Average Error: 0.2 → 0.2
Time: 23.5s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{\frac{\left(m \cdot \left(1 + m\right)\right) \cdot \left(1 - m\right)}{1 + m}}{v} - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{\frac{\left(m \cdot \left(1 + m\right)\right) \cdot \left(1 - m\right)}{1 + m}}{v} - 1\right) \cdot m
double f(double m, double v) {
        double r1364930 = m;
        double r1364931 = 1.0;
        double r1364932 = r1364931 - r1364930;
        double r1364933 = r1364930 * r1364932;
        double r1364934 = v;
        double r1364935 = r1364933 / r1364934;
        double r1364936 = r1364935 - r1364931;
        double r1364937 = r1364936 * r1364930;
        return r1364937;
}
↓
double f(double m, double v) {
        double r1364938 = m;
        double r1364939 = 1.0;
        double r1364940 = r1364939 + r1364938;
        double r1364941 = r1364938 * r1364940;
        double r1364942 = r1364939 - r1364938;
        double r1364943 = r1364941 * r1364942;
        double r1364944 = r1364943 / r1364940;
        double r1364945 = v;
        double r1364946 = r1364944 / r1364945;
        double r1364947 = r1364946 - r1364939;
        double r1364948 = r1364947 * r1364938;
        return r1364948;
}

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. Simplified0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019171 
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) m))