a parameter of renormalized beta distribution

Average Error: 0.2 → 0.2

Time: 3.9s

Precision: 64

\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]

Math

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

↓

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

C

double f(double m, double v) {
        double r9804 = m;
        double r9805 = 1.0;
        double r9806 = r9805 - r9804;
        double r9807 = r9804 * r9806;
        double r9808 = v;
        double r9809 = r9807 / r9808;
        double r9810 = r9809 - r9805;
        double r9811 = r9810 * r9804;
        return r9811;
}

↓

double f(double m, double v) {
        double r9812 = m;
        double r9813 = 1.0;
        double r9814 = r9813 - r9812;
        double r9815 = r9812 * r9814;
        double r9816 = v;
        double r9817 = r9815 / r9816;
        double r9818 = r9817 - r9813;
        double r9819 = r9818 * r9812;
        return r9819;
}

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

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

4. Applied times-frac 0.2

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

5. Simplified 0.2

   \[\leadsto \left(\color{blue}{m} \cdot \frac{1 - m}{v} - 1\right) \cdot m\]
6. Using strategy rm

7. Applied associate-*r/ 0.2

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

8. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019354 +o rules:numerics
(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))