Average Error: 38.7 → 0.0
Time: 1.7s
Precision: binary64
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[x \cdot x + x \cdot 2\]
\left(x + 1\right) \cdot \left(x + 1\right) - 1
↓
x \cdot x + x \cdot 2
(FPCore (x) :precision binary64 (- (* (+ x 1.0) (+ x 1.0)) 1.0))
↓
(FPCore (x) :precision binary64 (+ (* x x) (* x 2.0)))
double code(double x) {
	return ((double) (((double) (((double) (x + 1.0)) * ((double) (x + 1.0)))) - 1.0));
}
↓
double code(double x) {
	return ((double) (((double) (x * x)) + ((double) (x * 2.0))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 38.7

    \[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{{x}^{2} + 2 \cdot x}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{x \cdot \left(x + 2\right)}\]
  4. Using strategy rm

  5. Applied distribute-lft-in_binary640.0

    \[\leadsto \color{blue}{x \cdot x + x \cdot 2}\]

  6. Final simplification0.0

    \[\leadsto x \cdot x + x \cdot 2\]

Reproduce

herbie shell --seed 2020210 
(FPCore (x)
  :name "Expanding a square"
  :precision binary64
  (- (* (+ x 1.0) (+ x 1.0)) 1.0))