Average Error: 0.2 → 0.2
Time: 4.3s
Precision: binary64
\[0 < m \land 0 < v \land v < 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m \]
↓
\[m \cdot \frac{{m}^{3} - m}{v \cdot \left(-1 - m\right)} - m \]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
m \cdot \frac{{m}^{3} - m}{v \cdot \left(-1 - m\right)} - m

(FPCore (m v) :precision binary64 (* (- (/ (* m (- 1.0 m)) v) 1.0) m))
↓
(FPCore (m v)
 :precision binary64
 (- (* m (/ (- (pow m 3.0) m) (* v (- -1.0 m)))) m))
double code(double m, double v) {
	return (((m * (1.0 - m)) / v) - 1.0) * m;
}
↓
double code(double m, double v) {
	return (m * ((pow(m, 3.0) - m) / (v * (-1.0 - m)))) - 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 flip--_binary640.2

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

  4. Applied associate-*r/_binary640.2

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

  5. Applied associate-/l/_binary640.2

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

  6. Simplified0.2

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

  7. Taylor expanded around 0 7.2

    \[\leadsto \color{blue}{\frac{{m}^{2}}{v \cdot \left(1 + m\right)} - \left(\frac{{m}^{4}}{v \cdot \left(1 + m\right)} + m\right)} \]

  8. Simplified0.2

    \[\leadsto \color{blue}{m \cdot \frac{m - {m}^{3}}{v \cdot \left(m + 1\right)} - m} \]
  9. Using strategy rm

  10. Applied frac-2neg_binary640.2

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

  11. Simplified0.2

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

  12. Simplified0.2

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

  13. Final simplification0.2

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

Reproduce

herbie shell --seed 2021204 
(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))