Average Error: 0.1 → 0.1
Time: 15.2s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(-m\right) \cdot \left(\frac{m}{\frac{v}{1 - m}} - 1\right) + \left(\frac{m}{\frac{v}{1 - m}} - 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(-m\right) \cdot \left(\frac{m}{\frac{v}{1 - m}} - 1\right) + \left(\frac{m}{\frac{v}{1 - m}} - 1\right)
double f(double m, double v) {
        double r463847 = m;
        double r463848 = 1.0;
        double r463849 = r463848 - r463847;
        double r463850 = r463847 * r463849;
        double r463851 = v;
        double r463852 = r463850 / r463851;
        double r463853 = r463852 - r463848;
        double r463854 = r463853 * r463849;
        return r463854;
}
↓
double f(double m, double v) {
        double r463855 = m;
        double r463856 = -r463855;
        double r463857 = v;
        double r463858 = 1.0;
        double r463859 = r463858 - r463855;
        double r463860 = r463857 / r463859;
        double r463861 = r463855 / r463860;
        double r463862 = r463861 - r463858;
        double r463863 = r463856 * r463862;
        double r463864 = r463863 + r463862;
        return r463864;
}

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-rgt-in0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019153 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))