Average Error: 0.2 → 0.2
Time: 4.8s
Precision: binary64
\[0 < m \land 0 < v \land v < 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[m \cdot \left(\frac{1}{\frac{\frac{v}{m}}{1 - m}} - 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
m \cdot \left(\frac{1}{\frac{\frac{v}{m}}{1 - m}} - 1\right)
(FPCore (m v) :precision binary64 (* (- (/ (* m (- 1.0 m)) v) 1.0) m))
↓
(FPCore (m v) :precision binary64 (* m (- (/ 1.0 (/ (/ v m) (- 1.0 m))) 1.0)))
double code(double m, double v) {
	return (((m * (1.0 - m)) / v) - 1.0) * m;
}
↓
double code(double m, double v) {
	return m * ((1.0 / ((v / m) / (1.0 - m))) - 1.0);
}

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 0.2

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

  3. Applied clear-num_binary64_4180.2

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

  5. Applied associate-/r*_binary64_3630.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020353 
(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))