Average Error: 0.0 → 0.0
Time: 1.0s
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003\]
↓
\[\mathsf{fma}\left(y, x, 0.918938533204673003\right) - \mathsf{fma}\left(x, 1, y \cdot 0.5\right)\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003
↓
\mathsf{fma}\left(y, x, 0.918938533204673003\right) - \mathsf{fma}\left(x, 1, y \cdot 0.5\right)
double f(double x, double y) {
        double r39408 = x;
        double r39409 = y;
        double r39410 = 1.0;
        double r39411 = r39409 - r39410;
        double r39412 = r39408 * r39411;
        double r39413 = 0.5;
        double r39414 = r39409 * r39413;
        double r39415 = r39412 - r39414;
        double r39416 = 0.918938533204673;
        double r39417 = r39415 + r39416;
        return r39417;
}
↓
double f(double x, double y) {
        double r39418 = y;
        double r39419 = x;
        double r39420 = 0.918938533204673;
        double r39421 = fma(r39418, r39419, r39420);
        double r39422 = 1.0;
        double r39423 = 0.5;
        double r39424 = r39418 * r39423;
        double r39425 = fma(r39419, r39422, r39424);
        double r39426 = r39421 - r39425;
        return r39426;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020089 +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))