Average Error: 0.1 → 0.1
Time: 9.8s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{1 + m}}{v} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{1 + m}}{v} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r32751 = m;
        double r32752 = 1.0;
        double r32753 = r32752 - r32751;
        double r32754 = r32751 * r32753;
        double r32755 = v;
        double r32756 = r32754 / r32755;
        double r32757 = r32756 - r32752;
        double r32758 = r32757 * r32753;
        return r32758;
}
↓
double f(double m, double v) {
        double r32759 = m;
        double r32760 = 1.0;
        double r32761 = r32760 * r32760;
        double r32762 = r32759 * r32759;
        double r32763 = r32761 - r32762;
        double r32764 = r32759 * r32763;
        double r32765 = r32760 + r32759;
        double r32766 = r32764 / r32765;
        double r32767 = v;
        double r32768 = r32766 / r32767;
        double r32769 = r32768 - r32760;
        double r32770 = r32760 - r32759;
        double r32771 = r32769 * r32770;
        return r32771;
}

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 flip--0.1

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

  4. Applied associate-*r/0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020003 +o rules:numerics
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))