b parameter of renormalized beta distribution

Average Error: 0.1 → 0.1

Time: 35.7s

Precision: 64

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

Math

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

↓

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

C

double f(double m, double v) {
        double r1458682 = m;
        double r1458683 = 1.0;
        double r1458684 = r1458683 - r1458682;
        double r1458685 = r1458682 * r1458684;
        double r1458686 = v;
        double r1458687 = r1458685 / r1458686;
        double r1458688 = r1458687 - r1458683;
        double r1458689 = r1458688 * r1458684;
        return r1458689;
}

↓

double f(double m, double v) {
        double r1458690 = 1.0;
        double r1458691 = m;
        double r1458692 = r1458690 - r1458691;
        double r1458693 = v;
        double r1458694 = r1458693 / r1458692;
        double r1458695 = r1458691 / r1458694;
        double r1458696 = -r1458690;
        double r1458697 = r1458695 + r1458696;
        double r1458698 = r1458692 * r1458697;
        return r1458698;
}

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. Using strategy rm

5. Applied sub-neg 0.1

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

6. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m)))