All three tests pass

- `uniform` `toPointSet` method has been changed for numerical
stability.

Value: [1e-1 to 1.75e0]

packages/squiggle-lang/__tests__/Distributions/KlDivergence_test.res

@@ -70,13 +70,14 @@ describe("kl divergence", () => {
     let prediction =
       normalMakeR(mean1, stdev1)->E.R2.errMap(s => DistributionTypes.ArgumentError(s))
     let answer = normalMakeR(mean2, stdev2)->E.R2.errMap(s => DistributionTypes.ArgumentError(s))
+    // https://stats.stackexchange.com/questions/7440/kl-divergence-between-two-univariate-gaussians
     let analyticalKl =
       Js.Math.log(stdev1 /. stdev2) +.
       (stdev2 ** 2.0 +. (mean2 -. mean1) ** 2.0) /. (2.0 *. stdev1 ** 2.0) -. 0.5
     let kl = E.R.liftJoin2(klDivergence, prediction, answer)
 
-    Js.Console.log2("Analytical: ", analyticalKl)
-    Js.Console.log2("Computed: ", kl)
+    // Js.Console.log2("Analytical: ", analyticalKl)
+    // Js.Console.log2("Computed: ", kl)
 
     switch kl {
     | Ok(kl') => kl'->expect->toBeCloseTo(analyticalKl)
@@ -91,7 +92,7 @@ describe("kl divergence", () => {
 describe("combine along support test", () => {
   Skip.test("combine along support test", _ => {
     // doesn't matter
-    let combineAlongSupportOfSecondArgument = XYShape.PointwiseCombination.combineAlongSupportOfSecondArgument
+    let combineAlongSupportOfSecondArgument = XYShape.PointwiseCombination.combineAlongSupportOfSecondArgument0
     let lowAnswer = 0.0
     let highAnswer = 1.0
     let lowPrediction = 0.0

packages/squiggle-lang/src/rescript/Distributions/PointSetDist/Continuous.res

@@ -271,38 +271,30 @@ module T = Dist({
   let variance = (t: t): float =>
     XYShape.Analysis.getVarianceDangerously(t, mean, Analysis.getMeanOfSquares)
 
-  let klDivergence0 = (prediction: t, answer: t) => {
-    combinePointwise(
-      ~combiner=XYShape.PointwiseCombination.combineAlongSupportOfSecondArgument,
-      PointSetDist_Scoring.KLDivergence.integrand,
-      prediction,
-      answer,
-    )
-    |> E.R.fmap(shapeMap(XYShape.T.filterYValues(Js.Float.isFinite)))
-    |> E.R.fmap(integralEndY)
-  }
+  // let klDivergence0 = (prediction: t, answer: t) => {
+  //   combinePointwise(
+  //     ~combiner=XYShape.PointwiseCombination.combineAlongSupportOfSecondArgument,
+  //     PointSetDist_Scoring.KLDivergence.integrand,
+  //     prediction,
+  //     answer,
+  //   )
+  //   |> E.R.fmap(shapeMap(XYShape.T.filterYValues(Js.Float.isFinite)))
+  //   |> E.R.fmap(integralEndY)
+  // }
 
   let klDivergence = (prediction: t, answer: t) => {
-    let newShape = XYShape.PointwiseCombination.combineAlongSupportOfSecondArgument2(
+    let newShape = XYShape.PointwiseCombination.combineAlongSupportOfSecondArgument(
       PointSetDist_Scoring.KLDivergence.integrand,
       prediction.xyShape,
       answer.xyShape,
     )
-    let generateContinuousDistFromXYShape: XYShape.xyShape => t = xyShape => {
+    let xyShapeToContinuous: XYShape.xyShape => t = xyShape => {
       xyShape: xyShape,
       interpolation: #Linear,
       integralSumCache: None,
       integralCache: None,
     }
-    let _ = Js.Console.log2("prediction", prediction)
-    let _ = Js.Console.log2("answer", answer)
-    let _ = Js.Console.log2("newShape", newShape)
-    switch newShape {
-    | Ok(tshape) => Ok(integralEndY(generateContinuousDistFromXYShape(tshape)))
-    | Error(errormessage) => Error(errormessage)
-    }
-    //|> E.R.fmap(shapeMap(XYShape.T.filterYValues(Js.Float.isFinite)))
-    //|> E.R.fmap(integralEndY)
+    newShape->E.R2.fmap(x => x->xyShapeToContinuous->integralEndY)
   }
 })
 

packages/squiggle-lang/src/rescript/Distributions/PointSetDist/Discrete.res

@@ -230,7 +230,7 @@ module T = Dist({
 
   let klDivergence = (prediction: t, answer: t) => {
     combinePointwise(
-      ~combiner=XYShape.PointwiseCombination.combineAlongSupportOfSecondArgument,
+      ~combiner=XYShape.PointwiseCombination.combineAlongSupportOfSecondArgument0,
       ~fn=PointSetDist_Scoring.KLDivergence.integrand,
       prediction,
       answer,

packages/squiggle-lang/src/rescript/Distributions/SymbolicDist/SymbolicDist.res

@@ -396,8 +396,9 @@ module T = {
     | (#ByWeight, #Uniform(n)) =>
       // In `ByWeight mode, uniform distributions get special treatment because we need two x's
       // on either side for proper rendering (just left and right of the discontinuities).
-      let dx = 0.00001 *. (n.high -. n.low)
-      [n.low -. dx, n.low +. dx, n.high -. dx, n.high +. dx]
+      let distance = n.high -. n.low
+      let dx = MagicNumbers.Epsilon.ten *. distance
+      [n.low -. dx, n.low, n.low +. dx, n.high -. dx, n.high, n.high +. dx]
     | (#ByWeight, _) =>
       let ys = E.A.Floats.range(minCdfValue, maxCdfValue, n)
       ys |> E.A.fmap(y => inv(y, dist))

packages/squiggle-lang/src/rescript/Utility/XYShape.res

@@ -391,7 +391,7 @@ module PointwiseCombination = {
     `)
 
   // This function is used for kl divergence
-  let combineAlongSupportOfSecondArgument: (
+  let combineAlongSupportOfSecondArgument0: (
     (float, float) => result<float, Operation.Error.t>,
     interpolator,
     T.t,
@@ -455,14 +455,14 @@ module PointwiseCombination = {
     T.filterOkYs(newXs, newYs)->Ok
   }
 
-  let getApproximatePdfOfContinuousDistributionAtPoint: (xyShape, float) => option<float> = (
-    dist: xyShape,
-    point: float,
+  let approximatePdfOfContinuousDistributionAtPoint: (xyShape, float) => option<float> = (
+    distShape,
+    point,
   ) => {
-    let closestFromBelowIndex = E.A.reducei(dist.xs, None, (accumulator, item, index) =>
+    let closestFromBelowIndex = E.A.reducei(distShape.xs, None, (accumulator, item, index) =>
       item < point ? Some(index) : accumulator
     ) // This could be made more efficient by taking advantage of the fact that these are ordered
-    let closestFromAboveIndexOption = Belt.Array.getIndexBy(dist.xs, item => item > point)
+    let closestFromAboveIndexOption = Belt.Array.getIndexBy(distShape.xs, item => item > point)
 
     let weightedMean = (
       point: float,
@@ -480,30 +480,28 @@ module PointwiseCombination = {
 
     let result = switch (closestFromBelowIndex, closestFromAboveIndexOption) {
     | (None, None) => None // all are smaller, and all are larger
-    | (None, Some(i)) => Some(0.0) // none are smaller, all are larger
-    | (Some(i), None) => Some(0.0) // all are smaller, none are larger
+    | (None, Some(_)) => Some(0.0) // none are smaller, all are larger
+    | (Some(_), None) => Some(0.0) // all are smaller, none are larger
     | (Some(i), Some(j)) =>
-      Some(weightedMean(point, dist.xs[i], dist.xs[j], dist.ys[i], dist.ys[j])) // there is a lowerBound and an upperBound.
+      Some(weightedMean(point, distShape.xs[i], distShape.xs[j], distShape.ys[i], distShape.ys[j])) // there is a lowerBound and an upperBound.
     }
 
     result
   }
 
-  let combineAlongSupportOfSecondArgument2: (
+  let combineAlongSupportOfSecondArgument: (
     (float, float) => result<float, Operation.Error.t>,
     T.t,
     T.t,
   ) => result<T.t, Operation.Error.t> = (fn, prediction, answer) => {
-    let combineWithFn = (x: float, i: int) => {
-      let answerX = x
+    let combineWithFn = (answerX: float, i: int) => {
       let answerY = answer.ys[i]
-      let predictionY = getApproximatePdfOfContinuousDistributionAtPoint(prediction, answerX)
+      let predictionY = approximatePdfOfContinuousDistributionAtPoint(prediction, answerX)
       let wrappedResult = E.O.fmap(x => fn(x, answerY), predictionY)
-      let result = switch wrappedResult {
+      switch wrappedResult {
       | Some(x) => x
       | None => Error(Operation.LogicallyInconsistentPathwayError)
       }
-      result
     }
     let newYsWithError = Js.Array.mapi((x, i) => combineWithFn(x, i), answer.xs)
     let newYsOrError = E.A.R.firstErrorOrOpen(newYsWithError)
@@ -512,7 +510,6 @@ module PointwiseCombination = {
     | Error(b) => Error(b)
     }
 
-    // T.filterOkYs(newXs, newYs)->Ok
     result
   }