b parameter of renormalized beta distribution

Average Error: 0.1 → 0.1

Time: 3.4m

Precision: 64

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

Math

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

↓

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

C

double f(double m, double v) {
        double r8913888 = m;
        double r8913889 = 1.0;
        double r8913890 = r8913889 - r8913888;
        double r8913891 = r8913888 * r8913890;
        double r8913892 = v;
        double r8913893 = r8913891 / r8913892;
        double r8913894 = r8913893 - r8913889;
        double r8913895 = r8913894 * r8913890;
        return r8913895;
}

↓

double f(double m, double v) {
        double r8913896 = 1.0;
        double r8913897 = m;
        double r8913898 = r8913896 - r8913897;
        double r8913899 = v;
        double r8913900 = r8913899 / r8913898;
        double r8913901 = r8913897 / r8913900;
        double r8913902 = r8913901 - r8913896;
        double r8913903 = r8913898 * r8913902;
        return r8913903;
}

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 2019104 +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)))