Average Error: 0.2 → 0.2
Time: 3.7s
Precision: binary64
\[0 < m \land 0 < v \land v < 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\frac{m}{\frac{v}{m \cdot \left(1 - m\right)}} - m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\frac{m}{\frac{v}{m \cdot \left(1 - m\right)}} - m
(FPCore (m v) :precision binary64 (* (- (/ (* m (- 1.0 m)) v) 1.0) m))
↓
(FPCore (m v) :precision binary64 (- (/ m (/ v (* m (- 1.0 m)))) m))
double code(double m, double v) {
	return (((m * (1.0 - m)) / v) - 1.0) * m;
}
↓
double code(double m, double v) {
	return (m / (v / (m * (1.0 - m)))) - 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 clear-num_binary640.2

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

  4. Taylor expanded around 0 7.0

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

  5. Simplified0.2

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

  7. Applied associate-/l*_binary640.2

    \[\leadsto \color{blue}{\frac{m}{\frac{\frac{v}{m}}{1 - m}}} - m\]

  8. Simplified0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2020273 
(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))