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 r64221 = x;
        double r64222 = y;
        double r64223 = 1.0;
        double r64224 = r64222 - r64223;
        double r64225 = r64221 * r64224;
        double r64226 = 0.5;
        double r64227 = r64222 * r64226;
        double r64228 = r64225 - r64227;
        double r64229 = 0.918938533204673;
        double r64230 = r64228 + r64229;
        return r64230;
}
↓
double f(double x, double y) {
        double r64231 = y;
        double r64232 = x;
        double r64233 = 0.918938533204673;
        double r64234 = fma(r64231, r64232, r64233);
        double r64235 = 1.0;
        double r64236 = 0.5;
        double r64237 = r64231 * r64236;
        double r64238 = fma(r64232, r64235, r64237);
        double r64239 = r64234 - r64238;
        return r64239;
}

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 2020027 +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))