Average Error: 0.2 → 0.2
Time: 4.5s
Precision: binary64
\[0 < m \land 0 < v \land v < 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(m \cdot \frac{m}{v} + \frac{{\left(-m\right)}^{3}}{v}\right) - m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(m \cdot \frac{m}{v} + \frac{{\left(-m\right)}^{3}}{v}\right) - m
(FPCore (m v) :precision binary64 (* (- (/ (* m (- 1.0 m)) v) 1.0) m))
↓
(FPCore (m v)
 :precision binary64
 (- (+ (* m (/ m v)) (/ (pow (- m) 3.0) v)) m))
double code(double m, double v) {
	return (((m * (1.0 - m)) / v) - 1.0) * m;
}
↓
double code(double m, double v) {
	return ((m * (m / v)) + (pow(-m, 3.0) / v)) - m;
}

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 0.2

    \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt_binary64_4410.4

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

  4. Applied times-frac_binary64_4250.4

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

  5. Taylor expanded around 0 6.8

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

  6. Simplified0.2

    \[\leadsto \color{blue}{\frac{m}{v} \cdot \left(m - m \cdot m\right) - m}\]
  7. Using strategy rm

  8. Applied sub-neg_binary64_4120.2

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

  9. Applied distribute-rgt-in_binary64_3690.2

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

  10. Simplified0.2

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

  11. Final simplification0.2

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

Reproduce

herbie shell --seed 2020357 
(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))