srecord noeq ProbabilisticBinaryMaximumSearch(

  IF1<Double> scoreFunction,

  IVF1<WithProbability<Double>> action,

  DoubleRange startRange) extends Probabilistic {

  double featureSize = 1.0; // stop when range is shorter than twice this

  double defaultRecursionProbability = 1.0; //0.99;

  bool probabilitiesCanGoUp = true;

  bool verbose;

  // sigmoid function (R to (0; 1))

  swappable double scoreToProbability(double score) {

    ret arctanSigmoid_zeroToOne(score);

  }

  double probabilityScore(double x) {

    ret scoreToProbability(scoreFunction.get(x));

  }

  WithProbability<Double> probabilityScored(double x) {

    ret WithProbability(probabilityScore(x), x);

  }

  swappable double recursionProbability(DoubleRange r) {

    ret halfLength(r) >= featureSize ? defaultRecursionProbability : 0.0;

  }

  run {

    lookAtRange(startRange);

  }

  selfType verbose(bool verbose) { this.verbose = verbose; this; }

  void lookAtRange(DoubleRange r) {

    double previousP = probabilitiesCanGoUp ? 1.0 : ps.currentProbability();

    double x = chooseMiddlePoint(r);

    double score = scoreFunction.get(x);

    double scoreP = scoreToProbability(score);

    double actionP = previousP * scoreP;

    if (verbose) printVars lookAtRange(+r, +x, +score, +scoreP, +previousP, +actionP);

    at(actionP, () -> action.get(withProbability(scoreP, x)));

    double recP_raw = recursionProbability(r);

    double recP = actionP * recP_raw;

    if (verbose) printVars ("lookAtRange  ", +recP_raw, +recP);

    at(recP, () -> lookAtRange(lowerHalf(r)));

    at(recP, () -> lookAtRange(upperHalf(r)));

  }

  // You can adjust this, for example to look at integer coordinates only

  swappable double chooseMiddlePoint(DoubleRange r) {

    ret center(r);

  }

}