Average Error: 0.2 → 0.2
Time: 17.2s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{m}{\frac{v}{m}} - m\right) - \frac{1}{\frac{v}{m \cdot \left(m \cdot m\right)}}\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{m}{\frac{v}{m}} - m\right) - \frac{1}{\frac{v}{m \cdot \left(m \cdot m\right)}}
double f(double m, double v) {
        double r927409 = m;
        double r927410 = 1.0;
        double r927411 = r927410 - r927409;
        double r927412 = r927409 * r927411;
        double r927413 = v;
        double r927414 = r927412 / r927413;
        double r927415 = r927414 - r927410;
        double r927416 = r927415 * r927409;
        return r927416;
}
↓
double f(double m, double v) {
        double r927417 = m;
        double r927418 = v;
        double r927419 = r927418 / r927417;
        double r927420 = r927417 / r927419;
        double r927421 = r927420 - r927417;
        double r927422 = 1.0;
        double r927423 = r927417 * r927417;
        double r927424 = r927417 * r927423;
        double r927425 = r927418 / r927424;
        double r927426 = r927422 / r927425;
        double r927427 = r927421 - r927426;
        return r927427;
}

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 6.7

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

  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 clear-num0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019168 
(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))