b parameter of renormalized beta distribution

Average Error: 0.1 → 0.1

Time: 17.1s

Precision: 64

\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]

Math

\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]

↓

\[\left(1 - m\right) \cdot \left(\frac{m}{\frac{v}{1 - m}} - 1\right)\]

C

double f(double m, double v) {
        double r20749 = m;
        double r20750 = 1.0;
        double r20751 = r20750 - r20749;
        double r20752 = r20749 * r20751;
        double r20753 = v;
        double r20754 = r20752 / r20753;
        double r20755 = r20754 - r20750;
        double r20756 = r20755 * r20751;
        return r20756;
}

↓

double f(double m, double v) {
        double r20757 = 1.0;
        double r20758 = m;
        double r20759 = r20757 - r20758;
        double r20760 = v;
        double r20761 = r20760 / r20759;
        double r20762 = r20758 / r20761;
        double r20763 = r20762 - r20757;
        double r20764 = r20759 * r20763;
        return r20764;
}

Error

Bits error versus m

Bits error versus v

Derivation

1. Initial program 0.1

   \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
2. Using strategy rm

3. Applied associate-/l* 0.1

   \[\leadsto \left(\color{blue}{\frac{m}{\frac{v}{1 - m}}} - 1\right) \cdot \left(1 - m\right)\]

4. Final simplification 0.1

   \[\leadsto \left(1 - m\right) \cdot \left(\frac{m}{\frac{v}{1 - m}} - 1\right)\]

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m)))