Add example of new AST API

examples/build.gradle.kts

@@ -19,7 +19,8 @@ repositories {
 sourceSets.register("benchmarks")
 
 dependencies {
-//    implementation(project(":kmath-ast"))
+    implementation(project(":kmath-ast"))
+    implementation(project(":kmath-ast-kotlingrad"))
     implementation(project(":kmath-core"))
     implementation(project(":kmath-coroutines"))
     implementation(project(":kmath-commons"))

examples/src/main/kotlin/kscience/kmath/ast/ExpressionsInterpretersBenchmark.kt

@@ -1,70 +1,80 @@
 package kscience.kmath.ast
-//
-//import kscience.kmath.asm.compile
-//import kscience.kmath.expressions.Expression
-//import kscience.kmath.expressions.expressionInField
-//import kscience.kmath.expressions.invoke
-//import kscience.kmath.operations.Field
-//import kscience.kmath.operations.RealField
-//import kotlin.random.Random
-//import kotlin.system.measureTimeMillis
-//
-//class ExpressionsInterpretersBenchmark {
-//    private val algebra: Field<Double> = RealField
-//    fun functionalExpression() {
-//        val expr = algebra.expressionInField {
-//            variable("x") * const(2.0) + const(2.0) / variable("x") - const(16.0)
-//        }
-//
-//        invokeAndSum(expr)
-//    }
-//
-//    fun mstExpression() {
-//        val expr = algebra.mstInField {
-//            symbol("x") * number(2.0) + number(2.0) / symbol("x") - number(16.0)
-//        }
-//
-//        invokeAndSum(expr)
-//    }
-//
-//    fun asmExpression() {
-//        val expr = algebra.mstInField {
-//            symbol("x") * number(2.0) + number(2.0) / symbol("x") - number(16.0)
-//        }.compile()
-//
-//        invokeAndSum(expr)
-//    }
-//
-//    private fun invokeAndSum(expr: Expression<Double>) {
-//        val random = Random(0)
-//        var sum = 0.0
-//
-//        repeat(1000000) {
-//            sum += expr("x" to random.nextDouble())
-//        }
-//
-//        println(sum)
-//    }
-//}
-//
-//fun main() {
-//    val benchmark = ExpressionsInterpretersBenchmark()
-//
-//    val fe = measureTimeMillis {
-//        benchmark.functionalExpression()
-//    }
-//
-//    println("fe=$fe")
-//
-//    val mst = measureTimeMillis {
-//        benchmark.mstExpression()
-//    }
-//
-//    println("mst=$mst")
-//
-//    val asm = measureTimeMillis {
-//        benchmark.asmExpression()
-//    }
-//
-//    println("asm=$asm")
-//}
+
+import kscience.kmath.asm.compile
+import kscience.kmath.expressions.Expression
+import kscience.kmath.expressions.expressionInField
+import kscience.kmath.expressions.invoke
+import kscience.kmath.operations.Field
+import kscience.kmath.operations.RealField
+import kotlin.random.Random
+import kotlin.system.measureTimeMillis
+
+internal class ExpressionsInterpretersBenchmark {
+    private val algebra: Field<Double> = RealField
+    fun functionalExpression() {
+        val expr = algebra.expressionInField {
+            variable("x") * const(2.0) + const(2.0) / variable("x") - const(16.0)
+        }
+
+        invokeAndSum(expr)
+    }
+
+    fun mstExpression() {
+        val expr = algebra.mstInField {
+            symbol("x") * number(2.0) + number(2.0) / symbol("x") - number(16.0)
+        }
+
+        invokeAndSum(expr)
+    }
+
+    fun asmExpression() {
+        val expr = algebra.mstInField {
+            symbol("x") * number(2.0) + number(2.0) / symbol("x") - number(16.0)
+        }.compile()
+
+        invokeAndSum(expr)
+    }
+
+    private fun invokeAndSum(expr: Expression<Double>) {
+        val random = Random(0)
+        var sum = 0.0
+
+        repeat(1000000) {
+            sum += expr("x" to random.nextDouble())
+        }
+
+        println(sum)
+    }
+}
+
+/**
+ * This benchmark compares basically evaluation of simple function with MstExpression interpreter, ASM backend and
+ * core FunctionalExpressions API.
+ *
+ * The expected rating is:
+ *
+ * 1. ASM.
+ * 2. MST.
+ * 3. FE.
+ */
+fun main() {
+    val benchmark = ExpressionsInterpretersBenchmark()
+
+    val fe = measureTimeMillis {
+        benchmark.functionalExpression()
+    }
+
+    println("fe=$fe")
+
+    val mst = measureTimeMillis {
+        benchmark.mstExpression()
+    }
+
+    println("mst=$mst")
+
+    val asm = measureTimeMillis {
+        benchmark.asmExpression()
+    }
+
+    println("asm=$asm")
+}

examples/src/main/kotlin/kscience/kmath/ast/KotlingradSupport.kt

@@ -0,0 +1,22 @@
+package kscience.kmath.ast
+
+import edu.umontreal.kotlingrad.experimental.DoublePrecision
+import kscience.kmath.asm.compile
+import kscience.kmath.ast.kotlingrad.mst
+import kscience.kmath.ast.kotlingrad.sfun
+import kscience.kmath.ast.kotlingrad.svar
+import kscience.kmath.expressions.invoke
+import kscience.kmath.operations.RealField
+
+/**
+ * In this example, x^2-4*x-44 function is differentiated with Kotlin∇, and the autodiff result is compared with
+ * valid derivative.
+ */
+fun main() {
+    val proto = DoublePrecision.prototype
+    val x by MstAlgebra.symbol("x").svar(proto)
+    val quadratic = "x^2-4*x-44".parseMath().sfun(proto)
+    val actualDerivative = MstExpression(RealField, quadratic.d(x).mst()).compile()
+    val expectedDerivative = MstExpression(RealField, "2*x-4".parseMath()).compile()
+    assert(actualDerivative("x" to 123.0) == expectedDerivative("x" to 123.0))
+}