Average Error: 0.1 → 0.1
Time: 18.7s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m}{\frac{v}{1 - m}} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{m}{\frac{v}{1 - m}} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r21460 = m;
        double r21461 = 1.0;
        double r21462 = r21461 - r21460;
        double r21463 = r21460 * r21462;
        double r21464 = v;
        double r21465 = r21463 / r21464;
        double r21466 = r21465 - r21461;
        double r21467 = r21466 * r21462;
        return r21467;
}
↓
double f(double m, double v) {
        double r21468 = m;
        double r21469 = v;
        double r21470 = 1.0;
        double r21471 = r21470 - r21468;
        double r21472 = r21469 / r21471;
        double r21473 = r21468 / r21472;
        double r21474 = r21473 - r21470;
        double r21475 = r21474 * r21471;
        return r21475;
}

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 associate-/l*0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019306 +o rules:numerics
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))