a parameter of renormalized beta distribution

Average Error: 0.2 → 0.2

Time: 13.1s

Precision: 64

\[0 \lt m \land 0 \lt v \land v \lt 0.25\]

Math

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

↓

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

C

double f(double m, double v) {
        double r375909 = m;
        double r375910 = 1.0;
        double r375911 = r375910 - r375909;
        double r375912 = r375909 * r375911;
        double r375913 = v;
        double r375914 = r375912 / r375913;
        double r375915 = r375914 - r375910;
        double r375916 = r375915 * r375909;
        return r375916;
}

↓

double f(double m, double v) {
        double r375917 = m;
        double r375918 = v;
        double r375919 = r375917 / r375918;
        double r375920 = 1.0;
        double r375921 = r375919 - r375920;
        double r375922 = r375918 / r375917;
        double r375923 = r375917 / r375922;
        double r375924 = r375921 - r375923;
        double r375925 = r375924 * r375917;
        return r375925;
}

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 clear-num 0.2

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

4. Taylor expanded around 0 0.2

   \[\leadsto \color{blue}{\left(\frac{m}{v} - \left(\frac{{m}^{2}}{v} + 1\right)\right)} \cdot m\]

5. Simplified 0.2

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

6. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019153 
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) m))