Average Error: 39.0 → 0.0
Time: 1.4s
Precision: binary64
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[x \cdot x + \left(x + x\right)\]
\left(x + 1\right) \cdot \left(x + 1\right) - 1
↓
x \cdot x + \left(x + x\right)
(FPCore (x) :precision binary64 (- (* (+ x 1.0) (+ x 1.0)) 1.0))
↓
(FPCore (x) :precision binary64 (+ (* x x) (+ x x)))
double code(double x) {
	return ((x + 1.0) * (x + 1.0)) - 1.0;
}
↓
double code(double x) {
	return (x * x) + (x + x);
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 39.0

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

  2. Simplified0.0

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

  4. Applied distribute-rgt-in_binary640.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020253 
(FPCore (x)
  :name "Expanding a square"
  :precision binary64
  (- (* (+ x 1.0) (+ x 1.0)) 1.0))