a parameter of renormalized beta distribution

Average Error: 0.2 → 0.2

Time: 20.0s

Precision: 64

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

Math

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

↓

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

C

double f(double m, double v) {
        double r872174 = m;
        double r872175 = 1.0;
        double r872176 = r872175 - r872174;
        double r872177 = r872174 * r872176;
        double r872178 = v;
        double r872179 = r872177 / r872178;
        double r872180 = r872179 - r872175;
        double r872181 = r872180 * r872174;
        return r872181;
}

↓

double f(double m, double v) {
        double r872182 = m;
        double r872183 = v;
        double r872184 = r872183 / r872182;
        double r872185 = r872182 / r872184;
        double r872186 = r872185 - r872182;
        double r872187 = r872182 * r872182;
        double r872188 = r872187 * r872182;
        double r872189 = r872188 / r872183;
        double r872190 = r872186 - r872189;
        return r872190;
}

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 6.6

   \[\leadsto \color{blue}{\frac{{m}^{2}}{v} - \left(m + \frac{{m}^{3}}{v}\right)}\]

5. Simplified 0.2

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

6. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019158 
(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))