a parameter of renormalized beta distribution

Average Error: 0.2 → 0.2

Time: 4.7s

Precision: 64

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

Math

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

↓

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

C

double f(double m, double v) {
        double r12541 = m;
        double r12542 = 1.0;
        double r12543 = r12542 - r12541;
        double r12544 = r12541 * r12543;
        double r12545 = v;
        double r12546 = r12544 / r12545;
        double r12547 = r12546 - r12542;
        double r12548 = r12547 * r12541;
        return r12548;
}

↓

double f(double m, double v) {
        double r12549 = m;
        double r12550 = 1.0;
        double r12551 = r12550 - r12549;
        double r12552 = r12549 * r12551;
        double r12553 = 1.0;
        double r12554 = pow(r12552, r12553);
        double r12555 = v;
        double r12556 = r12554 / r12555;
        double r12557 = r12556 - r12550;
        double r12558 = r12557 * r12549;
        return r12558;
}

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 pow1 0.2

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

4. Applied pow1 0.2

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

5. Applied pow-prod-down 0.2

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

6. Final simplification 0.2

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

Reproduce

herbie shell --seed 2020047 
(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))