b parameter of renormalized beta distribution

Average Error: 0.1 → 0.1

Time: 21.5s

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 r1221762 = m;
        double r1221763 = 1.0;
        double r1221764 = r1221763 - r1221762;
        double r1221765 = r1221762 * r1221764;
        double r1221766 = v;
        double r1221767 = r1221765 / r1221766;
        double r1221768 = r1221767 - r1221763;
        double r1221769 = r1221768 * r1221764;
        return r1221769;
}

↓

double f(double m, double v) {
        double r1221770 = 1.0;
        double r1221771 = m;
        double r1221772 = r1221770 - r1221771;
        double r1221773 = v;
        double r1221774 = r1221773 / r1221772;
        double r1221775 = r1221771 / r1221774;
        double r1221776 = r1221775 - r1221770;
        double r1221777 = r1221772 * r1221776;
        return r1221777;
}

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 *-un-lft-identity 0.1

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

4. Applied associate-*r* 0.1

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

5. Simplified 0.1

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

6. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019162 
(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)))