a parameter of renormalized beta distribution

Average Error: 0.2 → 0.2

Time: 51.7s

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 r2442592 = m;
        double r2442593 = 1.0;
        double r2442594 = r2442593 - r2442592;
        double r2442595 = r2442592 * r2442594;
        double r2442596 = v;
        double r2442597 = r2442595 / r2442596;
        double r2442598 = r2442597 - r2442593;
        double r2442599 = r2442598 * r2442592;
        return r2442599;
}

↓

double f(double m, double v) {
        double r2442600 = m;
        double r2442601 = v;
        double r2442602 = 1.0;
        double r2442603 = r2442602 - r2442600;
        double r2442604 = r2442601 / r2442603;
        double r2442605 = r2442600 / r2442604;
        double r2442606 = r2442605 - r2442602;
        double r2442607 = r2442600 * r2442606;
        return r2442607;
}

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 2019107 
(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))