Three rows for numerical evaluation at a fresh point in the inter-version benchmark, with their baseline

Sources/Tests/DotnetBenchmark/CommonFunctionsInterVersion.cs

@@ -76,6 +76,32 @@ [Benchmark] public void EvalTrigPrecise()
         private static readonly EContext fiveHundredDigits =
             new(500, ERounding.HalfUp, -500, 5000, false);
 
+        // Numerical evaluation of an expression at a point, which is what a plot or a
+        // root-finder asks for thousands of times: the expression is built once and the
+        // point substituted afresh on every call, so the per-node cost of the evaluation is
+        // what is measured and not the cache of a previous answer. A polynomial, for the
+        // arithmetic alone, and a logarithm times an arctangent, for the series behind the
+        // transcendental functions; the polynomial once more at fifteen digits, since how
+        // much of the cost is the width of the numbers and how much is the evaluator's own
+        // overhead is the question https://github.com/asc-community/AngouriMath/issues/1338
+        // asks. The point is a decimal that is not within the downcasting tolerance of a
+        // small rational -- an exact `37/100` would be evaluated in rational arithmetic and
+        // never touch a decimal, and a binary double's fifty-three-digit expansion of 0.37
+        // is not what anybody means by it.
+        [Benchmark] public void EvalPolynomialFresh() => evalPolynomial.Substitute(evalX, evalAt).EvalNumerical();
+        [Benchmark] public void EvalTranscendentalFresh() => evalTranscendental.Substitute(evalX, evalAt).EvalNumerical();
+        [Benchmark] public void EvalPolynomialFresh15Digits()
+        {
+            using var _ = MathS.Settings.DecimalPrecisionContext.Set(fifteenDigits);
+            evalPolynomial.Substitute(evalX, evalAt).EvalNumerical();
+        }
+        private static readonly Entity.Variable evalX = MathS.Var("x");
+        private static readonly Entity evalAt = Entity.Number.Real.Create(EDecimal.FromString("0.37000000000001234"));
+        private static readonly Entity evalPolynomial = "x^3 + 2*x^2 - x + 1";
+        private static readonly Entity evalTranscendental = "ln(1 + x^2)*arctan(x)";
+        private static readonly EContext fifteenDigits =
+            new(15, ERounding.HalfUp, -100, 1000, false);
+
         // Testing compilation
         [Benchmark] public void CompileEasy() => toCompileEasy.Compile<Complex, Complex>("x");
         private static readonly Entity toCompileEasy = "x + x / 2 + sin(x)";

Sources/Tests/DotnetBenchmark/performance-baseline.json

@@ -22,6 +22,18 @@
       "allocatedBytes": 0,
       "meanNanoseconds": 1.8813217676555116
     },
+    "EvalPolynomialFresh": {
+      "allocatedBytes": 650888,
+      "meanNanoseconds": 348863.79150390625
+    },
+    "EvalPolynomialFresh15Digits": {
+      "allocatedBytes": 265816,
+      "meanNanoseconds": 83712.6138671875
+    },
+    "EvalTranscendentalFresh": {
+      "allocatedBytes": 5668395,
+      "meanNanoseconds": 3248098.8828125
+    },
     "EvalTrig": {
       "allocatedBytes": 1341457,
       "meanNanoseconds": 709052.2509114583