Average Error: 0.0 → 0.0
Time: 5.6s
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003\]
↓
\[\mathsf{fma}\left(x, y - 1, \mathsf{fma}\left(0.5, -y, 0.918938533204673003\right)\right)\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003
↓
\mathsf{fma}\left(x, y - 1, \mathsf{fma}\left(0.5, -y, 0.918938533204673003\right)\right)
double f(double x, double y) {
        double r37529 = x;
        double r37530 = y;
        double r37531 = 1.0;
        double r37532 = r37530 - r37531;
        double r37533 = r37529 * r37532;
        double r37534 = 0.5;
        double r37535 = r37530 * r37534;
        double r37536 = r37533 - r37535;
        double r37537 = 0.918938533204673;
        double r37538 = r37536 + r37537;
        return r37538;
}
↓
double f(double x, double y) {
        double r37539 = x;
        double r37540 = y;
        double r37541 = 1.0;
        double r37542 = r37540 - r37541;
        double r37543 = 0.5;
        double r37544 = -r37540;
        double r37545 = 0.918938533204673;
        double r37546 = fma(r37543, r37544, r37545);
        double r37547 = fma(r37539, r37542, r37546);
        return r37547;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y - 1, \mathsf{fma}\left(0.5, -y, 0.918938533204673003\right)\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, y - 1, \mathsf{fma}\left(0.5, -y, 0.918938533204673003\right)\right)\]

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (* x (- y 1)) (* y 0.5)) 0.918938533204673))