b parameter of renormalized beta distribution

Average Error: 0.1 → 0.1

Time: 19.1s

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 r20998 = m;
        double r20999 = 1.0;
        double r21000 = r20999 - r20998;
        double r21001 = r20998 * r21000;
        double r21002 = v;
        double r21003 = r21001 / r21002;
        double r21004 = r21003 - r20999;
        double r21005 = r21004 * r21000;
        return r21005;
}

↓

double f(double m, double v) {
        double r21006 = m;
        double r21007 = v;
        double r21008 = 1.0;
        double r21009 = r21008 - r21006;
        double r21010 = r21007 / r21009;
        double r21011 = r21006 / r21010;
        double r21012 = r21011 - r21008;
        double r21013 = r21012 * r21009;
        return r21013;
}

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 2019306 
(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)))