Average Error: 0.2 → 0.2
Time: 16.9s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{m}{\frac{v}{m}} - m\right) - \frac{m \cdot m}{\frac{v}{m}}\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{m}{\frac{v}{m}} - m\right) - \frac{m \cdot m}{\frac{v}{m}}
double f(double m, double v) {
        double r866452 = m;
        double r866453 = 1.0;
        double r866454 = r866453 - r866452;
        double r866455 = r866452 * r866454;
        double r866456 = v;
        double r866457 = r866455 / r866456;
        double r866458 = r866457 - r866453;
        double r866459 = r866458 * r866452;
        return r866459;
}
↓
double f(double m, double v) {
        double r866460 = m;
        double r866461 = v;
        double r866462 = r866461 / r866460;
        double r866463 = r866460 / r866462;
        double r866464 = r866463 - r866460;
        double r866465 = r866460 * r866460;
        double r866466 = r866465 / r866462;
        double r866467 = r866464 - r866466;
        return r866467;
}

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 clear-num0.2

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

  4. Taylor expanded around 0 6.9

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

  5. Simplified0.2

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

  7. Applied associate-/l*0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019163 
(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))