Average Error: 0.2 → 0.2
Time: 12.1s
Precision: binary64
\[0 < m \land 0 < v \land v < 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[m \cdot \left(\frac{m \cdot \left(1 - m \cdot m\right)}{v \cdot \left(m + 1\right)} - 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
m \cdot \left(\frac{m \cdot \left(1 - m \cdot m\right)}{v \cdot \left(m + 1\right)} - 1\right)
(FPCore (m v) :precision binary64 (* (- (/ (* m (- 1.0 m)) v) 1.0) m))
↓
(FPCore (m v)
 :precision binary64
 (* m (- (/ (* m (- 1.0 (* m m))) (* v (+ m 1.0))) 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 * (((m * (1.0 - (m * m))) / (v * (m + 1.0))) - 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. Using strategy rm

  3. Applied flip--_binary64_7350.2

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

  4. Applied associate-*r/_binary64_7020.2

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

  5. Applied associate-/l/_binary64_7070.2

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

  6. Final simplification0.2

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

Alternatives

Reproduce

herbie shell --seed 2021102 
(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))