Sample code for only generating enough noise octaves to know the sign of the final value (simplified from a small WIP MC mod of mine)

computeGoodEnoughNoise.java

    private double computeGoodEnoughNoise(int worldX, int worldY, int worldZ, double startingValue) {

        // Final noise value begins with the threshold.
        double value = startingValue; // e.g. -heightThreshold (negative)

        double freq = BASE_FREQUENCY; // e.g. 1.0/256.0
        double amp = BASE_AMPLITUDE; // e.g. 64.0
        for (int i = 0; i < nOctaves && actualValue > -uncertaintyBounds[i] && actualValue < uncertaintyBounds[i]; i++) {
            value += octaves[i].noise3_XZBeforeY(worldX * hScale * freq, worldY * vScale * freq, worldZ * hScale * freq) * amp;
            freq *= 2.0;
            amp /= 2.0;
        }
        return actualValue;
    }

/////////////////////////////////

    // Pregenerate this in a constructor, or somewhere.
    // for nOctaves=4, this would generate
    // { BASE_AMPLITUDE * (1.0 + 0.5 + 0.25 + 0.125), BASE_AMPLITUDE * (0.5 + 0.25 + 0.125), BASE_AMPLITUDE * (0.25 + 0.125), BASE_AMPLITUDE * (0.125) };
    uncertaintyBounds = new double[nOctaves];
    {
        double boundBase = 0.0;
        for (int i = nOctaves - 1; i >= 0; i--) {
            boundBase += 1.0 / (1 << i);
            uncertaintyBounds[i] = OUTPUT_NOISE_MAIN_AMPLITUDE * boundBase;
        }
    }