Average Error: 0.1 → 0.1
Time: 6.3s
Precision: binary64
\[0 < m \land 0 < v \land v < 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(m + \left(\frac{m - \left(m \cdot m\right) \cdot 2}{v} + -1\right)\right) + \frac{1}{\frac{v}{{m}^{3}}}\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(m + \left(\frac{m - \left(m \cdot m\right) \cdot 2}{v} + -1\right)\right) + \frac{1}{\frac{v}{{m}^{3}}}
(FPCore (m v) :precision binary64 (* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m)))
↓
(FPCore (m v)
 :precision binary64
 (+ (+ m (+ (/ (- m (* (* m m) 2.0)) v) -1.0)) (/ 1.0 (/ v (pow m 3.0)))))
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 - ((m * m) * 2.0)) / v) + -1.0)) + (1.0 / (v / pow(m, 3.0)));
}

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. Simplified0.1

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

  5. Applied clear-num_binary640.1

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

  7. Applied associate--l+_binary640.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020356 
(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)))