b parameter of renormalized beta distribution

Average Error: 0.1 → 0.1

Time: 16.9s

Precision: 64

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

Math

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

↓

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

C

double f(double m, double v) {
        double r1384516 = m;
        double r1384517 = 1.0;
        double r1384518 = r1384517 - r1384516;
        double r1384519 = r1384516 * r1384518;
        double r1384520 = v;
        double r1384521 = r1384519 / r1384520;
        double r1384522 = r1384521 - r1384517;
        double r1384523 = r1384522 * r1384518;
        return r1384523;
}

↓

double f(double m, double v) {
        double r1384524 = 1.0;
        double r1384525 = m;
        double r1384526 = r1384524 - r1384525;
        double r1384527 = v;
        double r1384528 = r1384525 / r1384527;
        double r1384529 = r1384526 * r1384528;
        double r1384530 = r1384529 - r1384524;
        double r1384531 = r1384530 * r1384526;
        return r1384531;
}

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. Using strategy rm

5. Applied associate-/r/ 0.1

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

6. Final simplification 0.1

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

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)))