Average Error: 0.1 → 0.1
Time: 20.4s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{\left(\left(\sqrt{m} + \sqrt{1}\right) \cdot m\right) \cdot \left(\sqrt{1} - \sqrt{m}\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{\left(\left(\sqrt{m} + \sqrt{1}\right) \cdot m\right) \cdot \left(\sqrt{1} - \sqrt{m}\right)}{v} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r1432128 = m;
        double r1432129 = 1.0;
        double r1432130 = r1432129 - r1432128;
        double r1432131 = r1432128 * r1432130;
        double r1432132 = v;
        double r1432133 = r1432131 / r1432132;
        double r1432134 = r1432133 - r1432129;
        double r1432135 = r1432134 * r1432130;
        return r1432135;
}
↓
double f(double m, double v) {
        double r1432136 = m;
        double r1432137 = sqrt(r1432136);
        double r1432138 = 1.0;
        double r1432139 = sqrt(r1432138);
        double r1432140 = r1432137 + r1432139;
        double r1432141 = r1432140 * r1432136;
        double r1432142 = r1432139 - r1432137;
        double r1432143 = r1432141 * r1432142;
        double r1432144 = v;
        double r1432145 = r1432143 / r1432144;
        double r1432146 = r1432145 - r1432138;
        double r1432147 = r1432138 - r1432136;
        double r1432148 = r1432146 * r1432147;
        return r1432148;
}

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 add-sqr-sqrt0.1

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

  4. Applied add-sqr-sqrt0.1

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

  5. Applied difference-of-squares0.1

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

  6. Applied associate-*r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m)))