Average Error: 0.2 → 0.2
Time: 20.9s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{\left(1 - m\right) \cdot m}{v} - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{\left(1 - m\right) \cdot m}{v} - 1\right) \cdot m
double f(double m, double v) {
        double r1033075 = m;
        double r1033076 = 1.0;
        double r1033077 = r1033076 - r1033075;
        double r1033078 = r1033075 * r1033077;
        double r1033079 = v;
        double r1033080 = r1033078 / r1033079;
        double r1033081 = r1033080 - r1033076;
        double r1033082 = r1033081 * r1033075;
        return r1033082;
}
↓
double f(double m, double v) {
        double r1033083 = 1.0;
        double r1033084 = m;
        double r1033085 = r1033083 - r1033084;
        double r1033086 = r1033085 * r1033084;
        double r1033087 = v;
        double r1033088 = r1033086 / r1033087;
        double r1033089 = r1033088 - r1033083;
        double r1033090 = r1033089 * r1033084;
        return r1033090;
}

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 *-un-lft-identity0.2

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

  4. Applied associate-/r*0.2

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

  5. Simplified0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019170 +o rules:numerics
(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))