Average Error: 0.2 → 0.2
Time: 4.8s
Precision: binary64
\[0 < m \land 0 < v \land v < 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[m \cdot \frac{m}{\frac{v}{1 - m}} - m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
m \cdot \frac{m}{\frac{v}{1 - m}} - m
(FPCore (m v) :precision binary64 (* (- (/ (* m (- 1.0 m)) v) 1.0) m))
↓
(FPCore (m v) :precision binary64 (- (* m (/ m (/ v (- 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 * (m / (v / (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. Simplified0.2

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

  5. Taylor expanded around 0 7.3

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

  6. Simplified0.2

    \[\leadsto \color{blue}{m \cdot \frac{m - m \cdot m}{v} - m}\]
  7. Using strategy rm

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

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

  9. Applied distribute-rgt-out--_binary640.2

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

  10. Applied associate-/l*_binary640.2

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

  11. Final simplification0.2

    \[\leadsto m \cdot \frac{m}{\frac{v}{1 - m}} - m\]

Alternatives

Reproduce

herbie shell --seed 2021113 
(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))