Average Error: 0.1 → 0.1
Time: 6.6s
Precision: binary64
Cost: 7680
\[0 < m \land 0 < v \land v < 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\left(m + \frac{m}{v}\right) - \left(1 + 2 \cdot \left(m \cdot \frac{m}{v}\right)\right)\right) + \frac{{m}^{3}}{v}\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\left(m + \frac{m}{v}\right) - \left(1 + 2 \cdot \left(m \cdot \frac{m}{v}\right)\right)\right) + \frac{{m}^{3}}{v}
(FPCore (m v) :precision binary64 (* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m)))
↓
(FPCore (m v)
 :precision binary64
 (+ (- (+ m (/ m v)) (+ 1.0 (* 2.0 (* m (/ m v))))) (/ (pow m 3.0) v)))
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 + (m / v)) - (1.0 + (2.0 * (m * (m / v))))) + (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

Alternatives

Alternative 1
Error0.1
Cost832
\[\left(1 - m\right) \cdot \left(-1 + \frac{m}{\frac{v}{1 - m}}\right)\]
Alternative 2
Error0.1
Cost832
\[\left(1 - m\right) \cdot \left(-1 + \frac{m - m \cdot m}{v}\right)\]
Alternative 3
Error0.3
Cost1025
\[\begin{array}{l} \mathbf{if}\;m \leq 3.577168187192135 \cdot 10^{-11}:\\ \;\;\;\;\left(m + \frac{m}{v}\right) + -1\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - m}{\frac{v}{m - m \cdot m}}\\ \end{array}\]
Alternative 4
Error0.3
Cost1025
\[\begin{array}{l} \mathbf{if}\;m \leq 3.1628156974903413 \cdot 10^{-12}:\\ \;\;\;\;\left(m + \frac{m}{v}\right) + -1\\ \mathbf{else}:\\ \;\;\;\;\left(1 - m\right) \cdot \left(m \cdot \frac{1 - m}{v}\right)\\ \end{array}\]
Alternative 5
Error2.3
Cost897
\[\begin{array}{l} \mathbf{if}\;m \leq 2.90526406314691:\\ \;\;\;\;\left(m + \frac{m}{v}\right) + -1\\ \mathbf{else}:\\ \;\;\;\;\left(m \cdot \frac{m}{v}\right) \cdot \left(m + -1\right)\\ \end{array}\]
Alternative 6
Error9.6
Cost448
\[\left(m + \frac{m}{v}\right) + -1\]
Alternative 7
Error37.2
Cost64
\[-1\]
Alternative 8
Error61.4
Cost64
\[1\]

Error

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 around 0 0.1

    \[\leadsto \color{blue}{\left(m + \left(\frac{m}{v} + \frac{{m}^{3}}{v}\right)\right) - \left(2 \cdot \frac{{m}^{2}}{v} + 1\right)}\]

  3. Simplified0.1

    \[\leadsto \color{blue}{\left(\left(m + \frac{m}{v}\right) - \left(1 + 2 \cdot \left(\frac{m}{v} \cdot m\right)\right)\right) + \frac{{m}^{3}}{v}}\]

  4. Simplified0.1

    \[\leadsto \color{blue}{\left(\left(m + \frac{m}{v}\right) - \left(1 + 2 \cdot \left(m \cdot \frac{m}{v}\right)\right)\right) + \frac{{m}^{3}}{v}}\]

  5. Final simplification0.1

    \[\leadsto \left(\left(m + \frac{m}{v}\right) - \left(1 + 2 \cdot \left(m \cdot \frac{m}{v}\right)\right)\right) + \frac{{m}^{3}}{v}\]

Reproduce

herbie shell --seed 2021044 
(FPCore (m v)
  :name "b 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) (- 1.0 m)))