Average Error: 0.2 → 0.2
Time: 22.0s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(m - m \cdot m\right) \cdot \frac{m}{v} - m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(m - m \cdot m\right) \cdot \frac{m}{v} - m
double f(double m, double v) {
        double r584180 = m;
        double r584181 = 1.0;
        double r584182 = r584181 - r584180;
        double r584183 = r584180 * r584182;
        double r584184 = v;
        double r584185 = r584183 / r584184;
        double r584186 = r584185 - r584181;
        double r584187 = r584186 * r584180;
        return r584187;
}
↓
double f(double m, double v) {
        double r584188 = m;
        double r584189 = r584188 * r584188;
        double r584190 = r584188 - r584189;
        double r584191 = v;
        double r584192 = r584188 / r584191;
        double r584193 = r584190 * r584192;
        double r584194 = r584193 - r584188;
        return r584194;
}

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 6.9

    \[\leadsto \color{blue}{\frac{{m}^{2}}{v} - \left(m + \frac{{m}^{3}}{v}\right)}\]

  3. Simplified0.2

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

  4. Taylor expanded around inf 6.9

    \[\leadsto \color{blue}{\frac{{m}^{2}}{v} - \left(m + \frac{{m}^{3}}{v}\right)}\]

  5. Simplified0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019149 
(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))