Average Error: 0.0 → 0.0
Time: 1.5s
Precision: binary64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673 \]
↓
\[\mathsf{fma}\left(x, y - 1, y \cdot -0.5\right) + 0.918938533204673 \]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673
↓
\mathsf{fma}\left(x, y - 1, y \cdot -0.5\right) + 0.918938533204673

(FPCore (x y)
 :precision binary64
 (+ (- (* x (- y 1.0)) (* y 0.5)) 0.918938533204673))
↓
(FPCore (x y)
 :precision binary64
 (+ (fma x (- y 1.0) (* y -0.5)) 0.918938533204673))
double code(double x, double y) {
	return ((x * (y - 1.0)) - (y * 0.5)) + 0.918938533204673;
}
↓
double code(double x, double y) {
	return fma(x, (y - 1.0), (y * -0.5)) + 0.918938533204673;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673 \]

  2. Applied fma-neg_binary640.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y - 1, -y \cdot 0.5\right)} + 0.918938533204673 \]

  3. Simplified0.0

    \[\leadsto \mathsf{fma}\left(x, y - 1, \color{blue}{-0.5 \cdot y}\right) + 0.918938533204673 \]

  4. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, y - 1, y \cdot -0.5\right) + 0.918938533204673 \]

Reproduce

herbie shell --seed 2022077 
(FPCore (x y)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (* x (- y 1.0)) (* y 0.5)) 0.918938533204673))