a parameter of renormalized beta distribution

Average Error: 0.2 → 0.2

Time: 32.1s

Precision: 64

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

Math

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

↓

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

C

double f(double m, double v) {
        double r1272079 = m;
        double r1272080 = 1.0;
        double r1272081 = r1272080 - r1272079;
        double r1272082 = r1272079 * r1272081;
        double r1272083 = v;
        double r1272084 = r1272082 / r1272083;
        double r1272085 = r1272084 - r1272080;
        double r1272086 = r1272085 * r1272079;
        return r1272086;
}

↓

double f(double m, double v) {
        double r1272087 = 1.0;
        double r1272088 = v;
        double r1272089 = 1.0;
        double r1272090 = m;
        double r1272091 = r1272089 - r1272090;
        double r1272092 = r1272088 / r1272091;
        double r1272093 = r1272092 / r1272090;
        double r1272094 = r1272087 / r1272093;
        double r1272095 = r1272094 - r1272089;
        double r1272096 = r1272095 * r1272090;
        return r1272096;
}

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. Using strategy rm

5. Applied clear-num 0.2

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

6. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) m))