Average Error: 0.0 → 0.0
Time: 870.0ms
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003\]
↓
\[\mathsf{fma}\left(x, y, -\mathsf{fma}\left(1, x, 0.5 \cdot y\right)\right) + 0.918938533204673003\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003
↓
\mathsf{fma}\left(x, y, -\mathsf{fma}\left(1, x, 0.5 \cdot y\right)\right) + 0.918938533204673003
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, -fma(1.0, x, (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. Taylor expanded around 0 0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020092 +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))