Average Error: 0.2 → 0.4
Time: 3.7s
Precision: binary64
\[0 < m \land 0 < v \land v < 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\frac{m}{\sqrt{v}} \cdot \frac{m - m \cdot m}{\sqrt{v}} - m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\frac{m}{\sqrt{v}} \cdot \frac{m - m \cdot m}{\sqrt{v}} - m
(FPCore (m v) :precision binary64 (* (- (/ (* m (- 1.0 m)) v) 1.0) m))
↓
(FPCore (m v)
 :precision binary64
 (- (* (/ m (sqrt v)) (/ (- m (* m m)) (sqrt 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 / sqrt(v)) * ((m - (m * m)) / sqrt(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 frac-2neg_binary640.2

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

  4. Simplified0.2

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

  5. Taylor expanded around 0 7.0

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

  6. Simplified0.2

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

  8. Applied add-sqr-sqrt_binary640.3

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

  9. Applied *-un-lft-identity_binary640.3

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

  10. Applied times-frac_binary640.4

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

  11. Applied associate-*r*_binary640.4

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

  12. Simplified0.4

    \[\leadsto \color{blue}{\frac{-m}{\sqrt{v}}} \cdot \frac{m \cdot m - m}{\sqrt{v}} - m\]

  13. Final simplification0.4

    \[\leadsto \frac{m}{\sqrt{v}} \cdot \frac{m - m \cdot m}{\sqrt{v}} - m\]

Reproduce

herbie shell --seed 2020262 
(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))