Average Error: 0.2 → 0.2
Time: 14.2s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[m \cdot \left(\frac{m - m \cdot m}{v} - 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
m \cdot \left(\frac{m - m \cdot m}{v} - 1\right)
double f(double m, double v) {
        double r374170 = m;
        double r374171 = 1.0;
        double r374172 = r374171 - r374170;
        double r374173 = r374170 * r374172;
        double r374174 = v;
        double r374175 = r374173 / r374174;
        double r374176 = r374175 - r374171;
        double r374177 = r374176 * r374170;
        return r374177;
}
↓
double f(double m, double v) {
        double r374178 = m;
        double r374179 = r374178 * r374178;
        double r374180 = r374178 - r374179;
        double r374181 = v;
        double r374182 = r374180 / r374181;
        double r374183 = 1.0;
        double r374184 = r374182 - r374183;
        double r374185 = r374178 * r374184;
        return r374185;
}

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 0.2

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

  2. Taylor expanded around 0 0.2

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

  3. Simplified0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019155 
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) m))