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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 : scheduler.currentProbability();
    double x = center(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)));
  }
}