Average Error: 0.1 → 0.1
Time: 1.1m
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\left(1 - m\right) \cdot \frac{m}{v} + \left(-\left(\left(1 - m\right) \cdot m\right) \cdot \frac{m}{v}\right)\right) - \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\left(1 - m\right) \cdot \frac{m}{v} + \left(-\left(\left(1 - m\right) \cdot m\right) \cdot \frac{m}{v}\right)\right) - \left(1 - m\right)
double f(double m, double v) {
        double r4287861 = m;
        double r4287862 = 1.0;
        double r4287863 = r4287862 - r4287861;
        double r4287864 = r4287861 * r4287863;
        double r4287865 = v;
        double r4287866 = r4287864 / r4287865;
        double r4287867 = r4287866 - r4287862;
        double r4287868 = r4287867 * r4287863;
        return r4287868;
}
↓
double f(double m, double v) {
        double r4287869 = 1.0;
        double r4287870 = m;
        double r4287871 = r4287869 - r4287870;
        double r4287872 = v;
        double r4287873 = r4287870 / r4287872;
        double r4287874 = r4287871 * r4287873;
        double r4287875 = r4287871 * r4287870;
        double r4287876 = r4287875 * r4287873;
        double r4287877 = -r4287876;
        double r4287878 = r4287874 + r4287877;
        double r4287879 = r4287878 - r4287871;
        return r4287879;
}

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. Taylor expanded around -inf 0.1

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

  3. Simplified0.1

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

  5. Applied pow10.1

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

  6. Applied pow10.1

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

  7. Applied pow-prod-down0.1

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

  8. Simplified0.1

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

  10. Applied sub-neg0.1

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

  11. Applied distribute-rgt-in0.1

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

  12. Applied distribute-rgt-in0.1

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

  13. Final simplification0.1

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

Reproduce

herbie shell --seed 2019120 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))