b parameter of renormalized beta distribution

Average Error: 0.1 → 0.1

Time: 1.9m

Precision: 64

\[0 \lt m \land 0 \lt v \land v \lt 0.25\]

Math

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

↓

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

C

double f(double m, double v) {
        double r1037908 = m;
        double r1037909 = 1.0;
        double r1037910 = r1037909 - r1037908;
        double r1037911 = r1037908 * r1037910;
        double r1037912 = v;
        double r1037913 = r1037911 / r1037912;
        double r1037914 = r1037913 - r1037909;
        double r1037915 = r1037914 * r1037910;
        return r1037915;
}

↓

double f(double m, double v) {
        double r1037916 = 1.0;
        double r1037917 = m;
        double r1037918 = r1037916 - r1037917;
        double r1037919 = r1037918 * r1037917;
        double r1037920 = v;
        double r1037921 = r1037919 / r1037920;
        double r1037922 = r1037921 - r1037916;
        double r1037923 = r1037922 * r1037918;
        return r1037923;
}

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 *-commutative 0.1

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

4. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019143 +o rules:numerics
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))