Average Error: 0.2 → 0.2
Time: 3.7s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\mathsf{fma}\left(1, \frac{m}{\frac{v}{m}}, -\mathsf{fma}\left(1, m, \frac{{m}^{3}}{v}\right)\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\mathsf{fma}\left(1, \frac{m}{\frac{v}{m}}, -\mathsf{fma}\left(1, m, \frac{{m}^{3}}{v}\right)\right)
double code(double m, double v) {
	return ((((m * (1.0 - m)) / v) - 1.0) * m);
}
↓
double code(double m, double v) {
	return fma(1.0, (m / (v / m)), -fma(1.0, m, (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. Taylor expanded around 0 7.1

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

  3. Simplified7.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(1, \frac{{m}^{2}}{v}, -\mathsf{fma}\left(1, m, \frac{{m}^{3}}{v}\right)\right)}\]
  4. Using strategy rm

  5. Applied unpow27.1

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

  6. Applied associate-/l*0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2020105 +o rules:numerics
(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))