Average Error: 0.2 → 0.2
Time: 3.5s
Precision: binary64
\[0 < m \land 0 < v \land v < 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[m \cdot \left(m \cdot \frac{1 - m}{v}\right) - m \cdot 1\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
m \cdot \left(m \cdot \frac{1 - m}{v}\right) - m \cdot 1
(FPCore (m v) :precision binary64 (* (- (/ (* m (- 1.0 m)) v) 1.0) m))
↓
(FPCore (m v) :precision binary64 (- (* m (* m (/ (- 1.0 m) v))) (* m 1.0)))
double code(double m, double v) {
	return ((double) (((double) ((((double) (m * ((double) (1.0 - m)))) / v) - 1.0)) * m));
}
↓
double code(double m, double v) {
	return ((double) (((double) (m * ((double) (m * (((double) (1.0 - m)) / v))))) - ((double) (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 Error: 0.2 bits

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

  2. SimplifiedError: 0.2 bits

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

  4. Applied sub-negError: 0.2 bits

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

  5. Applied distribute-lft-inError: 0.2 bits

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

  6. Final simplificationError: 0.2 bits

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

Reproduce

herbie shell --seed 2020204 
(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))