Average Error: 0.1 → 0.1
Time: 4.4s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m}{v} \cdot \left(1 - m\right) - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{m}{v} \cdot \left(1 - m\right) - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r12161 = m;
        double r12162 = 1.0;
        double r12163 = r12162 - r12161;
        double r12164 = r12161 * r12163;
        double r12165 = v;
        double r12166 = r12164 / r12165;
        double r12167 = r12166 - r12162;
        double r12168 = r12167 * r12163;
        return r12168;
}
↓
double f(double m, double v) {
        double r12169 = m;
        double r12170 = v;
        double r12171 = r12169 / r12170;
        double r12172 = 1.0;
        double r12173 = r12172 - r12169;
        double r12174 = r12171 * r12173;
        double r12175 = r12174 - r12172;
        double r12176 = r12175 * r12173;
        return r12176;
}

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 associate-/l*0.1

    \[\leadsto \left(\color{blue}{\frac{m}{\frac{v}{1 - m}}} - 1\right) \cdot \left(1 - m\right)\]
  4. Using strategy rm

  5. Applied associate-/r/0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020033 
(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)))