Average Error: 0.1 → 0.1
Time: 4.8s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{1 + m}}{v} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{1 + m}}{v} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r20323 = m;
        double r20324 = 1.0;
        double r20325 = r20324 - r20323;
        double r20326 = r20323 * r20325;
        double r20327 = v;
        double r20328 = r20326 / r20327;
        double r20329 = r20328 - r20324;
        double r20330 = r20329 * r20325;
        return r20330;
}
↓
double f(double m, double v) {
        double r20331 = m;
        double r20332 = 1.0;
        double r20333 = r20332 * r20332;
        double r20334 = r20331 * r20331;
        double r20335 = r20333 - r20334;
        double r20336 = r20331 * r20335;
        double r20337 = r20332 + r20331;
        double r20338 = r20336 / r20337;
        double r20339 = v;
        double r20340 = r20338 / r20339;
        double r20341 = r20340 - r20332;
        double r20342 = r20332 - r20331;
        double r20343 = r20341 * r20342;
        return r20343;
}

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 flip--0.1

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

  4. Applied associate-*r/0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020025 
(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)))