Average Error: 0.2 → 0.2
Time: 28.2s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{v \cdot \left(1 + m\right)} - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{v \cdot \left(1 + m\right)} - 1\right) \cdot m
double f(double m, double v) {
        double r22289 = m;
        double r22290 = 1.0;
        double r22291 = r22290 - r22289;
        double r22292 = r22289 * r22291;
        double r22293 = v;
        double r22294 = r22292 / r22293;
        double r22295 = r22294 - r22290;
        double r22296 = r22295 * r22289;
        return r22296;
}
↓
double f(double m, double v) {
        double r22297 = m;
        double r22298 = 1.0;
        double r22299 = r22298 * r22298;
        double r22300 = r22297 * r22297;
        double r22301 = r22299 - r22300;
        double r22302 = r22297 * r22301;
        double r22303 = v;
        double r22304 = r22298 + r22297;
        double r22305 = r22303 * r22304;
        double r22306 = r22302 / r22305;
        double r22307 = r22306 - r22298;
        double r22308 = r22307 * r22297;
        return r22308;
}

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 0.2

    \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
  2. Using strategy rm

  3. Applied flip--0.2

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

  4. Applied associate-*r/0.2

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

  5. Applied associate-/l/0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) m))