Average Error: 0.1 → 0.1
Time: 50.1s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\left(\sqrt{1} + \sqrt{m}\right) \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)\right) \cdot \left(\sqrt{1} - \sqrt{m}\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\left(\sqrt{1} + \sqrt{m}\right) \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)\right) \cdot \left(\sqrt{1} - \sqrt{m}\right)
double f(double m, double v) {
        double r2023825 = m;
        double r2023826 = 1.0;
        double r2023827 = r2023826 - r2023825;
        double r2023828 = r2023825 * r2023827;
        double r2023829 = v;
        double r2023830 = r2023828 / r2023829;
        double r2023831 = r2023830 - r2023826;
        double r2023832 = r2023831 * r2023827;
        return r2023832;
}
↓
double f(double m, double v) {
        double r2023833 = 1.0;
        double r2023834 = sqrt(r2023833);
        double r2023835 = m;
        double r2023836 = sqrt(r2023835);
        double r2023837 = r2023834 + r2023836;
        double r2023838 = r2023833 - r2023835;
        double r2023839 = r2023835 * r2023838;
        double r2023840 = v;
        double r2023841 = r2023839 / r2023840;
        double r2023842 = r2023841 - r2023833;
        double r2023843 = r2023837 * r2023842;
        double r2023844 = r2023834 - r2023836;
        double r2023845 = r2023843 * r2023844;
        return r2023845;
}

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

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

Reproduce

herbie shell --seed 2019168 +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)))