Average Error: 0.1 → 0.1
Time: 21.0s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\left(\frac{\left(1 - m\right) \cdot m}{v} - 1\right) \cdot \left(1 + \sqrt{m}\right)\right) \cdot \left(-\sqrt{m}\right) + \left(\frac{\left(1 - m\right) \cdot m}{v} - 1\right) \cdot \left(1 + \sqrt{m}\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\left(\frac{\left(1 - m\right) \cdot m}{v} - 1\right) \cdot \left(1 + \sqrt{m}\right)\right) \cdot \left(-\sqrt{m}\right) + \left(\frac{\left(1 - m\right) \cdot m}{v} - 1\right) \cdot \left(1 + \sqrt{m}\right)
double f(double m, double v) {
        double r546831 = m;
        double r546832 = 1.0;
        double r546833 = r546832 - r546831;
        double r546834 = r546831 * r546833;
        double r546835 = v;
        double r546836 = r546834 / r546835;
        double r546837 = r546836 - r546832;
        double r546838 = r546837 * r546833;
        return r546838;
}
↓
double f(double m, double v) {
        double r546839 = 1.0;
        double r546840 = m;
        double r546841 = r546839 - r546840;
        double r546842 = r546841 * r546840;
        double r546843 = v;
        double r546844 = r546842 / r546843;
        double r546845 = r546844 - r546839;
        double r546846 = sqrt(r546840);
        double r546847 = r546839 + r546846;
        double r546848 = r546845 * r546847;
        double r546849 = -r546846;
        double r546850 = r546848 * r546849;
        double r546851 = r546850 + r546848;
        return r546851;
}

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 add-sqr-sqrt0.1

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

  4. Applied *-un-lft-identity0.1

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

  5. Applied difference-of-squares0.1

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

  6. Applied associate-*r*0.1

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

  8. Applied sub-neg0.1

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

  9. Applied distribute-rgt-in0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019152 
(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)))