a parameter of renormalized beta distribution

Average Error: 0.2 → 0.2

Time: 23.5s

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 r24556 = m;
        double r24557 = 1.0;
        double r24558 = r24557 - r24556;
        double r24559 = r24556 * r24558;
        double r24560 = v;
        double r24561 = r24559 / r24560;
        double r24562 = r24561 - r24557;
        double r24563 = r24562 * r24556;
        return r24563;
}

↓

double f(double m, double v) {
        double r24564 = m;
        double r24565 = v;
        double r24566 = 1.0;
        double r24567 = r24566 - r24564;
        double r24568 = r24565 / r24567;
        double r24569 = r24564 / r24568;
        double r24570 = r24569 - r24566;
        double r24571 = r24570 * r24564;
        return r24571;
}

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))