Average Error: 38.6 → 0.0
Time: 1.6s
Precision: binary64
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[2 \cdot x + {x}^{2}\]
\left(x + 1\right) \cdot \left(x + 1\right) - 1
↓
2 \cdot x + {x}^{2}
(FPCore (x) :precision binary64 (- (* (+ x 1.0) (+ x 1.0)) 1.0))
↓
(FPCore (x) :precision binary64 (+ (* 2.0 x) (pow x 2.0)))
double code(double x) {
	return ((x + 1.0) * (x + 1.0)) - 1.0;
}
↓
double code(double x) {
	return (2.0 * x) + pow(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 38.6

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

  2. Simplified0.0

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

  3. Taylor expanded around 0 0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2021044 
(FPCore (x)
  :name "Expanding a square"
  :precision binary64
  (- (* (+ x 1.0) (+ x 1.0)) 1.0))