Average Error: 0.1 → 0.1
Time: 22.2s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{1}{\frac{v}{\left(1 - m\right) \cdot m}} - 1\right) \cdot \left(-m\right) + \left(\frac{m}{\frac{v}{1 - m}} - 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{1}{\frac{v}{\left(1 - m\right) \cdot m}} - 1\right) \cdot \left(-m\right) + \left(\frac{m}{\frac{v}{1 - m}} - 1\right)
double f(double m, double v) {
        double r983702 = m;
        double r983703 = 1.0;
        double r983704 = r983703 - r983702;
        double r983705 = r983702 * r983704;
        double r983706 = v;
        double r983707 = r983705 / r983706;
        double r983708 = r983707 - r983703;
        double r983709 = r983708 * r983704;
        return r983709;
}
↓
double f(double m, double v) {
        double r983710 = 1.0;
        double r983711 = v;
        double r983712 = m;
        double r983713 = r983710 - r983712;
        double r983714 = r983713 * r983712;
        double r983715 = r983711 / r983714;
        double r983716 = r983710 / r983715;
        double r983717 = r983716 - r983710;
        double r983718 = -r983712;
        double r983719 = r983717 * r983718;
        double r983720 = r983711 / r983713;
        double r983721 = r983712 / r983720;
        double r983722 = r983721 - r983710;
        double r983723 = r983719 + r983722;
        return r983723;
}

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 clear-num0.1

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

  8. Applied associate-/l*0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019139 
(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)))