Average Error: 0.1 → 0.1
Time: 3.3min
Precision: binary64
Cost: 832
\[0 < m \land 0 < v \land v < 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(1 - m\right) \cdot \left(\frac{m}{\frac{v}{1 - m}} + -1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(1 - m\right) \cdot \left(\frac{m}{\frac{v}{1 - m}} + -1\right)
(FPCore (m v) :precision binary64 (* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m)))
↓
(FPCore (m v) :precision binary64 (* (- 1.0 m) (+ (/ m (/ v (- 1.0 m))) -1.0)))
double code(double m, double v) {
	return (((m * (1.0 - m)) / v) - 1.0) * (1.0 - m);
}
↓
double code(double m, double v) {
	return (1.0 - m) * ((m / (v / (1.0 - m))) + -1.0);
}

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
Cost1153
\[\begin{array}{l} \mathbf{if}\;m \leq 6.567017411048897 \cdot 10^{-09}:\\ \;\;\;\;\left(1 - m\right) \cdot \left(-1 + \frac{m}{v + m \cdot v}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - m\right) \cdot \frac{m}{\frac{v}{1 - m}}\\ \end{array}\]
Alternative 2
Error0.3
Cost1025
\[\begin{array}{l} \mathbf{if}\;m \leq 1.9167553917159296 \cdot 10^{-21}:\\ \;\;\;\;-1 + \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;\left(1 - m\right) \cdot \frac{m}{\frac{v}{1 - m}}\\ \end{array}\]
Alternative 3
Error0.2
Cost1025
\[\begin{array}{l} \mathbf{if}\;m \leq 1.9167553917159296 \cdot 10^{-21}:\\ \;\;\;\;-1 + \frac{m}{v}\\ \mathbf{else}:\\ \;\;\;\;\frac{m + \left(m \cdot m\right) \cdot \left(m + -2\right)}{v}\\ \end{array}\]
Alternative 4
Error2.2
Cost897
\[\begin{array}{l} \mathbf{if}\;m \leq 1.4447632799732713:\\ \;\;\;\;\left(1 - m\right) \cdot \left(-1 + \frac{m}{v}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(m + -1\right) \cdot \left(m \cdot \frac{m}{v}\right)\\ \end{array}\]
Alternative 5
Error9.4
Cost448
\[-1 + \left(m + \frac{m}{v}\right)\]
Alternative 6
Error9.4
Cost320
\[-1 + \frac{m}{v}\]
Alternative 7
Error24.4
Cost652
\[\begin{array}{l} \mathbf{if}\;m \leq 4.141189497662956 \cdot 10^{-180} \lor \neg \left(m \leq 1.0933772138230144 \cdot 10^{-151}\right) \land m \leq 1.7266281413804802 \cdot 10^{-140}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;\frac{m}{v}\\ \end{array}\]
Alternative 8
Error36.8
Cost192
\[m + -1\]
Alternative 9
Error37.1
Cost64
\[-1\]

Error

Time

Derivation

  1. Initial program 0.1

    \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
  2. Using strategy rm

  3. Applied associate-/l*_binary640.1

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

  5. Applied sub-neg_binary640.1

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

  6. Simplified0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2021040 
(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)))