "-")
         {
-            this.reinit(mixin("rhs.data" ~ op ~ "lhs.data"), op[0], [lhs, rhs], &opBackwardAddSub);
+            this.reinit(mixin("lhs.data" ~ op ~ "rhs.data"), op[0], [lhs, rhs], &opBackwardAddSub);
         }
         else static if (op == "*" || op == "/")
         {
-            this.reinit(mixin("rhs.data" ~ op ~ "lhs.data"), op[0], [lhs, rhs], &opBackwardMulDiv);
+            this.reinit(mixin("lhs.data" ~ op ~ "rhs.data"), op[0], [lhs, rhs], &opBackwardMulDiv);
         }
         else static assert(0, "Operator <"~op~"> not supported!");
     }