Formula solver seems to work, now the UI should be reworked

lib/formula_evaluator.dart

@@ -117,9 +117,7 @@ class FormulaEvaluator {
     } catch (e, stack) {
       // SPECIAL CASE: If the error message starts with signalMagicString, treat it as a signal message and return it instead of throwing an exception
       // SEE signal() function in the generated d4rt code above for how this is used
-      print("#######################");
       if (e.toString().contains(signalMagicString)) {
-        print("***********************");
         final signalMessage = e.toString().split(signalMagicString).last.trim();
         return signalMessage;
       }
@@ -295,6 +293,52 @@ class FormulaEvaluator {
   }
 }
 
+Number formulaSolver(Formula formula,
+    String variableToSolve,
+    Map<String, dynamic> fixedInputValues, {
+      Number hint = 0,
+      Number step = 10,
+      Number maxDelta = 0.01,
+      int maxTries = 100,
+    }) {
+  
+  if( variableToSolve == formula.output.name ){
+    return FormulaEvaluator().evaluate(formula, fixedInputValues);
+  }
+  
+  if (!formula.inputVarNames().contains(variableToSolve) ){
+    throw ArgumentError(
+      'Variable "$variableToSolve" is not an input or output variable of the formula "${formula
+          .name}".',
+    );
+  }
+
+
+  final modifiedInputValues = Map<String, dynamic>.from(fixedInputValues);
+  var evaluator = FormulaEvaluator();
+  Number f(Number x) {
+    modifiedInputValues[variableToSolve] = x;
+    final result = evaluator.evaluate(formula, modifiedInputValues);
+    if (result is Number) {
+      return result;
+    } else {
+      throw FormulaEvaluationException(
+        'Expected formula evaluation to return a number, but got: $result ${result.runtimeType}',
+      );
+    }
+  }
+
+  var fixedFormulaOutput = fixedInputValues[formula.output.name];
+
+  return functionSolver(
+    (Number x) => f(x) - fixedFormulaOutput,
+    hint: hint,
+    step: step,
+    maxDelta: maxDelta,
+    maxTries: maxTries,
+  );
+}
+
 class NoSolutionException implements Exception {
   final String message;
 

test/formula_solver_test.dart

@@ -5,6 +5,26 @@ import 'dart:math' as Math;
 
 
 void main() {
+
+  group("Formulas", (){
+
+    test("Solve x^2 formula", () {
+      final formula = Formula(
+        name: 'Test x^2',
+        input: [
+          VariableSpec(name: 'x', unit: 'scalar'),
+        ],
+        output: VariableSpec(name: 'y', unit: 'scalar'),
+        d4rtCode: 'y = x*x;',
+      );
+
+      var solution = formulaSolver(formula, "x", {"y": 25}, maxDelta: 1e-10);
+      expect( solution, closeTo(5, 1e-10));
+    });
+
+  });
+
+  group('Native functions', () {
     test("Solve x^2", () {
       Number f(Number x) => x * x;
       var root = functionSolver(f, hint: 10, step: 1);
@@ -21,7 +41,8 @@ void main() {
     test("Solve x^2 + 1", () {
       Number f(Number x) => x * x + 1;
 
-    expect(()=> functionSolver(f, hint: 10, step: 1), throwsA(isA<NoSolutionException>()));
+      expect(() => functionSolver(f, hint: 10, step: 1),
+          throwsA(isA<NoSolutionException>()));
     });
 
     test("Solve (x-2)(x-10", () {
@@ -53,5 +74,6 @@ void main() {
       var root = functionSolver(f, hint: 1, step: 1);
       expect(root, closeTo(Math.log(2), 0.01));
     });
+  });
 
 }