Average Error: 0.1 → 0.1
Time: 5.1s
Precision: binary64
\[0 < m \land 0 < v \land v < 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(m + \left(\frac{m}{v} + \frac{{m}^{3}}{v}\right)\right) - \left(2 \cdot \frac{{m}^{2}}{v} + 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(m + \left(\frac{m}{v} + \frac{{m}^{3}}{v}\right)\right) - \left(2 \cdot \frac{{m}^{2}}{v} + 1\right)
(FPCore (m v) :precision binary64 (* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m)))
↓
(FPCore (m v)
 :precision binary64
 (- (+ m (+ (/ m v) (/ (pow m 3.0) v))) (+ (* 2.0 (/ (pow m 2.0) v)) 1.0)))
double code(double m, double v) {
	return (((m * (1.0 - m)) / v) - 1.0) * (1.0 - m);
}
↓
double code(double m, double v) {
	return (m + ((m / v) + (pow(m, 3.0) / v))) - ((2.0 * (pow(m, 2.0) / v)) + 1.0);
}

Error

Bits error versus m

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  2. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{\left(m + \left(\frac{m}{v} + \frac{{m}^{3}}{v}\right)\right) - \left(2 \cdot \frac{{m}^{2}}{v} + 1\right)}\]

  3. Final simplification0.1

    \[\leadsto \left(m + \left(\frac{m}{v} + \frac{{m}^{3}}{v}\right)\right) - \left(2 \cdot \frac{{m}^{2}}{v} + 1\right)\]

Reproduce

herbie shell --seed 2021013 
(FPCore (m v)
  :name "b 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) (- 1.0 m)))