Average Error: 0.1 → 0.1
Time: 4.9s
Precision: binary64
\[0 < m \land 0 < v \land v < 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(-1 + \frac{m}{v} \cdot \left(1 - m\right)\right) + m \cdot \left(1 - \frac{m}{v} \cdot \left(1 - m\right)\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(-1 + \frac{m}{v} \cdot \left(1 - m\right)\right) + m \cdot \left(1 - \frac{m}{v} \cdot \left(1 - m\right)\right)
(FPCore (m v) :precision binary64 (* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m)))
↓
(FPCore (m v)
 :precision binary64
 (+ (+ -1.0 (* (/ m v) (- 1.0 m))) (* m (- 1.0 (* (/ m v) (- 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 (-1.0 + ((m / v) * (1.0 - m))) + (m * (1.0 - ((m / v) * (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 sub-neg_binary640.1

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

  4. Applied distribute-rgt-in_binary640.1

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

  5. Simplified0.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Alternatives

Reproduce

herbie shell --seed 2021118 
(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)))