Average Error: 0.1 → 0.1
Time: 20.3s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(1 - m\right) \cdot \left(\frac{m}{\frac{v}{1 - m}} - 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(1 - m\right) \cdot \left(\frac{m}{\frac{v}{1 - m}} - 1\right)
double f(double m, double v) {
        double r1496221 = m;
        double r1496222 = 1.0;
        double r1496223 = r1496222 - r1496221;
        double r1496224 = r1496221 * r1496223;
        double r1496225 = v;
        double r1496226 = r1496224 / r1496225;
        double r1496227 = r1496226 - r1496222;
        double r1496228 = r1496227 * r1496223;
        return r1496228;
}
↓
double f(double m, double v) {
        double r1496229 = 1.0;
        double r1496230 = m;
        double r1496231 = r1496229 - r1496230;
        double r1496232 = v;
        double r1496233 = r1496232 / r1496231;
        double r1496234 = r1496230 / r1496233;
        double r1496235 = r1496234 - r1496229;
        double r1496236 = r1496231 * r1496235;
        return r1496236;
}

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 *-un-lft-identity0.1

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

  4. Applied associate-*r*0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019179 
(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)))