Average Error: 0.0 → 0.0
Time: 1.4s
Precision: binary64
\[2 \cdot \left(x \cdot x + x \cdot y\right) \]
↓
\[x \cdot \left(2 \cdot \left(x + y\right)\right) \]
2 \cdot \left(x \cdot x + x \cdot y\right)
↓
x \cdot \left(2 \cdot \left(x + y\right)\right)

(FPCore (x y) :precision binary64 (* 2.0 (+ (* x x) (* x y))))
↓
(FPCore (x y) :precision binary64 (* x (* 2.0 (+ x y))))
double code(double x, double y) {
	return 2.0 * ((x * x) + (x * y));
}
↓
double code(double x, double y) {
	return x * (2.0 * (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. Simplified0.0

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

  3. Taylor expanded in x around 0 0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

    \[\leadsto x \cdot \left(2 \cdot \left(x + y\right)\right) \]

Reproduce

herbie shell --seed 2022121 
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (* (* x 2.0) (+ x y))

  (* 2.0 (+ (* x x) (* x y))))