Average Error: 38.4 → 0.0
Time: 4.6s
Precision: 64
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[x \cdot \left(2 + x\right)\]
\left(x + 1\right) \cdot \left(x + 1\right) - 1
↓
x \cdot \left(2 + x\right)
double f(double x) {
        double r439746 = x;
        double r439747 = 1.0;
        double r439748 = r439746 + r439747;
        double r439749 = r439748 * r439748;
        double r439750 = r439749 - r439747;
        return r439750;
}
↓
double f(double x) {
        double r439751 = x;
        double r439752 = 2.0;
        double r439753 = r439752 + r439751;
        double r439754 = r439751 * r439753;
        return r439754;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 38.4

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))