diff --git a/kmath-commons/src/main/kotlin/scientifik/kmath/expressions/DiffExpression.kt b/kmath-commons/src/main/kotlin/scientifik/kmath/expressions/DiffExpression.kt
index 6c1759d54..5f6d0d8fe 100644
--- a/kmath-commons/src/main/kotlin/scientifik/kmath/expressions/DiffExpression.kt
+++ b/kmath-commons/src/main/kotlin/scientifik/kmath/expressions/DiffExpression.kt
@@ -2,7 +2,6 @@ package scientifik.kmath.expressions
 
 import org.apache.commons.math3.analysis.differentiation.DerivativeStructure
 import scientifik.kmath.operations.ExtendedField
-import scientifik.kmath.operations.ExtendedFieldOperations
 import scientifik.kmath.operations.Field
 import kotlin.properties.ReadOnlyProperty
 import kotlin.reflect.KProperty
@@ -10,8 +9,10 @@ import kotlin.reflect.KProperty
 /**
  * A field wrapping commons-math derivative structures
  */
-class DerivativeStructureField(val order: Int, val parameters: Map<String, Double>) :
-    ExtendedField<DerivativeStructure> {
+class DerivativeStructureField(
+    val order: Int,
+    val parameters: Map<String, Double>
+) : ExtendedField<DerivativeStructure> {
 
     override val zero: DerivativeStructure by lazy { DerivativeStructure(order, parameters.size) }
 
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/misc/AutoDiff.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/misc/AutoDiff.kt
index 91256d114..ed77054cf 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/misc/AutoDiff.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/misc/AutoDiff.kt
@@ -20,7 +20,7 @@ open class Variable<T : Any>(val value: T)
 class DerivationResult<T : Any>(
     value: T,
     val deriv: Map<Variable<T>, T>,
-    val context: ExtendedField<T>
+    val context: Field<T>
 ) : Variable<T>(value) {
     fun deriv(variable: Variable<T>) = deriv[variable] ?: context.zero
 
@@ -52,8 +52,8 @@ class DerivationResult<T : Any>(
  * assertEquals(9.0, x.d)  // dy/dx
  * ```
  */
-fun <T : Any> ExtendedField<T>.deriv(body: AutoDiffField<T>.() -> Variable<T>): DerivationResult<T> =
-    AutoDiffContext<T>(this).run {
+fun <T : Any, F : Field<T>> F.deriv(body: AutoDiffField<T, F>.() -> Variable<T>): DerivationResult<T> =
+    AutoDiffContext<T, F>(this).run {
         val result = body()
         result.d = context.one// computing derivative w.r.t result
         runBackwardPass()
@@ -61,9 +61,9 @@ fun <T : Any> ExtendedField<T>.deriv(body: AutoDiffField<T>.() -> Variable<T>):
     }
 
 
-abstract class AutoDiffField<T : Any> : Field<Variable<T>> {
+abstract class AutoDiffField<T : Any, F : Field<T>> : Field<Variable<T>> {
 
-    abstract val context: ExtendedField<T>
+    abstract val context: F
 
     /**
      * Performs update of derivative after the rest of the formula in the back-pass.
@@ -76,7 +76,7 @@ abstract class AutoDiffField<T : Any> : Field<Variable<T>> {
      * }
      * ```
      */
-    abstract fun <R> derive(value: R, block: ExtendedField<T>.(R) -> Unit): R
+    abstract fun <R> derive(value: R, block: F.(R) -> Unit): R
 
     /**
      * A variable accessing inner state of derivatives.
@@ -86,7 +86,7 @@ abstract class AutoDiffField<T : Any> : Field<Variable<T>> {
 
     abstract fun variable(value: T): Variable<T>
 
-    inline fun variable(block: ExtendedField<T>.() -> T) = variable(context.block())
+    inline fun variable(block: F.() -> T) = variable(context.block())
 
     // Overloads for Double constants
 
@@ -111,7 +111,7 @@ abstract class AutoDiffField<T : Any> : Field<Variable<T>> {
 /**
  * Automatic Differentiation context class.
  */
-private class AutoDiffContext<T : Any>(override val context: ExtendedField<T>) : AutoDiffField<T>() {
+private class AutoDiffContext<T : Any, F : Field<T>>(override val context: F) : AutoDiffField<T, F>() {
 
     // this stack contains pairs of blocks and values to apply them to
     private var stack = arrayOfNulls<Any?>(8)
@@ -123,11 +123,11 @@ private class AutoDiffContext<T : Any>(override val context: ExtendedField<T>) :
     /**
      * A variable coupled with its derivative. For internal use only
      */
-    inner class VariableWithDeriv(x: T, var d: T = context.zero) : Variable<T>(x)
+    private class VariableWithDeriv<T : Any>(x: T, var d: T) : Variable<T>(x)
 
 
     override fun variable(value: T): Variable<T> =
-        VariableWithDeriv(value)
+        VariableWithDeriv(value, context.zero)
 
     override var Variable<T>.d: T
         get() = (this as? VariableWithDeriv)?.d ?: derivatives[this] ?: context.zero
@@ -140,7 +140,7 @@ private class AutoDiffContext<T : Any>(override val context: ExtendedField<T>) :
         }
 
     @Suppress("UNCHECKED_CAST")
-    override fun <R> derive(value: R, block: ExtendedField<T>.(R) -> Unit): R {
+    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
@@ -152,7 +152,7 @@ private class AutoDiffContext<T : Any>(override val context: ExtendedField<T>) :
     fun runBackwardPass() {
         while (sp > 0) {
             val value = stack[--sp]
-            val block = stack[--sp] as ExtendedField<T>.(Any?) -> Unit
+            val block = stack[--sp] as F.(Any?) -> Unit
             context.block(value)
         }
     }
@@ -190,44 +190,50 @@ private class AutoDiffContext<T : Any>(override val context: ExtendedField<T>) :
 // Extensions for differentiation of various basic mathematical functions
 
 // x ^ 2
-fun <T : Any> AutoDiffField<T>.sqr(x: Variable<T>): Variable<T> = derive(variable { x.value * x.value }) { z ->
-    x.d += z.d * 2 * x.value
-}
+fun <T : Any, F : Field<T>> AutoDiffField<T, F>.sqr(x: Variable<T>): Variable<T> =
+    derive(variable { x.value * x.value }) { z ->
+        x.d += z.d * 2 * x.value
+    }
 
 // x ^ 1/2
-fun <T : Any> AutoDiffField<T>.sqrt(x: Variable<T>): Variable<T> = derive(variable { sqrt(x.value) }) { z ->
-    x.d += z.d * 0.5 / z.value
-}
+fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.sqrt(x: Variable<T>): Variable<T> =
+    derive(variable { sqrt(x.value) }) { z ->
+        x.d += z.d * 0.5 / z.value
+    }
 
 // x ^ y (const)
-fun <T : Any> AutoDiffField<T>.pow(x: Variable<T>, y: Double): Variable<T> =
+fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.pow(x: Variable<T>, y: Double): Variable<T> =
     derive(variable { power(x.value, y) }) { z ->
         x.d += z.d * y * power(x.value, y - 1)
     }
 
-fun <T : Any> AutoDiffField<T>.pow(x: Variable<T>, y: Int): Variable<T> = pow(x, y.toDouble())
+fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.pow(x: Variable<T>, y: Int): Variable<T> = pow(x, y.toDouble())
 
 // exp(x)
-fun <T : Any> AutoDiffField<T>.exp(x: Variable<T>): Variable<T> = derive(variable { exp(x.value) }) { z ->
-    x.d += z.d * z.value
-}
+fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.exp(x: Variable<T>): Variable<T> =
+    derive(variable { exp(x.value) }) { z ->
+        x.d += z.d * z.value
+    }
 
 // ln(x)
-fun <T : Any> AutoDiffField<T>.ln(x: Variable<T>): Variable<T> = derive(
+fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.ln(x: Variable<T>): Variable<T> = derive(
     variable { ln(x.value) }
 ) { z ->
     x.d += z.d / x.value
 }
 
 // x ^ y (any)
-fun <T : Any> AutoDiffField<T>.pow(x: Variable<T>, y: Variable<T>): Variable<T> = exp(y * ln(x))
+fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.pow(x: Variable<T>, y: Variable<T>): Variable<T> =
+    exp(y * ln(x))
 
 // sin(x)
-fun <T : Any> AutoDiffField<T>.sin(x: Variable<T>): Variable<T> = derive(variable { sin(x.value) }) { z ->
-    x.d += z.d * cos(x.value)
-}
+fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.sin(x: Variable<T>): Variable<T> =
+    derive(variable { sin(x.value) }) { z ->
+        x.d += z.d * cos(x.value)
+    }
 
 // cos(x)
-fun <T : Any> AutoDiffField<T>.cos(x: Variable<T>): Variable<T> = derive(variable { cos(x.value) }) { z ->
-    x.d -= z.d * sin(x.value)
-}
\ No newline at end of file
+fun <T : Any, F : ExtendedField<T>> AutoDiffField<T, F>.cos(x: Variable<T>): Variable<T> =
+    derive(variable { cos(x.value) }) { z ->
+        x.d -= z.d * sin(x.value)
+    }
\ No newline at end of file
diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealBufferField.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealBufferField.kt
index b56f42717..88c8c29db 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealBufferField.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/structures/RealBufferField.kt
@@ -1,7 +1,7 @@
 package scientifik.kmath.structures
 
+import scientifik.kmath.operations.ExtendedField
 import scientifik.kmath.operations.ExtendedFieldOperations
-import scientifik.kmath.operations.Field
 import kotlin.math.*
 
 
@@ -98,7 +98,7 @@ object RealBufferFieldOperations : ExtendedFieldOperations<Buffer<Double>> {
     }
 }
 
-class RealBufferField(val size: Int) : Field<Buffer<Double>>, ExtendedFieldOperations<Buffer<Double>> {
+class RealBufferField(val size: Int) : ExtendedField<Buffer<Double>> {
 
     override val zero: Buffer<Double> by lazy { DoubleBuffer(size) { 0.0 } }
 
diff --git a/kmath-core/src/commonTest/kotlin/scientifik/kmath/misc/AutoDiffTest.kt b/kmath-core/src/commonTest/kotlin/scientifik/kmath/misc/AutoDiffTest.kt
index 9a2597737..9dc8f5ef7 100644
--- a/kmath-core/src/commonTest/kotlin/scientifik/kmath/misc/AutoDiffTest.kt
+++ b/kmath-core/src/commonTest/kotlin/scientifik/kmath/misc/AutoDiffTest.kt
@@ -11,7 +11,7 @@ class AutoDiffTest {
 
     fun Variable(int: Int) = Variable(int.toDouble())
 
-    fun deriv(body: AutoDiffField<Double>.() -> Variable<Double>) = RealField.deriv(body)
+    fun deriv(body: AutoDiffField<Double, RealField>.() -> Variable<Double>) = RealField.deriv(body)
 
     @Test
     fun testPlusX2() {