Average Error: 0.2 → 0.2
Time: 16.8s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{v \cdot \left(1 + m\right)} - 1\right) \cdot m\]
\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 r20027 = m;
        double r20028 = 1.0;
        double r20029 = r20028 - r20027;
        double r20030 = r20027 * r20029;
        double r20031 = v;
        double r20032 = r20030 / r20031;
        double r20033 = r20032 - r20028;
        double r20034 = r20033 * r20027;
        return r20034;
}
↓
double f(double m, double v) {
        double r20035 = m;
        double r20036 = 1.0;
        double r20037 = r20036 * r20036;
        double r20038 = r20035 * r20035;
        double r20039 = r20037 - r20038;
        double r20040 = r20035 * r20039;
        double r20041 = v;
        double r20042 = r20036 + r20035;
        double r20043 = r20041 * r20042;
        double r20044 = r20040 / r20043;
        double r20045 = r20044 - r20036;
        double r20046 = r20045 * r20035;
        return r20046;
}

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 2019208 +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))