a parameter of renormalized beta distribution

Average Error: 0.2 → 0.2

Time: 5.5s

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 r15648 = m;
        double r15649 = 1.0;
        double r15650 = r15649 - r15648;
        double r15651 = r15648 * r15650;
        double r15652 = v;
        double r15653 = r15651 / r15652;
        double r15654 = r15653 - r15649;
        double r15655 = r15654 * r15648;
        return r15655;
}

↓

double f(double m, double v) {
        double r15656 = m;
        double r15657 = v;
        double r15658 = 1.0;
        double r15659 = r15658 - r15656;
        double r15660 = r15657 / r15659;
        double r15661 = r15656 / r15660;
        double r15662 = r15661 - r15658;
        double r15663 = r15662 * r15656;
        return r15663;
}

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 2020024 
(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))