Average Error: 0.2 → 0.7
Time: 3.7s
Precision: binary64
\[0 < m \land 0 < v \land v < 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[m \cdot \left(\frac{m \cdot \left({1}^{3} - {m}^{3}\right)}{v \cdot \left(m \cdot m + 1 \cdot \left(m + 1\right)\right)} - 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
m \cdot \left(\frac{m \cdot \left({1}^{3} - {m}^{3}\right)}{v \cdot \left(m \cdot m + 1 \cdot \left(m + 1\right)\right)} - 1\right)
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) (m * ((double) ((((double) (m * ((double) (((double) pow(1.0, 3.0)) - ((double) pow(m, 3.0)))))) / ((double) (v * ((double) (((double) (m * m)) + ((double) (1.0 * ((double) (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 flip3--0.2

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

  4. Applied associate-*r/0.7

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

  5. Applied associate-/l/0.7

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

  6. Simplified0.7

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

  7. Final simplification0.7

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

Reproduce

herbie shell --seed 2020196 
(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))