a parameter of renormalized beta distribution

Average Error: 0.2 → 0.2

Time: 24.4s

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 r24509 = m;
        double r24510 = 1.0;
        double r24511 = r24510 - r24509;
        double r24512 = r24509 * r24511;
        double r24513 = v;
        double r24514 = r24512 / r24513;
        double r24515 = r24514 - r24510;
        double r24516 = r24515 * r24509;
        return r24516;
}

↓

double f(double m, double v) {
        double r24517 = m;
        double r24518 = v;
        double r24519 = 1.0;
        double r24520 = r24519 - r24517;
        double r24521 = r24518 / r24520;
        double r24522 = r24517 / r24521;
        double r24523 = r24522 - r24519;
        double r24524 = r24523 * r24517;
        return r24524;
}

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 2019325 
(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))