a parameter of renormalized beta distribution

Average Error: 0.2 → 0.2

Time: 14.9s

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 r501614 = m;
        double r501615 = 1.0;
        double r501616 = r501615 - r501614;
        double r501617 = r501614 * r501616;
        double r501618 = v;
        double r501619 = r501617 / r501618;
        double r501620 = r501619 - r501615;
        double r501621 = r501620 * r501614;
        return r501621;
}

↓

double f(double m, double v) {
        double r501622 = m;
        double r501623 = v;
        double r501624 = 1.0;
        double r501625 = r501624 - r501622;
        double r501626 = r501623 / r501625;
        double r501627 = r501622 / r501626;
        double r501628 = r501627 - r501624;
        double r501629 = r501622 * r501628;
        return r501629;
}

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 2019154 
(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))