Average Error: 0.2 → 0.2
Time: 3.5s
Precision: binary64
\[0 < m \land 0 < v \land v < 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[1 \cdot \left(m \cdot \frac{m}{v} - m\right) - \frac{{m}^{3}}{v}\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
1 \cdot \left(m \cdot \frac{m}{v} - m\right) - \frac{{m}^{3}}{v}
double code(double m, double v) {
	return ((double) (((double) ((((double) (m * ((double) (1.0 - m)))) / v) - 1.0)) * m));
}
↓
double code(double m, double v) {
	return ((double) (((double) (1.0 * ((double) (((double) (m * (m / v))) - m)))) - (((double) pow(m, 3.0)) / v)));
}

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 associate-/l*0.2

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

  4. Taylor expanded around 0 7.1

    \[\leadsto \color{blue}{1 \cdot \frac{{m}^{2}}{v} - \left(1 \cdot m + \frac{{m}^{3}}{v}\right)}\]

  5. Simplified0.2

    \[\leadsto \color{blue}{1 \cdot \left(m \cdot \frac{m}{v} - m\right) - \frac{{m}^{3}}{v}}\]

  6. Final simplification0.2

    \[\leadsto 1 \cdot \left(m \cdot \frac{m}{v} - m\right) - \frac{{m}^{3}}{v}\]

Reproduce

herbie shell --seed 2020199 
(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))