a parameter of renormalized beta distribution

Average Error: 0.2 → 0.2

Time: 5.2s

Precision: 64

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

Math

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

↓

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

C

double f(double m, double v) {
        double r13469 = m;
        double r13470 = 1.0;
        double r13471 = r13470 - r13469;
        double r13472 = r13469 * r13471;
        double r13473 = v;
        double r13474 = r13472 / r13473;
        double r13475 = r13474 - r13470;
        double r13476 = r13475 * r13469;
        return r13476;
}

↓

double f(double m, double v) {
        double r13477 = 1.0;
        double r13478 = v;
        double r13479 = m;
        double r13480 = 1.0;
        double r13481 = r13480 - r13479;
        double r13482 = r13479 * r13481;
        double r13483 = r13478 / r13482;
        double r13484 = r13477 / r13483;
        double r13485 = r13484 - r13480;
        double r13486 = r13485 * r13479;
        return r13486;
}

Error

Bits error versus m

Bits error versus v

Derivation

1. Initial program 0.2

   \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
2. Using strategy rm

3. Applied clear-num 0.2

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

4. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019347 
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) m))