Average Error: 0.2 → 0.2
Time: 13.5s
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 r451393 = m;
        double r451394 = 1.0;
        double r451395 = r451394 - r451393;
        double r451396 = r451393 * r451395;
        double r451397 = v;
        double r451398 = r451396 / r451397;
        double r451399 = r451398 - r451394;
        double r451400 = r451399 * r451393;
        return r451400;
}
↓
double f(double m, double v) {
        double r451401 = m;
        double r451402 = v;
        double r451403 = r451401 / r451402;
        double r451404 = 1.0;
        double r451405 = r451404 - r451401;
        double r451406 = -1.0;
        double r451407 = fma(r451403, r451405, r451406);
        double r451408 = r451401 * r451407;
        return r451408;
}

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 2019154 +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))