Average Error: 0.3 → 0.3
Time: 2.4s
Precision: binary64
\[\left(x \cdot 27\right) \cdot y \]
↓
\[27 \cdot \left(y \cdot x\right) \]
\left(x \cdot 27\right) \cdot y
↓
27 \cdot \left(y \cdot x\right)

(FPCore (x y) :precision binary64 (* (* x 27.0) y))
↓
(FPCore (x y) :precision binary64 (* 27.0 (* y x)))
double code(double x, double y) {
	return (x * 27.0) * y;
}
↓
double code(double x, double y) {
	return 27.0 * (y * x);
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.3

    \[\left(x \cdot 27\right) \cdot y \]

  2. Taylor expanded in x around 0 0.3

    \[\leadsto \color{blue}{27 \cdot \left(y \cdot x\right)} \]

  3. Final simplification0.3

    \[\leadsto 27 \cdot \left(y \cdot x\right) \]

Reproduce

herbie shell --seed 2021275 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, F"
  :precision binary64
  (* (* x 27.0) y))