Average Error: 0.2 → 0.2
Time: 15.6s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[m \cdot \mathsf{fma}\left(\frac{m}{v}, 1 - m, -1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
m \cdot \mathsf{fma}\left(\frac{m}{v}, 1 - m, -1\right)
double f(double m, double v) {
        double r549090 = m;
        double r549091 = 1.0;
        double r549092 = r549091 - r549090;
        double r549093 = r549090 * r549092;
        double r549094 = v;
        double r549095 = r549093 / r549094;
        double r549096 = r549095 - r549091;
        double r549097 = r549096 * r549090;
        return r549097;
}
↓
double f(double m, double v) {
        double r549098 = m;
        double r549099 = v;
        double r549100 = r549098 / r549099;
        double r549101 = 1.0;
        double r549102 = r549101 - r549098;
        double r549103 = -1.0;
        double r549104 = fma(r549100, r549102, r549103);
        double r549105 = r549098 * r549104;
        return r549105;
}

Error

Bits error versus m

Bits error versus v

Derivation

  1. Initial program 0.2

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

  2. Simplified0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019153 +o rules:numerics
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) m))