Average Error: 0.0 → 0.0
Time: 1.6s
Precision: 64
\[2 \cdot \left(x \cdot x - x \cdot y\right)\]
↓
\[2 \cdot \mathsf{fma}\left(x, x, -x \cdot y\right)\]
2 \cdot \left(x \cdot x - x \cdot y\right)
↓
2 \cdot \mathsf{fma}\left(x, x, -x \cdot y\right)
double code(double x, double y) {
	return (2.0 * ((x * x) - (x * y)));
}
↓
double code(double x, double y) {
	return (2.0 * fma(x, x, -(x * y)));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[\left(x \cdot 2\right) \cdot \left(x - y\right)\]

Derivation

  1. Initial program 0.0

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

  3. Applied fma-neg0.0

    \[\leadsto 2 \cdot \color{blue}{\mathsf{fma}\left(x, x, -x \cdot y\right)}\]

  4. Final simplification0.0

    \[\leadsto 2 \cdot \mathsf{fma}\left(x, x, -x \cdot y\right)\]

Reproduce

herbie shell --seed 2020078 +o rules:numerics
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (* (* x 2) (- x y))

  (* 2 (- (* x x) (* x y))))