Average Error: 0.0 → 0.0
Time: 1.0s
Precision: binary64
\[x \cdot \left(y + y\right) \]
↓
\[2 \cdot \left(y \cdot x\right) \]
x \cdot \left(y + y\right)
↓
2 \cdot \left(y \cdot x\right)

(FPCore (x y) :precision binary64 (* x (+ y y)))
↓
(FPCore (x y) :precision binary64 (* 2.0 (* y x)))
double code(double x, double y) {
	return x * (y + y);
}
↓
double code(double x, double y) {
	return 2.0 * (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 0.0

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

  2. Taylor expanded in x around 0 0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2022077 
(FPCore (x y)
  :name "Numeric.Integration.TanhSinh:simpson  from integration-0.2.1"
  :precision binary64
  (* x (+ y y)))