Average Error: 0.2 → 0.2
Time: 11.2s
Precision: binary64
\[0 < m \land 0 < v \land v < 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[m \cdot \left(\left(-1 + \frac{m}{v}\right) - \frac{m}{\frac{v}{m}}\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
m \cdot \left(\left(-1 + \frac{m}{v}\right) - \frac{m}{\frac{v}{m}}\right)
(FPCore (m v) :precision binary64 (* (- (/ (* m (- 1.0 m)) v) 1.0) m))
↓
(FPCore (m v) :precision binary64 (* m (- (+ -1.0 (/ m v)) (/ m (/ v m)))))
double code(double m, double v) {
	return (((m * (1.0 - m)) / v) - 1.0) * m;
}
↓
double code(double m, double v) {
	return m * ((-1.0 + (m / v)) - (m / (v / 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. Taylor expanded around 0 6.9

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

  3. Simplified0.2

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

  5. Applied div-sub_binary64_7650.2

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

  6. Applied associate-+r-_binary64_6940.2

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

  8. Applied associate-/l*_binary64_7050.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2021091 
(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))