a parameter of renormalized beta distribution

Average Error: 0.2 → 0.2

Time: 27.9s

Precision: 64

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

Math

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

↓

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

C

double f(double m, double v) {
        double r26039 = m;
        double r26040 = 1.0;
        double r26041 = r26040 - r26039;
        double r26042 = r26039 * r26041;
        double r26043 = v;
        double r26044 = r26042 / r26043;
        double r26045 = r26044 - r26040;
        double r26046 = r26045 * r26039;
        return r26046;
}

↓

double f(double m, double v) {
        double r26047 = 1.0;
        double r26048 = m;
        double r26049 = v;
        double r26050 = r26048 / r26049;
        double r26051 = r26047 * r26050;
        double r26052 = 2.0;
        double r26053 = pow(r26048, r26052);
        double r26054 = r26053 / r26049;
        double r26055 = r26051 - r26054;
        double r26056 = r26055 - r26047;
        double r26057 = r26056 * r26048;
        return r26057;
}

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. Taylor expanded around 0 0.2

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

5. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019304 
(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))