b parameter of renormalized beta distribution

Average Error: 0.1 → 0.1

Time: 35.2s

Precision: 64

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

Math

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

↓

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

C

double f(double m, double v) {
        double r1451110 = m;
        double r1451111 = 1.0;
        double r1451112 = r1451111 - r1451110;
        double r1451113 = r1451110 * r1451112;
        double r1451114 = v;
        double r1451115 = r1451113 / r1451114;
        double r1451116 = r1451115 - r1451111;
        double r1451117 = r1451116 * r1451112;
        return r1451117;
}

↓

double f(double m, double v) {
        double r1451118 = m;
        double r1451119 = v;
        double r1451120 = 1.0;
        double r1451121 = r1451120 - r1451118;
        double r1451122 = r1451119 / r1451121;
        double r1451123 = r1451118 / r1451122;
        double r1451124 = r1451123 - r1451120;
        double r1451125 = r1451124 * r1451121;
        return r1451125;
}

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

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

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m)))