Average Error: 0.1 → 0.1
Time: 4.4s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m}{\frac{v}{1 - m}} - 1\right) \cdot 1 + \left(\frac{m}{\frac{v}{1 - m}} - 1\right) \cdot \left(-m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{m}{\frac{v}{1 - m}} - 1\right) \cdot 1 + \left(\frac{m}{\frac{v}{1 - m}} - 1\right) \cdot \left(-m\right)
double f(double m, double v) {
        double r14904 = m;
        double r14905 = 1.0;
        double r14906 = r14905 - r14904;
        double r14907 = r14904 * r14906;
        double r14908 = v;
        double r14909 = r14907 / r14908;
        double r14910 = r14909 - r14905;
        double r14911 = r14910 * r14906;
        return r14911;
}
↓
double f(double m, double v) {
        double r14912 = m;
        double r14913 = v;
        double r14914 = 1.0;
        double r14915 = r14914 - r14912;
        double r14916 = r14913 / r14915;
        double r14917 = r14912 / r14916;
        double r14918 = r14917 - r14914;
        double r14919 = r14918 * r14914;
        double r14920 = -r14912;
        double r14921 = r14918 * r14920;
        double r14922 = r14919 + r14921;
        return r14922;
}

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. Using strategy rm

  3. Applied associate-/l*0.1

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

  5. Applied sub-neg0.1

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

  6. Applied distribute-lft-in0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020065 
(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 m)) v) 1) (- 1 m)))