Average Error: 0.1 → 0.1
Time: 3.2s
Precision: binary64
\[\left(0 < m \land 0 < v\right) \land v < 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right) \]
↓
\[\left(\frac{m \cdot \left(1 - {m}^{2}\right)}{v \cdot \left(1 + m\right)} - 1\right) \cdot \left(1 - m\right) \]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{m \cdot \left(1 - {m}^{2}\right)}{v \cdot \left(1 + m\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 (- 1.0 (pow m 2.0))) (* v (+ 1.0 m))) 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 * (1.0 - pow(m, 2.0))) / (v * (1.0 + m))) - 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. Applied egg-rr0.1

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

  3. Taylor expanded in v around 0 0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2022129 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (and (< 0.0 m) (< 0.0 v)) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m)))