Average Error: 0.2 → 0.2
Time: 18.5s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{m}{\frac{v}{m}} - m\right) - \frac{m \cdot m}{\frac{v}{m}}\]
\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 r866449 = m;
        double r866450 = 1.0;
        double r866451 = r866450 - r866449;
        double r866452 = r866449 * r866451;
        double r866453 = v;
        double r866454 = r866452 / r866453;
        double r866455 = r866454 - r866450;
        double r866456 = r866455 * r866449;
        return r866456;
}
↓
double f(double m, double v) {
        double r866457 = m;
        double r866458 = v;
        double r866459 = r866458 / r866457;
        double r866460 = r866457 / r866459;
        double r866461 = r866460 - r866457;
        double r866462 = r866457 * r866457;
        double r866463 = r866462 / r866459;
        double r866464 = r866461 - r866463;
        return r866464;
}

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))