b parameter of renormalized beta distribution

Average Error: 0.1 → 0.1

Time: 18.5s

Precision: 64

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

Math

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

↓

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

C

double f(double m, double v) {
        double r1526213 = m;
        double r1526214 = 1.0;
        double r1526215 = r1526214 - r1526213;
        double r1526216 = r1526213 * r1526215;
        double r1526217 = v;
        double r1526218 = r1526216 / r1526217;
        double r1526219 = r1526218 - r1526214;
        double r1526220 = r1526219 * r1526215;
        return r1526220;
}

↓

double f(double m, double v) {
        double r1526221 = 1.0;
        double r1526222 = m;
        double r1526223 = r1526221 - r1526222;
        double r1526224 = v;
        double r1526225 = r1526224 / r1526223;
        double r1526226 = r1526222 / r1526225;
        double r1526227 = r1526226 - r1526221;
        double r1526228 = r1526223 * r1526227;
        return r1526228;
}

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 2019171 
(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)))