Average Error: 39.4 → 0.0
Time: 1.3s
Precision: binary64
Cost: 320
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[x \cdot \left(x + 2\right)\]
\left(x + 1\right) \cdot \left(x + 1\right) - 1
↓
x \cdot \left(x + 2\right)
(FPCore (x) :precision binary64 (- (* (+ x 1.0) (+ x 1.0)) 1.0))
↓
(FPCore (x) :precision binary64 (* x (+ x 2.0)))
double code(double x) {
	return ((x + 1.0) * (x + 1.0)) - 1.0;
}
↓
double code(double x) {
	return x * (x + 2.0);
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error39.4
Cost576
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
Alternative 2
Error61.2
Cost64
\[1\]
Alternative 3
Error61.2
Cost64
\[0\]
Alternative 4
Error62.1
Cost64
\[-1\]

Error

Derivation

  1. Initial program 39.4

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

  2. Simplified0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2021042 
(FPCore (x)
  :name "Expanding a square"
  :precision binary64
  (- (* (+ x 1.0) (+ x 1.0)) 1.0))