a parameter of renormalized beta distribution

Average Error: 0.2 → 0.2

Time: 20.5s

Precision: 64

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

Math

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

↓

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

C

double f(double m, double v) {
        double r813461 = m;
        double r813462 = 1.0;
        double r813463 = r813462 - r813461;
        double r813464 = r813461 * r813463;
        double r813465 = v;
        double r813466 = r813464 / r813465;
        double r813467 = r813466 - r813462;
        double r813468 = r813467 * r813461;
        return r813468;
}

↓

double f(double m, double v) {
        double r813469 = 1.0;
        double r813470 = v;
        double r813471 = m;
        double r813472 = r813469 - r813471;
        double r813473 = r813471 * r813472;
        double r813474 = r813470 / r813473;
        double r813475 = r813469 / r813474;
        double r813476 = r813475 - r813469;
        double r813477 = r813476 * r813471;
        return r813477;
}

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 2019158 +o rules:numerics
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) m))