Average Error: 0.1 → 0.1
Time: 14.3s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(1 - m\right) \cdot \left(\left(\frac{m}{v} \cdot 1 - \frac{m \cdot m}{v}\right) - 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(1 - m\right) \cdot \left(\left(\frac{m}{v} \cdot 1 - \frac{m \cdot m}{v}\right) - 1\right)
double f(double m, double v) {
        double r24779 = m;
        double r24780 = 1.0;
        double r24781 = r24780 - r24779;
        double r24782 = r24779 * r24781;
        double r24783 = v;
        double r24784 = r24782 / r24783;
        double r24785 = r24784 - r24780;
        double r24786 = r24785 * r24781;
        return r24786;
}
↓
double f(double m, double v) {
        double r24787 = 1.0;
        double r24788 = m;
        double r24789 = r24787 - r24788;
        double r24790 = v;
        double r24791 = r24788 / r24790;
        double r24792 = r24791 * r24787;
        double r24793 = r24788 * r24788;
        double r24794 = r24793 / r24790;
        double r24795 = r24792 - r24794;
        double r24796 = r24795 - r24787;
        double r24797 = r24789 * r24796;
        return r24797;
}

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. Taylor expanded around 0 0.1

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

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019179 
(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)))