a parameter of renormalized beta distribution

Average Error: 0.2 → 0.2

Time: 25.6s

Precision: 64

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

Math

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

↓

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

C

double f(double m, double v) {
        double r487885 = m;
        double r487886 = 1.0;
        double r487887 = r487886 - r487885;
        double r487888 = r487885 * r487887;
        double r487889 = v;
        double r487890 = r487888 / r487889;
        double r487891 = r487890 - r487886;
        double r487892 = r487891 * r487885;
        return r487892;
}

↓

double f(double m, double v) {
        double r487893 = m;
        double r487894 = 1.0;
        double r487895 = r487894 - r487893;
        double r487896 = r487893 * r487895;
        double r487897 = v;
        double r487898 = r487896 / r487897;
        double r487899 = r487898 - r487894;
        double r487900 = r487893 * r487899;
        return r487900;
}

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 *-un-lft-identity 0.2

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

4. Applied associate-*r* 0.2

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

5. Simplified 0.2

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

6. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019143 +o rules:numerics
(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))