Average Error: 0.0 → 0.0
Time: 7.8s
Precision: 64
\[\left(x \cdot \left(y - 1.0\right) - y \cdot 0.5\right) + 0.918938533204673\]
↓
\[\mathsf{fma}\left(y - 1.0, x, 0.918938533204673 - 0.5 \cdot y\right)\]
\left(x \cdot \left(y - 1.0\right) - y \cdot 0.5\right) + 0.918938533204673
↓
\mathsf{fma}\left(y - 1.0, x, 0.918938533204673 - 0.5 \cdot y\right)
double f(double x, double y) {
        double r1264263 = x;
        double r1264264 = y;
        double r1264265 = 1.0;
        double r1264266 = r1264264 - r1264265;
        double r1264267 = r1264263 * r1264266;
        double r1264268 = 0.5;
        double r1264269 = r1264264 * r1264268;
        double r1264270 = r1264267 - r1264269;
        double r1264271 = 0.918938533204673;
        double r1264272 = r1264270 + r1264271;
        return r1264272;
}
↓
double f(double x, double y) {
        double r1264273 = y;
        double r1264274 = 1.0;
        double r1264275 = r1264273 - r1264274;
        double r1264276 = x;
        double r1264277 = 0.918938533204673;
        double r1264278 = 0.5;
        double r1264279 = r1264278 * r1264273;
        double r1264280 = r1264277 - r1264279;
        double r1264281 = fma(r1264275, r1264276, r1264280);
        return r1264281;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[\left(x \cdot \left(y - 1.0\right) - y \cdot 0.5\right) + 0.918938533204673\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(y - 1.0, x, 0.918938533204673 - y \cdot 0.5\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y - 1.0, x, 0.918938533204673 - 0.5 \cdot y\right)\]

Reproduce

herbie shell --seed 2019164 +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))