a parameter of renormalized beta distribution

Average Error: 0.2 → 0.2

Time: 3.3s

Precision: binary64

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

Math

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

↓

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

FPCore

(FPCore (m v) :precision binary64 (* (- (/ (* m (- 1.0 m)) v) 1.0) m))

↓

(FPCore (m v) :precision binary64 (* m (- (/ (- (* m m) m) (- v)) 1.0)))

C

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

↓

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

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 frac-2neg_binary64 0.2

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

4. Simplified 0.2

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

5. Final simplification 0.2

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

Reproduce

herbie shell --seed 2020219 
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) m))