Average Error: 0.2 → 0.2
Time: 3.3s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{m}{v} \cdot \left(1 - m\right) - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{m}{v} \cdot \left(1 - m\right) - 1\right) \cdot m
double code(double m, double v) {
	return ((((m * (1.0 - m)) / v) - 1.0) * m);
}
↓
double code(double m, double v) {
	return ((((m / v) * (1.0 - m)) - 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 0.2

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

  3. Applied flip--0.2

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

  4. Applied associate-*r/0.2

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

  5. Applied associate-/l/0.2

    \[\leadsto \left(\color{blue}{\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{v \cdot \left(1 + m\right)}} - 1\right) \cdot m\]
  6. Using strategy rm

  7. Applied flip-+0.2

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

  8. Applied associate-*r/0.2

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

  9. Applied associate-/r/0.2

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

  10. Simplified0.2

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

  11. Final simplification0.2

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

Reproduce

herbie shell --seed 2020066 
(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 m)) v) 1) m))