a parameter of renormalized beta distribution

Average Error: 0.2 → 0.2

Time: 3.8s

Precision: 64

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

Math

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

↓

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

C

double code(double m, double v) {
	return ((((m * (1.0 - m)) / v) - 1.0) * m);
}

↓

double code(double m, double v) {
	return ((((m * (1.0 - m)) * (1.0 / v)) - 1.0) * m);
}

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 div-inv 0.2

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

4. Final simplification 0.2

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

Reproduce

herbie shell --seed 2020103 +o rules:numerics
(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))