Average Error: 0.0 → 0.0
Time: 945.0ms
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003\]
↓
\[\mathsf{fma}\left(x, y - 1, -0.5 \cdot y\right) + 0.918938533204673003\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003
↓
\mathsf{fma}\left(x, y - 1, -0.5 \cdot y\right) + 0.918938533204673003
double code(double x, double y) {
	return ((double) (((double) (((double) (x * ((double) (y - 1.0)))) - ((double) (y * 0.5)))) + 0.918938533204673));
}
↓
double code(double x, double y) {
	return ((double) (((double) fma(x, ((double) (y - 1.0)), ((double) -(((double) (0.5 * y)))))) + 0.918938533204673));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003\]
  2. Using strategy rm

  3. Applied fma-neg0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y - 1, -y \cdot 0.5\right)} + 0.918938533204673003\]

  4. Simplified0.0

    \[\leadsto \mathsf{fma}\left(x, y - 1, \color{blue}{-0.5 \cdot y}\right) + 0.918938533204673003\]

  5. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, y - 1, -0.5 \cdot y\right) + 0.918938533204673003\]

Reproduce

herbie shell --seed 2020113 +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))