Average Error: 0.1 → 0.1
Time: 47.4s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(1 - m\right) \cdot \left(\frac{m}{\frac{v}{1 - m}} - 1\right)\]
\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 r729342 = m;
        double r729343 = 1.0;
        double r729344 = r729343 - r729342;
        double r729345 = r729342 * r729344;
        double r729346 = v;
        double r729347 = r729345 / r729346;
        double r729348 = r729347 - r729343;
        double r729349 = r729348 * r729344;
        return r729349;
}
↓
double f(double m, double v) {
        double r729350 = 1.0;
        double r729351 = m;
        double r729352 = r729350 - r729351;
        double r729353 = v;
        double r729354 = r729353 / r729352;
        double r729355 = r729351 / r729354;
        double r729356 = r729355 - r729350;
        double r729357 = r729352 * r729356;
        return r729357;
}

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

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

Reproduce

herbie shell --seed 2019142 +o rules:numerics
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))