b parameter of renormalized beta distribution

Average Error: 0.1 → 0.1

Time: 5.1s

Precision: 64

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

Math

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

↓

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

C

double f(double m, double v) {
        double r21139 = m;
        double r21140 = 1.0;
        double r21141 = r21140 - r21139;
        double r21142 = r21139 * r21141;
        double r21143 = v;
        double r21144 = r21142 / r21143;
        double r21145 = r21144 - r21140;
        double r21146 = r21145 * r21141;
        return r21146;
}

↓

double f(double m, double v) {
        double r21147 = m;
        double r21148 = v;
        double r21149 = 1.0;
        double r21150 = r21149 - r21147;
        double r21151 = r21148 / r21150;
        double r21152 = r21147 / r21151;
        double r21153 = r21152 - r21149;
        double r21154 = r21153 * r21150;
        return r21154;
}

Error

Bits error versus m

Bits error versus v

Derivation

1. Initial program 0.1

   \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
2. Using strategy rm

3. Applied associate-/l* 0.1

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

4. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020036 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))