Average Error: 0.1 → 0.1
Time: 5.0s
Precision: binary64
\[0 < m \land 0 < v \land v < 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right) \]
↓
\[\begin{array}{l} t_0 := \frac{m \cdot \left(1 - m\right)}{v}\\ \left(t_0 - 1\right) + m \cdot \left(1 - t_0\right) \end{array} \]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\begin{array}{l}
t_0 := \frac{m \cdot \left(1 - m\right)}{v}\\
\left(t_0 - 1\right) + m \cdot \left(1 - t_0\right)
\end{array}

(FPCore (m v) :precision binary64 (* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m)))
↓
(FPCore (m v)
 :precision binary64
 (let* ((t_0 (/ (* m (- 1.0 m)) v))) (+ (- t_0 1.0) (* m (- 1.0 t_0)))))
double code(double m, double v) {
	return (((m * (1.0 - m)) / v) - 1.0) * (1.0 - m);
}
↓
double code(double m, double v) {
	double t_0 = (m * (1.0 - m)) / v;
	return (t_0 - 1.0) + (m * (1.0 - t_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 0.1

    \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right) \]
  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-lft-in_binary640.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2021190 
(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)))