Average Error: 0.2 → 0.2
Time: 3.5s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
double f(double m, double v) {
        double r7128 = m;
        double r7129 = 1.0;
        double r7130 = r7129 - r7128;
        double r7131 = r7128 * r7130;
        double r7132 = v;
        double r7133 = r7131 / r7132;
        double r7134 = r7133 - r7129;
        double r7135 = r7134 * r7128;
        return r7135;
}
↓
double f(double m, double v) {
        double r7136 = m;
        double r7137 = 1.0;
        double r7138 = r7137 - r7136;
        double r7139 = r7136 * r7138;
        double r7140 = v;
        double r7141 = r7139 / r7140;
        double r7142 = r7141 - r7137;
        double r7143 = r7142 * r7136;
        return r7143;
}

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 clear-num0.2

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

  4. Taylor expanded around 0 0.2

    \[\leadsto \left(\color{blue}{\left(1 \cdot \frac{m}{v} - \frac{{m}^{2}}{v}\right)} - 1\right) \cdot m\]

  5. Simplified0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020034 +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))