Average Error: 0.1 → 0.1
Time: 21.7s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{\left(m \cdot \left(\sqrt{1} + \sqrt{m}\right)\right) \cdot \left(\sqrt{1} - \sqrt{m}\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{\left(m \cdot \left(\sqrt{1} + \sqrt{m}\right)\right) \cdot \left(\sqrt{1} - \sqrt{m}\right)}{v} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r2010854 = m;
        double r2010855 = 1.0;
        double r2010856 = r2010855 - r2010854;
        double r2010857 = r2010854 * r2010856;
        double r2010858 = v;
        double r2010859 = r2010857 / r2010858;
        double r2010860 = r2010859 - r2010855;
        double r2010861 = r2010860 * r2010856;
        return r2010861;
}
↓
double f(double m, double v) {
        double r2010862 = m;
        double r2010863 = 1.0;
        double r2010864 = sqrt(r2010863);
        double r2010865 = sqrt(r2010862);
        double r2010866 = r2010864 + r2010865;
        double r2010867 = r2010862 * r2010866;
        double r2010868 = r2010864 - r2010865;
        double r2010869 = r2010867 * r2010868;
        double r2010870 = v;
        double r2010871 = r2010869 / r2010870;
        double r2010872 = r2010871 - r2010863;
        double r2010873 = r2010863 - r2010862;
        double r2010874 = r2010872 * r2010873;
        return r2010874;
}

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

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

  4. Applied add-sqr-sqrt0.1

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

  5. Applied difference-of-squares0.1

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

  6. Applied associate-*r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m)))