a parameter of renormalized beta distribution

Average Error: 0.2 → 0.2

Time: 24.9s

Precision: 64

\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]

Math

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

↓

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

C

double f(double m, double v) {
        double r24046 = m;
        double r24047 = 1.0;
        double r24048 = r24047 - r24046;
        double r24049 = r24046 * r24048;
        double r24050 = v;
        double r24051 = r24049 / r24050;
        double r24052 = r24051 - r24047;
        double r24053 = r24052 * r24046;
        return r24053;
}

↓

double f(double m, double v) {
        double r24054 = m;
        double r24055 = v;
        double r24056 = 1.0;
        double r24057 = r24056 - r24054;
        double r24058 = r24055 / r24057;
        double r24059 = r24054 / r24058;
        double r24060 = r24059 - r24056;
        double r24061 = r24060 * r24054;
        return r24061;
}

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

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

Reproduce

herbie shell --seed 2019306 
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) m))