Average Error: 0.1 → 0.1
Time: 3.6s
Precision: binary64
\[\left(0 < m \land 0 < v\right) \land v < 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right) \]
↓
\[\left(\left(\frac{m}{v} - \sqrt{m} \cdot \frac{{m}^{1.5}}{v}\right) - 1\right) \cdot \left(1 - m\right) \]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\left(\frac{m}{v} - \sqrt{m} \cdot \frac{{m}^{1.5}}{v}\right) - 1\right) \cdot \left(1 - m\right)

(FPCore (m v) :precision binary64 (* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m)))
↓
(FPCore (m v)
 :precision binary64
 (* (- (- (/ m v) (* (sqrt m) (/ (pow m 1.5) v))) 1.0) (- 1.0 m)))
double code(double m, double v) {
	return (((m * (1.0 - m)) / v) - 1.0) * (1.0 - m);
}
↓
double code(double m, double v) {
	return (((m / v) - (sqrt(m) * (pow(m, 1.5) / v))) - 1.0) * (1.0 - 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 0.1

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

  2. Taylor expanded in v around inf 0.1

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

  3. Applied div-sub_binary640.1

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

  4. Simplified0.1

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

  5. Applied *-un-lft-identity_binary640.1

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

  6. Applied add-sqr-sqrt_binary640.1

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

  7. Applied times-frac_binary640.1

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

  8. Applied associate-*l*_binary640.1

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

  9. Simplified0.1

    \[\leadsto \left(\left(\frac{m}{v} - \frac{\sqrt{m}}{1} \cdot \color{blue}{\frac{{m}^{1.5}}{v}}\right) - 1\right) \cdot \left(1 - m\right) \]

  10. Final simplification0.1

    \[\leadsto \left(\left(\frac{m}{v} - \sqrt{m} \cdot \frac{{m}^{1.5}}{v}\right) - 1\right) \cdot \left(1 - m\right) \]

Reproduce

herbie shell --seed 2022082 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (and (< 0.0 m) (< 0.0 v)) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m)))