a parameter of renormalized beta distribution

Average Error: 0.2 → 0.2

Time: 50.7s

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 r2267944 = m;
        double r2267945 = 1.0;
        double r2267946 = r2267945 - r2267944;
        double r2267947 = r2267944 * r2267946;
        double r2267948 = v;
        double r2267949 = r2267947 / r2267948;
        double r2267950 = r2267949 - r2267945;
        double r2267951 = r2267950 * r2267944;
        return r2267951;
}

↓

double f(double m, double v) {
        double r2267952 = m;
        double r2267953 = v;
        double r2267954 = 1.0;
        double r2267955 = r2267954 - r2267952;
        double r2267956 = r2267953 / r2267955;
        double r2267957 = r2267952 / r2267956;
        double r2267958 = r2267957 - r2267954;
        double r2267959 = r2267952 * r2267958;
        return r2267959;
}

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 2019119 
(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))