Average Error: 0.1 → 0.1
Time: 5.5s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\left(1 \cdot \frac{m}{v} - \frac{{m}^{2}}{v}\right) - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\left(1 \cdot \frac{m}{v} - \frac{{m}^{2}}{v}\right) - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r11907 = m;
        double r11908 = 1.0;
        double r11909 = r11908 - r11907;
        double r11910 = r11907 * r11909;
        double r11911 = v;
        double r11912 = r11910 / r11911;
        double r11913 = r11912 - r11908;
        double r11914 = r11913 * r11909;
        return r11914;
}
↓
double f(double m, double v) {
        double r11915 = 1.0;
        double r11916 = m;
        double r11917 = v;
        double r11918 = r11916 / r11917;
        double r11919 = r11915 * r11918;
        double r11920 = 2.0;
        double r11921 = pow(r11916, r11920);
        double r11922 = r11921 / r11917;
        double r11923 = r11919 - r11922;
        double r11924 = r11923 - r11915;
        double r11925 = r11915 - r11916;
        double r11926 = r11924 * r11925;
        return r11926;
}

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 associate-/l*0.1

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

  4. Taylor expanded around 0 0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020034 +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)))