a parameter of renormalized beta distribution

Average Error: 0.2 → 0.2

Time: 55.4s

Precision: 64

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

Math

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

↓

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

C

double f(double m, double v) {
        double r2159894 = m;
        double r2159895 = 1.0;
        double r2159896 = r2159895 - r2159894;
        double r2159897 = r2159894 * r2159896;
        double r2159898 = v;
        double r2159899 = r2159897 / r2159898;
        double r2159900 = r2159899 - r2159895;
        double r2159901 = r2159900 * r2159894;
        return r2159901;
}

↓

double f(double m, double v) {
        double r2159902 = m;
        double r2159903 = v;
        double r2159904 = 1.0;
        double r2159905 = r2159904 - r2159902;
        double r2159906 = r2159903 / r2159905;
        double r2159907 = r2159902 / r2159906;
        double r2159908 = r2159907 - r2159904;
        double r2159909 = r2159902 * r2159908;
        return r2159909;
}

Error

Bits error versus m

Bits error versus v

Derivation

1. Initial program 0.2

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

3. Applied associate-/l* 0.2

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

4. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019120 +o rules:numerics
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) m))