b parameter of renormalized beta distribution

Average Error: 0.1 → 0.1

Time: 15.0s

Precision: 64

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

Math

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

↓

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

C

double f(double m, double v) {
        double r19141 = m;
        double r19142 = 1.0;
        double r19143 = r19142 - r19141;
        double r19144 = r19141 * r19143;
        double r19145 = v;
        double r19146 = r19144 / r19145;
        double r19147 = r19146 - r19142;
        double r19148 = r19147 * r19143;
        return r19148;
}

↓

double f(double m, double v) {
        double r19149 = m;
        double r19150 = 1.0;
        double r19151 = r19149 * r19150;
        double r19152 = -r19149;
        double r19153 = r19149 * r19152;
        double r19154 = r19151 + r19153;
        double r19155 = v;
        double r19156 = r19154 / r19155;
        double r19157 = r19156 - r19150;
        double r19158 = r19150 - r19149;
        double r19159 = r19157 * r19158;
        return r19159;
}

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 sub-neg 0.1

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

4. Applied distribute-lft-in 0.1

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

5. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019208 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))