Average Error: 0.2 → 0.2
Time: 10.2s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\left(1 \cdot \frac{m}{v} - {m}^{2} \cdot \frac{1}{v}\right) - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\left(1 \cdot \frac{m}{v} - {m}^{2} \cdot \frac{1}{v}\right) - 1\right) \cdot m
double f(double m, double v) {
        double r9726 = m;
        double r9727 = 1.0;
        double r9728 = r9727 - r9726;
        double r9729 = r9726 * r9728;
        double r9730 = v;
        double r9731 = r9729 / r9730;
        double r9732 = r9731 - r9727;
        double r9733 = r9732 * r9726;
        return r9733;
}
↓
double f(double m, double v) {
        double r9734 = 1.0;
        double r9735 = m;
        double r9736 = v;
        double r9737 = r9735 / r9736;
        double r9738 = r9734 * r9737;
        double r9739 = 2.0;
        double r9740 = pow(r9735, r9739);
        double r9741 = 1.0;
        double r9742 = r9741 / r9736;
        double r9743 = r9740 * r9742;
        double r9744 = r9738 - r9743;
        double r9745 = r9744 - r9734;
        double r9746 = r9745 * r9735;
        return r9746;
}

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. Using strategy rm

  4. Applied div-inv0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2020046 
(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))