Average Error: 0.1 → 0.1
Time: 9.0s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(\sqrt{1} + \sqrt{m}\right)\right) \cdot \left(\sqrt{1} - \sqrt{m}\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(\sqrt{1} + \sqrt{m}\right)\right) \cdot \left(\sqrt{1} - \sqrt{m}\right)
double f(double m, double v) {
        double r13850 = m;
        double r13851 = 1.0;
        double r13852 = r13851 - r13850;
        double r13853 = r13850 * r13852;
        double r13854 = v;
        double r13855 = r13853 / r13854;
        double r13856 = r13855 - r13851;
        double r13857 = r13856 * r13852;
        return r13857;
}
↓
double f(double m, double v) {
        double r13858 = m;
        double r13859 = 1.0;
        double r13860 = r13859 - r13858;
        double r13861 = r13858 * r13860;
        double r13862 = v;
        double r13863 = r13861 / r13862;
        double r13864 = r13863 - r13859;
        double r13865 = sqrt(r13859);
        double r13866 = sqrt(r13858);
        double r13867 = r13865 + r13866;
        double r13868 = r13864 * r13867;
        double r13869 = r13865 - r13866;
        double r13870 = r13868 * r13869;
        return r13870;
}

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 add-sqr-sqrt0.1

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

  5. Applied difference-of-squares0.1

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

  6. Applied associate-*r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(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)))