Average Error: 0.0 → 0.0
Time: 1.7s
Precision: 64
\[2 \cdot \left(x \cdot x + x \cdot y\right)\]
↓
\[2 \cdot \mathsf{fma}\left(y, x, {x}^{2}\right)\]
2 \cdot \left(x \cdot x + x \cdot y\right)
↓
2 \cdot \mathsf{fma}\left(y, x, {x}^{2}\right)
double code(double x, double y) {
	return (2.0 * ((x * x) + (x * y)));
}
↓
double code(double x, double y) {
	return (2.0 * fma(y, x, pow(x, 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. Using strategy rm

  3. Applied flip-+31.6

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

  4. Simplified42.6

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

  5. Simplified42.6

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

  6. Taylor expanded around 0 0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020079 +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))))