Average Error: 0.0 → 0.0
Time: 17.3s
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 r3067193 = x;
        double r3067194 = y;
        double r3067195 = 1.0;
        double r3067196 = r3067194 - r3067195;
        double r3067197 = r3067193 * r3067196;
        double r3067198 = 0.5;
        double r3067199 = r3067194 * r3067198;
        double r3067200 = r3067197 - r3067199;
        double r3067201 = 0.918938533204673;
        double r3067202 = r3067200 + r3067201;
        return r3067202;
}
↓
double f(double x, double y) {
        double r3067203 = y;
        double r3067204 = 1.0;
        double r3067205 = r3067203 - r3067204;
        double r3067206 = x;
        double r3067207 = 0.918938533204673;
        double r3067208 = 0.5;
        double r3067209 = r3067208 * r3067203;
        double r3067210 = r3067207 - r3067209;
        double r3067211 = fma(r3067205, r3067206, r3067210);
        return r3067211;
}

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 2019165 +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))