Average Error: 0.2 → 0.2
Time: 21.0s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{m}{\frac{v}{m}} - m\right) - \frac{{m}^{3}}{v}\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{m}{\frac{v}{m}} - m\right) - \frac{{m}^{3}}{v}
double f(double m, double v) {
        double r394744 = m;
        double r394745 = 1.0;
        double r394746 = r394745 - r394744;
        double r394747 = r394744 * r394746;
        double r394748 = v;
        double r394749 = r394747 / r394748;
        double r394750 = r394749 - r394745;
        double r394751 = r394750 * r394744;
        return r394751;
}
↓
double f(double m, double v) {
        double r394752 = m;
        double r394753 = v;
        double r394754 = r394753 / r394752;
        double r394755 = r394752 / r394754;
        double r394756 = r394755 - r394752;
        double r394757 = 3.0;
        double r394758 = pow(r394752, r394757);
        double r394759 = r394758 / r394753;
        double r394760 = r394756 - r394759;
        return r394760;
}

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

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

  3. Simplified0.2

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

  4. Taylor expanded around 0 6.8

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

  5. Simplified0.2

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

  7. Applied pow10.2

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

  8. Applied pow10.2

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

  9. Applied pow10.2

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

  10. Applied pow-prod-up0.2

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

  11. Applied pow-prod-up0.2

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

  12. Simplified0.2

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

  13. Final simplification0.2

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

Reproduce

herbie shell --seed 2019155 +o rules:numerics
(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))