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

  3. Applied *-un-lft-identity_binary640.2

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

  4. Applied times-frac_binary640.2

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

  5. Simplified0.2

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

  7. Applied add-sqr-sqrt_binary640.6

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

  8. Applied associate-*r*_binary640.6

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

  9. Simplified0.6

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

  10. Taylor expanded around 0 7.2

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

  11. Simplified0.2

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

  12. Final simplification0.2

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

Reproduce

herbie shell --seed 2020232 
(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))