b parameter of renormalized beta distribution

Average Error: 0.1 → 0.1

Time: 16.2s

Precision: 64

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

Math

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

↓

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

C

double f(double m, double v) {
        double r1181070 = m;
        double r1181071 = 1.0;
        double r1181072 = r1181071 - r1181070;
        double r1181073 = r1181070 * r1181072;
        double r1181074 = v;
        double r1181075 = r1181073 / r1181074;
        double r1181076 = r1181075 - r1181071;
        double r1181077 = r1181076 * r1181072;
        return r1181077;
}

↓

double f(double m, double v) {
        double r1181078 = 1.0;
        double r1181079 = m;
        double r1181080 = r1181078 - r1181079;
        double r1181081 = r1181080 * r1181079;
        double r1181082 = v;
        double r1181083 = r1181081 / r1181082;
        double r1181084 = r1181083 - r1181078;
        double r1181085 = r1181084 * r1181080;
        return r1181085;
}

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 *-commutative 0.1

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

4. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019163 
(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)))