Average Error: 0.0 → 0.0
Time: 1.3s
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 r64307 = x;
        double r64308 = y;
        double r64309 = 1.0;
        double r64310 = r64308 - r64309;
        double r64311 = r64307 * r64310;
        double r64312 = 0.5;
        double r64313 = r64308 * r64312;
        double r64314 = r64311 - r64313;
        double r64315 = 0.918938533204673;
        double r64316 = r64314 + r64315;
        return r64316;
}
↓
double f(double x, double y) {
        double r64317 = y;
        double r64318 = x;
        double r64319 = 0.918938533204673;
        double r64320 = fma(r64317, r64318, r64319);
        double r64321 = 1.0;
        double r64322 = 0.5;
        double r64323 = r64317 * r64322;
        double r64324 = fma(r64318, r64321, r64323);
        double r64325 = r64320 - r64324;
        return r64325;
}

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 2020100 +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))