Average Error: 0.1 → 0.1
Time: 4.0s
Precision: binary64
\[\left(0 < m \land 0 < v\right) \land v < 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right) \]
↓
\[\left({m}^{3} \cdot \frac{1}{v} + \left(m + \frac{m}{v}\right)\right) - \left(1 + 2 \cdot \frac{{m}^{2}}{v}\right) \]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left({m}^{3} \cdot \frac{1}{v} + \left(m + \frac{m}{v}\right)\right) - \left(1 + 2 \cdot \frac{{m}^{2}}{v}\right)

(FPCore (m v) :precision binary64 (* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m)))
↓
(FPCore (m v)
 :precision binary64
 (-
  (+ (* (pow m 3.0) (/ 1.0 v)) (+ m (/ m v)))
  (+ 1.0 (* 2.0 (/ (pow m 2.0) v)))))
double code(double m, double v) {
	return (((m * (1.0 - m)) / v) - 1.0) * (1.0 - m);
}
↓
double code(double m, double v) {
	return ((pow(m, 3.0) * (1.0 / v)) + (m + (m / v))) - (1.0 + (2.0 * (pow(m, 2.0) / v)));
}

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 in m around 0 0.1

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

  3. Applied div-inv_binary640.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2021307 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (and (< 0.0 m) (< 0.0 v)) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m)))