Average Error: 0.2 → 0.2
Time: 4.0s
Precision: binary64
\[0 < m \land 0 < v \land v < 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m \]
↓
\[m \cdot \frac{m - m \cdot m}{v} - m \]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
m \cdot \frac{m - m \cdot m}{v} - m

(FPCore (m v) :precision binary64 (* (- (/ (* m (- 1.0 m)) v) 1.0) m))
↓
(FPCore (m v) :precision binary64 (- (* m (/ (- m (* m m)) 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 * ((m - (m * m)) / 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 clear-num_binary640.2

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

  4. Simplified0.2

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

  6. Applied *-un-lft-identity_binary640.2

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

  7. Applied associate-*l*_binary640.2

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

  8. Simplified0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2021197 
(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))