b parameter of renormalized beta distribution

Average Error: 0.1 → 0.1

Time: 29.2s

Precision: 64

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

Math

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

↓

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

C

double f(double m, double v) {
        double r849852 = m;
        double r849853 = 1.0;
        double r849854 = r849853 - r849852;
        double r849855 = r849852 * r849854;
        double r849856 = v;
        double r849857 = r849855 / r849856;
        double r849858 = r849857 - r849853;
        double r849859 = r849858 * r849854;
        return r849859;
}

↓

double f(double m, double v) {
        double r849860 = 1.0;
        double r849861 = m;
        double r849862 = r849860 - r849861;
        double r849863 = v;
        double r849864 = r849863 / r849862;
        double r849865 = r849861 / r849864;
        double r849866 = r849865 - r849860;
        double r849867 = r849862 * r849866;
        return r849867;
}

Error

Bits error versus m

Bits error versus v

Derivation

1. Initial program 0.1

   \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
2. Using strategy rm

3. Applied associate-/l* 0.1

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

4. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019141 +o rules:numerics
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))