b parameter of renormalized beta distribution

Average Error: 0.1 → 0.1

Time: 15.7s

Precision: 64

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

Math

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

↓

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

C

double f(double m, double v) {
        double r21469 = m;
        double r21470 = 1.0;
        double r21471 = r21470 - r21469;
        double r21472 = r21469 * r21471;
        double r21473 = v;
        double r21474 = r21472 / r21473;
        double r21475 = r21474 - r21470;
        double r21476 = r21475 * r21471;
        return r21476;
}

↓

double f(double m, double v) {
        double r21477 = 1.0;
        double r21478 = m;
        double r21479 = r21477 * r21478;
        double r21480 = -r21478;
        double r21481 = r21480 * r21478;
        double r21482 = r21479 + r21481;
        double r21483 = v;
        double r21484 = r21482 / r21483;
        double r21485 = r21484 - r21477;
        double r21486 = r21477 - r21478;
        double r21487 = r21485 * r21486;
        return r21487;
}

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-rgt-in 0.1

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

5. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019305 
(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)))