b parameter of renormalized beta distribution

Average Error: 0.1 → 0.1

Time: 18.8s

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 r21059 = m;
        double r21060 = 1.0;
        double r21061 = r21060 - r21059;
        double r21062 = r21059 * r21061;
        double r21063 = v;
        double r21064 = r21062 / r21063;
        double r21065 = r21064 - r21060;
        double r21066 = r21065 * r21061;
        return r21066;
}

↓

double f(double m, double v) {
        double r21067 = m;
        double r21068 = 1.0;
        double r21069 = r21067 * r21068;
        double r21070 = -r21067;
        double r21071 = r21067 * r21070;
        double r21072 = r21069 + r21071;
        double r21073 = v;
        double r21074 = r21072 / r21073;
        double r21075 = r21074 - r21068;
        double r21076 = r21068 - r21067;
        double r21077 = r21075 * r21076;
        return r21077;
}

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 +o rules:numerics
(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)))