Average Error: 0.1 → 0.1
Time: 1.1m
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{\left(1 - m\right) \cdot m}{v} - 1\right) \cdot \left(-m\right) + \left(\frac{\left(1 - m\right) \cdot m}{v} - 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{\left(1 - m\right) \cdot m}{v} - 1\right) \cdot \left(-m\right) + \left(\frac{\left(1 - m\right) \cdot m}{v} - 1\right)
double f(double m, double v) {
        double r5247074 = m;
        double r5247075 = 1.0;
        double r5247076 = r5247075 - r5247074;
        double r5247077 = r5247074 * r5247076;
        double r5247078 = v;
        double r5247079 = r5247077 / r5247078;
        double r5247080 = r5247079 - r5247075;
        double r5247081 = r5247080 * r5247076;
        return r5247081;
}
↓
double f(double m, double v) {
        double r5247082 = 1.0;
        double r5247083 = m;
        double r5247084 = r5247082 - r5247083;
        double r5247085 = r5247084 * r5247083;
        double r5247086 = v;
        double r5247087 = r5247085 / r5247086;
        double r5247088 = r5247087 - r5247082;
        double r5247089 = -r5247083;
        double r5247090 = r5247088 * r5247089;
        double r5247091 = r5247090 + r5247088;
        return r5247091;
}

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 sub-neg0.1

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

  4. Applied distribute-rgt-in0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019112 
(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)))