Average Error: 0.2 → 0.2
Time: 3.0s
Precision: binary64
\[0 < m \land 0 < v \land v < 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[1 \cdot \left(\frac{m}{\frac{v}{m}} - m\right) - \frac{m \cdot m}{\frac{v}{m}}\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
1 \cdot \left(\frac{m}{\frac{v}{m}} - m\right) - \frac{m \cdot m}{\frac{v}{m}}
(FPCore (m v) :precision binary64 (* (- (/ (* m (- 1.0 m)) v) 1.0) m))
↓
(FPCore (m v)
 :precision binary64
 (- (* 1.0 (- (/ m (/ v m)) m)) (/ (* m m) (/ v m))))
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) ((m / (v / m)) - m)))) - (((double) (m * 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. Using strategy rm

  3. Applied associate-/l*_binary640.2

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

  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. Using strategy rm

  7. Applied unpow3_binary640.2

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

  8. Applied associate-/l*_binary640.2

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

  9. Taylor expanded around 0 7.1

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

  10. Simplified0.2

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

  11. Final simplification0.2

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

Reproduce

herbie shell --seed 2020210 
(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))