Average Error: 0.1 → 0.1
Time: 27.7s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\left(\frac{m}{v} - \frac{m}{\frac{v}{m}}\right) - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\left(\frac{m}{v} - \frac{m}{\frac{v}{m}}\right) - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r716760 = m;
        double r716761 = 1.0;
        double r716762 = r716761 - r716760;
        double r716763 = r716760 * r716762;
        double r716764 = v;
        double r716765 = r716763 / r716764;
        double r716766 = r716765 - r716761;
        double r716767 = r716766 * r716762;
        return r716767;
}
↓
double f(double m, double v) {
        double r716768 = m;
        double r716769 = v;
        double r716770 = r716768 / r716769;
        double r716771 = r716769 / r716768;
        double r716772 = r716768 / r716771;
        double r716773 = r716770 - r716772;
        double r716774 = 1.0;
        double r716775 = r716773 - r716774;
        double r716776 = r716774 - r716768;
        double r716777 = r716775 * r716776;
        return r716777;
}

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. Simplified0.1

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

  3. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{\left(\frac{m}{v} - \left(\frac{{m}^{2}}{v} + 1\right)\right)} \cdot \left(1 - m\right)\]

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(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)))