Average Error: 0.0 → 0.0
Time: 1.1s
Precision: 64
\[2 \cdot \left(x \cdot x + x \cdot y\right)\]
↓
\[\mathsf{fma}\left(y, x, {x}^{2}\right) \cdot 2\]
2 \cdot \left(x \cdot x + x \cdot y\right)
↓
\mathsf{fma}\left(y, x, {x}^{2}\right) \cdot 2
double code(double x, double y) {
	return (2.0 * ((x * x) + (x * y)));
}
↓
double code(double x, double y) {
	return (fma(y, x, pow(x, 2.0)) * 2.0);
}

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. Simplified0.0

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

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{2 \cdot {x}^{2} + 2 \cdot \left(x \cdot y\right)}\]

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020071 +o rules:numerics
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, B"
  :precision binary64

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

  (* 2 (+ (* x x) (* x y))))