Average Error: 0.2 → 0.2
Time: 3.8s
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. Taylor expanded around 0 7.0

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

  7. Simplified0.2

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

  9. Applied sub-neg_binary640.2

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

  10. Applied distribute-lft-in_binary640.2

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

  11. Applied associate--l+_binary640.2

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

  12. Simplified0.2

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

  13. Final simplification0.2

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

Reproduce

herbie shell --seed 2021139 
(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))