Average Error: 0.1 → 0.1
Time: 4.6s
Precision: binary64
\[0 < m \land 0 < v \land v < 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right) \]
↓
\[\left(\left(\frac{m}{v} - \frac{m \cdot m}{v}\right) - 1\right) \cdot \left(1 - m\right) \]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\left(\frac{m}{v} - \frac{m \cdot m}{v}\right) - 1\right) \cdot \left(1 - m\right)

(FPCore (m v) :precision binary64 (* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m)))
↓
(FPCore (m v)
 :precision binary64
 (* (- (- (/ m v) (/ (* m m) v)) 1.0) (- 1.0 m)))
double code(double m, double v) {
	return (((m * (1.0 - m)) / v) - 1.0) * (1.0 - m);
}
↓
double code(double m, double v) {
	return (((m / v) - ((m * m) / v)) - 1.0) * (1.0 - 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 0.1

    \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right) \]
  2. Using strategy rm

  3. Applied flip3--_binary640.1

    \[\leadsto \left(\frac{m \cdot \color{blue}{\frac{{1}^{3} - {m}^{3}}{1 \cdot 1 + \left(m \cdot m + 1 \cdot m\right)}}}{v} - 1\right) \cdot \left(1 - m\right) \]

  4. Applied associate-*r/_binary640.7

    \[\leadsto \left(\frac{\color{blue}{\frac{m \cdot \left({1}^{3} - {m}^{3}\right)}{1 \cdot 1 + \left(m \cdot m + 1 \cdot m\right)}}}{v} - 1\right) \cdot \left(1 - m\right) \]

  5. Simplified0.7

    \[\leadsto \left(\frac{\frac{\color{blue}{m + \left(-{m}^{4}\right)}}{1 \cdot 1 + \left(m \cdot m + 1 \cdot m\right)}}{v} - 1\right) \cdot \left(1 - m\right) \]

  6. Taylor expanded around 0 0.1

    \[\leadsto \left(\color{blue}{\left(\frac{m}{v} - \frac{{m}^{2}}{v}\right)} - 1\right) \cdot \left(1 - m\right) \]

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2021198 
(FPCore (m v)
  :name "b 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) (- 1.0 m)))