Average Error: 39.2 → 0.0
Time: 1.6s
Precision: 64
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[{x}^{2} + x \cdot 2\]
\left(x + 1\right) \cdot \left(x + 1\right) - 1
↓
{x}^{2} + x \cdot 2
double code(double x) {
	return ((double) (((double) (((double) (x + 1.0)) * ((double) (x + 1.0)))) - 1.0));
}
↓
double code(double x) {
	return ((double) (((double) pow(x, 2.0)) + ((double) (x * 2.0))));
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 39.2

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

  2. Taylor expanded around 0 0.0

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

  3. Simplified0.0

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

  5. Applied +-commutative0.0

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

  6. Applied distribute-lft-in0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020113 
(FPCore (x)
  :name "Expanding a square"
  :precision binary64
  (- (* (+ x 1) (+ x 1)) 1))