Average Error: 0.2 → 0.2
Time: 38.5s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\frac{m}{\frac{v}{m}} - \left(m + \frac{\left(m \cdot m\right) \cdot m}{v}\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\frac{m}{\frac{v}{m}} - \left(m + \frac{\left(m \cdot m\right) \cdot m}{v}\right)
double f(double m, double v) {
        double r554367 = m;
        double r554368 = 1.0;
        double r554369 = r554368 - r554367;
        double r554370 = r554367 * r554369;
        double r554371 = v;
        double r554372 = r554370 / r554371;
        double r554373 = r554372 - r554368;
        double r554374 = r554373 * r554367;
        return r554374;
}
↓
double f(double m, double v) {
        double r554375 = m;
        double r554376 = v;
        double r554377 = r554376 / r554375;
        double r554378 = r554375 / r554377;
        double r554379 = r554375 * r554375;
        double r554380 = r554379 * r554375;
        double r554381 = r554380 / r554376;
        double r554382 = r554375 + r554381;
        double r554383 = r554378 - r554382;
        return r554383;
}

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 associate-/l*0.2

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

  5. Applied clear-num0.2

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

  6. Taylor expanded around 0 6.6

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

  7. Simplified0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019146 
(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))