a parameter of renormalized beta distribution

Average Error: 0.2 → 0.2

Time: 22.8s

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 r628089 = m;
        double r628090 = 1.0;
        double r628091 = r628090 - r628089;
        double r628092 = r628089 * r628091;
        double r628093 = v;
        double r628094 = r628092 / r628093;
        double r628095 = r628094 - r628090;
        double r628096 = r628095 * r628089;
        return r628096;
}

↓

double f(double m, double v) {
        double r628097 = m;
        double r628098 = v;
        double r628099 = 1.0;
        double r628100 = r628099 - r628097;
        double r628101 = r628098 / r628100;
        double r628102 = r628097 / r628101;
        double r628103 = r628102 - r628099;
        double r628104 = r628097 * r628103;
        return r628104;
}

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 2019133 +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))