Average Error: 0.2 → 0.2
Time: 19.1s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\left(\frac{1 \cdot m}{v} - \frac{m}{v} \cdot m\right) - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\left(\frac{1 \cdot m}{v} - \frac{m}{v} \cdot m\right) - 1\right) \cdot m
double f(double m, double v) {
        double r956554 = m;
        double r956555 = 1.0;
        double r956556 = r956555 - r956554;
        double r956557 = r956554 * r956556;
        double r956558 = v;
        double r956559 = r956557 / r956558;
        double r956560 = r956559 - r956555;
        double r956561 = r956560 * r956554;
        return r956561;
}
↓
double f(double m, double v) {
        double r956562 = 1.0;
        double r956563 = m;
        double r956564 = r956562 * r956563;
        double r956565 = v;
        double r956566 = r956564 / r956565;
        double r956567 = r956563 / r956565;
        double r956568 = r956567 * r956563;
        double r956569 = r956566 - r956568;
        double r956570 = r956569 - r956562;
        double r956571 = r956570 * r956563;
        return r956571;
}

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. Simplified0.2

    \[\leadsto \left(\color{blue}{\left(\frac{1 \cdot m}{v} - \frac{m}{\frac{v}{m}}\right)} - 1\right) \cdot m\]
  4. Using strategy rm

  5. Applied associate-/r/0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019174 
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) m))