a parameter of renormalized beta distribution

Average Error: 0.2 → 0.2

Time: 17.3s

Precision: 64

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

Math

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

↓

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

C

double f(double m, double v) {
        double r399018 = m;
        double r399019 = 1.0;
        double r399020 = r399019 - r399018;
        double r399021 = r399018 * r399020;
        double r399022 = v;
        double r399023 = r399021 / r399022;
        double r399024 = r399023 - r399019;
        double r399025 = r399024 * r399018;
        return r399025;
}

↓

double f(double m, double v) {
        double r399026 = m;
        double r399027 = v;
        double r399028 = r399027 / r399026;
        double r399029 = r399026 / r399028;
        double r399030 = r399029 - r399026;
        double r399031 = r399026 * r399026;
        double r399032 = r399031 * r399026;
        double r399033 = r399032 / r399027;
        double r399034 = r399030 - r399033;
        return r399034;
}

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 clear-num 0.2

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

4. Taylor expanded around 0 7.0

   \[\leadsto \color{blue}{\frac{{m}^{2}}{v} - \left(m + \frac{{m}^{3}}{v}\right)}\]

5. Simplified 0.2

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

6. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019151 
(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))