Average Error: 0.2 → 0.2
Time: 17.1s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{m}{\frac{v}{m}} - m\right) \cdot 1 - \frac{m \cdot m}{\frac{v}{m}}\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{m}{\frac{v}{m}} - m\right) \cdot 1 - \frac{m \cdot m}{\frac{v}{m}}
double f(double m, double v) {
        double r25867 = m;
        double r25868 = 1.0;
        double r25869 = r25868 - r25867;
        double r25870 = r25867 * r25869;
        double r25871 = v;
        double r25872 = r25870 / r25871;
        double r25873 = r25872 - r25868;
        double r25874 = r25873 * r25867;
        return r25874;
}
↓
double f(double m, double v) {
        double r25875 = m;
        double r25876 = v;
        double r25877 = r25876 / r25875;
        double r25878 = r25875 / r25877;
        double r25879 = r25878 - r25875;
        double r25880 = 1.0;
        double r25881 = r25879 * r25880;
        double r25882 = r25875 * r25875;
        double r25883 = r25882 / r25877;
        double r25884 = r25881 - r25883;
        return r25884;
}

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 add-sqr-sqrt0.6

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

  4. Applied associate-*r*0.5

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

  5. Simplified0.6

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

  6. Taylor expanded around 0 7.1

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

  7. Simplified0.2

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

  9. Applied unpow30.2

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

  10. Applied associate-/l*0.2

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

  11. Final simplification0.2

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

Reproduce

herbie shell --seed 2019195 +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))