Average Error: 0.2 → 0.2
Time: 6.5s
Precision: binary64
\[0 < m \land 0 < v \land v < 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m \]
↓
\[m \cdot \left(-1 + \frac{m}{\frac{-v}{m + -1}}\right) \]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
m \cdot \left(-1 + \frac{m}{\frac{-v}{m + -1}}\right)

(FPCore (m v) :precision binary64 (* (- (/ (* m (- 1.0 m)) v) 1.0) m))
↓
(FPCore (m v) :precision binary64 (* m (+ -1.0 (/ m (/ (- v) (+ 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 + (m / (-v / (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. Applied frac-2neg_binary640.2

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

  3. Simplified0.2

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

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

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

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

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

  6. Applied associate-/l*_binary640.2

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

  7. Simplified0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2021220 
(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))