Average Error: 0.2 → 0.2
Time: 41.1s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1.0 - m\right)}{v} - 1.0\right) \cdot m\]
↓
\[m \cdot \left(\frac{\left(\left(\sqrt{m} + \sqrt{1.0}\right) \cdot m\right) \cdot \left(\sqrt{1.0} - \sqrt{m}\right)}{v} - 1.0\right)\]
\left(\frac{m \cdot \left(1.0 - m\right)}{v} - 1.0\right) \cdot m
↓
m \cdot \left(\frac{\left(\left(\sqrt{m} + \sqrt{1.0}\right) \cdot m\right) \cdot \left(\sqrt{1.0} - \sqrt{m}\right)}{v} - 1.0\right)
double f(double m, double v) {
        double r1087704 = m;
        double r1087705 = 1.0;
        double r1087706 = r1087705 - r1087704;
        double r1087707 = r1087704 * r1087706;
        double r1087708 = v;
        double r1087709 = r1087707 / r1087708;
        double r1087710 = r1087709 - r1087705;
        double r1087711 = r1087710 * r1087704;
        return r1087711;
}
↓
double f(double m, double v) {
        double r1087712 = m;
        double r1087713 = sqrt(r1087712);
        double r1087714 = 1.0;
        double r1087715 = sqrt(r1087714);
        double r1087716 = r1087713 + r1087715;
        double r1087717 = r1087716 * r1087712;
        double r1087718 = r1087715 - r1087713;
        double r1087719 = r1087717 * r1087718;
        double r1087720 = v;
        double r1087721 = r1087719 / r1087720;
        double r1087722 = r1087721 - r1087714;
        double r1087723 = r1087712 * r1087722;
        return r1087723;
}

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

    \[\left(\frac{m \cdot \left(1.0 - m\right)}{v} - 1.0\right) \cdot m\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.2

    \[\leadsto \left(\frac{m \cdot \left(1.0 - \color{blue}{\sqrt{m} \cdot \sqrt{m}}\right)}{v} - 1.0\right) \cdot m\]

  4. Applied add-sqr-sqrt0.2

    \[\leadsto \left(\frac{m \cdot \left(\color{blue}{\sqrt{1.0} \cdot \sqrt{1.0}} - \sqrt{m} \cdot \sqrt{m}\right)}{v} - 1.0\right) \cdot m\]

  5. Applied difference-of-squares0.2

    \[\leadsto \left(\frac{m \cdot \color{blue}{\left(\left(\sqrt{1.0} + \sqrt{m}\right) \cdot \left(\sqrt{1.0} - \sqrt{m}\right)\right)}}{v} - 1.0\right) \cdot m\]

  6. Applied associate-*r*0.2

    \[\leadsto \left(\frac{\color{blue}{\left(m \cdot \left(\sqrt{1.0} + \sqrt{m}\right)\right) \cdot \left(\sqrt{1.0} - \sqrt{m}\right)}}{v} - 1.0\right) \cdot m\]

  7. Final simplification0.2

    \[\leadsto m \cdot \left(\frac{\left(\left(\sqrt{m} + \sqrt{1.0}\right) \cdot m\right) \cdot \left(\sqrt{1.0} - \sqrt{m}\right)}{v} - 1.0\right)\]

Reproduce

herbie shell --seed 2019165 
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) m))