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

↓

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

double f(double m, double v) {
        double r1301602 = m;
        double r1301603 = 1.0;
        double r1301604 = r1301603 - r1301602;
        double r1301605 = r1301602 * r1301604;
        double r1301606 = v;
        double r1301607 = r1301605 / r1301606;
        double r1301608 = r1301607 - r1301603;
        double r1301609 = r1301608 * r1301602;
        return r1301609;
}

↓

double f(double m, double v) {
        double r1301610 = m;
        double r1301611 = r1301610 * r1301610;
        double r1301612 = r1301610 - r1301611;
        double r1301613 = v;
        double r1301614 = r1301610 / r1301613;
        double r1301615 = r1301612 * r1301614;
        double r1301616 = r1301615 - r1301610;
        return r1301616;
}

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

↓

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

Derivation

Initial program 0.2
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
Simplified0.2
\[\leadsto \color{blue}{\frac{m}{v} \cdot \left(m - m \cdot m\right) - m}\]
Taylor expanded around 0 0.2
\[\leadsto \frac{m}{v} \cdot \color{blue}{\left(m - {m}^{2}\right)} - m\]
Simplified0.2
\[\leadsto \frac{m}{v} \cdot \color{blue}{\left(m - m \cdot m\right)} - m\]
Final simplification0.2
\[\leadsto \left(m - m \cdot m\right) \cdot \frac{m}{v} - m\]

Reproduce

herbie shell --seed 2019101 
(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))

Error

Derivation

Reproduce