Average Error: 0.2 → 0.2
Time: 22.2s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{m}{\frac{v}{m}} - m\right) \cdot 1 - \left(m \cdot m\right) \cdot \frac{m}{v}\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{m}{\frac{v}{m}} - m\right) \cdot 1 - \left(m \cdot m\right) \cdot \frac{m}{v}
double f(double m, double v) {
        double r33618 = m;
        double r33619 = 1.0;
        double r33620 = r33619 - r33618;
        double r33621 = r33618 * r33620;
        double r33622 = v;
        double r33623 = r33621 / r33622;
        double r33624 = r33623 - r33619;
        double r33625 = r33624 * r33618;
        return r33625;
}
↓
double f(double m, double v) {
        double r33626 = m;
        double r33627 = v;
        double r33628 = r33627 / r33626;
        double r33629 = r33626 / r33628;
        double r33630 = r33629 - r33626;
        double r33631 = 1.0;
        double r33632 = r33630 * r33631;
        double r33633 = r33626 * r33626;
        double r33634 = r33626 / r33627;
        double r33635 = r33633 * r33634;
        double r33636 = r33632 - r33635;
        return r33636;
}

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. Using strategy rm

  3. Applied sub-neg0.2

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

  4. Applied distribute-lft-in0.2

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

  5. Simplified0.2

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

  6. Simplified0.2

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

  7. Taylor expanded around 0 6.7

    \[\leadsto \color{blue}{1 \cdot \frac{{m}^{2}}{v} - \left(1 \cdot m + \frac{{m}^{3}}{v}\right)}\]

  8. Simplified0.2

    \[\leadsto \color{blue}{1 \cdot \left(\frac{m}{\frac{v}{m}} - m\right) - \frac{{m}^{3}}{v}}\]
  9. Using strategy rm

  10. Applied *-un-lft-identity0.2

    \[\leadsto 1 \cdot \left(\frac{m}{\frac{v}{m}} - m\right) - \frac{{m}^{3}}{\color{blue}{1 \cdot v}}\]

  11. Applied add-cube-cbrt0.5

    \[\leadsto 1 \cdot \left(\frac{m}{\frac{v}{m}} - m\right) - \frac{{\color{blue}{\left(\left(\sqrt[3]{m} \cdot \sqrt[3]{m}\right) \cdot \sqrt[3]{m}\right)}}^{3}}{1 \cdot v}\]

  12. Applied unpow-prod-down0.5

    \[\leadsto 1 \cdot \left(\frac{m}{\frac{v}{m}} - m\right) - \frac{\color{blue}{{\left(\sqrt[3]{m} \cdot \sqrt[3]{m}\right)}^{3} \cdot {\left(\sqrt[3]{m}\right)}^{3}}}{1 \cdot v}\]

  13. Applied times-frac0.5

    \[\leadsto 1 \cdot \left(\frac{m}{\frac{v}{m}} - m\right) - \color{blue}{\frac{{\left(\sqrt[3]{m} \cdot \sqrt[3]{m}\right)}^{3}}{1} \cdot \frac{{\left(\sqrt[3]{m}\right)}^{3}}{v}}\]

  14. Simplified0.3

    \[\leadsto 1 \cdot \left(\frac{m}{\frac{v}{m}} - m\right) - \color{blue}{\left(m \cdot m\right)} \cdot \frac{{\left(\sqrt[3]{m}\right)}^{3}}{v}\]

  15. Simplified0.2

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

  16. Final simplification0.2

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(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))