Average Error: 0.2 → 0.2
Time: 24.7s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(-\frac{{m}^{3}}{v}\right) + \left(\frac{m}{\frac{v}{m}} - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(-\frac{{m}^{3}}{v}\right) + \left(\frac{m}{\frac{v}{m}} - m\right)
double f(double m, double v) {
        double r859893 = m;
        double r859894 = 1.0;
        double r859895 = r859894 - r859893;
        double r859896 = r859893 * r859895;
        double r859897 = v;
        double r859898 = r859896 / r859897;
        double r859899 = r859898 - r859894;
        double r859900 = r859899 * r859893;
        return r859900;
}
↓
double f(double m, double v) {
        double r859901 = m;
        double r859902 = 3.0;
        double r859903 = pow(r859901, r859902);
        double r859904 = v;
        double r859905 = r859903 / r859904;
        double r859906 = -r859905;
        double r859907 = r859904 / r859901;
        double r859908 = r859901 / r859907;
        double r859909 = r859908 - r859901;
        double r859910 = r859906 + r859909;
        return r859910;
}

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 7.2

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

  3. Simplified0.2

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

  5. Applied associate-/l*0.2

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

  6. Taylor expanded around 0 0.2

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

  7. Simplified0.2

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

  9. Applied pow20.2

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

  10. Applied pow10.2

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

  11. Applied pow-prod-up0.2

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

  12. Simplified0.2

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

  13. Final simplification0.2

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

Reproduce

herbie shell --seed 2019135 
(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))