Average Error: 0.1 → 0.1
Time: 20.0s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m}{v} \cdot \frac{1 \cdot 1 - m \cdot m}{1 + m} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{m}{v} \cdot \frac{1 \cdot 1 - m \cdot m}{1 + m} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r23693 = m;
        double r23694 = 1.0;
        double r23695 = r23694 - r23693;
        double r23696 = r23693 * r23695;
        double r23697 = v;
        double r23698 = r23696 / r23697;
        double r23699 = r23698 - r23694;
        double r23700 = r23699 * r23695;
        return r23700;
}
↓
double f(double m, double v) {
        double r23701 = m;
        double r23702 = v;
        double r23703 = r23701 / r23702;
        double r23704 = 1.0;
        double r23705 = r23704 * r23704;
        double r23706 = r23701 * r23701;
        double r23707 = r23705 - r23706;
        double r23708 = r23704 + r23701;
        double r23709 = r23707 / r23708;
        double r23710 = r23703 * r23709;
        double r23711 = r23710 - r23704;
        double r23712 = r23704 - r23701;
        double r23713 = r23711 * r23712;
        return r23713;
}

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 0.1

    \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
  2. Using strategy rm

  3. Applied flip--0.1

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

  4. Applied associate-*r/0.1

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

  5. Applied associate-/l/0.1

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

  7. Applied times-frac0.1

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

  8. Final simplification0.1

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

Reproduce

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