Average Error: 0.1 → 0.1
Time: 23.4s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(\sqrt{m} + 1\right)\right) \cdot \left(1 - \sqrt{m}\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(\sqrt{m} + 1\right)\right) \cdot \left(1 - \sqrt{m}\right)
double f(double m, double v) {
        double r837810 = m;
        double r837811 = 1.0;
        double r837812 = r837811 - r837810;
        double r837813 = r837810 * r837812;
        double r837814 = v;
        double r837815 = r837813 / r837814;
        double r837816 = r837815 - r837811;
        double r837817 = r837816 * r837812;
        return r837817;
}
↓
double f(double m, double v) {
        double r837818 = m;
        double r837819 = 1.0;
        double r837820 = r837819 - r837818;
        double r837821 = r837818 * r837820;
        double r837822 = v;
        double r837823 = r837821 / r837822;
        double r837824 = r837823 - r837819;
        double r837825 = sqrt(r837818);
        double r837826 = r837825 + r837819;
        double r837827 = r837824 * r837826;
        double r837828 = r837819 - r837825;
        double r837829 = r837827 * r837828;
        return r837829;
}

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. Final simplification0.1

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

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)))