Average Error: 0.2 → 0.2
Time: 5.3s
Precision: binary64
Cost: 704
\[0 < m \land 0 < v \land v < 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[m \cdot \left(\frac{m}{\frac{v}{1 - m}} - 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
m \cdot \left(\frac{m}{\frac{v}{1 - m}} - 1\right)
(FPCore (m v) :precision binary64 (* (- (/ (* m (- 1.0 m)) v) 1.0) m))
↓
(FPCore (m v) :precision binary64 (* m (- (/ m (/ v (- 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 * ((m / (v / (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

Alternatives

Alternative 1
Error0.2
Cost704
\[m \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)\]
Alternative 2
Error0.4
Cost897
\[\begin{array}{l} \mathbf{if}\;m \leq 3.577168187192135 \cdot 10^{-11}:\\ \;\;\;\;\frac{m}{\frac{v}{m}} - m\\ \mathbf{else}:\\ \;\;\;\;m \cdot \frac{m}{\frac{v}{1 - m}}\\ \end{array}\]
Alternative 3
Error2.4
Cost833
\[\begin{array}{l} \mathbf{if}\;m \leq 1.0658776399970118:\\ \;\;\;\;\frac{m}{\frac{v}{m}} - m\\ \mathbf{else}:\\ \;\;\;\;m \cdot \left(\frac{m}{v} \cdot \left(-m\right)\right)\\ \end{array}\]
Alternative 4
Error10.3
Cost448
\[\frac{m}{\frac{v}{m}} - m\]
Alternative 5
Error10.3
Cost448
\[m \cdot \frac{m}{v} - m\]
Alternative 6
Error36.6
Cost128
\[-m\]
Alternative 7
Error61.1
Cost64
\[0\]
Alternative 8
Error61.4
Cost64
\[1\]

Error

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 associate-/l*_binary64_3640.2

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

  4. Simplified0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2021044 
(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))