Average Error: 0.0 → 0.0
Time: 6.3s
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931\]
↓
\[\mathsf{fma}\left(y - 1, x, 0.9189385332046730026078762421093415468931 - 0.5 \cdot y\right)\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931
↓
\mathsf{fma}\left(y - 1, x, 0.9189385332046730026078762421093415468931 - 0.5 \cdot y\right)
double f(double x, double y) {
        double r1798380 = x;
        double r1798381 = y;
        double r1798382 = 1.0;
        double r1798383 = r1798381 - r1798382;
        double r1798384 = r1798380 * r1798383;
        double r1798385 = 0.5;
        double r1798386 = r1798381 * r1798385;
        double r1798387 = r1798384 - r1798386;
        double r1798388 = 0.918938533204673;
        double r1798389 = r1798387 + r1798388;
        return r1798389;
}
↓
double f(double x, double y) {
        double r1798390 = y;
        double r1798391 = 1.0;
        double r1798392 = r1798390 - r1798391;
        double r1798393 = x;
        double r1798394 = 0.918938533204673;
        double r1798395 = 0.5;
        double r1798396 = r1798395 * r1798390;
        double r1798397 = r1798394 - r1798396;
        double r1798398 = fma(r1798392, r1798393, r1798397);
        return r1798398;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(y - 1, x, 0.9189385332046730026078762421093415468931 - y \cdot 0.5\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y - 1, x, 0.9189385332046730026078762421093415468931 - 0.5 \cdot y\right)\]

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, A"
  (+ (- (* x (- y 1.0)) (* y 0.5)) 0.918938533204673))