Average Error: 0.1 → 0.1
Time: 47.9s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\left(\sqrt{1} + \sqrt{m}\right) \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)\right) \cdot \left(\sqrt{1} - \sqrt{m}\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\left(\sqrt{1} + \sqrt{m}\right) \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)\right) \cdot \left(\sqrt{1} - \sqrt{m}\right)
double f(double m, double v) {
        double r2324031 = m;
        double r2324032 = 1.0;
        double r2324033 = r2324032 - r2324031;
        double r2324034 = r2324031 * r2324033;
        double r2324035 = v;
        double r2324036 = r2324034 / r2324035;
        double r2324037 = r2324036 - r2324032;
        double r2324038 = r2324037 * r2324033;
        return r2324038;
}
↓
double f(double m, double v) {
        double r2324039 = 1.0;
        double r2324040 = sqrt(r2324039);
        double r2324041 = m;
        double r2324042 = sqrt(r2324041);
        double r2324043 = r2324040 + r2324042;
        double r2324044 = r2324039 - r2324041;
        double r2324045 = r2324041 * r2324044;
        double r2324046 = v;
        double r2324047 = r2324045 / r2324046;
        double r2324048 = r2324047 - r2324039;
        double r2324049 = r2324043 * r2324048;
        double r2324050 = r2324040 - r2324042;
        double r2324051 = r2324049 * r2324050;
        return r2324051;
}

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

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

  4. Applied add-sqr-sqrt0.1

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

  5. Applied difference-of-squares0.1

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

  6. Applied associate-*r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019168 
(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)))