Average Error: 0.0 → 0.0
Time: 1.3s
Precision: binary64
Cost: 576
\[2 \cdot \left(x \cdot x - x \cdot y\right)\]
↓
\[2 \cdot \left(x \cdot x - x \cdot y\right)\]
2 \cdot \left(x \cdot x - x \cdot y\right)
↓
2 \cdot \left(x \cdot x - x \cdot y\right)
(FPCore (x y) :precision binary64 (* 2.0 (- (* x x) (* x y))))
↓
(FPCore (x y) :precision binary64 (* 2.0 (- (* x x) (* x y))))
double code(double x, double y) {
	return 2.0 * ((x * x) - (x * y));
}
↓
double code(double x, double y) {
	return 2.0 * ((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
\[\left(x \cdot 2\right) \cdot \left(x - y\right)\]

Alternatives

Alternative 1
Error0.0
Cost448
\[2 \cdot \left(x \cdot \left(x - y\right)\right)\]
Alternative 2
Error8.1
Cost648
\[\begin{array}{l} \mathbf{if}\;y \leq -7.349671524913476 \cdot 10^{-14} \lor \neg \left(y \leq 2.8835203175836237 \cdot 10^{-77}\right):\\ \;\;\;\;\left(x \cdot y\right) \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot x\right)\\ \end{array}\]
Alternative 3
Error21.7
Cost320
\[\left(x \cdot y\right) \cdot -2\]
Alternative 4
Error54.0
Cost64
\[0\]
Alternative 5
Error61.3
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.0

    \[2 \cdot \left(x \cdot x - x \cdot y\right)\]

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2021044 
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, A"
  :precision binary64

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

  (* 2.0 (- (* x x) (* x y))))