Average Error: 0.2 → 0.3
Time: 23.7s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{1 - m}{v} \cdot m - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{1 - m}{v} \cdot m - 1\right) \cdot m
double f(double m, double v) {
        double r19120 = m;
        double r19121 = 1.0;
        double r19122 = r19121 - r19120;
        double r19123 = r19120 * r19122;
        double r19124 = v;
        double r19125 = r19123 / r19124;
        double r19126 = r19125 - r19121;
        double r19127 = r19126 * r19120;
        return r19127;
}
↓
double f(double m, double v) {
        double r19128 = 1.0;
        double r19129 = m;
        double r19130 = r19128 - r19129;
        double r19131 = v;
        double r19132 = r19130 / r19131;
        double r19133 = r19132 * r19129;
        double r19134 = r19133 - r19128;
        double r19135 = r19134 * r19129;
        return r19135;
}

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

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

  3. Simplified0.3

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

  4. Final simplification0.3

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

Reproduce

herbie shell --seed 2019323 
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) m))