a parameter of renormalized beta distribution

Average Error: 0.2 → 0.2

Time: 14.8s

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 r319166 = m;
        double r319167 = 1.0;
        double r319168 = r319167 - r319166;
        double r319169 = r319166 * r319168;
        double r319170 = v;
        double r319171 = r319169 / r319170;
        double r319172 = r319171 - r319167;
        double r319173 = r319172 * r319166;
        return r319173;
}

↓

double f(double m, double v) {
        double r319174 = m;
        double r319175 = v;
        double r319176 = 1.0;
        double r319177 = r319176 - r319174;
        double r319178 = r319175 / r319177;
        double r319179 = r319174 / r319178;
        double r319180 = r319179 - r319176;
        double r319181 = r319174 * r319180;
        return r319181;
}

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 2019128 +o rules:numerics
(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))