Average Error: 0.1 → 0.1
Time: 28.2s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\left(\frac{m \cdot \left(m \cdot m\right)}{v} - \frac{m \cdot m}{v}\right) + m\right) + \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\left(\frac{m \cdot \left(m \cdot m\right)}{v} - \frac{m \cdot m}{v}\right) + m\right) + \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)
double f(double m, double v) {
        double r974474 = m;
        double r974475 = 1.0;
        double r974476 = r974475 - r974474;
        double r974477 = r974474 * r974476;
        double r974478 = v;
        double r974479 = r974477 / r974478;
        double r974480 = r974479 - r974475;
        double r974481 = r974480 * r974476;
        return r974481;
}
↓
double f(double m, double v) {
        double r974482 = m;
        double r974483 = r974482 * r974482;
        double r974484 = r974482 * r974483;
        double r974485 = v;
        double r974486 = r974484 / r974485;
        double r974487 = r974483 / r974485;
        double r974488 = r974486 - r974487;
        double r974489 = r974488 + r974482;
        double r974490 = 1.0;
        double r974491 = r974490 - r974482;
        double r974492 = r974482 * r974491;
        double r974493 = r974492 / r974485;
        double r974494 = r974493 - r974490;
        double r974495 = r974489 + r974494;
        return r974495;
}

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 0.1

    \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.1

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

  4. Applied distribute-lft-in0.1

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

  6. Applied associate-/l*0.1

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

  7. Taylor expanded around 0 0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019146 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))