b parameter of renormalized beta distribution

Average Error: 0.1 → 0.1

Time: 2.6m

Precision: 64

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

Math

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

↓

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

C

double f(double m, double v) {
        double r12201430 = m;
        double r12201431 = 1.0;
        double r12201432 = r12201431 - r12201430;
        double r12201433 = r12201430 * r12201432;
        double r12201434 = v;
        double r12201435 = r12201433 / r12201434;
        double r12201436 = r12201435 - r12201431;
        double r12201437 = r12201436 * r12201432;
        return r12201437;
}

↓

double f(double m, double v) {
        double r12201438 = 1.0;
        double r12201439 = m;
        double r12201440 = r12201438 - r12201439;
        double r12201441 = v;
        double r12201442 = r12201441 / r12201440;
        double r12201443 = r12201439 / r12201442;
        double r12201444 = r12201443 - r12201438;
        double r12201445 = r12201440 * r12201444;
        return r12201445;
}

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 2019124 +o rules:numerics
(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)))