kmath-commons/src/main/kotlin/kscience/kmath/commons/expressions/DerivativeStructureExpression.kt

@@ -1,9 +1,6 @@
 package kscience.kmath.commons.expressions
 
-import kscience.kmath.expressions.DifferentiableExpression
+import kscience.kmath.expressions.*
-import kscience.kmath.expressions.Expression
-import kscience.kmath.expressions.ExpressionAlgebra
-import kscience.kmath.expressions.Symbol
 import kscience.kmath.operations.ExtendedField
 import org.apache.commons.math3.analysis.differentiation.DerivativeStructure
 
@@ -92,6 +89,12 @@ public class DerivativeStructureField(
     public override operator fun DerivativeStructure.minus(b: Number): DerivativeStructure = subtract(b.toDouble())
     public override operator fun Number.plus(b: DerivativeStructure): DerivativeStructure = b + this
     public override operator fun Number.minus(b: DerivativeStructure): DerivativeStructure = b - this
+
+    public companion object : AutoDiffProcessor<Double, DerivativeStructure, DerivativeStructureField> {
+        override fun process(function: DerivativeStructureField.() -> DerivativeStructure): DifferentiableExpression<Double> {
+            return DerivativeStructureExpression(function)
+        }
+    }
 }
 
 /**

kmath-commons/src/main/kotlin/kscience/kmath/commons/optimization/CMFit.kt

@@ -71,12 +71,8 @@ public object CMFit {
 public fun Expression<Double>.optimize(
     vararg symbols: Symbol,
     configuration: CMOptimizationProblem.() -> Unit,
-): OptimizationResult<Double> {
+): OptimizationResult<Double> = optimizeWith(CMOptimizationProblem, symbols = symbols, configuration)
-    require(symbols.isNotEmpty()) { "Must provide a list of symbols for optimization" }
+
-    val problem = CMOptimizationProblem(symbols.toList()).apply(configuration)
-    problem.expression(this)
-    return problem.optimize()
-}
 
 /**
  * Optimize differentiable expression
@@ -84,12 +80,7 @@ public fun Expression<Double>.optimize(
 public fun DifferentiableExpression<Double>.optimize(
     vararg symbols: Symbol,
     configuration: CMOptimizationProblem.() -> Unit,
-): OptimizationResult<Double> {
+): OptimizationResult<Double> = optimizeWith(CMOptimizationProblem, symbols = symbols, configuration)
-    require(symbols.isNotEmpty()) { "Must provide a list of symbols for optimization" }
-    val problem = CMOptimizationProblem(symbols.toList()).apply(configuration)
-    problem.diffExpression(this)
-    return problem.optimize()
-}
 
 public fun DifferentiableExpression<Double>.minimize(
     vararg startPoint: Pair<Symbol, Double>,

kmath-commons/src/main/kotlin/kscience/kmath/commons/optimization/CMOptimizationProblem.kt

@@ -33,7 +33,7 @@ public class CMOptimizationProblem(
 
     public fun exportOptimizationData(): List<OptimizationData> = optimizationData.values.toList()
 
-    public fun initialGuess(map: Map<Symbol, Double>): Unit {
+    public override fun initialGuess(map: Map<Symbol, Double>): Unit {
         addOptimizationData(InitialGuess(map.toDoubleArray()))
     }
 
@@ -94,10 +94,12 @@ public class CMOptimizationProblem(
         return OptimizationResult(point.toMap(), value, setOf(this))
     }
 
-    public companion object {
+    public companion object : OptimizationProblemFactory<Double, CMOptimizationProblem> {
         public const val DEFAULT_RELATIVE_TOLERANCE: Double = 1e-4
         public const val DEFAULT_ABSOLUTE_TOLERANCE: Double = 1e-4
         public const val DEFAULT_MAX_ITER: Int = 1000
+
+        override fun build(symbols: List<Symbol>): CMOptimizationProblem = CMOptimizationProblem(symbols)
     }
 }
 

kmath-commons/src/main/kotlin/kscience/kmath/commons/optimization/OptimizationProblem.kt

@@ -1,37 +0,0 @@
-package kscience.kmath.commons.optimization
-
-import kscience.kmath.expressions.DifferentiableExpression
-import kscience.kmath.expressions.Expression
-import kscience.kmath.expressions.Symbol
-
-public interface OptimizationFeature
-
-//TODO move to prob/stat
-
-public class OptimizationResult<T>(
-    public val point: Map<Symbol, T>,
-    public val value: T,
-    public val features: Set<OptimizationFeature> = emptySet(),
-){
-    override fun toString(): String {
-        return "OptimizationResult(point=$point, value=$value)"
-    }
-}
-
-/**
- * A configuration builder for optimization problem
- */
-public interface OptimizationProblem<T : Any> {
-    /**
-     * Set an objective function expression
-     */
-    public fun expression(expression: Expression<Double>): Unit
-
-    /**
-     *
-     */
-    public fun diffExpression(expression: DifferentiableExpression<Double>): Unit
-    public fun update(result: OptimizationResult<T>)
-    public fun optimize(): OptimizationResult<T>
-}
-

kmath-core/src/commonMain/kotlin/kscience/kmath/expressions/DifferentiableExpression.kt

@@ -23,10 +23,9 @@ public fun <T> DifferentiableExpression<T>.derivative(symbol: Symbol): Expressio
 public fun <T> DifferentiableExpression<T>.derivative(name: String): Expression<T> =
     derivative(StringSymbol(name) to 1)
 
-//public interface DifferentiableExpressionBuilder<T, E, A : ExpressionAlgebra<T, E>>: ExpressionBuilder<T,E,A> {
+/**
-//    public override fun expression(block: A.() -> E): DifferentiableExpression<T>
+ * A [DifferentiableExpression] that defines only first derivatives
-//}
+ */
-
 public abstract class FirstDerivativeExpression<T> : DifferentiableExpression<T> {
 
     public abstract fun derivativeOrNull(symbol: Symbol): Expression<T>?
@@ -36,3 +35,10 @@ public abstract class FirstDerivativeExpression<T> : DifferentiableExpression<T>
         return derivativeOrNull(dSymbol)
     }
 }
+
+/**
+ * A factory that converts an expression in autodiff variables to a [DifferentiableExpression]
+ */
+public interface AutoDiffProcessor<T : Any, I : Any, A : ExpressionAlgebra<T, I>> {
+    public fun process(function: A.() -> I): DifferentiableExpression<T>
+}

kmath-core/src/commonMain/kotlin/kscience/kmath/expressions/SimpleAutoDiff.kt

@@ -47,7 +47,7 @@ public fun <T : Any> DerivationResult<T>.grad(vararg variables: Symbol): Point<T
 }
 
 /**
- * Runs differentiation and establishes [AutoDiffField] context inside the block of code.
+ * Runs differentiation and establishes [SimpleAutoDiffField] context inside the block of code.
  *
  * The partial derivatives are placed in argument `d` variable
  *
@@ -59,36 +59,90 @@ public fun <T : Any> DerivationResult<T>.grad(vararg variables: Symbol): Point<T
  * assertEquals(9.0, x.d)  // dy/dx
  * ```
  *
- * @param body the action in [AutoDiffField] context returning [AutoDiffVariable] to differentiate with respect to.
+ * @param body the action in [SimpleAutoDiffField] context returning [AutoDiffVariable] to differentiate with respect to.
  * @return the result of differentiation.
  */
 public fun <T : Any, F : Field<T>> F.simpleAutoDiff(
     bindings: Map<Symbol, T>,
-    body: AutoDiffField<T, F>.() -> AutoDiffValue<T>,
+    body: SimpleAutoDiffField<T, F>.() -> AutoDiffValue<T>,
 ): DerivationResult<T> {
     contract { callsInPlace(body, InvocationKind.EXACTLY_ONCE) }
 
-    return AutoDiffContext(this, bindings).derivate(body)
+    return SimpleAutoDiffField(this, bindings).derivate(body)
 }
 
 public fun <T : Any, F : Field<T>> F.simpleAutoDiff(
     vararg bindings: Pair<Symbol, T>,
-    body: AutoDiffField<T, F>.() -> AutoDiffValue<T>,
+    body: SimpleAutoDiffField<T, F>.() -> AutoDiffValue<T>,
 ): DerivationResult<T> = simpleAutoDiff(bindings.toMap(), body)
 
 /**
  * Represents field in context of which functions can be derived.
  */
-public abstract class AutoDiffField<T : Any, F : Field<T>>
+public open class SimpleAutoDiffField<T : Any, F : Field<T>>(
-    : Field<AutoDiffValue<T>>, ExpressionAlgebra<T, AutoDiffValue<T>> {
+    public val context: F,
+    bindings: Map<Symbol, T>,
+) : Field<AutoDiffValue<T>>, ExpressionAlgebra<T, AutoDiffValue<T>> {
 
-    public abstract val context: F
+    // this stack contains pairs of blocks and values to apply them to
+    private var stack: Array<Any?> = arrayOfNulls<Any?>(8)
+    private var sp: Int = 0
+    private val derivatives: MutableMap<AutoDiffValue<T>, T> = hashMapOf()
+
+    /**
+     * Differentiable variable with value and derivative of differentiation ([simpleAutoDiff]) result
+     * with respect to this variable.
+     *
+     * @param T the non-nullable type of value.
+     * @property value The value of this variable.
+     */
+    private class AutoDiffVariableWithDerivative<T : Any>(
+        override val identity: String,
+        value: T,
+        var d: T,
+    ) : AutoDiffValue<T>(value), Symbol {
+        override fun toString(): String = identity
+        override fun equals(other: Any?): Boolean = this.identity == (other as? Symbol)?.identity
+        override fun hashCode(): Int = identity.hashCode()
+    }
+
+    private val bindings: Map<String, AutoDiffVariableWithDerivative<T>> = bindings.entries.associate {
+        it.key.identity to AutoDiffVariableWithDerivative(it.key.identity, it.value, context.zero)
+    }
+
+    override fun bindOrNull(symbol: Symbol): AutoDiffValue<T>? = bindings[symbol.identity]
+
+    private fun getDerivative(variable: AutoDiffValue<T>): T =
+        (variable as? AutoDiffVariableWithDerivative)?.d ?: derivatives[variable] ?: context.zero
+
+    private fun setDerivative(variable: AutoDiffValue<T>, value: T) {
+        if (variable is AutoDiffVariableWithDerivative) variable.d = value else derivatives[variable] = value
+    }
+
+
+    @Suppress("UNCHECKED_CAST")
+    private fun runBackwardPass() {
+        while (sp > 0) {
+            val value = stack[--sp]
+            val block = stack[--sp] as F.(Any?) -> Unit
+            context.block(value)
+        }
+    }
+
+    override val zero: AutoDiffValue<T> get() = const(context.zero)
+    override val one: AutoDiffValue<T> get() = const(context.one)
+
+    override fun const(value: T): AutoDiffValue<T> = AutoDiffValue(value)
 
     /**
      * A variable accessing inner state of derivatives.
      * Use this value in inner builders to avoid creating additional derivative bindings.
      */
-    public abstract var AutoDiffValue<T>.d: T
+    public var AutoDiffValue<T>.d: T
+        get() = getDerivative(this)
+        set(value) = setDerivative(this, value)
+
+    public inline fun const(block: F.() -> T): AutoDiffValue<T> = const(context.block())
 
     /**
      * Performs update of derivative after the rest of the formula in the back-pass.
@@ -101,9 +155,22 @@ public abstract class AutoDiffField<T : Any, F : Field<T>>
      * }
      * ```
      */
-    public abstract fun <R> derive(value: R, block: F.(R) -> Unit): R
+    @Suppress("UNCHECKED_CAST")
+    public fun <R> derive(value: R, block: F.(R) -> Unit): R {
+        // save block to stack for backward pass
+        if (sp >= stack.size) stack = stack.copyOf(stack.size * 2)
+        stack[sp++] = block
+        stack[sp++] = value
+        return value
+    }
 
-    public inline fun const(block: F.() -> T): AutoDiffValue<T> = const(context.block())
+
+    internal fun derivate(function: SimpleAutoDiffField<T, F>.() -> AutoDiffValue<T>): DerivationResult<T> {
+        val result = function()
+        result.d = context.one // computing derivative w.r.t result
+        runBackwardPass()
+        return DerivationResult(result.value, bindings.mapValues { it.value.d }, context)
+    }
 
     // Overloads for Double constants
 
@@ -119,68 +186,7 @@ public abstract class AutoDiffField<T : Any, F : Field<T>>
 
     override operator fun AutoDiffValue<T>.minus(b: Number): AutoDiffValue<T> =
         derive(const { this@minus.value - one * b.toDouble() }) { z -> this@minus.d += z.d }
-}
 
-/**
- * Automatic Differentiation context class.
- */
-private class AutoDiffContext<T : Any, F : Field<T>>(
-    override val context: F,
-    bindings: Map<Symbol, T>,
-) : AutoDiffField<T, F>() {
-    // this stack contains pairs of blocks and values to apply them to
-    private var stack: Array<Any?> = arrayOfNulls<Any?>(8)
-    private var sp: Int = 0
-    private val derivatives: MutableMap<AutoDiffValue<T>, T> = hashMapOf()
-    override val zero: AutoDiffValue<T> get() = const(context.zero)
-    override val one: AutoDiffValue<T> get() = const(context.one)
-
-    /**
-     * Differentiable variable with value and derivative of differentiation ([simpleAutoDiff]) result
-     * with respect to this variable.
-     *
-     * @param T the non-nullable type of value.
-     * @property value The value of this variable.
-     */
-    private class AutoDiffVariableWithDeriv<T : Any>(
-        override val identity: String,
-        value: T,
-        var d: T,
-    ) : AutoDiffValue<T>(value), Symbol{
-        override fun toString(): String = identity
-        override fun equals(other: Any?): Boolean = this.identity == (other as? Symbol)?.identity
-        override fun hashCode(): Int = identity.hashCode()
-    }
-
-    private val bindings: Map<String, AutoDiffVariableWithDeriv<T>> = bindings.entries.associate {
-        it.key.identity to AutoDiffVariableWithDeriv(it.key.identity, it.value, context.zero)
-    }
-
-    override fun bindOrNull(symbol: Symbol): AutoDiffVariableWithDeriv<T>? = bindings[symbol.identity]
-
-    override fun const(value: T): AutoDiffValue<T> = AutoDiffValue(value)
-
-    override var AutoDiffValue<T>.d: T
-        get() = (this as? AutoDiffVariableWithDeriv)?.d ?: derivatives[this] ?: context.zero
-        set(value) = if (this is AutoDiffVariableWithDeriv) d = value else derivatives[this] = value
-
-    @Suppress("UNCHECKED_CAST")
-    override fun <R> derive(value: R, block: F.(R) -> Unit): R {
-        // save block to stack for backward pass
-        if (sp >= stack.size) stack = stack.copyOf(stack.size * 2)
-        stack[sp++] = block
-        stack[sp++] = value
-        return value
-    }
-
-    @Suppress("UNCHECKED_CAST")
-    fun runBackwardPass() {
-        while (sp > 0) {
-            val value = stack[--sp]
-            val block = stack[--sp] as F.(Any?) -> Unit
-            context.block(value)
-        }
-    }
 
     // Basic math (+, -, *, /)
 
@@ -206,13 +212,6 @@ private class AutoDiffContext<T : Any, F : Field<T>>(
         derive(const { k.toDouble() * a.value }) { z ->
             a.d += z.d * k.toDouble()
         }
-
-    inline fun derivate(function: AutoDiffField<T, F>.() -> AutoDiffValue<T>): DerivationResult<T> {
-        val result = function()
-        result.d = context.one // computing derivative w.r.t result
-        runBackwardPass()
-        return DerivationResult(result.value, bindings.mapValues { it.value.d }, context)
-    }
 }
 
 /**
@@ -220,99 +219,178 @@ private class AutoDiffContext<T : Any, F : Field<T>>(
  */
 public class SimpleAutoDiffExpression<T : Any, F : Field<T>>(
     public val field: F,
-    public val function: AutoDiffField<T, F>.() -> AutoDiffValue<T>,
+    public val function: SimpleAutoDiffField<T, F>.() -> AutoDiffValue<T>,
 ) : FirstDerivativeExpression<T>() {
     public override operator fun invoke(arguments: Map<Symbol, T>): T {
         //val bindings = arguments.entries.map { it.key.bind(it.value) }
-        return AutoDiffContext(field, arguments).function().value
+        return SimpleAutoDiffField(field, arguments).function().value
     }
 
     override fun derivativeOrNull(symbol: Symbol): Expression<T> = Expression { arguments ->
         //val bindings = arguments.entries.map { it.key.bind(it.value) }
-        val derivationResult = AutoDiffContext(field, arguments).derivate(function)
+        val derivationResult = SimpleAutoDiffField(field, arguments).derivate(function)
         derivationResult.derivative(symbol)
     }
 }
 
+/**
+ * Generate [AutoDiffProcessor] for [SimpleAutoDiffExpression]
+ */
+public fun <T : Any, F : Field<T>> simpleAutoDiff(field: F): AutoDiffProcessor<T, AutoDiffValue<T>, SimpleAutoDiffField<T, F>> {
+    return object : AutoDiffProcessor<T, AutoDiffValue<T>, SimpleAutoDiffField<T, F>> {
+        override fun process(function: SimpleAutoDiffField<T, F>.() -> AutoDiffValue<T>): DifferentiableExpression<T> {
+            return SimpleAutoDiffExpression(field, function)
+        }
+    }
+}
+
 
 // Extensions for differentiation of various basic mathematical functions
 
 // x ^ 2
-public fun <T : Any, F : Field<T>> AutoDiffField<T, F>.sqr(x: AutoDiffValue<T>): AutoDiffValue<T> =
+public fun <T : Any, F : Field<T>> SimpleAutoDiffField<T, F>.sqr(x: AutoDiffValue<T>): AutoDiffValue<T> =
     derive(const { x.value * x.value }) { z -> x.d += z.d * 2 * x.value }
 
 // x ^ 1/2
-public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.sqrt(x: AutoDiffValue<T>): AutoDiffValue<T> =
+public fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.sqrt(x: AutoDiffValue<T>): AutoDiffValue<T> =
     derive(const { sqrt(x.value) }) { z -> x.d += z.d * 0.5 / z.value }
 
 // x ^ y (const)
-public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.pow(
+public fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.pow(
     x: AutoDiffValue<T>,
     y: Double,
 ): AutoDiffValue<T> =
     derive(const { power(x.value, y) }) { z -> x.d += z.d * y * power(x.value, y - 1) }
 
-public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.pow(
+public fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.pow(
     x: AutoDiffValue<T>,
     y: Int,
 ): AutoDiffValue<T> = pow(x, y.toDouble())
 
 // exp(x)
-public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.exp(x: AutoDiffValue<T>): AutoDiffValue<T> =
+public fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.exp(x: AutoDiffValue<T>): AutoDiffValue<T> =
     derive(const { exp(x.value) }) { z -> x.d += z.d * z.value }
 
 // ln(x)
-public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.ln(x: AutoDiffValue<T>): AutoDiffValue<T> =
+public fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.ln(x: AutoDiffValue<T>): AutoDiffValue<T> =
     derive(const { ln(x.value) }) { z -> x.d += z.d / x.value }
 
 // x ^ y (any)
-public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.pow(
+public fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.pow(
     x: AutoDiffValue<T>,
     y: AutoDiffValue<T>,
 ): AutoDiffValue<T> =
     exp(y * ln(x))
 
 // sin(x)
-public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.sin(x: AutoDiffValue<T>): AutoDiffValue<T> =
+public fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.sin(x: AutoDiffValue<T>): AutoDiffValue<T> =
     derive(const { sin(x.value) }) { z -> x.d += z.d * cos(x.value) }
 
 // cos(x)
-public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.cos(x: AutoDiffValue<T>): AutoDiffValue<T> =
+public fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.cos(x: AutoDiffValue<T>): AutoDiffValue<T> =
     derive(const { cos(x.value) }) { z -> x.d -= z.d * sin(x.value) }
 
-public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.tan(x: AutoDiffValue<T>): AutoDiffValue<T> =
+public fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.tan(x: AutoDiffValue<T>): AutoDiffValue<T> =
     derive(const { tan(x.value) }) { z ->
         val c = cos(x.value)
         x.d += z.d / (c * c)
     }
 
-public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.asin(x: AutoDiffValue<T>): AutoDiffValue<T> =
+public fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.asin(x: AutoDiffValue<T>): AutoDiffValue<T> =
     derive(const { asin(x.value) }) { z -> x.d += z.d / sqrt(one - x.value * x.value) }
 
-public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.acos(x: AutoDiffValue<T>): AutoDiffValue<T> =
+public fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.acos(x: AutoDiffValue<T>): AutoDiffValue<T> =
     derive(const { acos(x.value) }) { z -> x.d -= z.d / sqrt(one - x.value * x.value) }
 
-public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.atan(x: AutoDiffValue<T>): AutoDiffValue<T> =
+public fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.atan(x: AutoDiffValue<T>): AutoDiffValue<T> =
     derive(const { atan(x.value) }) { z -> x.d += z.d / (one + x.value * x.value) }
 
-public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.sinh(x: AutoDiffValue<T>): AutoDiffValue<T> =
+public fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.sinh(x: AutoDiffValue<T>): AutoDiffValue<T> =
-    derive(const { sin(x.value) }) { z -> x.d += z.d * cosh(x.value) }
+    derive(const { sinh(x.value) }) { z -> x.d += z.d * cosh(x.value) }
 
-public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.cosh(x: AutoDiffValue<T>): AutoDiffValue<T> =
+public fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.cosh(x: AutoDiffValue<T>): AutoDiffValue<T> =
-    derive(const { cos(x.value) }) { z -> x.d += z.d * sinh(x.value) }
+    derive(const { cosh(x.value) }) { z -> x.d += z.d * sinh(x.value) }
 
-public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.tanh(x: AutoDiffValue<T>): AutoDiffValue<T> =
+public fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.tanh(x: AutoDiffValue<T>): AutoDiffValue<T> =
-    derive(const { tan(x.value) }) { z ->
+    derive(const { tanh(x.value) }) { z ->
         val c = cosh(x.value)
         x.d += z.d / (c * c)
     }
 
-public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.asinh(x: AutoDiffValue<T>): AutoDiffValue<T> =
+public fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.asinh(x: AutoDiffValue<T>): AutoDiffValue<T> =
     derive(const { asinh(x.value) }) { z -> x.d += z.d / sqrt(one + x.value * x.value) }
 
-public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.acosh(x: AutoDiffValue<T>): AutoDiffValue<T> =
+public fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.acosh(x: AutoDiffValue<T>): AutoDiffValue<T> =
     derive(const { acosh(x.value) }) { z -> x.d += z.d / (sqrt((x.value - one) * (x.value + one))) }
 
-public fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.atanh(x: AutoDiffValue<T>): AutoDiffValue<T> =
+public fun <T : Any, F : ExtendedField<T>> SimpleAutoDiffField<T, F>.atanh(x: AutoDiffValue<T>): AutoDiffValue<T> =
     derive(const { atanh(x.value) }) { z -> x.d += z.d / (one - x.value * x.value) }
 
+public class SimpleAutoDiffExtendedField<T : Any, F : ExtendedField<T>>(
+    context: F,
+    bindings: Map<Symbol, T>,
+) : ExtendedField<AutoDiffValue<T>>, SimpleAutoDiffField<T, F>(context, bindings) {
+    // x ^ 2
+    public fun sqr(x: AutoDiffValue<T>): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).sqr(x)
+
+    // x ^ 1/2
+    public override fun sqrt(arg: AutoDiffValue<T>): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).sqrt(arg)
+
+    // x ^ y (const)
+    public override fun power(arg: AutoDiffValue<T>, pow: Number): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).pow(arg, pow.toDouble())
+
+    // exp(x)
+    public override fun exp(arg: AutoDiffValue<T>): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).exp(arg)
+
+    // ln(x)
+    public override fun ln(arg: AutoDiffValue<T>): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).ln(arg)
+
+    // x ^ y (any)
+    public fun pow(
+        x: AutoDiffValue<T>,
+        y: AutoDiffValue<T>,
+    ): AutoDiffValue<T> = exp(y * ln(x))
+
+    // sin(x)
+    public override fun sin(arg: AutoDiffValue<T>): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).sin(arg)
+
+    // cos(x)
+    public override fun cos(arg: AutoDiffValue<T>): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).cos(arg)
+
+    public override fun tan(arg: AutoDiffValue<T>): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).tan(arg)
+
+    public override fun asin(arg: AutoDiffValue<T>): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).asin(arg)
+
+    public override fun acos(arg: AutoDiffValue<T>): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).acos(arg)
+
+    public override fun atan(arg: AutoDiffValue<T>): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).atan(arg)
+
+    public override fun sinh(arg: AutoDiffValue<T>): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).sinh(arg)
+
+    public override fun cosh(arg: AutoDiffValue<T>): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).cosh(arg)
+
+    public override fun tanh(arg: AutoDiffValue<T>): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).tanh(arg)
+
+    public override fun asinh(arg: AutoDiffValue<T>): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).asinh(arg)
+
+    public override fun acosh(arg: AutoDiffValue<T>): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).acosh(arg)
+
+    public override fun atanh(arg: AutoDiffValue<T>): AutoDiffValue<T> =
+        (this as SimpleAutoDiffField<T, F>).atanh(arg)
+}

kmath-core/src/commonMain/kotlin/kscience/kmath/expressions/expressionBuilders.kt

@@ -8,11 +8,6 @@ import kotlin.contracts.InvocationKind
 import kotlin.contracts.contract
 
 
-//public interface ExpressionBuilder<T, E, A : ExpressionAlgebra<T, E>> {
-//    public fun expression(block: A.() -> E): Expression<T>
-//}
-
-
 /**
  * Creates a functional expression with this [Space].
  */

kmath-core/src/commonTest/kotlin/kscience/kmath/expressions/SimpleAutoDiffTest.kt

@@ -2,6 +2,7 @@ package kscience.kmath.expressions
 
 import kscience.kmath.operations.RealField
 import kscience.kmath.structures.asBuffer
+import kotlin.math.E
 import kotlin.math.PI
 import kotlin.math.pow
 import kotlin.math.sqrt
@@ -13,18 +14,18 @@ class SimpleAutoDiffTest {
 
     fun dx(
         xBinding: Pair<Symbol, Double>,
-        body: AutoDiffField<Double, RealField>.(x: AutoDiffValue<Double>) -> AutoDiffValue<Double>,
+        body: SimpleAutoDiffField<Double, RealField>.(x: AutoDiffValue<Double>) -> AutoDiffValue<Double>,
     ): DerivationResult<Double> = RealField.simpleAutoDiff(xBinding) { body(bind(xBinding.first)) }
 
     fun dxy(
         xBinding: Pair<Symbol, Double>,
         yBinding: Pair<Symbol, Double>,
-        body: AutoDiffField<Double, RealField>.(x: AutoDiffValue<Double>, y: AutoDiffValue<Double>) -> AutoDiffValue<Double>,
+        body: SimpleAutoDiffField<Double, RealField>.(x: AutoDiffValue<Double>, y: AutoDiffValue<Double>) -> AutoDiffValue<Double>,
     ): DerivationResult<Double> = RealField.simpleAutoDiff(xBinding, yBinding) {
         body(bind(xBinding.first), bind(yBinding.first))
     }
 
-    fun diff(block: AutoDiffField<Double, RealField>.() -> AutoDiffValue<Double>): SimpleAutoDiffExpression<Double, RealField> {
+    fun diff(block: SimpleAutoDiffField<Double, RealField>.() -> AutoDiffValue<Double>): SimpleAutoDiffExpression<Double, RealField> {
         return SimpleAutoDiffExpression(RealField, block)
     }
 
@@ -245,9 +246,9 @@ class SimpleAutoDiffTest {
 
     @Test
     fun testTanh() {
-        val y = dx(x to PI / 6) { x -> tanh(x) }
+        val y = dx(x to 1.0) { x -> tanh(x) }
-        assertApprox(1.0 / sqrt(3.0), y.value) // y = tanh(pi/6)
+        assertApprox((E * E - 1) / (E * E + 1), y.value) // y = tanh(pi/6)
-        assertApprox(1.0 / kotlin.math.cosh(PI / 6.0).pow(2), y.derivative(x)) // dy/dx = sech(pi/6)^2
+        assertApprox(1.0 / kotlin.math.cosh(1.0).pow(2), y.derivative(x)) // dy/dx = sech(pi/6)^2
     }
 
     @Test